Three-dimensional angular deviation and diffraction efficiency of a grating in Littrow-configuration ECDL

We consider in this paper the angular deviation and diffraction efficiency of the reflection gratings in Littrow-configuration for applications of external cavity diode laser using the rigorous coupled-wave analysis method. We consider the three-dimensional diffraction case in general, where the incidence plane is un-parallel with the grating vector, i.e. conical diffraction. The angular tolerance of arbitrary gratings under plane and conical diffraction are thus derived and presented. A typical blazed grating is chosen as an example to calculate its diffraction efficiency using the rigorous coupled-wave analysis method. Furthermore, we point out that the angular tolerance and reflection efficiency can be improved if the appropriate parameter settings are selected for Littrow-configuration devices, including incidence angle, diffraction order, grating period and blazed angle. Otherwise, a tiny slanting angle of the grating vector deviated from the incidence plane will deviate the feedback light away from entering the laser-diode-chip and halt laser oscillation in the external cavity. Finally, a general rule for the parameter settings in Littrow-configuration is provided as a benchmark.