G.R. Hadley

Transparent boundary condition for the beam propagation method

A new boundary condition is presented for use in beam propagation calculations that passes outgoing radiation freely with minimum reflection coefficient (as low as 3*10/sup -8/). In conjunction with a standard Crank-Nicholson finite difference scheme, the assumption that the radiation field behaves as a complex exponential near the boundary is shown to result in a specific transparent boundary condition algorithm. In contrast to the commonly used absorber method, this algorithm contains no adjustable parameters, and is thus problem independent. It is shown to be accurate and robust for both two- and three-dimensional problems. >

Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers

This paper discusses the issues involving the design and fabrication of vertical-cavity surface-emitting lasers (VCSELs). A review of the basic experimental structures is given, with emphasis on recent developments in distributed Bragg reflectors, gain media, as well as current and optical confinement techniques. The paper describes present VCSEL performance, in particular, those involving selective oxidation and visible wavelength operation.

Comprehensive numerical modeling of vertical-cavity surface-emitting lasers

We present a comprehensive numerical model for vertical-cavity surface-emitting lasers that includes all major processes affecting cw operation of axisymmetric devices. In particular, our model includes a description of the 2-D transport of electrons and holes through the cladding layers to the quantum well(s), diffusion and recombination of these carriers within the wells, the 2-D transport of heat throughout the device, and a multilateral-mode effective index optical model. The optical gain acquired by photons traversing the quantum wells is computed including the effects of strained band structure and quantum confinement. We employ our model to predict the behavior of higher-order lateral modes in proton-implanted devices and to provide an understanding of index-guiding in devices fabricated using selective oxidation.

Scalability of small-aperture selectively oxidized vertical cavity lasers

We analyze the threshold properties of small area selectively oxidized vertical cavity lasers. Agreement for threshold gain versus laser size is found using the experimental intrinsic threshold voltage matched with a gain theory, as compared to a two-dimensional optical cavity simulation. Our analysis indicates the increasing threshold current density of small area lasers arises from both increasing threshold gain and the concomitant increasing leakage current. We further show that the optical loss can be reduced for lasers with areas as small as 0.25 μm2 while maintaining sufficient transverse optical confinement by displacing the apertures longitudinally away from the cavity and reducing the oxide thickness.

High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners

For part I see ibid., p. 1210, 2002. We present a discussion of the behavior of the electric and magnetic fields satisfying the two-dimensional Helmholtz equation for waveguides in the vicinity of a dielectric corner. Although certain components of the electric field have long been known to be infinite at the corner, it is shown that all components of the magnetic field are finite, and that finite-difference equations may be derived for these fields that satisfy correct boundary conditions at the corner. These finite-difference equations have been combined with those derived in the previous paper to form a full-vector waveguide solution algorithm of unprecedented accuracy. This algorithm is employed to provide highly accurate solutions for the fundamental modes of a previously studied standard rib waveguide structure.

Coherent beams from high efficiency two‐dimensional surface‐emitting semiconductor laser arrays

We have fabricated and operated large two‐dimensional (2D) arrays of phase‐locked surface‐emitting semiconductor lasers. The arrays were fabricated by reactive ion beam etching of epitaxial Fabry–Perot resonators comprising GaAs/AlGaAs quantum wells surrounded by AlAs‐AlGaAs quarter‐wave mirrors. Different arrays corresponding to different pixel size (2–5 μm) and spacing (1–2 μm) were produced to investigate evanescent coupling between pixels. The arrays were photopumped so that the array size could be conveniently varied from 1×1, 2×2,... up to 20×20. Except for the 1×1 which emits a circular pattern, all arrays exhibit a well‐defined four‐lobed far‐field pattern in agreement with our theoretical analysis of the optical modes which predicts domination by the 2D out‐of‐phase eigenmode. As a consequence this pattern can be understood with simple Fraunhofer diffraction theory. The angular spread of the lobes, determined by the periodicity of the array elements, is 10° for the array with element size/spacing...

On-axis far-field emission from two-dimensional phase-locked vertical cavity surface-emitting laser arrays with an integrated phase-corrector

We have fabricated large, two‐dimensional (2D) arrays of optically pumped, phase‐locked vertical cavity surface‐emitting lasers that emit more than 50% of their light in a central on‐axis lobe. The emission of the arrays was modified from the usual four‐lobed far‐field of 2D coupled arrays by incorporation of a binary phase‐shift mask on the surface of the array. The array consists of Fabry–Perot resonators comprising GaAs/AlGaAs quantum wells surrounded by AlAs/AlGaAs quarterwave mirrors with a multiple order AlGaAs phase‐delay layer on the top mirror stack. The phase‐shift layer was etched away on alternating elements of the array. The resulting on‐axis emission had an angular width of 2° for an array of approximately 100 elements.

Single‐frequency continuous‐wave operation of ring resonator diode lasers

We report continuous‐wave room‐temperature operation of a semiconductor ring resonator diode laser with a single Y‐junction outcoupling waveguide. This device with a 150 μm radius and 8‐μm‐wide etched‐rib waveguide has a threshold current of 72 mA and emits up to 1 mW of single‐frequency output. The side‐mode‐rejection ratio of this laser exceeds 22 dBm over a ≳50 mA current range corresponding to a stable operating mode of the laser. Studies of the emission behavior in this and other similar ring lasers suggest that the ring is lasing in ‘‘whispering gallery’’ modes, and also that the Y junction is affecting mode selection in the ring.

High-accuracy finite-difference equations for dielectric waveguide analysis I: uniform regions and dielectric interfaces

A methodology is presented that allows the derivation of low-truncation-error finite-difference representations or the two-dimensional Helmholtz equation, specific to waveguide analysis. This methodology is derived from the formal infinite series solution involving Bessel functions and sines and cosines. The resulting finite-difference equations are valid everywhere except at dielectric corners, and are highly accurate (from fourth to sixth order, depending on the type of grid employed). None the less, they utilize only a nine-point stencil, and thus lead to only minor increases in numerical effort compared with the standard Crank-Nicolson equations.

Comprehensive modeling of diode arrays and broad-area devices with applications to lateral index tailoring

A numerical model for calculating the emission characteristics of diode laser arrays and broad-area devices operating well above threshold is discussed. This model uses the beam propagation technique for determining the field intensities for several lateral modes, while simultaneously and self-consistently solving for the two-dimensional current flow through the laser structure and the subsequent carrier diffusion in the active region. The active-region temperature distribution is also computed in a self-consistent manner, based on the flow of heat generated in the active region through the layered device structure to a constant-temperature heat sink. The model is applied by investigating the sensitivity of the lasing modes of a broad-area diode laser to variations in the lateral temperature distribution. >