光在复折射率介质界面的反射与折射
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摘要
通过研究光在复折射率介质中的传播,获得光波在复折射率介质中传播和衰减的有效折射率N_s和N_q的表达式,它们的值由介质的复折射率、等幅面和等相面的单位矢量q和s之间的夹角决定;折射边的有效折射率除了与折射边的复折射率有关外,还与入射光的入射角和入射介质的有效折射率有关。根据光的传播表达式,分别运用相应的Snell定律,获得了光在两复折射率介质界面的菲涅耳(Fresnel)公式,可知反射和透射系数与入射角、吸收性介质的复折射率有关,而且与入射光两单位矢量之间的夹角有关,并将Fresnel公式推广至任意两界面组合的情况下,且光通过两复折射率介质的Fresnel公式可退化为介质/介质的特殊情况。
The light propagation within an absorbing medium are studied,the light propagation and attenuation effective refractive indices N_s and N_q have been obtained,their values depend not only on the complex refractive index but also on the angle between the planes of constant phase and of constant amplitude.But the effective refractive indices of refraction medium depend on the refractive index of the refracted medium and the parameters of incident wave.With the expression for the light propagation,using the corresponding boundary conditions,the Fresnel formula of the light through the interface of two absorbing medium have been obtained.This work can be applied to the interface of the media,wherein either/both of them is/are absorbing or transparent.
The light propagation within an absorbing medium are studied,the light propagation and attenuation effective refractive indices N_s and N_q have been obtained,their values depend not only on the complex refractive index but also on the angle between the planes of constant phase and of constant amplitude.But the effective refractive indices of refraction medium depend on the refractive index of the refracted medium and the parameters of incident wave.With the expression for the light propagation,using the corresponding boundary conditions,the Fresnel formula of the light through the interface of two absorbing medium have been obtained.This work can be applied to the interface of the media,wherein either/both of them is/are absorbing or transparent.
引文
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[16]LI X,HAN X,LI R et al.Geometrical-optics approximation of forward scattering by gradient-index spheres[J].Applied Optics.2007,46(22):5241-5247.
[17]XU F,RRN K F,CAI X S.Extension of geometrical-optics approximation to on-axis Gaussian beam scattering.I.By a spherical particle[J].Applied Optics,2006,45(20):4990-4999.
[18]徐峰,蔡小舒,沈嘉祺.米氏理论的近似及在粒度测量中的应用[J].光学学报,2003,23(12):1464-1469.
[19]HE H,LI W,ZHANG X,et al.Light scattering by a spheroidal bubble with geometrical optics approximation[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2012,113(12):1467-1475.
[20]YANG P,LIOUK N.Light scattering by hexagonal ice crystals:comparison of finite-difference time domain and geometric optics models[J].Journal of the Optical Society of America A,1995,12(1):162-176.
[21]YANG P,LIOUK N.Effective refractive index for determining ray propagation in an absorbing dielectric particle[J].Journal of Quantitative Spectroscopy&Radiative Transfer,2009,110:300-306.
[22]XU F,CAI X S,REN K F.Geometrical optics approximation of forward scattering by coated particles[J].Applied Optics.2004,43:1870-1879.
[23]郭硕鸿.电动力学[M].2版.北京:高等教育出版社,1997:122-123.
[2]姚启钧.光学教程[M].3版.北京:高等教育出版社,2002:78-80.
[3]赵凯华,钟锡华.光学[M].北京:北京大学出版社,2003:246-249.
[4]CHIU M H,LEE J Y,SU D C.Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry[J].Applied Optics,1997,36(13):2936-2939.
[5]陈强华,罗会甫,王素梅,等.基于表面等离子体共振和双频激光干涉相位测量的空气折射率测量[J].中国激光,2013,40(1):180-186.
[6]马利祥,李范鸣,牛继勇,等.基于复折射率的偏振模型及其应用[J].激光与红外,2013,43(10):1138-1141.
[7]CHIU M H,LEE J Y,SU D C.Complex refractive-index measurement based on Fresnel's equations and the uses of heterodyne interferometry[J].Applied Optics,1999,38(19):4047-4052.
[8]马科斯·玻恩,埃米尔·沃耳夫.光学原理[M].5版.杨葭荪,译.北京:科学出版社,1978:618-619.
[9]GARCIAPOMAR J L,NIETOVESPERINAS M.Transmission study of prisms and slabs of lossy negative index media[J].Optic Express,2004,12(10):2081-2095.
[10]顾闻,邬云骅,陈岳瑞,等.光在金属界面的传输特性研究[J].红外与毫米波学报,2009,28(1):31-34.
[11]张秋长.光在金属界面传播的实折射角计算[J].厦门大学学报(自然科学版),2015,54(2):242-246.
[12]DAVIS G E.Scattering of light by an air bubble in water[J].Journal of the Optical Soc.Am.1955,45(7):572-581.
[13]HULST H C V D.Light scattering by small particles[M].New York:John Wiley&Sons,1957:470.
[14]HOVENAC E A.Calculation of far-field scattering from nonspherical particles using ageometrical optics approach[J].Applied Optics.1991(30):4739-4746.
[15]ADEN A L,KERKER M.Scattering of electromagnetic waves by two concentric spheres[J].Journal of Applied Physics.1951,22:1242-1246.
[16]LI X,HAN X,LI R et al.Geometrical-optics approximation of forward scattering by gradient-index spheres[J].Applied Optics.2007,46(22):5241-5247.
[17]XU F,RRN K F,CAI X S.Extension of geometrical-optics approximation to on-axis Gaussian beam scattering.I.By a spherical particle[J].Applied Optics,2006,45(20):4990-4999.
[18]徐峰,蔡小舒,沈嘉祺.米氏理论的近似及在粒度测量中的应用[J].光学学报,2003,23(12):1464-1469.
[19]HE H,LI W,ZHANG X,et al.Light scattering by a spheroidal bubble with geometrical optics approximation[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2012,113(12):1467-1475.
[20]YANG P,LIOUK N.Light scattering by hexagonal ice crystals:comparison of finite-difference time domain and geometric optics models[J].Journal of the Optical Society of America A,1995,12(1):162-176.
[21]YANG P,LIOUK N.Effective refractive index for determining ray propagation in an absorbing dielectric particle[J].Journal of Quantitative Spectroscopy&Radiative Transfer,2009,110:300-306.
[22]XU F,CAI X S,REN K F.Geometrical optics approximation of forward scattering by coated particles[J].Applied Optics.2004,43:1870-1879.
[23]郭硕鸿.电动力学[M].2版.北京:高等教育出版社,1997:122-123.