吸收介质中光传播与反射折射事件研究

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"这篇文章研究了光在吸收介质中的传播以及两个吸收介质之间的反射和折射事件。通过使用表示恒定场振幅和平面的单位向量，以及表示恒定相位的单位向量，作者描述了光的传播和衰减，这依赖于介质的复折射率和单位向量之间的角度。利用光传播的表达式，得出了相应的斯涅尔定律和菲涅耳系数的公式，可用于描述任意透明与吸收介质界面的反射-折射现象。" 文章深入探讨了光在吸收介质内的行为，这是光学领域的一个重要主题。在非理想情况下，如当光穿过具有吸收特性的材料时，光的传播路径和强度会受到显著影响。这里，作者使用了单位矢量的概念来分析光的传播特性，这些单位矢量分别代表了恒定场振幅和相位的平面。这种方法揭示了光传播和衰减的过程，其中有效折射指数起到了关键作用。有效折射指数不仅与介质的复折射率有关，还与光传播方向（即单位向量之间的角度）紧密关联。复折射率是描述介质对光的吸收和散射能力的重要参数，它包含实部和虚部。实部表示介质的折射率，而虚部则与介质的吸收系数相关。通过这种方式，作者能够精确地描述光在吸收介质内部的衰减过程。文章进一步发展了斯涅尔定律，这是描述光在不同介质间传播时发生折射的基本定律。在吸收介质的背景下，斯涅尔定律需要考虑介质的吸收特性，这使得定律的适用范围扩大到包括吸收介质在内的各种组合。同时，菲涅耳系数的表达式也被推导出来，它们用于计算光在界面处反射和折射的相对强度，这对于理解和预测光在复杂环境中的行为至关重要。此外，文章提到了几个光学信息科学（OCIS）代码，这些代码通常用于分类和检索光学领域的研究论文。给出的代码260.2110、120.5700、120.5710和080.1510可能分别对应于光学中的特定子领域，如光学材料、光学器件、光波传播以及光学测量技术。这篇文章提供了一个详尽的框架，用于理解和计算光在吸收介质中的传播，以及在吸收介质界面发生的反射和折射现象。这对于光学工程、材料科学、物理光学等领域有着重要的理论和实际应用价值。

January 10, 2010 / Vol. 8, No. 1 / CHINESE OPTICS LETTERS 111

Light propagation and reﬂection-refraction event in

absorbing media

Jianqi Shen (!!!ïïïjjj)

∗

, Haitao Yu (uuu°°°777), and Jindeng Lu (©©©???)

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

∗

E-mail: shenjq@online.sh.cn

Received February 12, 2009

The light propagation within an absorbing medium and the reﬂection and refraction at the interface of two

absorbing media are studied. By using the unit vectors denoting the planes of constant field amplitude and

constant phase respectively, the light propagation and attenuation are described by the effective refractive

indices which depend on both the complex refractive index of the medium and the angle between the unit

vectors. With the expression for the light propagation, the corresponding Snell’s law and the expression

of Fresnel coefficients are obtained, which can be applied to describe the reﬂection-refraction event at the

interface b etween an arbitrary combination of transparent and absorbing media.

OCIS co des: 260.2110, 120.5700, 120.5710, 080.1510.

doi: 10.3788/COL20100801.0111.

Geometrical optics approximation (GOA) of light scat-

tering by large particles with the size much larger than

the wavelength of the incident light is considered as a

good method by avoiding difficulties in Lorenz-Mie cal-

culation. Studies on the GOA of light scattering have

been of interest to many researchers during the past sev-

eral decades

[1−12]

. Most of the publications treat the

light scattering by transparent particles. As far as we

know, the GOA calculations of light scattering by ab-

sorbing particles are rare due to the difficulties in calcu-

lating the propagation of light in the absorbing medium

and its Fresnel coefficients at the interface of the me-

dia. This problem was recently investigated by Yang

et al.

[13,14]

by introducing the effective refractive in-

dex, and they presented the formulae for calculating the

Fresnel coefficients at the interface of the transparent-

absorbing media, which was based on the assumption of

the plane of constant amplitude being parallel to the in-

terface.

The assumption of Yang et al. is reasonable for the

reﬂection-refraction event while the incident light hits the

absorbing particle suspended in air, as p = 0 in Fig. 1.

However, for the high order reﬂection-refraction events

(i.e., p = 1,2,···) in which the light within the particle

is reﬂected and refracted at the interface, the plane of

constant amplitude is usually unparallel to the interface.

Besides, if one would calculate the coated particles con-

taining absorbing core and shell, he has to account for

the interface between absorbing-absorbing media.

In this letter, we study the light propagation in an ab-

sorbing medium and the reﬂection-refraction event of the

light at the interface of absorbing-absorbing media. The

media are assumed to be uniform and isotropic. The pa-

rameters such as the permeability ε, the permittivity µ,

and the conductivity σ are time-independent. The time

dependence of the light wave is expressed in the form exp

(iωt), where ω is the angular frequency and t is the time.

Substituting the time-harmonic wave (i.e., E (r, t) =

E (r) exp (iωt) and H (r, t) = H (r) exp (iωt)) into the

Maxwell equations (in SI units)

[15,16]

, we may obtain

∇ × E (r) = −iωµH (r)

∇ × H (r) = iωˆεE (r)

, (1)

∇

E (r) + k

ˆm

E (r) = 0

∇

H (r) + k

ˆm

H (r) = 0

, (2)

where ˆε = ε −i

is the equivalent complex permeability,

is the wave number in vacuum. The complex refrac-

tive index ˆm is defined by ˆm

= (ω/k

)

ˆεµ = c

ˆεµ (c

is the light speed in vacuum), whose real and imaginary

parts m

and m

are obtained as











ˆm = m

− i · m

= c

+ µε

= c

− µε

. (3)

Fig. 1. Schematic illustration of the reﬂection-refraction

events of the light in an absorbing sphere.

1671-7694/2010/010111-04

° 2010 Chinese Optics Letters

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