Optimal design of radial Bragg cavities and lasers

We present a new and optimal design approach for obtaining maximal confinement of the field in radial Bragg cavities and lasers for TM polarization. The presented approach outperforms substantially the previously employed periodic and semi-periodic design schemes of such lasers. We show that in order to obtain maximal confinement, it is essential to consider the complete reflection properties (amplitude and phase) of the propagating radial waves at the interfaces between Bragg layers. When these properties are taken into account, we find that it is necessary to introduce a wider ("half-wavelength") layer at a specific radius in the "quarter-wavelength" radial Bragg stack. It is shown that this radius corresponds to the cylindrical equivalent of Brewster's angle. The confinement and field profile are calculated numerically by means of transfer matrix method.