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

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 info for Computational Methods for Electromagnetic and Optical Systems, Second Edition

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21. 24) where n0 denotes the intrinsic refractive index of the medium, and n(2) is a measure of the gradation in the refractive index. 3 Contour plots showing periodic focusing of an initial Gaussian profile. 3. The contour plots show the initial (Gaussian) beam profile, the beam profile where the initial Gaussian attains its minimum waist during propagation before returning back to its original shape again, due to periodic focusing by the graded index distribution. Note that there exists a specific eigenmode (a Gaussian of a specific width, related to the refractive index gradient) for which the beam propagates through the material without a change in shape as a result of a balance between the diffraction of the beam and the guiding due to the parabolic gradient index profile.

From Nehmetallah, G. A. O. , Research Signpost, Trivandrum, India, 2007. ) exp{Sˆ Δz} = exp − j γ ʹ ue Δz . As expected, the “pulse” remains unchanged with propagation. 30 in one transverse dimension (x). The result is a spatial soliton. 9. The split-step technique has also been applied to analyze propagation of profiles in two transverse dimensions [11], and also to analyze propagation of optical fields that are pulsed in time and have a spatial profile in the transverse dimension [12]. 37) During the last stages of self-focusing, the assumptions about slowly varying amplitude and the paraxial approximation may not be valid for large focusing angles.

100, 166, 1993. ) 32 Computational Methods for Electromagnetic and Optical Systems Before comparing the thin sample results with the findings for the thick sample case, we will, at this point, provide a simple alternate explanation for the observed behavior of DBF when monitored as a function of the intensity. Our explanation is based on the examination of the spectrum of the phase modulation exp(−jk0Δn(x)L). The far-field pattern is the convolution of the above spectrum with that of the input profile.

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