The theoretical analysis of antiphase, surface-emitting, complex-coupled, distributed feedback ͑SE-CC-DFB͒ lasers is presented. The specific configuration chosen for analysis is relatively simple: a metallic second order grating placed atop a diode-laser structure. This type of SE-CC-DFB structure can be fabricated by a lift-off and evaporation process; can operate in a single-lobed, orthonormal beam with a rather uniform near-field intensity pattern, and external differential quantum efficiency, d , values in excess of 30%. The dependence of the gain threshold on grating duty cycle for both the symmetric and antisymmetric ͑longitudinal͒ modes is presented and discussed. The external differential quantum efficiency for the symmetric mode is found to steadily increase with grating length at the expense of the degree of near-field-pattern uniformity. © 1996 American Institute of Physics. ͓S0003-6951͑96͒00345-2͔Complex-coupled, distributed-feedback ͑CC-DFB͒ edgeemitting lasers consisting of periodic variations of both the refractive index and gain have recently received considerable theoretical and experimental attention as potential light sources in advanced optical-communication systems.1-9 We have previously reported on the theoretical analysis of inphase, second-order, surface-emitting CC-DFB lasers.10 In this letter, we present a treatment of antiphase ͑i.e., excess gain preferentially placed in low-index regions͒, CC-DFB lasers. The device analyzed is simply composed of a metallic second-order Bragg grating placed atop a diode-laser structure. We show that an antiphase, surface-emitting ͑SE-CC-DFB͒ laser can provide a single-lobed, orthonormal far-field radiation profile as well as a symmetric, nearly uniform nearfield intensity pattern.While we have already demonstrated 10 that in-phase type SE-CC-DFB devices can fundamentally favor symmetric ͑i.e., single-lobe͒ mode operation, the designed structure involves a biharmonic-like grating, a feature impractical to fabricate and incorporate into a semiconductor-laser device. Therefore, knowing that resonant-optical-waveguide ͑ROW͒ arrays 11 are analogous to second-order antiphase, CC-DFB lasers, 12 we proceeded to analyze antiphase-type SE-CC-DFB's; which, as shown below, can be designed to be made in practical configurations. In particular, we choose to analyze a metal-grating second-order DFB, due to its simplicity of fabrication, and no need to process the semiconductor material itself. The latter feature is particularly attractive if one has to make GaN-based blue/green diode lasers. Metal-grating first-order, loss-coupled DFB lasers have already been demonstrated, 14 with excellent results ͑i.e., single-longitudinal-mode operation with good side-mode suppression ratio and no danger of self-pulsation, since light absorption in the metal is nonsaturatable͒. However, those devices were edge emitters. Here we present an analysis of a second-order metal-grating DFB laser that primarily acts to efficiently outcouple light in a direction orthornomal to the wafer pl...