Simulation and analysis of volume holographic gratings integrated in collimation optics for wavelength stabilization

Integrating volume holographic gratings into micro-optical components such as cylindrical fast-axis collimation lenses (VHG-FAC) for diode lasers constitutes a promising concept for wavelength stabilization by forming an external cavity laser. Compared to standard wavelength stabilization configurations the integrated element reduces the alignment complexity and is furthermore insensitive to the smile-error of diode laser bars. In order to configure and optimize these components the diffraction of the divergent field distribution of a broad area semiconductor laser must be calculated. The present paper presents the extension of the coupled-mode theory in order to calculate the spectral distribution of the diffracted field and the coupling efficiency within the external cavity. The model was extended to three-dimensional space and supplemented to include surface effects, polarization dependency and wave-optical propagation. The asymmetric spectral distribution emitted by an external cavity laser with VBG-FAC is tracked back to the feedback of highly divergent radiation diffracted at the holographic grating. Power losses due to the coupling efficiency within the cavity are also calculated for various field distributions and compared with experimental data. In summary the mathematical model allows to estimate the minimum spectral width and the losses using a VHG-FAC in an external cavity. Thus the injection locking concept using the VHG-FAC can be compared to the spectral characteristics and estimated power losses of standard wavelength stabilization configurations, e.g. the alignment of the grating in the collimated beam.