Complex coupling coefficient in laterally coupled microcavity laser diode arrays

Abstract

The complex component of the coupling coefficient κ=κr+iκi, used to describe the coupling between adjacent semiconductor microcavity laser diodes, is studied. The complex component κi represents the gain or loss difference between the coherent in-phase and out-of-phase array supermodes obtained from two laterally coupled lasers. Steady-state analysis reveals that the threshold of the preferred coherent supermode is lower than that of an individual laser mode in proportion to κi. We show that the complex component κi can be experimentally extracted from a simple output power vs current measurement. Furthermore, the change in the lasing threshold at the onset of optical coupling perturbs the differential resistance of the coupled lasers. Therefore, an electrical signature of optical coupling can be detected in the diode array series resistance.

Dynamics of Evanescently-Coupled Laser Pairs With Unequal Pumping: Analysis Using a Three-Variable Reduction of the Coupled Rate Equations

“…For this we needed the value of τ N which is not given in [12]; since in other publications, e.g. [8,17,25], these authors use τ N = 2 ns, that value was assumed here. Our results indicate that only the out-of-phase case shows stability and moreover the range of stable solutions, as bounded these bifurcations, is very limited for this array.…”

“…The steady state solutions of ( 5) -( 7) can be found explicitly by using the approximation sinψ s ≅−q which is consistent with ητ p << 1, m s << 1, where the subscript 's' denotes the steady-state value. The results can then be written as In the limit of equal pumping Q A = Q B , q = 0, (9) and (11) reduce to the forms in (25), (26) and (29) of [16], whilst (10) reduces to the forms of ( 27) and (28) of [16] but without the terms of order ητ p which appear in the latter. Since we assume ητ p << 1, this omission should only result in a very small error in the accuracy of (10).…”

Supermode Switching in Coherently-Coupled Vertical Cavity Surface Emitting Laser Diode Arrays

“…where α diff is the differential gain, τ N is the carrier lifetime, τ P is the cavity photon lifetime, α m is the mirror loss, V a is the active volume of the laser array [14]. These latter parameters are considered constant while ΔP and P uncoupled are the two experimental variables that dictate |κ i |.…”

“…Furthermore, the gain of the lowest loss array supermode will be less than that of a single cavity individual mode. As a consequence, when the VCSEL array is tuned into coherent operation, an increase of the coherent array output power is observed and has recently been characterized [14].…”

Complex Waveguide Supermode Analysis of Coherently-Coupled Microcavity Laser Arrays

“…The imaginary part of the coupling coefficient represents the gain difference between the elements, which dictates which of the nearly degenerate supermodes is dominant [5]. We recently reported a technique to experimentally measure both the real and imaginary components of the coupling coefficient using simultaneous measurements of output power, near-field intensity, and far-field profile [14,15]. In this work we will focus on a 2D waveguide model corresponding to 2×1 photonic crystal VCSEL array structures and evaluate the effects of a few key design parameters on the complex coupling coefficient.…”