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研究设计了基于光通信C波段旋电材料的矩形波导, 利用有效折射率法对波导有效折射率及横向电场分布进行求解, 得到矩形波导中
$ {\rm{E}}_{mn}^x$ 导模的色散方程. 研究了在外磁场作用下表面磁等离子体激元的非互易传播特性. 还研究了结构参数和材料折射率对非互易色散关系、时延特性的影响. 结果表明: 其色散曲线随波导宽度的递增逐渐趋向平面波导; 群速度vg与波导宽度、传播常数、工作波长相关; 矩形波导芯区宽度在140—233.5 nm范围内的波导工艺容差较大; vg与矩形波导y方向包层材料折射率成正相关, 当材料为金属银时慢光效应最明显, 传输速度最小可以达到2.8 × 10–3c.A C-band rectangular waveguide with gyroelectric semiconductor is designed to study the non-reciprocal propagation characteristics of surface magnetoplasmons (SMPs), which are generated by an external magnetic field. The effective refractive index method is used to obtain the effective refractive index and transverse electric field distribution of the waveguide, and a two-dimensional rectangular waveguide is approximately regarded as a combination of two one-dimensional planar waveguides. The dispersion equation of planar waveguide with$ {\rm{E}}_{mn}^x$ mode in rectangular waveguide is derived. The influences of the structural parameters of rectangular waveguide and the refractive index of material on the non-reciprocal dispersion relation and time-delay characteristics are analyzed by numerical method. Due to the effect of external magnetic field, the off-diagonal elements of dielectric tensor in magnetic photonic crystal are changed. The generation of electrical anisotropy leads the time reversal symmetry to be broken. As a result, the dispersion curves of the rectangular waveguide are asymmetric with respect to propagation constant, and the complete one-way transmission of SMPs can be realized in the asymmetric frequency region. The dispersion curve tends to be a dispersion curve of planar waveguide as the width of rectangular waveguide increases, but the non-reciprocal frequency range is approximately unchanged. The width of the core region and the refractive index of the side material have a significant influence on the non-reciprocal dispersion characteristics: the group velocity of SMPs decreases with ω and propagation constant decreasing. The group velocity is related to the waveguide width, propagation constant and the operating wavelength. The relationship between the normalized group velocity and the width of the waveguide separately operating at 1530, 1550 and 1565 nm are studied. The group velocity is relatively slow when the width of waveguide’s core region is between 140 nm and 233.5 nm, and the minimum group velocity reaches 5.43 × 10－2c. As for the slow light effect, the rectangular waveguide is better than planar waveguide. The rectangular waveguide has a large engineering tolerance in the width of core region, which is 93.5 nm. In addition, the dispersion curves of the rectangular waveguide with SiO2, Air, Au and Ag as the left and right cladding layers are calculated. As a result, the group velocity is proportional to the refractive index of the side material in the y direction of the rectangular waveguide. The slow light effect is the most obvious when the material is silver, and the minimum transmission speed can reach 2.8 × 10－3c.-
Keywords:
- rectangular waveguide /
- effective refractive index /
- surface magnetoplasmons /
- nonreciprocal properties
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Wang J 2003 Wave Guiding Optics (Beijing: Tsinghua University Press) p57 (in Chinese)
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图 1 基于光通信C波段旋电材料的矩形波导结构
Fig. 1. Structure of rectangular waveguide with gyroelectric material in C-band.
图 2 有效折射率法的两个等效平面波导截面图 (a) x方向受约束的平面波导PW1; (b) y方向受约束的平面波导PW2
Fig. 2. Sectional views of two equivalent planar waveguides by effective refractive index method: (a) Planar waveguide PW1 with x direction constraint; (b) planar waveguide PW2 with y direction constraint.
图 3 (a)不同芯区宽度的矩形波导色散曲线; (b)不同芯区宽度的矩形波导中SMPs波单向传输区域的群速度; (c)不同波长的SMPs波群速度随芯区宽度的变化
Fig. 3. (a) Dispersion curves of rectangular waveguide with different core widths; (b) group velocity of one-way SMPs transmission region in rectangular waveguide with different widths; (c) variation of group velocity of SMPs with different wavelengths with different core widths.
图 4 (a)不同材料的矩形波导色散曲线; (b)不同材料的矩形波导中SMPs波单向传输区域的群速度曲线
Fig. 4. (a) Dispersion curves of rectangular waveguide with different materials; (b) group velocity of one-way SMPs transmission region in rectangular waveguide with different materials.
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[1] Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904
Google Scholar
[2] Wang Z, Chong Y D, Joannopoulos J D, Soljačić M 2008 Phys. Rev. Lett. 100 013905
Google Scholar
[3] Wang Z, Chong Y, Joannopoulos J D, Soljačić M 2009 Nature 461 772
Google Scholar
[4] Fan F, Chen S, Wang X H, Chang S J 2013 Opt. Express 21 8614
Google Scholar
[5] Armelles G, Cebollada A, García-Martín A, González M U 2013 Adv. Opt. Mater. 1 10
Google Scholar
[6] Brion J J, Wallis R F, Hartstein A, Burstein E 1972 Phys. Rev. Lett. 28 1455
Google Scholar
[7] Shen L, Wang Z, Deng X, Wu J J, Yang T J 2015 Opt. Lett. 40 1853
Google Scholar
[8] Shoji Y, Mizumoto T 2014 Sci. Technol. Adv. Mater. 15 014602
Google Scholar
[9] Chen S, Fan F, Wang X, Wu P, Zhang H, Chang S 2015 Opt. Express 23 1015
Google Scholar
[10] Shoji Y, Mizumoto T 2018 Opt. Mater. Express 8 2387
Google Scholar
[11] Jawad G N, Duff C I, Sloan R 2017 Trans. Microw. Theory Tech. 65 1249
Google Scholar
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Google Scholar
[13] Śmigaj W, Romero-Vivas J, Gralak B, Magdenko L, Dagens B, Vanwolleghem M 2010 Opt. Lett. 35 568
Google Scholar
[14] Qiu W, Wang Z, Soljačić M 2011 Opt. Express 19 22248
Google Scholar
[15] Shoji Y, Miura K, Mizumoto T 2015 J. Opt. 18 013001
[16] Huang D, Pintus P, Zhang C, Morton P, Shoji Y, Mizumoto T, Bowers J E 2017 Optica 4 23
Google Scholar
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Google Scholar
[18] Haddadpour A, Nezhad V F, Yu Z, Veronis G 2016 Opt. Lett. 41 4340
Google Scholar
[19] Shen L, You Y, Wang Z, Deng X 2015 Opt. Express 23 950
Google Scholar
[20] Tsakmakidis K L, Shen L, Schulz S A, Zheng X, Upham J, Deng X, Boyd R W 2017 Science 356 1260
Google Scholar
[21] 王健 2010 导波光学 (北京: 清华大学出版社) 第57页
Wang J 2003 Wave Guiding Optics (Beijing: Tsinghua University Press) p57 (in Chinese)
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