] 2 M ar 1 99 9 Surface and internal scattering in microspheres : limits imposed on the Q - factor and mode splitting

Accurate calculation of internal and surface scattering losses in fused silica microspheres is done. We show that in microspheres internal scattering is partly inhibited as compared to losses in the bulk material. We pay attention on the effect of frozen thermodynamical capillary waves on surface roughness. We calculate also the value of mode splitting due to backscattering and other effects of this backscattering. Optical microsphere resonators 1 working on whispering gallery modes combine several unique features – very high quality factor, small size and effective volume of field localization with low cost, that make them very attractive for future applications in optoelectronics and measurement science. Such microresonators may be for example used as interferometers and filters with record finesse 2,3 , for QED experiments 1,4,5 and for diode laser stabilization 6. The last application as for now looks the most intriguing as it allows to create centimeter size cheap tunable laser with kilohertz linewidth. Microspheres are prepared from fused silica or other pure glassy medium by autoforming under the action of surface tension in the flame of a microburner or in the CO 2 beam. The properties of the microspheres are analyzed theoretically and experimentally rather wide. The theory of whispering gallery modes is well known from electrodynamics 11 and methods of optimal coupling with them were elaborated and experimentally confirmed 7. In 8 nonlinear properties of fused silica microspheres were investigated theoretically and experimentally. Mechanisms limiting the quality factor of microspheres were outlined in several papers. It was shown that the main factor preventing the obtaining and preservation of high Q-factor is surface atmospheric water adsorption 9. However, values as high as Q ≃ 8 × 10 9 – very close to fundamental limit of internal losses were obtained at He-Ne and near IR region 9,3. Attempts to obtain higher Q moving to minimum of losses of fused silica 1.55µm, were as for now unsuccessful. Besides chemosorbed water the reason may be surface scattering on inhomogeneities. Problems of scattering inside the microsphere and on its surface were analyzed formerly incompletely. Scattering leads not only to the limitation of the Q-factor but also lifts degeneracy between degenerate sine and cosine modes. This effect may be observed as mode doublets 8,10. Especially badly explored are questions of surface scattering. In different papers one may find expressions leading not only to different numerical estimates but to different functional dependencies from the size …