First-Order Grating TM Coupling Coefficients for Distributed Feedback Quantum Cascade Lasers

A ray optics (RO) technique utilizing diffraction grating theory and a transfer matrix method is used to derive a closed form expression for the 1
^st
-order distributed feedback coupling coefficient in practical quantum cascade laser structures. Values of the coupling coefficient obtained using a full-wave finite element numerical method (COMSOL Multiphysics) are in good agreement with those obtained using the RO-derived expression.