Electromagnetically induced negative refractive index in a V-type four-level atomic system

We propose a scheme for realizing negative refractive index in a V-type four-level atomic system. It is shown that the negative refractive index can be achieved in a wide frequency band based on the effect of quantum coherence. It is also found that the frequency band of negative refractive index and the absorption property of left-handed material are manipulated by the pump and control fields. Furthermore, left-handed material with reduced absorption is possible by choosing appropriate parameters. (c) 2006 Elsevier B.V. All rights reserved.

Double injection: high frequency noise and temperature dependence

Noise measurements from 140°K to 350°K ambient temperature and between 10kHz and 22MHz performed on a double injection silicon diode as a function of operating point indicate that the high frequency noise depends linearly on the ambient temperature T and on the differential conductance g measured at the same frequency. The noise is represented quantitatively by〈i^2〉 = α•4kTgΔf. A new interpretation demands Nyquist noise with α ≡ 1 in these devices at high frequencies. This is in accord with an equivalent circuit derived for the double injection process. The effects of diode geometry on the static I-V characteristic as well as on the ac properties are illustrated. Investigation of the temperature dependence of double injection yields measurements of the temperature variation of the common high-level lifetime τ(τ ∝ T^2), the hole conductivity mobility µ_p (µ_p ∝ T^(-2.18)) and the electron conductivity mobility µ_n(µ_n ∝ T^(-1.75)).

Equivalent differential equations for nonlinear dynamical systems

A technique for obtaining approximate periodic solutions to nonlinear ordinary differential equations is investigated. The approach is based on defining an equivalent differential equation whose exact periodic solution is known. Emphasis is placed on the mathematical justification of the approach. The relationship between the differential equation error and the solution error is investigated, and, under certain conditions, bounds are obtained on the latter. The technique employed is to consider the equation governing the exact solution error as a two point boundary value problem. Among other things, the analysis indicates that if an exact periodic solution to the original system exists, it is always possible to bound the error by selecting an appropriate equivalent system.

Three equivalence criteria for minimizing the differential equation error are compared, namely, minimum mean square error, minimum mean absolute value error, and minimum maximum absolute value error. The problem is analyzed by way of example, and it is concluded that, on the average, the minimum mean square error is the most appropriate criterion to use.

A comparison is made between the use of linear and cubic auxiliary systems for obtaining approximate solutions. In the examples considered, the cubic system provides noticeable improvement over the linear system in describing periodic response.

A comparison of the present approach to some of the more classical techniques is included. It is shown that certain of the standard approaches where a solution form is assumed can yield erroneous qualitative results.

Anomalous behaviour of photorefractive grating erasure owing to existence of both negative and positive carriers

In LiNbO3:Fe, anomalous behaviour of grating erasure is observed with different wavelenghts, i.e. rapid grating erasure in the short wavelength range, which deviates from the results predicted by the electron transport band model. The deviation is related to the coexistance of electrons and holes in photorefraction, and charge-transfer process including electrons and hole has been proposed. The electron and hole contributions to photo-excitation coefficient S of the Fe centre on the wavelength.

Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

An investigation of the reaction negative K¯p → K¯π⁺ at P_(lab) = 2 Gev/c

The reaction K^-p→K^-π⁺n has been studied for incident kaon momenta of 2.0 GeV/c. A sample of 19,881 events was obtained by a measurement of film taken as part of the K-63 experiment in the Berkeley 72 inch bubble chamber.

Based upon our analysis, we have reached four conclusions. (1) The magnitude of the extrapolated Kπ cross section differs by a factor of 2 from the P-wave unitarity prediction and the K⁺n results; this is probably due to absorptive effects. (2) Fits to the moments yield precise values for the Kπ S-wave which agree with other recent statistically accurate experiments. (3) An anomalous peak is present in our backward K^-p→(π+n) K^- u-distribution. (4) We find a non-linear enhancement due to interference similiar to the one found by Bland et al. (Bland 1966).

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .2. TIME-DEPENDENT TRANSMISSION THEORY

By generalization of the methods presented in Part I of the study [J. Opt. Soc. Am. A 12, 600 (1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions. (c) 2006 Elsevier Ltd. All rights reserved.

The tunable negative refractive index in granular composite

The effective refractive index of a kind of granular composite, which consists of granular metallic and magnetic inclusions with different radius embedded in a host medium, is theoretically investigated. Results show that for certain volume fractions of these two inclusions, the negative permittivity peak shifts to low frequency and the peak value increases with increasing radius ratio of the radius of magnetic granulae to that of metallic granulae. Simultaneously, peak value of permeability decreases with the radius ratio, and value peak shifts to high frequency with increasing volume fraction of magnetic inclusion. Therefore, the radius ratio can affect the effective refractive index considerably, and it is found that by adjusting the radius ratio, the refractive index may change between negative and positive values for certain volume fractions of the two inclusions. (c) 2005 Elsevier B.V. All rights reserved.

Negative refraction via domain wall resonances in a homogeneous mixture of ferro- and nonmagnetic substances

We deliver the general conditions on the synthetic proportions for a homogeneous mixture of ferro- and nonmagnetic substances to become left-handed. As an alternative for left-handed metamaterials, we consider mixing ferromagnetic materials with nonmagnetic microscopic particles. In the mixture, the ferromagnetic material provides the needed permeability via domain wall resonances at high frequencies, whereas the nonmagnetic material gives the required permittivity. Using the effective medium theory, we have found that when the concentration of the nonmagnetic particles falls into a certain range, the refractive index of the mixture is negative, n < 0, which includes the double negative ( epsilon < 0 and mu < 0) and other cases ( e. g. epsilon < 0 and mu > 0). We finally give the requirements on the microscopic material properties for the ferromagnetic materials to reach the domain wall resonances at high frequencies.