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

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

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

General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond

We derive general expansion formulas in vibrational coordinates for all bimodal Jahn–Teller and pseudo-Jahn–Teller Hamiltonians in tetragonal symmetry. Symmetry information of all the vibronic Hamiltonian matrix elements is fully carried by up to only 4 eigenvalues of symmetry operators. This problem-to-eigenvalue reduction enables us to handle thousands of vibronic problems in one work. The derived bimodal formulas can be easily extended to cover problems with one or more than two vibrational modes. They lay a solid foundation for future vibronic coupling studies of tetragonal systems. More importantly, the efficient derivation can be applied to handle (pseudo-)Jahn–Teller Hamiltonians for all problems with one principal symmetry axis

Modal analysis of semiconductor lasers with nonplanar mirrors

We present a formalism for analyzing laser resonators which possess nonplanar mirrors and lateral waveguiding [e.g., an unstable resonator semiconductor laser (URSL)]. The electric field is expanded in lateral modes of the complex-index waveguide and is required to reproduce itself after, one roundtrip of the cavity. We show how the waveguide modes, their gain and loss, and hence the criterion for truncation of the infinite set of modes can be derived from the Green's function of the one-dimensional eigenvalue equation for the waveguide. Examples are presented for three cases of interest - a purely gain-guided URSL, an index-guided URSL, and a gain-guided tilted-mirror resonator. We compare theoretical calculations to previous experiments