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Oscillatory Vertical Coupling between a Whispering-Gallery Resonator and a Bus Waveguide

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Physical Review Letters · Journal article · 15 April 2013
M. Ghulinyan, F. Ramiro-Manzano, N. Prtljaga, R. Guider, I. Carusotto, A. Pitanti, G. Pucker and L. Pavesi
Physical Review Letters
Volume 110
Issue 16
Article 163901
2013
DOI · 10.1103/PhysRevLett.110.163901 View article at APS Physical Review Letters journal
Abstract
We report on a theoretical and experimental study of the optical coupling between a whispering-gallery type resonator and a waveguide lying on different planes. In contrast to the usual in-plane geometry, the present vertical one is characterized by an oscillatory behavior of the effective coupling as a function of the vertical gap. This behavior manifests itself as oscillations in both the resonance peak waveguide transmission and the mode quality factor. An analytical description based on coupled-mode theory and a two-port beam-splitter model of the waveguide-resonator vertical coupling is developed for arbitrary phase-matching conditions and is successfully used to interpret the experimental observations.
How to cite
Initials first
M. Ghulinyan, F. Ramiro-Manzano, N. Prtljaga, R. Guider, I. Carusotto, A. Pitanti, G. Pucker and L. Pavesi. “Oscillatory Vertical Coupling between a Whispering-Gallery Resonator and a Bus Waveguide.” Phys. Rev. Lett. 110(16), 163901 (2013). DOI: 10.1103/PhysRevLett.110.163901.
Family name first
Ghulinyan, M., Ramiro-Manzano, F., Prtljaga, N., Guider, R., Carusotto, I., Pitanti, A., Pucker, G. and Pavesi, L. “Oscillatory Vertical Coupling between a Whispering-Gallery Resonator and a Bus Waveguide.” Phys. Rev. Lett. 110(16), 163901 (2013). DOI: 10.1103/PhysRevLett.110.163901.
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Figures
Figure 1: in-plane and vertical waveguide-resonator coupling geometries, optical micrograph and separation profiles
Figure 1. In-plane and vertical resonator-waveguide coupling geometries, an optical image of the vertically coupled device, and the corresponding separation profiles.
From M. Ghulinyan et al., Physical Review Letters 110, 163901 (2013), DOI 10.1103/PhysRevLett.110.163901. © 2013 American Physical Society.
Figure 2: theoretical vertical-coupling length, beam-splitter model, transmission and quality factor
Figure 2. Coupled-mode description of the vertical geometry, including the flat-zone length, beam-splitter model, resonant transmission and quality factor.
From M. Ghulinyan et al., Physical Review Letters 110, 163901 (2013), DOI 10.1103/PhysRevLett.110.163901. © 2013 American Physical Society.
Figure 3: experimental transmission spectrum of vertically coupled whispering-gallery resonator modes
Figure 3. Experimental transmission spectrum for a device with a nominal vertical gap of 814 nm, compared with the theoretical response of two radial-mode families.
From M. Ghulinyan et al., Physical Review Letters 110, 163901 (2013), DOI 10.1103/PhysRevLett.110.163901. © 2013 American Physical Society.
Figure 4: transmission and quality factor versus vertical gap with representative resonance spectra
Figure 4. Measured and calculated transmission and quality factor as functions of the vertical gap, with representative resonance spectra across the coupling regimes.
From M. Ghulinyan et al., Physical Review Letters 110, 163901 (2013), DOI 10.1103/PhysRevLett.110.163901. © 2013 American Physical Society.