Abstract : Nonlinear optics is the area of optics that studies the interaction of light with matter in the regime where the response of the material system to the applied electromagnetic field is nonlinear in the amplitude of this field. Here, we are concerned with numerical modeling of nonlinear optical phenomena. Of particular interest to this minisymposium are recent advances on general numerical methods such as finite difference methods, finite element methods, discontinuous Galerkin methods, etc. that have been tailored to the mathematical models of nonlinear optics with emphasis on achieving high order accuracy, adaptivity and efficient handling of multiscale features.
[03183] High-Order Accurate Approaches for Maxwell's Equations with Nonlinear Active Media on Overlapping Grids
Format : Talk at Waseda University
Author(s) :
Jeffrey Banks (Rensselaer Polytechnic Institute)
Gregor Kovacic (Rensselaer Polytechnic Institute)
William Henshaw (Rensselaer Polytechnic Institute)
Donald Schwendeman (Rensselaer Polytechnic Institute)
Qing Xia (KTH Royal Institute of Technology)
Alexander Kildeshev (Purdue University)
Ludmila Prokopeva (Purdue University)
Abstract : Here I discuss efficient numerical methods for Maxwell's equations in nonlinear active media. Complex geometry is treated with overlapping grids, and interfaces between different materials are accurately and efficiently treated using compatibility coupling conditions. A novel hierarchical modified equation (ME) approach leads to an explicit scheme that does not require nonlinear iteration, and also gives local update equations without any tangential coupling along interfaces that would otherwise occur using a traditional high-order ME time stepper.
[02203] Energy stability and active Q-factor control in numerical models of nonlinear electromagnetic resonance effects
Format : Online Talk on Zoom
Author(s) :
Lutz Angermann (Clausthal University of Technology)
Abstract : The talk deals with the modeling and some properties of mathematical models to describe the excitation of a nonlinear material by electromagnetic waves, including typical questions such as the existence and uniqueness of a solution, the derivation of energy laws or estimates, the evaluation of the resonance quality and the transfer of these properties to numerical models.
[02291] Energy stable finite element method for nonlinear Maxwell's equations
Format : Talk at Waseda University
Author(s) :
Maohui Lyu (Beijing University of Posts and Telecommunications)
Vrushali Bokil (Oregon State University)
Yingda Cheng (Michigan State University)
Fengyan Li (Rensselaer Polytechnic Institute)
Weiying Zheng (LSEC, Chinese academy of sciences)
Abstract : In this talk, we consider the time-domain nonlinear Maxwell’s equations in multi-dimensions. With special discretizations for the nonlinear terms, we introduce a class of provably energy stable finite element method. Numerical experiments are provided to validate the performance of the proposed methods.
[03742] High Order Energy Stable FDTD Methods for Maxwell Duffing models in Nonlinear Photonics
Format : Talk at Waseda University
Author(s) :
Vrushali A Bokil (Oregon State University)
Daniel Appelo (Michigan State University)
Yingda Cheng (Michigan State University)
Fengyan Li (Rensselaer Polytechnic Institute)
Abstract : We present electromagnetic models that describe nonlinear optical phenomenon in which the nonlinear polarization is driven by the electric field
and modeled as an anharmonic oscillator(s). The models for the nonlinear polarization are given by Duffing equations and incorporate both nonlinearity and dispersion. Using the auxiliary differential equation approach, we present discretizations of the coupled Maxwell-Duffing models which are high order and energy stable methods based on finite difference time domain (FDTD) techniques.
Constantin Carle (Karlsruhe Institute of Technology)
Marlis Hochbruck (Karlsruhe Institute of Technology)
Abstract : For the spatially discretized acoustic wave equation, stability of explicit time integration schemes such as the leapfrog scheme can only be guaranteed under a CFL condition. In the case of locally refined meshes, this condition is the main bottleneck for the efficiency of explicit schemes.
To overcome this issue, we introduce local time-stepping and locally implicit schemes and present a rigorous error analysis.
[02186] Discontinuous Galerkin Time-Domain methods for nonlinear active media on unstructured grids
Abstract : We present a Discontinuous Galerkin Time-Domain method for solving the system of Maxwell equations coupled to the rate equations modeling light interaction with gain media.
