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

15The Q factor is dictated by the length of time for which a photon can be stored withinthe cavity and is limited by several other factors apart from the WGM losses. In fact,WGM losses have an appreciable eect only for radii less than about 7 m [29].The losses within a microsphere resonator arise due to both internal and externalmechanisms. The internal losses result from WGM losses and material losses fromthe cavity such as surface scattering, water absorption and bulk absorption of thematerial.Coupling losses, Q coupling , depend on the coupling technique and on the ability toachieve good phase matching between the coupler and the microsphere. We typicallyuse 1-2 m diameter taper bres for coupling due to their near ideal performance[25]. These bres are fabricated by heating and stretching a strand of single modebre down to a diameter of 1 m. An evanescent eld forms in this region whichis then coupled into an adjacent microsphere. The coupling Q factor is governed bythe overlap of the evanescent elds of the bre taper and the sphere (c.f. page 28 formore details) [30]. The interaction strength between the cavity mode and bre modegovern Q coupling . 1It has been found [31] that the Q factor shows an initial rapid decay within therst two to three minutes of fabrication of microspheres. This is due to one or twomonolayers of water forming on the surface. Ideally, fabrication should be performedin a vacuum environment. The formula for losses due to water absorption [32] isQ w s2a8n 3 s1 w; (1.8)where 0.2 nm is the thickness of the monolayers of water, and w is the absorption1 Q coupling is maximised when the mode matching is optimised in terms of the spatial modes andthe propagation constants of the microsphere and bre taper.