Three classes of array modes of closely spaced antiguides are analyzed: coupled fundamental (element) modes, coupled first-order (element) modes, and modes adjacent to coupled fundamental modes. The behavior of coupled fundamental modes as a function of lateral index step is analyzed and explained from a ray-optics point of view. It is found that at resonance, for both coupled fundamental and first-order modes, the array-mode propagation constant is virtually identical to the propagation constant of the mode of a single, unperturbed antiguide. Several types of mode discrimination mechanisms are discussed. For devices with 3- mu m-wide antiguide cores and 1- mu m interelement spacing, intermodal discrimination values of 15-20 cm/sup -1/ can be achieved. Excellent agreement is found between experimental data and theoretical predictions based on the effective-index method. >

Phase-locked arrays of antiguides: model content and discrimination

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. >

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

All-monolithic phase-locked arrays of antiguided diode lasers have recently demonstrated exceptionally high diffraction-limited powers: 0.5 W continuous wave (CW) and 2.1 W peak pulsed. An overview of theoretical and experimental work to date is presented. The performance of antiguided arrays is compared to the best results from conventional array types (evanescent-wave, Y-junction, diffraction). The two basic types of array modes: evanescent-wave and leaky-wave are discussed. Resonant leaky-wave coupling in antiguided arrays is explained and interpreted. One key new insight is revealed: when gain is placed in the low-index regions of large arrays (≥10 elements) the array mode favoured to lase is the leaky mode (in-phase or out-of-phase) closest to its respective resonance. Thus the ‘classic’ prediction of coupled-mode theory that high gain in low-index regions automatically favours in-phase mode operation is incorrect. The intrinsic array modal discrimination mechanisms (mode overlap with the gain regions [i.e. the Γ effect]; edge radiation loss, and interelement loss) as well as Talbot-type spatial filtering are briefly explained, and their respective effects on resonant and nonresonant devices are discussed. Results of rigorous modelling of antiguided arrays using two-dimensional analysis are discussed and compared, for the first time, to results obtained via the effective-index method. Finally, key electro-optical characteristics of 20-and 40-element arrays are described.

High-power monolithic phase-locked arrays of antiguided semiconductor diode lasers

We present a numerical model for directly calculating the eigenmodes of multiple-stripe gain-guided diode laser arrays, which includes the effects of both carrier diffusion and heating in the active region. Comprehensive calculations of the eigenmodes of a CW gain-guided array using this model are directly compared to experimental observations on commercial ten-stripe arrays. These numerical and experimental results show that, contrary to popular wisdom, gain-guided arrays are characterized by a large number of eigenmodes, not limited to the number of elements in the array. In addition, our results show the importance of including the refractive index perturbation arising from junction heating, which dramatically alters both the character and the gain of the array modes.

Free-running modes for gain-guided diode laser arrays

The Bloch‐function method is used to provide a simple, yet accurate treatment of the leaky modes of infinite‐extent antiguided arrays. Laterally resonant modes of infinite arrays are described for the first time. Bloch‐function solutions for infinite arrays are used to explain key characteristics of the modes of finite‐extent antiguided arrays. It is found that the resonant modes of antiguided arrays satisfy the second‐order lateral Bragg condition, and consequently are analogous to the modes of second‐order distributed‐feedback (DFB) lasers. In effect, the resonant‐optical‐waveguide (ROW) array is a second‐order lateral DFB structure with the radiative component along the longitudinal device axis, and zero stopband.

Simple description of laterally resonant, distributed‐feedback‐like modes of arrays of antiguides

A method for analyzing arbitrary one-dimensional waveguides is described and applied to find the lateral modes of gain-guided laser arrays directly, without the need for a coupled-mode approximation. Detailed results are given for a four-element array for which experimental results are available, and the effect of varying device parameters on the relative gains of the modes is considered. The results show differences between gain-guided and real-index guided arrays which are not evident in prior analyses.

W. Marshall

Papers

Direct analysis of gain-guided phase-locked semiconductor laser arrays