Maxwell Wave Equation Research Articles

Influence of phase matching on the Cooper minimum in Ar high-order harmonic spectra

We study the influence of phase matching on interference minima in high harmonic spectra. We concentrate on structures in atoms due to interference of different angular momentum channels during recombination. We use the Cooper minimum (CM) in argon at 47 eV as a marker in the harmonic spectrum. We measure 2d harmonic spectra in argon as a function of wavelength and angular divergence. While we identify a clear CM in the spectrum when the target gas jet is placed after the laser focus, we find that the appearance of the CM varies with angular divergence and can even be completely washed out when the gas jet is placed closer to the focus. We also show that the argon CM appears at different wavelengths in harmonic and photo-absorption spectra measured under conditions independent of any wavelength calibration. We model the experiment with a simulation based on coupled solutions of the time-dependent Schr\"odinger equation and the Maxwell wave equation, including both the single atom response and macroscopic effects of propagation. The single atom calculations confirm that the ground state of argon can be represented by its field free $p$ symmetry, despite the strong laser field used in high harmonic generation. Because of this, the CM structure in the harmonic spectrum can be described as the interference of continuum $s$ and $d$ channels, whose relative phase jumps by $\pi$ at the CM energy, resulting in a minimum shifted from the photoionization result. We also show that the full calculations reproduce the dependence of the CM on the macroscopic conditions. We calculate simple phase matching factors as a function of harmonic order and explain our experimental and theoretical observation in terms of the effect of phase matching on the shape of the harmonic spectrum. Phase matching must be taken into account to fully understand spectral features related to HHG spectroscopy.

Effect of photoconductivity and oscillation frequency shift on the signal beam intensity in two beam coupling in photorefractive materials

A general theory of the two-beam coupling between a pump beam and a signal beam in photorefractive materials is presented. The coupled wave equations describing the non-linear two beam coupling are derived, based on Maxwell's wave equation. The coupled equation for the intensities of the two beams in the photorefractive crystals with the absorbing properties have been derived analytically. The intensity of the signal beam increases with the increasing crystal thickness, reaches a maximum and then decreases. The influence of energy beam coupling coefficient, oscillation frequency shift, crystal thickness, absorption coefficient and the input beam intensity ratio on the signal beam intensity have been studied in details. The effect of the photoconductivity of the materials on the intensities of the two beams in both the co-directional as well as contra-directional two beam coupling cases have been studied.

空气中氧分子吸附作用对紫外光丝传输特性的影响

From the Maxwell wave equation,the beam propagation equation,which includes several nonlinear effects,such as the attachment of oxygen,was obtained.The filamentation dynamics was homologous to the problem of particles moving in a potential well.The initial conditions in which the laser beam becomes a stationary filamentation were analyzed.By the numerical simulation,the influences of beam size,power and phase on the attachment of oxygen in the filament propagation were discussed.The conclusions indicate that the power is rather consumed by the attachment of oxygen,which results in the beam size decreasing in oscillation process.The results qualitatively explain the relationship between beam size and power.

Ultra-low loss Si_3N_4 waveguides with low nonlinearity and high power handling capability

We investigate the nonlinearity of ultra-low loss Si3N4-core and SiO2-cladding rectangular waveguides. The nonlinearity is modeled using Maxwell's wave equation with a small amount of refractive index perturbation. Effective n2 is used to describe the third-order nonlinearity, which is linearly proportional to the optical intensity. The effective n2 measured using continuous-wave self-phase modulation shows agreement with the theoretical calculation. The waveguide with 2.8-μm wide and 80-nm thick Si3N4 core has low loss and high power handling capability, with an effective n2 of about 9×10(-16) cm2/W.

Derivation of coupled Maxwell-Schrödinger equations describing matter-laser interaction from first principles of quantum electrodynamics

We study the general problem of matter-laser interaction within the framework of nonrelativistic quantum electrodynamics, with particular emphasis on strong laser field effects. Consequently, we formulate a well-defined approximation leading in a straightforward manner toward the conventional semiclassical mode of description. Namely, we arrive naturally to two coupled equations of motion: (i) the Schr\"odinger equation which governs the quantum dynamics of an atomic system driven by classically described radiation field (composed of an incoming laser pulse plus radiation emitted from the atom), and (ii) the classical Maxwell wave equation which describes the emission of radiation from the mentioned atomic source. Employing the formalism of adiabatic Floquet theory, we derive a simple criterion of validity of the just described semiclassical approach. It shows that the semiclassical treatment is justified in most situations. On the other hand, it turns out that the semiclassical approximation breaks down completely in certain special but realistic cases, regardless of the fact that the incoming laser pulse contains a huge number of photons. Under such special circumstances, we anticipate new effects arising due to the quantized nature of the radiation field, to be observable, for example, in harmonic generation spectra. Our considerations are illustrated more explicitly using a simple model of a two-level atom strongly driven by a laser. The quantum dynamics of this model problem is resolved within the framework of quantum electrodynamics while adopting well-defined and physically justifiable approximations. As an outcome, analytic formulas are found serving as a quantitative criterion of (non)applicability of the semiclassical approach and demonstrating the breakdown of semiclassical theory under well-defined conditions. An illustrative numerical calculation is provided.

Earth Sciences Push Radiative Transfer Theory: 2009 International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics; Saratoga Springs, New York, 4–7 May 2009

The theories of radiative transfer and particle—particularly neutron—transport are grounded in distinctive microscale physics that deals with either optics or particle dynamics. However, it is not practical to track every wave or particle in macroscopic systems, nor do all of these details matter. That is why Newton's laws, which describe individual particles, are replaced by those of Euler, Navier‐Stokes, Maxwell, Boltzmann, Gibbs, and others, which describe the collective behavior of vast numbers of particles. And that is why the radiative transfer (RT) equation is used to describe the flow of radiation through geophysical‐scale systems, leaving to Maxwell's wave equations only the task of providing the optical properties of the medium, be it air, water, snow, ice, or biomass. Interestingly, particle transport is determined by the linear transport equation, which is mathematically identical to the RT equation, so geophysicists and nuclear scientists are interested in the same mathematics and computational techniques.

Modal propagation characteristics of EM waves in ternary one-dimensional plasma photonic crystals

We have theoretically studied the modal dispersion characteristics, group velocity, and effective group as well as phase index of refraction of ternary one-dimensional (1D) plasma photonic band gap (PBG) structure having periodic multilayers of three different materials in one unit cell. The dispersion characteristics related for such structure is derived by solving Maxwell wave equation based on principle of Kronig–Penny model. From the computed results we observe that the dispersion characteristics of such structure also show the frequency gap and cutoffs as found in (binary) one-dimensional plasma photonic crystal. The frequency gap is shown to become larger with the increase of plasma frequency as well as plasma width. It is seen that such structure provide additional degree of freedom to control dispersion characteristic, group velocity and effective index of refraction compared to conventional one-dimensional plasma photonic crystal.

The effect of grana and inter-grana components of chloroplasts on green light transmission: A preliminary study

In this paper we simulate for the first time the propagation of green light through grana and inter-grana components of chloroplasts. Those components are nano-metric structures and thus regular estimation of the propagation of light cannot be exact without taking into account diffraction effects. The numerical investigation presented in this paper solves Maxwell wave equation using the finite-difference time-domain (FDTD) numerical approach to analyze the propagation of light through a chloroplast model.

A general theory of two-wave mixing in nonlinear media

A general theory of two-wave mixing (TWM) in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of TWM are derived based on Maxwell's wave equation. The coupled-wave equations can be decoupled as coupled equations for the intensity and coupled equations for the phase of both beams, and these two sets of coupled equations can be solved analytically by using average total intensity in the medium instead of using the total intensity. Compared with the previous theory of TWM, the theory presented here is more general, and the applications of the theory to photorefractive materials, Kerr media, and semiconductor broad-area amplifiers are described.

A generalized modeling strategy of quantum-cascade structures with resonance-enhanced harmonic oscillations

In this work, the modeling strategy of quantum-cascade lasers is generalized to including the harmonic-resonance-enhanced nonlinear oscillations up to the third order. In addition to the lasing power at fundamental frequency, the second-harmonic and third-harmonic output power can all be evaluated through the model. The model is built on the rate-equations for subband electrons and photons, in connection with Maxwell wave equations for propagation coupling between different emission modes. Various radiative and nonradiative carrier scattering mechanisms are accounted in the model. In addition to single-photon processes, multi-photon processes in the nonlinear cascades are also accounted. The model is based on a full cascade structure containing the injector, active region, and collector in order to account for the nonideal injection efficiency between periodic stages of quantum-cascade lasers. The simulation results on two fabricated quantum-cascade structures capable of nonlinearly harmonic generations agree well with the experiment measurements. The model can be used to evaluate and further optimize the nonlinear performances of quantum-cascade lasers.

MODAL DISPERSION CHARACTERISTICS OF A BRAGG FIBER HAVING PLASMA IN THE CLADDING REGIONS

The modal dispersion relation of electromagnetic waves in a Bragg fiber having plasma in the cladding regions is investigated analytically. The proposed Bragg fiber consists of a low index central region having air surrounded by a large number of periodic cladding layers of alternating high and low refractive indices of dielectric and plasma respectively. The modal dispersion relation is obtained by solving Maxwell wave equations using a simple boundary matching method. The analysis shows that the normalized frequency parameter (also called V -number) is frequency independent. This indicates that the proposed Bragg fiber may be used for single mode operation without high frequency limitation as well as with little loss of energy compared to the conventional dielectric waveguide.

On the Choice Between Transmission Line Equations and Full-Wave Maxwell's Equations for Transient Analysis of Buried Wires

In this paper, we evaluate the validity of transmission line (TL) solutions in the study of interaction of lightning transients with buried wires. The considered transients have frequencies between a few kilohertz to a few megahertz with risetimes 0.1-10 mus. Comparative simulations using TL equations and full- wave Maxwell's equations are carried out in the paper, and the solutions to both the equations are based on the finite-difference time-domain method. It is found that TL solutions are sufficiently accurate for lightning transient analysis of buried wires. It is also claimed that the TL approach remains valid for all transients having frequencies lower than those of lightning. TL solutions are computationally efficient, particularly when dealing with distributed power and railway systems. The TL approach is valid as long as the transverse electromagnetic mode (TEM) is dominant. However, other modes of propagation, classified as antenna modes, might be present depending upon the type of excitation source, its location, frequency, and the associated media. A possible approximate formula for the frequency above which the validity of TL solutions for buried systems is questionable is proposed based on the concept of penetration depth of fields into the soil. Discussions presented in the paper could motivate the application of TL solutions for electromagnetic transient analyses of the buried conductors of power, railway, and telecommunication systems.

Nonlinear gain amplification due to two-wave mixing in a broad-area semiconductor amplifier with moving gratings

The two-wave mixing in a broad-area semiconductor amplifier with moving gratings is investigated theoretically, where a pump beam and a signal beam with different frequencies are considered, thus both a moving phase grating and a moving gain grating are induced in the amplifier. The coupled-wave equations of two-wave mixing are derived based on the Maxwell's wave equation and rate equation of the carrier density. The analytical solutions of the coupled-wave equations are obtained in the condition of small signal when the total intensity is far below the saturation intensity of the amplifier. The results show that the optical gain of the amplifier is affected by both the moving phase grating and the moving gain grating, and there is energy exchange between the pump and signal beams. Depending on the moving direction of the gratings and the anti-guiding parameter, the optical gain may increase or decrease due to the two-wave mixing.

Two-wave mixing in a broad-area semiconductor amplifier

The two-wave mixing in the broad-area semiconductor amplifier was investigated, both theoretically and experimentally. In detail we investigated how the optical gain is affected by the presence of the two-wave mixing interference grating. In the experimental setup we are able to turn on and off the interference pattern in the semiconductor amplifier. This arrangement allows us to determine the two-wave mixing gain. The coupled-wave equations of two-wave mixing were derived based on the Maxwell's wave equation and rate equation of the carrier density. The analytical solutions of the coupled-wave equations were obtained in the condition of small signal and the total intensity is far below the saturation intensity of the amplifier. The results show that when the amplifier is operated below transparency we obtain an increase in the optical gain, and when the amplifier is operated above transparency we obtain a decrease in the optical gain. The experimental results obtained in an 810 nm, 200 microm wide GaAlAs amplifier show good agreement with the theory. A diffusion length of 2.0 microm is determined from the experiment.

Optical pumping of the electron spin polarization in bulk CuCl

In CuCl bulk crystal negatively charged excitons (trions $X^-$) can be induced by the resonant optical excitation of extra electrons in conduction band minimum. In the case of light polarization and due to the top valence band structure of CuCl only the electrons with spin antiparallel to the direction of the light propagation contribute to the formation of $X^-$, while the emerging $X^-$ can recombine into both possible electron states, with spin parallel and antiparallel to the direction of light propagation. We propose to use this mechanism for optical electronic spin pumping. We describe the dynamics of pumping in terms of density matrix formalism. The coherent pumping laser pulse propagating through the sample is described by Maxwell wave equation coupled to the density matrix evolution equations. The results of our approximate simple model calculations suggest that spin polarization close to 100% can be achieved in time shorter than 100ps.

Theoretical and experimental studies of polarization mode dispersion of an electro-optic Mach–Zehnder modulator

A theoretical model is developed to study the polarization mode dispersion effect in an electro-optic Mach-Zehnder interferometric (MZI) modulator. The Stokes parameters and differential group delay (DGD) of the output light of a MZI modulator can be analytically derived with the proposed model, which is based on a three-dimensional Maxwell's wave equation approach. The theoretical model is validated to the extent possible by comparing the theoretical results of the Stokes parameters and DGD with experimental measurements that are based on the wavelength-scanning method and the Jones matrix eigenanalysis method.

A new model for complex dynamic laser modeling

We present a new distributed time domain model (DTDM) for use in complex laser modeling. Like several other models, we use Maxwell's wave equations, but with a time dependent polarization in the form of classical electron oscillators (CEO). It is based on the neoclassical rate equations of A. E. Siegman. The unique feature of our model is the use of a virtual electric field used to simulate random spontaneous emission. This approach has not been used before. The model includes effects such as gain suppression, optically induced gratings, and excess noise. We discuss our results and compare and contrast them with other published work.

Eikonal approximation to 5D wave equations as geodesic motion in a curved 4D spacetime

We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the symplectic structure of the corresponding mechanics. We then apply an analogous method to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics to demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. Finally we discuss the case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg-Schr\"odinger equation. This construction provides a model for an underlying quantum mechanical structure for classical dynamical motion along geodesics on a pseudo-Riemannian manifold. The locally symplectic structure which emerges is that of Stueckelberg's covariant mechanics on this manifold.

The application of Euler deconvolution to airborne EM datay

Euler's equation has traditionally not been used with electromagnetic fields because of a belief that it does not apply, because EM data obey Maxwell's wave equations rather than Laplace's equation. However if two approximations are employed then this is not the case. The approximations are ; 1) the effects of displacement currents are neglected; and 2) the contribution of the country rock is assumed to be small, due to its much lower conductivity than the target. In these situations then the wave equation reduces to Laplace?s equation. With frequencies <5000 Hz and an overburden:target conductivity ratio of <0.05 this approximation is valid. If Laplace's equation is valid then Euler's equation is also valid, and it may be used as a semi-automatic interpretation method in a similar manner to that with which it is used with magnetic and gravity data. It also allows for the downward continuation of EM data. The application of Euler deconvolution to airborne EM data is demonstrated both on data from synthetic models, and on real data over massive Ni-Cu sulphides associated with basic intrusive rocks.

On the electro-optic measurements in organic single-crystal films

We present a detailed study of the electro-optic modulation in single-crystal thin films of organic materials, taking into account the effects due to multiple internal reflections and absorption of optical radiation in the crystal film and the substrate. Optical transmission expressions are derived for the widely employed field-induced birefringence measurement configuration by developing a coupled optical cavity formalism and incorporating complex electro-optic coefficient tensor elements and refractive indices in Maxwell's wave equation. This treatment is applied to the electro-optic measurements in the single-crystal films of an important and popular organic molecular salt, 4′-dimethylamino-N-methyl-4-stilbazolium tosylate. The results show that the conventional interpretation of the measured responses, where the aforesaid effects are neglected for simplicity, would lead to substantial errors in the determination of the electro-optic coefficients, which is validated by the wide variation of reported experimental results in the literature.