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

xiiiList of Figures1.1 WGM in a microsphere. (a) Ray propagation around the sphere byTIR; (b) Spherical coordinate system. . . . . . . . . . . . . . . . . . . 91.2 Calculated intensity distribution of the TM mode in the equatorialplane (a) for n = 1 and l = 30 with x = 24.623 (b) and for n = 2 andl = 30 with x = 27.978. The wavelength is 1.55 m, and the sphereradius and intensity are normalised to unity in both cases. . . . . . . 121.3 Azimuthal intensity distribution for TM modes with (a) n = 1; l jmj =1, (b) n = 2; l jmj = 1, (c) n = 1; l jmj = 2, (d) n = 2; l jmj = 1.The wavelength is 980 m, and the sphere radius is normalised to unity. 131.4 Total quality factor and individual quality factors as a function ofsphere diameter at a wavelength of 980 nm. Water absorption limitsthe Q in silica. In (b), the statistical correlation length, B, and theaverage standard deviation of the surface roughness, , are increased bya factor of about three to simulate the estimated poorer surface qualityin our doped microspheres (B = 7 nm and = 15 nm). Coupling losseswith a tapered bre have been neglected. . . . . . . . . . . . . . . . . 181.5 Mode volume for a doped microsphere with n s = 1:5 for = 1550nm (squares) and 980 nm (diamonds). The TE modes have a slightlysmaller mode volume. In contrast, the nonlinear mode volume (greenmarkers) is at variance with the quantum mode volumes (red and bluemarkers). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21