Post on 08-Feb-2016
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Chapter 3 & 4Beam Optics + Fourier Optics
Comments 第二章的延续 非平面波
主要沿 z方向传播 在横截面( xy)里,电磁场为非均匀分布
3.1 THE GAUSSIAN BEAM
Under paraxial Helmholtz equation
Properties
W0 ~ z01/2
束缚越强,扩散越大!
Gouy Phase
Divergence and Gouy Phase
Dispersion Relation kx
2+ky2+kz
2=k02
Isotropic media
Divergence and Gouy Phase
Confinement in x-y w(z)
Broadening in kx-ky
1/w(z)
Divergence and Gouy Phase
Gouy Phasekx
2 + ky2 + kz
2 = k2
OL 26, 485 (2001)
源于量子受限效应
Problems Broadening in wavevector?
Could explain the divergence! Wrong for Gouy phase
Weights of different Fourier components do not vary with distance z!
Why? Paraxial Approximation
A dilemma exists! 也许值得探讨
3.2 TRANSMISSION THROUGH OPTICAL COMPONENTS
光路设计上很重要
3.4 LAGUERRE-GAUSSIAN AND BESSEL BEAMS
伴随着 l,存在环状能流,在光学蜗旋上、光镊里起到关键作用!
Vortex
Generation
Applications
Bessel Beams
< k, Gouy Phase
Non-integrable
FOURIER OPTICS
based on harmonic analysis (the Fourier transform) linear systems
Expansion Methods Fourier Optics
Expansion based on the solutions of wave equation -- plane waves
Paraxial Optics? LG waves HG waves
Expansion based on the orthogonal and complete sets
4.1 PROPAGATION OF LIGHT IN FREE SPACE
算法实现 周期边界性条件
取样区域的尺寸大小 A为周期 Fourier Transformation中 , k=n2π/A, 取分立值
可调用 Fast Fourier Transformation (FFT)命令
4.2 OPTICAL FOURIER TRANSFORM
4.3 DIFFRACTION OF LIGHT
WHY?
x
kx
Sharp edge high spatial frequency
Problem?
We must utilize the components with higher wavevectors kx, ky>k kz become pure imaginary!
Evanescent waves & surface waves
Bigger k smaller wavelength 电镜 , x-ray
SNOM
Perfect lense / superlensePhys. Rev. Lett. 85, 3966–3969 (2000), cited by 4500 times
用左手材料 /负折射率( left-handed materials or negative refractive media)材料可以实现超聚焦
science_308_534 (2005)
END
Homework Plot the curves of Eqs. (3.1-8) to (3.1-10)
versus z, and explain what they means
EXERCISE 3.1-3
EXERCISE 3.1-2
Homework EXERCISE 4.1-1
What is Fresnel Approximation and Fraunhofer approximation? Explain their difference
EXERCISE 4.2-2
EXERCISE 4.3-3