The modal characteristics of dual-core photonic crystal fibers(PCFs) are analyzed by a full vector supercell lattice overlapping model. The fundamental and second-order modes of dual-core PCFs consist of a pair of even and odd modes with different polarization. The parity properties of the modal electric field for the fundamental and second-order modes are discussed. Based on the analysis of parity of the modal electric fields, we investigated the vector modal interference in dual-core PCFs.It is the interference between two same polarized modes that conributes to the inter-core coupling of power. It is shown that the optical power will oscillate from one core to the other and the phase difference between both cores is about π/2. The dependence of coupling coefficients for different polarization on wavelength is discussed.
The modal characteristics of dual-core photonic crystal fibers(PCFs) are analyzed by a full vector supercell lattice overlapping model. The fundamental and second-order modes of dual-core PCFs consist of a pair of even and odd modes with different polarization. The parity properties of the modal electric field for the fundamental and second-order modes are discussed. Based on the analysis of parity of the modal electric fields, we investigated the vector modal interference in dual-core PCFs.It is the interference between two same polarized modes that conributes to the inter-core coupling of power. It is shown that the optical power will oscillate from one core to the other and the phase difference between both cores is about π/2. The dependence of coupling coefficients for different polarization on wavelength is discussed.
A variable separation approach is applied to obtain the new exact explicit solution of (2+1)dimensional nonlinear Burgers equations. Using a B-cklund transformation and the variable separation technique, we find the variable separation solution of the (2+1)dimensional Burgers equations by the entrance of there arbitrary functions (one condition function) for the seed solution. Some special type of the kink soliton solution, periodic soliton solutions and lattice soliton solutions are discussed by selecting the arbitrary functions appropriately.
A variable separation approach is applied to obtain the new exact explicit solution of (2+1)dimensional nonlinear Burgers equations. Using a B-cklund transformation and the variable separation technique, we find the variable separation solution of the (2+1)dimensional Burgers equations by the entrance of there arbitrary functions (one condition function) for the seed solution. Some special type of the kink soliton solution, periodic soliton solutions and lattice soliton solutions are discussed by selecting the arbitrary functions appropriately.
A non-Noether conserved quantity, i.e. Hojman conserved quantity,constructed by using a form invariance for the nonholonomic mechanical systems is presented. Under special infinitesimal transformations in which the time is not changed, the determining equations of the special form invariance, the constrained restriction equations, the additional restriction equations, and the definitions of the weak form invariance and the strong form invariance of the nonholonomic mechanical systems are given. The condition under which the special form invariance is a special Lie symmetry are obtained. From the special form invariance, the Hojman conserved quantity of the corresponding holonomic systems, the weak Hojman conserved quantity and the strong Hojman conserved quantity of the nonholonomic systems are obtained. And two examples are given to illustrate the application of the result.
A non-Noether conserved quantity, i.e. Hojman conserved quantity,constructed by using a form invariance for the nonholonomic mechanical systems is presented. Under special infinitesimal transformations in which the time is not changed, the determining equations of the special form invariance, the constrained restriction equations, the additional restriction equations, and the definitions of the weak form invariance and the strong form invariance of the nonholonomic mechanical systems are given. The condition under which the special form invariance is a special Lie symmetry are obtained. From the special form invariance, the Hojman conserved quantity of the corresponding holonomic systems, the weak Hojman conserved quantity and the strong Hojman conserved quantity of the nonholonomic systems are obtained. And two examples are given to illustrate the application of the result.
The problem on stability of equilibrium of a thin elastic rod in view of dynamics is discussed in this paper. The dynamical equations of the rod is established, and the definitions of Lyapunov stability for a discrete dynamical system with arc-coordinate s and time t as double arguments are proposed. As an example, the stability of straight equilibrium of a rod with noncircular cross-section and intrinsic twisting is analyzed by use of the first approximation method. It was proved that the straight equilibrium of the rod is stable dynamically when the conditions of stability are satisfied within the scope of statics.
The problem on stability of equilibrium of a thin elastic rod in view of dynamics is discussed in this paper. The dynamical equations of the rod is established, and the definitions of Lyapunov stability for a discrete dynamical system with arc-coordinate s and time t as double arguments are proposed. As an example, the stability of straight equilibrium of a rod with noncircular cross-section and intrinsic twisting is analyzed by use of the first approximation method. It was proved that the straight equilibrium of the rod is stable dynamically when the conditions of stability are satisfied within the scope of statics.
The study on gas flow characteristics in a long-constant-area microchannel in mixed Kn-regime flows has not only theoretical meaning, but also important application in controlling the system of outer space aerocrafts. Flow characteristics were studied based on experiments and approximate theoretical analysis. The inlet pressure was 130, 250 and 320?kPa, and the outlet pressure ranged from 9 to 100?kPa. Five pressure measuring points were distributed along the microchannel and the temperature sensors were located at the inlet and outlet. The pressure distribution and the volume flow rate of air were measured experimentally. An approximate theoretical model based on Poiseuille flow was adopted. Experimental investigations with the long-constant-area microchannel indicate that the mass flow rate through the microchannel changes little as the inlet-to-outlet pressure ratio reaches a certain critical value. The phenomenon is defined as sub-choking and the corresponding pressure ratio is defined as the sub-choking-critical-pressure-ratio. The phenomenon of sub-choking is due to the surface effects. Moreover, the effects of the ratio of surface to volume on the critical pressure ratio are studied.
The study on gas flow characteristics in a long-constant-area microchannel in mixed Kn-regime flows has not only theoretical meaning, but also important application in controlling the system of outer space aerocrafts. Flow characteristics were studied based on experiments and approximate theoretical analysis. The inlet pressure was 130, 250 and 320?kPa, and the outlet pressure ranged from 9 to 100?kPa. Five pressure measuring points were distributed along the microchannel and the temperature sensors were located at the inlet and outlet. The pressure distribution and the volume flow rate of air were measured experimentally. An approximate theoretical model based on Poiseuille flow was adopted. Experimental investigations with the long-constant-area microchannel indicate that the mass flow rate through the microchannel changes little as the inlet-to-outlet pressure ratio reaches a certain critical value. The phenomenon is defined as sub-choking and the corresponding pressure ratio is defined as the sub-choking-critical-pressure-ratio. The phenomenon of sub-choking is due to the surface effects. Moreover, the effects of the ratio of surface to volume on the critical pressure ratio are studied.
With the aid of symbolic computation system Maple and by using the extended hyperbolic function method, the exact solitary wave solutions of Zakharov equations are obtained which include bell-shaped soliton solutions, kink-shaped soliton solutions, envelop soliton solutions, singular soliton solutions and a new type of soliton solutions. The method can be also used to solve other nonlinear wave equations.
With the aid of symbolic computation system Maple and by using the extended hyperbolic function method, the exact solitary wave solutions of Zakharov equations are obtained which include bell-shaped soliton solutions, kink-shaped soliton solutions, envelop soliton solutions, singular soliton solutions and a new type of soliton solutions. The method can be also used to solve other nonlinear wave equations.
A new nanoindentation creep test, i.e. a steady-state loading segment followed by the constant load for long period of time, has been proposed by combining a constant loading rate divided by the load (const.P·/P) with a constant load test (const.P). The method is applicable not only to the materials with lower melting temperature and higher creep ability, but also to those materials with higher melting temperature and lower creep ability and an indentation size effect. The strain rate sensitivity m of Cu at room temperature determined by the method is about 0.01. It is also found that the previous loading schemes, including the values of the P·/P used during loading segment and the maximum depths h-max at the end of the loading segment, have no obvious influence on the values of the strain rate sensitivity m.
A new nanoindentation creep test, i.e. a steady-state loading segment followed by the constant load for long period of time, has been proposed by combining a constant loading rate divided by the load (const.P·/P) with a constant load test (const.P). The method is applicable not only to the materials with lower melting temperature and higher creep ability, but also to those materials with higher melting temperature and lower creep ability and an indentation size effect. The strain rate sensitivity m of Cu at room temperature determined by the method is about 0.01. It is also found that the previous loading schemes, including the values of the P·/P used during loading segment and the maximum depths h-max at the end of the loading segment, have no obvious influence on the values of the strain rate sensitivity m.
A new quantum spectrum function is defined using the eigenvalues and eigenfunctions of the system considered. We study the two-dimensional rectangular billiard,and find that the Fourier transform of the spectrum function reveals the classical orbits from one point to another.
A new quantum spectrum function is defined using the eigenvalues and eigenfunctions of the system considered. We study the two-dimensional rectangular billiard,and find that the Fourier transform of the spectrum function reveals the classical orbits from one point to another.
A general scalar chaotic signal synchronization system is proposed in this paper. For the system in the “strict-feedback' form with variant parameters and variant weights of artificial control terms, a feedback controller and associated parameter adaptive laws are constructed via adaptive backstepping design with tuning functions. Using the controller and parameter adaptive laws proposed in this paper, the output of the general system asymptotically synchronizes with the output of any chaotic system with a known structure. Both theory analysis and computer simulation results illustrate the validity of the general scalar chaotic signal synchronization system and its controller.
A general scalar chaotic signal synchronization system is proposed in this paper. For the system in the “strict-feedback' form with variant parameters and variant weights of artificial control terms, a feedback controller and associated parameter adaptive laws are constructed via adaptive backstepping design with tuning functions. Using the controller and parameter adaptive laws proposed in this paper, the output of the general system asymptotically synchronizes with the output of any chaotic system with a known structure. Both theory analysis and computer simulation results illustrate the validity of the general scalar chaotic signal synchronization system and its controller.
The sheet resistance for a microarea in a large silicon wafers was measured by using a modified Rymaszewski's formulas for a square four-point probe technique. An improved Rymaszewski's formulas was deduced taking into account the shift of probes in square four-point probe measurement. The equation of resistivity for square four-point probe measurement when there were shifts of the probes and there was no shift of the probes was deduced theoretically. A possible error produced by the shift of the probes was analyzed in theory and expressed with graphs. The effect upon measuring results arising from the shift of probes was also discussed. Practical-measurement of a specimen has been tested using a self-established equipment of square four-point probes. An equal-value-line graph was plotted for the measurement-results.
The sheet resistance for a microarea in a large silicon wafers was measured by using a modified Rymaszewski's formulas for a square four-point probe technique. An improved Rymaszewski's formulas was deduced taking into account the shift of probes in square four-point probe measurement. The equation of resistivity for square four-point probe measurement when there were shifts of the probes and there was no shift of the probes was deduced theoretically. A possible error produced by the shift of the probes was analyzed in theory and expressed with graphs. The effect upon measuring results arising from the shift of probes was also discussed. Practical-measurement of a specimen has been tested using a self-established equipment of square four-point probes. An equal-value-line graph was plotted for the measurement-results.
Triple-axis x-ray diffraction (TXRD) and photoluminescence (PL) spectra are used to assess the influence of the ratio of TMIn flow to group Ⅲ flow on structural defects, such as dislocations and interface roughness, and optical properties of multiple quantum wells(MQWs). In this paper the mean densities of edge and screw dislocations in InGaN/GaN MQWs are obtained by ωscan of every satellite peak of (0002) symmetric and (1012) asymmetric diffractions. At the same time, the interface roughness is measured by the radio of the full width at half maximum of satellite peaks to the peak orders. The experimental results showed that the density of dislocation, especially of edge dislocation, and interface roughness increase with the increase of the ratio, which leads to the decrease of PL properties. It also can be concluded that the edge dislocation acts as nonradiative recombination centers in InGaN/GaN MQWs. Also noticed is that the variation of the ratio has more influence on edge dislocation than on screw dislocation.
Triple-axis x-ray diffraction (TXRD) and photoluminescence (PL) spectra are used to assess the influence of the ratio of TMIn flow to group Ⅲ flow on structural defects, such as dislocations and interface roughness, and optical properties of multiple quantum wells(MQWs). In this paper the mean densities of edge and screw dislocations in InGaN/GaN MQWs are obtained by ωscan of every satellite peak of (0002) symmetric and (1012) asymmetric diffractions. At the same time, the interface roughness is measured by the radio of the full width at half maximum of satellite peaks to the peak orders. The experimental results showed that the density of dislocation, especially of edge dislocation, and interface roughness increase with the increase of the ratio, which leads to the decrease of PL properties. It also can be concluded that the edge dislocation acts as nonradiative recombination centers in InGaN/GaN MQWs. Also noticed is that the variation of the ratio has more influence on edge dislocation than on screw dislocation.
Based on the Faddeev formalism of path-integral quantization for a constrained Hamiltonian system, the Casimir effect between two non-parallel lines in the (2+1)-dimensional space is calculated by using conformal mapping and Plana summation formula in the theory of complex variable function. Without introducing any cutoff of parameter, the finite analytical expression is obtained.
Based on the Faddeev formalism of path-integral quantization for a constrained Hamiltonian system, the Casimir effect between two non-parallel lines in the (2+1)-dimensional space is calculated by using conformal mapping and Plana summation formula in the theory of complex variable function. Without introducing any cutoff of parameter, the finite analytical expression is obtained.
Based on the character in which both the intermediate and final states are intimately related with the vacuum properties of strong-interactions,we have discussed from an alternative point of view the processes of both the radiative production of glueball and the annihilation into electron-positron pair in J/ψ decays.Using the modified field theory model of pomeron in high-energy soft strong processes and the consequent hypothesis of the maximum non-perturbative strong interaction as well as the relevant changes of parameters of the model connecting with the large inner-structure difference between light and heavy constituent quarks,we proposed another mechanism for these two decay processes and calculated their partial width.The coupling constant between the glueballs and the non-perturbative gluons has been estimated.
Based on the character in which both the intermediate and final states are intimately related with the vacuum properties of strong-interactions,we have discussed from an alternative point of view the processes of both the radiative production of glueball and the annihilation into electron-positron pair in J/ψ decays.Using the modified field theory model of pomeron in high-energy soft strong processes and the consequent hypothesis of the maximum non-perturbative strong interaction as well as the relevant changes of parameters of the model connecting with the large inner-structure difference between light and heavy constituent quarks,we proposed another mechanism for these two decay processes and calculated their partial width.The coupling constant between the glueballs and the non-perturbative gluons has been estimated.
By including the electron correlation and the relaxation effects,the energy level structures of the 4d core excited configuration 4d9 5s25p5,final radiative configuration 4d105s25p4 and final Auger configurations 4d105s25p3 and 4d105s15p4 of the Cs Ⅳ ion and all possible decay dynamic processes related to these configurations are systematically studied using multi-configuration Dirac-Fock method. The present study not only provides satisfactory results for the radiative transition energies,oscillator strengths and line widths in comp arison with the existing semi-empirical calculations and related experiments,but also predicts some dominant features of the Auger electron spectrum emitted by the Auger decay process of the 4d95s25p5 core excited states.
By including the electron correlation and the relaxation effects,the energy level structures of the 4d core excited configuration 4d9 5s25p5,final radiative configuration 4d105s25p4 and final Auger configurations 4d105s25p3 and 4d105s15p4 of the Cs Ⅳ ion and all possible decay dynamic processes related to these configurations are systematically studied using multi-configuration Dirac-Fock method. The present study not only provides satisfactory results for the radiative transition energies,oscillator strengths and line widths in comp arison with the existing semi-empirical calculations and related experiments,but also predicts some dominant features of the Auger electron spectrum emitted by the Auger decay process of the 4d95s25p5 core excited states.
The structure changes of a Cu Σ=5(310)/[001] symmetrical tilt grain boundary are investigated using the molecular dynamics method by heating and quenching. The simulated results showed that with increasing temperature,there are structure changes of the grain boundary. At a temperature significantly below the bulk melting point of copper,the grain boundary undergoes a structure change,and there exists the crystal-melt coexistence in the grain boundary zone. The grain boundary structures can be changed by quenching,which are compared to those at the same temperatures by heating.
The structure changes of a Cu Σ=5(310)/[001] symmetrical tilt grain boundary are investigated using the molecular dynamics method by heating and quenching. The simulated results showed that with increasing temperature,there are structure changes of the grain boundary. At a temperature significantly below the bulk melting point of copper,the grain boundary undergoes a structure change,and there exists the crystal-melt coexistence in the grain boundary zone. The grain boundary structures can be changed by quenching,which are compared to those at the same temperatures by heating.
In this paper,we study the errors caused by an intense excitation beam in fluorescence correlation spectroscopy (FCS). Saturated excitation induced by an intense excitation beam will alter the spatial distribution function of the laser-induced fluorescence; therefore it changes the results of FCS measurements. Using the theory for saturated excitation,we derived a general expression for the effective detection volume as a function of the excitation laser intensity. Quantitative relations between the particle number and diffusion time,both obtained from FCS measurements,and the excitation laser intensity are established and used to remove the systematic error due to saturated excitation. The success of this technique is demonstrated in both Monte-Carlo simulations and experiments.
In this paper,we study the errors caused by an intense excitation beam in fluorescence correlation spectroscopy (FCS). Saturated excitation induced by an intense excitation beam will alter the spatial distribution function of the laser-induced fluorescence; therefore it changes the results of FCS measurements. Using the theory for saturated excitation,we derived a general expression for the effective detection volume as a function of the excitation laser intensity. Quantitative relations between the particle number and diffusion time,both obtained from FCS measurements,and the excitation laser intensity are established and used to remove the systematic error due to saturated excitation. The success of this technique is demonstrated in both Monte-Carlo simulations and experiments.
The enhancement of stimulated Raman scattering (SRS) of minority species of binary mixture is demonstrated in pendant drops by overlapping the Stokes wavelengths of the Raman modes of minority species with Rhodamine 640 dye lasing gain.The limit of detectable concentration for the minority species,methanol in methanol-ethanol and ethanol in ethanol-water mixtures,is greatly reduced. Based on the theory of SRS,the mechanism for enhancing SRS of minority species is explained.
The enhancement of stimulated Raman scattering (SRS) of minority species of binary mixture is demonstrated in pendant drops by overlapping the Stokes wavelengths of the Raman modes of minority species with Rhodamine 640 dye lasing gain.The limit of detectable concentration for the minority species,methanol in methanol-ethanol and ethanol in ethanol-water mixtures,is greatly reduced. Based on the theory of SRS,the mechanism for enhancing SRS of minority species is explained.
A new method for realizing the optical tomography of bio-tissue by using a δ sound field and a near infrared laser is presented. A δ sound field is cons tructed and is acted upon the tissue, and this causes some variations of optical properties at the action spot . A perturbation of the light intensity distribution on the tissue surface is measured. The inherent relations between the perturbation and the variations of optical properties are discussed. The optical property distribution in the tissue volume can be extracted from the light distributions on the tissue surface by scanning the action spot at the layer to be constructed. The present method is useful for clinic applications and diagnoses of breast cancers at early stage.
A new method for realizing the optical tomography of bio-tissue by using a δ sound field and a near infrared laser is presented. A δ sound field is cons tructed and is acted upon the tissue, and this causes some variations of optical properties at the action spot . A perturbation of the light intensity distribution on the tissue surface is measured. The inherent relations between the perturbation and the variations of optical properties are discussed. The optical property distribution in the tissue volume can be extracted from the light distributions on the tissue surface by scanning the action spot at the layer to be constructed. The present method is useful for clinic applications and diagnoses of breast cancers at early stage.
The angular and wavelength selectivities of band gaps of holographic photonic crystals were calculated using transfer matrix method for different polarizations.It showed that the width of the band gaps for P-polarization is narrower than that for S-polarization. About the angular selectivity, the changing trends for different polarizations are the same, but with different degree of variations. About the wavelength selectivity, the changing trends for different polarizations are in an opposite way. A \!general Brewster's angle\' is introduced. The theoretical analysis shows that when a beam incident on a photonic crystal just at the general Brewster's angle\', the forbidden band of S-polarization will still exist as it is, while the forbidden band of P-polarization will vanish. Therefore , a \!defect mode\' can be obtained in the forbidden band of S-polarization by i lluminating the photonic crystal with P-polarization beam at the \!general Brews ter's angle\'. The experimental results for verifying the theoretical calculatio ns were given.
The angular and wavelength selectivities of band gaps of holographic photonic crystals were calculated using transfer matrix method for different polarizations.It showed that the width of the band gaps for P-polarization is narrower than that for S-polarization. About the angular selectivity, the changing trends for different polarizations are the same, but with different degree of variations. About the wavelength selectivity, the changing trends for different polarizations are in an opposite way. A \!general Brewster's angle\' is introduced. The theoretical analysis shows that when a beam incident on a photonic crystal just at the general Brewster's angle\', the forbidden band of S-polarization will still exist as it is, while the forbidden band of P-polarization will vanish. Therefore , a \!defect mode\' can be obtained in the forbidden band of S-polarization by i lluminating the photonic crystal with P-polarization beam at the \!general Brews ter's angle\'. The experimental results for verifying the theoretical calculatio ns were given.
The conventional holography met with three unsolvable difficulties,such as coherence of light source,spatial resolution and sensitivity of detector,when applied in atomic imaging. This paper is intended to explain how the inside source holography can overcome all these difficulties,and to investigate the recording and reconstruction procedures of the inside source holography. The reconstruction formula of inside source spherical hologram and the δ-functions describing reconstructed atomic images in spherical-symmetrical and energy-irrelevent approximations of atomic scattering factor are deduced
The conventional holography met with three unsolvable difficulties,such as coherence of light source,spatial resolution and sensitivity of detector,when applied in atomic imaging. This paper is intended to explain how the inside source holography can overcome all these difficulties,and to investigate the recording and reconstruction procedures of the inside source holography. The reconstruction formula of inside source spherical hologram and the δ-functions describing reconstructed atomic images in spherical-symmetrical and energy-irrelevent approximations of atomic scattering factor are deduced
A scheme is presented for preparing the superposition of coherent states,i.e.,Schr?dinger cat states. These states can be generated by the action of an external impulse functional signal on initial vaccum state of a mesoscopic LC circuit. The nonclassical squeezing properties appear in the circuit under the Schr?dinger cat states.
A scheme is presented for preparing the superposition of coherent states,i.e.,Schr?dinger cat states. These states can be generated by the action of an external impulse functional signal on initial vaccum state of a mesoscopic LC circuit. The nonclassical squeezing properties appear in the circuit under the Schr?dinger cat states.
The evolution properties of the entropy of a single-mode light field interacting with the V-type three-level atom via intensity-dependent coupling have been studied. The discussion is centered on the influence of detuning and initial photon number on the field entropy evolution. The results show that the behavi or of the field entropy is non-periodic for the cases of small detuning and weak initial light field,being similar to the single-photon Jaynes-Cummings model (JCM). On the contrary,the field entropy evolution is periodic for the cases of large detuning or strong initial light field,being similar to the two-photon JCM
The evolution properties of the entropy of a single-mode light field interacting with the V-type three-level atom via intensity-dependent coupling have been studied. The discussion is centered on the influence of detuning and initial photon number on the field entropy evolution. The results show that the behavi or of the field entropy is non-periodic for the cases of small detuning and weak initial light field,being similar to the single-photon Jaynes-Cummings model (JCM). On the contrary,the field entropy evolution is periodic for the cases of large detuning or strong initial light field,being similar to the two-photon JCM
In this paper we reveal that the constructive interference of atomic coherence on absorption leads to electromagnetically induced absorption,which is in sharp contrast to the case in which destructive interference of atomic coherence gives rise to electromagnetically induced transparency. A four-level atomic system is employed in which three transitions are in N configuration and the middle transition is used as a probe transition. In the dressed states representation the probe transition is split into four transitions that are coupled to each other. The coupling originates from the spontaneous emission of the atomic medium and the spontaneous transfer from excited state coherence to ground state coherence. The former leads to couplings between all transitions with the same sign and to the absorption reduction. The latter results in couplings,of which t wo terms have positive sign and another two have negative sign. It is due to the couplings with positive and negative signs that significant modification of the contribution of dressed coherence to absorption occurs,i.e., absorption inhibition is changed to absorption enhancement.
In this paper we reveal that the constructive interference of atomic coherence on absorption leads to electromagnetically induced absorption,which is in sharp contrast to the case in which destructive interference of atomic coherence gives rise to electromagnetically induced transparency. A four-level atomic system is employed in which three transitions are in N configuration and the middle transition is used as a probe transition. In the dressed states representation the probe transition is split into four transitions that are coupled to each other. The coupling originates from the spontaneous emission of the atomic medium and the spontaneous transfer from excited state coherence to ground state coherence. The former leads to couplings between all transitions with the same sign and to the absorption reduction. The latter results in couplings,of which t wo terms have positive sign and another two have negative sign. It is due to the couplings with positive and negative signs that significant modification of the contribution of dressed coherence to absorption occurs,i.e., absorption inhibition is changed to absorption enhancement.
We present an analytic investigation of the signal-to-noise ratio of output intensity in a loss-noise model of a single-mode laser system driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. Stochastic resonance (SR) in the curve of signal-to-noise ratio R versus the pump noise self-correlation time τ,signal frequency Ω,and cross-correlation coefficient between the real and imaginary parts of the quantum noise λq are found. It extends the conclusion of the typical SR,that is, \!there is a maximum in the curve of R vs noise intensity\'. Moreover,we detect that,when the parameter Ω increases,the shape of the Rτ curve will exhibit a change process of multiform SR: the curve experienced from simulta neous existence of resonances and suppressions to single-peak SR and finally to the monotonous rise. And when the parameter τincreases,the shape of theRΩcurve also exhibit a change process of multiform SR: the curve experienced from the monotonous rise to the simultaneous existence of resonances and suppressions and finally to the monotonous descending. For the Rλq curve,it appears an acute single-peak form.
We present an analytic investigation of the signal-to-noise ratio of output intensity in a loss-noise model of a single-mode laser system driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. Stochastic resonance (SR) in the curve of signal-to-noise ratio R versus the pump noise self-correlation time τ,signal frequency Ω,and cross-correlation coefficient between the real and imaginary parts of the quantum noise λq are found. It extends the conclusion of the typical SR,that is, \!there is a maximum in the curve of R vs noise intensity\'. Moreover,we detect that,when the parameter Ω increases,the shape of the Rτ curve will exhibit a change process of multiform SR: the curve experienced from simulta neous existence of resonances and suppressions to single-peak SR and finally to the monotonous rise. And when the parameter τincreases,the shape of theRΩcurve also exhibit a change process of multiform SR: the curve experienced from the monotonous rise to the simultaneous existence of resonances and suppressions and finally to the monotonous descending. For the Rλq curve,it appears an acute single-peak form.
The cavity field spectrum of a cascade three-level atom interacting with a single-mode field in an ideal cavity is investigated. When the atom is in the upper level and the field is vacuum initially,the number of Rabi peaks changes according to 2→6→4→2→4 with the increase of R=g2/g1,and all Rabi peaks disappear for R1 Three-peak,five-peak or seven-peak structure appear for weak initial fields,and single resonance peak appears for a st rong field. When the atom is in the middle level initially,the cavity field spectrum is of a two-peak structure with R=1 as the spectrum of Jaynes-Cummings model.
The cavity field spectrum of a cascade three-level atom interacting with a single-mode field in an ideal cavity is investigated. When the atom is in the upper level and the field is vacuum initially,the number of Rabi peaks changes according to 2→6→4→2→4 with the increase of R=g2/g1,and all Rabi peaks disappear for R1 Three-peak,five-peak or seven-peak structure appear for weak initial fields,and single resonance peak appears for a st rong field. When the atom is in the middle level initially,the cavity field spectrum is of a two-peak structure with R=1 as the spectrum of Jaynes-Cummings model.
Exemplifying the three-level systems in the V configuration, we investigate the role of selective excitation of dressed populations in lasing without inversion. Incoherent driving field transfers population from either of the dressed states to excited state when the level spacing between dressed states produced by the coherent field is much larger than the spectral width of the incoherent driving field. With atomic decay pathways,unidirectional channel of population transfer is formed and selective excitation of dressed populations is established. Employing selective excitation of dressed populations,three severe limits are relaxed. First,it is no longer required that the decay rate of the low-frequency driving transition is larger than that of high-frequency laser transition. Second,the threshold for incoherent driving rate is remarkably lowered. Third,linear gain of the laser without inversion is no longer inversely proportional to the coherent driving field intensity, and the gain is significantly enhanced.
Exemplifying the three-level systems in the V configuration, we investigate the role of selective excitation of dressed populations in lasing without inversion. Incoherent driving field transfers population from either of the dressed states to excited state when the level spacing between dressed states produced by the coherent field is much larger than the spectral width of the incoherent driving field. With atomic decay pathways,unidirectional channel of population transfer is formed and selective excitation of dressed populations is established. Employing selective excitation of dressed populations,three severe limits are relaxed. First,it is no longer required that the decay rate of the low-frequency driving transition is larger than that of high-frequency laser transition. Second,the threshold for incoherent driving rate is remarkably lowered. Third,linear gain of the laser without inversion is no longer inversely proportional to the coherent driving field intensity, and the gain is significantly enhanced.
In this paper,a novel eigenvector method (EM) for calculation of optical resonator modes and beam propagation is introduced,in which the new transit matrix of an optical resonator is obtained by dividing the mirror into finite grids based on Fresnel-Kirchhoff diffracted integral equation. Then,the eigenvectors of the transit matrix,representing the multi-mode characteristics of the resonator,can be calculated by solving the matrix eigen-equation. The field distributions inside or outside the resonator,resulting from the known eigenvectors on the resonator mirror,can be derived by EM. The merits of EM include that the consider ably simpler procedure for solution of eigenvectors of the matrix eigen-equation replaces the complicated iteration in traditional methods,and there is no depen dence on the initial field distribution,and a number of modes can be derived on ce and the discrimination capability of the resonator can be evaluated easily. T he example of using EM to simulate the confocal resonator is given,and the calculated results,well matched with the Fox-Li method and Laguerre-Gaussian approx imatie analytical solution,prove that EM is highly effective and reasonable.
In this paper,a novel eigenvector method (EM) for calculation of optical resonator modes and beam propagation is introduced,in which the new transit matrix of an optical resonator is obtained by dividing the mirror into finite grids based on Fresnel-Kirchhoff diffracted integral equation. Then,the eigenvectors of the transit matrix,representing the multi-mode characteristics of the resonator,can be calculated by solving the matrix eigen-equation. The field distributions inside or outside the resonator,resulting from the known eigenvectors on the resonator mirror,can be derived by EM. The merits of EM include that the consider ably simpler procedure for solution of eigenvectors of the matrix eigen-equation replaces the complicated iteration in traditional methods,and there is no depen dence on the initial field distribution,and a number of modes can be derived on ce and the discrimination capability of the resonator can be evaluated easily. T he example of using EM to simulate the confocal resonator is given,and the calculated results,well matched with the Fox-Li method and Laguerre-Gaussian approx imatie analytical solution,prove that EM is highly effective and reasonable.
A planar waveguide array, whose structure is similar to a volume phase grating,can be fabricated in a congruent SBN:Cr (Sr0.61Ba0.39Nb2O6:Cr) crystal by irradiation of two-beam interference pattern,and,simultaneously, by applying an appropriate direct electrical field along the c-axis of the crystal. The transversal index profile of the waveguide array is measured in real-time using a Mach-Zehnder interferometer,and the maximum index change in the waveguide region is close to 10-4. The initial guiding tests show that it is feasible to write a dynamic planar waveguide array in the SBN:Cr crystal by using irradiation of period structure-light,due to the rapid response property of SBN:Cr crystals. And the dynamic control of the waveg uide can be realized by switching the writing lights on or off,or adjusting the angle of the two interferent beams. Moreover,the waveguide parameter such as the index profile in the waveguide zone can be effectively controlled by varying the external electric field.
A planar waveguide array, whose structure is similar to a volume phase grating,can be fabricated in a congruent SBN:Cr (Sr0.61Ba0.39Nb2O6:Cr) crystal by irradiation of two-beam interference pattern,and,simultaneously, by applying an appropriate direct electrical field along the c-axis of the crystal. The transversal index profile of the waveguide array is measured in real-time using a Mach-Zehnder interferometer,and the maximum index change in the waveguide region is close to 10-4. The initial guiding tests show that it is feasible to write a dynamic planar waveguide array in the SBN:Cr crystal by using irradiation of period structure-light,due to the rapid response property of SBN:Cr crystals. And the dynamic control of the waveg uide can be realized by switching the writing lights on or off,or adjusting the angle of the two interferent beams. Moreover,the waveguide parameter such as the index profile in the waveguide zone can be effectively controlled by varying the external electric field.
This paper analyzes theoretically various nonlinear phenomena caused by focusing a laser beam into high-pressure gas, and the interaction and interference produced, measures the relationship among output energy, input energy, gas pressure and focal length when the fourth harmonic Nd:YAG laser is focused into the Raman cell filled with methane. Experimental results are in agreement with theoretical ones qualitatively. Based on these we can optimize and use the stimulated Raman scattering.
This paper analyzes theoretically various nonlinear phenomena caused by focusing a laser beam into high-pressure gas, and the interaction and interference produced, measures the relationship among output energy, input energy, gas pressure and focal length when the fourth harmonic Nd:YAG laser is focused into the Raman cell filled with methane. Experimental results are in agreement with theoretical ones qualitatively. Based on these we can optimize and use the stimulated Raman scattering.
Based on the technology of spatial phase modulation, a simple scheme to steer optical Gaussian beams in photovoltaic media is presented. Numerical simulations show that we can realize the self-deflection, soliton like propagation, divergence and splitting of Gaussian beams in photovoltaic media. The relationship between the intensity profile of the incident beam and the modulation parameters is also discussed.
Based on the technology of spatial phase modulation, a simple scheme to steer optical Gaussian beams in photovoltaic media is presented. Numerical simulations show that we can realize the self-deflection, soliton like propagation, divergence and splitting of Gaussian beams in photovoltaic media. The relationship between the intensity profile of the incident beam and the modulation parameters is also discussed.
Nearfield acoustic holography (NAH) based on wave superposition approach (WSA) is proposed and applied to radiation analysis of sound sources with arbitrarily shaped surface. In problem of calculating acoustic radiation, boundary element method (BEM) is realized by discretizing acoustic and position variables on the boundary surface, while WSA is accomplished by superposing wave fields generated by simple sources interior to the radiator. Therefore, there are no problems such as parameters interpolation, singular integration etc. in WSAbased acoustic holography, which are inherent to BEMbased NAH. The principle of WSAbased acoustic holography is easier to understand, and it is more amiable to implement on the computer. The results of the experiment show that satisfactory precision has been obtained in the reconstruction of sound field using WSAbasedacoustic holography.
Nearfield acoustic holography (NAH) based on wave superposition approach (WSA) is proposed and applied to radiation analysis of sound sources with arbitrarily shaped surface. In problem of calculating acoustic radiation, boundary element method (BEM) is realized by discretizing acoustic and position variables on the boundary surface, while WSA is accomplished by superposing wave fields generated by simple sources interior to the radiator. Therefore, there are no problems such as parameters interpolation, singular integration etc. in WSAbased acoustic holography, which are inherent to BEMbased NAH. The principle of WSAbased acoustic holography is easier to understand, and it is more amiable to implement on the computer. The results of the experiment show that satisfactory precision has been obtained in the reconstruction of sound field using WSAbasedacoustic holography.
The transitional primary dynamical processes, which were constructed in the experiment in a transitional boundary layer, were used to make further analysis on the turbulent cascade patterns. The quantitative results obtained from the measurement data in the transitional boundary layer experiment described the link between the turbulent cascade patterns and a sequence of transitional primary dynamics processes. This may be helpful for us to understand the turbulent cascade more deeply.
The transitional primary dynamical processes, which were constructed in the experiment in a transitional boundary layer, were used to make further analysis on the turbulent cascade patterns. The quantitative results obtained from the measurement data in the transitional boundary layer experiment described the link between the turbulent cascade patterns and a sequence of transitional primary dynamics processes. This may be helpful for us to understand the turbulent cascade more deeply.
The angular distribution and the energy spectrum of hot electrons with energy over 50keV emitted from ethanol droplets irradiated by linearly polarized 150 fs laser pulses at the intensity of 10 16W/cm2 have been measured. The angular distribution of hot electrons is found to be dependent on the laser polarization. Two hot electron jets like double leaves symmetrically with respect to the laser propagation direction are observed within the polarization plane. The maximum energy of the hot electrons is found to be more than 750 keV. A model based on the resonance absorption can be used to interpret the above distribution. The calculation agrees well with the experimental results.
The angular distribution and the energy spectrum of hot electrons with energy over 50keV emitted from ethanol droplets irradiated by linearly polarized 150 fs laser pulses at the intensity of 10 16W/cm2 have been measured. The angular distribution of hot electrons is found to be dependent on the laser polarization. Two hot electron jets like double leaves symmetrically with respect to the laser propagation direction are observed within the polarization plane. The maximum energy of the hot electrons is found to be more than 750 keV. A model based on the resonance absorption can be used to interpret the above distribution. The calculation agrees well with the experimental results.
A PLJERC-FDTD algorithm is applied to the study of the scattering of perfectly conducting cube covered with homogeneous isotropic plasmas. The effects of plasma thickness, density and collision frequency on the radar cross section(RCS) of the conducting cube scatterer have been obtained. The results illustrate that the plasma cloaking can greatly reduce the RCS of radar targets, and the RCS of the perfectly conducting cube scatterer decreases with increasing plasma thickness when the plasma frequency is greatly less than the electromagnetic(EM) wave frequency; the RCS of the perfectly conducting cube scatterer decreases with increasing plasma thickness and plasma collision frequency when the plasma frequency is almost half as much as the EM wave frequency; the effects of plasma thickness and collision frequency on the RCS of the perfectly conducting cube scatterer is small when the plasma frequency is close to the EM wave frequency.
A PLJERC-FDTD algorithm is applied to the study of the scattering of perfectly conducting cube covered with homogeneous isotropic plasmas. The effects of plasma thickness, density and collision frequency on the radar cross section(RCS) of the conducting cube scatterer have been obtained. The results illustrate that the plasma cloaking can greatly reduce the RCS of radar targets, and the RCS of the perfectly conducting cube scatterer decreases with increasing plasma thickness when the plasma frequency is greatly less than the electromagnetic(EM) wave frequency; the RCS of the perfectly conducting cube scatterer decreases with increasing plasma thickness and plasma collision frequency when the plasma frequency is almost half as much as the EM wave frequency; the effects of plasma thickness and collision frequency on the RCS of the perfectly conducting cube scatterer is small when the plasma frequency is close to the EM wave frequency.
Numerical simulation results are presented in this paper concerning the heat transfer and fluid flow within the supersonic plasma jet, which is produced by the converging diverging plasma torch. The full NaiverStokes equations, which take into account the gas viscous effects, temperature and pressure dependent properties, and compressible effects, are employed in this simulation and the PHOENICS software is used to solve the set of nonlinear equations. The shock structure within the supersonic plasma jet is analysed in detail,and the effects of ambient pressure on the jet flow field are studied. Results show that the supersonic plasma flow interacts with the ambient gas and forms a series of compression and expansion waves in the region near the torch nozzle exit.
Numerical simulation results are presented in this paper concerning the heat transfer and fluid flow within the supersonic plasma jet, which is produced by the converging diverging plasma torch. The full NaiverStokes equations, which take into account the gas viscous effects, temperature and pressure dependent properties, and compressible effects, are employed in this simulation and the PHOENICS software is used to solve the set of nonlinear equations. The shock structure within the supersonic plasma jet is analysed in detail,and the effects of ambient pressure on the jet flow field are studied. Results show that the supersonic plasma flow interacts with the ambient gas and forms a series of compression and expansion waves in the region near the torch nozzle exit.
Linear dispersion properties and waves of collisionless plasma current sheet at small scales are discussed, using 25dimensional, collisionless and incompressible magnetohydrodynamic (MHD) models with the full electron pressure tensor. General dispersion relations are very complex. Two special cases, i.e., the central region of current sheet and the electronβ*e=0, are analytically studied here. The main results are as follows. (1) In the ioninertial region (kdi>1), there are fast magnetosonic-kinetic Alfven waves and obliquely Alfven-whistler waves, and the electron magnetohydrodynamic (EMHD) model is a precise MHD model. In the long wavelength region (kdi<1), there are Alfven waves and ion acoustic waves, and the ideal MHD model is valid. (2) When electron β*e=0, the results drop off some modes, e.g., the fast magnetosonic-kinetic Alfven wave and ion acoustic wave. This case is not exactly valid for the current sheet plasma. (3) At central region of current sheet, results from both of physical models have fast magnetosonic kinetic Alfven waves.
Linear dispersion properties and waves of collisionless plasma current sheet at small scales are discussed, using 25dimensional, collisionless and incompressible magnetohydrodynamic (MHD) models with the full electron pressure tensor. General dispersion relations are very complex. Two special cases, i.e., the central region of current sheet and the electronβ*e=0, are analytically studied here. The main results are as follows. (1) In the ioninertial region (kdi>1), there are fast magnetosonic-kinetic Alfven waves and obliquely Alfven-whistler waves, and the electron magnetohydrodynamic (EMHD) model is a precise MHD model. In the long wavelength region (kdi<1), there are Alfven waves and ion acoustic waves, and the ideal MHD model is valid. (2) When electron β*e=0, the results drop off some modes, e.g., the fast magnetosonic-kinetic Alfven wave and ion acoustic wave. This case is not exactly valid for the current sheet plasma. (3) At central region of current sheet, results from both of physical models have fast magnetosonic kinetic Alfven waves.
A two-dimensional, three-temperature radiation magneto-hydrodynamics model is applied to the simulation of tungsten wire-array plasma implosion based on the real experimental parameters of the Qiangguang1 generator. The spatial-temporal evolutions of the plasma density and temperature are presented, and the characteristic of the magnetic field and current density is analyzed and summarized. The calculated x-ray power curve is approximately in agreement with the corresponding measured one. All these predicted quantities are conducive to the plas ma diagnoses of Z pinches. In addition, some of physical parameters and numerical schemes related to this simulation are discussed also.
A two-dimensional, three-temperature radiation magneto-hydrodynamics model is applied to the simulation of tungsten wire-array plasma implosion based on the real experimental parameters of the Qiangguang1 generator. The spatial-temporal evolutions of the plasma density and temperature are presented, and the characteristic of the magnetic field and current density is analyzed and summarized. The calculated x-ray power curve is approximately in agreement with the corresponding measured one. All these predicted quantities are conducive to the plas ma diagnoses of Z pinches. In addition, some of physical parameters and numerical schemes related to this simulation are discussed also.
For most reactive radio-frequency plasma etching processing, the plasma sheaths near two electrodes are asymmetric due to the powered electrode area being smaller than the grounded electrode area. Taking collisional effects of ions with neutrals in the sheaths into account, a selfconsistent dynamic model is proposed here to describe the characteristics of radio-frequency sheaths. Numerical results show the collisional effects on some physical quantities, such as instantaneous voltages on the electrodes, instantaneous thicknesses of the electron sheathes, spatial distributions of the ion density and the electric field in the sheaths, and instantaneous voltage difference between two electrodes.
For most reactive radio-frequency plasma etching processing, the plasma sheaths near two electrodes are asymmetric due to the powered electrode area being smaller than the grounded electrode area. Taking collisional effects of ions with neutrals in the sheaths into account, a selfconsistent dynamic model is proposed here to describe the characteristics of radio-frequency sheaths. Numerical results show the collisional effects on some physical quantities, such as instantaneous voltages on the electrodes, instantaneous thicknesses of the electron sheathes, spatial distributions of the ion density and the electric field in the sheaths, and instantaneous voltage difference between two electrodes.
Using the one-dimensional dynamic sheath model, the effects of charging at a planar dielectric surface in plasma immersion ion implantation are studied. The temporal evolution of the sheath thickness, the effective potential at the surface of the dielectric and the ion dose accumulated on it are obtained for different plasma densities and dielectric thicknesses. The numerical results demonstrated that due to the charging effects, the plasma density has a profound impact on doping result during plasma immersion ion implantation, but the thickness of the dielectric has no significant effect on it.
Using the one-dimensional dynamic sheath model, the effects of charging at a planar dielectric surface in plasma immersion ion implantation are studied. The temporal evolution of the sheath thickness, the effective potential at the surface of the dielectric and the ion dose accumulated on it are obtained for different plasma densities and dielectric thicknesses. The numerical results demonstrated that due to the charging effects, the plasma density has a profound impact on doping result during plasma immersion ion implantation, but the thickness of the dielectric has no significant effect on it.
Base on successful solution of the problems in judging whether the surface elastic term K13 of nematic liquid crystal exists or not, the equilibrium equation and boundary condition of the director have been obtained by the methods of analytical derivation and numerical calculation. The influence of the surface elastic energy term K13 on the properties of Fréedericksz transition of weak anchoring nematic liquid crystal cell under a magnetic field has been investigated in detail. The results show that the existence of K13 has influence on the free energy of the liquid crystal system so great as to change the property of the transition and induce a first-order Fréedericksz transition. The conditions for this transition are obtained. They depend on the surface elastic energy term K13 besides the structure and material of the system. The method of judging whether K13 term exists or not by Fréedericksz transition has been given.
Base on successful solution of the problems in judging whether the surface elastic term K13 of nematic liquid crystal exists or not, the equilibrium equation and boundary condition of the director have been obtained by the methods of analytical derivation and numerical calculation. The influence of the surface elastic energy term K13 on the properties of Fréedericksz transition of weak anchoring nematic liquid crystal cell under a magnetic field has been investigated in detail. The results show that the existence of K13 has influence on the free energy of the liquid crystal system so great as to change the property of the transition and induce a first-order Fréedericksz transition. The conditions for this transition are obtained. They depend on the surface elastic energy term K13 besides the structure and material of the system. The method of judging whether K13 term exists or not by Fréedericksz transition has been given.
The polycrystalline VO2 film was directly prepared from V2O5 powder using the modified ion beam enhanced deposition (IBED) method and a suitable annealing. Testing results show that the IBED polycrystalline VO2 film has a single orientation, an obvious phase transition, a compact structure, and favorable processing properties. The temperature coefficient of resistance (TCR) of the film was up to more 4% and adhered hard to the substrate. The mechanism of the IBED film with higher TCR was discussed in detail. The reason why the film has a high TCR could be as follows: the oxygen vacancy and crystalline boundary in the film was decreased due to the IBED technology; with single oriented and dense texture the activation energy of electrical conduction of the IBED polycrystalline VO2 film was closer to the activation energy of VO2 crystalline in semiconductor phase which is higher than that of the VOx films prepared by other methods
The polycrystalline VO2 film was directly prepared from V2O5 powder using the modified ion beam enhanced deposition (IBED) method and a suitable annealing. Testing results show that the IBED polycrystalline VO2 film has a single orientation, an obvious phase transition, a compact structure, and favorable processing properties. The temperature coefficient of resistance (TCR) of the film was up to more 4% and adhered hard to the substrate. The mechanism of the IBED film with higher TCR was discussed in detail. The reason why the film has a high TCR could be as follows: the oxygen vacancy and crystalline boundary in the film was decreased due to the IBED technology; with single oriented and dense texture the activation energy of electrical conduction of the IBED polycrystalline VO2 film was closer to the activation energy of VO2 crystalline in semiconductor phase which is higher than that of the VOx films prepared by other methods
A three-dimensional kinetic Monte-Carlo technique has been developed for simulating the growth of thin Cu films. The model involves incident atom attachments, diffusion of the atoms on the growing surface, and the detachment of the atoms from the growing surface. Related effects due to surface atom diffusion was taken into account. A great improvement was made on calculation of the activation energy for atom diffusion based on a reasonable assumption of interaction potential between atoms. The results showed that as the substrate temperature is raised or the deposited rate decreased, the diffusion of particles causes the particles grouping into islands (more than three atoms). The higher the temperature or the lower the deposition rate, the larger the size of the islands. Also we observed the island shape transition from two-dimensional islands to three-dimensional ones. There exist three optimum growth temperatures at a given deposition rate, namely Tn at which the nucleation rate is maximum, Tr at which the surface roughness minimizes and Td at which the relative density approaches to saturation. They all increase with the increase of substrate temperature, and these variations almost superpose on each other. The simulation results also showed that the relative density decreases with increasing deposition rate. But the nucleation rate is close to a steadiness at a lower temperature while it increases at a higher temperature. The surface roughness increases at a lower temperature while it decreases at a higher temperature.
A three-dimensional kinetic Monte-Carlo technique has been developed for simulating the growth of thin Cu films. The model involves incident atom attachments, diffusion of the atoms on the growing surface, and the detachment of the atoms from the growing surface. Related effects due to surface atom diffusion was taken into account. A great improvement was made on calculation of the activation energy for atom diffusion based on a reasonable assumption of interaction potential between atoms. The results showed that as the substrate temperature is raised or the deposited rate decreased, the diffusion of particles causes the particles grouping into islands (more than three atoms). The higher the temperature or the lower the deposition rate, the larger the size of the islands. Also we observed the island shape transition from two-dimensional islands to three-dimensional ones. There exist three optimum growth temperatures at a given deposition rate, namely Tn at which the nucleation rate is maximum, Tr at which the surface roughness minimizes and Td at which the relative density approaches to saturation. They all increase with the increase of substrate temperature, and these variations almost superpose on each other. The simulation results also showed that the relative density decreases with increasing deposition rate. But the nucleation rate is close to a steadiness at a lower temperature while it increases at a higher temperature. The surface roughness increases at a lower temperature while it decreases at a higher temperature.
The SiC:Tb films were deposited on porous silicon substrate by rfsputtering. The samples prepared were annealed in N2 atmosphere at different temperatures, and Fourier transform infrared has been used to characterize the structure of them. We observed a strong photoluminescence(PL) spectrum at room temperature in the ultraviolet(UV) and visible regions. We found that the UV emission has obvious changed and a slight blue shift was observed with the change of annealing temperature. The UV and visible PLs were attributed to oxygen deficit center(ODC) and Tb3+ respectively.
The SiC:Tb films were deposited on porous silicon substrate by rfsputtering. The samples prepared were annealed in N2 atmosphere at different temperatures, and Fourier transform infrared has been used to characterize the structure of them. We observed a strong photoluminescence(PL) spectrum at room temperature in the ultraviolet(UV) and visible regions. We found that the UV emission has obvious changed and a slight blue shift was observed with the change of annealing temperature. The UV and visible PLs were attributed to oxygen deficit center(ODC) and Tb3+ respectively.
The effect of lattice mismatch between the substrate and the heteroepitaxial film on the initial process of ultra-thin film growth, such as the nuclear density, the average size of cluster, the scale behavior and the growth mode, is studied by the kinetic Monte-Carlo method. It is found that the negative (positive) mismatch, corresponding to the compressive (tensile) strain, can induce the growth process transferring from the nucleation stage to the intermediate one earlier (later). The larger the mismatch, the more apparent the above behavior. Under the same deposition condition, the negative mismatch can bring about lower nuclear density and larger average cluster size than the positive mismatch does. Furthermore, the nuclear density is found to follow the power law of Ns≈(F/D)χ, andχdecreases from 0.37 to 0.33 while the mismatch changes from –0.04 to 0.02. This behavior indicates that the growth mode of the ultra-thin film changes from including dimer diffusion into excluding dimer diffusion. Additionally, the scale theory of the cluster size is found to be valid even for the heteroepitaxial growth.
The effect of lattice mismatch between the substrate and the heteroepitaxial film on the initial process of ultra-thin film growth, such as the nuclear density, the average size of cluster, the scale behavior and the growth mode, is studied by the kinetic Monte-Carlo method. It is found that the negative (positive) mismatch, corresponding to the compressive (tensile) strain, can induce the growth process transferring from the nucleation stage to the intermediate one earlier (later). The larger the mismatch, the more apparent the above behavior. Under the same deposition condition, the negative mismatch can bring about lower nuclear density and larger average cluster size than the positive mismatch does. Furthermore, the nuclear density is found to follow the power law of Ns≈(F/D)χ, andχdecreases from 0.37 to 0.33 while the mismatch changes from –0.04 to 0.02. This behavior indicates that the growth mode of the ultra-thin film changes from including dimer diffusion into excluding dimer diffusion. Additionally, the scale theory of the cluster size is found to be valid even for the heteroepitaxial growth.
Zinc oxide films doped with various contents of copper were deposited on silicon (111) substrates by rf reactive sputtering. The photoluminescent(PL) spectra of the ZnO films were measuered at room temperature. Results showed that each of the samples had a blue band at about 435nm (2.85eV) and the intensities of these blue bands were changed with the variation of content and sputtering power. It was observed that there is a stronger blue bi-peak when the power reaches 150W and the copper content is equal to 2.5%, and there is a stronger blue peak at 437?nm when the power was 100?W and copper content is 1.5% on the PL spectra of ZnO films, the latter had a good c axis orientation. We have investigated the PL properties for various Cu-doped contents and different sputtering powers, and the mechanism of blue emission was also discussed in this paper.
Zinc oxide films doped with various contents of copper were deposited on silicon (111) substrates by rf reactive sputtering. The photoluminescent(PL) spectra of the ZnO films were measuered at room temperature. Results showed that each of the samples had a blue band at about 435nm (2.85eV) and the intensities of these blue bands were changed with the variation of content and sputtering power. It was observed that there is a stronger blue bi-peak when the power reaches 150W and the copper content is equal to 2.5%, and there is a stronger blue peak at 437?nm when the power was 100?W and copper content is 1.5% on the PL spectra of ZnO films, the latter had a good c axis orientation. We have investigated the PL properties for various Cu-doped contents and different sputtering powers, and the mechanism of blue emission was also discussed in this paper.
The hydrogen-adsorbed diamond (001) surface is studied by ab initio pseudopotential method. The bare and monohydride surface configurations are calculated.The alteration of the charge density redistribution of the monohydride surface shows the formation of the C—H bonding, which leads to electron transfer from carbon atoms in the surface layer to the absorbed H atoms. The mechanism of alteration for charge density redistribution is discussed, which provides a theoretical background for the previous experimental observations and the model of electrical properties of diamond surface.
The hydrogen-adsorbed diamond (001) surface is studied by ab initio pseudopotential method. The bare and monohydride surface configurations are calculated.The alteration of the charge density redistribution of the monohydride surface shows the formation of the C—H bonding, which leads to electron transfer from carbon atoms in the surface layer to the absorbed H atoms. The mechanism of alteration for charge density redistribution is discussed, which provides a theoretical background for the previous experimental observations and the model of electrical properties of diamond surface.
The electret hybrid film consisting of porous PTFE and Teflon FEP is prepared through co-melting method at high temperature and with corona charging.Their piezoelectric responses are investigated by means of decay measurement of isothermal piezoelectric coefficient and charge density.The piezoelectric mechanism is discussed according to the theoretical model proposed by Kacprzyk et al.The results indicate that the piezoelectric responses not only result from charge density but also correlate to the charge distribution in the bulk of hybrid film.
The electret hybrid film consisting of porous PTFE and Teflon FEP is prepared through co-melting method at high temperature and with corona charging.Their piezoelectric responses are investigated by means of decay measurement of isothermal piezoelectric coefficient and charge density.The piezoelectric mechanism is discussed according to the theoretical model proposed by Kacprzyk et al.The results indicate that the piezoelectric responses not only result from charge density but also correlate to the charge distribution in the bulk of hybrid film.
WO3 films are well known for the change of their color through electro, photo and thermochromism. We report here that the nanostructured WO3 bulk has an obvious electrochromic effect, which does not exist in ordinary WO3 bulk. The sample turns to a deep blue color upon changing from anode to cathode when external voltage is applied. There is no difference of the microstructure and phase structure between the colored and uncolored samples. X-ray photoelectron spectroscopy analysis shows that low valence state of tungsten ion (W5+) existed in the colored samples. Based on the experimental results, it is concluded that the coloration is an electron-injection effect. The high valence state of tungsten ion (W6+) in nanostructured WO3 bulk has enough activity to combine with electron and turns to the low valence state counterpart because of the surface effects of nanostructured materials. As a consequence, the sample changes its color.
WO3 films are well known for the change of their color through electro, photo and thermochromism. We report here that the nanostructured WO3 bulk has an obvious electrochromic effect, which does not exist in ordinary WO3 bulk. The sample turns to a deep blue color upon changing from anode to cathode when external voltage is applied. There is no difference of the microstructure and phase structure between the colored and uncolored samples. X-ray photoelectron spectroscopy analysis shows that low valence state of tungsten ion (W5+) existed in the colored samples. Based on the experimental results, it is concluded that the coloration is an electron-injection effect. The high valence state of tungsten ion (W6+) in nanostructured WO3 bulk has enough activity to combine with electron and turns to the low valence state counterpart because of the surface effects of nanostructured materials. As a consequence, the sample changes its color.
The system charge density distribution was investigated by the self-consistent theory. Using the exciton theory, the frequency spectrum of surface plasmon and polariton(SPP) was derived by analyzing charge density matrix. Then, the electric transport matrix formed on the basis of atom orbit functions was classified into polynomial by the frequency spectrum of SPP. Moreover, the physics mechanism of negative resistance caused by the effect of SPP on electric transport was discussed.
The system charge density distribution was investigated by the self-consistent theory. Using the exciton theory, the frequency spectrum of surface plasmon and polariton(SPP) was derived by analyzing charge density matrix. Then, the electric transport matrix formed on the basis of atom orbit functions was classified into polynomial by the frequency spectrum of SPP. Moreover, the physics mechanism of negative resistance caused by the effect of SPP on electric transport was discussed.
The master equation of the single-electron triple-barrier tunnel-junction(TBTJ) model is developed based on the orthodox theory. The steady distribution of electrons on the Coulomb islands is obtained with the linear system of equations method and the I-V curves through the simulation method are presented in this paper. Discontinuities of the slope of the curve at the flat-form of Coulomb staircase compared to double barrier tunnel-junction system, which is caused by the change of the electron numbers on the second Coulomb island, are found. The system temperature requirement can be reduced in the TBTJ system, and the maximum temperature at which Coulomb staircase can be resolved is estimated using the energy spacing at the Fermi energy.
The master equation of the single-electron triple-barrier tunnel-junction(TBTJ) model is developed based on the orthodox theory. The steady distribution of electrons on the Coulomb islands is obtained with the linear system of equations method and the I-V curves through the simulation method are presented in this paper. Discontinuities of the slope of the curve at the flat-form of Coulomb staircase compared to double barrier tunnel-junction system, which is caused by the change of the electron numbers on the second Coulomb island, are found. The system temperature requirement can be reduced in the TBTJ system, and the maximum temperature at which Coulomb staircase can be resolved is estimated using the energy spacing at the Fermi energy.
Four types of pinned magnetic tunnel junctions (MTJs) with threekeylayer structures of Py/Al2O3/Py,Py/Al2O3/Co,Co/Al2O3/Py,Co/Al2O3/Co were fabricated using a contact shadow mask method and an antiferromagnetically pinned layer of Ir22Mn78.The slit width of the shadow mask is 100μm, and the composition of permalloy is Py=Ni79Fe21.For example, the MTJs of Co/Al2O3/Co with a tunneling magnetoresistance (TMR) ratio of 17.2%, the junction resistance of 76?Ω, the resistance area product RS of 760?kΩμm2, and the freelayer reversal field of 1114A·m-1 defined as the field where the TMR rises to 50% of the total jump were achieved at the as deposited state at room temperature. Furthermore, when the magnetic field increases from 0 to 1114?A·m-1 the TMR ratio jumps from 0 to 17.2% with one step, which shows that the magnetic field sensitivity of the junction reached at 0.1%/(103A·m-1). While, the TMR vs external filed H curves for the pinned MTJs of Co/Al2O3/Py show a good rectangular shape with a small free-layer reversal filed of 1114?A·m-1. Our exprimental results show that such MTJs can be used to fabricate the magnetic field sensitive sensors or prototype demonstration devices of magnetoresistive random access memory.
Four types of pinned magnetic tunnel junctions (MTJs) with threekeylayer structures of Py/Al2O3/Py,Py/Al2O3/Co,Co/Al2O3/Py,Co/Al2O3/Co were fabricated using a contact shadow mask method and an antiferromagnetically pinned layer of Ir22Mn78.The slit width of the shadow mask is 100μm, and the composition of permalloy is Py=Ni79Fe21.For example, the MTJs of Co/Al2O3/Co with a tunneling magnetoresistance (TMR) ratio of 17.2%, the junction resistance of 76?Ω, the resistance area product RS of 760?kΩμm2, and the freelayer reversal field of 1114A·m-1 defined as the field where the TMR rises to 50% of the total jump were achieved at the as deposited state at room temperature. Furthermore, when the magnetic field increases from 0 to 1114?A·m-1 the TMR ratio jumps from 0 to 17.2% with one step, which shows that the magnetic field sensitivity of the junction reached at 0.1%/(103A·m-1). While, the TMR vs external filed H curves for the pinned MTJs of Co/Al2O3/Py show a good rectangular shape with a small free-layer reversal filed of 1114?A·m-1. Our exprimental results show that such MTJs can be used to fabricate the magnetic field sensitive sensors or prototype demonstration devices of magnetoresistive random access memory.
a-Si:H/SiO2 multilayers were layer by layer deposited and in situ plasma oxidized in a plasma-enhanced chemical vapor deposition system. Strong and stable blue photoluminescence at room temperature was observed from the as fabricated a-Si:H/SiO2 multilayers. By controlling the thickness of the a-Si:H sublayer from 4 to 1.5nm,the photoluminescence peak blueshifts from 465 to 435?nm. X-ray photo electron spectroscopy indicates that the oxide layer is of stoichiometric SiO2. Good passivation of a-Si:H/SiO2 interface is testified by C-V. Periodical structure and sharp a-Si:H/SiO2 interface is shown by transmission electron microscope. Combined with the measurements of absorption and photoluminescence, the origin of blue photoluminescence is attributed to the recombination of electrons and holes near the band-tail in a-Si:H sublayer under one-dimensional quantum confinement effect.
a-Si:H/SiO2 multilayers were layer by layer deposited and in situ plasma oxidized in a plasma-enhanced chemical vapor deposition system. Strong and stable blue photoluminescence at room temperature was observed from the as fabricated a-Si:H/SiO2 multilayers. By controlling the thickness of the a-Si:H sublayer from 4 to 1.5nm,the photoluminescence peak blueshifts from 465 to 435?nm. X-ray photo electron spectroscopy indicates that the oxide layer is of stoichiometric SiO2. Good passivation of a-Si:H/SiO2 interface is testified by C-V. Periodical structure and sharp a-Si:H/SiO2 interface is shown by transmission electron microscope. Combined with the measurements of absorption and photoluminescence, the origin of blue photoluminescence is attributed to the recombination of electrons and holes near the band-tail in a-Si:H sublayer under one-dimensional quantum confinement effect.
Using finite-temperature molecular dynamic simulations, we study the lower-frequency voltage noise in two-dimensional random-pinning-vortex lattices. We calculate the voltage noise spectrum of the vortex motion, and obtain the broadband noise (BBN) as a function of the driving current, pinning strength, and temperature. It is found that BBN increases with the pinning strength, and decreases with increasing temperature. These results are consistent with experiments and may be understood in terms of the microscopic dynamics of vortex motion.
Using finite-temperature molecular dynamic simulations, we study the lower-frequency voltage noise in two-dimensional random-pinning-vortex lattices. We calculate the voltage noise spectrum of the vortex motion, and obtain the broadband noise (BBN) as a function of the driving current, pinning strength, and temperature. It is found that BBN increases with the pinning strength, and decreases with increasing temperature. These results are consistent with experiments and may be understood in terms of the microscopic dynamics of vortex motion.
In this paper,we study the effect of impurity on the thermal entanglement between the normal lattice in three-qubit Heisenberg XX chain,and give the analytical expression of the concurrence.According to the discussion of our result,we find that the impurity parameter has a great effect on the pairwise thermal entanglement,it even can change the characters of the entanglement to some degree.
In this paper,we study the effect of impurity on the thermal entanglement between the normal lattice in three-qubit Heisenberg XX chain,and give the analytical expression of the concurrence.According to the discussion of our result,we find that the impurity parameter has a great effect on the pairwise thermal entanglement,it even can change the characters of the entanglement to some degree.
Co-Pt-C grain films with in plan magnetic anisotropy and large coercivity Hc were prepared by sputtering on Si substrates in multilayer form,with post-annealing in vacuum at 700℃ for 1?h. After annealing, Co-Pt particles trans form from amorphous to fcc CoPt3 and fct CoPt, and C remains in disorder state. Effects of Pt and C concentration on the magnetic properties of the films are studied. The maximum Hc is 430kA/m when the content of Pt is 70 vol% and the thickness of C layer is 0.4nm. The shoulder developed on the hysteresis loop is analyzed.
Co-Pt-C grain films with in plan magnetic anisotropy and large coercivity Hc were prepared by sputtering on Si substrates in multilayer form,with post-annealing in vacuum at 700℃ for 1?h. After annealing, Co-Pt particles trans form from amorphous to fcc CoPt3 and fct CoPt, and C remains in disorder state. Effects of Pt and C concentration on the magnetic properties of the films are studied. The maximum Hc is 430kA/m when the content of Pt is 70 vol% and the thickness of C layer is 0.4nm. The shoulder developed on the hysteresis loop is analyzed.
By the Green's function technique, we obtain the analytic expressions of the effective magnetoelectric property of composites and calculate the effective magnetoelectric properties of the threephase particulate composites made of rare earth-iron alloys, piezoelectric ceramics and polymer (Terfenol-D/PZT/PVDF). Our results show a strong influence of composite microstructure including the phase composition, aspect ratio of particles, orientation of polarization in PZT particles and applied bias field on the magnetoelectric properties. These numerical results provide guidelines for experimental design of the composites. After optimum design, the magnetoelectric voltage coefficient of these composites may reach as high as hundreds mV/A. As a new kind of magnetoelectric composite, such three-phase composites are expected to be a novel important kind of magnetoelectric materials because of their good magnetic-electrical response and easy fabrication.
By the Green's function technique, we obtain the analytic expressions of the effective magnetoelectric property of composites and calculate the effective magnetoelectric properties of the threephase particulate composites made of rare earth-iron alloys, piezoelectric ceramics and polymer (Terfenol-D/PZT/PVDF). Our results show a strong influence of composite microstructure including the phase composition, aspect ratio of particles, orientation of polarization in PZT particles and applied bias field on the magnetoelectric properties. These numerical results provide guidelines for experimental design of the composites. After optimum design, the magnetoelectric voltage coefficient of these composites may reach as high as hundreds mV/A. As a new kind of magnetoelectric composite, such three-phase composites are expected to be a novel important kind of magnetoelectric materials because of their good magnetic-electrical response and easy fabrication.
High k dielectric HfO2 films were deposited on p-type Si(100) substrates by e-beam evaporation. The composition of the films is determined to be stoichiometric. The structure changes from almost amorphous to polycrystalline after annealing. The films have very flat surface(rms roughness less than 0.3nm) and no voids appear even after high-temperature annealing, indicating a good thermal stability. The refractive index of HfO2 film is 2.09 (at 600?nm). The dielectric constant is 19. All the characteristics show that e-beam evaporation is a good method to deposit HfO2 thin films as dielectric.
High k dielectric HfO2 films were deposited on p-type Si(100) substrates by e-beam evaporation. The composition of the films is determined to be stoichiometric. The structure changes from almost amorphous to polycrystalline after annealing. The films have very flat surface(rms roughness less than 0.3nm) and no voids appear even after high-temperature annealing, indicating a good thermal stability. The refractive index of HfO2 film is 2.09 (at 600?nm). The dielectric constant is 19. All the characteristics show that e-beam evaporation is a good method to deposit HfO2 thin films as dielectric.
CdS0.13Se0.87 nanocrystals of different sizes were grown by annealing glass contained Cd,Se and S at 650—800℃ for 4?h. The absorption spectra, photoluminescence spectra and electroabsorption spectra of the nanocrystals were measured. The energy of part of the electronic states was determined. Dependence of the optical properties of nanocrystals on their size was discussed. With the increase of nanocrystal size, the absorption, photoluminescence and eletroabsorption shifted red due to the weakening of quantum size Stark effects. The electroabsorption of small nanocrystals was due to the quantumconfined Stark effects whereas the electroabsorption line shape of larger nanocrystals was similar to that of bulk materials. With the increase of nanocrystal size, the electroabsor ption is enhanced. All nanocrystals have the third\|order optical susceptibility.
CdS0.13Se0.87 nanocrystals of different sizes were grown by annealing glass contained Cd,Se and S at 650—800℃ for 4?h. The absorption spectra, photoluminescence spectra and electroabsorption spectra of the nanocrystals were measured. The energy of part of the electronic states was determined. Dependence of the optical properties of nanocrystals on their size was discussed. With the increase of nanocrystal size, the absorption, photoluminescence and eletroabsorption shifted red due to the weakening of quantum size Stark effects. The electroabsorption of small nanocrystals was due to the quantumconfined Stark effects whereas the electroabsorption line shape of larger nanocrystals was similar to that of bulk materials. With the increase of nanocrystal size, the electroabsor ption is enhanced. All nanocrystals have the third\|order optical susceptibility.
SiC films were deposited on Si(111) substrates by radio-frequency (RF) sputtering method. High-resolution x-ray diffraction and infrared (IR) absorption spectroscopy were used to investigate the composition and bonding structures of the SiC films. The analysis indicated that the samples deposited at high temperatures (>800℃) were found to consist of 4HSiC or 3CSiC crystallites, while the amorphous films were obtained at lower temperatures. IR spectra suggested that the main absorption property was caused by Si—Cb ondings. Furthermore, atomic force microscopy was used to examine the surface morphology of the SiC films and the field emission properties of the films were studied.
SiC films were deposited on Si(111) substrates by radio-frequency (RF) sputtering method. High-resolution x-ray diffraction and infrared (IR) absorption spectroscopy were used to investigate the composition and bonding structures of the SiC films. The analysis indicated that the samples deposited at high temperatures (>800℃) were found to consist of 4HSiC or 3CSiC crystallites, while the amorphous films were obtained at lower temperatures. IR spectra suggested that the main absorption property was caused by Si—Cb ondings. Furthermore, atomic force microscopy was used to examine the surface morphology of the SiC films and the field emission properties of the films were studied.
Aligned CNx nanotubes were fabricated by pyrolyzing ethylenediamine on p-type Si(111) substrates deposited by Fe catalysts. Scanning electron microscopy, high-resolution transmission electron microscopy and Raman spectroscopy were used to characterize the CNx nanotubes. The CNx nanotubes about 20μm in length and 50-100?nm in diameter have the “bamboo-like” structure and worse crystallinity. Field emission measurements of the CNx nanotubes indicated that 20μA/cm2 current densities were observed at an electric field of 1.4V/μm,and 1.280mA/cm2 were obtained at 2.54V/μm. No current saturation was found under higher electric field. The CNx nanotubes exhibit better field emission properties than carbon nanotubes and BCN nanotubes that have been grown under same experiment conditions only using different precursor solution. The emission mechanism of CNx nanotubes is also discussed based on their “bamboo-like” structures.
Aligned CNx nanotubes were fabricated by pyrolyzing ethylenediamine on p-type Si(111) substrates deposited by Fe catalysts. Scanning electron microscopy, high-resolution transmission electron microscopy and Raman spectroscopy were used to characterize the CNx nanotubes. The CNx nanotubes about 20μm in length and 50-100?nm in diameter have the “bamboo-like” structure and worse crystallinity. Field emission measurements of the CNx nanotubes indicated that 20μA/cm2 current densities were observed at an electric field of 1.4V/μm,and 1.280mA/cm2 were obtained at 2.54V/μm. No current saturation was found under higher electric field. The CNx nanotubes exhibit better field emission properties than carbon nanotubes and BCN nanotubes that have been grown under same experiment conditions only using different precursor solution. The emission mechanism of CNx nanotubes is also discussed based on their “bamboo-like” structures.
The itinerancy of π electrons included in DNA molecules is related to their structures and configurations. The variation of the itinerant electrons will affect the band structure of this kind of soft material to some extent. In the frame work of the tight binding model, we calculated the band structure and the electronic density of states of a DNA chain. It was found that the band gap at the Fermi level depends sensitively upon the number of the itinerant electrons. The conductance of the DNA molecule in different orders of duplex pairs with possible combinations was discussed.
The itinerancy of π electrons included in DNA molecules is related to their structures and configurations. The variation of the itinerant electrons will affect the band structure of this kind of soft material to some extent. In the frame work of the tight binding model, we calculated the band structure and the electronic density of states of a DNA chain. It was found that the band gap at the Fermi level depends sensitively upon the number of the itinerant electrons. The conductance of the DNA molecule in different orders of duplex pairs with possible combinations was discussed.
Metropolis molecular dynamics simulation combined with bond-fluctuation method was employed to study the dynamic process of single DNA chain through an entropic trapping channel driven by an electric field. It was found that the single DNA chain experienced the processes such as random transfer, entropic trapping and fast transfer etc. The mobility of DNA increased with the increase of electric field and reached the conformation-independent mobility μ0 at a high electric field. In particular, a clear linear relationship between lnτ and 1/Eav (the reciprocal of electric field) could be seen. The simulation result was in agreement with the experimental result presented by Han et al qualitatively. In addition, the simulation provided a detailed dynamic process of the single DNA chain driven through an entropic trapping channel,which could not be observed in the experiment.
Metropolis molecular dynamics simulation combined with bond-fluctuation method was employed to study the dynamic process of single DNA chain through an entropic trapping channel driven by an electric field. It was found that the single DNA chain experienced the processes such as random transfer, entropic trapping and fast transfer etc. The mobility of DNA increased with the increase of electric field and reached the conformation-independent mobility μ0 at a high electric field. In particular, a clear linear relationship between lnτ and 1/Eav (the reciprocal of electric field) could be seen. The simulation result was in agreement with the experimental result presented by Han et al qualitatively. In addition, the simulation provided a detailed dynamic process of the single DNA chain driven through an entropic trapping channel,which could not be observed in the experiment.
In the field of the oil exploration, the research is focused on the fracture detection in recent years. The difficulty is how to determine the orientation of the crack. To solve this problem, the relationship between the wave equations and the orientation of the crack should be determined. Unfortunately, the existing wave equations cannot completely reveal these relations. This paper studies the fractured media with arbitrary azimuthal angles. The convolution integral is solved incrementally, and then the corresponding time-domain wave equations are presented. The wave equations may be solved to model the wave propagation in the azimuthally anisotropic and viscoelastic media and to reveal the mechanisms of seismic multi-wave propagation in fractured media.
In the field of the oil exploration, the research is focused on the fracture detection in recent years. The difficulty is how to determine the orientation of the crack. To solve this problem, the relationship between the wave equations and the orientation of the crack should be determined. Unfortunately, the existing wave equations cannot completely reveal these relations. This paper studies the fractured media with arbitrary azimuthal angles. The convolution integral is solved incrementally, and then the corresponding time-domain wave equations are presented. The wave equations may be solved to model the wave propagation in the azimuthally anisotropic and viscoelastic media and to reveal the mechanisms of seismic multi-wave propagation in fractured media.