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.
© 2009 Optical Society of America
Original Manuscript: June 30, 2009
Revised Manuscript: September 28, 2009
Manuscript Accepted: October 2, 2009
Published: October 28, 2009
Alexander V. Kildishev, Yonatan Sivan, Natalia M. Litchinitser, and Vladimir M. Shalaev, "Frequency-domain modeling of TM wave propagation in optical nanostructures with a third-order nonlinear response," Opt. Lett. 34, 3364-3366 (2009)