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By Banerjee, Partha P.; Jarem, John M

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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.

In this respect, the nature of the optical nonlinearity in a PR material is more involved as compared to that in a nonlinear Kerr-type material. We point out that in a Kerr-type material for instance, only an asymmetric beam profile can cause beam bending, as reported in [32], while a symmetric beam undergoes self-focusing or defocusing. 31 Scalar EM Beam Propagation in Inhomogeneous Media In what follows, we first provide results for the far-field beam profiles by assuming the PR material to be a thin sample, in the sense that we neglect the effects of propagational diffraction through the material.

16a. The resulting far-field pattern which is the convolution of the Gaussian spectrum and the Airy pattern generally exhibits decreased DBF when the Airy pattern has a (denormalized) width much smaller than that of the Gaussian spectrum (which may occur, for instance, for both small and large W). 16. Appreciable DBF occurs in the region where the normalized spectral width is greater than unity. 5 mW, maximum beam fanning, defined by the maximum of the ratio of the peak value of the sidelobe and that of the mainlobe, occurs when W = 30 μm.

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