Analysis of surface-emitting second-order distributed feedback lasers with central grating phaseshift

Abstract

An analysis of 2nd-order distributed feedback lasers (DFB) with central grating phaseshift is performed. The devices have an active grating (ie, DFB) section, passive grating sections (ie, DBRs); and the active grating is formed at a metal-semiconductor interface. Coupled-mode theory and the transfer matrix method are employed. It is found that a central grating phaseshift, Δϕ, of 180° causes the laser to radiate in a beam of symmetric near-field amplitude profile, in sharp contrast to conventional second-order DFB lasers which radiate in beams of asymmetric near-field amplitude profile. In turn the far-field profile becomes a single-lobe beam pattern. Thus, a means to fundamentally obtain surface emission in an orthonormal single-lobe beam from a 2nd-order DFB/DBR device has been found. The orthornomal-beam emission is achieved at no penalty in device efficiency. External differential quantum efficiencies, η <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> , in excess of 70% can be obtained, and the guided-field intensity profile is substantially uniform. The effects of the lengths of the DFB section (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DFB</sub> ) and of each of the DBR sections (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DBR</sub> ) on device performance are analyzed and optimal values are found to occur for L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DFB</sub> in the 500-700 μm range and for L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DBR</sub> in the 600-700 μm range. One can obtain η <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> values as high as 76% from devices with 80% of the energy in the central lobe, and moderate threshold gains (ie, 40 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ). Threshold gains as low as 25 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> can also be obtained from highly efficient devices (ie, η <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> ≅70%), at some penalty in guided-field uniformity. In either case the intermodal discrimination is quite high (70-75 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ). Gratings with half-wave (ie, π) phaseshifts have been fabricated by using the dual-tone photoresist method, and the concept has been experimentally proven: orthonormal, single-lobe emission in a diffraction-limited beam from 1500 μm-long devices. Extension to two-dimensional (2-D) large-aperture: 200 μm×1500 μm; surface emitters is quite possible, which should allow for the emission of watts of coherent CW power in a stable, single mode. The 2-D structure represents a defect-free, second-order active photonic lattice.