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Beam Propagation Method

Beam Propagation Method. Devang Parekh 3/2/04 EE290F. Outline . What is it? FFT FDM Conclusion. Beam Propagation Method. Used to investigate linear and nonlinear phenomena in lightwave propagation Helmholtz’s Equation. BPM (cont.). Separating variables. Substituting back in.

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Beam Propagation Method

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  1. Beam Propagation Method Devang Parekh 3/2/04 EE290F

  2. Outline • What is it? • FFT • FDM • Conclusion

  3. Beam Propagation Method • Used to investigate linear and nonlinear phenomena in lightwave propagation • Helmholtz’s Equation

  4. BPM (cont.) • Separating variables • Substituting back in

  5. BPM (cont.) • Nonlinear Schrödinger Equation • Optical pulse envelope • Switch to moving reference frame

  6. BPM (cont.) • Substituting again • First two-linear; last-nonlinear

  7. Fast Fourier Transform (FFTBPM) • Use operators to simplify • Solution

  8. Fast Fourier Transform (FFTBPM) • A represents linear propagation • Switch to frequency domain

  9. Fast Fourier Transform (FFTBPM) • Solving back for the time domain • Plug in at h/2

  10. Fast Fourier Transform (FFTBPM) • Similarly for B(nonlinear) • Using this we can find the envelope at z+h

  11. Fast Fourier Transform (FFTBPM) • Three step process 1. Linear propagation through h/2 2. Nonlinear over h 3. Linear propagation through h/2

  12. Fast Fourier Transform (FFTBPM) • Numerically solving • Discrete Fourier Transform • Fast Fourier Transform • Divide and conquer method

  13. Fast Fourier Transform (FFTBPM) • Cool Pictures

  14. Fast Fourier Transform (FFTBPM)

  15. Finite Difference Method (FDMBPM) • Represent as differential equation • Apply Finite Difference Method

  16. Finite Difference Method (FDMBPM)

  17. Finite Difference Method (FDMBPM) • Cool Pictures

  18. Finite Difference Method (FDMBPM)

  19. Conclusion • Can be used for linear and nonlinear propagation • Either method depending on computational complexity can be used • Generates nice graphs of light propagation

  20. Reference • Okamoto K. 2000 Fundamentals of Optical Waveguides (San Diego, CA: Academic)

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