圆偏振光在左手介质表面的Imbert-Fedorov位移
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摘要
近来,人们发现当光在左手材料中传播时会表现出一些奇异的电磁特性,因此,左手介质表面的Imbert-Fedorov位移也受到了人们越来越多的关注。本文采用能流法的思想,在理论上分别对圆偏振光入射时,各向同性均匀左手介质、各向异性左手介质和弱吸收左手介质表面的Imbert-Fedorov位移进行了研究。
1.运用能流法推导出了圆偏振光从右手介质入射到各向同性均匀的左手介质表面时Imbert-Fedorov位移的表达式。并在此基础上讨论了Imbert-Fedorov位移随入射角度的变化关系以及圆偏振光的旋向不同对Imbert-Fedorov位移的影响。
2 .分别对单轴各向异性左手介质和双轴各向异性左手介质表面的Imbert-Fedorov位移进行研究。在对单轴各向异性左手介质表面的Imbert-Fedorov位移进行讨论时发现,Imbert-Fedorov位移不仅与入射光束的性质和入射角度有关,而且与光轴的方向也有很大的关系。另外,给出了双轴各向异性左手介质表面的Imbert-Fedorov位移的表达式,并且讨论了当介电常数和磁导率不相同时,Imbert-Fedorov位移的变化趋势。
3.讨论了弱吸收左手介质表面的Imbert-Fedorov位移。分别分析了Imbert-Fedorov位移随着介电常数的实部和虚部的变化规律,以及在单层膜结构下膜的厚度对Imbert-Fedorov位移的影响。
There will be some particular electromagnetic characteristics when light beam propagates in left-handed materials . Therefore, Imbert-Fedorov shift at the interface between right-handed material and left-handed material received more and more attention. This thesis deal with the Imbert-Fedorov shift on the surface of homogeneous isotropic left-handed medium, anisotropic left-handed medium and weakly absorbing left-handed medium based on the Renard model when an circularly polarized light beam propagates in the medium theoretically.
Firstly, the expression about Imbert-Fedorov shift is presented when an circularly polarized light beam is totally reflected at the interface between right-handed material and homogeneous isotropic left-handed material. On this basis, the relation between Imbert-Fedorov shift and the incident angle, the difference of Imbert-Fedorov shift when the circularly polarization is switched from left-hand to right-hand is also discussed.
Secondly, the Imbert-Fedorov shift on the surface of uniaxially anisotropic left-handed material and biaxial anisotropic left-handed material is investigated theoretically. The results show that the displacement depends not only on the polarization and incident angle of the incident beam, but also on the orientation of the optical axis. In addition, the expression of Imbert-Fedorov shift on the surface of biaxial anisotropic left-handed material is presented. And does some discussion about state of Imbert-Fedorov shift when the permittivity and permeability are difference.
Finally, Imbert-Fedorov shift on the surface of weakly absorbing left-handed medium is discussed. The thesis presents the behavior of Imbert-Fedorov shift with the variation of real and imaginary part of permittivity. At last, the relationship between the thickness of the dielectric film and the shift in the configuration of single layer film.
1.运用能流法推导出了圆偏振光从右手介质入射到各向同性均匀的左手介质表面时Imbert-Fedorov位移的表达式。并在此基础上讨论了Imbert-Fedorov位移随入射角度的变化关系以及圆偏振光的旋向不同对Imbert-Fedorov位移的影响。
2 .分别对单轴各向异性左手介质和双轴各向异性左手介质表面的Imbert-Fedorov位移进行研究。在对单轴各向异性左手介质表面的Imbert-Fedorov位移进行讨论时发现,Imbert-Fedorov位移不仅与入射光束的性质和入射角度有关,而且与光轴的方向也有很大的关系。另外,给出了双轴各向异性左手介质表面的Imbert-Fedorov位移的表达式,并且讨论了当介电常数和磁导率不相同时,Imbert-Fedorov位移的变化趋势。
3.讨论了弱吸收左手介质表面的Imbert-Fedorov位移。分别分析了Imbert-Fedorov位移随着介电常数的实部和虚部的变化规律,以及在单层膜结构下膜的厚度对Imbert-Fedorov位移的影响。
There will be some particular electromagnetic characteristics when light beam propagates in left-handed materials . Therefore, Imbert-Fedorov shift at the interface between right-handed material and left-handed material received more and more attention. This thesis deal with the Imbert-Fedorov shift on the surface of homogeneous isotropic left-handed medium, anisotropic left-handed medium and weakly absorbing left-handed medium based on the Renard model when an circularly polarized light beam propagates in the medium theoretically.
Firstly, the expression about Imbert-Fedorov shift is presented when an circularly polarized light beam is totally reflected at the interface between right-handed material and homogeneous isotropic left-handed material. On this basis, the relation between Imbert-Fedorov shift and the incident angle, the difference of Imbert-Fedorov shift when the circularly polarization is switched from left-hand to right-hand is also discussed.
Secondly, the Imbert-Fedorov shift on the surface of uniaxially anisotropic left-handed material and biaxial anisotropic left-handed material is investigated theoretically. The results show that the displacement depends not only on the polarization and incident angle of the incident beam, but also on the orientation of the optical axis. In addition, the expression of Imbert-Fedorov shift on the surface of biaxial anisotropic left-handed material is presented. And does some discussion about state of Imbert-Fedorov shift when the permittivity and permeability are difference.
Finally, Imbert-Fedorov shift on the surface of weakly absorbing left-handed medium is discussed. The thesis presents the behavior of Imbert-Fedorov shift with the variation of real and imaginary part of permittivity. At last, the relationship between the thickness of the dielectric film and the shift in the configuration of single layer film.
引文
[1] Goos F, Hanchen H. Ein Neuer und Fundamentaler Versuch Zur Total Reflexion. Ann. Phys. 1947, 1: 333-3461
[2] Chih-Wei Chen, Wen-Chi Lin, Lu-Shing Liao. Optical Temperature Sensing Based on the Goos–H?nchen Effect [J]. Applied Optics, 2007, 46(22): 5347-535
[3] Li C F. Unified Theory for Goos-Hanchen and Imbert-Fedorov Effects. Phys. Rev. A, 2007, 76(1): 013811(7)
[4] Imbert C. Calculation and Experimental Proof of the Transverse Shift Induced by Total Internal Reflection of a Circularly Polarized Light Beam. Phys. Rev. D, 1972, 5(4): 787-798
[5] Imbert C. Quantizes Longitudinal and Transverse Shifts Associated With Total Internal Reflection [J]. Phys. Rev. D, 1972, 28(18): 1211-1213
[6] Renard R H. Total Reflection: A New Evaluation of the Goos-Hanchen Shift. J. Opt. Soc. Am, 1964, 54(10): 1190-1197
[7] Aiello A, Woerdman J P. Role of Beam Propagation in Goos-Hanchen and Imber-Fedorov Shifts. Opt. Lett., 2008, 33(13): 1437-1439
[8] Born M, Wolf E. Principles of Optics, 7th ed. [M]. America: Cambridge U. Press, 2003.
[9] Bliokh K Y, Shadrivov I V, Kivshar Y S. Goos-Hanchen and Imbert-Fedorov Shifts of Polarized Vortex Beams. Opt. Lett., 2009, 34(3): 389-391
[10] Nasalski W. Polarization Versus Spatial Characteristics of Optical Beams at a Planar Isotropic Interface [J]. Phys. Rev. E, 2006, 74: 056613(16)
[11] Bliokh K Y, Bliokh Y P. Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Re?ection and Refraction of an Electromagnetic Wave Packet [J]. Phys. Rev. Lett., 2006, 96(7): 073903(4)
[12] Lai H M, Kwok C W, Loo Y W. Energy-flux Pattern in the Goos-Hanchen Effect [J]. Phys. Rev. E, 2000, 62(5): 7330-7339.
[13] Aiello A, Woerdman J P. Theory of Angular Goos-H¨anchen Shift near BrewsterIncidence [J]. Physics.Optics, 2007: 1-13
[14] Pillon F, Gilles H, Girard S. Experimental Observation of the Imbert-FedorovTransverse Displacement after a Single Total Reflection. Applied Optics.2004, 43(9): 1863-1869
[15] O. Hosten, P. Kwiat. Observation of the Spin Hall Effect of Light via Weak Measurements [J]. Science, 2008, 319(5864): 787-790
[16] V. G.. Veselago. The Electrodynamics of Substances with Simultaneously Negative Values ofεandμ. Soviet Phys Uspekhi. 1968, 10: 509-514
[17]张永强.左手介质中Goos-Hanchen位移及多层膜色散特性的研究[D].哈尔滨:哈尔滨工业大学,2006
[18] Pendary J B. Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett.,2000, 85: 3966-3969
[19] Antoniades M A, Eleftheriades G. V. Compact Linear Lead/Lag Metamaterial Phase Shifters for Broadband Applications. IEEE Antennas Wireless Propagat. Lett., 2003, 2: 103-106
[20] Shadrivov I V, Sukhorukov A A, Kivshar Y S. Guide Modes in Negative-refractive-index Waveguides. Phys. Rev. E, 2003, 67(5): 057602(4)
[21] F. I. Fedorov. Theory of Total Reflection[J]. Dokl. Akad. Nauk. SSSR. 1955, 105: 465-468
[22] Yasumoto K, Oishi Y. A New Evaluation of the Goos-Hanchen Shift and Associated Time Delay. J. Appl. Phys., 1983, 54(5): 2170-2176
[23] Menzel C, Rockstuhl C, Paul T, et al. Imbert-Fedorov Shift at Metamaterial Interfaces [J]. Phys. Rev. A, 2008, 77(1): 013810(7)
[24]周惠玲,陈玺,李春芳.任意偏振态光束全反射时的横向和侧向位移.光学学报,2006, 26(12):1852-1856
[25] Luo H L, Wen S C, Shu W X, et al. Spin Hall Effect of Light Beam in Left-handed Materials. Phys. Rev. A 2009, 40(4): 1-6
[26] Qin Y, Li Y, Feng X B, et al. Spin Hall Effect of Reflected Light at the Air-uniaxial Crystal Interface. Optics Express, 2010, 18(16): 16832-16839
[27]尹红芳,罗海陆,文双春.光自旋霍尔效应中横移的影响因素研究.光学学报2011, 31(3): 0326002(7)
[28]徐旭明,方利光,刘念华.含负折射率层的多体系的反常光子隧穿[J].光学学报,2005, 25(12): 1676-1681
[29]董海霞,江海涛,石云龙,等.负折射率缺陷的光量子阱的透射特性及理论模拟[J].光学学报,2007, 25(12): 2245-2249
[30]张志伟.棱镜反射光技术与工程应用[M].北京:国防工业出版社,2009: 36-37
[31] Zel’dovich B Y. Observed Transverse Shift of a Focal Spot Upon a Change in the Sign of Circular Polarization . JETP Lett, 1944, 59(11): 766-769
[32] Fadeyeva T A, Rubass A F, Volyar A V. Transverse Shift of a High-order Paraxial Vortex-beam Induced by a Homogeneous Anisotropic Medium. Phys. Rev. A, 2009, 79(5): 053815(12)
[33] Hu L B, Chui S T. Characteristics of Electromagnetic Wave Propagation in Uniaxially Anisotropic Left-handed Materials. Phys. Rev. B, 2002, 66(8): 085108(7)
[34]冷光尧.吸收媒质界面上反射束的非镜像纵向位移[J].光学学报, 1994, 14(6):646-649.
[35] Shen J Q, Yu H T, Lu J D. Light Propagation and Reflection-reflection Event in Absorbing Media. Chinese Optics Letters, 2010, 8(1): 111-114
[36] Yang P, Liou K N. Effective Refractive Index for Determining Ray Propagation in an Absorbing Dielectric Particle. J. Quant. Spectrosc. Radiat. Transfer, 2009, 110: 300-306
[37] Yang P, Liou K N. Light Scattering by Hexagonal Ice Crystals: Comparison of Finite-difference Time Domain and Geometric Optics Models. J. Opt. Soc. Am. A, 1995 12(1): 162-176
[38] Lai H M, Chan S W. Large and Negative Goos–H?nchen Shift near the Brewster Dip on Reflection from Weakly Absorbing Media. Opt. Lett., 2002, 27(9): 680-682
[39] Horowitz B R, Tamir T. Lateral Displacement of a Light Beam at a Dielectric Interface. J. Opt. Soc. Am, 1971, 61(5): 586-594
[40] Xiang Y J, Dai X Y, Wen S C. Large Goos-Hanchen Shifts from an Asymmetric Configuration with Single-negative Materials Due to Surface Polariton Resonance. Proc of SPIE, 2006, 6352: 63522N(8)
[41] Wang L G., Liu N H, Lin Q, et al. Propagation of Coherent and Partially Coherent Pulses through One-dimensional Photonic Crystals. Phys. Rev. E, 2004, 70(1): 016601 (12)
[42] Wang L G, Chen H, Zhu S Y. Large Negative Goos–H?nchen Shift from a Weakly Absorbing Dielectric Slab. Opt. Lett., 2005, 30(21): 2936-293
[2] Chih-Wei Chen, Wen-Chi Lin, Lu-Shing Liao. Optical Temperature Sensing Based on the Goos–H?nchen Effect [J]. Applied Optics, 2007, 46(22): 5347-535
[3] Li C F. Unified Theory for Goos-Hanchen and Imbert-Fedorov Effects. Phys. Rev. A, 2007, 76(1): 013811(7)
[4] Imbert C. Calculation and Experimental Proof of the Transverse Shift Induced by Total Internal Reflection of a Circularly Polarized Light Beam. Phys. Rev. D, 1972, 5(4): 787-798
[5] Imbert C. Quantizes Longitudinal and Transverse Shifts Associated With Total Internal Reflection [J]. Phys. Rev. D, 1972, 28(18): 1211-1213
[6] Renard R H. Total Reflection: A New Evaluation of the Goos-Hanchen Shift. J. Opt. Soc. Am, 1964, 54(10): 1190-1197
[7] Aiello A, Woerdman J P. Role of Beam Propagation in Goos-Hanchen and Imber-Fedorov Shifts. Opt. Lett., 2008, 33(13): 1437-1439
[8] Born M, Wolf E. Principles of Optics, 7th ed. [M]. America: Cambridge U. Press, 2003.
[9] Bliokh K Y, Shadrivov I V, Kivshar Y S. Goos-Hanchen and Imbert-Fedorov Shifts of Polarized Vortex Beams. Opt. Lett., 2009, 34(3): 389-391
[10] Nasalski W. Polarization Versus Spatial Characteristics of Optical Beams at a Planar Isotropic Interface [J]. Phys. Rev. E, 2006, 74: 056613(16)
[11] Bliokh K Y, Bliokh Y P. Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Re?ection and Refraction of an Electromagnetic Wave Packet [J]. Phys. Rev. Lett., 2006, 96(7): 073903(4)
[12] Lai H M, Kwok C W, Loo Y W. Energy-flux Pattern in the Goos-Hanchen Effect [J]. Phys. Rev. E, 2000, 62(5): 7330-7339.
[13] Aiello A, Woerdman J P. Theory of Angular Goos-H¨anchen Shift near BrewsterIncidence [J]. Physics.Optics, 2007: 1-13
[14] Pillon F, Gilles H, Girard S. Experimental Observation of the Imbert-FedorovTransverse Displacement after a Single Total Reflection. Applied Optics.2004, 43(9): 1863-1869
[15] O. Hosten, P. Kwiat. Observation of the Spin Hall Effect of Light via Weak Measurements [J]. Science, 2008, 319(5864): 787-790
[16] V. G.. Veselago. The Electrodynamics of Substances with Simultaneously Negative Values ofεandμ. Soviet Phys Uspekhi. 1968, 10: 509-514
[17]张永强.左手介质中Goos-Hanchen位移及多层膜色散特性的研究[D].哈尔滨:哈尔滨工业大学,2006
[18] Pendary J B. Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett.,2000, 85: 3966-3969
[19] Antoniades M A, Eleftheriades G. V. Compact Linear Lead/Lag Metamaterial Phase Shifters for Broadband Applications. IEEE Antennas Wireless Propagat. Lett., 2003, 2: 103-106
[20] Shadrivov I V, Sukhorukov A A, Kivshar Y S. Guide Modes in Negative-refractive-index Waveguides. Phys. Rev. E, 2003, 67(5): 057602(4)
[21] F. I. Fedorov. Theory of Total Reflection[J]. Dokl. Akad. Nauk. SSSR. 1955, 105: 465-468
[22] Yasumoto K, Oishi Y. A New Evaluation of the Goos-Hanchen Shift and Associated Time Delay. J. Appl. Phys., 1983, 54(5): 2170-2176
[23] Menzel C, Rockstuhl C, Paul T, et al. Imbert-Fedorov Shift at Metamaterial Interfaces [J]. Phys. Rev. A, 2008, 77(1): 013810(7)
[24]周惠玲,陈玺,李春芳.任意偏振态光束全反射时的横向和侧向位移.光学学报,2006, 26(12):1852-1856
[25] Luo H L, Wen S C, Shu W X, et al. Spin Hall Effect of Light Beam in Left-handed Materials. Phys. Rev. A 2009, 40(4): 1-6
[26] Qin Y, Li Y, Feng X B, et al. Spin Hall Effect of Reflected Light at the Air-uniaxial Crystal Interface. Optics Express, 2010, 18(16): 16832-16839
[27]尹红芳,罗海陆,文双春.光自旋霍尔效应中横移的影响因素研究.光学学报2011, 31(3): 0326002(7)
[28]徐旭明,方利光,刘念华.含负折射率层的多体系的反常光子隧穿[J].光学学报,2005, 25(12): 1676-1681
[29]董海霞,江海涛,石云龙,等.负折射率缺陷的光量子阱的透射特性及理论模拟[J].光学学报,2007, 25(12): 2245-2249
[30]张志伟.棱镜反射光技术与工程应用[M].北京:国防工业出版社,2009: 36-37
[31] Zel’dovich B Y. Observed Transverse Shift of a Focal Spot Upon a Change in the Sign of Circular Polarization . JETP Lett, 1944, 59(11): 766-769
[32] Fadeyeva T A, Rubass A F, Volyar A V. Transverse Shift of a High-order Paraxial Vortex-beam Induced by a Homogeneous Anisotropic Medium. Phys. Rev. A, 2009, 79(5): 053815(12)
[33] Hu L B, Chui S T. Characteristics of Electromagnetic Wave Propagation in Uniaxially Anisotropic Left-handed Materials. Phys. Rev. B, 2002, 66(8): 085108(7)
[34]冷光尧.吸收媒质界面上反射束的非镜像纵向位移[J].光学学报, 1994, 14(6):646-649.
[35] Shen J Q, Yu H T, Lu J D. Light Propagation and Reflection-reflection Event in Absorbing Media. Chinese Optics Letters, 2010, 8(1): 111-114
[36] Yang P, Liou K N. Effective Refractive Index for Determining Ray Propagation in an Absorbing Dielectric Particle. J. Quant. Spectrosc. Radiat. Transfer, 2009, 110: 300-306
[37] Yang P, Liou K N. Light Scattering by Hexagonal Ice Crystals: Comparison of Finite-difference Time Domain and Geometric Optics Models. J. Opt. Soc. Am. A, 1995 12(1): 162-176
[38] Lai H M, Chan S W. Large and Negative Goos–H?nchen Shift near the Brewster Dip on Reflection from Weakly Absorbing Media. Opt. Lett., 2002, 27(9): 680-682
[39] Horowitz B R, Tamir T. Lateral Displacement of a Light Beam at a Dielectric Interface. J. Opt. Soc. Am, 1971, 61(5): 586-594
[40] Xiang Y J, Dai X Y, Wen S C. Large Goos-Hanchen Shifts from an Asymmetric Configuration with Single-negative Materials Due to Surface Polariton Resonance. Proc of SPIE, 2006, 6352: 63522N(8)
[41] Wang L G., Liu N H, Lin Q, et al. Propagation of Coherent and Partially Coherent Pulses through One-dimensional Photonic Crystals. Phys. Rev. E, 2004, 70(1): 016601 (12)
[42] Wang L G, Chen H, Zhu S Y. Large Negative Goos–H?nchen Shift from a Weakly Absorbing Dielectric Slab. Opt. Lett., 2005, 30(21): 2936-293