arXiv subjects

R. H. Goodman

Publications and source records attributed to R. H. Goodman.

4 recordsLinked to original sources

arXiv2023

Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

We pose the problem of transferring a Bose-Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross-Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using another Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.

nlin.PS↗

arXiv2023

Apodizer Design to Efficiently Couple Light into a Fiber Bragg Grating

We provide an optimal control framework for efficiently coupling light in a bare fiber into Bragg gratings with a cubic nonlinearity. The light-grating interaction excites gap solitons, a type of localized nonlinear coherent state which propagates with a central frequency in the forbidden band gap, resulting in a dramatically slower group velocity. Due to the nature of the band gap, a substantial amount of light is back-reflected by the grating's strong reflective properties. We optimize, via a projected gradient descent method, the transmission efficiency of previously designed nonuniform grating structures in order to couple more slow light into the grating. We further explore the space of possible grating designs, using genetic algorithms, along with a previously unexplored design parameter: the grating chirp. Through these methods, we find structures that couple a greater fraction of light into the grating with the added bonus of creating slower pulses.

physics.optics↗

arXiv2003

Strong NLS Soliton-Defect Interactions

We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected, transmitted, or captured by the defect. We propose a mechanism of resonant energy transfer to a nonlinear standing wave mode supported by the defect. Following Forinash et al, we derive a finite-dimensional model for the interaction of the soliton with the defect via a collective coordinates method. The system thus derived is a three degree-of-freedom Hamiltonian with an additional conserved quantity. We study this system using the tools of dynamical systems theory, and find that it exhibits a variety of interesting behaviors, largely determined by the structures of stable and unstable manifolds of special classes of periodic orbits. We use this geometrical understanding to interpret the simulations.

nlin.PS↗

arXiv2001

Stopping Light on a Defect

Gap solitons are localized nonlinear coherent states which have been shown both theoretically and experimentally to propagate in periodic structures. Although theory allows for their propagation at any speed $v$, $0\le v\le c$, they have been observed in experiments at speeds of approximately 50% of $c$. It is of scientific and technological interest to trap gap solitons. We first introduce an explicit multiparameter family of periodic structures with localized defects, which support linear defect modes. These linear defect modes are shown to persist into the nonlinear regime, as {\it nonlinear defect modes}. Using mathematical analysis and numerical simulations we then investigate the capture of an incident gap soliton by these defects. The mechanism of capture of a gap soliton is resonant transfer of its energy to nonlinear defect modes. We introduce a useful bifurcation diagram from which information on the parameter regimes of gap soliton capture, reflection and transmission can be obtained by simple conservation of energy and resonant energy transfer principles.

nlin.PS↗