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Chapter 3 & 4

Chapter 3 & 4. Beam 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. W 0 ~ z 0 1/2. 束缚越强，扩散越大！. Gouy Phase. Divergence and Gouy Phase. Dispersion Relation

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Chapter 3 & 4

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  1. Chapter 3 & 4 Beam Optics + Fourier Optics

  2. 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. 3.1 THE GAUSSIAN BEAM

  4. Under paraxial Helmholtz equation

  5. Properties W0 ~ z01/2 束缚越强，扩散越大！

  6. Gouy Phase

  7. Divergence and Gouy Phase • Dispersion Relation • kx2+ky2+kz2=k02 • Isotropic media

  8. Divergence and Gouy Phase • Confinement in x-y • w(z) • Broadening in kx-ky • 1/w(z) • Divergence and Gouy Phase

  9. Gouy Phase OL 26, 485 (2001) • kx2 + ky2 + kz2 = k2 源于量子受限效应

  10. 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

  11. 3.2 TRANSMISSION THROUGH OPTICAL COMPONENTS

  12. 光路设计上很重要

  13. 3.4 LAGUERRE-GAUSSIAN AND BESSEL BEAMS

  14. 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！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！

  15. Vortex

  16. Generation

  17. Applications

  18. Bessel Beams < k, Gouy Phase Non-integrable

  19. Fourier Optics

  20. based on • harmonic analysis (the Fourier transform) • linear systems

  21. 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

  22. 4.1 PROPAGATION OF LIGHT IN FREE SPACE

  23. 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

  24. 4.2 OPTICAL FOURIER TRANSFORM

  25. 4.3 DIFFRACTION OF LIGHT

  26. WHY? Sharp edge  high spatial frequency x kx

  27. Problem? • Wemust utilize the components with higher wavevectorskx, ky>k • kz become pure imaginary! • Evanescent waves & surface waves • Bigger k  smaller wavelength • 电镜, x-ray

  28. SNOM

  29. 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

  30. science_308_534 (2005)

  31. END

  32. Homework • Develop Eq. (3.1-5) • Explain the meaning of each factor in Eq. (3.1-23) • EXERCISE 3.1-1 • EXERCISE 3.1-2

  33. Homework • EXERCISE 4.1-2 • EXERCISE 4.2-2 • Problems 4.1-3

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