Mean Field Theory for Lossy Nonlinear Composites

The mean-field theory for lossy nonlinear composites, described by complex and field-dependent dielectric functions, is presented. By using the spectral representation of linear composites with identical microstructure, we develop self-consistent equations for the effective response. We examine two types of microstructure, namely, the Maxwell-Garnett approximation and the effective medium approximation to illustrate the theory.Comment: 11 pages, LaTeX format, 2 figures, accepted for publication by Solid State Communications 18 November 199

Reply to Comments of P. W. Smith, Jr.

In his comments on this subject, Smith has put emphasis on the special nature of the plane-wave solution in acoustic problems. It is perhaps unnecessary to defend the importance of the plane-wave solution in a linear theory

On the Propagation of Sound in a Liquid Containing Gas Bubbles

The theory of the propagation of sound in a homogeneous gas including the effect of heat conduction is presented for the purpose of clarifying the underlying thermodynamic process. The propagation of sound in a liquid with a homogeneous and isotropic distribution of gas bubbles is then considered. The bubbles are assumed to be sufficiently small and numerous so that the mixture can be taken to be a uniform medium. The effect of heat conduction is included. If f is the ratio of gas volume in the mixture to liquid volume, it is shown for the range of f of general interest that the acoustic condensations and rarefactions of the gaseous portion of the medium are essentially isothermal. It is also found that the attenuation of an acoustic disturbance by heat conduction is quite small

Theory of the acoustic absorption by a gas bubble in a liquid

A complete analysis of acoustic absorption by a spherical gas bubble is developed by the application of the classical Rayleigh method. The absorption considered is that due to the viscosity and heat conduction of the gas bubble. Specific results are presented for the S-wave scatter and absorption for the case of an air bubble in water, and the absorption effects of viscosity and heat conduction alone are calculated explicitly. The results found here are of similar magnitude to those found by Pfriem and Spitzer who used an approximate procedure

Theory of gas bubble dynamics in oscillating pressure fields

The behavior of a permanent gas bubble in a liquid with an oscillating pressure field is analyzed with a linearized theory. If the assumption is made that conditions within the bubble are uniform, the thermodynamic relations found are as expected; i.e., at low frequencies the bubble behaves isothermally and at high frequencies the behavior becomes adiabatic. However, a more detailed analysis, which allows the bubble interior to vary not only in time but also in space, leads to an average isothermal behavior for the bubble even in the high-frequency limit

Spectral representation of the effective dielectric constant of graded composites

We generalize the Bergman-Milton spectral representation, originally derived for a two-component composite, to extract the spectral density function for the effective dielectric constant of a graded composite. This work has been motivated by a recent study of the optical absorption spectrum of a graded metallic film [Applied Physics Letters, 85, 94 (2004)] in which a broad surface-plasmon absorption band has been shown to be responsible for enhanced nonlinear optical response as well as an attractive figure of merit. It turns out that, unlike in the case of homogeneous constituent components, the characteristic function of a graded composite is a continuous function because of the continuous variation of the dielectric function within the constituent components. Analytic generalization to three dimensional graded composites is discussed, and numerical calculations of multilayered composites are given as a simple application.Comment: Physical Review E, submitted for publication

Effective conductivity of composites of graded spherical particles

We have employed the first-principles approach to compute the effective response of composites of graded spherical particles of arbitrary conductivity profiles. We solve the boundary-value problem for the polarizability of the graded particles and obtain the dipole moment as well as the multipole moments. We provide a rigorous proof of an {\em ad hoc} approximate method based on the differential effective multipole moment approximation (DEMMA) in which the differential effective dipole approximation (DEDA) is a special case. The method will be applied to an exactly solvable graded profile. We show that DEDA and DEMMA are indeed exact for graded spherical particles.Comment: submitted for publication

Scheme for Attophysics Experiments at a X-ray SASE FEL

We propose a concept for production of high power coherent attosecond pulses in X-ray range. An approach is based on generation of 8th harmonic of radiation in a multistage HGHG FEL (high gain high harmonic free electron laser) configuration starting from shot noise. Single-spike phenomena occurs when electron bunch is passed through the sequence of four relatively short undulators. The first stage is a conventional "long" wavelength (0.8 nm) SASE FEL which operates in the high-gain linear regime. The 0.1 nm wavelength range is reached by successive multiplication (0.8 nm $\to$ 0.4 nm $\to$ 0.2 nm $\to$ 0.1 nm) in a stage sequence. Our study shows that the statistical properties of the high-harmonic radiation from the SASE FEL, operating in linear regime, can be used for selection of radiation pulses with a single spike in time domain. The duration of the spikes is in attosecond range. Selection of single-spike high-harmonic pulses is achieved by using a special trigger in data acquisition system. The potential of X-ray SASE FEL at TESLA at DESY for generating attosecond pulses is demonstrated. Since the design of XFEL laboratory at TESLA is based on the use of long SASE undulators with tunable gap, no special place nor additional FEL undulators are required for attophysics experiments. The use of a 10 GW-level attosecond X-ray pulses at X-ray SASE FEL facility will enable us to track processes inside atoms.Comment: 21 pages, 12 figures, submitted to Optics Communication

Parity violating cylindrical shell in the framework of QED

We present calculations of Casimir energy (CE) in a system of quantized electromagnetic (EM) field interacting with an infinite circular cylindrical shell (which we call `the defect'). Interaction is described in the only QFT-consistent way by Chern-Simon action concentrated on the defect, with a single coupling constant $a$. For regularization of UV divergencies of the theory we use % physically motivated Pauli-Villars regularization of the free EM action. The divergencies are extracted as a polynomial in regularization mass $M$, and they renormalize classical part of the surface action. We reveal the dependence of CE on the coupling constant $a$. Corresponding Casimir force is attractive for all values of $a$. For $a\to\infty$ we reproduce the known results for CE for perfectly conducting cylindrical shell first obtained by DeRaad and Milton.Comment: Typos corrected. Some references adde