We have measured the spectrum of the amplified spontaneous emission of two coupled vertical-cavity semiconductor lasers. The spectrum shows a triplet structure consisting of a central peak at the lasing frequency and two sidebands. Theoretical analysis shows that the sidebands are due to spatial relaxation oscillations; the triplet structure is a result of spatial hole burning which occurs due to interference between the lasing supermode and the fluctuations in the nonlasing supermode.PACS number͑s͒: 42.55.Sa, 42.55.Px, 42.60.Da, 42.50.Lc Phase-locked semiconductor laser arrays are of interest as sources to produce high output power in a coherent beam and for applications in one-or two-dimensional devices. These arrays usually exhibit stable antiphase locking, i.e., all the lasers oscillate in the same frequency with each one being out-of-phase with respect to the neighboring ones. This mode is usually referred to as the antisymmetric supermode and has been experimentally observed in various semiconductor laser arrays ͓1-3͔. Theoretically, the dominance of the out-of-phase supermode is generally explained using simple coupled-mode analysis ͓4,5͔. However, the interaction between the optical field and the carrier density results in complex dynamics between the lasers, where the amplitude ͑and phase͒ fluctuations in one laser can lead to amplitude and phase changes in the second laser, which in turn can destabilize the phase locking between the lasers ͓6,7͔. These theories refer to arrays of both edge emitting and verticalcavity surface-emitting lasers ͑VCSELs͒. Presently, the interest is mainly in VCSEL arrays in view of their tremendous potential for 2D integration.One way to investigate the dynamics of semiconductor lasers in general and semiconductor laser arrays in particular is via measurements of the spontaneous emission into the nonlasing modes. The investigation of the nonlasing modes has been a powerful tool to understand the dynamics of surface-emitting lasers. In this paper, we demonstrate experimentally predictions of the theoretical model of Hofmann and Hess ͓8͔ which relates the dynamics of two coupled VCSELs with the spectrum of the nonlasing mode. As will be shown below, this spectrum can be directly measured, and information about the coupling between the lasers can be deduced.We first review briefly in qualitative terms the model of Hofmann and Hess ͓8͔. The dynamic equations of the field and the carrier densities of a two-laser array are derived in terms of the symmetric and antisymmetric supermodes. This model, also referred as split-density model, redivides the carrier densities of the individual lasers into two distinct density pools. The total carrier density, i.e., the sum of the carrier densities of both lasers, interacts equally strong with both supermodes, whereas the carrier density difference of the lasers ͑due to spatial hole-burning effects͒ couples the two supermodes. The symmetric and antisymmetric supermodes, the total carrier density and the difference carrier density form a s...
