As one of the most popular micro pattern gaseous detectors, gas electron multiplier (GEM) has been extensively studied and applied in recent years. The studies of the detector gain measurement and simulation are important, especially on a low gain scale. Traditionally, the gain measurement is realized by measuring the current or the pulse height spectrum. The former needs complicated electronic chain calibration and the latter needs necessarily to calculate the primary electron number. In this paper, an alternative method to determine the effective gain of GEM is introduced. The GEM gain can be precisely achieved through a gaseous detector of hybrid structure which combines GEM with micro-mesh gaseous structure (MM). The hybrid structure is called GEM-MM for short. The GEM-MM detector consists of drift cathode, standard GEM foil, stainless steel micro mesh, and readout anode. In this detector, the space between the cathode and the GEM foil is called drift gap and the other space between the GEM foil and the mesh is named transfer gap. When the X-rays irradiate into the gas volume of GEM-MM, the primary ionization occurs in both regions. Photoelectrons in the drift gap transfer from the drift region to amplification sensitive areas of the GEM and the MM detector while those in the transfer region are only amplified by the MM detector. In the energy spectrum of 55Fe, there is a clear energy profile including two sets of peaks. The gain of GEM can be easily obtained from the energy spectrum. Meanwhile, detailed simulations are carried out with Garfield++ software package. Simulation of the electron transport parameters has been optimized. and the gains of GEM detector are also calculated for three different gas mixtures. Experimental results of the gains ranging from 3 to 24 are obtained. The gains of GEM under different working voltages are studied precisely from the spectrum measurements. The Penning transfer rate could reach 0.32±0.01 when the simulated value matches the measurement within 1σ error.

Surface plasmons as the collective electrons oscillation at the interface of metal and dielectric materials, have induced tremendous applications for the nanoscale light focusing, waveguiding, coupling, and photodetection. As the development of the modern technology, cathodoluminescence (CL) has been successfully applied to describe the plasmon resonance within the nanoscale. Usually, the CL detection system is combined with a high resolution scanning electron microscope (SEM). The fabricated plasmonic nanostructure is directly excited by the electron beam, and detected by an ultra-sensitive spectrometer and photodetector. Under the high energy electron stimulation, all of the plasmon resonances of the metallic nanostructure can be excited. Because of the high spatial resolution of the SEM, the detected CL can be used to analyze the details of plasmon resonance modes.In this review, we first briefly introduced the physical mechanism for the CL generation, and then discussed the CL emission of single plasmonic nanostructures such as different nanowires, nanoantennas, nanodisks and nanocavities, where the CL only describes the individual plasmon resonance modes. Second, the plasmon coupling behavior for the ensemble measurement was compared and analyzed for the CL detection. Finally, the CL detection with other advanced technologies were concluded. We believe with the development of the nanophotonics community, CL detection as a unique technique with ultra-high energy and spatial resolution has potential applications for the future plasmonic structure design and characterization.

Optical near field enhancement on substrate can be achieved by localizing femtosecond laser energy with nanoparticles. The enhanced field is located in the region between nanoparticles and the substrate. The localized femtosecond optical field is of great significance for fabricating the micro/nano structure with characteristic size beyond the diffraction limit. Up to now, femtosecond processing nanohole assisted by particle array is only possible for metal particle (Au) and low-refractive-index dielectric polystyrene particle. However, previous research results show that it cannot be realized for metal particle arrays (Au) to form periodic nanohole arrays, and it is limited for polystyrene particle to choose the corresponding substrate. In this paper, a novel method is proposed, in which high refractive index TiO2 arrayed particles are placed on the substrate to achieve laser induced near field enhancement. This makes feasible the nanoscale processing beyond the diffraction limit. In this paper, near field distributions of TiO2 particle array on Si, Pt and SiO2 substrates are simulated by the finite-difference time-domain (FDTD) method. The results show that TiO2 particles concentrate the laser energy to a region with a diameter of 100 nm around the particle and the near field enhancement is 140 times higher than the incident laser intensity, which is beneficial to fabricating the nanostructure of super diffraction limit, such as sub-hundred nanometer nanohole ablation by femtosecond laser. For Si substrate, the near field enhancement is only about 30% lower for TiO2 particle array than that for single TiO2 particle. In order to explore the influence mechanism of the substrate material parameters on the near field enhancement of TiO2 nanoparticle array, we further simulate the enhancement factor for the substrates of different refractive indices. It is found that the near field is enhanced with the increase of substrate refractive index, and this is attributed to an increased interaction of the particle with the near field of substrate and the scattering effect in which the TiO2 particle supports forward near field intensity pattern. Moreover, the image charge model is introduced to analyze the effect of substrate optical parameters on local field enhancement. Results in this paper can be applied to most metals as well as dielectric substrate surfaces, and they open a new way for femtosecond laser near field nano-processing with characteristic size beyond the diffraction limit.

Surface plasmon polaritons (SPPs), the electromagnetic waves traveling along metal-dielectric or metal-air interface, which originate from the interactions between light and collective electron oscillations on metal surface, have received considerable attention for their promising applications in the future optical field, such as image, breaking diffraction limit, subwavelength-optics microscopy, lithography, etc. However, one of the fundamental issues in plasmonics is how to actively manipulate the propagation direction of SPPs. In this paper, we propose and numerically investigate a graphene-based unidirectional SPP coupler, which is composed of asymmetric plasmonic nanoantenna pairs with a graphene sheet separated by a SiO2 spacer from the gold substrate. The device geometry facilitates the simultaneous excitation of two localized surface plasmon resonances in the entire structure, and consequently, the asymmetric nanoantenna pairs can be considered as being composed of two oscillating magnetic dipoles or as two SPP sources. Because the resonance of the plasmonic antenna pairs depends on the bias voltage applied across graphene sheet and back-gated Au, the phase difference between radiated electromagnetic waves induced by the antenna can be tuned through varying the Fermi level of graphene. Here, approximately a n/2 phase difference between radiated electromagnetic (EM) waves can be acquired at EF 0.81 eV, which indicates that the radiated EM waves can interfere constructively along the direction of the x-axis while interfere destructively along the opposite direction. This directional propagation of EM wave leads to the unidirectional propagation of SPPs. Furthermore, electric field distribution of the cavity demonstrates that the tunability of plasmonic antenna is proportional to the electric field intensity in the vicinity of the graphene region. For our designed structure, the left cavity can provide a significantly larger tunable range than the right one. With this result, we can quantitatively analyze the tuning behavior of graphene-loaded plasmonic antenna based on equivalent circuit model, and draw the conclusions that the unidirectional SPP propagation effect originates from the interference mechanism. In addition, compared with the device reported previously, our proposed device possesses a huge extinction ratio (2600) and more broadband tunable wavelength range (6.3-7.5 m). In addition, it is possible to make up for the deficiencies of current nanofabrication technologies by utilizing its actively controlled capability. All the above results indicate that the proposed active device promises to realize a compactable, tunable, and broadband terahertz plasmonic light source. It will play an important role in future photonic integrations and optoelectronics.

Sapphire has shown broad application prospects in military and medical fields, due to its high hardness, excellent corrosion resistance and high transmission in the infrared band. However, these characteristics have also brought about lots of difficulties in machining or chemical etching the material. Femtosecond laser processing with excellent characteristics including small heat-affected zones and high processing resolution ratio, has become an emerging field. Therefore, it has important application prospects and has found increasingly wide applications in the fields of material modification and high-quality fabrication of three-dimensional micro-nano structures and devices. In this paper, we propose a method in which femtosecond laser processing based on multi-photon absorption is used to process sapphire beyond the optical diffraction limit. In this work, femtosecond laser with a central wavelength of 343 nm is focused on the sapphire and the surface of sapphire is scanned with the high-precision piezoelectric positioning stages. Nano structures each with a width of about 61 nm are obtained, and the minimum space between the nano structures could be as short as about 142 nm. Further, the influences on the processing resolution from laser power and scanning speed are investigated and the generation mechanism for the nano-ripple structure is discussed. Finally, femtosecond laser processing on the sapphire with a resolution beyond the optical diffraction limit is achieved. This work provides a reference for processing the hard and brittle materials by femtosecond laser.

Structural vibration is commonly seen in engineering, which can cause resonance and fatigue damage in structure. Therefore, it is very desirable in vibration control techniques to achieve structure with low-frequency and broadband damping feature. In this paper, we design a phononic crystal (PC) beam with X-shaped locally resonant metadamping (X-LRMD) structures. Based on the PC theory, the flexural wave propagation in X-LRMD beam is studied. The equivalent dynamic properties of the X LRMD structure are analyzed by Lagrange equation. It is shown that due to its geometric nonlinearity, the X LRMD can effectively increase the damping of the system, which is validated by the transfer matrix method. The influence of structural parameters of X LRMD on band gap characteristics of the PC beam is then discussed in detail by using the finite element method with COMSOL multiphysics software in conjunction with Matlab, where the PC beam with X LRMD is modeled with the multi-body dynamic module within COMSOL and the band gap characteristics are calculated. The damping properties of the system are studied also using the finite element method. It is shown that compared with the equivalent structures, the PC beam with X LRMD can magnify the damping of the structure system, demonstrating a meta-damping phenomenon. The X LRMD in the PC beam can not only generate lower frequency and wider range band gaps but also suppress the vibration in passband ranges. This can bring a new design for reducing the vibration of structural systems.

In the field of optical imaging, the conventional imaging resolution is about 200 nm due to the diffraction limit. The higher resolution is urgently needed for further developing scientific research. Therefore, how to break through this limitation to acquire high quality and high resolution image has become a hot research topic. The microspheres with the size of tens of micrometers exhibit the ability to improve the imaging resolution of the conventional optical microscope by locating them directly on the sample surface. Due to its simplicity, the microsphere optical nanoscope technology is widely studied. This paper introduces the research background of the optical microscope and the research progress of microsphere optical nanoscope technology. At the same time, approaches to adjusting the photonic nanojet generated by the microspheres by fabricating concentric ringing, central mask, and surface coating of microspheres are reviewed. The possible reasons for this improved resolution are discussed. The applications and development of the microsphere ultra-microscopic technology in the future are discussed.

Surface plasmon polariton has attracted more and more attention and has been studied extensively in the recent decades, owing to its ability to confine the electro-magnetic field to a sub-wavelength scale near the metal-dielectric interface. On one hand, the tightly confined surface plasmonic modes can reduce the size of integrated optical device beyond the diffraction limit; on the other hand, it provides an approach to enhancing the interaction between light and matter. With the development of experimental and numerical simulation techniques, its investigation at a quantum level has become possible. In the recent experiments, scientists have realized quantum interference between single plasmons in a nanoscale waveguide circuit and achieved the strong coupling between photons and single molecules by using plasmonic structure, which demonstrates its superiority over the traditional optics. Here, we review the theoretical and experimental researches of surface plasmon polariton in the field of quantum information processing. First, we introduce the experiments on the basic quantum properties of surface plasmons, including the preservation of photonic entanglement, wave-particle duality and quantum statistical property. Second, we review the research work relating to the generation, manipulation and detection of surface plasmons in a quantum plasmonic integrated circuit. Then, we present the research of the interaction between surface plasmons and single quantum emitters and its potential applications. Finally, we make a discussion on how the intrinsic loss affects the quantum interference of single plasmons and the coupling between quantum emitters. The collision and combination of quantum optical and plasmonic fields open up possibilities for investigating the fundamental quantum physical properties of surface plasmons. It can be used to make ultra-compact quantum photonic integrated circuits and enhance the interaction strength between photons and quantum emitters.

The diffraction limit of traditional optical device greatly restricts the further development of optical super-resolution systems. It is a great challenge to overcome the diffraction limit at a device level, and achieve label-free far-field super-resolution imaging. Optical super-oscillation provides a new way to realize super-resolution since it allows the generation of arbitrary small structures in optical fields in the absence of evanescent waves. The researches of optical super-oscillation and super-oscillatory optical devices have grown rapidly in recent decades. Optical super-oscillation and super-oscillatory optical devices have been demonstrated theoretically and experimentally to show great potential applications in label-free far-field optical microscopy, far-field imaging and high-density data storage. In this paper, we gives a broad review of recent development in optical super-oscillation and super-oscillatory optical devices, including basic concepts, design tools and methods, testing techniques for super-oscillatory optical field, and their applications.

Due to the fundamental laws of wave optics, the spatial resolution of traditional optical microscopy is limited by the Rayleigh criterion. Enormous efforts have been made in the past decades to break through the diffraction limit barrier and in depth understand the dynamic processes and static properties. A growing array of super-resolution techniques by distinct approaches have been invented, which can be assigned to two categories: near-field and far-field super-resolution techniques. The near-field techniques, including near-field scanning optical microscopy, superlens, hyperlens, etc., could break through the diffraction limit and realize super-resolution imaging by collecting and modulating the evanescent wave. However, near-field technique suffers a limitation of very short working distances because of the confined propagation distance of evanescent wave, and certainly produces a mechanical damage to the specimen. The super-resolution fluorescence microscopy methods, such as STED, STORM, PALM, etc., could successfully surpass the diffractive limit in far field by selectively activating or deactivating fluorophores rooted in the nonlinear response to excitation light. But those techniques heavily rely on the properties of the fluorophores, and the labelling process makes them only suitable for narrow class samples. Developing a novel approach which could break through the diffraction limit in far field without any near-field operation or labelling processes is of significance for not only scientific research but also industrial production. Recently, the planar metalenses emerge as a promising approach, owing to the theoretical innovation, flexible design, and merits of high efficiency, integratable and so forth. In this review, the most recent progress of planar metalenses is briefly summarized in the aspects of sub-diffractive limit focusing and super-resolution imaging. In addition, the challenge to transforming this academic concept into practical applications, and the future development in the field of planar metalenses are also discussed briefly.

Electromagnetic metamaterials are artificial structures engineered on a subwavelength scale to have optical properties that are not observed in their constituent materials and may not be found in nature either, such as negative refractive index. They have enabled unprecedented flexibility in manipulating light waves and producing various novel optical functionalities. Since the beginning of this century, with the development of nanofabrication and characterization technologies, there has been aroused a tremendous growing interest in the study of electromagnetic metamaterials and their potential applications in different fields including super-resolution imaging, optical biosensing, electromagnetic cloaking, photonic circuits and data storage. Electromagnetic metasurfaces are two-dimensional metamaterials composed of subwavelength planar building blocks. Although metasurfaces sacrifice some functionalities compared with their bulk counterparts, they provide us with distinct possibility to fully control light wave with ultrathin planar structures. Based on Huygens principle, the metasurfaces are able to arbitrarily manipulate the phases, amplitudes or polarizations of optical waves. For example, metasurfaces made of gold nanoantenna-arrays are able to create phase discontinuities for light propagating through the interfaces and drastically change the flows of reflected and refracted light at infrared frequencies. Comparing traditional dielectric optic elements, the thickness values of metasurface-based optical devices are much smaller. In addition to the control of free-space incident light, metasurfaces can also be used to precisely control and manipulate surface electromagnetic waves. In this review, we introduce the generalized Snell's law and the fundamental principles to modulate phase by using metasurfaces. Research progress of a variety of imaging technologies based on metasurfaces is then presented, including plasmonic metasurface, all-dielectric metasurface and metal/insulator hybrid metasurface. Finally, we summarize several frontier problems associated with metasurface, which maybe provide some references for the future researches and applications.

For a semiconductor material, the characterization of its electronic band structure is very important for analyzing its physical properties and applications in semiconductor-based devices. Photoreflectance spectroscopy is a contactless and highly sensitive method of characterizing electronic band structures of semiconductor materials. In the photoreflectance spectroscopy, the modulation of pumping laser can cause a change in material dielectric function particularly around the singularity points of joint density of states. Thus the information about the critical points in electronic band structure can be obtained by measuring these subtle changes. However, in the conventional single-modulated photoreflectance spectroscopy, Rayleigh scattering and inevitable photoluminescence signals originating from the pumping laser strongly disturb the line shape fitting of photoreflectance signal and influence the determination of critical point numbers. Thus, experimental technique of photoreflectance spectroscopy needs further optimizing. In this work, we make some improvements on the basis of traditional measurement technique of photoreflectance spectroscopy. We set an additional optical chopper for the pumping laser which can modulate the amplitude of the photoreflectance signal. We use a dual-channel lock-in amplifier to demodulate both the unmodulated reflectance signals and the subtle changes in modulated reflectance signals at the same time, which avoids the systematic errors derived from multiple measurements compared with the single-modulated photoreflectance measurement. The combination of dual-modulated technique and dual-channel lock-in amplifier can successfully eliminate the disturbances from Rayleigh scattering and photoluminescence, thus improving the signal-to-noise ratio of the system. Under a visible laser (2.33 eV) pumping, we measure the room-temperature dual-modulated photoreflectance spectrum of semi-insulating GaAs in a region from near-infrared to ultraviolet (1.1 ～6.0 eV) and obtain several optical features which correspond to certain critical points in its electronic band structure. Besides the unambiguously resolved energy level transition of E0 and E0+0 around the bandgap, we also obtain several high-energy optical features above the energy of pumping laser which are related to high-energy level transitions of E1, E1+1, E0' and E2 in the electronic band structure of GaAs. This is consistent with the results from ellipsometric spectroscopy and electroreflectance spectroscopy. The results demonstrate that for those high-energy optical features, the mechanism for photoreflectance is that the photon-generated carriers modulate the build-in electric field which affects the overall electronic band structures, rather than the band filling effect around those critical points. This indicates that dual-modulated photoreflectance performs better in the characterization of semiconductors electronic band structure at critical point around and above its bandgap.

Structure illumination microscopy (SIM) is a novel imaging technique with advantages of high spatial resolution, wide imaging field and fast imaging speed. By illuminating the sample with patterned light and analyzing the information about Moir fringes outside the normal range of observation, SIM can achieve about 2-fold higher in resolution than the diffraction limit, thus it has played an important role in the field of biomedical imaging. In recent years, to further improve the resolution of SIM, people have proposed a new technique called plasmonic SIM (PSIM), in which the dynamically tunable sub-wavelength surface plasmon fringes are used as the structured illuminating light and thus the resolution reaches to 3-4 times higher than the diffraction limit. The PSIM technique can also suppress the background noise and improve the signal-to-noise ratio, showing great potential applications in near-surface biomedical imaging. In this review paper, we introduce the principle and research progress of PSIM. In Section 1, we first review the development of optical microscope, including several important near-field and far-field microscopy techniques, and then introduce the history and recent development of SIM and PSIM techniques. In Section 2, we present the basic theory of PSIM, including the dispersion relation and excitation methods of surface plasmon, the principle and imaging process of SIM, and the principle of increasing resolution by PSIM. In Section 3, we review the recent research progress of two types of PSIMs in detail. The first type is the nanostructure-assisted PSIM, in which the periodic metallic nanostructures such as grating or antenna array are used to excite the surface plasmon fringes, and then the shift of fringes is modulated by changing the angle of incident light. The resolution of such a type of PSIM is mainly dependent on the period of nanostructure, thus can be improved to a few tens of nanometers with deep-subwavelength structure period. The other type is the all-optically controlled PSIM, in which the structured light with designed distribution of phase or polarization (e.g. optical vortex) is used as the incident light to excite the surface plasmon fringes on a flat metal film, and then the fringes are dynamically controlled by modulating the phase or polarization of incident light. Without the help of nanostructure, such a type of PSIM usually has a resolution of about 100 nm, but benefits from the structureless excitation of plasmonic fringes in an all-optical configuration, thereby showing more dynamic regulation and reducing the need to fabricate nanometer-sized complex structures. In the final Section, we summarize the features of PSIM and discuss the outlook for this technique. Further studies are needed to improve the performance of PSIM and to expand the scope of practical applications in biomedical imaging.

Optical microscope has been giving impetus to the development of modern technology. As the advancement of these techniques, high resolution microscopy becomes crucial in biological and material researches. However, the diffraction limit restricts the resolution of conventional microscopy. In 1968, confocal microscopy, the first pointwise scanning superresolution method, appeared. It improves the imaging resolution, enhances the contrast, and thus breaks through the diffraction limit. Since then many superresolution methods have come into being, among which the pointwise scanning superresolution method earns reputation for its high imaging resolution and contrast. The stimulated emission depletion microscopy becomes the most prominent method with an achievable resolution of about 2.4 nm and then widely used. Besides, the newly developed fluorescence emission difference microscopy (FED) and the saturated absorption competition microscopy (SAC) have their advantages of non-constraint on fluorescent dyes, low saturated beam power, simplified optical setups, while they achieve a resolution of lower than /6. Further explorations of FED will be keen on vivo biological observations by using it, while that of SAC can concentrate on enhancing the resolution on a nanoscale and reducing the signal-to-noise ratio. In addition, the Airyscan technique in which a detector array is used for image acquisition, can serve as a complementary tool to further enhance the imaging quality of pointwise scanning superresolution method. The detector-array enables both the narrowed size of pinhole and the increasing of the acquired signal intensity by 1.84 folds. The other methods, e.g. superoscillation lens and high-index resolution enhancement by scattering, have the potentialities to obtain superresolved image in material science or deep tissues. After being developed in the past three decades, the superresolution methods now encounter a new bottleneck. Further improvement of the current methods is aimed at imaging depth, and being used more practically and diversely. In this review, we detailedly describe the above pointwise scanning superresolution methods, and explain their principles and techniques. In addition, the deficiencies and potentialities of these methods are presented in this review. Finally, we compare the existing methods and envision the next generation of the pointwise scanning superresolution methods.

As a fundamental property of waves, diffraction plays an important role in many physical problems. However, diffraction makes waves in free space unable to be focused into an arbitrarily small space, setting a fundamental limit (the so-called diffraction limit) to applications such as imaging, lithography, optical recording and waveguiding, etc. Although the diffraction effect can be suppressed by increasing the refractive index of the surrounding medium in which the electromagnetic and optical waves propagate, such a technology is restricted by the fact that natural medium has a limited refractive index. In the past decades, surface plasmon polaritons (SPPs) have received special attention, owing to its ability to break through the diffraction limit by shrinking the effective wavelength in the form of collective excitation of free electrons. By combining the short wavelength property of SPPs and subwavelength structure in the two-dimensional space, many exotic optical effects, such as extraordinary light transmission and optical spin Hall effect have been discovered and utilized to realize functionalities that control the electromagnetic characteristics (amplitudes, phases, and polarizations etc.) on demand. Based on SPPs and artificial subwavelength structures, a new discipline called subwavelength electromagnetics emerged in recent years, thus opening a door for the next-generation integrated and miniaturized electromagnetic and optical devices and systems.In this paper, we review the theories and methods used to break through the diffraction limit by briefly introducing the history from the viewpoint of electromagnetic optics. It is shown that by constructing plasmonic metamaterials and metasurfaces on a subwavelength scale, one can realize the localized phase modulation and broadband dispersion engineering, which could surpass many limits of traditional theory and lay the basis of high-performance electromagnetic and optical functional devices. For instance, by constructing gradient phase on the metasurfaces, the traditional laws of reflection and refraction can be rewritten, while the electromagnetic and geometric shapes could be decoupled, both of which are essential for realizing the planar and conformal lenses and other functional devices. At the end of this paper, we discuss the future development trends of subwavelength electromagnetics. Based on the fact that different concepts, such as plasmonics, metamaterials and photonic crystals, are closely related to each other on a subwavelength scale, we think, the future advancements and even revolutions in subwavelength electromagnetics may rise from the in-depth intersection of physical, chemical and even biological areas. Additionally, we envision that the material genome initiative can be borrowed to promote the information exchange between different engineering and scientific teams and to enable the fast designing and implementing of subwavelength structured materials.

Laser is recognized as one of the top technological achievements of 20th century and plays an important role in many fields, such as medicine, industry, entertainment and so on. Laser processing technology is one of the earliest and most developed applications of laser. With the rapid development of nanoscience and nanotechnology and micro/nano electronic devices, the micro/nanofabrication technologies become increasingly demanding in manufacturing industries. In order to realize low-cost, large-area and especially high-precision micro-nanofabrication, it has great scientific significance and application value to study and develop the laser fabrication technologies that can break the diffraction limit. In this article, the super resolution laser fabrication technologies are classified into two groups, far-filed laser direct writing technologies and near-field laser fabrication technologies. Firstly, the mechanisms and progress of several far-field laser direct writing technologies beyond the diffraction limit are summarized, which are attributed to the lasermatter nonlinear interaction. The super-diffraction laser ablation was achieved for the temperature-dependent reaction of materials with the Gaussian distribution laser, and the super-diffraction laser-induced oxidation in Metal-Transparent Metallic Oxide grayscale photomasks was realized by the laser-induced Cabrera-Mott oxidation process. Besides, the multi-photon polymerization techniques including degenerate/non-degenerate two-photon polymerization are introduced and the resolution beyond the diffraction limit was achieved based on the third-order nonlinear optical process. Moreover, the latest stimulated emission depletion technique used in the laser super-resolution fabrication is also introduced. Secondly, the mechanisms and recent advances of novel super diffraction near-field laser fabrication technologies based on the evanescent waves or surface plasmon polaritons are recommended. Scanning near-field lithography used a near-field scanning optical microscope coupled with a laser to create nanoscale structures with a resolution beyond 100 nm. Besides, near-field optical lithography beyond the diffraction limit could also be achieved through super resolution near-field structures, such as a bow-tie nanostructure. The interference by the surface plasmon polariton waves could lead to the fabrication of super diffraction interference fringe structures with a period smaller than 100 nm. Moreover, a femtosecond laser beam could also excite and interfere with surface plasmon polaritons to form laser-induced periodic surface structures. Furthermore, the super-resolution superlens and hyperlens imaging lithography are introduced. Evanescent waves could be amplified by using the superlens of metal film to improve the optical lithography resolution beyond the diffraction resolution. The unique anisotropic dispersion of hyperlens could provide the high wave vector component without the resonance relationship, which could also realize the super resolution imaging. Finally, prospective research and development tend of super diffraction laser fabrication technologies are presented. It is necessary to expand the range of materials which can be fabricated by laser beyond the diffraction limit, especially 2D materials.

In the last few decades, nanoscience and nanotechnology have been growing with breath taking speed, and how to break through the diffraction limit and tame the light on a nanoscale have become the major challenges in optics. In this field, several super-resolution optical nanoscopy techniques have been developed, leading to a series of breakthroughs in physics, chemistry, and life sciences. In the work, we give a retrospect of the newly developed techniques in diffraction theory of linear optical systems, including the solid immersion lens, structured light illumination microscopy, scanning near-field optical microscopy, metamaterial-based wide field near-field imaging technique and super-oscillatory lens. Brief discussion on their principles, advantages and applications is also provided.

Nanophotonics focuses on the study of the behavior of light and the interaction between light and matter on a nanometer scale. It has often involved metallic nanostructures which can concentrate and guide the light beyond the diffraction limit due to the unique surface plasmons (SPs). Manipulation of light can be accomplished through controlling the morphologies and components of metallic nanostructures to incur special surface plasmons. However, it is still a severe challenge to achieve exquisite control over the morphologies or components of metallic nanostructures: chemical methods can provide anisotropic but highly symmetric metallic nanostructures; lithographic methods have a limited resolution, especially for three-dimensional metallic nanostructures. By comparison, DNA self-assembly-based fabrication of metallic nanostructures is not restricted to these confinements. With the high-fidelity Waston-Crick base pairing, DNA can self-assemble into arbitrary shapes ranging from the simplest double strands to the most sophisticated DNA origami. Due to the electrostatic interactions between negatively charged phosphate backbones and positively charged metal ions, DNA of any shapes can affect the metal ions or atoms to a certain degree. Depending on the shape and base, DNA self-assembly nanostructures can exert different influences on the growth of metallic nanoparticles, which in turn gives rise to deliberately controllable metallic nanostructures. Besides, DNA self-assembly nanostructures can act as ideal templates for the organization of metallic nanoparticles to construct special metallic nanostructures. In this case, DNA-modified metallic nanoparticles are immobilized on DNA self-assembly nanostructures carrying complementary sticky ends. The geometry and component arrangements of metallic nanostructures both can be precisely dictated on the DNA nanostructures by programming the sticky end arrays. Complicated metallic nanostructures which can be hardly fabricated with conventional chemical or lithographic methods have been readily prepared with the DNA self-assembly-based fabrication method, thereby greatly promoting the development of nanophotonics. Therefore, the studies of DNA self-assembly-based fabrication of metallic nanostructures and related nanophotonics have received rapidly growing attention in recent years. This review first gives a brief introduction of the mechanism for breaking the diffraction limit of light with metallic nanostructures based on SPs. Then we give a systematic review on DNA self-assembly-based fabrication of metallic nanostructures and related nanophotonics, which is divided into several parts according to the different pathways by which DNA self-assembly can influence the morphologies or components of metallic nanostructures. Finally, the remaining problems and limitations for the existing DNA self-assembly-based fabrication of metallic nanostructures are presented and an outlook on the future trend of the field is given as well.

In linear optical regime, many novel optical functions have been demonstrated by using ultrathin photonic metasurfaces. The main concept of metasurface is to appropriately assembly the spatially variant meta-atoms on a subwavelength scale, and realize the manipulations of polarization, phase and amplitude of light. Recently, the nonlinear optical properties of photonic metasurfaces have attracted a lot of attention. In this review, we discuss the design, material selection, symmetry consideration of the meta-atoms, as well as the applications such as nonlinear chiral optics, nonlinear geometric Berry phase and nonlinear wavefront engineering. Lastly, we point out the challenges and potentials of nonlinear photonic metasurfaces for manipulating the light-matter interactions.

The diffraction of the finite aperture in the optical imaging system restricts further improvement of the resolution of optical microscopy, which is called the diffraction limit. Since raised by Ernst Abbe in 1873, the problem of diffraction limit has been one of the foci of academic research. In recent years, with the rapid development of related fields such as the development of optoelectronic devices including high energy lasers and high sensitivity detectors and the development of new fluorescent probes, the problem of diffraction limit in optical microscopy ushered in a new opportunity, and super-resolution microscopy (SRM) has made remarkable achievements in the past decade. The basic principles of diffraction limited resolution in both space and frequency domains are reviewed, and on this basis, the mechanisms for the various SRM technologies to circumvent the diffraction limit and improve the resolution are explained in detail. The development trends and research directions of various SRM techniques are also introduced. As a new and important development trend of SRM, correlative super-resolution microscopy and its recent progress are reviewed, including correlative studies on SRM and time-lapse live cell fluorescence microscopy, fluorescence lifetime imaging microscopy, spectrometry and spectroscopy, electron microscopy, atomic force microscopy, etc. The role and significance of various correlative super-resolution microscopy are discussed. The future development of super-resolution microscopy and correlative super-resolution microscopy is also prospected.

Structured illumination microscopy (SIM) is one of the most promising super-resolution techniques, owing to its advantages of fast imaging speed and weak photo bleaching. The quality of the SIM image is greatly dependent on the contrast of the sinusoidal fringe illumination patterns. Low fringe contrast illumination will seriously affect the super-resolution result and lead to additional artifacts. The generation of fringe patterns with high contrast is the key requirement in hardware for the SIM technique. This can be done by the interference of two laser beams diffracted from the phase gratings addressed on a spatial light modulator. Meanwhile, for maximal interference contrast, precise polarization control to maintain s-polarization for different fringe orientations is critical. In this paper, we review several typical polarization control methods in SIM, and propose a new method by using a zero-order vortex half-wave retarder (VHR). Compared with the other methods, the presented VHR-based polarization control method is very efficient in terms of simple system configuration, ease of use, and high light energy utilization efficiency near to 100%.

Accurate measurement of the ionization cross section of the target atom induced by collision between ions and atoms is of great significance for studying the atomic shell process and establishing a suitable theoretical model. The experimental data and the theoretical models mostly concentrate on the cases in the low energy region at present. Only a few experimental data of high energy region are reported due to the limitation of experimental conditions. Which theory is more suitable to describe the ionization cross section of the inner shell of the target atom caused by the high energy heavy ions, is necessarily studied experimentally. The C6+ ions provided by the Heavy Ion Research Facility in Lanzhou Electron Cooling Storage Ring, are used to bombard the Ni target, in which the K-shell X-ray of Ni is measured. The incident energies of C6+ ions are 165, 300, 350 and 430 MeV/u respectively. Through analyzing the intensity ratio of K/K X-ray of Ni, it is found that the influence of incident energy on the intensity ratio of K/K X-ray is not obvious. The intensity ratios of this experiment are greater than the experimental values of incident proton and the calculated values based on the Hartree-Slater theory, which may be caused by the multiple-ionization of the L shell. The production cross sections of Ni K-shell X-ray are calculated by the binary encounter approximation (BEA) model, the plane wave Born approximation (PWBA) model and the energy-loss coulomb-repulsion perturbed-stationary-state relativistic (ECPSSR) theory respectively, which are compared with the experimental results in this paper. It is found that the experimental cross section increases with the increasing incident energy, which is consistent with the trend of BEA model estimation, but the experimental value is obviously lower than the theoretical value. We think that BEA model needs to be modified when describing the ionization process in the high energy region.

The generation, propagation and application of optical vortex have been hot research topics in recent years. Optical vortex carries orbital angular momentum (OAM) that potentially increases the capacity and the spectral efficiency of optical communication system as a new degree of freedom. The optical vortex can be used not only as information carrier for space-division multiplexing, but also for encoding/decoding. We present a novel free-space optical communication system based on hybrid optical mode array encoding/decoding. The array includes four modes that can easily be identified by image processing. The four modes are Gaussian beam, single optical vortex, and two different composite optical vortices. In this paper, the computer generated hologram (CGH) of the hybrid optical mode array is generated based on the object-oriented conjugate-symmetric extension Fourier holography. When the CGH is loaded onto the electronic addressing reflection-type spatial light modulator (SLM), a single light beam illuminates the SLM, and the desired hybrid optical mode array is generated. In the experiment, a m 32 pixel32 pixel Lena gray image is transferred. At the transmitter, the Lena gray image is scanned line by line. The gray value (0-255) of each pixel with 8-bit information is extracted from the image and converted into a 22 hybrid optical mode array, which is encoded into the CGH. Hence, the m 32 pixel32 pixel Lena gray image is corresponding to a sequence with 1024 CGHs. By switching the CGHs loaded onto the SLM, the Lena gray image is transmitted in the form of the hybrid optical mode array. At the receiver, each hybrid optical mode array is decoded to a pixel value. To distinguish different modes conveniently, two cross lines are set at the center of each mode. By counting the peaks of two intensity distribution lines, the modes can easily be identified. We demonstrate the image reproduction of Lena with zero bit error rate (BER). The experimental result shows the favorable performance of the free-space optical communication link based on hybrid optical mode array encoding/decoding. Compared to that of the traditional single-vortex encoding communication system, the information capacity of our system with 22 hybrid optical mode array increases by four times. In addition, the presented experimental system is feasible and has strong expansibility. The information capacity can increase by 16 times with a 44 hybrid optical mode array based on the same experimental setup. Therefore, the presented free-space optical communication system using hybrid optical mode array encoding/decoding has great significance for improving the capacity of free-space optical communication system.

Like the spin in spintronics, the valley index in graphene can be viewed as a new carrier of information, which is useful for designing modern electronic devices. Recently, we have applied the concept of valleytronics to photonic graphene, revealed valley-dependent beam splitting effect and realized pseudomagnetic field. The pseudomagnetic field enables a novel manipulation of photons. In this paper, the photonic analogy of valley Hall effect in uniaxially distorted photonic graphene is investigated. It is found that photons in two valleys are subjected to pseudomagnetic fields that are equal in strength but opposite in sign. With the increasing of distortion, the valley Hall effect becomes stronger. In addition, it is found that the photonic valley Hall effect can still be maintained under the influence of loss, although the beam intensity decreases. The photonic analogy of valley Hall effect induced by pseudomagnetic field in uniaxially distorted photonic graphene may be very useful for controlling the flow of light in future valley-polarized devices.

Self-accelerating beam is a kind of light beam capable of self-bending in free space without any external potential, of which a typical one is the well-known Airy beam. Such a beam has gained great attention for its extraordinary properties, including nondiffracting, self-accelerating and self-healing, which may have versatile applications in the delivery and guiding of energy, information and objects using light, such as particle manipulation, micro-machining, optical routing, super-resolution imaging, etc. However, since Airy beam can only propagate along parabolic trajectory, which reduces the flexibility in practical applications, thus how to design accelerating beams propagating along arbitrary trajectory is still a crucial problem in this area. One scheme is to keep on finding other analytical solutions of the wave equation besides Airy beam, such as semi-Bessel accelerating beams, Mathius beams, and Weber beams, moving along circular, elliptical, or parabolic trajectories, but it becomes increasingly difficult to find out any more solutions. A more effective solution to this problem is based on the caustic method, which associates the predesigned trajectory with an optical caustics and then obtains the necessary initial field distribution by performing a light-ray analysis of the caustics. This method has been implemented in real space and Fourier space based on Fresnel diffraction integral and angular-spectrum integral, respectively. It has been found recently that they can be unified by constructing Wigner distribution function in phase space. Based on the caustic method, accelerating beams were constructed to propagate along arbitrary convex trajectories in two-dimensional space at first. With continuous development of this method, the types of accelerating beams available have been extending from convex trajectories to nonconvex trajectories, from two-dimensional trajectories to three-dimensional trajectories, and from one main lobe to multiple main lobes, which opens up more possibilities for emerging applications based on accelerating beams. In future, previous researches and applications based on Airy beams will certainly be generalized to all these new types of accelerating beams, and owing to the great flexibility in designing accelerating beams, more application scenarios may emerge in this process with huge development potential. Thus in this paper, we review the principle and progress of the caustic method in designing accelerating beams.

Inertial confinement fusion utilizes sufficient laser beams to directly illuminate a spherical capsule, or convert the laser into thermal X-rays inside a high Z hohlraum to drive capsule implosion. The direct drive implosion is one of ways toward central ignition and similar to the indirect drive implosion, but has higher laser energy coupling efficiency and the potential for higher-gain implosion than indirect drive, and needs stringent laser condition. In order to develop and execute the direct drive experiment on the laser facility, which is configured initially for indirect drive, the polar direct drive has been proposed and validated on the Omega laser facility and the National Ignition Facility. The polar direct drive repoints some of the beams toward the polar and equator of the target, thus increasing the drive energy on the polar and equator of capsule and achieving the most uniform irradiation. The present article focuses on the laser irradiation uniformity of the target in polar direct drive on ShenGuangIII (SGIII) facility. Firstly, the laser beam configuration of the SGIII, the characteristics of laser spots, the laser beam repointing strategy and the principle of optimization are introduced. The 48 laser beams are distributed over four cones per hemisphere and the beam centerlines are repointed in polar direct drive. The continuous phase plates (CPPs) of the SGIII are designed to have unique shape to make the laser beam with a 250 m-radius circular section at the laser entrance hole in indirect drive, and thus the laser beams have ellipse cross sections with fixed major axis and different minor axes in different cones. Then, the irradiation uniformity of 540 m target is optimized by the three-dimensional (3D) view factor method on the assumption that the laser intensity distribution is super-Gaussian with three and five orders, and the energy deposition distributions are expressed as cos2 and cos . The irradiation nonuniformity of less than 5% on the polar direct drive capsule of 540 m in diameter is achieved. The pressure distribution of the hot spot at the neutron bang time with the optimized parameter is also simulated by Multi2D, and the results of 2D hydrodynamics simulation indicate that the hot spot under the assumption of cos distribution is more symmetric. Finally, the effects on irradiation uniformity of the beam-to-beam power imbalance, the repointing error and the target pointing error are estimated by the Monte Carlo method. According to the simulation results, the laser root mean square nonuniformity on the target will not become worse observably when the maximal beam-to-beam power imbalance is limited to a value of 5%, and the repointing error and the target pointing error are better than 7 m.

The MAX phase has attracted much attention due to its unique properties combined with the merits of both metal and ceramic, including the low density, high electrical conductivity and good oxidation resistance, which makes it significant for possible applications in various high temperature or other environments. There is a lot of research work on Ti2AlX (X=C, N). However little research about thermodynamic properties at high pressure is carried out. So we study the structural, mechanical and thermodynamic properties of Ti2AlC and Ti2AlN at various pressures and temperatures.The first-principles calculations based on electronic density-functional theory framework are used to investigate the properties at various pressures. The cut-off energy is 350 eV. Converged results are achieved with 10102 special K-point meshes. The self-consistent convergence of total energy is set to be 5.010-6 eV/atom.According to the calculated structural parameters at various pressures, we can find that the ratios V/V0 (V0 denotes the system volume at 0 GPa) of Ti2AlX are reduced by 20.59% and 18.93%, respectively, so the compressibility of the system is strong. As the internal pressure increases, the curves of V/V0 become gentle. Then we calculate elastic constants at pressures ranging from 0 to 50 GPa in steps of 10 GPa. It is obvious that the Ti2AlX is mechanically stable because all of the elastic constants satisfy the Born stability criteria. The bulk modulus, shear modulus and Young's modulus linearly increase with internal pressure increasing, implying that the pressure can improve the resistance to volume deformation. The ductility and brittleness can be judged according to Pugh's criterion (ratio of bulk modulus to shear modulus B/G), and the brittle nature turns into ductile nature in a pressure range of 40-50 GPa for the Ti2AlX since the value of B/G exceeds 1.75. Finally, we study the thermodynamic properties at various pressures and temperatures based on the quasi-harmonic Debye approximation theory, including the bulk modulus, heat capacity and thermal expansion coefficient. The bulk modulus decreases with temperature increasing but increases with pressure increasing. The heat capacity at constant volume Cv and the heat capacity at constant pressure Cp have the same variation tendency, while Cv obeys the Dulong-Petit limit. It is easy to see that temperature and pressure have opposite influences on heat capacity and the effect of temperature is more significant than that of pressure. The effects of temperature and pressure on linear expansion coefficient mainly occur at low temperature and the effect of pressure is not so considerable when the pressure exceeds 30 GPa. Above all, the effects of temperature and pressure on thermodynamic properties are inverse.

The dynamic response of iron, especially the phase transformation from the ambient body-centered-cubic (bcc) up-phase to the hexagonal-closed packed (hcp) -phase, has been studied extensively in the last 60 years due to its importance in industry and its role as a main constituent of Earth. Recently, this topic has attracted a lot of attention in the aspects of the kinetic characteristics and mechanism of the shock-induced phase transition, including orientation-, temperature-, time- and strain rate-dependences. But only a few data have been published on the crystal orientation effect. The systematic experimental results to identify the predictions of the non-equilibrium molecular dynamics (NEMD) simulation are still lacking. For this reason, we study the shock responses of the [100], [110] and [111] orientated iron single crystals by using a three-independent-sample method in one shot. Unlike previously reported [001] single-crystal iron, a clear three-wave structure consisting of a PEL wave (elastic wave), a P1 wave (plastic wave) and a P2 wave (phase transition wave) is observed in the measured wave profiles for all single-crystal iron samples. The elastic-plastic transition process is in accordance with the numerical simulation of dislocation-based constitutive model for visco-plastic deformation. It is found that the values of Hugoniot elastic limit HEL ((111)/(HEL) (110)/(HEL) (100)/(HEL)) are greater than 6 GPa and dependent on the initial crystal orientation. Such a high yield strength is consistent with the nanosecond X-ray diffraction of [001] single-crystal iron where the uniaxial compression of the lattice has been observed at a shock pressure of about 5.4 GPa. Moreover, the onset pressures PPT for the phase transition are obtained to be 13.890.57 GPa, 14.530.53 GPa and 16.050.67 GPa along the [100], [110], and [111] directions, respectively. Based on these results, it is concluded that the crystal orientation effect of PPT is consistent with the reported NEMD calculations. However, the measured values are lower. In addition, the transition strain-ratio of singlecrystal iron is found to be higher than that of polycrystalline iron, reflecting the influence of the transformation kinetics (i.e., transformation kinetics coefficient) on the wave profile evolution. Our observations indicate that the strong coupling between plasticity and phase transition in single crystal iron might be a key point for understanding the origin of the phase transition and also for ending the controversy of metastable -phase. The fine multi-wave profiles also provide an important experimental reference for improving the phase field modeling of shock-induced phase transition.

Since electromagnetic waves were discovered, effectively controlling them has been a goal and radiators with better characteristics have always been chased by researchers. However, limited by the electromagnetic properties of nature materials, traditional radiation technology is reaching its bottleneck. For example, traditional microwave antenna has the disadvantages of large volume, heavy weight, narrow operating frequency band, etc., and cannot satisfy the development requirement of modern communication systems. Therefore, the state-of-art radiation technology meets the challenge of minimizing the size and broadening the bandwidth of radiators, and constructingmulti-functional and reconfigurable antennas. In recent years, metamaterials have aroused great interest due to the extraordinary diffraction manipulation on a subwavelength scale. Fruitful bizarre electromagnetic phenomena, such as negative refraction index, planar optics, perfect lens, etc. have been observed in metamaterials, and the corresponding theories improve the fundamental principle systems of electromagnetics. Based on these novel theories, a series of new radiators has been proposed, which has effectively overcome the difficulties in traditional radiation technology and broken through the limits of natural electromagnetic materials. The relating theory and technology may greatly promote the development of electromagnetics, optics, materials.In this article, we mainly review the recent progress in the novel electromagnetic radiation technology based on metamaterials, which is named meta-antenna, including the principle of diffraction manipulation of metamaterial to control the amplitude, phase and polarization of the incident electromagnetic waves. Subsequently, a series of radiation devices is introduced, including the new phased array antenna on the concept of phase manipulating metamaterial, and the high directivity antenna based on zero refraction index metamaterial and photonic crystal, and the low RCS antenna simultaneously has the functions of gain enhancement and stealth ability. Besides, the polarization manipulation characteristics of metamaterial are also reviewed. The anisotropic and chiral metamaterials are analyzed, and several polarizers with broadband characteristics and reconfigurable ability are introduced. Furthermore, due to the importance as future radiation sources, nanolasers that work on a subwavelengh scale are demonstrated. Finally, we point out the current problems and future trend of the radiation technology based on metamaterials.

Super diffraction imaging has been a research hotspot for a long time. We realize the super diffraction imaging with a metasurface structure, which is consisted of asymmetrically split rings. Based on the wave vector selectivity of the metasurface, radiation can be transmitted through it only in a narrow range of the incident angular. The metasurface acts as a high frequency spatial filter, reduces the diffraction effect, and obtains the super diffraction resolution. Numerical simulation results demonstrate the validity of this method.

Lithography is one of most important technologies for fabricating micro- and nano-structures. Limited by the light diffraction limit, it becomes more and more difficult to reduce the feature size of lithography. Surface plasmon polariton (SPP) is due to the interaction between electromagnetic wave and oscillation of free-electron on metal surface. For the shorter wavelength, higher field intensity and abnormal dispersion relation, the SPP would play an important role in breaking through the diffraction limit and realizing nanolithography. In this paper, we theoretically and experimentally study the optical nonlinear effect of SPP (two-SPP-absorption) in the photoresist and its application of nanolithography with large field. First, the concept and features of two-SPP-absorption are introduced. Like two-photo-absorption, the two-SPP-absorption based lithography is able to realize nanopatterns beyond the diffraction limit: 1) the absorption rate quadratically depends on the light intensity, which can further squeeze the exposure spot; 2) the pronounced power threshold provides a possibility for precisely controlling the linewidth by manipulating the illumination power. Nevertheless, unlike the two-photo-absorption lithography which focuses light onto a single spot and scans point by point, the two-SPP-absorption method could obtain the subwavelength field pattern by simply illuminating the plasmonic mask. The subwavelength field pattern due to the short wavelength of SPP would further result in the overcoming-diffraction-limit resist pattern. Besides, the highly concentrated SPP field leads to the strong electromagnetic field enhancement at the metal-dielectric interface, which could reduce the input power density of exposure source or enlarge the exposure area. Then the two-SPP absorption is realized under the illuminations of femtosecond lasers with vacuum wavelengths of 800 nm and 400 nm. Meanwhile, the interference periodic patternis realized and it is observed that the linewidth could be adjusted by controlling the exposure dose. The minimum linewidth of resist pattern is only one tenth of the vacuum wavelength. By utilizing the features of two-SPP-absorption, namely shorter wavelength, enhanced field and threshold effect, the lithography field could be of millimeter size, which is about four to five orders of magnitude larger than the characteristic size of nanostructure. Therefore, this two-SPP-absorption scheme could be used for large-area plasmonic lithography beyond the diffraction limit with the help of various plasmonic structures and modes.

Enormous efforts have been made to manipulate the light-matter interactions, especially in sub-diffraction-limited space, leading to miniaturized and integrated photonic devices. In physics, an elementary excitation, called polariton, which is the quantum of the coupled photon and polar elementary excitation wave field, underlies the light-matter interaction. In the dispersion relation, polaritons behave as anti-crossing interacting resonance. Surface polaritons provide ultra-confinement of electromagnetic field at the interface, opening up possibilities for sub-diffraction-limited devices, and various field enhancement effects. In the electromagnetic spectra, terahertz (THz) regime was called THz gap before the 1990s, but has now been thrust into the limelight with great significance. This review is devoted to the emerging but rapidly developing field of sub-diffraction-limited THz photonics, with an emphasis on the materials and the physics of surface polaritons. A large breadth of different flavours of materials and surface polaritonic modes have been summarized. The former includes metallic, dielectric, semiconductor, two-dimensional (2D) materials, metamaterials, etc.; the latter covers surface phonon-, plasmon-, and hybrid polaritons. In the THz regime, 2D surface plasmon polariton and artificial surface phonon polaritons offer more attractive advantages in ability to obtain low-loss, tunable, ultracompact light-matter modes.

In order to investigate the influence of the chromatic aberration on the performance of multi-junction solar cells, the performance of the triple-junction GaInP/GaInAs/Ge solar cell under high concentration condition is investigated by a three-dimensional (3D) model based on distributed circuit units. Moreover, the effects of chromatic aberration on the performance of solar cells with different sizes are studied by analyzing the distributions of the voltage, the dark current and the transverse current in each layer. It is indicated that the photo-generated current is mismatched in local region of multi-junction solar cell, which is caused by chromatic aberration. However, the mismatched photo-generated current can be compensated for by the form of transverse current, and the current can be better matched when the size of solar cell is reduced. When the size of solar cell is as big as 20 mm20 mm, the mismatched photo-generated current is large, so are the transverse current and the dark current. But the transverse current is far less than the dark current, only 12% of the mismatched photo-generated carriers can flow from the edge to the center of the cell through the transverse resistance between the sub-cells, the rest of the photo-generated carriers are lost in the form of dark current, and the cell is in a state of current mismatching. Finally, the chromatic aberration gives rise to a reduction in the short-circuit current density, and the efficiency is only 94% as high as that of non-chromatic aberration. When the size of the cell decreases, the mismatched photo-generated current and the transverse current also decrease gradually, but the dark current caused by the chromatic aberration exponentially decreases more quickly, and the ratio of the transverse current to the mismatched photo-generated current increases gradually. Therefore, the overall state of the current mismatching is alleviated, and the short-circuit current density is increased gradually. Moreover, when the size of solar cell is 2 mm2 mm, the transverse current is much larger than the dark current, 99.98% of the mismatched photo-generated carriers can be compensated for in the form of transverse current. Although the photo-generated current of the cell is mismatched in local region, the overall is still in the state of current matching. The short-circuit current densities with and without chromatic aberration are equal, but the filling factor is reduced due to the transverse resistor. When the size of cell is further reduced, the mismatched photo-generated current is very small, and the influence of the transverse series resistance decreases gradually. Therefore, the value of the filling factor gradually approaches to the value without chromatic aberration. Furthermore, the performance of solar cell with and without chromatic aberration is nearly the same when the size of solar cell is as small as 0.4 mm0.4 mm. The efficiencies are both about 34.5% and the effects of chromatic aberration can be ignored.