On the number and location of short geodesics in moduli space

A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.Comment: 23 pages, 1 figur

Abstract commensurators of braid groups

Let B_n be the braid group on n strands, with n at least 4, and let Mod(S) be the extended mapping class group of the sphere with n+1 punctures. We show that the abstract commensurator of B_n is isomorphic to a semidirect product of Mod(S) with a group we refer to as the transvection subgroup, Tv(B_n). We also show that Tv(B_n) is itself isomorphic to a semidirect product of an infinite dimensional rational vector space with the multiplicative group of nonzero rational numbers.Comment: 10 page

Arrangement for damping the resonance in a laser diode

An arrangement for damping the resonance in a laser diode is described. This arrangement includes an additional layer which together with the conventional laser diode form a structure (35) of a bipolar transistor. Therein, the additional layer serves as the collector, the cladding layer next to it as the base, and the active region and the other cladding layer as the emitter. A capacitor is connected across the base and the collector. It is chosen so that at any frequency above a certain selected frequency which is far below the resonance frequency the capacitor impedance is very low, effectively shorting the base to the collector

Diffraction coupled phase-locked semiconductor laser array

A new monolithic, diffraction coupled phase-locked semiconductor laser array has been fabricated. Stable narrow far-field patterns (~3°) and peak power levels of 1 W have been obtained for 100-µm-wide devices with threshold currents as low as 250 mA. Such devices may be useful in applications where high power levels and stable radiation patterns are needed

Double heterostructure lasers with facets formed by a hybrid wet and reactive-ion-etching technique

Double heterostructure lasers were fabricated in which one of the laser facets was produced by a hybrid wet and reactive-ion-etching technique. This technique is suitable for GaAs/GaAlAs heterostructure lasers and utilizes the selectivity of the plasma in preferentially etching GaAs over GaAlAs. Lasers fabricated by this technique are compatible with optoelectronic integration and have threshold currents and quantum efficiency comparable to lasers with both mirrors formed by cleaving. The technique enables the use of relatively higher pressures of noncorrosive gases in the etch plasma resulting in smoother mirror surfaces and further eliminates the nonreproducibility inherent in the etching of GaAlAs layers

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

Tilted-mirror semiconductor lasers

Broad-area GaAs heterostructure lasers with a tilted mirror were demonstrated for the first time, with the tilted mirror fabricated by etching. These lasers operate in a smooth and stable single lateral mode with a high degree of spatial coherence. The suppression of filamentation manifests itself in a high degree of reproducibility in the near-field pattern