Computational analysis of dispersive and nonlinear 2D materials by using a GS-FDTD method

In this paper, we propose a novel numerical method for modeling nanostructures containing dispersive and nonlinear two-dimensional (2D) materials, by incorporating a nonlinear generalized source (GS) into the finite-difference time-domain (FDTD) method. Starting from the expressions of nonlinear currents characterizing nonlinear processes in 2D materials, such as second- and third-harmonic generation, we prove that the nonlinear response of such nanostructures can be rigorously determined using two linear simulations. In the first simulation, one computes the linear response of the system upon its excitation by a pulsed incoming wave, whereas in the second one the system is excited by a nonlinear GS, which is determined by the linear near-field calculated in the first linear simulation. This new method is particularly suitable for the analysis of dispersive and nonlinear 2D materials, such as graphene and transition-metal dichalcogenides, chiefly because, unlike the case of most alternative approaches, it does not require the thickness of the 2D material. To investigate the accuracy of the proposed GS-FDTD method and illustrate its versatility, the linear and nonlinear responses of graphene gratings have been calculated and compared to results obtained using alternative methods. Importantly, the proposed GS-FDTD can be extended to three-dimensional bulk nonlinearities, rendering it a powerful tool for the design and analysis of more complicated nanodevices

Generalized source method for modeling nonlinear diffraction in planar periodic structures

We present a new numerical method for the analysis of second-harmonic generation (SHG) in one-and twodimensional (1D, 2D) diffraction gratings with arbitrary profile made of non-centrosymmetric optical materials. Our method extends the generalized source method (GSM), which is a highly efficient alternative to the conventional Fourier modal method, to quadratically nonlinear diffraction gratings. The proposed method consists of a two-stage algorithm. Initially, the electromagnetic field at the fundamental frequency is computed in order to obtain the second-harmonic polarization using the known second-order nonlinear susceptibility. Then the optical field at the second-harmonic frequency is computed using this polarization as an additional source term in the GSM. We show how to integrate this source term into the GSM framework without changing the structure of the basic algorithm. We use the proposed algorithm to investigate a doubly resonant mechanism that leads to strong enhancement of SHG in a nonlinear 2D circular GaAs grating mounted on top of a GaAs slab waveguide. We design this optical device such that slab waveguide modes at the fundamental and second-harmonic are simultaneously excited and phase matched by the grating. The numerically obtained resonance frequencies show good agreement with analytically computed resonance frequencies of the unperturbed slab waveguide. © 2014 SPIE

Numerical investigation of Littrow lasing in open resonator photonic crystal waveguides

We present a numerical analysis of in-plane lasing in open resonator photonic crystal (PhC) waveguides in the Littrow configuration. The intensity spectra corresponding to the resonant modes of PhC waveguide lasers are determined and agree closely with resonant modes in the band diagram of the waveguide. We investigate the dependence of the lasing behavior on the properties of the waveguide. In particular, our method allows for the determination of the lasing threshold, for which an optimal waveguide width is found. Because of the good reflectivity of the PhC mirrors the concept of open resonator waveguides holds promise for laterally small lasers

Gigabit Pulse Position Bistability in Semiconductor Lasers

The paper briefly reviews the major forms of optical bistability in active optical devices compatible for use in gigabit optical communication systems, and reports an entirely new optical bistability for the first time. Unlike previous devices, the two bistable states of the optical device are each a series of picosecond optical pulses at 1 GHz or greater repetition rates, and are distinguished by a half period temporal shift between their temporal positions in relation to a clock pulse. The bistable device is based on a gain switched semiconductor laser. Theoretical studies suggest 100-ps switching speeds might be achieved, and experimental results are reported indicating optically triggered switching times of 500 ps. © 1987, American Medical Association. All rights reserved