Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer

Abstract

The interaction of whispering gallery modes (WGM) of optical microresonators with subwavelength imperfections has been studied both experimentally and theoretically. This interaction is responsible for the formation of spectral doublets in place of single resonance peaks, and for degrading of Q-factors of the resonances. Within the currently accepted framework the spectral doublets are explained as a result of degeneracy removal of clockwise and counterclockwise WGMs due to their coupling caused by defect-induced backscattering, while the degrading of the Q-factor is described phenomenologically as an additional contribution to the overall decay rate of WGM due to coupling between WGM and radiative modes. Here we show that the existing understanding of this phenomenon is conceptually wrong and develop an exact theory of WGM interaction with a single defect, which provides a unified treatment for both aspects of this interaction explaining existing experiments and predicting new phenomena.Elastic (with no change in frequency) scattering of light due to small (compared to wavelength) particles is one of the most fundamental and intensively studied optical phenomena. Its modern history began almost one hundred fifty years ago with the explanation of the blue color of sky in a series of papers by Lord Rayleigh[1], where the now famous 1/λ 4 cross section law, where λ is the wavelength of light in vacuum, was derived. Since then it has been customary to refer to processes of elastic interaction of light with subwavelength particles as Rayleigh scattering. Besides providing us with beautiful blue skies and red sunsets, Rayleigh scattering is important for a large number of fundamental optical phenomena as well as for numerous applications. Recent developments in optics and photonics have created new situations in which the manifestations of Rayleigh scattering are significantly modified. Particularly drastic modification of this process is expected when light is confined in all three dimensions inside optical microresonators in the form of whispering gallery modes (WGM) [2]. Given the fundamental nature of this process it is not surprising that it has attracted a significant amount of attention in recent years [3,4,5,6,7].While whispering gallery modes can occur in various types of geometries [8] we will focus on spherical microresonators. WGMs in this case correspond to Mie resonances [9] with ultra narrow widths, γ ls ≪ ω ls , where ω ls is the frequency of the mode, and respectively high (up to 10 9 for silica microspheres [8]) Q-factors defined as Q ls = ω ls /γ ls . WGMs are characterized by polar and azimuthal indexes, l and m, and a radial number s determining, respectively, the angular and radial dependence of the fields in a spherical coordinate system centered at the sphere. The resonance frequency ω ls does not depend on the azimuthal number, which reflects the degeneracy of the resonances due to full spherical symmetry of the problem. WGMs are also characterized by their the mode volume, which can be very d...

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