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We obtain optimal dynamic contests for environments where the designer monitors effort through coarse, binary signals—Poisson successes—and aims to elicit maximum effort, ideally in the least amount of time possible, given a fixed prize. The designer has a vast set of contests to choose from, featuring termination and prize-allocation rules together with real-time feedback for the contestants. Every effort-maximizing contest (which also maximizes total expected successes) has a history-dependent termination rule, a feedback policy that keeps agents fully apprised of their own success, and a prize-allocation rule that grants them, in expectation, a time-invariant share of the prize if they succeed. Any contest that achieves this effort in the shortest possible time must in addition be what we call second chance: once a pre-specified number of successes arrive, the contest enters a countdown phase where contestants are given one last chance to succeed.

We present a full operator approach to treatment of the cross-Kerr interaction combined with parametric amplification. It is shown that this problem can be exactly integrated using the method of higher-order operators. While the initial basis is infinite-dimensional, an orthogonal transformation can reduce the problem exactly into a six-dimensional basis which can be integrated conveniently.

Public, private, and not-for-profit organizations find advanced technology and product development projects challenging to manage due to the time and budget pressures, and turn to their development partners and suppliers to address their development needs. We study how dynamic development contests with enriched rank-based incentives and carefully-tailored information design can help these organizations outsource their development projects at the minimum project lead time by stimulating competition among suppliers. We show that an organization can use dynamically adjusted flexible rewards to achieve the absolute minimum expected project lead time at a significantly lower cost than a fixed-reward policy. Importantly, our flexible-reward policy pays the absolute minimum expected reward (i.e., achieves the first best). We further study the case where the organization does not have sufficient budget to offer a reward that attains the absolute minimum expected lead time. We propose that in this case, the organization can dynamically increase the contest reward until its budget constraint binds and then use information sharing as a strategic tool to incentivize suppliers. Specifically, we propose an easy-to-implement random-update policy where the organization periodically monitors the status of suppliers at random times and immediately discloses any partial progress. We show that such a random-update policy outperforms other canonical information disclosure strategies. Our results indicate that dynamic rewards and strategic information disclosure are powerful tools to help organizations outsource their development needs swiftly and cost effectively.

Problem definition: Firms seek to use the contest format to source solutions from a broader network of outside solvers. However, contests end without satisfactory solutions in case of complex problems with significant solution development costs, in part due to the lack of sufficient effort from solvers. To address this lack of solver engagement, we study when and how a firm’s finely-tuned screening of contestant submissions encourages contestant effort for solving complex problems. Methodology/results: We present an application-driven game-theoretic model to capture imperfections in screening using the true positive rate (Sensitivity) and the true negative rate (Specificity). Specifically, we consider a two-stage contest with a screening decision by the firm between the stages. Solvers face uncertainty about their probability of fit and the final quality of the solution is dependent on the performance across both stages. We identify two mechanisms through which screening induces greater effort, namely the encouragement effect and the competitive contest effect, and characterize how screening should be tuned to the problem setting. We consider the special case of single-stage contest to study how screening can benefit firms, finding that limiting contestant entry can be optimal for solution-seeking firms. Our results indicate that in case of problems with less upfront complexity, coarse (imperfect) screening is beneficial in order to manage competition and stimulate greater effort, but it behooves the firm to resort to more accurate screening otherwise. We also derive nuanced results for the case when a Seeker faces screening limits and must balance screening sensitivity and specificity. Managerial implications: Our work provides firms an additional degree of freedom, in terms of specific and sensitive screening to design and run contests and to better engage outside solvers. We derive actionable results and translate them into a managerial framework to help fine-tune the screening mechanism for improved contest performance.

This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second order operators which constitute an exactly closed commutators. We consider both types of standard position-field and the recently predicted non-standard momentum-field quadratic interactions, which is significant when the ratio of mechanical frequency to optical frequency is not negligible. This unexplored regime of large mechanical frequency can be investigated in few platforms including the superconducting electromechanics and simulating quantum cavity electrodynamic circuits. It has been shown that the existence of non-standard quadratic interaction could be observable under appropriate conditions.

Frequency shifts of red- and blue-scattered (Stokes/anti-Stokes) side-bands in quantum optomechanics are shown to be counter-intuitively inequal, resulting in an unexpected symmetry breaking. This difference is referred to as Side-band Inequivalenve (SI), which normally leans towards red, and being a nonlinear effect it depends on optical power or intracavity photon number. Also there exists a maximum attainable SI at an optimal operation point. The mathematical method employed here is a combination of operator algebra equipped with harmonic balance, which allows a clear understanding of the associated nonlinear process. This reveals the existence of three distinct operation regimes in terms of pump power, two of which have immeasurably small SI. Compelling evidence from various experiments sharing similar interaction Hamiltonians, including quantum optomechanics, ion/Paul traps, electrooptic modulation, Brillouin scattering, and Raman scattering unambiguously confirm existence of a previously unnoticed SI., Comment: This is the final version including Supplementary Information; Comments are utmostly welcome

Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an exact formulaion of coupled mode theory for interaction between elastic and photonic Bloch waves moving along an optomechanical waveguide. In general, an optical wavefront is strongly diffracted by an elastic wave in frequency and wavevector, and thus infinite modes with different frequencies and wavevectors appear. We discuss resonance and mode conversion conditions, and present a rigorous method to derive coupling rates and mode profiles. We also find a conservation law which rules over total optical power from interacting individual modes. We present application examples to the theory to optomechanical waveguides and cavities, as well as non-reciprocal transmission of light and optomechanical switches., to appear in IEEE Journal of Quantum Electronics

The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a bit less accurate than WKB solutions but much easier to work with because of their algebraic form. Furthermore, these bases exactly satisfy the initial conditions and may go over the turning points without the divergent behavior of WKB solutions. The findings of this paper allow explicit evaluation of eigenvalues of confined modes with high precision, as demonstrated by few examples.

We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics., Comment: 16 equations, 11 pages, 88 references, with 21 pages of Supplementary Information. Experimental observations were dropped. This final version with total restructuring under a new title appears in Scientific Reports

We present quantum yield measurements of single layer $\textrm{WSe}_2$ (1L-$\textrm{WSe}_2$) integrated with high-Q ($Q>10^6$) optical microdisk cavities, using an efficient ($��>$90%) near-field coupling scheme based on a tapered optical fiber. Coupling of the excitonic emission is achieved by placing 1L-WSe$_2$ to the evanescent cavity field. This preserves the microresonator high intrinsic quality factor ($Q>10^6$) below the bandgap of 1L-WSe$_2$. The nonlinear excitation power dependence of the cavity quantum yield is in agreement with an exciton-exciton annihilation model. The cavity quantum yield is $\textrm{QY}_\textrm{c}\sim10^{-3}$, consistent with operation in the \textit{broad emitter} regime (i.e. the emission lifetime of 1L-WSe$_2$ is significantly shorter than the bare cavity decay time). This scheme can serve as a precise measurement tool for the excitonic emission of layered materials into cavity modes, for both in plane and out of plane excitation.

We introduce a new scalable cavity quantum electrodynamics platform which can be used for quantum computing. This system is composed of coupled photonic crystal (PC) cavities which their modes lie on a Dirac cone in the whole super crystal band structure. Quantum information is stored in quantum dots that are positioned inside the cavities. We show if there is just one quantum dot in the system, energy as photon is exchanged between the quantum dot and the Dirac modes sinusoidally. Meanwhile the quantum dot becomes entangled with Dirac modes. If we insert more quantum dots into the system, they also become entangled with each other.

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer Two-Dimensional (2D) Transition-Metal Dichalcogenides (TMDCs), having the formula $\textrm{MX}_2$ with M=Mo,W and X=S,Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semiclassical perturbation analysis of response functions. We numerically calculate the linear $\chi_{\mu\nu}^{(1)}(-\omega;\omega)$ and nonlinear surface susceptibility tensors $\chi_{\mu\nu\zeta\eta}^{(3)} (-\omega_\Sigma;\omega_r,\omega_s,\omega_t)$ with $\omega_\Sigma=\omega_r+\omega_s+\omega_t$. Both non-degenerate and degenerate cases are studied for third-harmonic generation and nonlinear refractive index, respectively. Computational results obtained \textit{with no external fitting parameters} are discussed regarding two recent reported experiments on ${\rm MoS}_2$, and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a $\frac{\pi}{4}-$rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and high-harmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.

An educational robot is described, which is designed and constructed for use in the laboratory of Principles of Electrical Engineering. The discrete nature of design, conforming to a simple block strategy, allows fairly easy introduction of basic and fundamental concepts of Electrical Engineering to the freshman students, including control, actuation, wireless signal transmission, and analogue/digital conversions. Each block or module represents one or few engineering ideas, and helps the students to understand the interplay and connection between system divisions, and enhance their creative thinking. Circuits are designed and implemented that both the structure and functionality of each module are clearly presented. Inputs and outputs as well as major signals can be traced and measured through several test points

Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in studying photonic and phononic (phoxonic) crystals in full three dimensions is not suitable for slab analysis in its standard form, because of convergence and stability issues. Here, we propose a modification to this method which overcomes these limitations. This improved method can be utilized for calculation of both photonic and phononic modes in phoxonic slabs. While in the standard three-dimensional PWE, Fourier series are used to estimate the field dependence across the normal component of the slab, we expand the fields across the third dimension using eigenmodes of a plain unstructured slab. Despite its approximate nature, this approach is observed to be both much faster and more accurate than the conventional PWE method and can give a very accurate estimation of confined propagating modes. As an application example of the proposed method we investigate a non-reciprocal photonic device. This device is a phoxonic slab waveguide which changes modes of optical waves by elastic waves and can be used as an optical insulator or mode converter., accepted to Journal of Lightwave Technology

Phoxonic crystal as a means of guiding and confining electromagnetic and elastic waves has already attracted attentions. Lack of exact knowledge on how these two types of waves interact inside this crystal and how electromagnetic wave evolves through this interaction has increased this field complexity. Here we explain how an elastic wave affects an electromagnetic wave through photo-elasticity and interface displacement mechanisms in a phoxonic crystal slab waveguide. We obtain a master equation which can describe electromagnetic wave evolution. In this equation we define a coupling parameter and calculate its value for different modes of electromagnetic and elastic waves and show it vanishes for some types of modes . Finally we solve the master equation for a typical phoxonic crystal slab waveguide and illustrate the electromagnetic wave evolution.

There has been a rapidly growing interest in optoelectronic properties of graphene and associated structures. Despite the general belief on absence of spontaneous emission in graphene, which is normally attributed to its unique ultrafast carrier momentum relaxation mechanisms, there exist a few recent evidences of strong optical gain and spontaneous light emission from mono-layer graphene, supported by observations of dominant role of out-of-plane excitons in polycyclic aromatic hydrocarbons. In this article, we develop a novel concept of light emission and optical gain from simple vertical graphene/dielectric tunnel junctions. It is theoretically shown that the possible optical gain or emission spectrum will be easily tunable by the applied voltage. We present details of quantum mechanical calculations and perform an exact analysis of field-assisted tunneling using transfer matrices combined with expansion on Airy's functions.

We study the effects of recombination and generation process on the operation of bipolar junction transistor based on two-dimensional materials, and in particular, graphone. Here, we use Shockley–Read–Hall model to study these process. First, we investigate the current–voltage characteristics of a graphone p–n junction considering generation and recombination process. Then, we calculate the estimated changes in current gain, cutoff frequency, and output characteristics of a graphone bipolar junction transistor designed in a recent study.

The cavity quantum electrodynamics of various complex systems is here analyzed using a general versatile code developed in this research. Such quantum multi-partite systems normally consist of an arbitrary number of quantum dots in interaction with an arbitrary number of cavity modes. As an example, a nine-partition system is simulated under different coupling regimes, consisting of eight emitters interacting with one cavity mode. Two-level emitters (e.g. quantum dots) are assumed to have an arrangement in the form of a linear chain, defining the mutual dipole–dipole interactions. It was observed that plotting the system trajectory in the phase space reveals a chaotic behavior in the so-called ultrastrong-coupling regime. This result is mathematically confirmed by detailed calculation of the Kolmogorov entropy, as a measure of chaotic behavior. In order to study the computational complexity of our code, various multi-partite systems consisting of one to eight quantum dots in interaction with one cavity mode were solved individually. Computation run times and the allocated memory for each system were measured.

We show a methodology for how to construct Dirac points that occur at the corners of Brillouin zone as the Photonic counterparts of graphene. We use a triangular lattice with circular holes on a silicon substrate to create a Coupled Photonic Crystal Resonator Array (CPCRA) which its cavity resonators play the role of carbon atoms in graphene. At first we draw the band structure of our CPCRA using the tight-binding method. For this purpose we first designed a cavity which its resonant frequency is approximately at the middle of the first H-polarization band gap of the basis triangular lattice. Then we obtained dipole modes and magnetic field distribution of this cavity using the Finite Element Method (FEM). Finally we drew the two bands that construct the Dirac points together with the frequency contour plots for both bands and compared with the Plane Wave Expansion (PWE) and FEM results to prove the existence of Dirac point in the H-polarization band structure of lattices with air holes.

It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

We present an explicit solution of carrier and field distributions in abrupt PN junctions under equilibrium. An accurate logarithmic numerical method is implemented and results are compared to the analytical solutions. Analysis of results shows reasonable agreement with numerical solution as well as the depletion layer approximation. We discuss extensions to the asymmetric junctions. Approximate relations for differential capacitance C-V and current-voltage I–V characteristics are also found under non-zero external bias.

The exact numerical solution of the nonlinear Ginzburg–Landau equation for Josephson junctions is obtained, from which the precise nontrivial current density and effective potential of the Josephson junctions are found. Based on the resulting potential well, the tunneling probabilities of the associated bound states are computed which are in complete agreement with the reported experimental data. The effects of junction and bias parameters such as thickness of the insulating barrier, cross sectional area, bias current, and magnetic field are fully investigated using a successive perturbation approach. We define and compute figures of merit for achieving optimal operation of phase qubits and measurements of the corresponding states. Particularly, it is found that Josephson junctions with thicker barriers yield better performance in measurements of phase qubits. The variations of characteristic parameters such as life time of the states due to the above considered parameters are also studied and discussed to obtain the appropriate configuration setup.

We investigate the potential of plasmonic resonance in metal nanocomposite materials for the design of photonic crystal all optical switches by numerical methods. We study the absorption effect of the plasmonic resonance on the Fano resonances of one dimensional photonic crystal slabs covered by a metal nanocomposite layer. It is shown that the absorption reduces the contrast of the Fano resonances. However, for adequate metal nanoparticle concentrations it is possible to achieve both sufficiently sharp Fano resonance and strong Kerr nonlinearity, which provides a suitable condition for the design of high contrast and low threshold switches.

A different approach in the calculation of two-dimensional local density of states has been presented for a two-dimensional finite rectangular-lattice photonic crystal with a separable profile of permittivity. Approximate staircase structures are already shown to be useful for their ability to reproduce actual properties of practical square lattice photonic crystals. Using the effective resonance approach in a Fabry–Perot resonator and transfer matrix method an analytical expression for calculating a two-dimensional local density of states can be derived for both polarisations in the structure. It is shown that for this geometry one can resolve the modes as a product of two separate functions each being a function of x- and y-coordinates. The results have been investigated for the two-dimensional local density of states in the ordered finite structure and in the disordered structure. The main advantage of this method in calculating the local density of states is its extremely efficient numerical evaluatio...

Enhancement of interaction between optical and mechanical fields is one of the main goals of cavity optomechanics as a newly founded physics context. If the coupling rate between these fields exceeds their decay rates from the cavity, then preparation of quantum entangled states between photons of the electromagnetic field and phonons of the mechanical field becomes feasible. Among different types of cavities, phoxonic crystal (PxC) cavities have attracted attention in recent years because they can confine optical and mechanical fields simultaneously. In this paper, we introduce four PxC slabs which exhibit simultaneous photonic and phononic bandgaps. All of these crystals have a triangular lattice pattern and are formed of periodic air holes inside a silicon slab. Then, we create cavities inside these crystals by filling air holes of a unit cell with silicon and then study the coupling strength between their photonic and phononic modes. We deduce that the crystal slab with circular holes can enhance the coupling strength more than others. We further show that if this crystal can be manufactured with lattice constant a=400 nm, then a single-photon coupling rate of g0≃14 MHz is predicted, which is the greatest value reported for a PxC slab cavity to the best of our knowledge. This cavity would have an effective mass of meff≃35 fg.

In this paper, we present an envelope function analysis in order to design the emission spectra of a white quantum well light emitting diode. The nanometric heterostructure that we are dealing with is a multiple quantum well, consisting periods of three single quantum wells with various well thicknesses. With the aid of 6x6 Luttinger Hamiltonian, we employ the combination of two methods, k.p perturbation and transfer matrix method, to acquire electron and hole wavefunctions analytically. The envelope function approximation was considered to obtain these wavefunctions for a special basis set. While adjacent valence subbands have been studied exactly, the conduction bands are approximated as parabolic. The effect of Stokes shift has been also taken into account. The dipole moment matrix elements for interband atomic transitions are evaluated via correlation between electron and hole envelope functions, for both orthogonal polarizations. This has simplified the calculation of photoluminescence intensity. Spatial variations in hole/electron wavefunctions have been examined with the introduction of piezoelectric and spontaneous polarizations internal field. We theoretically establish the possibility of a highly efficient InGaN red emitter, resulting in a uniform luminescence in red, green and blue emissions from the while light emitting diode, through adjusting material composition, potential slope, and thickness.

Most electromechanical devices are in two-dimensional metallic drums under high tensile stress, which causes increased mechanical frequency and quality factor. However, high mechanical frequencies lead to small zero-point displacements $x_{\rm zp}$, which limits the single-photon interaction rate $g_0$. For applications which demand large $g_0$, any design with increased $x_{\rm zp}$ is desirable. It is shown that a patterned drum by spiral shape can resolve this difficulty, which is obtained by a reduction of mechanical frequency while the motion mass is kept almost constant. An order of magnitude increase in $g_0$, and agreement between simulations and interferometric measurements is observed.

In contrast to graphene, which is a gapless semiconductor, graphane, the hydrogenated graphene, is a semiconductor with an energy gap. Together with the 2-D geometry, unique transport features of graphene, and the possibility of doping graphane, p and n regions can be defined so that 2-D p-n junctions become feasible with small reverse currents. This paper introduces a basic analysis to obtain the current-voltage characteristics of such a 2-D p-n junction based on graphane. As we show, within the approximation of Shockley's law of junctions, an ideal I-V characteristic for this p-n junction is to be expected.

The superprism effects of higher bands, i.e., for normal frequencies of higher than one, in two-dimensional (2D) polymer photonic crystals (PCs) are investigated. It is shown that in a polymer PC of triangular symmetry with filling factor of about 31%, the gradual transition of the hexagonal into triangular equi-frequency dispersion contours leads to a strong superprism in the 6th band at a normal frequency of 1.2. This dispersion is more prominent than those observed in the lower bands in 2D PCs. Also, this requires a lattice constant longer than the concerned wavelength. Furthermore, in a 2D polymer PC with a filling factor of about 83% a strong discontinuous superprism effect occurs at normal frequencies higher than one, which is due to an abrupt transition between two modes with the refraction angles of opposite signs. The effect can be exploited for switching applications as demonstrated in the paper.

A terahertz modulator based on the Type-II superconductor flux flow oscillator has been proposed. Analytical calculations are presented and the effects of intrinsic and extrinsic parameters such as disorder strength of crystal, penetration depth, frequency, and amplitude of the modulated current on the radiation power spectrum have been studied. The proposed structure also exhibits a mixer-like behavior, in the sense that its output harmonics range from the washboard frequency up to the superconductor gap frequency, so the input signal is practically mixed with the washboard frequency and its harmonics. The modulation index for each harmonic of this modulator has also been investigated. This well-featured modulator has a potential to be used in next-generation terahertz integrated transceivers.

We present a new approach for analytical modeling and calculating the response of high-T c superconductive transition edge sensors in a wide range of modulation frequencies for different configurations of the film patterns. The method used here is based on solving the heat transfer differential equation for two different time varying heat sources, which are related to the absorbed radiated power. The used method employs two-dimensional boundary conditions for describing meander-line patterned devices. The results from the applied method are in better agreement with those obtained from the frequency response measurements of the characterized samples, than the previously developed models. In addition, the method is capable of being used for analysing the effect of the device configurative parameters on its ultimate sensitivity. Therefore, it has also been applied to investigate the effects of changing track and spacing width, substrate thickness, and absorption coefficient of the absorber layer on the magnitude of bolometric response. In this calculation, the effect of surface absorption caused by the superconducting thin film and absorber layer, as well as bulk absorption in the depth of the substrate are considered simultaneously. Analytical results are presented and compared with previous analytical works and measured data from YBCO samples. Through extensive numerical calculations, we demonstrate that the responsivity of superconductor bolometers is a strong function of geometry, and there exists an optimal track width to spacing ratio of about 0.2.

Magnetohydrodynamic (MHD) equilibrium is vulnerable to numerous destabilizing mechanisms. Instabilities introduce distortions to the plasma magnetic surfaces and its boundaries, their driving force being the radial gradient of plasma toroidal current density. For certain modal numbers, internal kink modes may develop, and their study is feasible according to the energy principle, in which the change in total potential energy due to the disturbance is evaluated. In this article, we present a totally new analysis of MHD equilibrium and stability, and apply it to Damavand tokamak which has a large aspect ratio. For this purpose, we combine perturbation and Green’s function methods to solve for the equilibrium configuration. At this stage, plasma profiles are found explicitly in terms of Bessel functions, and we present a simple expression for estimation of total toroidal plasma current. Then the rest of plasma profiles, including poloidal magnetic flux, safety factor, and toroidal current density, are obtained and plotted. In the next step, we turn to the stability calculations and show that Damavand plasma is resistant to most of the disturbances.

A rigorous, fast and efficient method is proposed for analytical extraction of guided defect modes in two-dimensional photonic crystals, where each Bloch spatial harmonic is expanded in terms of Hermite–Gauss functions. This expansion, after being substituted in Maxwell’s equations, is analytically projected in the Hilbert space spanned by the Hermite–Gauss basis functions, and then a new set of first order coupled linear ordinary differential equations with non-constant coefficients is obtained. This set of equations is solved by employing successive differential transfer matrices, whereupon defect modes, i.e. the guided modes propagating in the straight line-defect photonic crystal waveguides and coupled resonator optical waveguides, are analytically derived. In this fashion, the governing differential equations are converted into an algebraic and easy to solve matrix eigenvalue problem. Thanks to the analyticity of the proposed approach, the eigenmodes of these structures can be extracted very quickly. The validity of the obtained results is however justified by comparing them to those derived by using the standard finite-difference time-domain method.

We have performed a numerical solution for band structure of an Abrikosov vortex lattice in type-II superconductors forming a periodic array in two dimensions for applications of incorporating the photonic crystals concept into superconducting materials with possibilities for optical electronics. The implemented numerical method is based on the extensive numerical solution of the Ginzburg–Landau equation for calculating the parameters of the two-fluid model and obtaining the band structure from the permittivity for both orthogonal polarizations, which depends on the above parameters and the frequency. This is while the characteristics of such crystals highly vary with an externally applied static normal magnetic field, leading to nonlinear behavior of the band structure, which also has nonlinear dependence on the temperature. The similar analysis for every arbitrary lattice structure is also possible to be developed by this approach as presented in this work. We also present some examples and discuss the results. 2007 Elsevier B.V. All rights reserved.

Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and pseudo-periodic with respect to the other. An additional kind of symmetry between r-space and k-space exists between the envelope and eignfunctions not apparently noticed before, which allows to define new invertible modified Wannier functions. As opposed to the Wannier functions in r-space, these modified Wannier functions are defined in the k-spaces, but satisfy similar basic properties. These could result in new algorithms and other novel applications in the computational tools of periodic structures.

We propose a new method based on variational principle for analysis of photonic crystal (PC) slabs. Most of the methods used today treat PC slab as a three-dimensional (3D) crystal and this makes them very time and/or memory consuming. In this method we use Bloch theorem to expand the field on infinite plane waves which their amplitudes depend on the component perpendicular to the slab surface. By approximating these amplitudes with appropriate functions, we can find modes of PC slabs almost as fast as we can find modes of a two-dimensional (2D) crystal. Besides this advantage, we can also calculate radiation modes with this method which is not feasible with 3D Plane Wave Expansion (PWE) method., Comment: accepted to Materials Research Express

A two-dimensional (2-D) finite-difference time-domain (FDTD) code for the study of nonlinear optical phenomena, in which both the slowly varying and the rapidly varying components of the electromagnetic fields are considered, has been developed. The algorithm solves vectorial Maxwell's equations for all field components and uses the nonlinear constitutive relation in matrix form as the equations required to describe the nonlinear system. The stability of the code is discussed and its effectiveness is demonstrated through the simulations of self-phase modulation (SPM) and second-harmonic generation (SHG). The authors also show that the combination of nonlinear effects with PCs can result in a significant improvement in device size and integrability, using the example of a Mach-Zehnder interferometer (MZI).

In this paper, the excitation of surface waves in 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 a limited range of millimetre waves to far infrared.

In this paper, we present a new approach for the exact calculation of band structure in one-dimensional periodic media, such as photonic crystals and superlattices, based on the recently reported differential transfer matrix method (DTMM). The media analyzed in this paper can have arbitrary profile of refractive index. We derive a closed form dispersion equation using differential transfer matrix formalism, and simplify it under the assumptions of even symmetry and real-valued wavenumber. We also show that under normal incidence both TE and TM modes must have the same band structure. Several numerical test cases are also studied and discussed.

In this paper, the effect of two-dimensional electron plasma formed on the surface of a semiconductor on the refraction phase of an optical beam is investigated. Both the density and effective mass of the surface state electrons can be controlled by a transverse electric field. While the surface density of electrons varies slowly with the applied field, their effective mass changes instantaneously. Therefore, a high bandwidth for the phase modulation can be obtained. It is expected that the device operates in the far-infrared region with a semiconductor as the base material. GaAs is one of the best candidates having both large dynamic range, and large ratio of free electron to the crystal effective mass. The device operates in a waveguide configuration, as discussed throughout the paper. The electron effective mass is found through quantum mechanical calculations, and the interaction with the incident light beam is treated classically. Finally, a waveguide light phase modulator is proposed.

We present a new analytical method for solution of non-homogeneous anisotropic optical systems, based on the extension of transfer matrices into differential form. This approach can be used for exact calculation of various functions including reflection and transmission coefficients, band structures and bound states. We discuss improvements of the method for infinite periodic structures and bounded modes. Then simplifications of the approach are considered for the TE and TM polarized isotropic structures, pseudo-isotropic and uniaxial non-magnetic media. Moreover a general variational representation of bound states is introduced. As application examples, we consider the reflection from inhomogeneous structures, the band structure of infinite periodic media and bounded modes in inhomogeneous anisotropic waveguides. Excellent agreement between the results from our differential transfer matrix method and other methods is observed where comparison is possible.

Feasibility of a new integrated amplitude modulator/switch operating up to the visible spectrum, based on the absorption of light due to the linear interaction of the incident laser and a two-dimensional plasma layer is demonstrated. Plasma layers are generated via the Muller effect at the waveguide's interfaces. A plasma wave is excited in the two-dimensional gas when it is illuminated by electromagnetic radiation. Thus, due to the energy transfer from the electromagnetic wave to the plasma wave, the output light intensity can be controlled. The device is capable of amplitude modulation of guided beams in dielectric waveguides. Analysis based on both full-classical and semiclassical approaches are performed and are compared.