We calculate the optimum refractive index and thickness for a single layer antireflection coating as a function of active layer thickness of a laser diode using three different simplified numerical methods. The difference of the results using three methods comes from that of the effective refractive index of a laser used in three methods. We compare three simplified methods to an exact method to check the validity of the simplified methods. We conclude that the simplified method, choosing the effective index of a laser diode as a function of incidence angle of each plane wave composing of a guided mode agree well to an exact method for both TE and TM modes and the cases of strongly and weakly guiding.