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TM Wave Propagation in Optical Nanostructures with a Third-Order Nonlinear Response: Modeling and Validation with COMSOL

A. Kildishev[1], E. E. Narimanov[1]
[1]Birck Nanotechnology Center, School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana, USA

An enhanced method is used for analysis of third-order nonlinearities in optical nanostructures with scalar TM (H-field) frequency domain formulation. After embedding it in COMSOL Multiphysics it is shown to produce fast and accurate results without superfluous vector E-field formalism. A standard TM representation based on cubic non-linear susceptibility χ(3) results in an intractable implicit equation, but our technique alleviates this problem. In addition to a universal approach, simpler, more efficient solutions are proposed for media with χ(3) having solely either the real part (lossless Kerr-type medium) or the imaginary part (non-linear absorbing medium).