John M. Jarem

Rigorous coupled-wave analysis of photorefractive reflection gratings

Rigorous coupled-wave reflection grating analysis and Kukhtarev’s equations have been solved in the time domain to determine the optical intensity, electron density, and dielectric modulation in BaTiO3. A novel Green’s-function approach has been developed to analyze Kukhtarev’s material equations. The Green’s-function approach allowed Kukhtarev’s equations to be reduced to a matrix form, from which the electron density could be obtained. A temporal state variable matrix equation was also developed from which full time-dependent solutions of Kukhtarev’s equations could be determined. An electron balance equation was developed from which the different terms in Kukhtarev’s equation could be studied and compared. Numerical simulations were carried out that showed the growth of a photorefractive BaTiO3 reflection grating. The simulation showed that an asymmetric, blazelike pattern resulted for the dielectric modulation. The blazelike pattern was shown to arise from spatial differentiation of a cusplike shape that the electron-density function assumed for its solution.

Exact, Dynamical Analysis of the Kukhtarev Equations in Photorefractive Barium Titanate using Rigorous Coupled-Wave Diffraction Theory

Rigorous coupled-wave diffraction theory is used to analyze two-wave and multiwave mixing in diffusion-controlled photorefractive barium titanate, which is modeled by the Kukhtarev equations. These equations are partially decoupled to yield a system of two equations between the electron density and the electrostatic field (and hence the induced refractive index profile). The transmitted and reflected optical fields, the dielectric modulation, the electrostatic field, and the electron density are studied for the cases in which the interfering, incident optical fields have equal and unequal amplitudes for different values of the linear refractive index mismatch and for different values of photorefractive crystal length. In each case the exact longitudinal inhomogeneity in the photorefractive medium is analyzed with the use of rigorous coupled-wave diffraction theory and an exact Kukhtarev analysis. We compare the evolution of the diffracted orders for different sample lengths to show that the nature of the steady state (oscillatory or nonoscillatory) critically depends on the sample length. Our computations study in BaTiO3 the conditions for temporal instability resulting in self-pulsation and for anisotropic diffraction contributing to significant generation of higher orders (assuming that two plane waves are incident on the photorefractive material).

Transient wave mixing and recording kinetics in photorefractive barium titanate: a nonlinear coupled mode approach

By using rigorous coupled-wave diffraction theory along with a time-dependent nonlinear formulation, we analyze two- and multiple-wave coupling and the grating kinetics in BaTiO 3 with different boundary interfaces. Efffects of electrostatic and optical anisotropy have been included in the analysis. Significant mode conversion to higher orders is observed only when the boundary interfaces are highly mismatched.

Application of the complex Poynting theorem to diffraction gratings

The complex Poynting theorem has been used to study power flow and energy storage for the case in which a plane wave (polarization wherein the electric field is in the plane of incidence) is scattered from a generally lossy, anisotropic, non-Hermitian diffraction grating. The full electromagnetic fields of the diffraction grating system were specified, and, in applying the complex Poynting theorem to the grating system, a full calculation of the diffraction efficiency, the electromagnetic (electric and magnetic) energy, and the real, reactive, dissipative, and evanescent power of the grating was made. A step profile grating was used to test numerical examples, and, in all cases considered, the complex Poynting theorem was obeyed to a high degree of numerical accuracy. In the study the effects that anisotropy and lossiness of the grating system had on the complex power of the system were illustrated. A comparison of the complex power that resulted from scattering from diffraction gratings composed of Hermitian and non-Hermitian anisotropic materials was numerically studied.

A Nonlinear, Transient Analysis of Two- and Multi-Wave Mixing in a Photorefractive Material using Rigorous Coupled-Wave Diffraction Theory

Rigorous coupled-wave diffraction theory is used to analyze two- and multi-wave mixing in a diffusion-controlled photorefractive material which is modeled by the Kukhtarev equations. These equations are first decoupled to yield a nonlinear time-dependent differential equation for the induced refractive index profile. The transmitted and reflected field coupling coefficients are studied for the cases when the incident optical fields are coherent and partially coherent, for materials with different gain constants, and for different values of the linear refractive index mismatch. In each case, the exact longitudinal inhomogeneity in the photorefractive medium is analyzed using rigorous coupled-wave diffraction theory. Our computations predict a possible temporal instability resulting in self-pulsation and anisotropic diffraction contributing to a significant generation of higher orders when two plane waves are incident on photorefractive materials. Six-wave coupling in index mismatched barium titanate is studied.

U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development

The advent of missile seekers with dual-mode millimeter wave and infrared common-aperture sensors has led to a requirement to develop the simulation tools necessary to test these systems. Traditionally, one of the most important techniques for supporting systems development has been a full seeker hardware-in-the-loop simulation. The development of simulation facilities capable of supporting the new generation of advanced dual-mode guided systems has been limited due to some major technological challenges which are yet to be solved. This paper provides an overview of the development of such a simulation facility at the U.S. Army Missile Command for supporting hardware-in-the-loop simulations of dual-mode systems. The major technological challenges which limit common-aperture dual-mode simulator development are presented with the current approaches which are being taken to overcome these challenges.

Convergence of Electromagnetic Field Components across Discontinuous Permittivity Profiles

We provide further insight into why the inverse rule [J. Opt. Soc. Am. A 13, 1870 (1996)] for multiplying two finite Fourier series of two pairwise discontinuous functions yields correct results at the point of discontinuity.

Time domain state variable analysis of induced reflection gratings in photorefractive materials

We apply the multilayer rigorous coupled wave theory to analyze reflection gratings in a photorefractive material of an arbitrary thickness. In particular, we study the effect of varying the overall material length over a few thousand grating wavelengths, and also study the effect of layer detuning on reflection grating formation. Furthermore, convergence of the numerical method is rigorously analyzed.

Determination of the mutual coherence function and determination of the point-spread function in a transversely and longitudinally inhomogeneous aero-optic turbulence layer

The mutual coherence function (MCF) of strong-fluctuation theory as a result of optical energy passing through a transversely and longitudinally inhomogeneous aero-optic turbulent layer is studied. Solutions for the MCF equation are determined by decomposing the MCF solution into coherent and incoherent parts and by solving separately the equations that result from this decomposition. The MCF equations for an arbitrary three-dimensional inhomogeneous layer are presented. A simplified version of these equations for the case in which the turbulence inhomogeneity is longitudinally inhomogeneous and is transversely inhomogeneous in one dimension is also presented. A numerical method for solving the parabolic MCF equations by the Lax-Wendroff explicit finite-difference algorithm is given, and numerical examples of the MCF solution for three different inhomogeneous aero-optic layers are discussed. Equations to relate the point-spread function, the optical transfer function, and image formation to the MCF of an inhomogeneous aero-optic turbulence layer are derived. An approximate MCF Fourier integral solution is presented and compared with the exact finite-difference solution. A formula to estimate the validity of the approximate integral solution is given.

Propagation of the mutual coherence function in inhomogeneous turbulent media

An inhomogeneous turbulent medium is characterized by a refractive index spectrum that varies from point to point. The mutual coherence function (MCF) is used to analyze the distortion that electromagnetic waves suffer when they propagate through such a medium. In this paper, we analyze the MCF in two dimensions for an incoherent line source. We show that the MCF consists of delta and non-delta components and derive the differential equations that each component must satisfy. Finally, we present results obtained by a numerical solution of these differential equations.