title: Frequency-domain modeling of TM wave propagation in optical nanostructures with a third-order nonlinear response.
abstract: 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.
authors.affiliation: Birck Nanotechnology Center, School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA. kildishev@purdue.edu
authors.forename: Alexander V
authors.initials: AV
authors.lastname: Kildishev
authors.forename: Yonatan
authors.initials: Y
authors.lastname: Sivan
authors.forename: Natalia M
authors.initials: NM
authors.lastname: Litchinitser
authors.forename: Vladimir M
authors.initials: VM
authors.lastname: Shalaev