A note on an exact solution for the optical absorbance by thin films

The Babu-Barouch solution of Berning's difference equation for the electromagnetic fields within optical thin films is shown to converge in the continuum limit to a solution (expressed as a converging series) of the limiting differential equation.Supported in part by the NSF Grant #ECS 8611298 and the mathematics division of AFOSR.     

Difference frequency generation in GaAs microdisks

Semiconductor-based whispering-gallery-mode microcavities are very promising for nonlinear optics applications, thanks to the high optical quality factors attainable with today's technology. We propose to exploit this advantage to generate cw light through phase-matched difference frequency generation in a triply resonant GaAs microdisk. A proper choice of the microdisk radius and thickness allows one to select the generated wavelength in the band of 2.5-2.9 mum. Besides illustrating the design features, we numerically show that temperature can be effectively used to compensate for wavelength shifts induced on the generated field by fabrication errors.     

表面等离子体激元微盘的优化设计及应用

表面等离子体激元(SPP)微腔具有很高的品质因子和极小的模式体积,在光电子器件研究方面具有重要的应用价值。采用有限元法对表面等离子体激元的金属覆盖介质微盘谐振腔进行理论模拟,研究考虑微盘底半径、介质层厚度及金属膜厚度等参数对微盘表面等离子体模的品质因子及模体积的影响。研究表明,在光通信波段1550nm附近获得高品质因子(1000以上),极低模式体积的表面等离子体微盘。最后研究了利用优化设计的微盘进行折射率传感的应用,获得了高达300nm/RIU的折射率传感灵敏度。     

Transformation of laser light by a semiconductor microcylinder

Theoretical simulation of the transformation of the electromagnetic field by microcavities in the shape of homogeneous semiconductor microcylinders has shown that the morphology of microcavities affects the transformation of the optical radiation in modes of the microlaser in a rather complicated way. We show that, in homogeneous semiconductor microcylinders, there can be realized the regime of single- or two-mode lasing on morphological resonances differing both by the quality factor and by the spatial structure of the electromagnetic field. The region of single- or two-mode lasing is determined by the ratio of the gain and loss factors and by the field magnitudes in the spatial structure of morphological resonances.     

Green's function for a three-dimensional oscillator in a variable uniform electromagnetic field

By means of the Feynman integral along trajectories, an exact expression is found for Green's function in the Cauchy problem involving the Schrödinger equation, which describes the behavior of a three-dimensional variable-frequency oscillator in a variable uniform electromagnetic field. The problem reduces to that of finding the fundamental solution to a secondorder ordinary linear differential equation with variable coefficients.     

Kinetic theory of the interaction in an electron current-electromagnetic wave system

The interaction between an electron beam and a retarded electromagnetic field with an accelerating electrostatic field (traveling wave tube with bunching) is considered. An exact steady-state solution of the kinetic equation is found for the case of a zero electrostatic field and an approximate solution is found for the case of a slowly varying electrostatic potential. A theory is constructed for the amplification of the electromagnetic wave; a critical value is indicated for the power of the amplified wave, above which stable amplification is possible. The dependence of the differential efficiency on the power of the amplified wave is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 17–21, April, 1982.     

The magneto-elastic subharmonic resonance of current-conducting thin plate in magnetic filed

Based on Maxwell equations and corresponding electromagnetic constitutive relations, the electrodynamic equations and electromagnetic force expressions of a current-conducting thin plate in electromagnetic field are deduced. Nonlinear magneto-elastic vibration equations of the thin plate are given. In addition, nonlinear subharmonic resonances of the thin plate with two opposite sides simply supported which is under the mechanic live loads and in constant transverse magnetic field are studied. The corresponding vibration differential equation of Duffing type is deduced by the Galerkin method. The method of multiple scales is used to solve the equation, and the frequency-response equation of the system in steady motion under subharmonic responses is obtained, and the stability of solution is analyzed. According to the Liapunov stability theory, the critical conditions of stability are obtained. By the numerical calculation, the curves of resonance amplitude changing with the detuning parameter, the excitation amplitude and the magnetic intensity and corresponding state planes are obtained. The existing regions of nontrivial solutions and the changing law of stable and unstable solutions are analyzed. The time history response plots, the phase charts and the Poincare mapping charts are plotted. And the effect of the magnetic intensity on the system is discussed, and some complex dynamic performances as period-doubling motion and quasi-period motion are analyzed.     

Spontaneous emission in micro- and nano-structures

Spontaneous emission of emitters governing the performance of optoelectronic devices is a fundamental phenomenon, and it has strong environment-dependent characteristics. In this article, we mainly review the experimental and theoretical progresses in the control of spontaneous emission by manipulating optical modes with photonic crystals, optical microcavities and metallic nanostructures. The spontaneous emission from emitters in photonic crystals can be modified by the local density of states, and by employing photonic crystals, the devices’ efficiency is enhanced, the angular radiation pattern can be engineered, and highly efficient optoelectronic devices are achieved through decreasing the radiative lifetime. In quantum optical devices, microcavities would alter the lifetime of an excited state through tuning the resonance in the frequency and positioning between the emitters and cavity field, and inducing the emitters to emit spontaneous photons in a desired direction. The emerging enhanced electromagnetic field near metallic nanostructures can help to control and manipulate the spontaneous emission of an emitter. The use of micro- and nano-structures to manipulate spontaneous emission will open unprecedented opportunities for realizing functional photonic devices.     

Spontaneous emission in micro- and nano-structures

Spontaneous emission of emitters governing the performance of optoelectronic devices is a fundamental phenomenon, and it has strong environment-dependent characteristics. In this article, we mainly review the experimental and theoretical progresses in the control of spontaneous emission by manipulating optical modes with photonic crystals, optical microcavities and metallic nanostructures. The spontaneous emission from emitters in photonic crystals can be modified by the local density of states, and by employing photonic crystals, the devices’ efficiency is enhanced, the angular radiation pattern can be engineered, and highly efficient optoelectronic devices are achieved through decreasing the radiative lifetime. In quantum optical devices, microcavities would alter the lifetime of an excited state through tuning the resonance in the frequency and positioning between the emitters and cavity field, and inducing the emitters to emit spontaneous photons in a desired direction. The emerging enhanced electromagnetic field near metallic nanostructures can help to control and manipulate the spontaneous emission of an emitter. The use of micro- and nano-structures to manipulate spontaneous emission will open unprecedented opportunities for realizing functional photonic devices.     

Analytic-numerical approach to non-linear problems in dielectric waveguides

A combined analytic-numerical approach is presented for investigations of electromagnetic signal propagation in dielectric waveguides containing a non-linear medium. The approach is based on the resolvent method for the Volterra integral equation describing an electromagnetic process. The proposed algorithm uses the exact expression for the solution to the integral equation for the electromagnetic field in the planar waveguide with time jump changing of the medium properties. In the case of a non-linear dielectric as the waveguide core the continuous change of the medium parameters is replaced by jump changes of the latter. This is the only approximation made in the algorithm. The resolvents that are constructed give the exact solution on each jump step. The results from some example numerical calculations are presented.     

Dynamical aspects in the optical bloch equations

In quantum optics, some models are considered to describe many aspects of the dynamics of atoms coupled to an electromagnetic field (laser). The simplest atomic model is of course the two-level-atom which is governed by the Bloch optical equations. In general this system is solved in the steady state or by using some approximations. An extended analytic approach is considered for this coupled equations. The separation approach of coupled differential equations is always possible with a sequence of special transformation into nonlinear differential equations. The conditions that permit an exact solution of three coupled systems are extracted in a natural manner. The case of sodium atom moving along the axis of a standing-wave is investigated in some details.     

Exact solution of Maxwell's equations for optical interactions with a macroscopic random medium

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations.     

金属-电介质约束的半导体微盘激光器

设计了一种以半导体材料InGaAsP作为核心结构的器件表面蒸镀二氧化硅膜层,在其上蒸镀金膜层,构成金属-电介质半导体微盘激光器结构,盘面的厚度为2 μm,盘面半径为6 μm,盘壁侧表面与底面的夹角为45°.使用有限元法对该结构器件的回音壁模式进行数值研究,利用所谓"偏微分方程的弱项形式"有效地抑制了许多局域不变性相关的"伪解".通过数值求解弱项型矢量亥姆霍兹方程,得到微盘激光器回音壁模式的横磁场分布,在此基础上讨论了其品质因数(Q值)、模体积、不同金属和电介质膜厚度对器件品质因数的影响、盘的半径和其品质因素的关系等相关量.理论计算表明,这种结构的器件较直接在介质表面蒸镀金属膜层结构的器件的品质因数高2～3倍.实验还获得了基阶和高阶的表面等离子体波模式,以及品质因数最大达到约5 400的光学-电介质基模.     

Controlling spontaneous emission and threshold-less laser oscillation with optical microcavities

We describe the alteration of spontaneous emission of materials in optical microcavities having dimensions on the order of the emitted wavelength. Particular attention is paid to one-dimensional optical confinement structures with pairs of planar reflectors (planar microcavities). The presence of the cavity causes great modifications in the emission spectrum and spatial emission intensity distribution accompanied by changes in the spontaneous emission lifetime. Experimental results are shown for planar microcavities containing GaAs quantum wells or organic dye-embedded Langmuir-Brodgett films as light emitting layers. Also discussed are the laser oscillation properties of microcavities. A remarkable increase in the spontaneous emission coupling into the laser oscillation mode is expected in microcavity lasers. A rate equation analysis shows that increasing the coupling of spontaneous emission into the cavity mode causes the disappearance of the lasing threshold in the input-output curve. Experimentally verification is presented using planar optical microcavities confining an organic dye solution. The coupling ratio of spontaneous emission into a laser mode increases to be as large as 0.2 for a cavity having a half wavelength distance between a pair of mirrors. At this point, the threshold becomes quite fuzzy. Differences between the spontaneous emission dominant regime and the stimulated emission dominant regime are examined with emission spectra and emission lifetime analyses.     

Pair production and vacuum polarization of vector particles with electric dipole moments and anomalous magnetic moments

The matrix 8-component Dirac-like form of the P-odd equations for boson fields of spin 1 and 0 are obtained and the symmetry group of the equations is derived. We found exact solutions of the field equation for vector particles with arbitrary electric and magnetic moments in external constant and uniform electromagnetic fields. The differential probability of pair production of vector particles with electric dipole moments and anomalous magnetic moments by an external constant and uniform electromagnetic field has been found using exact solutions. We have calculated the imaginary and real parts of the electromagnetic field Lagrangian that takes into account the vacuum polarization of vector particles. Received: 14 April 2001 / Revised version: 13 July 2001 / Published online: 19 September 2001     

Integration of the dirac equation,which does not presume complete separation of variables,in Stäckel spaces

The method of noncommutative integration of linear differential equations is used to construct an exact solution of the Dirac equation, which does not presume complete separation of variables, in Stäckel spaces. The Dirac equation in an external electromagnetic field is integrated by this method, using one example. The Stäckel space under consideration does not enable one to solve this equation exactly within the framework of the theory of separation of variables.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 31–37, January, 1996.     

Neutrino radiation in gravitational fields

A differential equation representing radiation solutions of the general relativistic Weyl equation is derived. Their optical properties and the group of motion of the corresponding energy-momentum tensor are studied. If there exists neutrino radiation the Riemann space must be algebraically special and the propagation of the neutrinos occurs only along one of the principal null directions. Gravitational- and neutrinopp-waves taken together, represent an exact solution of the Weyl-Einstein system of field equations.     

An exact solution of the relativistic equation of motion of acharged particle driven by a circularly polarized electromagnetic waveand a constant magnetic field

An exact solution is found for the relativistic equation of motion of a charged particle driven by a circularly polarized electromagnetic wave and a constant magnetic field. The explicit expressions of particle position and velocity are obtained for certain initial conditions. The results are of interest to the interaction of the high-power laser with the magnetized plasma, electromagnetically pumped free-electron laser with a guide magnetic field, propagation of electromagnetic wave signals through a re-entry plasma sheath in the presence of a strong magnetic field, and magnetic confinement plasmas     

Photon BLOCH oscillations in porous silicon optical superlattices

We report the first observation of oscillations of the electromagnetic field in an optical superlattice based on porous silicon. These oscillations are an optical equivalent of well-known electronic Bloch oscillations in crystals. Elementary cells of our structure are composed by microcavities whose coupling gives rise to the extended collective modes forming optical minigaps and minibands. By varying thicknesses of the cavities along the structure axis, we have created an effective electric field for photons. A very high quality factor of the confined optical state of the Wannier-Stark ladder may allow lasing in porous silicon-based superlattices.     

Fabrication of the Fully Hybrid Microcavities Based on Zn(S)Se Epilayers and Amorphous Dielectrics

A technique of fabrication of fully-hybrid microcavities using II-VI semiconductor compound epilayers and distributed Bragg reflectors based on amorphous dielectric coating is described. The fully hybrid microcavities with Zn(S)Se epilayers are created. High structural and optical quality of the embedded Zn(S)Se thin films was established by atomic-force microscopy and optic studies. The analysis of excitonic spectra for Zn(S)Se epilayers embedded in the fully hybrid microcavities indicates that such structure can be perspective for creation of a new type of light-emitting devices – polariton lasers.