Chen-Wen Tarn

Spatial Fourier transform approach to the study of polarization changing and beam profile deformation of light during Bragg acousto-optic interaction with longitudinal and shear ultrasonic waves in isotropic media

A spatial Fourier transform approach is proposed to investigate the polarization changing and the beam profile deformation of light during the acousto-optic (AO) interaction in isotropic media. Two basic types of sound waves are considered, namely, longitudinal and shear waves interacting with the light in an AO bulk cell. The perturbation of the permittivity is then caused by these kinds of acoustic waves and can be expressed in tensor forms. The evolution of two different orders of scattered light under the Bragg condition can be properly described by a couple of solutions that are derived from the wave equation by using a spatial Fourier transform approach. The solutions explicitly comprise the effects of polarization changing, beam deformation, and propagational diffraction. It is shown that the spatial beam profiles of the scattered light are distorted during the process because of the effects of the AO interaction and the propagational diffraction. For both cases of longitudinal and shear sound waves, the degree of the profile deformation can be controlled by changing the amplitude and the frequency of the sound. It is also shown that the polarization states of the scattered light are different from those of the input light on account of the AO effect. The degree of difference of the polarization states, which depend on the propagation type, frequency, and amplitude of the sound wave, can be examined through the use of two polarization parameters, the ellipticity and the orientation of the major axis of the scattered light. Detailed numerical simulations, including Fourier-transforming the incident light profile to calculate the spectra and the on-axis values of ellipticity and orientation of the scattered light in space with use of the inverse Fourier transform, are presented.

Two-Dimensional Strong, Acousto-Optic Interaction between Arbitrary Light and Sound Profiles: A Fourier Transform Approach

Abstract A spatial Fourier transform approach is employed to investigate the acoustooptic interaction with cw, profiled sound and an incident light beam. Two coupled differential equations which describe the near Bragg interaction are derived in the spatial frequency domain. Since there is no analytic solution for these coupled equations, a well-known numerical technique, viz., the Range-Kutta method is used to solve the equations. Detailed numerical simulation, involving Fourier transforming the input light beam profile to calculate the spectra of the scattered light beams and, hence, their profiles in space using the inverse transform, are presented.

Spatial coherence property of a laser beam during acousto-optic diffraction

The spatial coherence property of a partially coherent light during the Bragg acousto-optic interaction is investigated. Starting from the wave equation, four coupled, parabolic equations that can describe the evolution and the propagation of mutual intensity functions of the diffracted light during the acousto-optic interaction are derived. A partially coherent light beam with arbitrary spatial profile and complex degree of spatial coherence is assumed to be incident on the Bragg acousto-optic cell. With the use of a statistical theory of linear systems, a general formalism of angular-correlation functions for zero-order and minus-one-order light can be derived. The corresponding mutual intensity and complex coherence factor functions are hence implemented numerically. From the solutions one can note that, through the acousto-optic interaction, the degrees of spatial coherence of the diffracted light beams are controllable by the intensity and the frequency of the sound wave.

Polarization changing and beam profile deformation of light during the isotropic Raman-nath acousto-optic interaction.

A spatial Fourier transform approach is used to study the phenomena of polarization changing and beam profile deformation of light during the Raman-Nath, acousto-optic interaction in isotropic media. Starting from the vector version of the well-known Raman-Nath interaction equation and using a spatial Fourier transform allows analytic solutions that encompass the effects of polarization changing and beam-profile deformation for the multiple scattered light to be found in the spatial-frequency domain. Two kinds of sound wave, longitudinal and shear, are assumed to be interacted with the light, whose transverse spatial profile and state of polarization are arbitrary. It is shown that, for light with an arbitrary spatial profile after interaction with the sound wave in the Raman-Nath regime, the spatial profiles of the scattered light are almost the same shape as those of the input light. For the polarization changing part, it is found that the state of polarization and the direction of rotation can alter, depending not only on the sound amplitude but also on the propagation mode of the sound wave. Simulation results are provided to confirm the validity of this approach.

Gaussian-beam profile deformation via anisotropic photorefractive gratings formed by diffusive, photovoltaic, and drift mechanisms: a system transfer function approach

Light-beam profile deformation during scattering with the pho- torefractive grating formed by the diffusive, photovoltaic, and drift mechanisms is investigated in the case of anisotropic Bragg diffraction for the incident light with arbitrary spatial beam profile under the frame- work of a three-dimensional configuration. A set of three-dimensional coupled-wave equations that can properly describe the interaction is de- rived from Maxwells equations. In the wave equations, the permittivity profile, which is perturbed by the diffusive, photovoltaic, and drift mecha- nisms, can be correctly plotted by employing Kukhtarevs material model. Using a spatial Fourier transform technique identical to the one used in deriving the spatial transfer function from the paraxial wave equation for free-space propagation, a steady-state solution for the out- put light beams diffracted by this initially stored grating can be calculated in the spatial frequency domain. The nature of the dependence of beam profiles on the material properties, sample thickness, and incident angle, under the combined effects of propagational diffraction, diffusion, photo- voltaicity, and drifting, is presented.

General formalism for Bragg acousto-optic interaction beyond the paraxial approximation

Most of the conventional studies of acousto-optics (AO) are under the paraxial approximation; that is, the propagation directions of the scattered light are almost along the optic axis of the AO system, or, equivalently, the envelope of the light wave varies slowly with respect to the direction of propagation. This assumption should not, however, be carried too far in the cases in which the incident or the Bragg angles are large enough that the scattered light waves do not propagate closely along the optic axis of the AO system. We study the Bragg AO effect beyond the paraxial assumption for small- and large-Bragg-angle incidence. Starting from the wave equations, which are derived from Maxwells equations, a set of coupled equations that depict the AO interaction are derived in the Bragg regime without the paraxial assumption; i.e., the second derivative terms of the scattered-light amplitudes with respect to the propagation direction are nonnegligible. Analytic solutions that describe the evolution of the scattered light that is due to the acousto-optic effect beyond the paraxial approximation can then be found from the coupled equations. Simulation results are provided to check the validity of our solutions.

Laser beam profile deformation effect during Bragg acousto-optic interaction: a non-paraxial approximation

Doungchin CaoUniversity of Alabama in HuntsvilleDepartment of Electrical andComputer EngineeringHuntsville, Alabama 35899Abstract. It is commonly known that the spatial profiles of the diffractedlight beams during Bragg acousto-optic interaction are distorted due tothe Bragg angle selection mechanism. All the conventional studies onthis effect use the paraxial approximation. But this approximation shouldbe amended when the incident angle of the light is large enough that thediffracted light waves do not propagate closely along the optic axis of theacousto-optic diffraction system. By using a spatial Fourier transformapproach, we rigorously study the light beam profile deformation effect ofthe diffracted light during the Bragg acousto-optic interaction beyond theparaxial approximation. Starting from the wave equation, a set ofcoupled-wave equations is derived to depict the acousto-optic effect.Analytic solutions that describe the profiles of the diffracted light arederived from the acousto-optic coupled-wave equations. From the solu-tions, differences can be found between the ones with and withoutparaxial approximation.

Real-time polarization mode dispersion monitoring system for a multiple-erbium-doped fiber amplifier, dense wavelength division multiplexing optical fiber transmission by amplified spontaneous emission modulation and acousto-optic tunable fiber scanning techniques.

Without interruption or affecting the transmission of ordinary payload channels, we propose a real time polarization mode dispersion (PMD) monitoring system for long-haul, multiple erbium-doped fiber amplifier (EDFA), dense wavelength division multiplexing (DWDM) optical fiber transmission using modulated amplified spontaneous emission (ASE) of one of the EDFAs as the supervisory (SV) signal source. An acousto-optic tunable filter (AOTF) at the receiver side is adopted to scan the spectrum of the transmitted ASE SV signal. Using the fixed-analyzer method, PMDs of different wavelength bands that range from 1545 to 1580 nm of a DWDM fiber-optic communication system can be found by adaptively changing the radio frequency of the AOTF. The resolution and the measuring range of the proposed monitoring system can be significantly improved by cascading the AOTFs at the receiver side.

Theoretical and experimental studies of polarization mode dispersion of an electro-optic Mach-Zehnder modulator

A theoretical model is developed to study the polarization mode dispersion effect in an electro-optic Mach-Zehnder interferometric (MZI) modulator. The Stokes parameters and differential group delay (DGD) of the output light of a MZI modulator can be analytically derived with the proposed model, which is based on a three-dimensional Maxwells wave equation approach. The theoretical model is validated to the extent possible by comparing the theoretical results of the Stokes parameters and DGD with experimental measurements that are based on the wavelength-scanning method and the Jones matrix eigenanalysis method.

Theoretical and experimental analysis of the near-Bragg acousto-optic effect

A spatial Fourier transform approach is employed to investi- gate the acousto-optic interaction in the near-Bragg regime with cw pla- nar sound and a light beam of arbitrary spatial profile. Four coupled differential equations that can exactly describe the near-Bragg acousto- optic interaction are derived from Maxwells equations. A spatial Fourier transform approach is applied to the coupled-wave equations to express the interaction in the spatial frequency domain. The spatial Fourier trans- form approach used here is identical to the technique for solving the paraxial wave equation to derive the transfer function of propagation and hence the Fresnel diffraction formula during free-space propagation of a light beam in the presence of diffraction. Since there are no analytic solutions for these coupled equations, a well-known numerical method, viz., the Runge-Kutta-Fehlberg, is used to solve the equations. Detailed numerical simulation is performed, which involves spatially Fourier- transforming the input light beam profile to calculate the spectra of the diffracted light beam and hence their profiles in the space, using the inverse transform. Experimental results are also presented to check the validity of our approach.