KEYWORDS: Image resolution, 3D image processing, Integral imaging, Frequency division multiplexing, Quantization, 3D displays, Numerical analysis, Imaging systems, 3D image reconstruction, Spatial frequencies
Integral imaging could be considered as one of the prospective methods for recording and displaying 3D images
based on its distinct features. Some of the most important challenges with this approach are the field of view
and resolution limitation. In this work we investigate using frequency division multiple access (FDMA) idea for
solving this problem. Simulation results show an increase of more than ten percent in the performance of the
3D reconstructed images using the proposed method.
Effect of relaxation time on the performance of photonic crystal optical bistable switches based on Kerr nolinearity is
discussed. This paper deals with optical pulses with the duration of about 50 ps. In such cases the steady state response
of the optical device can be used to approximate the pulse evolution if the nonlinearity is assumed instantaneous, hence
analytical solutions such as the coupled mode theory can be used to obtain the time evolution of the electromagnetic
fields. However if the relaxation time of the material nonlinear response is also considered, changes in the power levels
and in the shape of the hystersis loop is observed. In this case, we use the nonlinear finite difference time domain method
(NL-FDTD) to follow the system dynamics and get the bistability hystersis loop. Codes are developed to analyze the
instantaneous Kerr materials and the Kerr materials with finite response times. Depending on the material, the relaxation
times of the order of 1-10fs should be considered in studying bistability to obtain the right shape of the output pulses. It
is observed that the relaxation leads to larger input power and threshold and hence degrades the performance of the
switch in pulse shaping.
KEYWORDS: Spatial frequencies, Image filtering, Principal component analysis, Modulation transfer functions, Amplitude modulation, Imaging systems, Signal to noise ratio, Phase modulation, 3D image processing, Modulation
In this paper we present a novel approach to generate images of extended depth of field (DOF) without compromising
the lateral resolution to support realization of three-dimensional imaging systems such as integral imaging.
In our approach in extending DOF, we take advantage of the spatial frequency spectrum of the object specific to
the task in hand. The pupil function is thus engineered in such a fashion that the modulation transfer function
(MTF) is maximized only in these selected spatial frequencies. We extract these high energy spatial frequencies
using PCA method. The advantage of our approach is illustrated using an amplitude modulation and a phase
modulation example. In these examples, we split the pupil filter and choose the optimum transmission/phase
value of each section in the filter in a way that the response of the system in all the DOF range as well as
spatial frequencies of interest is optimized. Consequently, we have optimized the DOF extension process with
blocking the minimum possible area in the pupil plane. This maximizes the output image quality (e.g. 10% DOF
improvement) compared to the existing methods where non-optimal blocking of the lens area may cause more
degradation in output image quality. Experimental results are presented to illustrate our proposed approach.
Many authors simply use band structure of infinite photonic crystals to predict the beam's direction in a finite structure.
The validity of this approximation for high frequencies has been questioned by Felbacq (PRL 92, 193902) and instead a
dressed (by evanescent waves) transfer matrix has been suggested. In this work, we show through numerical examples
that the direction obtained by conventional band structure is more accurate than that of dressed transfer matrix of Felbacq
et. al. We also demonstrate that this approximation can be improved by taking the effect of evanescent Bloch modes into
consideration. The effect of these modes leads to a constant shift of beam's center inside and far enough from the PC's
interface.
In this work, an optimum frequency is found for the operation of single cavity photonic switches. At this optimum point,
the transmission contrast of ON and OFF states takes its highest value, while keeping the device power threshold
relatively low and the device speed acceptably high. Then, the dynamic behavior of a typical single cavity all optical
switch is investigated in the optimum operation point through temporal Coupled Mode Theory. Switching speed and
power are discussed, and the device is shown to be applicable for telecommunication and data processing applications.
The analysis is quite general, and can be used for resonant structures, such as photonic crystals and microring resonators,
in both side coupled and direct coupled configurations.
Low power operation and high speed have always been desirable in applications such as data processing and
telecommunications. While achieving these two goals simultaneously, however, one encounters the well-known powerbandwidth
trade-off. This is here discussed in a typical bistable switch based on a two-dimensional photonic crystal
with Kerr type nonlinearity. The discussion is supported by the nonlinear finite difference time domain (FDTD)
simulation of a direct coupled structure with a home-developed code. Two cases of working near resonant and offresonant
are simulated to compare the power and the speed of the device in the two cases. It is shown that working nearresonance
reduces the power levels at the expense of reducing the settling time, i.e. the bandwidth limitation. The
hystersis loops for the device are also obtained with both coupled-mode theory and quasi-steady state FDTD simulation.
The impact of operating near/off resonance on the shape of the hystersis loop is discussed as a confirmation of the
previous results. Alternative ways of reducing the power while saving the bandwidth are also examined. The discussion
is general and one may investigate other optical switches to obtain similar results.
Optical code division multiple access (OCDMA) is a promising multiple-access technique for future all optical networks.
In this manuscript, the usefulness of exploiting bistable optical elements as threshold devices in coherent OCDMA
systems is analytically investigated, in which the bistability effect is modeled by a simple square loop.
Using polynomial expansion of electromagnetic fields has been already reported for extraction of E polarized defect
modes in two-dimensional photonic crystals. This approach is now applied to straight single-line defect optical
waveguides, where H polarized defect modes are analytically extracted for the first time. Electromagnetic fields are
expanded in accordance with the Floquet theorem, where each Floquet order is itself expanded in terms of Hermite
polynomials and finally a new set of linear ordinary differential equations with non-constant coefficients is obtained.
This set of equations is handled by employing differential transfer matrix method. In this fashion, algebraic and easy to
solve dispersion equations are derived, where each mode is effectively sought out in the Hilbert space spanned by
Hermite polynomials. Effective index theory based on static field approximation is also presented to show the strong
similarity between eigenmodes of photonic bandgap waveguides and those of slab waveguides with uniaxial anisotropic
claddings.
Recently, interaction of electromagnetic waves with conducting interfaces has been studied and several applications have been proposed. For instance, new type of photonic crystals similar to Kronig-Penny electronic crystals has been implemented by using these structures. In these structures a free two dimensional interface charge layer is generated at the dielectric interfaces and interesting phenomena are observed. In this manuscript, the effect of finite charge layer thickness and its asymptotic behavior toward conducting interface, where the thin charge layer is modelled via a surface conductivity σs, is numerically studied for the first time. Two different regimes are considered: first, propagation of optical waves through sub-wavelength free charge layers and its corresponding reflection and transmission coefficients for both major polarizations TE and TM; second, propagation of optical slow waves localized at the interface of two dielectrics with interface conducting layer between them..
In this paper optical filters based on photonic resonant tunneling effect are analyzed by using the polynomial expansion method. Amplitude and phase response together with their dependency on the physical parameters of the filters are also investigated. These steep-edge filters show low insertion loss amplitude response, and linear phase variation in their passband, a suitable feature for WDM and DWDM applications where constant time delay and dispersion free devices are needed. Two kinds of filters, namely discrete level and continuous profile filters are introduced. These structures can be analyzed and designed by using Transfer Matrix Method. However, this approach suffers from inaccuracy and numerical instability when narrow linewidth filters are desired. Moreover, analyzing the continuous profile filters using this method calls for breaking the structure into many homogeneous sublayers. Here, a method based on Legendre expansion of electromagnetic fields is adopted to design and analyze the proposed filters. Not only the method relieves some numerical problems peculiar to conventional methods, but also can be applied for holistic analysis of filters having continuous refractive index profile and therefore eliminates the need for cumbersome multilayer analysis.
Analytical analysis of straight single-line defect optical waveguides in two dimensional photonic crystals based on expanding electromagnetic fields in terms of Hermite polynomials is reported. This novel electromagnetic field expression is substituted in Helmholtz equation, a new set of linear ordinary differential equations with variable coefficients are obtained, and by employing differential transfer matrix method; defect modes, i.e. the guided modes propagating in the line defect waveguide, are analytically derived. The validity of the results obtained by applying the proposed approach are confirmed by comparing them to those derived by using finite difference time domain method.
Free electron lasers have been the subject of intensive interest during the recent decades. In this paper, free electron laser having sheet electron beam with arbitrary inhomogeneous profile of transverse distribution of the beam current density is studied in the linear regime, whereas a novel approach based on the Legendre polynomial expansion of eigenfunctions, already used in analyzing optical structures including stratified structures and diffraction gratings, is adapted to find the eigenfunctions and eigenvalues of the structure. As for this method is unconditionally stable, it works pretty well even in those cases in which the conventional transfer matrix method suffers from numerical instability, i.e. the detuning parameter is negative with a large absolute value. Though the used formulation, obtained by solving Maxwell's and Vlasov's equations simultaneously, is limited to the linear regime, it includes the effects of energy spread and space charge fields.
Three-dimensional vectorial diffraction analysis of phase and amplitude gratings in conical mounting is presented based on Legendre expansion of electromagnetic fields. In the so-called conical mounting, different fields components are coupled and the solution is not separable in terms of independent TE and TM cases. In contrast to conventional RCWA in which the solution is obtained using state variables representation of the coupled wave amplitudes by expanding space harmonic amplitudes of the fields in terms of the eigenfunctions and eigenvectors of the coefficient matrix defined by
rigorous coupled wave equations, here the solution of first order coupled Maxwell's equations is expanded in terms of Legendre polynomials. This approach yields well-behaved algebraic equations for deriving diffraction efficiencies and electromagnetic field profiles. It can nicely handle the cases in which conventional methods face the problem of numerical instability and inevitable round off errors; also, it yields accurate results to any desired level of accuracy. The method is applied to phase and amplitude gratings in conical mountings, comparison to other methods already reported in the literature is made, and the presented approach is justified and its usefulness in cases that other methods usually fail
is demonstrated. This general method applies well even in such cases as thick gratings, non-Bragg incidence, and cases in which higher diffracted orders are needed to be retained, or evanescent orders corresponding to real eigenvalues have to be included. The efficacy of the proposed method relies on the fact that although Legendre polynomials span a complete space, they are not eigensolutions and hence each polynomial basis function bears a weighted projection of all eigenfunctions. Thus no modal information is completely missed in the ineluctable truncation process. In deriving the formulation, a rigorous approach is followed.
Optical measurement of voltage because of its excellent advantages is studied by several research groups. In this paper, two optically voltage measurement method based on periodic structure have been introduced. First one is based on Bragg reflection effect. The coefficient of reflection from a periodic layered medium depends on properties of periodic structure. In this work a periodic structure on LiNbO3 substrate was considered and under a high voltage electric field perpendicular to surface of layers, refractive indices of substrate have been changed. Performance of reflection versus applied electric field was calculated. Second method was based on Guided-mode resonance effect. Guided mode resonance effects in waveguide grating structures results in sharp variations in the intensity of the observable propagation waves. When a waveguide grating structure is illuminated with an incident light beam, part of the beam is directly transmitted and part is diffracted and trapped in waveguide layer. The trapped light is then rediffracted and it
can interfere destructively with the transmitted or reflected light and show transmission or reflection anomalies. This phenomenon is sensitive to constitutive parameters of structure; therefore, it can be used in order to electro-optic voltage measurement.
Coupling efficiency in a directional coupler is influenced by the change of refractive index of substrate. It can be modulated by applying electric field and changing the coupling constant in an electro optic substrate. In this work a Ypropagating Ti:LiNbO3 channel waveguide fabricated in a Z-cut LiNbO3 substrate is simulated. Then, two waveguides with an enough separation gap are considered. Solving Maxwell’s equations and applying boundary conditions yields new eigenmodes of this structure. Using these new eigenmodes, coupling constant is obtained. For obtaining eigenmodes of coupled system, a recently reported variational approach has been used. Then, performance of the sensor was studied by applying electric field. It changes refractive indices in this structure, which gives new eigenmodes and new coupling constants. Simulation results show variations in coupling constant with the change of electric field; these changes of output optical power level can be used to measure the applied electric field.
In several recent papers, layered waveguide structures with conductive interfaces have been discussed, whose propagation properties are controlled by a transverse voltage. These structures can be used as a dynamic optical read/write memory cell, and programmable optical diffractive element. In this paper, the excitation of surface waves with the presence of interface charges is discussed. Interface charges affect the dispersion of surface waves, and therefore they can be used in various applications such as optical modulators, switches, sensors and filters. These waves can be superior to surface plasmon waves since they are not lossy. The lossless property is satisfied in limited range: millimeter waves to far infrared.
In this article, polynomial expansion approach for extraction of guided and leaky modes in layered waveguides in which loss and gain can be present simultaneously is proposed. To verify the method, results of analysis of a typical test case have been compared to the other references, proving a good agreement. Polynomial expansion is a nonharmonic expansion and does not involve harmonic functions or intrinsic modes of homogenous layers. This approach has the benefit of leading to algebraic dispersion equations rather than transcendental dispersion equation; therefore, it will be easier to solve compared with other methods such as argument principle method (APM), reflection pole method (RPM) or wavevector density method (WDM), which are solving the transcendental equation via integral methods. Besides, algebraic dispersion equation will be obtained without any numerical stability problem, while ordinary transcendental dispersion equation, which is usually derived by transfer matrix method, is difficult to obtain due to stability problem in multiplying transfer matrices.
The electromagnetic interface states formed in a heterostructure composed of two semi-infinite Kronig-Penny photonic crystals have been studied. Modified transfer matrices have been used for study of Kronig-Penny photonic crystals (heterostructures with conducting interfaces) to show strong similarity between solid-state physics and electromagnetics. Our calculations are limited to TE polarization.
We present a new analytical method for solution of 1-D quantum and optical systems, based on the differential transfer matrices. This approach can be used for exact calculation of various functions including reflection and transmission coefficients, band structures as well as bound states. We show the consistency of WKB method with out approach and discuss improvements for even symmetry and infinite periodic structures. Moreover a general variational representation of bound states is introduced. As application examples, we consider several test cases including the reflection and band structure of gratings as well as bounded states of inhomogeneous waveguides. An excellent agreement between the results from our differential transfer matrix method with other methods is observed where possible.
In this article, a new variational approach for extraction of leaky modes in layered waveguides is proposed. To verify the method, results of analysis of a typical test case is compared to the other references, being in agreement with them. The efficiency of the proposed approach is compared to other reported methods.
In several recent papers, layered waveguide structures with conductive interfaces have been discussed, whose propagation properties are controlled by a transverse voltage. These structures have wide range of applications. In this paper, surface wave excitation on one-dimensional photonic crystals at the presence of interface conductivity is discussed. It is shown that excitation of electromagnetic surface waves can be controlled by the interface conductivity. This property can be used in constructing miscellaneous optical devices such as optical modulators, switches and tunable optical filters. Devices based on these waves can be superior to surface plasmon waves since they are not lossy. The lossless property is satisfied in limited range: millimeter waves to far infra red.
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