Modal properties of two-dimensional antiguided vertical-cavity surface-emitting laser arrays

We present a detailed analysis on 2-D (4 × 4 square-lattice) antiguided vertical-cavity surface-emitting laser (VCSEL) arrays based on the effective-index model. The calculation shows that the array can operate under 2-D resonant coupling, provided that the resonance condition in both the horizontal and vertical directions is satisfied. Consequently, the resonant-mode edge radiation loss is inversely proportional to the number of array elements along one direction for a N × N array. Low-edge-loss out-of-phase and adjacent array modes are found to compete with the in-phase resonant mode. While the 3-D gain overlap is not a significant factor in modal discrimination, the introduction of inter-element loss allows the in-phase mode to exhibit the lowest threshold gain for a wide range of inter-element width, s (Δ₈ ≈ 0.5 μm for 980-nm wavelength devices). The 2-D antiguided array results from shifting the cavity resonance between the element and inter-element regions and is fabricated by selective chemical etching and two-step metalorganic chemical vapor deposition growth. Diffraction-limited in-phase and out-of-phase array mode operation is observed from top-emitting arrays, depending on the inter-element width. Substrate-emitting array structures are investigated as a means to lower heating and increase the coherent output power