Improved simulation of surface gratings of higher Bragg order
Fig. 1: SEM picture of a dry-etched surface grating
Fig. 2: Calculated maximum reflectivity of a 10th order Bragg grating as a function of number of steps approximating the slopes of the grooves for a 35° etch angle
Fig. 3: Calculated maximum reflectivity of a 10th order Bragg grating as a function of number of steps approximating the slopes of the grooves for a 10° etch angle
The spectral emission width of semiconductor lasers can be significantly reduced from typically a few nanometers down to the femtometer scale by implementing periodical structures (Bragg gratings) into the resonator. This feature makes the efficient semiconductor light sources also attractive for narrow-band applications such as spectroscopy. An established method for grating integration is to introduce periodical grooves with defined depth, shape, and period into the laser surface. These gratings can be defined using either i-line stepper lithography or electron beam lithography and are transferred into the semiconductor surface by dry etching.
Utilizing such gratings as a back mirror requires a grating reflectivity as high as possible, which necessitates extensive numerical simulations to optimize shape and depth of the gratings. The corresponding reflectivity spectra are calculated by solving Maxwell equations in two spatial dimensions. The scattering matrix method used bases on the expansion of the optical field in terms of local waveguide modes. This method can be most efficiently implemented for rectangular shaped grooves. The simulation results obtained in such a manner reveal that a high reflectivity can be only achieved with gratings of a higher Bragg order (>3) if their duty cycle is larger than 90%. The widths of the grooves must therefore be smaller than 100 nm. Due to the limited resolution of lithography and the high etch depths of more than 1000 nm needed it is difficult to fabricate such gratings. This is the reason why the grooves are etched V-shaped and tapered towards the active region. However, it has not been possible to simulate such gratings at the FBH until now.
Therefore, the existing FBH tool to simulate the surface gratings has been extended in such a way that reflections spectra of V-shaped grooves can be calculated, too. To this end, both slopes of the grooves are approximated by steps. Their number can be chosen arbitrarily. The simulations reveal that each slope must be approximated by at least 20 steps in order to obtain correct values for the reflection coefficient. The rise of the grating reflectivity with decreasing etch angle can be attributed to an increase of the effective duty cycle.
Publications:
J. Fricke, A. Klehr, O. Brox, W. John, A. Ginolas, P. Ressel, L. Weixelbaum, G. Erbert, "Y-branch coupled DFB-lasers based on high-order Bragg gratings for wavelength stabilization", Semicond. Sci. Technol., 28, 035009 (2013).
J. Fricke, H. Wenzel, F. Bugge, O.P. Brox, A. Ginolas, W. John, P. Ressel, L. Weixelbaum, G. Erbert, "High-Power Distributed Feedback Lasers With Surface Gratings", IEEE Photonics Technol. Lett., vol. 24 , no. 16, pp. 1443-1445 (2012).
J. Fricke, W. John, A. Klehr, P. Ressel, L. Weixelbaum, H. Wenzel, G. Erbert, "Properties and fabrication of high-order Bragg gratings for wavelength stabilization of diode lasers", Semicond. Sci. Technol., vol. 27, no. 055009 (2012).
FBH research: 25.03.2014