Notes on Certain (0,2) Correlation Functions

In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations. Ordinary quantum chiral rings reflect worldsheet instanton corrections to correlation functions involving products of Dolbeault cohomology groups on the target space. The heterotic generalization described here involves computing worldsheet instanton corrections to correlation functions defined by products of elements of sheaf cohomology groups. One must not only compactify moduli spaces of rational curves, but also extend a sheaf (determined by the gauge bundle) over the compactification, and linear sigma models provide natural mechanisms for doing both. Euler classes of obstruction bundles generalize to this language in an interesting way.Comment: 51 pages, LaTeX; v2: typos fixed; v3: more typos fixe

Spectra of D-branes with Higgs vevs

In this paper we continue previous work on counting open string states between D-branes by considering open strings between D-branes with nonzero Higgs vevs, and in particular, nilpotent Higgs vevs, as arise, for example, when studying D-branes in orbifolds. Ordinarily Higgs vevs can be interpreted as moving the D-brane, but nilpotent Higgs vevs have zero eigenvalues, and so their interpretation is more interesting -- for example, they often correspond to nonreduced schemes, which furnishes an important link in understanding old results relating classical D-brane moduli spaces in orbifolds to Hilbert schemes, resolutions of quotient spaces, and the McKay correspondence. We give a sheaf-theoretic description of D-branes with Higgs vevs, including nilpotent Higgs vevs, and check that description by noting that Ext groups between the sheaves modelling the D-branes, do in fact correctly count open string states. In particular, our analysis expands the types of sheaves which admit on-shell physical interpretations, which is an important step for making derived categories useful for physics.Comment: 46 pages, LaTeX; v2: typos fixed; v3: more typos fixe

D-branes, B fields, and Ext groups

In this paper we extend previous work on calculating massless boundary Ramond sector spectra of open strings to include cases with nonzero flat B fields. In such cases, D-branes are no longer well-modelled precisely by sheaves, but rather they are replaced by `twisted' sheaves, reflecting the fact that gauge transformations of the B field act as affine translations of the Chan-Paton factors. As in previous work, we find that the massless boundary Ramond sector states are counted by Ext groups -- this time, Ext groups of twisted sheaves. As before, the computation of BRST cohomology relies on physically realizing some spectral sequences. Subtleties that cropped up in previous work also appear here.Comment: 23 pages, LaTeX; v2: typos fixed; v3: reference adde

Linearized Gravity in Brane Backgrounds

A treatment of linearized gravity is given in the Randall-Sundrum background. The graviton propagator is found in terms of the scalar propagator, for which an explicit integral expression is provided. This reduces to the four-dimensional propagator at long distances along the brane, and provides estimates of subleading corrections. Asymptotics of the propagator off the brane yields exponential falloff of gravitational fields due to matter on the brane. This implies that black holes bound to the brane have a "pancake"-like shape in the extra dimension, and indicates validity of a perturbative treatment off the brane. Some connections with the AdS/CFT correspondence are described.Comment: 31 pages, harvmac. v2: minor typo and reference corrections. v3: minor corrections to eqs and discussio

Recent Developments In Monolithic Phase-Locked Semiconductor Laser Arrays

Coherent combination of the power of several semiconductor lasers fabricated on the same substrate has been the subject of an intense research effort in recent years, the main motivation being to obtain higher power levels than those available from a single laser in a stable radiation pattern. Best results reported so far include 2.6 Watts cw emitted power and less than 10 far-field angle (in the array plane) in arrays where all the lasers are electrically connected in parallel. A different type of coherent array, where each element has a separate contact, has been recently demonstrated. While requiring the more complex two-level metallization technology, applying a separate contact to each laser provides an additional degree of freedom in the design and the operation of monolithic arrays. The separate contacts can be employed to tailor the near-field and far-field distributions and to compensate for device-to-device nonuniformities. Furthermore, the control of the currents of the array elements allows the performance of a variety of other functions, such as beam scanning, spectral mode control, wavelength tuning and control of the mutual coherence between array elements

Controlled fundamental supermode operation of phase-locked arrays of gain-guided diode lasers

Uniform semiconductor laser arrays tend to oscillate in a superposition of their supermodes, thus leading to large beam divergence and spectral spread. Discrimination among the supermodes in phase-locked arrays is discussed theoretically. It is shown that supermode discrimination in gain-guided arrays, in favor of the fundamental supermode, is made possible by the near-field interference patterns which result from the complex optical fields of the gain-guided lasers. A fundamental supermode operation is demonstrated, for the first time, in GaAlAs/GaAs gain-guided laser arrays. This is achieved by control of the current (gain) profile across the array by means of individual laser contacts

Longitudinal-mode control in integrated semiconductor laser phased arrays by phase velocity matching

The spectrum of semiconductor laser arrays with separate contacts is investigated. It is demonstrated that the individual laser currents can be selected such that the array operates in a single longitudinal mode in contrast to the multimode nature of its individual constituents. Moreover, it is possible to tune the lasing frequency by varying the laser currents. Wavelength tuning range of ~50 Å, with tuning rate of ~5 Å/mA, is demonstrated. It is suggested that these spectral features, characteristic of lasers which are coupled in parallel, result from the strong frequency dependence of their spatial mode pattern near the phase-matching frequency of their coupled waveguides

Dynamic modeling of spacecraft in a collisionless plasma

A new computational model is described which can simulate the charging of complex geometrical objects in three dimensions. Two sample calculations are presented. In the first problem, the capacitance to infinity of a complex object similar to a satellite with solar array paddles is calculated. The second problem concerns the dynamical charging of a conducting cube partially covered with a thin dielectric film. In this calculation, the photoemission results in differential charging of the object

Chirped arrays of diode lasers for supermode control

We propose nonuniform structures of phase-locked diode lasers, which make it possible to discriminate efficiently against all the higher order array supermodes (lateral modes). In these nonuniform arrays, the effective mode index in each channel varies across the array. Consequently, the envelopes of the various supermodes, including the highest order one, differ significantly from each other. Thus, by proper tailoring of the gain distribution across the array, one can conveniently select the fundamental supermode. Such fundamental supermode oscillation is essential in order to obtain single lobe, diffraction limited beams and minimal spectral spread from phase-locked laser arrays