Theory and practical calculation of antireflection coatings on semiconductor laser diode optical amplifiers

The reflectivity of the end facet of a 3-D dielectric waveguide can be easily calculated, in case of weak guidance, by replacing the waveguide with a homogeneous medium of refractive index n_eq while the incident electric (or magnetic) field remains that of the guided mode. The calculation is done through a plane-wave expansion of the incident field; a practical algorithm is given to cope with multidielectric coatings. This process naturally emerges when exact equations are expanded in terms of powers of the weak guidance parameter and it leads to a 1st-order approximation of the reflectivity (i.e. within 2nd-order error) when n_eq is suitably chosen. The facet can be normal or angled with respect to the waveguide axis