介质参数对左右手材料光波导传输性能的影响
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摘要
构建芯层为左手材料包裹层为右手材料的光波导模型,利用转移矩阵方法对模式本征方程进行多模式求解,研究介质参数对传输性能的影响。结果表明:当归一化频率极限小时,左右手材料对称光波导的基模不会消失;ε'μ'>εμ(ε'和μ'、ε和μ依次分别为芯层、包裹层介质的介电常数和磁导率),总波矢的平方差R~2=0. 5、-μ/μ'=0. 8的光波导能产生1个的表面波,R~2=1. 15、-μ/μ'=1. 1的光波导能产生3个表面波,0 0. 78 cm的奇数模能量被局域在导波层外侧;频率为4. 75 GHz、ε'μ'>εμ、-1 <μ'<0、-μ/μ'> 1时,D=0. 7 cm、传播常数为4 cm~(-1)的光波导能承载3个导波模式;频率为5. 50 GHz、ε'μ'<εμ、μ'<-1、-μ/μ'> 1时,D <0. 11 cm的光波导的两个分界面上能产生2个表面波,D> 0. 11 cm的光波导两个分界面上不产生表面波,D=0. 11 cm表面波的正归一化能量被局域在导波层外表面,而表面波的负归一化能量被局域在导波层内表面,正能量振幅衰减较慢于负能量;模系数m对表面波和导波模式的电场分布有着显著的影响。
The optical waveguide model with core layer as the left-hand material and wrapping layer as the right hand material is used to solve the pattern eigenvalue equation by using the transfer matrix method,and the influence of dielectric parameters on the transmission performance is studied. Results show: when normalized frequency is extremely small,the fundamental mode of the symmetric optical waveguide of LHM and RHM will not disappear;when ε'μ' > εμ( ε' and μ',ε and μ represent the dielectric constants and magnetic permeabilities of the core layer and the cladding layer,respectively),the optical waveguide with difference of squares of total wave vector R~2=0. 5,-μ/μ' = 0. 8 will generate 1 surface wave,the optical waveguide with R~2= 1. 15,-μ/μ' = 1. 1 will generate3 surface waves,the energy of the even-mode with 0 < D < 0. 68 cm( D is the thickness of the core layer) is localized inside the guided wave layer,while that of the odd-mode with D > 0. 78 cm is localized out of the guided wave layer; when the frequency is 4. 75 GHz,ε' μ' > εμ,-1 < μ' < 0,-μ/μ' > 1,the optical waveguide with D = 0. 7 cm,propagation constant is 4 cm~(-1) can carry 3 guided wave modes; when the frequency is 5. 50 GHz,ε'μ' < εμ,μ' <-1,-μ/μ' > 1,the two interfaces of the optical waveguide with D > 0. 11 cm will not generate any surface wave,the positively normalized energy of the surface wave with D = 0. 11 cm is localized on the outer surface of the waveguide layer,while the negatively normalized energy of the surface wave is localized on the inner surface of the guided wave layer,the amplitude of the positive energy attenuates at a rate less than that of the negative energy; the mode coefficient m has a significant influence on the electric field distribution of the surface waves and the guided wave modes.
The optical waveguide model with core layer as the left-hand material and wrapping layer as the right hand material is used to solve the pattern eigenvalue equation by using the transfer matrix method,and the influence of dielectric parameters on the transmission performance is studied. Results show: when normalized frequency is extremely small,the fundamental mode of the symmetric optical waveguide of LHM and RHM will not disappear;when ε'μ' > εμ( ε' and μ',ε and μ represent the dielectric constants and magnetic permeabilities of the core layer and the cladding layer,respectively),the optical waveguide with difference of squares of total wave vector R~2=0. 5,-μ/μ' = 0. 8 will generate 1 surface wave,the optical waveguide with R~2= 1. 15,-μ/μ' = 1. 1 will generate3 surface waves,the energy of the even-mode with 0 < D < 0. 68 cm( D is the thickness of the core layer) is localized inside the guided wave layer,while that of the odd-mode with D > 0. 78 cm is localized out of the guided wave layer; when the frequency is 4. 75 GHz,ε' μ' > εμ,-1 < μ' < 0,-μ/μ' > 1,the optical waveguide with D = 0. 7 cm,propagation constant is 4 cm~(-1) can carry 3 guided wave modes; when the frequency is 5. 50 GHz,ε'μ' < εμ,μ' <-1,-μ/μ' > 1,the two interfaces of the optical waveguide with D > 0. 11 cm will not generate any surface wave,the positively normalized energy of the surface wave with D = 0. 11 cm is localized on the outer surface of the waveguide layer,while the negatively normalized energy of the surface wave is localized on the inner surface of the guided wave layer,the amplitude of the positive energy attenuates at a rate less than that of the negative energy; the mode coefficient m has a significant influence on the electric field distribution of the surface waves and the guided wave modes.
引文
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10 Veselago V G.The electrodynamics of substances with simultaneously negative values ofεandμ[J].Soviet Physics Uspekhi,1968,10(4):509-514
12 Zharov A A,Shadrivov I V,Kivshar Y S.Nonlinear properties of left-handed metamaterials[J].Physical Review Letters,2003,91(3):037401
12 He Y,Zhang X,Yang Y F,et al.Guided modes in asymmetric metalcladding left-handed material waveguides[J].Chinese Optics Letters,2011,9(5):70-73
13许江勇,徐静,王元章,等.一维二元光子晶体量子阱的透射谱分析[J].科学技术与工程,2014,14(10):111-114Xu Jiangyong,Xu Jing,Wang Yuanzhang,et al.Analysis of transmission spectrum of one-dimensional dual photonic crystal quantum well[J].Science Technology and Engineering,2014,14(10):111-114
14刘文莉,唐婷婷,何修军.微波段左手材料光子晶体带隙特性研究[J].光子学报,2016,45(2):0216002Liu Wenli,Tang Tingting,He Xiujun.Band gap characteristics of photonic crystals consisted of left-handed material in the microwave band[J].Acta Photonica Sinica,2016,45(2):0216002
15 Shelby R A,Smith D R,Schultz S.Experimental verification of a negative index of refraction[J].Science,2001,5514(292):77-79
16 Berrier A,Mulot M,Swillo M,et al.Negative refraction at infrared wavelengths in a two-dimensional photonic crystal[J].Physical Review Letters,2004,93(7):073902
17 Lu Z,Murakowski J A,Schuetz C A,et al.Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies[J].Physical Review Letters,2005,95(15):153901
18 Moussa R,Foteinopoulou S,Zhang L,et al.Negative refraction and superlens behavior in a two-dimensional photonic crystal[J].Physical Review B,2005,71(8):085106
19 Zhang S,Fan W,Malloy K J,et al.Near-infrared double negative metamaterials.[J].Optics Express,2005,13(13):4922-4930
20 Liu L,Ao X,Wosinski L,et al.Compact polarization beam splitter employing positive/negative refraction based on photonic crystals of pillar type[J].Asia-Pacific Optical Communications,2006,6352(4):74-81
21 Dolling G,Wegener M,Soukoulis C M,et al.Negative-index metamaterial at 780 nm wavelength.[J].Optics Letters,2007,32(1):53-55
22 Notomi M.Theory of light propagation in strongly modulated photonic crystals:Refractionlike behavior in the vicinity of the photonic band gap[J].Physical Review B,2000,62(16):10696-10705
23 Cubukcu E,Aydin K,Ozbay E,et al.Electromagnetic waves:Negative refraction by photonic crystals[J].Nature,2003,423(6940):604-605
24 Ozbay E,Bulu I,Guven K,et al.Observation of negative refraction and focusing in two-dimensional photonic crystals[J].Japanese Journal of Applied Physics,2006,45(8A):6064-6070
25 Ao X,Liu L,Wosinski L,et al.Polarization beam splitter based on a two-dimensional photonic crystal of pillar type[J].Applied Physics Letters,2006,89(17):171115
26 Ruan Z C,He S L.Open cavity formed by a photonic crystal with negative effective index of refraction[J].Optics letters,2005,30(17):2308-2310
27 Zhang X D.Tunable non-near-field focus and imaging of an unpolarized electromagnetic wave[J].Physical Review B,2005,71(23):235103
28 Feng S,Li Z Y,Feng Z F,et al.Imaging properties of an ellipticalrod photonic-crystal slab lens[J].Physical Review B,2005,72(7):75101
2 Cho I K,Yoon K B,Ahn S H,et al.Experimental demonstration of10 Gbit/s transmission with an optical backplane system using optical slots[J].Optics Letters,2005,30(13):1635-1637
3 Taubenblatt M A.Optical interconnects for high-performance computing[J].Journal of Lightwave Technology,2011,30(4):448-457
4刘涛,李志山,蒋志,等.有机聚合物光波导制作工艺综述[J].激光与红外,2015,45(6):599-604Liu Tao,Li Zhishan,Jiang Zhi,et al.Fabrication process of organic polymer optical waveguide[J].Laser&Infrared,2015,45(6):599-604
5唐海泉,张辉,冀健龙,等.光波导器件应用及其表面光滑化研究综述[J].河北科技大学学报,2017,38(1):26-31Tang Haiquan,Zhang Hui,Ji Jianlong,et al.Review of applications and surface smoothing mechanisms of optical waveguide devices[J].Journal of Hebei University of Science&Technology,2017,38(1):26-31
6 Pendrydag J B,Holdenddag A J,Robbinsddag D J,et al.Low frequency plasmons in thin-wire structures[J].Journal of Physics:Condensed Matter,1998,10(22):4785-4809
7 Shadrivov I V,Sukhorukov A A,Kivshar Y S.Guided modes in negative-refractive-index waveguides[J].Physical Review E:Statistical Nonlinear&Soft Matter Physics,2003,67(5):57602
8许江勇,苏安,潘继环,等.双负介质对一维光子晶体量子阱透射谱的影响[J].红外与激光工程,2013,42(8):2156-2161Xu Jiangyong,Su An,Pan Jihua,et al.Effect of double negative medium on the transmission spectra of one-dimensional photonic crystal quantum well[J].Infrared&Laser Engineering,2013,42(8):2156-2161
9吴良威,张正平.基于多开口田字形宽频带低损耗左手材料[J].物理学报,2016,65(16):164101Wu Liangwei,Zhang Zhengping.Broadband and low-loss left-handed materials based on multi-opening cross shape structures[J].Acta Physica Sinica,2016,65(16):164101
10 Veselago V G.The electrodynamics of substances with simultaneously negative values ofεandμ[J].Soviet Physics Uspekhi,1968,10(4):509-514
12 Zharov A A,Shadrivov I V,Kivshar Y S.Nonlinear properties of left-handed metamaterials[J].Physical Review Letters,2003,91(3):037401
12 He Y,Zhang X,Yang Y F,et al.Guided modes in asymmetric metalcladding left-handed material waveguides[J].Chinese Optics Letters,2011,9(5):70-73
13许江勇,徐静,王元章,等.一维二元光子晶体量子阱的透射谱分析[J].科学技术与工程,2014,14(10):111-114Xu Jiangyong,Xu Jing,Wang Yuanzhang,et al.Analysis of transmission spectrum of one-dimensional dual photonic crystal quantum well[J].Science Technology and Engineering,2014,14(10):111-114
14刘文莉,唐婷婷,何修军.微波段左手材料光子晶体带隙特性研究[J].光子学报,2016,45(2):0216002Liu Wenli,Tang Tingting,He Xiujun.Band gap characteristics of photonic crystals consisted of left-handed material in the microwave band[J].Acta Photonica Sinica,2016,45(2):0216002
15 Shelby R A,Smith D R,Schultz S.Experimental verification of a negative index of refraction[J].Science,2001,5514(292):77-79
16 Berrier A,Mulot M,Swillo M,et al.Negative refraction at infrared wavelengths in a two-dimensional photonic crystal[J].Physical Review Letters,2004,93(7):073902
17 Lu Z,Murakowski J A,Schuetz C A,et al.Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies[J].Physical Review Letters,2005,95(15):153901
18 Moussa R,Foteinopoulou S,Zhang L,et al.Negative refraction and superlens behavior in a two-dimensional photonic crystal[J].Physical Review B,2005,71(8):085106
19 Zhang S,Fan W,Malloy K J,et al.Near-infrared double negative metamaterials.[J].Optics Express,2005,13(13):4922-4930
20 Liu L,Ao X,Wosinski L,et al.Compact polarization beam splitter employing positive/negative refraction based on photonic crystals of pillar type[J].Asia-Pacific Optical Communications,2006,6352(4):74-81
21 Dolling G,Wegener M,Soukoulis C M,et al.Negative-index metamaterial at 780 nm wavelength.[J].Optics Letters,2007,32(1):53-55
22 Notomi M.Theory of light propagation in strongly modulated photonic crystals:Refractionlike behavior in the vicinity of the photonic band gap[J].Physical Review B,2000,62(16):10696-10705
23 Cubukcu E,Aydin K,Ozbay E,et al.Electromagnetic waves:Negative refraction by photonic crystals[J].Nature,2003,423(6940):604-605
24 Ozbay E,Bulu I,Guven K,et al.Observation of negative refraction and focusing in two-dimensional photonic crystals[J].Japanese Journal of Applied Physics,2006,45(8A):6064-6070
25 Ao X,Liu L,Wosinski L,et al.Polarization beam splitter based on a two-dimensional photonic crystal of pillar type[J].Applied Physics Letters,2006,89(17):171115
26 Ruan Z C,He S L.Open cavity formed by a photonic crystal with negative effective index of refraction[J].Optics letters,2005,30(17):2308-2310
27 Zhang X D.Tunable non-near-field focus and imaging of an unpolarized electromagnetic wave[J].Physical Review B,2005,71(23):235103
28 Feng S,Li Z Y,Feng Z F,et al.Imaging properties of an ellipticalrod photonic-crystal slab lens[J].Physical Review B,2005,72(7):75101
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