Antireflective behavior of a facet in a multilayer waveguide-based laser with a surface-trapped mode

We address theoretically edge-emitting semiconductor lasers based on a multilayer waveguide structure in a form of a distributed Bragg reflector (DBR) and emitting laser light in a TM-polarized surface-trapped optical mode (optical Tamm state, OTS) which decays exponentially into the air and decays in an oscillatory way into the DBR. The effective refractive index of the lasing mode is close to 1, which renders the mode reflectivity from an uncoated (as-cleaved) facet anomalously small. The facet reflectivity is calculated exactly by the finite difference frequency domain method. We show that the exact reflectivity differs drastically from the value found in the Fresnel approximation. The reflectivity in a range of 0.01--0.07 shows that the uncoated facet is naturally antireflective for the lasing surface-trapped mode. A strong dependence of the facet reflectivity on the wavelength of light affects the threshold lasing conditions and the wavelength at which the lasing first occurs. A metal bar mounted on top of the DBR close to the rear facet forms a moderately highly reflecting mirror for the surface-trapped mode. The model structure of a semiconductor laser is proposed, in which the TM-polarized OTS has the preferred conditions for the lasing versus all other modes. Two types of lasers are considered: (i) a laser with the naturally antireflective uncoated front facet and a metal bar mirror on the top surface close to the rear facet and (ii) a laser with metal bar mirrors close to both facets. For a laser emitting at $\ensuremath{\lambda}\ensuremath{\approx}1\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}$ the lasing mode has the penetration depth to the air about $0.7--1.3\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}$ which allows an efficient near-field outcoupling to an external waveguide or to an optical fiber placed in the vicinity of the DBR surface.