Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 3 & 4 Beam Optics + Fourier Optics 1 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 kx2+ky2+kz2=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 Phase OL 26, 485 (2001) kx2 + ky2 + kz2 = k2 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 Paraxial Optics? Expansion based on the solutions of wave equation -- plane waves 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? Sharp edge high spatial frequency x kx 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 Phys. Rev. Lett. 85, 3966–3969 (2000), cited by 4500 times Perfect lense / superlense 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