CALCULATION OF LIFETIME DEPENDENCE OF ER3+ ON CAVITY LENGTH IN DIELECTRIC HALF-WAVE AND FULL-WAVE MICROCAVITIES

Angular spontaneous emission rates and lifetimes of Er3+ in Si/SiO2 Microcavities are calculated for cavity lengths close to full and half-wavelengths. For a half-wavelength cavity, the calculations show that the spontaneous lifetime is sensitive to the variation of cavity length, and agrees very well with the experimental data measured by Vredenberg, Hunt, Schubert, Jacobson, Poate, and Zydzik [Phys. Rev. Lett. 71, 517 (1993)]. This variation comes from a coupling rate change into the cavity normal. For a full wavelength cavity, the lifetime is less sensitive to cavity length due to strong coupling of spontaneous emission to a fundamental waveguide mode.