Electromagnetic Density Of Modes Research Articles

Anisotropic Light Scattering in Nanoporous Materials: A Photon Density of States Effect

Similar to spontaneous emission of photons and inelastic (Raman) scattering, elastic (Rayleigh) scattering of light is controlled by spectral and spatial distribution of photon density of states, DOS (density of electromagnetic modes). However, to date Rayleigh scattering in nanoporous media has not become the subject of discussion in the context of photon DOS effects. In this paper, we consider light scattering in porous materials in the context of spectral, spatial, and angular redistribution of photon DOS in materials with pores whose size and spacing are of the order of light wavelength. The DOS effect results in predictable and controllable modification of scattering and can be purposefully used in certain light harvesting and illumination systems. A possible role of the effect in the cornea of eye is outlined for seeing at grazing incidence of light beams with respect to an eye pupil.

Electromagnetic density of modes for a finite-size three-dimensional structure.

The concept of the density of modes has been lacking a precise mathematical definition for a finite-size structure. With the explosive growth in the fabrication of photonic crystals and nanostructures, which are inherently finite in size, a workable definition is imperative. We give a simple and physically intuitive definition of the electromagnetic density of modes based on the Green's function for a generic three-dimensional open cavity filled with a linear, isotropic, dielectric material.

Electromagnetic mode density at the band edge of a 1D graded periodic dielectric structure

Analytical expressions are derived for electromagnetic mode density in 1D periodic dielectric structures consisting of dielectric slabs of different dielectric constants. Firstly, the Maxwell's equation is solved for a dielectric scatterer block that contains two dielectric slabs of different dielectric constants, and then it is solved for a dielectric scatterer block that contains three dielectric slabs of different dielectric constants. Finally, a generalized expression for the dielectric scatterer block, containing n dielectric slabs of different dielectric constants, is written. The dependence of the photonic band gap upon the dielectric contrast, dimensions of the unit cell, and number of periods is investigated. The various properties of mode density at the band edge are discussed for both the quarter-wave stack as well as the generalized case. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005.

Multiple-wavelength lasing in one-dimensional bandgap structures: implementation with active n–i–p–i layers

We study the optical localized states in a one-dimensional system of strongly coupled defect microcavities for the case when a tight-binding approximation is not valid. Transmission and electromagnetic mode density spectra as well as the distribution of light intensity inside the bandgap material are investigated. We report on the effect of splitting the fundamental coupled-cavity mode into several high-Q submodes to support perfect transmission of light at low group-velocity values. New types of laser microcavities that provide low-threshold lasing at multiple wavelengths and in opposite directions are proposed. Possible implementation of the laser systems with active n–i–p–i layers is discussed.

General electromagnetic density of modes for a one-dimensional photonic crystal

In this paper, we present more general, exact, and concise expressions for calculating the electromagnetic density of modes (EDOM) in one dimension photonic crystal (superlattice) for E and H polarizations. The expression is used for numerical computation of the EDOM in the lower-index (dielectric constant) layer. We discuss the difference between the EDOM in high- and low-index layers as due to the presence of waveguiding modes and evanescent-excited Bloch modes in the higher-index layer. Two methods of computation are presented to compute the EDOM in the lower-index layer. We suggest the possibility of using the EDOM to establish population inversion, which may be useful for higher-frequency lasers (e.g., x rays) and control any radiative processes. We also elaborate on the limitations of the results of Alvarado Rodriguez et al. as due to the approximation used in the evaluation of partial differentialomega/ partial differentialk(y,z) for nabla(k)omega and comment on the limitations of the one-dimensional EDOM expression of Bendickson et al.

Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures

We present a numerical study of second-harmonic (SH) generation in a one-dimensional, generic, photonic band-gap material that is doped with a nonlinear ${\ensuremath{\chi}}^{(2)}$ medium. We show that a 20-period, 12-\ensuremath{\mu}m structure can generate short SH pulses (similar in duration to pump pulses) whose energy and power levels may be 2--3 orders of magnitude larger than the energy and power levels produced by an equivalent length of a phase-matched, bulk medium. This phenomenon comes about as a result of the combination of high electromagnetic mode density of states, low group velocity, and spatial phase locking of the fields near the photonic band edge. The structure is designed so that the pump pulse is tuned near the first-order photonic band edge, and the SH signal is generated near the band edge of the second-order gap. This maximizes the density of available field modes for both the pump and SH field. Our results show that the ${\ensuremath{\chi}}^{(2)}$ response is effectively enhanced by several orders of magnitude. Therefore, mm- or cm-long, quasi-phase-matched devices could be replaced by these simple layered structures of only a few micrometers in length. This has important applications to high-energy lasers, Raman-type sources, and frequency up- and down-conversion schemes.

Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures.

We derive an exact expression for the electromagnetic mode density, and hence the group velocity, for a finite, N-period, one-dimensional, photonic band-gap structure. We begin by deriving a general formula for the mode density in terms of the complex transmission coefficient of an arbitrary index profile. Then we develop a specific formula that gives the N-period mode density in terms of the complex transmission coefficient of the unit cell. The special cases of mode-density enhancement and suppression at the photonic band edge and also at midgap, respectively, are derived. The specific example of a quarter-wave stack is analyzed, and applications to three-dimensional structures, spontaneous emission control, delay lines, band-edge lasers, and superluminal tunneling times are discussed. \textcopyright{} 1996 The American Physical Society.

Probing femtosecond dynamics in solution on a picosecond time scale. Cavity enhancement of spontaneous emission rates in microdroplets

Fluorescence decay rate enhancement of rhodamine 6G (R6G) in levitated ethylene glycol microdroplets (4–8 μm diam.) has been observed. This effect derives from an increase (relative to extended media) in electromagnetic mode density near resonance frequencies associated with the droplet. Unlike bulk solutions, fluorescence lifetimes ( T 1) in microcavities carry information on electronic polarization dephasing ( T 2) on a femtosecond time scale. Thus, femtosecond dynamics can be probed indirectly via fluorescence with a time resolution of several picoseconds. The value of T 2 in ethylene glycol estimated from our measurements agrees well with values obtained from direct femtosecond probes.

Progress in Weyl's problem achieved by computational methods

The smoothed eigenvalue distribution for the scalar, and the electromagnetic vector, wave equations are studied for large, but finite wavenumbers k by counting the first 10 6 eigenvalues for various shapes of the domain. The results have implications on the Fermi-gas model of nuclear matter, the electron gas as well as the long-wave acoustic vibration modes in small crystals, the laws of black-body radiation, the acoustics of complicated resonators, and the thermodynamics of perfect gases in a finite volume. The relevance of the computational procedure is compared to that of the analytical methods yielding asymptotic expansions for the eigenvalue distribution which are valid in the limit of infinite k. As an illustrative example for the computational procedure, we present the calculation of the electromagnetic mode density in a lossless cavity resonator with the shape of a circular cylinder. This calculation comprehends the computation of the first 10 4 zeros of the Bessel functions.