Monish Ranjan Chatterjee

Demonstration of Acousto-optic Bistability and Chaos by Direct Nonlinear Circuit Modeling

A novel technique involving nonlinear dependent sources expressed as convergent power series expansions of one or more variables representing the output fields of a Bragg-domain hybrid acousto-optic device with feedback is presented. Using some straightforward modifications of a basic circuit prototype, we show how optical bistability, possible multistability, and chaos may be generated for three fundamental types of tuning effects, i.e., feedback gain, bias voltage, and input amplitude. The results obtained are shown to compare favorably with the existing theory and experiments.

A numerical analysis and expository interpretation of the diffraction of light by ultrasonic waves in the Bragg and Raman-Nath regimes using multiple scattering theory

In this paper, we examine some of the fundamental properties of Bragg and Raman-Nath diffraction of light by ultrasonic waves by revisiting the well-known multiple plane wave scattering theory developed by Korpel and Poon in 1980. The purpose is to provide a clear and unambiguous insight into the variety of physical and geometrical configurations associated with the process of optical diffraction from Bragg and Raman-Nath ultrasonic cells, treating each domain separately. Despite well-established theoretical models, there is a tendency to sometimes erroneously associate general Bragg domain diffraction (as opposed to exact Bragg diffraction where the incident angle is Bragg-matched and the interaction width is infinite) with only two diffracted orders that vary sinusoidally with peak phase shift of the light and distance of propagation. In numerical analyses of the coupled equations, there is also a tendency to sometimes limit the number of orders to a few lower ones. With the enthusiasm to arrive at a solution, this truncation is sometimes applied in the Raman-Nath regime as well. In doing so, higher Raman-Nath-scattered orders are implicitly assumed to be progressively weaker and, therefore, negligible. In complex acoustooptic systems, such approximations can lead to serious errors. With an aim toward rectifying these and other common misconceptions, a thorough numerical analysis of uniform plane wave acoustooptic diffraction in the two well-known regimes is presented and the limits of such analysis are examined.

Dual-input hybrid acousto-optic set-reset flip-flop and its nonlinear dynamics

The characteristics of a dual-input hybrid acousto-optic device are investigated numerically and experimentally. The device, which operates as a set-reset flip-flop, uses the well-known bistable acousto-optic device with feedback to which two input beams are applied. The resulting flip-flop is analyzed numerically by use of nonlinear dynamical and nonlinear circuit-modeling techniques, and some of its properties are demonstrated experimentally.

Implementation of a spatially multiplexed pixelated three-dimensional display by use of a holographic optical element array

A pixelated holographic stereogram is proposed and experimentally studied for the emulation of a spatially multiplexed composite three-dimensional (3-D) pixel display. With this approach, pixelated holograms are utilized to compose spatially multiplexed images. Each composite pixel in the holographic optical element array has a diffraction pattern that scatters light into predefined spatial directions. Under reconstruction, each pixel generates different intensities along a range of viewing angles. When the composite holographic pixel array is assembled, it has the capability to deliver 3-D effects. The technique, together with a novel recording scheme that is designed to synthesize a computerized 3-D display system based on this concept, is described in some detail.

Examination of beam propagation in misaligned holographic gratings and comparison with the acousto-optic transfer function model for profiled beams

A transfer function formalism developed earlier for the propagation of profiled optical beams through acousto-optic Bragg cells is revisited and applied to a thick holographic grating. The results based on the holographic coupled wave model and the acousto-optic multiple scattering model are shown to be compatible, and equivalent parameters such as the Q and grating strength are defined for the two systems. Results for a Gaussian spatial profile are numerically computed and compared. For the holographic grating, a profiled beam may be interpreted as an angular misalignment or Bragg-angle mismatch problem. The case of Bragg-wavelength mismatch is also investigated for the case of a polychromatic READ beam with a uniform and a Gaussian amplitude spectrum. The resulting spatial amplitude distribution of the scattered order at the grating output is plotted as a function of the departure from the correct Bragg direction.

Feedback correction of angular error in grating READOUT

Angular and wavelength READ beam errors in holographic interconnection systems are often a recurrent problem. Several strategies have been proposed to minimize or eliminate such READOUT misalignments. Some years ago, Chatterjee and co-workers proposed a method involving READ beam wavelength tuning to correct output angular errors. In this paper, we investigate the possibility of using an acousto-optic (A-O) Bragg cell with optoelectronic feedback to dynamically correct the scattered beam for deviations in the incidence direction of the READ beam of a hologram. The concept here is based on an acoustic frequency feedback strategy used recently by Balakshy and Kazaryan for laser beam directional stabilization. In the dynamic and adaptive method being proposed here, an acousto-optic Bragg cell is placed between the READ beam and the hologram. A photo-detector placed after the Bragg cell enables the estimation of scattered efficiency and hence (from the READ dephasing-based diffraction efficiency), the amount of the angular deviation. An algorithm for implementing the above scheme, to be used in a practical setup, is proposed and the results of numerical simulations are presented along with possible extensions to wavelength error correction and other applications.

Spectral approach to optical propagation across a linear–nonlinear interface

Propagation of optical signals across a linear–nonlinear interface is investigated by using a spectral decomposition technique involving discrete sideband frequencies. The complexity of the analysis is shown to be appreciably reduced by assuming incommensurate discrete sidebands around the carrier. The efficacy of this formalism is tested for various cases, including discrete stationary modes, evolution of discrete sidebands assuming an undepleted carrier, and, finally, AM pulse propagation across the interface. Among several interesting results, the formation of a narrow-band FM pulse, spatially separated from the ubiquitous AM pulse, is demonstrated. The latter result may be interpreted as a test of the stability of the uniform plane-wave solution.

Nonlinear dynamics of a Bragg cell under intensity feedback in the near-Bragg, four-order regime

A detailed examination of the nonlinear dynamical behavior of an acousto-optic Bragg cell in the near-Bragg regime of operation for the case of four scattered orders under intensity feedback is carried out. This problem is an extension of the standard ideal-Bragg feedback model whereby traditionally bistability, hysteresis, and chaotic oscillations are observed under zeroth- or first-order feedback of the scattered light. For the present case, the closed-loop equations are developed from a priori knowledge of the open-loop analytical solutions for four-order near-Bragg scattering. The results, obtained via computer simulation, reveal a variety of interesting dynamics, including bistability, bifurcation, hysteresis, chaotic oscillations (including in this case the relatively uncommon period-three behavior, in addition to the more usual period-doubling phenomenon en route to chaos), and potentially useful parametric dependence of these features. The observed results are interpreted in terms of system behavior for varying feedback gain and bias, the so-called Klein-Cook parameter Q, and time delay, and are compared with earlier work based on the ideal Bragg regime.

Overview of Acousto-optic Bistability, Chaos, and Logical Applications

An overview is presented of the key results in the field of acousto-optic bistability in the past two decades. It is shown that the basic acousto-optic bistable device may be described as a nonlinear dynamical system which satisfies a quadratic map. Thereafter, details are presented of several analytical methods, computer modeling approaches, including the SPICE circuit modeling technique, and experiments that have been used to understand the phenomenon. Extensions to logical and digital applications are also discussed.

Derivation of impulse response and transfer function of an optical fiber under chromatic dispersion and application to a linear fiber-optic communication system

Treating the frequency-dependent time delay caused by the presence of chromatic dispersion in a fiber-optical channel of length L as a random variable, it is possible to obtain a simple expression for the impulse response of the channel. This idea is used to derive the impulse response in terms of parameters such as the zero-dispersion wavelength, the second derivative of the refractive index, and the linewidth of the source. The result indicates an asymmetrical impulse response, and the corresponding transfer function has a low-pass characteristic with a first-order pole which may be readily determined from the fiber parameters. The derived impulse response is applied to the case of a simple fiber-optic communication system configured as a phase diversity receiver, to illustrate how a linear systems approach, under certain approximations, may be used to predict and analyze the behavior of such a system. The analysis includes calculations involving the field amplitudes in (n*n) hybrid couplers, and how such couplers must be connected in order to obtain the desired optical components in the phase diversity scheme is described.<<ETX>>