Extended transfer matrix modeling of an erbium-doped cavity with SiO2/TiO2 Bragg reflectors

Following the earlier realisation by rf-sputtering technique of a one-dimensional dielectric photonic crystal activated by Er3+ ion [1], we developed a comprehensive modelling based on extended (3?3) Transfer Matrix Formalism including sources [2]. The cavity is made of an Er3+-doped SiO2 active layer inserted between two Bragg reflectors consisting of six pairs of SiO2/TiO2 layers. Near infrared (NIR) transmittance spectra indicate clear evidence of a stop-band from 1350 nm to 1850 nm, and a cavity resonance centred at 1537 nm in normal incidence, with a measured quality factor of 171. We report in Figure 1 the Er3+ luminescence spectrum emitted by the cavity when optically pumped by an Ar laser at ?P = 514.5 nm, as compared to the luminescence obtained from a single Er3+-doped SiO2 active layer without Bragg mirrors: an enhancement of 90 times is observed that can be attributed to the cavity effect. As a matter of fact, extended matrix simulation shows how the intrinsic spontaneous emission is projected into the resonance mode of the cavity [Figure 2]. The smallest possible theoretical value of the linewidth (for an ideal lossless cavity) would be close to 3 nm. Moreover, modeling shows that it is possible to optimize the design of an Er3+-doped SiO2/TiO2 microcavity in order to exploit a third-order resonance at the pump wavelength, for a suitable value of the incidence angle iP of the pump beam. This would open the way to stimulated gain or even laser effect. In the present configuration, the threshold gain is estimated at 275 cm-1; adding one more period to each DBR would suffice to divide it by two. Wavelength [nm] Figure 1. 4I13/2 ? 4I15/2 photoluminescence spectra of the cavity activated by Er3+ and of the single Er3+-doped SiO2 active layer without Bragg mirrors. The light is recorded at 5° from the normal on the samples upon excitation at 514.5 nm.Figure 2. Simulation by Extended (3?3) Transfer Matrix Formalism of the radiation emitted out of the cavity (in arbitrary units), as compared to the intrinsic spectral rate of spontaneous emission of Er3+ in SiO2. References [1]A. Chiasera et al., Appl. Phys. Lett. 89, 171910, 1-3 (2006). [2]Y.G. Boucher, J.E.O.S.-Rapid Pub. 1, 06027, 1-6 (2006).