The objective of this paper is to present an overview of topics related to one of the fundamental parameters for semiconductor lasers-the linewidth broadening factor α that describes the coupling between carrier-concentration-induced variations of real and imaginary parts of susceptibility. After introducing the definition of α and discussing its dependence on carrier concentration, photon energy, and temperature, we give a short historical summary on how the concept of α evolved over the past two decades. This is followed by a discussion of α dependence on device structure in gain-guided and subdimensional lasers (quantum wells and quantum wires). The bulk of the paper is devoted to a detailed review of laser properties influenced by α and of associated methods of estimating the value of α. Results of measurements reported to date are collected and the most reliable methods are indicated.

Linewidth broadening factor in semiconductor lasers--An overview

Beams of light interacting with nonlinear-optical materials naturally form complex transverse profiles. Self-focusing, filamentation, modulational instabilities, spontaneous pattern formation and symmetry breaking, nonlinear waveguiding, and transverse mode excitation are but some of the many phenomena that are observed in lasers, in optical bistability, and in the free interaction of beams. As an introduction to a special issue of the Journal of the Optical Society of America B on transverse effects in nonlinear-optical systems, we provide this overview of history and current work.

Overview of transverse effects in nonlinear-optical systems

The static characteristics of gain‐guided double‐heterostructure semiconductor lasers are modeled using a beam‐propagation method that is capable of including both the axial and lateral variations of the optical‐mode and carrier‐density profiles. The use of the fast‐Fourier‐transform algorithm for the lateral mode propagation results in a relatively fast numerical procedure to obtain the self‐consistent solution of the wave equation coupled to a nonlinear carrier‐diffusion equation. To compare it with previous work, the model is applied to study the above‐threshold behavior of an axially uniform AlGaAs laser. The inclusion of axial effects leads to minor (∼few percent) quantitative changes. As a novel application of the beam‐propagation model, a tapered‐stripe AlGaAs laser is analyzed in detail. In this axially nonuniform device the lateral profiles for the carrier density and the forward and backward waves exhibit considerable axial variations and affect the behavior both qualitatively and quantitatively. The calculated results are in reasonable agreement with the reported experimental observations.

Fast‐Fourier‐transform based beam‐propagation model for stripe‐geometry semiconductor lasers: Inclusion of axial effects

A two-dimensional model for quantum-well lasers that solves, self-consistently, the semiconductor equations together with the complex scalar wave equation is described. It incorporates a position- and wavelength-dependent gain function which is derived from a quantum mechanical calculation. Such a model enables one to predict the characteristics of a quantum-well laser with a minimal number of empirical parameters. The output of the model includes light-current characteristics, the current distribution, and the optical field intensity distribution, obtained simultaneously in the calculation. Examples for modeling GRIN-SCH SQW (graded-index separate confinement heterostructure single quantum well) ridge wave guide lasers are given, and good agreement with experimental results is obtained. The model is used to optimize the geometry of a GRIN-SCH SQW laser for minimum threshold current and maximum efficiency. >

A self-consistent two-dimensional model of quantum-well semiconductor lasers: optimization of a GRIN-SCH SQW laser structure

We report the light-current (L-I), spectral, and far-field characteristics of quantum cascade lasers (QCLs) with seven different wavelengths in the /spl lambda/=4.3 to 6.3 /spl mu/m range. In continuous-wave (CW) mode, the narrow-stripe (/spl ap/13 /spl mu/m) epitaxial- side-up devices operated at temperatures up to 340 K, while at 295 K the CW output power was as high as 640 mW with a wallplug efficiency of 4.5%. All devices with /spl lambda//spl ges/4.7 /spl mu/m achieved room-temperature CW operation, and at T=200 K several produced powers exceeding 1 W with /spl ap/10% wallplug efficiency. The data indicated both spectral and spatial instabilities of the optical modes. For example, minor variations of the current often produced nonmonotonic hopping between spectra with envelopes as narrow as 5-10 nm or as broad as 200-250 nm. Bistable beam steering, by far-field angles of up to /spl plusmn/12/spl deg/ from the facet normal, also occurred, although even in extreme cases the beam quality never became worse than twice the diffraction limit. The observed steering is consistent with a theory for interference and beating between the two lowest order lateral modes. We also describe simulations of a wide-stripe photonic-crystal distributed-feedback QCL, which based on the current material quality is projected to emit multiple watts of CW power into a single-mode beam at T=200 K.

Beam steering in high-power CW quantum-cascade lasers

The rate equations used to find carrier and photon densities in semiconductor lasers are extended to include a spatial variation of the carrier density in the junction plane and combined with a field equation for calculation of the intensity distribution. The equations are solved for both static and dynamic cases, and the model is able to account for nonlinear light current characteristics, near field displacements, and self-sustained pulsations in lasers without a built-in guiding mechanism. The results are compared to both experimental results and predictions from other models.

J. Buus

Papers

Models of the static and dynamic behavior of stripe geometry lasers