Fully vectorial simulation of light propagation through uniaxial and biaxial crystals

Nowadays, to achieve high accuracy in optical measurements, manufacturing and particle trap- ping, light { many of its aspects and especially the polarization - must be controlled precisely. Uniaxial and biaxial crystals, due to their birefringent properties, are probably the most suitable choices for manipulating light in a vectorial manner. For a better understanding and design of optical systems which include birefringent crystals, a fully vectorial simulation technique is needed. Several approaches have been put forward, but very often, they are restricted to either certain types of crystals or certain types of fields and solve the problems only in specific cases. We present, based on Berreman's 4x4 matrix formulation, a numerical simulation technique for the propagation of general fields through any uniaxial or biaxial crystal. With this technique, we demonstrate simulation examples including the generation of optical vortices with uniaxial crystals, the formation of configurable optical bottle beams with biaxial crystals, and so on. In addition, we also briefly introduce the simulation technique for the possible second-order nonlinear effects taking place in birefringent materials.

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