Quantitative method for measurement of the Goos-Hanchen effect based on source divergence considerations

In this paper we report on a method for quantitative measurement and characterization of the Goos-Hanchen effect based upon the real world performance of optical sources. A numerical model of a nonideal plane wave is developed in terms of uniform divergence properties. This model is applied to the Goos-Hanchen shift equations to determine beam shift displacement characteristics, which provides quantitative estimates of finite shifts near critical angle. As a potential technique for carrying out a meaningful comparison with experiments, a classical method of edge detection is discussed. To this end a line spread Green’s function is defined which can be used to determine the effective transfer function of the near critical angle behavior of divergent plane waves. The process yields a distributed (blurred) output with a line spread function characteristic of the inverse square root nature of the Goos-Hanchen shift equation. A parameter of interest for measurement is given by the edge shift function. Modern imaging and image processing methods provide suitable techniques for exploiting the edge shift phenomena to attain refractive index sensitivities of the order of 10−6, comparable with the recent results reported in the literature

Intrinsic chaos in a dc field biased quantum heterostructure

A closed, quantum, double barrier, GaAs/AlGaAs heterostructure is made chaotic by adding a nonlinear potential term, α〈Q(t)〉, to the time-dependent Schrödinger equation, and the dynamical behavior of an electron cloud moving in the heterostructure biased by a dc electric field is examined numerically. Using phase-space diagrams, power spectrums, and Lyapunov exponents, both qualitative and quantitative measures of the chaos in the system were taken. In general, for all values of α, the nonlinearity parameter, the Lyapunov exponent, λ, increases as the applied dc field, β, increases. However, for values of α ⩽ 1.376, we notice a sharp drop in λ for the value of β = −9.2×107 V/m corresponding to an average dc voltage of −.085 eV in the central well. This first order type transition to high values of λ for α\u3e1.376 corresponds to a similar increase in the mean charge trapped in the heterostructure and in the average nonlinear potential in the central well for that dc field. This behavior is attributed to the fact that for α ⩽ 1.376 and β = −9.2×107 V/m, the field effects dominate, but for α\u3e1.376, the nonlinearity term dominates

Quantitative method for measurement of the Goos-Hanchen effect based on source divergence considerations

In this paper we report on a method for quantitative measurement and characterization of the Goos-Hanchen effect based upon the real world performance of optical sources. A numerical model of a nonideal plane wave is developed in terms of uniform divergence properties. This model is applied to the Goos-Hanchen shift equations to determine beam shift displacement characteristics, which provides quantitative estimates of finite shifts near critical angle. As a potential technique for carrying out a meaningful comparison with experiments, a classical method of edge detection is discussed. To this end a line spread Green’s function is defined which can be used to determine the effective transfer function of the near critical angle behavior of divergent plane waves. The process yields a distributed (blurred) output with a line spread function characteristic of the inverse square root nature of the Goos-Hanchen shift equation. A parameter of interest for measurement is given by the edge shift function. Modern imaging and image processing methods provide suitable techniques for exploiting the edge shift phenomena to attain refractive index sensitivities of the order of 10−6, comparable with the recent results reported in the literature

Digital signal propagation in dispersive media.

In this article, the propagation of digital and analog signals through media which, in general, are both dissipative and dispersive is modeled using the one-dimensional telegraph equation. Input signals are represented using impulsive, Heaviside unit step, Gaussian, rectangular pulse, and both unmodulated and modulated sinusoidal pulse type boundary data. Applications to coaxial transmission lines and freshwater signal propagation, for both digital and analog signals, are included. The analysis presented here supports the finding that digital transmission in dispersive media is generally superior to that of analog. The boundary data (input signals) give rise to solutions of the telegraph equation which contain propagating discontinuities. It is shown that the magnitudes of these discontinuities, as a function of distance, can be found without the need of solving the governing equation. Thus, for digital signals in particular, signal strength at a given distance from the input source can be easily determined. Furthermore, the magnitudes of these discontinuities are found to be independent of both the dispersion coefficient k and the elastic coefficient b. In addition, it is shown that, depending on the algebraic sign of k, one of two distinct forms of dispersion is possible and that for small-time intervals, solutions are approximately independent of

Energy flow and fluorescence near a small metal particle

We examine the classical energy-balance equation for a fluorescing system consisting of a molecule near a small, spherical metal particle capable of sustaining electromagnetic resonances and irradiated with laser light. From the energy-flow distribution in the entire system, we obtain the enhancement factor for the fluorescence emission of the adsorbed molecule. Numerical results demonstrate that the electromagnetic interactions of the molecule and the surface can be understood in terms of energy flow through the entire system and applied to investigate spectroscopic properties of adsorbates in similar systems. Absorption and emission rates of the adsorbed molecule are determined considering the energy-flow distribution and its dependence on the substrate as well as molecular parameters. Such understanding is useful in predicting spectroscopic responses of adsorbates

Mirrorless optical bistability in a nonlinear absorbing dielectric film

The optical transmissivity of a mirrorless, nonlinear, absorbing dielectric thin film is investigated numerically. The dielectric function in the film region is dependent on the intensity of the electromagnetic field. Multivalued solutions of transmissivity as a function of incident power are calculated for the steady-state wave equation. The numerical solution is applied to two different model dielectric functions. As the absorption parameter is increased, larger values of incident intensity are required to switch the systems between stable output states. Also, the peak values of transmissivity are reduced as the absorption is increased

Aberration-free negative-refractive-index lens

The aberrations of a spherical lens composed of left-handed materials are studied in this letter. Five Seidel aberrations (spherical, coma, astigmatism, field curvature, and distortion) as a function of the refractive index n and shape factor q of the lens are considered. Our numerical calculations show that the negative refractive index gives much larger windows of small values of aberrations than the positive index, which will significantly enhance the flexibility for the design of an optical lens. Two possible regions with optimized aberrations are proposed: n = −1, q = −2.2 and n = −0.81 and q = 0.8

Causal implications of viscous damping in compressible fluid flows

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid

Causal implications of viscous damping in compressible fluid flows

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid