Modeling and Characterization by Experiment of Higher Order Surface Bragg Gratings for Ultra-Narrow Linewidth Diode Lasers

Bragg gratings for monolithic extended cavity diode lasers with ultra-narrow linewidth must exhibit a spectrally narrow resonance of the order of a few tens of gigahertz to enable longitudinal single mode operation. This requirement is met by higher order surface gratings in ridge-waveguides, combining a length of at least 2 mm with a small coupling coefficient. The modeling of such structures relies on major simplifications. In addition, the impact of uncertainties in the design and implementation is aggravated by the size of the grating. To optimize the design and evaluate the quality of the modeling and implementation, we developed and applied a procedure for the precise measurement of the grating reflectance and loss. In this work, we present our hybrid modeling approach based on eigenmode expansion complemented by coupled mode theory as well as our characterization procedure. We combine this with the analysis by scanning electron microscopy of our test structures. We find that measured spectra of gratings of up to 2 mm length agree well with the models, including the asymmetry of the loss vs. frequency caused by radiation effects. We also report a spectral filamentation of the reflectance spectrum of 4 mm long gratings with side features on the long wavelength side.