The whispering-gallery mode space of a cylindrically symmetric silicon micro-optic bottle resonator with an axial Gaussian dielectric profile is theoretically examined. Maxwell’s wave equation for the magnetic field, expressed in cylindrical coordinates, is converted into an eigenvalue problem using a Fourier–Bessel basis space to expand the inverse dielectric and field components. The order of the eigen-matrix is reduced using symmetry arguments and azimuthal order segmentation such that the matrix can be solved on a desktop PC. The eigen-space reveals that several states can be confined in the bottle region, whereas another set of states extends the axial length of the structure similar to ridge waveguide modes. The hollow core bottle is also presented as a design modification. The micro-optic bottle resonator structure size makes it directly compatible with silicon-based photonics increasing its potential as a key component in sensing, communication, and other applications.

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Keywords Bottle resonator, Eigen-matrix, Fourier-Bessel basis, Microresonator, Silicon photonics, Whispering-gallery modes
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Journal Journal of Micro/Nanolithography, MEMS, and MOEMS
Gauthier, R. (2013). Whispering-gallery modes of μ-optic silicon bottle resonator examined using a Fourier-Bessel eigen-state approach. Journal of Micro/Nanolithography, MEMS, and MOEMS, 12(4). doi:10.1117/1.JMM.12.4.043007