By Banerjee, Partha P.; Jarem, John M
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Additional info for Computational methods for electromagnetic and optical systems
The phenomenon of PR beam fanning, where the incident light beam is deflected and/or distorted when it passes through a high-gain PR crystal, has been observed in BaTiO3, LiNbO3, and SBN [26–28]. One of the ways this has been explained is through the fact that a symmetric beam may create an asymmetric refractive index profile, leading to beam distortion, or what we will call deterministic beam fanning (DBF) in the far field . This analysis has been done for a thin sample, meaning one where diffraction of the beam is neglected during its travel through the PR material, and by using a linearized theory to determine the induced refractive index profile.
Thus, for H < 0, the function V(z) vanishes at a distance zr = [V0 /−4H0]1/2 > 0. , when the nonlinear effect is stronger than diffraction, the beam self-focuses and collapse occurs at a distance zc ≤ zr. 1585(p − 1) for r0 = 1/ 2 , where p = N0/Nc and N 0 = c 2r0D . Note that the ub condition H = 0, which leads to Pc , leads to an overestimate of the actual critical power. We now outline our numerical adaptive spectral technique called the adaptive split-step fast Hankel transform (AFHTSS) used to track the solution of the NLS equation for σ = 1, D = 2 and variable ε.
36 Computational Methods for Electromagnetic and Optical Systems phase information at every propagation step. The paraxial approximation used in this split-step method allows us to simulate the propagation of beams with spot sizes as small as 3 μm without significant error . As the beam enters the crystal (at step 2), part of it is reflected (Eref). The transmitted beam (Ep) is propagated to the rear boundary, where part of this beam is transmitted (Ept) and remainder is reflected (Es) (at step n − 1).