楔形薄膜的大负Goos-Hänchen位移研究

150 浏览量更新于2024-08-27 收藏 1010KB PDF 举报

"这篇论文探讨了楔形薄膜对光反射的影响，特别是Goos-Hänchen（GH）位移现象。文章中，作者通过分析方法推导出了楔形薄膜反射的复振幅表达式，并针对平面波和非平面波（如高斯光束）两种情况进行了计算和模拟。" 在光学领域，Goos-Hänchen位移是一种非经典的光反射现象，它描述了光线在经过界面反射后，在垂直于入射方向上的偏移。这篇由Jianping Bai和Yaoju Zhang合作撰写的《Chinese Optics Letters》论文中，重点研究了这种现象在楔形薄膜中的表现。他们发现，即使在薄膜的反射率接近共振条件较低时，楔形薄膜也能产生显著的负向纵向GH位移。论文首先介绍了对于平面波入射的情况，利用简单的光线追踪方法来计算GH位移。这种方法直观且易于理解，适用于解析分析。然后，为了处理非平面波，如高斯光束的入射，作者采用了平面波的角谱方法进行数值模拟。这两种方法都表明，楔形薄膜能导致大的负向GH位移，这与真空中的平面平行薄膜相比，更容易被检测到。论文中提到的OCIS codes（Optical Society of America 的主题代码）260.1960 和 240.0310，分别对应“表面和薄膜光学”和“非线性光学材料和效应”。这些代码揭示了研究的核心内容：薄膜光学的非线性现象和表面光学特性。 doi:10.3788/COL20090709.0 是该论文的数字对象标识符（Digital Object Identifier），用于唯一识别和引用这篇论文。通过这个DOI，读者可以在相关数据库中找到原始文献，进一步深入学习和研究。该研究揭示了楔形薄膜对Goos-Hänchen位移的独特影响，提供了理论计算和实验验证的手段，这对于理解和控制光在复杂结构中的行为具有重要意义，可能在微纳光学、光通信、光电子技术等领域有潜在的应用价值。

September 10, 2009 / Vol. 7, No. 9 / CHINESE OPTICS LETTERS 845

Large negative Goos-H¨anchen shift from a wedge-shaped

thin ﬁlm

Jianping Bai (

xxx

ïïï

²²²

)

and Yaoju Zhang (

ÜÜÜ



ÞÞÞ

)

2∗

School of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 472000, China

College of Physics and Electronic Information, Wenzhou University, Wenzhou 325035, China

∗

E-mail: zhangyaoju@sohu.com

Received December 12, 2008

The analytical expression for the complex amplitude of light reﬂected from a wedge-shaped thin ﬁlm is

derived. For plane wave incidence, a simple ray tracing approach is used to calculate Goos-H¨anchen (GH)

shifts; and for non-plane wave incidence, for example, a Gaussian beam, th e angular spectrum approach of

plane wave is used in simulation. The two approaches predict that a wedge-shaped thin ﬁlm can produce

large negative longitudinal GH shifts. Although the reﬂectivity is small near the condition of resonance,

the large negative GH shifts can be more easily detected in comparison with the shift from a plane-parallel

ﬁlm in vacuum.

OCIS codes: 260.1960, 240.0310.

doi: 10.3788/COL20090709.0845.

Goos-H¨anchen (GH) eﬀect describes the spatial shift of

the reﬂected ray with respect to a point w here the ray of

incidence intersects the boundary, and the shift is called

the GH shift

[1]

. This phenomenon has been widely ana-

lyzed in theory

[2−13]

and veriﬁed in experiments

[14−17]

Recently, the GH shifts from plane-parallel dielectric

ﬁlms with the positive

[7−9]

and negative

[10−13]

refrac-

tive indices have attracted a grea t deal of attention.

However, to the best of our knowledge, the GH eﬀect

from a wedge-shaped dielectric ﬁlm has not been studied.

The wedge-shaped ﬁlm is a fundamental optical element,

which can be used in lasers, interferometers, and some

exp eriments

[18−22]

. Some electromagnetic properties of

the wedge-shaped ﬁlm have been analyzed

[23,24]

. In this

letter, we analyze the GH shift from a wedge-shaped thin

ﬁlm.

Consider a unit-amplitude and monochromatic plane

wave incident at an angle θ on a nonmagnetic wedge-

shaped thin ﬁlm with a small apex a ngle α (see Fig.

1(a)). The ﬁlm’s thickness at the point of incidence is

h and its refractive index is n. Because of multiple re-

ﬂections at the surfaces, the reﬂected light consists of

a se t of plane waves propagating in diﬀerent dire c tions.

If the a ngle of refraction for the ﬁrst time is denoted

as θ’, the pth wave of the reﬂected set emerg e s at an

angle θ

where, from the law of refraction and reﬂec-

tion, n sin θ

= n

′

sin [θ

′

+ 2(p − 1)α], with n

′

being

the refractive index of the wedge-shaped ﬁlm, and n

being the refractive index of the surrounding medium.

The virtual reﬂected wave-fronts W

, W

, . . . , W

, . . . ,

which contain the wedge apex , would be cophasal if

there is no phase change at reﬂection. At a point P

on the ﬁrst surface with a distance ρ from the apex

O, the diﬀerence of optical path of the pth wave and

the wave which is directly reﬂected (p=1) is therefore

∆S

= n(P N

− P N

) = nρ(sin θ

− sin θ

), where N

and N

are the feet of perpendicular from P to W

and

, respectively. In terms of the geometric relations,

the diﬀerence of optical path between two successively-

reﬂected rays is ∆s = n

′

(AB + BC) − nCD (se e Fig.

1(b)). Thus, the total phase diﬀerence δ

between the

pth wave and the dire c tly reﬂected wave is

2π

[∆S

+ (p − 1)∆s]

4π

′

hcos θ

′



sin(p − 1)α

tan α

{cos(p − 1)α

−tan θ

′

sin(p − 1)α} + (p − 1)β



, (1)

where λ is the wavelength in vacuum, h (= ρtan α) is the

thickness of the ﬁlm a t P , θ’ is determined from the law

of refraction n sin θ = n

′

sin θ

′

, and

β =

1 + tan θ

′

tan(θ

′

+ α)



1 +

cos θ

′

− sin θ

′

sin2(θ

′

+ α)

cos(θ

′

+ 2α)



. (2)

Let r be the Fresnel reﬂection coeﬃcient, t be

the Fresnel transmission coeﬃcient, and r

′

, t

′

be the

Fig. 1. Illustration for multiple reﬂections in a wedge.

1671-7694/2009/090845-04

 2009 Chinese Optics Letters

下载后可阅读完整内容，剩余3页未读，立即下载

weixin_38516270

粉丝: 3

楔形薄膜的大负Goos-Hänchen位移研究

磁光Goos-Hänchen效应在含磁性膜的多层结构中的折射率检测

Goos-Hanchen shift on transmission at the interface of a weakly absorbing medium

光在不同界面反射时的Goos-H?nchen位移 (2009年)

怎么通过命令行设置go goos

goland修改goos为linux

golang runtime goos

在 Windows 上使用 Go 命令构建可执行文件，命令为： 复制 CGO_ENABLED=1 GOOS=linux GOARCH=amd64 CC=x86_64-linux-gnu-gcc go build -o [可执行文件名] [代码路径] 如何操作

GOOS=linux : 无法将“GOOS=linux”项识别为 cmdlet、函数、脚本文件或可运行程序的名称。请检查名称的拼写，如果包括路径，请 确保路径正确，然后再试一次。 所在位置 行:1 字符: 1

$env:GOOS="linux"是什么意思

Redis Metrics Exporter v1.68.0,SHA1=b6015d582ca3132fd42f01a310dafc609725451a build date: sha1: [no-sha] Go: go1.24.1 GOOS: linux GOARCH: amd64" time="2025-03-13T06:45:09Z" level=info msg="Providing metrics at :9121/metrics"

最新资源

在 Windows 上使用 Go 命令构建可执行文件，命令为：复制 CGO_ENABLED=1 GOOS=linux GOARCH=amd64 CC=x86_64-linux-gnu-gcc go build -o [可执行文件名] [代码路径] 如何操作

GOOS=linux : 无法将“GOOS=linux”项识别为 cmdlet、函数、脚本文件或可运行程序的名称。请检查名称的拼写，如果包括路径，请确保路径正确，然后再试一次。所在位置行:1 字符: 1