optical characterisation of rare-earth doped fluoride and phosphate ...

19An issue closely related to Q factor is nesse, F, dened as the free spectral range(FSR) divided by the bandwidth of the resonances, or equivalently,F =Q2n s a : (1.11)To date, the highest reported nesse is 10 7at an optical wavelength, recorded bySavchenkov et al. in 2007 in a CaF 2 microtoroid [7]. As a comparison, the highestreported nesse in a super Fabry-Perot cavity is 10 5 at optical wavelengths [2].Each of these individual contributions to the cavity loss can be combined togetherto give a system Q factor asQ 1total = Q wgm 1 + Q 1material + Q 1coupling(1.12)Q 1material = Q ss 1 + Qwater 1 + Q 1bulk ;where Q wgm is the whispering gallery Q, and Q material is the material Q.1.6 Mode VolumeThe degree of modal connement in a sphere can be determined by integrating thevolume as shown in Fig. 1.3, and, optionally, choosing a 1=e 2 boundary for theintensity distribution. It is a non-trivial exercise to determine the volume based onthe set of formulae in Eqn. 1.2. Despite that, it can be shown that mode volumescan be as small as 1000-4000 m 3 , depending on microsphere size and wavelength.Such tightly propagating modes around the microsphere can easily develop very highexcitation densities ( 10 3 Vm1 ) as mentioned earlier. This is very important forstudying nonlinear processes and microlaser operation.The eective mode volume, V eff , is dened as the integral of the square of the