Stochastic coupled mode theory for partially coherent laser arrays

Abstract

Partially coherent, transversely coupled laser arrays are investigated within a stochastic coupled mode formalism. Predictions of the coherence or correlation functions in both the spectral and time domains are made. It is demonstrated that the coherence properties of the system in both domains are strongly dependent on the number and intensity of coupled modes. The theory can be useful for the study of semiconductor laser arrays, particularly vertical-cavity surface-emitting laser arrays.

Parity-time symmetry in coherently coupled vertical cavity laser arrays

“…While the study of PT-symmetric Hamiltonians traces to the seminal paper in 1998 [19], coherently coupled semiconductor laser arrays have been studied for more than three decades [20][21][22][23][24][25][26][27][28] for applications including high brightness beam generation [29][30][31][32], beam steering [21,27,33,34], and high bandwidth modulation [35,36]. Coupled mode theory has been used to describe the supermodes of the array [23,37,38], phase velocity matching [39], and dynamics [27,40]. However, in previous couple-mode analyses, the possibility of gain difference between the individual resonators was either not included or was implicit in a set of carrier density equations coupled to the optical field equations.…”

Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

“…Coherent optically-coupled semiconductor laser arrays have been studied experimentally and theoretically for more than four decades [1][2][3][4][5][6][7][8] . Coupled mode theory has been successful in describing the optical coupled modes and the mutual coherence in coupled laser arrays [9][10][11][12][13] . Coupled rate equations (CREs) combine coupled mode theory with semiconductor laser rate equations, and have been used for the study of temporal dynamics of optically-coupled semiconductor laser arrays 6,14 .…”

Investigating supermodes in coupled dual-element photonic crystal VCSEL arrays: a comparative analysis under strong and weak anti-guiding conditions

“…The injection current where supermodes exist is referred to as the coherently coupled regime and corresponds to roughly equal current injection into each element above threshold. The supermodes exist in two configurations: the first has the same phase in each cavity (referred to as in-phase), while the other has a π phase difference between cavities (referred to as out-of-phase) 16 as shown in Figure 2. In previous analyses, the assumption was made that ion implantation between the cavities would provide perfect electrical isolation, resulting in zero free carriers suppressing the real index in the region between cavities and the real refractive index between cavities was taken to be the same as in the field 17 .…”