By Banerjee, Partha P.; Jarem, John M
Read Online or Download Computational Methods for Electromagnetic and Optical Systems, Second Edition PDF
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Additional resources for Computational Methods for Electromagnetic and Optical Systems, Second Edition
Thus far we have analyzed the propagation of a single focused Gaussian beam in a diffusiondominated PR medium. When two beams are incident on such a medium with a small angle between each other, the induced refractive index profile is responsible for energy exchange between the two beams, a phenomenon referred to as TBC. This energy exchange occurs due to the phase shift between the intensity interference pattern and the induced refractive index pattern . We can effectively study the interaction and the resulting energy exchange between two focused Gaussian beams incident on the material numerically using the split-step method.
When two approximately co-propagating beams are incident on the PR material, they give rise to induced transmission gratings which facilitate the energy exchange. On the other hand when two approximately contra-propagating beams are incident on the PR material, they give rise to induced reflection gratings which also facilitate the energy exchange. This energy exchange occurs over and above the beam fanning described above. While the first model described below for induced refractive index is based on carrier diffusion, other effects such as the photovoltaic (PV) effect in materials such as LiNbO3 can also contribute to induced transmission and reflection gratings, as will be seen later.
12) if Dˆ , Sˆ are assumed to be z-independent. 13) according to the Baker–Hausdorff formula , where [Dˆ , Sˆ ] represents the commutation of Dˆ , Sˆ. 13 the diffraction and the inhomogeneous operators can be treated independent of each other. 14 is better understood in the spectral domain. Note that this is the propagation operator that takes into account the effect of diffraction between planes z and z + Δz. 8 with z replaced by Δz. 1 Flow diagram for the BPM split-step method. domain. 1. , the symmetrized split-step Fourier method, and the leap-frog techniques; these are discussed in detail elsewhere .