ABSTRACT
The finite angular spectral width of a 2D resonant grating mirror is adjusted to select the fundamental transverse mode of a laser and to filter out higher order modes. The selection principle is explained phenomenologically on a simplified 1D model. The 2D design is made so as to sustain the large field concentration in the grating slab-waveguide mirror, and the technology permitting to obtain the resonant reflection within the gain bandwidth of two types of laser is described. The blank experimental measurements by means of a white light supercontinuum are shown to match the targeted specifications on the resonance spectral position and angular width.
ABSTRACT
The Fourier modal method (FMM), often also referred to as rigorous coupled-wave analysis (RCWA), is known to suffer from numerical instabilities when applied to low-loss metallic gratings under TM incidence. This problem has so far been attributed to the imperfect conditioning of the matrices to be diagonalized. The present analysis based on a modal vision reveals that the so-called instabilities are true features of the solution of the mathematical problem of a binary metal grating dealt with by truncated Fourier representation of Maxwell's equations. The extreme sensitivity of this solution to the optogeometrical parameters is the result of the excitation, propagation, coupling, interference, and resonance of a finite number of very slow propagating spurious modes. An astute management of these modes permits a complete and safe removal of the numerical instabilities at the price of an arbitrarily small and controllable reduction in accuracy as compared with the referenced true-mode method.
