Computational Methods for Electromagnetic and Optical by Banerjee, Partha P.; Jarem, John M

By Banerjee, Partha P.; Jarem, John M

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Extra resources for Computational Methods for Electromagnetic and Optical Systems, Second Edition

Example text

In the case of pure charge diffusion, for the c-axis oriented along the direction of pump propagation, constructive interference occurs for the backscattered light, while the transmitted light suffers destructive interference. This interference occurs due to the phase difference between the interference and grating patterns, and the phase change in the scattered beams due to the reflections from the grating. The constructive and destructive interference directions are reversed when the crystal c-axis is reversed.

10 is to note that in the absence of diffraction (the first term on the RHS), the solution of the equation is of the form Ee ∝ exp[−jΔnk0z], which explicitly shows the additional phase change due to propagation in the perturbed refractive index. 10) is a partial differential equation (PDE) that does not always lend itself to analytical solutions, except for some very special cases involving special spatial variations of Δn, or when as in nonlinear optics, one looks for particular soliton solution of the resulting nonlinear PDE using exact integration or inverse scattering methods.

Hence, we have employed an alternate approximate method of simulating the interference with less computational load. We have saved only the peak of the field (instead of the whole transverse array) in the buffer. This results in an interference pattern without a transverse profile. This approximation does not result in any significance difference in our simulation, but has improved the required CPU time by two orders of magnitude. 21 shows the peak of the interference at every step in the longitudinal direction (each point of the plot represent the peak of the transverse profile at that step) for a thin LiNbO3 crystal.

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