Computer Engineering Commons^™

Examination Of Focused Beam Propagation Through A Finite Non-Reciprocal Planar Chiral Slab Using Complex Fresnel Coefficients And Dual Transforms, Monish Ranjan Chatterjee, Sumit Nema, Partha P. Banerjee

Monish R. Chatterjee

Recently, uniform plane wave propagation across a nonchiral-chiral interface was examined via the development of appropriate Fresnel coefficients. In this extension, propagation of focused uniform and profiled beams through a finite, planar nonreciprocal chiral slab is investigated using complex Fresnel coefficients via angular plane wave decomposition and dual transforms.

Experimental Investigations Of Wavelength And Angular Errors In Holographic Gratings With Non-Bragg-Matched Read Beams, Monish Ranjan Chatterjee, Vivek Ray

Monish R. Chatterjee

Perfect Bragg matching is generally desirable for accurate optical interconnections with holographic gratings. In reality, however, gratings may be illuminated by READ beams with non-Bragg-matched angles, or wavelengths, or both. In such cases, the scattered beams are generally misdirected, and may suffer loss of efficiency and possibly more serious errors such as crosstalk noise or missed connections. A conventional wave-vector triad method of analyzing the scattered beam errors leads readily to near-Bragg estimates of the output angular misalignment. However, the READ wave-vector triads appear to indicate a possible wavelength shift in the output beam even with a Bragg-matched READ wavelength, …

Examination Of Beam Propagation In Misaligned Holographic Gratings And Comparison With The Acousto-Optic Transfer Function Model For Profiled Beams, Monish Ranjan Chatterjee, David D. Reagan

Monish R. Chatterjee

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 …

Consideration Of Dispersion And Group Velocity Dispersion In The Determination Of Velocities Of Electromagnetic Propagation, Monish Ranjan Chatterjee, Partha P. Banerjee

Monish R. Chatterjee

Electromagnetic (EM) propagation velocities play an important role in the determination of power and energy flow in materials and interfaces. It is well known that group and phase velocities need to be in opposition in order to achieve negative refractive index. Recently, we have shown that considerable differences may exist in phase, group and signal/energy velocities for normal and anomalous dispersion, especially near dielectric resonances. This paper examines the phase and group velocities in the presence of normal and anomalous dispersion, and group velocity dispersion (GVD), which requires introduction of the second order coefficient in the permittivity and permeability models.

A Critical Study Of Nonlinear Echo Phenomena, Monish Ranjan Chatterjee

Monish R. Chatterjee

The present thesis attempts to give a concise and critical account of the evolution of the echo phenomena over the last thirty years. Starting with spin and photon echoes, which were among the earliest to be observed and studied, the thesis explores the experimental findings and the models proposed in connection with the more contemporary echo experiments, viz. those involving electroacoustic or polarization echoes in single and polycrystalline piezoelectric materials and in powders. Although the investigations regarding the various mechanisms of short and long term echo formation are by no means complete, a coherent picture is beginning to emerge as …

A Transfer Function Based Frequency Model For Propagation Of A Chaos Wave Through Modified Von Karman Turbulence Under Various Chaos And Turbulence Conditions, Monish Ranjan Chatterjee, Fathi H.A. Mohamed

Monish R. Chatterjee

Complex phasor fields for electromagnetic wave propagation through von Karman turbulence and acousto-optic RF chaos are derived en route to the effective transfer function between chaos and narrow turbulence. Results are tested for several turbulence and chaos conditions.

Chaotic Bandgaps In Hybrid Acousto-Optic Feedback And Their Implications, Monish Ranjan Chatterjee, Mohammed A. Al-Saedi

Monish R. Chatterjee

The nonlinear dynamics of a hybrid acousto-optic device was examined from the perspective of the Lyapunov exponent (LE) and bifurcation maps. The plots for LE versus system parameters and bifurcation maps have recently been examined against known simulation results including chaotic encryption experiments [1]. It is verified that the "loop gain" (feedback gain (β) times incident light amplitude (Iin) needs to be greater than one as a necessary , but not sufficient condition for the onset of chaos. It is found that for certain combinations of β, Iin, net bias voltage (αtοt), and the initial value of the first-order scattered …

Examination Of Energy And Group Velocities In Positive And Negative Index Chiral Materials With And Without Dispersion, Monish Ranjan Chatterjee, Partha P. Banerjee

Partha Banerjee

Concepts of energy and group velocities, Poynting and propagation vectors are examined for both positive and negative index materials. Known definitions for these entities are explored in terms of the interplay of chirality and dispersion.

Examination Of Focused Beam Propagation Through A Finite Non-Reciprocal Planar Chiral Slab Using Complex Fresnel Coefficients And Dual Transforms, Monish Ranjan Chatterjee, Sumit Nema, Partha P. Banerjee

Partha Banerjee

Recently, uniform plane wave propagation across a nonchiral-chiral interface was examined via the development of appropriate Fresnel coefficients. In this extension, propagation of focused uniform and profiled beams through a finite, planar nonreciprocal chiral slab is investigated using complex Fresnel coefficients via angular plane wave decomposition and dual transforms.

Consideration Of Dispersion And Group Velocity Dispersion In The Determination Of Velocities Of Electromagnetic Propagation, Monish Ranjan Chatterjee, Partha P. Banerjee

Partha Banerjee

Electromagnetic (EM) propagation velocities play an important role in the determination of power and energy flow in materials and interfaces. It is well known that group and phase velocities need to be in opposition in order to achieve negative refractive index. Recently, we have shown that considerable differences may exist in phase, group and signal/energy velocities for normal and anomalous dispersion, especially near dielectric resonances. This paper examines the phase and group velocities in the presence of normal and anomalous dispersion, and group velocity dispersion (GVD), which requires introduction of the second order coefficient in the permittivity and permeability models.

Investigation Of Negative Refractive Index In Reciprocal Chiral Materials, Monish Ranjan Chatterjee, Partha P. Banerjee, Pradeep R. Anugula

Partha Banerjee

It is well known that there exist both natural materials (such as milk or sugar solution) possessing chiral (or handed) properties, as well as an increasing list of man-made materials (such as sodium bromate) that exhibit chirality. One of the principal properties of chirality is that light of any arbitrary polarization, when propagating through a chiral material, splits up into two circular polarizations propagating in different directions. In the past decade or longer, researchers have investigated electromagnetic transverse (plane) wave propagation across a non-chiral/chiral interface, and determined the electromagnetic Fresnel coefficients for such propagation. Traditionally, such coefficients are derived under …

Analysis Of Beam Propagation In 90-Degree Holographic Recording And Readout Using Transfer Functions And Numerical 2-D-Laplace Inversion, Monish Ranjan Chatterjee, Partha P. Banerjee, George Nehmetallah

Partha Banerjee

Recently, 2-D-Laplace analysis of recording and readout of edge-holograms was reported. Numerical Laplace inversion was examined for simple test cases. Inversion algorithms are applied to examine beam shaping and distortion in photovoltaic and photorefractive materials.

Volume Holographic Recording And Readout For 90-Deg Geometry, Partha P. Banerjee, Monish Ranjan Chatterjee, Nickolai Kukhtarev, Tatiana Kukhtareva

Monish R. Chatterjee

When a prerecorded cross-beam hologram is reconstructed (so-called edge-lit readout) with a uniform plane wave and a point source, the resulting exact solutions reveal Bessel-function-type diffracted beam profiles, which are fundamentally modified under weak propagational diffraction. The case of a profiled beam readout with propagational diffraction may be analyzed using a transfer function approach based on 2-D Laplace transforms. In a second series of investigations, dynamic readout from a cross-beam volume hologram recorded with two orthogonal uniform plane waves is considered for various dependences of the refractive index modulation with intensity. Typically, refractive index profiles that are proportional to the …

Self‐Refraction Of Nonlinear Capillary‐Gravity Waves, Partha P. Banerjee, Adrianus Korpel, Karl E. Lonngren

Partha Banerjee

Self‐refraction effects have been observed during the propagation of deep‐water capillary‐gravity waves. The observations are shown to be in qualitative agreement with the theory of self‐focusing and defocusing in a cubically nonlinear medium in the presence of diffraction.

Self-Enhancement Of Dynamic Gratings In Photogalvanic Crystals, Nickolai Kukhtarev, Sergei F. Lyuksyutov, Preben Buchhave, Tatiana Kukhtareva, K. Sayano, Partha P. Banerjee

Partha Banerjee

We have developed a compact closed-form solution of the band transport model for high-contrast gratings in photogalvanic crystals. Our solution predicts the effect of the photoconductivity and the electric field grating enhancement due to the photogalvanic effect. We predict a pronounced dependence of the steady-state photogalvanic current on the contrast of the interference pattern and an increase of holographic storage time due to the enhancement of the photoconductivity grating contrast. In the high contrast limit and a large photogalvanic effect the refractive index grating will be shifted from the position of the intensity modulation pattern, contrary to the usually adopted …

Single-Beam Holographic Tomography Creates Images In Three Dimensions, George Nehmetallah, Partha P. Banerjee, Nickolai Kukhtarev

Partha Banerjee

In digital holography (DH), the interference between light scattered from an object and a reference wave is recorded using a CCD camera. DH has various advantages over analog holography: no film processing is needed, reconstruction is performed using numerical methods, and no further experimental setup is necessary. However, one of the disadvantages of DH is that current CCDs have a resolution of approximately 1,000 lines/mm, which is less than that of photographic film.

Subharmonic Generation By Resonant Three‐Wave Interaction Of Deep‐Water Capillary Waves, Partha P. Banerjee, Adrianus Korpel

Partha Banerjee

Subharmonic generation has been observed during the propagation of deep‐water capillary waves. The observations are shown to be in agreement with the theory of degenerate resonant noncollinear three‐wave interaction in a nonlinear, dispersive medium.

Time Dynamics Of Self-Pumped Reflection Gratings In A Photorefractive Polymer, Partha P. Banerjee, S. H. Buller, C. M. Liebig, S. A. Basun, Gary Cook, Dean R. Evans, Pierre-Alexandre Blanche, J. Thomas, Cory W. Christenson, N. Peyghambarian

Partha Banerjee

The time dynamics of self-pumped reflection gratings in a commonly used photorefractive polymer PDCST:PVK:ECZ-BBP:C60 with no additional electron sources or traps is investigated. While holes are normally the mobile charges and responsible for grating formation, our experimental observations, analyzed using multi-exponential fitting curves, show evidence of electrons in addition to holes as charge carriers, particularly above an applied field of 40 V/μm. The dependence of effective carrier mobilities on the applied electric field, deduced from experimental results, show stronger field dependence of electron mobility at high electric fields. At an applied field of 70 V/μm, electron and hole mobilities become …

Volume Holographic Recording And Readout For 90-Deg Geometry, Partha P. Banerjee, Monish Ranjan Chatterjee, Nickolai Kukhtarev, Tatiana Kukhtareva

Partha Banerjee

When a prerecorded cross-beam hologram is reconstructed (so-called edge-lit readout) with a uniform plane wave and a point source, the resulting exact solutions reveal Bessel-function-type diffracted beam profiles, which are fundamentally modified under weak propagational diffraction. The case of a profiled beam readout with propagational diffraction may be analyzed using a transfer function approach based on 2-D Laplace transforms. In a second series of investigations, dynamic readout from a cross-beam volume hologram recorded with two orthogonal uniform plane waves is considered for various dependences of the refractive index modulation with intensity. Typically, refractive index profiles that are proportional to the …

Rotation-Invariant Synthetic Discriminant Function Filter For Pattern Recognition, Vahid R. Riasati, Partha P. Banerjee, Mustafa A. G. Abushagur, Kenneth B. Howell

Partha Banerjee

The ring synthetic discriminant function (RSDF) filter for rotation-invariant response is discussed for pattern recognition. This method uses one half of a slice of the Fourier transform of the object to generate the transfer function of the filter. This is accomplished by rotating the one half of a slice in the Fourier domain through 2π rad about the zero-frequency point of the Fourier plane. This filter has the advantage of always matching at least one half of a slice of the Fourier transform of any rotation of the image. An analytical discussion of the filter construction and correlation results are …

Laser Beam Profile Deformation Effect During Bragg Acousto-Optic Interaction: A Non-Paraxial Approximation, Ray S. Huang, Chen-Wen Tarn, Partha P. Banerjee, Doungchin Cao

Partha Banerjee

It is commonly known that the spatial profiles of the diffracted light beams during Bragg acousto-optic interaction are distorted due to the Bragg angle selection mechanism. All the conventional studies on this effect use the paraxial approximation. But this approximation should be amended when the incident angle of the light is large enough that the diffracted light waves do not propagate closely along the optic axis of the acousto-optic diffraction system. By using a spatial Fourier transform approach, we rigorously study the light beam profile deformation effect of the diffracted light during the Bragg acousto-optic interaction beyond the paraxial approximation. …

Modeling And Characterization Of Adaptive Lanthanum-Modified Lead Zirconate Titanate (Plzt) Microlenses, Yasser A. Abdelaziez, Partha P. Banerjee

Partha Banerjee

We report the modeling and characterization of adaptive voltage controlled electro-optic microlenses. First, we utilize finite element analysis (FEA) to simulate the induced electro-optic effect in lanthanum-modified lead zirconate titanate (PLZT). FEA simulation provides microlens parameters such as phase and focal length. A simple z-scan method is developed to fully characterize the adaptive voltage controlled linear lens. Experimental z-scan results are shown to match the theoretical predictions from FEA.

Interaction Of Profiled Light With Contrapropagating Acoustic Waves: Fourier Transform Approach, Partha P. Banerjee, Chen-Wen Tarn, Jaw-Jueh Liu

Partha Banerjee

A straightforward Fourier-transform approach is employed to investigate acousto-optic interaction between an input optical beam with arbitrary profile and contrapropagating cw sound in the Bragg regime. The process can be analyzed in terms of the simultaneous scattering of light by the two sound waves in the interaction region. Analytic expressions for the equivalent transfer functions are obtained and the scattered light profiles are plotted.

Broadband Dynamic, Holographically Self-Recorded, And Static Hexagonal Scattering Patterns In Photorefractive Knbo3:Fe, Nickolai Kukhtarev, Tatiana V. Kukhtareva, John Caulfield, Partha P. Banerjee, Hsueh-Ling Yu, Lambertus Hesselink

Partha Banerjee

We have observed and explained three types of hexagon pattern formation in photo refractive crystal KNb03:Fe. These are:

• Dynamic (laser induced)
• Semipermanent (holographically stored)
• Permanent (induced by a static domain grid) over a wide wavelength range

Analysis Of Multifrequency Dispersive Optical Bistability And Switching In Nonlinear Ring Cavities With Large Medium-Response Times, Pawel Pliszka, Partha P. Banerjee

Partha Banerjee

Using a simple model of a ring cavity comprising a cubically nonlinear medium, we analyze dispersive optical bistability in the presence of more than one spectral component. We show the phenomenon of so-called competition for resonance. In addition to presenting cavity characteristics for the cases of two and three different frequencies, we also discuss the general method for finding steady-state solutions and checking their stability. A simple and efficient algorithm, based on a relaxation method, is devised to find steady-state solutions satisfying appropriate boundary conditions. The relaxation dynamics is physically related to a finite response time of the medium.

Study Of Soliton Stabilization In D+1 Dimensions Using Novel Analytical And Numerical Techniques, George Nehmetallah, Partha P. Banerjee

Partha Banerjee

In this Chapter, we provide a brief review of the underlying nonlinear Schrödinger and associated equations that model spatio-temporal propagation in one and higher dimensions in a nonlinear dispersive environment. Particular attention is given to fast adaptive numerical techniques to solve such equations, and in the presence of dispersion and nonlinearity management, saturating nonlinearity and nonparaxiality. A unique variational approach is also outlined which helps in determining the ranges of nonlinearity and dispersion parameters to ensure stable solutions of the nonlinear equations. The propagation of 3+1 dimensional spatio-temporal pulses, or optical bullets is also modeled using a fast adaptive split-step …

Signal Flow Analysis, Partha P. Banerjee

Partha Banerjee

Signal flow graphs are a viable alternative to block diagrammatic representation of a system. What makes signal flow graphs attractive is that certain features from graph theory can be applied to the simplification and the synthesis of complex systems.

Scalar Em Beam Propagation In Inhomogeneous Media, John M. Jarem, Partha P. Banerjee

Partha Banerjee

In the previous chapter, we reviewed some of the mathematical preliminaries that will be useful later on in the text. In this chapter, we discuss some of the basic concepts of scalar wave propagation, and discuss an important numerical method, called the beam propagation method (BPM), to study propagation in linear media and in media with induced nonlinearities. Furthermore, we also discuss propagation through induced gratings, both transmission and reflection type, in order to assess energy coupling between participating waves. Finally, we introduce readers to an important characterization method, called the z-scan method, which is often used to determine the …

Guest Editorial: Special Section On Photorefractive Nonlinear Optics, Partha P. Banerjee

Partha Banerjee

Hand in hand with experimental work in photorefractives, there is a lot of activity in modeling photorefractive materials and experimental observations in the open literature. This special section contains a paper by Banerjee and Jarem, who use a rigorous coupled wave theory to analyze two- and multiple-wave mixing photorefractive barium titanate, modeled through the Kukhtarev equations.

Guest Editorial: Special Section On Acousto-Optic Devices And Optical Information Processing: Research And Developments, Partha P. Banerjee, Ting-Chung Poon

Partha Banerjee

This guest editorial provides an overview of the topical area and an introduction to the articles featured in the special section.