Beam Propagation Method Devang Parekh 3204 EE 290
Beam Propagation Method Devang Parekh 3/2/04 EE 290 F
Outline What is it? n FFT n FDM n Conclusion n
Beam Propagation Method Used to investigate linear and nonlinear phenomena in lightwave propagation n Helmholtz’s Equation n
BPM (cont. ) n Separating variables n. Substituting back in
BPM (cont. ) n. Nonlinear Schrödinger Equation n. Optical pulse envelope n. Switch to moving reference frame
BPM (cont. ) n. Substituting n. First again two-linear; last-nonlinear
Fast Fourier Transform (FFTBPM) n. Use operators to simplify n. Solution
Fast Fourier Transform (FFTBPM) n. A represents linear propagation n. Switch to frequency domain
Fast Fourier Transform (FFTBPM) n. Solving n. Plug back for the time domain in at h/2
Fast Fourier Transform (FFTBPM) n. Similarly n. Using for B(nonlinear) this we can find the envelope at z+h
Fast Fourier Transform (FFTBPM) n. Three step process 1. Linear propagation through h/2 2. Nonlinear over h 3. Linear propagation through h/2
Fast Fourier Transform (FFTBPM) n. Numerically n. Discrete n. Fast solving Fourier Transform n. Divide and conquer method
Fast Fourier Transform (FFTBPM) n. Cool Pictures
Fast Fourier Transform (FFTBPM)
Finite Difference Method (FDMBPM) n. Represent n. Apply as differential equation Finite Difference Method
Finite Difference Method (FDMBPM)
Finite Difference Method (FDMBPM) n. Cool Pictures
Finite Difference Method (FDMBPM)
Conclusion Can be used for linear and nonlinear propagation n Either method depending on computational complexity can be used n Generates nice graphs of light propagation n
Reference n Okamoto K. 2000 Fundamentals of Optical Waveguides (San Diego, CA: Academic)
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