1 / 20

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.

rylee-may
Download Presentation

Beam Propagation Method

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related