Parapositronium atom in the field of annihilation and optical photons as a nonlinear quantum system

A parapositronium atom in an optical laser field is described beyond the perturbation theory framework by a closed system of Heisenberg equations on operators of atoms and photons. Wwe consider the annihilation of the parapositronium atom, which starts from one or two quantum states; optical quantum transitions between these states are caused by one or two optical photons. Mean occupation numbers of these states are governed by a system of two nonlinear equations. We investigated particular stationary and nonstationary solutions of this system and find that annihilation photons substantially affect the annihilation process. We show that definite optical laser radiation may stabilize the parapositronium atom and make its lifetime hundreds of times longer than the lifetime of the free parapositronium atom in the 1s state. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 1, pp. 148–168, July, 2000.     

Analytical Solution for the Deformation of a Cylinder under Tidal Gravitational Forces

Quite a few future high precision space missions for testing Special and General Relativity will use optical resonators which are used for laser frequency stabilisation. These devices are used for carrying out tests of the isotropy of light and of the universality of the gravitational redshift. As the resonator frequency not only depends on the speed of light but also on the resonator length, the quality of these measurements is very sensitive to elastic deformations of the optical resonator itself. As a consequence, a detailed knowledge about the deformations of the cavity is necessary. In this note we derive for the first time an analytical solution for the problem of an elastic, isotropic, homogeneous free–flying cylinder in space under the influence of a tidal gravitational force. A detailed derivation can be found in [4]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive grid refinement for a model of two confined and interacting atoms

We have applied adaptive grid refinement to solve a two-dimensional Schrödinger equation in order to study the feasibility of a quantum computer based on extremely-cold neutral alkali-metal atoms. Qubits are implemented as motional states of an atom trapped in a single well of an optical lattice of counter-propagating laser beams. Quantum gates are constructed by bringing two atoms together in a single well leaving the interaction between the atoms to cause entanglement. For special geometries of the optical lattices and thus shape of the wells, quantifying the entanglement reduces to solving for selected eigenfunctions of a Schrödinger equation that contains a two-dimensional Laplacian, a trapping potential that describes the optical well, and a short-ranged interaction potential. The desired eigenfunctions correspond to eigenvalues that are deep in the interior of the spectrum where the trapping potential becomes significant. The spatial range of the interaction potential is three orders of magnitude smaller than the spatial range of the trapping potential, necessitating the use of adaptive grid refinement.     

Optimization of a one dimensional hypertelescope for a direct imaging in astronomy

We describe an application of nonlinear optimization in interferometric optical astronomy. The aim is to find the relative positions of the output pupils and the modulus of the beams through each pupil of a linear array of telescopes in order to design an instrument capable of imaging exoplanets. The problem is modelized under the form of a semi-infinite nonlinear minimization problem. The model problem is transformed by a simple discretization into a minimization problem with a finite number of constraints, then it is solved by using a minimization solver. Numerical experiments are reported.     

Rotating Waves in a Parabolic Problem with a Transformed Argument

A study is made of the bifurcation of periodic, orbitally stable, spatially-inhomogeneous, rotating wave-type solutions generated from spatially-homogeneous, stationary solutions of a parabolic equation through transformation of a rotation of the spatial coordinate. This equation arises in modelling the self interaction of a light field in an optical resonator with distributed feedback.     

Eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide

One proves the existence of the eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide. One gives a normalization of the eigenfunctions of the continuous spectrum relative to an indefinite inner product. One defines the concept of the genus of the multipliers of a Hamiltonian equation, corresponding to the continuous spectrum of the optical waveguide.Translated from Problemy Matematicheskogo Analiza, No. 9, pp. 18–34, 1984.     

一类Fermi气体光晶格非线性机制的轨线研究

研究了一类Fermi气体光晶格轨线的非线性扰动模型.首先求得了Fermi气体光晶格在无扰动情形下模型轨线的精确解.然后引入一组广义泛函分析同伦映射,构造一组迭代系统,得到了Fermi气体光晶格非线性扰动模型轨线的任意次渐近解.最后讨论了一个微扰系统.该文在方法上可较方便地得到轨线的渐近表示式.     

Localized states in an ultracold atomic gas trapped in a bichromatic potential: The effect of a time-varying phase

Localization phenomena observed in an ultracold atomic gas trapped in a bichromatic optical lattice were found to be sensitive to the degree of lattice disorder, and are affected by the extent of interatomic interaction. In this work, I shall discuss the dependence of localization on the phase difference between the two superimposed optical waves. The step and sinusoidal phase functions in region III identified in the work by Larcher et al. [1], are studied. A step varying phase mildly distorts localization, whereas a sinusoidally varying phase will take the system to a unique form of localization, which we call logarithmic localization.     

Numerical Modeling of Solitons in a Low Birefringent Optical Fiber

A numerical investigation, based on the split-step Fourier transform algorithm of all optical switching of solitons in a low birefringent optical fiber is presented. The numerical algorithm is described in detail. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mathematical model of an optical antenna based on the discrete sources method

We consider an optical antenna that is a linear cluster of nanoparticles inside a metal film on a substrate. Based on discrete sources method has been developed and implemented a mathematical model of the optical antenna. Numerical results demonstrate the ability to control the width of the lobe, and directionality of the antenna radiation.     

A numerical validation approach of a finite element muscle model using optical data

Aim of this work is to obtain a convenient data set for the validation of a recently developed three-dimensional constitutive muscle model. Therefore, an optical measurement technique is used to reconstruct a geometrical model of a rabbit soleus muscle. Thus, the muscle geometry and also the generated force characteristics are measured. The proposed numerical model is able to reproduce the experimental results in an adequate manner. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inversion of solar transmitted radiance profiles for the atmospheric optical thickness

In a series of papers (Refs. [1–12]), quasilinearization and invariant imbedding have been successfully applied to an inversion of total spectral radiance profiles remotely sensed from space for determining the atmospheric optical properties and the ground albedo, in a least square sense. In the present paper, with the aid of quasilinearization and invariant imbedding, a statistical estimation of the atmospheric optical thickness is made, using solar noisy transmitted radiance measurements on the ground.     

Algorithms for solving inverse problems in the optics of layered media based on comparing the extrema of spectral characteristics

A new algorithm for determining the optical parameters of deposited multilayer optical coatings based on comparing the positions of the extrema of the optical characteristics of multilayer optical coatings is proposed. Two versions of this algorithm are compared. Using a series of numerical simulation experiments, the advantage of one of these versions is demonstrated. It is shown that this version decreases the influence of systematic errors in the spectral data.     

Electromagnetic scattering theorems for interior dipole excitation of a layered obstacle

A layered scatterer is excited by a time‐harmonic spherical electromagnetic wave, generated by a dipole located either in the interior or in the exterior of the scatterer. The scatterer's core may be perfect conducting, impedance or dielectric. This paper initiates the investigation of scattering theorems corresponding to the excitation of a layered scatterer by a dipole in its interior. We establish reciprocity and general scattering theorems relating the total electric fields with the corresponding far‐field patterns. The optical theorem, relating the scattering cross‐section with the electric field in the layer containing the dipole, is recovered as a corollary of the general scattering theorem. Furthermore, for a scatterer excited by a spherical and a plane wave, mixed scattering theorems are derived. Besides, all the derived theorems recover known results, concerning the excitation of a homogeneous scatterer by an exterior dipole. We also analyze numerical implementations of the optical theorem in certain concrete scattering applications. Copyright © 2007 John Wiley & Sons, Ltd.     

An idea of half-space thermal mirror

The paper describes a theoretical discussion of the optical reflecting properties of an isotropic thermoelastic half-space subjected to an instantaneous heat pulse at a point of its surface (such a system is called the half-space thermal mirror). The fundamental optical properties of the mirror so obtained (i.e.—its aberration characteristic, including optical power and focal length), and their time evolution are derived in the paper. The half-space thermal mirror represents an optical device suffering rather high aberrations; the paraxial optics approximation, and criteria of its applicability for such a mirror are given. Possibilities of an application of the thermal mirror for determining the temperature conductivity of a material are considered.     

The existence of solutions for the problem in the optical lattice with nonlocal nonlinearity

We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discuss the solitons solution for a class of nonlinear Schr?dinger equations in the optical lattice with nonlocal nonlinearity. We also show via a uniform priori estimate that existence and uniqueness of the global solution for the initial problem.     

Generalization of the optical theorem to multipole sources in the scattering theory of electromagnetic waves

Energy relations are used to generalize the Optical Theorem to the case of a local body excited by a multipole source, including in the presence of a half-space. It is shown that the extinction cross section can be represented in an explicit analytical form. This circumstance considerably facilitates the computation of the fluorescence quantum yield or the efficiency of an optical antenna.     

Numerical solution of the problem of image formation in two planes using the integral fresnel formula

The paper considers numerical solution of the problem of constructing a plane phase optical element which forms prespecified images in two focal planes when illuminated by a plane wave front. The propagation of radiation from the optical element to the focal planes obeys the integral Fresnel formula. The phase function defining the optical element, is from the space of feasible phase functions satisfying both computational and technological constraints. The computer algorithm is based on efficient numerical solution of the inverse directional diagram problem. The phase function is constructed using the projector on the space of feasible phase functions. The efficiency of the phase optical element produced by the proposed procedure is demonstrated by solving a prototype problem involving simulation of the direct operator. The corresponding optical element was manufactured by electron-beam lithography. Physical experiments with a laser source illuminating the element confirmed the findings of the numerical experiment. Translated from Prikladnaya Matematika i Informatika, No. 1, pp. 86–89, 1999.     

Raman like perturbation on an optical pulse propagation—a different outlook

Effect of Raman like perturbations on the propagation characteristics of an optical pulse in a fiber is simulated in different manner. The optical pulse is described by a modified NLS equation, which is coupled with a vibrational equation describing the Raman perturbation due to the molecular oscillation. Two different approaches are used to analyze the equation. In the first approach both the coupled equations are treated through projection operator technique to derive the ODE’s for describing the evolution of the pulse parameters. On the other hand in the later technique we could reduce the system to a new NLS equation which was then studied in a similar manner. The numerical results and the behaviour of the parameters predicted by both the methodologies reasonably tallies with each other. The detailed change of the amplitude, chirp, phase, and width of the pulse is analyzed. It is then shown how dispersion management partially restores the projected pulse. And lastly it is demonstrated that including a distance dependent amplification or an amplification map we can get back the required periodic structure required for a long haul transmission.     

An Exact Solution for the Optical Absorbance of Thin Films

The electric and magnetic fields within optical thin films are obtained exactly in closed form as solutions of a system of difference equations presented by Berning and utilized by Dill, Neureuther, Tuttle, and Walker in their sample program for modeling optical lithography. The solution allows an explicit closed form expression for the absorbance.