Rigorous electromagnetic study of diffraction loss in VCSEL mirrors

An electromagnetic model for the reflection properties of mirrors VCSEL is discussed. To this end the vectorial Maxwell equations are solved in a fully rigorous way in a layered structure, with proper care taken of the numerical treatment of thick structures. Since most VCSEL devices are circular the discussion is limited to this, class of geometries. The presented method is capable of dealing with complex structures, including lossy materials and circular gratings. The authors focus on the reflection properties of VCSEL Bragg mirrors to illustrate the theory. Numerical results are presented concerning the diffraction loss of a highly reflecting Bragg stack as experienced by different transverse VCSEL modes.