Modeling of circular-grating surface-emitting lasers

Grating-coupled surface-emitting lasers became an area of growing interest due to their salient features. Emission from a broad area normal to the wafer surface, makes them very well suited in high power applications and two-dimensional laser arrays. These new possibilities have caused an interest in different geometries to fully develop their potential. Among them, circular-grating lasers have the additional advantage of producing a narrow beam with a circular cross section. This special feature makes them ideal for coupling to optical fibers. All existing theoretical models dealing with circular-grating lasers only consider first-order gratings, or second-order gratings, neglecting surface emission.; In this thesis, the emphasis is to develop accurate models describing the laser performance by considering the radiation field. Toward this aim, and due to the importance of the radiation modes in surface-emitting structures, a theoretical study of these modes in multilayer planar structures has been done in a rigorous and systematic fashion. Problems like orthogonality of the radiation modes have been treated very accurately. We have considered the inner product of radiation modes using the distribution theory. Orthogonality of degenerate radiation modes is an important issue. We have examined its validity using the transfer matrix method. It has been shown that orthogonality of degenerate radiation modes in a very special case leads to the Brewster theorem. In addition, simple analytical formulas for the normalization of radiation modes have been derived. We have shown that radiation modes can be handled in a much easier way than has been thought before.; A closed-form spectral dyadic Green's function formulation of multilayer planar structures has been developed. In this formulation, both rectangular and cylindrical structures can be treated within the same mathematical framework. The Hankel transform of some auxiliary functions defined on a circular aperture has been used to obtain the far-field pattern of the aperture. It has been shown that the far-field patterns of all circular apertures except those with the first harmonic azimuthal variation have a dark spot at their centers.; Threshold analysis of circular-grating lasers has been performed by considering surface emission. In this study, we have assumed that the laser beam is circularly symmetric. Based on the large argument approximation of the Hankel functions, we have shown that the interaction between the amplitudes of the guided modes can be described by coupled-mode equations containing coupling factors to the radiation field. These factors have been obtained by using the Green's function approach. The transfer matrix method is essential in obtaining the Green's function.; The relationship between the input current and the output power of circular-grating lasers producing circularly symmetric beams has been derived by developing suitable rate equations for the total number of photons and the phase of the optical amplitude in the laser cavity. We have solved the rate equations above the threshold under steady state conditions. Formulas for radiating power and far-field patterns have also been presented.; The theoretical treatment of the radiation modes developed earlier makes it possible to include radiation modes in coupled-mode equations in cylindrical structures. We have done so to pave the way for treating laser fields that are not circularly symmetric. Among them, the laser fields that have the first harmonic azimuthal variation are highly desirable due to the nonzero value of the radiation field on the axis of the laser.