Rate Equations Analysis of Phase-Locked Semiconductor Laser Arrays Under Steady State Conditions

Rate equations analysis of phase-locked semiconductor laser arrays has been carried out. I t was found that for given (laser) current densities, the photon density distribution in the array elements is that pmticular one which maximizes the total photon density. Theresults of this analysis were then combined with the waveguiding properties of the laser array waveguide, yielding a basic model of phase-locked diode laser arrays. This model explains the effects of the variation of the current combination through the array elements on its mode structure that were observed recently. P HASE locking of semiconductor injection lasers has been the subject of widespread research effort recently, with most of the work implemented in various monolithic configurations of one-dimensional arrays [ I ] [ l o ] . The few theoretical investigations of such arrays, to date involve the evaluation of the array far-field pattern using an ad hoc presumed nearfield pattern [4 ] , and more recently, the construction of its optical field in terms of the array supermodes [ 111 (i.e., the eigenmodes of the array waveguide). Amore complete analysis of the array properties, however, should include the effect of the gain distribution among the different array elements, as determined by the carrier and photon densities, rather than considering just the “cold” cavity of the array. The effect of the saturated gain distribution is of particular importance in the case of multiple-stripe lasers. Whereas single-stripe lasers are designed mostly to support a single spatial mode, N-channel laser arrays are characterized by N (lateral) supermodes [ 111 . Since each of these supermodes exhibits, generally, different excitations of the different array channels [ 111 , it is clear that gain saturation effects are important in determining the modal gain of the supermodes and, hence, their relative excitation at various pumping levels. This, in turn, determines the array farfield pattern [ l 11 and its longitudinal mode structure [ 121 . Furthermore, as the control of the gain distribution among the array channels can be realized by providing each laser with a separate contact [ 101 , the results of this more complete Manuscript received January 26, 1984; revised April 6 , 1984. This work was performed by the Jet Propulsion Laboratory, California Institute of Technology under contract with the National Aeronautics and Space Administration, and by the Applied Physics Department, California Institute of Technology under contracts with the U.S. Office of Naval Research and the National Science Foundation. The work of E. Kapon was supported by the Weizmann Postdoctoral Fellowship. J . Katz is with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91 109. E. Kapon, S. Margalit, and A. Yariv are with the Applied Physics Department, California Institute of Technology, Pasadena, CA 91125. J1 ’2 J3