Strong and Short Bragg Waveguide Gratings With Trapezoidal-Shaped Grooves

In this study, we evaluate strong Bragg waveguide gratings formed of trapezoidal-shaped grooves, as typically produced in surface-etched structures, and we propose optimal groove shapes. We begin by validating our modelling approach, which is based on the finite-difference time-domain method, through comparisons with coupled mode theory applied to rectangular gratings. We then compute the reflectance, transmittance and loss of trapezoidal gratings as a function of Bragg order, and of the top and bottom widths of the grooves. Simulations reveal that the highest reflectance peaks are achieved for widths that are about λ/8, regardless of the Bragg order. We find that the characteristics of trapezoidal-grooved gratings are strongly dependent on the bottom width of the grooves, and that a very high reflectance can be achieved by carefully tailoring this width. We also calculate the coupling coefficients of infinitely long optimized structures, finding that they decrease with increasing Bragg order. Our results are of interest in the design of strong short gratings etched in the surface of semiconductor waveguides.