Coupled-mode analysis of phase-locked injection laser arrays

Abstract

A coupled-mode analysis has been developed to describe the output of phase-locked injection laser arrays. We show that an array of emitters with weak coupling can only operate in a set of discrete modes determined by the number and the spacing of the emitters. The interaction between emitters leads to a splitting of the common frequency of operation that can be estimated from the coupling strength. The coupled-mode analysis is compared to calculations based on simple diffraction theory. A consequence of the analysis is an explanation for the commonly observed discrepancy between experimentally observed far-field lobe(s) widths and those predicted by simple diffraction theory.

Linear tailored gain broad area semiconductor lasers

“…At this point we simply quote the relations for position of the near-field peak x, ( b ) half-width of the near-field distribution w, ( 6 ) 12 sin (7r/6 + cp) q cos (6' + P)…”

“…(1 + b2)li3 cos ( 2 p + 8/2) and far-field emission angle 8, ( 6 ) all expressed in terms of their values in the no anti-guiding case. The angles p and 8 are functions of b defined as…”

“…Although the array structure solves the filamentation problem by confining the filaments to individual laser channels, the lateral mode problem remains. The well-known undesirable twin-lobed far-field pattern of a uniformly spaced array of identical lasers [2]- [4] comes about because the lossy interchannel regions in the uniform array cause the highest order supermode to have the highest modal gain, and this mode has a twin-lobed far-field pattern [5], [6]. In principle, one method of achieving fundamental mode operation in an array would be to vary (e.g., chirp) the widths of the array elements so that the fundamental mode is localized in a different spatial region than the higher order modes [7].…”

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

“…In addition, all previously reported phase-locked 2-D VCSEL arrays operate in either the out-of-phase array mode or a mixture of various array modes. This behavior is characteristic of weakly-index guided or gain-guided phase-locked arrays in which the highest-order (i.e., out-of-phase mode) is always favored to lase over the in-phase mode [7]- [9], [41], [42], with poor intermodal discrimination and mode stability. By changing the phase relationships of adjacent array-elements, such as patterning the 2-D array surface with an external phase-shifter [10], "in-phase mode-like" emission was obtained from optically pumped VCSEL arrays, although the beam is quite broad (twice the diffraction-limit), indicating multi-mode operation.…”

“…Weak coupling and poor inter-modal discrimination found in evanescently coupled edge-emitting laser arrays has severely limited their single-mode output power [11]. According to the coupled-mode theory employed to calculate the modal behavior in weakly index-guided array systems, each element only couples with its nearest neighbors by their weak evanescent waves (series-coupling), and each array mode is a superposition of individual element modes [8], [41], [9], [42]. For an 2-D VCSEL array, the coupled modes can be labeled by the number of intensity nulls in each direction.…”