C. T. Law

Propagation dynamics of optical vortices

Optical vortices in linear and nonlinear media may exhibit propagation dynamics similar to hydrodynamic vortex phenomena. Analytical and numerical methods are used to describe and investigate the interaction between vortices and the background field. We demonstrate that optical vortices that have quasi-point core functions, such as optical vortex solitons, may orbit one another at rates that are orders of magnitude larger than those with nonlocalized cores.

Optical vortex solitons and the stability of dark soliton stripes

Dark soliton stripes are robust but can decay into optical vortex solitons when subjected to a persistent, long-period, transverse modulation. We explore the nonlinear dynamics of this symmetry-breaking process and determine growth rates, vortex densities, and other characteristics by conducting a nonlinear stability analysis that uses numerical techniques for several cases of special interest.

Waveguiding properties of optical vortex solitons.

An optical vortex soliton induces a graded-index waveguide over an extended propagation distance in a self-defocusing nonlinear optical medium. Using numerical techniques, we determine the waveguide dispersion and optimal size of the guided beam.

Polarized optical vortex solitons: Instabilities and dynamics in Kerr nonlinear media

Abstract Optical vortex solitons are known to be stable in a scalar nonlinear system, and they have even been observed. We now explore the effects of polarization on the vortices, and find that they are unstable in Kerr defocusing media, except when the beam is circularly polarized. Numerical simulations verify this and show remarkable beam evolution, including vortex shedding and reversal of topological charge.

X-ray transition radiation in a solid-state superlattice: photoabsorption, electron scattering, and radiation optimization

Soft x rays are generated when low-energy electron beams traverse a solid-state superlattice. We investigate the influence of x-ray absorption and electron scattering losses on the maximum power radiated, the required electron energy, and the optimum total thickness of the superlattice. We show that a moderate increase in the electron-beam energy compensates for the losses due to photoabsorption and electron scattering.

Nonparaxial propagation of a cylindrical beam with Lanczos reduction.

We discuss a numerical method based on Lanczos reduction of modeling nonparaxial propagation of a cylindrical symmetric beam. To illustrate the performance and demonstrate the significant difference between nonparaxial and paraxial beams, we consider Gaussian beam propagation in two different settings.

Propagation of nonparaxial beams with a modified Arnoldi method

We have developed a modified Arnoldi method that includes a complex square-root approximation, which excels at modeling the propagation of highly diverging beams in various media. Simulations of one transverse dimensional beam with an ultranarrow width and of cylindrical Gaussian beams with various divergence angles reveal the strength of this nonparaxial-beam propagation method.

Improving the self-defocusing optical limiter

The so-called defocusing limiter is one of the best configurations for achieving laser radiation protection over a broadband spectrum in a low fnumber system. Available nonlinear materials, however, can not provide maximum permissible exposure levels over a large dynamic range. On the other hand, we believe that novel nonlinear optical engineering techniques can be used to overcome these difficulties. We have recently discovered a rich class of nonlinear optical phenomena in defocusing media, which opens new opportunities to enhance the performance of defocusing limiters and to explore completely new limiting schemes. Here we show that a nonlinear mask can be used to improve the device performance by reducing the throughput power by 90% in an ff5 optical system. We have numerically modeled a generic nonlinear optical limiter to account for these effects. The code allows us to vary the parameters of the optical system and the nonlincar medium. In addition to obtaining the transmission data, we also determine the intensity distribution in the final focal plane.

Implementation of a package for optical limiter modeling

As our continuous effort to develop a package for modeling of beam propagation in nonlinear optical devices, we use different means to improve its user-friendliness, availability and capability. We have extended our model to include pulse propagation, i.e. 4-dimensional propagation of an optical beam. Currently, we have developed a few models for intensitydependent and fluence-dependent propagation of nonlinear wave, including various nonlinear absorption and refractive mechanisms such as thermal diffusion and reverse saturation absorption (RSA). These models can provide significant insight into the underlying optical processes which occur in nonlinear optical devices such as optical limiters. Here we will concentrate our discussion on thermal diffusion and reverse saturable absorption. To improve user-friendliness, availability and capability of the package, we have implemented two graphical user interfaces, a Internet version based on Hypertext Markup Language HTML/pen script and a standalone version based on TcIITk script. The two interfaces can be executed in a variety of computers (Macintosh, workstation or PC) while the actual simulation can be performed in a more powerful computer. The two interfaces have their own merits. The Tcl!Fk version can be easily modified and installed in a computer that has no access to the Internet. On the other hand, the web based version makes the package available to more users via world-wide web (WWW). The layouts of the interfaces are almost the same. They generate simulation results in text files for plotting as well as animation sequences which can be viewed with a free software, available from National Center for Supercomputing Applications.

Numerical Modeling of Nonlinear Beam Propagation Phenomena

A user-friendly beam propagation program has been developed for use over the worldwide- web to aid the optical limiting community in modeling the transmission of light through nonlinear refractive and absorptive media having local intensity-dependent or nonlocal fluencedependent mechanisms.