Complex Waveguide Supermode Analysis of Coherently-Coupled Microcavity Laser Arrays

Abstract

Coherently coupled microcavity lasers have desirable properties for emerging applications. We use 2-dimensional complex refractive index waveguide modeling of 2-element photonic crystal vertical cavity surface emitting laser arrays to analyze their supermodes. The complex modal effective indices are used in turn to calculate the complex coupling coefficient between the laser array elements. An analysis of the effects of array design parameters, such as photonic crystal period, fillfactor, or confinement, to engineer the coupling coefficient for the desired properties is given and example designs for 850nm arrays are presented.

Analysis of Coherence and Coupling in Vertical Cavity Surface Emitting Laser Arrays

“…V. Modeling and Theory We build on the previously proposed waveguide model of VCSEL arrays [8] by adjusting the model parameters to fit experimental device performance. The photonic crystal parameters are given Table I.…”

“…This modeling process flow is summarized in Fig. 9 and the details of the complex coupling coefficient estimation have been previously detailed [8].…”

“…Past theoretical analysis of coupled VCSEL arrays has primarily involved one-dimensional real refractive index waveguide models [5] for the analysis of the array modes and their (real) coupling coefficient, and coupling coefficient formulations of the laser rate equations for the analysis of dynamics [6,7]. A recently developed twodimensional complex index waveguide model improves on past work by enabling the calculation of the complex coupling coefficient as a function of physical array structure [8] and is used here.…”

Fourier beam analysis of photonic crystal coupled triangular VCSEL array

“…To identify the set of injection currents which will result in emission into one dominant supermode we perform Fourier analysis on the output beam of such a triangular array 15 . First, we compute the three supermodes from the complex waveguide modal simulation.…”

“…Finally we summarize that this numerical Fourier analysis technique can be useful to identify a dominant supermode for target applications. To compute the array supermodes we utilize the complex waveguide model shown in Figure 2 13,15,17 . The real and imaginary refractive indices of the complex model are portrayed in Figure 2(b) and 2(c) respectively.…”