Factor of spontaneous emission into the optical dielectric waveguide mode

Within the framework of a complete vector analysis, an expression for the factor of spontaneous emission into the transverse mode of a dielectric waveguide is found. The results are compared with those previously obtained in the framework of the scalar approximation. It is shown that their most significant quantitative difference is possible for waveguides used in diode lasers and amplifiers in which the transverse beam size is commensurable with the wavelength. The conditions for the applicability of the scalar approximation for calculating the spontaneous emission factor are obtained.