Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications

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Abstract
A perturbation theory is presented for the frequency shift of highly resonant photonic whispering gallery modes in a transparent sphere. Using a vector wave equation, we derive a general formula for the shifts in TE and TM polarization by adsorption of another dielectric medium. The adsorbed medium can have an arbitrary shape and refractive-index profile. The formula is applied to adsorption of a thin layer and deposition of a small spherical particle, many such particles, and thin cylindrical particles on the resonator surface. We found that the ratio of the TM mode shift to the TE mode shift is sensitive to the shape of the adsorbates and their orientation. Calculation results are discussed in terms of a dipolar field.