By Banerjee, Partha P.; Jarem, John M
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Extra info for Computational methods for electromagnetic and optical systems
The bi-directionality of the simulation (opposing directions of the pump and signal beams) is handled by treating the two counter-propagating directions in sequence and then using an iterative shooting method to find the converged solution. 20. 20 represent the front and rear surfaces of the PR material, respectively, and the crystal c-axis is perpendicular to these faces. In this work, we only consider the case of LiNbO3, which is a uniaxial crystal. For uniaxial crystals with light propagation along the polar axis, only one transverse polarization vector is required to be defined.
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.
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. 2 Induced Transmission Gratings It can be shown that the coupled set of simplified Kukhtarev equations  (see Chapter 6 for details) for a diffusion-dominated PR material can be decoupled in the steady state to yield an ODE for the space charge electric field .