Non-Hermitian aspects of coherently coupled vertical cavity laser arrays

Two by one (2 × 1) optically coupled electrically isolated vertical cavity surface emitting laser (VCSEL) arrays have been studied both theoretically and experimentally. Because of the tunable gain/loss profile in the array, the coupled laser system is non-Hermitian in analogy with non-Hermitian quantum mechanics. The experimentally observed optical mode tuning and beam steering are inherently connected to the non-Hermiticity of the system. Theoretical investigation of the mode tuning mechanism is conducted first by coupled mode analysis, and then in a more comprehensive coupled rate equation analysis. The theoretical analysis reveals the unique mode tuning mechanism in coupled VCSEL arrays and is shown to be in excellent agreement with experimental characterization. Experimentally, 2 × 1 optically coupled electrically isolated VCSEL arrays have been designed, fabricated, and characterized. We perform two-dimensional characterizations by varying the two independently controlled injection currents into each array and recording the laser output power, spectra, near-field intensity profile, and far-field intensity profile. Two-dimensional maps of the output optical power, interference visibility, and beam steering angles versus the two injection currents are plotted as concise representations of the mode tuning behavior controlled by the current tuning. Arrays with built-in asymmetry between the two lasers demonstrate that the mode tuning behavior can also be engineered by the degree of asymmetry. The coupling coefficient is extracted from the characterizations. The theoretical and experimental investigations presented in this work reveal the unique mode tuning mechanism in weakly coupled diode laser arrays and will guide the future pursuit of improved functionalities in coupled VCSEL arrays