Frequency-domain modeling of TM wave propagation in optical nanostructures with a third-order nonlinear response

Alexander V. Kildishev, Birck Nanotechnology Center, School of ECE
Yonatan Sivan, Purdue University - Main Campus
Natalia M. Litchinitser, SUNY Buffalo
V. M. Shalaev, Birck Nanotechnology Center and School of Electrical and Computer Engineering, Purdue University

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An enhanced method is developed for analysis of third-order nonlinearities in optical nanostructures with a scalar magnetic field frequency-domain formulation; it is shown to produce fast and accurate results for 2D problems without a superfluous vector electric field formalism. While a standard TM representation using cubic nonlinear susceptibility results in an intractable implicit equation, our technique alleviates this problem. In addition to a universal approach, simpler, more efficient solutions are proposed for media having solely either a real (lossless Kerr-type medium) or an imaginary (nonlinear absorbing medium) nonlinearity. Combining these solutions with a finite-element method, we show simulation examples validated with alternative approaches.


Engineering | Nanoscience and Nanotechnology