Self-collimated unstable resonator semiconductor laser

Self-collimation of the output is achieved in an unstable resonator semiconductor laser by providing a large concave mirror M sub 1 and a small convex mirror M sub 2 on opposite surfaces of a semiconductor body of a material having an effective index of refraction denoted by n, where the respective mirror radii R sub 1, R sub 2 and beam radii r sub 1, r sub 2 are chosen to satisfy a condition (R sub 2)/(1 + r sub 1) = (n - 1)/n, with a value of geometric magnification 1 less than or equal to M less than or equal to (n + 1)/(n - 1) where r sub 1 and r sub 2 are the radii of counterpropagating beams at respective mirrors of radii R sub 1 and R sub 2

Multiperiod-grating surface-emitting lasers

Surface-emitting distributed feedback (DFB) lasers are disclosed with hybrid gratings. A first-order grating is provided at one or both ends of the active region of the laser for retroreflection of light back into the active region, and a second-order or nonresonant grating is provided at the opposite end for coupling light out perpendicular to the surfaces of the laser or in some other selected direction. The gratings may be curved to focus light retroreflected into the active region and to focus light coupled out to a point. When so focused to a point, the DFB laser may be part of a monolithic read head for a laser recorded disk, or an optical coupler into an optical fiber

Shear viscosity from Kubo formalism: NJL-model study

A large-$N_{\rm c}$ expansion is combined with the Kubo formalism to study the shear viscosity $\eta$ of strongly interacting matter in the two-flavor NJL model. We discuss analytical and numerical approaches to $\eta$ and investigate systematically its strong dependence on the spectral width and the momentum-space cutoff. Thermal effects on the constituent quark mass from spontaneous chiral symmetry breaking are included. The ratio $\eta/s$ and its thermal dependence are derived for different parameterizations of the spectral width and for an explicit one-loop calculation including mesonic modes within the NJL model.Comment: 14 pages, 11 figures. Revision includes additionally the spectral width at one-loop level (chapter V) and Appendix A. Matches published versio

Semiclassical theory of noise in multielement semiconductor lasers

We present a derivation of the noise spectra of multielement semiconductor lasers. We model the noise by a set of Langevin sources which drive a system of small-signal field equations. The Langevin sources are normalized to transition rates within the laser and general formulas for relative intensity, frequency fluctuation, and field spectra are produced. We evaluate the formulas for several specific cases of interest, including those of a passive-active resonator and active-active coupled cavity resonator. In each case, the linewidth is governed by effective α-parameter(s) which generally differ from the material parameter. In the active-active cavity, the linewidth consists of two parts, one which is similar to the Schawlow-Townes linewidth, and a second which is proportional to the FM modulation index

Intermodal stability of a coupled-cavity semiconductor laser

We present an analysis of the steady-state operation of a two-element coupled-cavity laser near a mode hop. The equations of motion for the two cavities and two relevant modes of a longitudinally coupled-cavity laser are reduced to a system of nondimensional nonlinear ordinary differential equations which describe a general two-element laser. The equations are then solved and the stability of their solutions is analyzed. Depending upon the fill factors for the two modes, there exists an intrinsically multimode oscillation for operating conditions under which it was previously thought that no steady state existed. Under conditions where the multimode state is unstable, both of the single-mode states are stable with bistable transitions occurring only on the boundaries of the unstable multimode regimes

Coupling coefficients for coupled-cavity lasers

We derive simple, analytic formulas for the field coupling coefficients in a two-section coupled-cavity laser using a local field rate equation treatment. We show that there is a correction to the heuristic formulas based on power flow calculated by Marcuse; the correction is in agreement with numerical calculations from a coupled-mode approach

Beyond Megalopolis: Exploring America’s New “Megapolitan” Geography

The Metropolitan Institute at Virginia Tech identifies ten US “Megapolitan Areas”— clustered networks of metropolitan areas that exceed 10 million total residents (or will pass that mark by 2040) . Six Megapolitan Areas lie in the eastern half of the United States, while four more are found in the West. Megapolitan Areas extend into 35 states, including every state east of the Mississippi River except Vermont. Sixty percent of the Census Bureau’s “Consolidated Statistical Areas” are found in Megapolitan Areas, as are 39 of the nation’s 50 most populous metropolitan areas. As of 2003, Megapolitan Areas contained less than a fifth of all land area in the lower 48 states, but captured more than two-thirds of total US population with almost 200 million people. Megapolitan Areas are expected to add 83 million people (or the current population of Germany) by 2040, accounting for seven in every ten new Americans. By 2040, a projected 33 trillion dollars will be spent on Megapolitan building construction. The figure represents over three quarters of all the capital that will be expended nationally on private real estate development. In 2004, Democratic candidate John Kerry won the Megapolitan Area popular vote by 51.6 percent to 48.4 for President George W. Bush—or almost the exact reverse of the nation as a whole. Kerry received 46.4 million Megapolitan votes, while Bush won 43.5 million. Megapolitan geography reframes many planning and public policy debates, touching on such issues as environmental impact, transportation, and urban sprawl

An exact formulation of coupled-mode theory for coupled-cavity lasers

Coupled-mode rate equations for coupled-cavity lasers are derived using a novel approach. The method, based on the Mittag-Leffler theorem, is exact. The coupling coefficients are compared to those derived by several different approximations

Analysis of the dynamic response of multielement semiconductor lasers

We present a derivation of the dynamic response of a semiconductor laser consisting of more than one active element. We show that the amplitude and phase of the modulated cavity adiabatically follows the complex resonance of the composite cavity; and using this relation, plus linearized carrier equations, we calculate the parameters characterizing the modulation response of the composite system. In the process, "effective" differential gain constants and linewidth enhancement factors arise which take the place of the corresponding parameters in single-element lasers. In the case of a two-section laser, we show that frequency chirping under modulation is present except under special conditions; we identify those conditions and show how chirping can be avoided

Shear Viscosities from Kubo Formalism in a large-NcN_{\rm c} Nambu--Jona-Lasinio Model

In this work the shear viscosity of strongly interacting matter is calculated within a two-flavor Nambu--Jona-Lasinio model as a function of temperature and chemical potential. The general Kubo formula is applied, incorporating the full Dirac structure of the thermal quark spectral function and avoiding commonly used on-shell approximations. Mesonic fluctuations contributing via Fock diagrams provide the dominant dissipative processes. The resulting ratio $\eta/s$ (shear viscosity over entropy density) decreases with temperature and chemical potential. Interpolating between our NJL results at low temperatures and hard-thermal-loop results at high temperatures a minimum slightly above the AdS/CFT benchmark $\eta/s=1/4\pi$ is obtained.Comment: 15 pages, 11 figures. Revision with minor corrections matches published versio