Angular deviation and diffraction efficiency of Littrow-configuration ECDL for three-dimensional diffraction

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 (ECDL) using the rigorous coupled-wave analysis (RCWA) 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 (DE) using RCWA. {Furthermore}, we point out that the angular tolerance and reflection efficiency can be improved if the appropriate parameter settings are selected for Littrow-configuration ECDL, 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 LD-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.