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

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Presentation transcript:

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

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

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

Fast Fourier Transform (FFTBPM) Use operators to simplify Solution

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

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

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

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

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

Fast Fourier Transform (FFTBPM) Cool Pictures

Fast Fourier Transform (FFTBPM)

Finite Difference Method (FDMBPM) Represent as differential equation Apply Finite Difference Method

Finite Difference Method (FDMBPM)

Cool Pictures

Finite Difference Method (FDMBPM)

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

Reference Okamoto K Fundamentals of Optical Waveguides (San Diego, CA: Academic)