Abstract

Owing to their ability to confine electromagnetic energy in ultrasmall dielectric volumes, micro-disk, ring and toroid resonators hold interest for both specific applications and fundamental investigations. Generally, contributions from various loss channels within these devices lead to limited spectral windows (Q-bands) where highest mode Q-factors manifest. Here we describe a strategy for tuning Q-bands using a new class of micro-resonators, named micro-kylix resonators, in which engineered stress within an initially flat disk results in either concave or convex devices. To shift the Q-band by 60nm towards short wavelengths in flat micro-disks a 50% diameter reduction is required, which causes severe radiative losses suppressing Q’s. With a micro-kylix, we achieve similar tuning and even higher Q’s by two orders of magnitude smaller diameter modification (0.4%). The phenomenon relies on geometry-induced smart interplay between modified dispersions of material absorption and radiative loss-related Q-factors. Micro-kylix devices can provide new functionalities and novel technological solutions for photonics and micro-resonator physics.

© 2009 Optical Society of America

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  1. L. Rayleigh, "Further applications of Bessel’s functions of high order to the whispering gallery and allied problems," Philos. Mag. 27, 100-109 (1914).
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    [CrossRef]
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    [CrossRef]
  4. T. Krauss, P. J. R. Laybourn, and J. Roberts, "CW operation of semiconductor ring lasers," Electron. Lett. 26, 2095-2097 (1990).
    [CrossRef]
  5. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2008 (3)

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, "A Photon Turnstile Dynamically Regulated by One Atom," Science 319, 1062-1065 (2008).
[CrossRef] [PubMed]

M. Ghulinyan, D. Navarro-Urrios, A. Pitanti, A. Lui, G. Pucker, and L. Pavesi, "Whispering-gallery modes and light emission from a Si-nanocrystal-based single microdisk resonator," Opt. Express 16, 13218-13224 (2008).
[CrossRef] [PubMed]

2007 (3)

Zh. Zhang, L. Yang, V. Liu, T. Hong, K. Vahala, and A. Scherer, "Visible submicron microdisk lasers," Appl. Phys. Lett. 90, 111119 (2007).
[CrossRef]

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, "Trapping, corralling and spectral bonding of optical resonances through optically induced potentials," Nat. Photonics 1, 658-665 (2007).
[CrossRef]

2006 (3)

2003 (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

2002 (1)

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma enhanced chemical-vapour deposition grown Silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

2000 (1)

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, "Laser emission from quantum dots in microdisk structures," Appl. Phys. Lett. 77, 184-186 (2000).
[CrossRef]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

1990 (1)

T. Krauss, P. J. R. Laybourn, and J. Roberts, "CW operation of semiconductor ring lasers," Electron. Lett. 26, 2095-2097 (1990).
[CrossRef]

1914 (1)

L. Rayleigh, "Further applications of Bessel’s functions of high order to the whispering gallery and allied problems," Philos. Mag. 27, 100-109 (1914).

Aoki, T.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, "A Photon Turnstile Dynamically Regulated by One Atom," Science 319, 1062-1065 (2008).
[CrossRef] [PubMed]

Armani, A. M.

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Becher, C.

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, "Laser emission from quantum dots in microdisk structures," Appl. Phys. Lett. 77, 184-186 (2000).
[CrossRef]

Bermel, P.

Burr, G.

Cazzanelli, M.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma enhanced chemical-vapour deposition grown Silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

Daldosso, N.

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

Dayan, B.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, "A Photon Turnstile Dynamically Regulated by One Atom," Science 319, 1062-1065 (2008).
[CrossRef] [PubMed]

Farjadpour, A.

Ferraioli, L.

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

Gaburro, Z.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma enhanced chemical-vapour deposition grown Silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

Ghulinyan, M.

Hong, T.

Zh. Zhang, L. Yang, V. Liu, T. Hong, K. Vahala, and A. Scherer, "Visible submicron microdisk lasers," Appl. Phys. Lett. 90, 111119 (2007).
[CrossRef]

Hu, E.

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, "Laser emission from quantum dots in microdisk structures," Appl. Phys. Lett. 77, 184-186 (2000).
[CrossRef]

Iacona, F.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma enhanced chemical-vapour deposition grown Silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

Ibanescu, M.

Ilchenko, V. S.

A. B. Matsko, and V. S. Ilchenko, "Optical Resonators With Whispering-Gallery Modes Part I: Basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

Imamoglu, A.

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, "Laser emission from quantum dots in microdisk structures," Appl. Phys. Lett. 77, 184-186 (2000).
[CrossRef]

Ippen, E. P.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, "Trapping, corralling and spectral bonding of optical resonances through optically induced potentials," Nat. Photonics 1, 658-665 (2007).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kimble, H. J.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, "A Photon Turnstile Dynamically Regulated by One Atom," Science 319, 1062-1065 (2008).
[CrossRef] [PubMed]

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Kiraz, A.

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, "Laser emission from quantum dots in microdisk structures," Appl. Phys. Lett. 77, 184-186 (2000).
[CrossRef]

Kompocholis, C.

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

Krauss, T.

T. Krauss, P. J. R. Laybourn, and J. Roberts, "CW operation of semiconductor ring lasers," Electron. Lett. 26, 2095-2097 (1990).
[CrossRef]

Laybourn, P. J. R.

T. Krauss, P. J. R. Laybourn, and J. Roberts, "CW operation of semiconductor ring lasers," Electron. Lett. 26, 2095-2097 (1990).
[CrossRef]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Liu, V.

Zh. Zhang, L. Yang, V. Liu, T. Hong, K. Vahala, and A. Scherer, "Visible submicron microdisk lasers," Appl. Phys. Lett. 90, 111119 (2007).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Lui, A.

Matsko, A. B.

A. B. Matsko, and V. S. Ilchenko, "Optical Resonators With Whispering-Gallery Modes Part I: Basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Michler, P.

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, "Laser emission from quantum dots in microdisk structures," Appl. Phys. Lett. 77, 184-186 (2000).
[CrossRef]

Navarro-Urrios, D.

M. Ghulinyan, D. Navarro-Urrios, A. Pitanti, A. Lui, G. Pucker, and L. Pavesi, "Whispering-gallery modes and light emission from a Si-nanocrystal-based single microdisk resonator," Opt. Express 16, 13218-13224 (2008).
[CrossRef] [PubMed]

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

Ostby, E. P.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, "A Photon Turnstile Dynamically Regulated by One Atom," Science 319, 1062-1065 (2008).
[CrossRef] [PubMed]

Parkins, A. S.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, "A Photon Turnstile Dynamically Regulated by One Atom," Science 319, 1062-1065 (2008).
[CrossRef] [PubMed]

Pavesi, L.

M. Ghulinyan, D. Navarro-Urrios, A. Pitanti, A. Lui, G. Pucker, and L. Pavesi, "Whispering-gallery modes and light emission from a Si-nanocrystal-based single microdisk resonator," Opt. Express 16, 13218-13224 (2008).
[CrossRef] [PubMed]

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma enhanced chemical-vapour deposition grown Silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Pitanti, A.

Popovic, M. A.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, "Trapping, corralling and spectral bonding of optical resonances through optically induced potentials," Nat. Photonics 1, 658-665 (2007).
[CrossRef]

Prakash, G. V.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma enhanced chemical-vapour deposition grown Silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

Pucker, G.

Puker, G.

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

Rakich, P. T.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, "Trapping, corralling and spectral bonding of optical resonances through optically induced potentials," Nat. Photonics 1, 658-665 (2007).
[CrossRef]

Rayleigh, L.

L. Rayleigh, "Further applications of Bessel’s functions of high order to the whispering gallery and allied problems," Philos. Mag. 27, 100-109 (1914).

Roberts, J.

T. Krauss, P. J. R. Laybourn, and J. Roberts, "CW operation of semiconductor ring lasers," Electron. Lett. 26, 2095-2097 (1990).
[CrossRef]

Rodriguez, A.

Roundy, R.

Scherer, A.

Zh. Zhang, L. Yang, V. Liu, T. Hong, K. Vahala, and A. Scherer, "Visible submicron microdisk lasers," Appl. Phys. Lett. 90, 111119 (2007).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Solja?cic, M.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, "Trapping, corralling and spectral bonding of optical resonances through optically induced potentials," Nat. Photonics 1, 658-665 (2007).
[CrossRef]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Vahala, K.

Zh. Zhang, L. Yang, V. Liu, T. Hong, K. Vahala, and A. Scherer, "Visible submicron microdisk lasers," Appl. Phys. Lett. 90, 111119 (2007).
[CrossRef]

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, "A Photon Turnstile Dynamically Regulated by One Atom," Science 319, 1062-1065 (2008).
[CrossRef] [PubMed]

A. M. Armani and K. J. Vahala, "Heavy water detection using ultra-high-Q microcavities," Opt. Lett. 31, 1896-1898 (2006).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Wang, M.

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

Yang, L.

Zh. Zhang, L. Yang, V. Liu, T. Hong, K. Vahala, and A. Scherer, "Visible submicron microdisk lasers," Appl. Phys. Lett. 90, 111119 (2007).
[CrossRef]

Zhang, L.

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, "Laser emission from quantum dots in microdisk structures," Appl. Phys. Lett. 77, 184-186 (2000).
[CrossRef]

Zhang, Zh.

Zh. Zhang, L. Yang, V. Liu, T. Hong, K. Vahala, and A. Scherer, "Visible submicron microdisk lasers," Appl. Phys. Lett. 90, 111119 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

P. Michler, A. Kiraz, L. Zhang, C. Becher, E. Hu, and A. Imamoglu, "Laser emission from quantum dots in microdisk structures," Appl. Phys. Lett. 77, 184-186 (2000).
[CrossRef]

Zh. Zhang, L. Yang, V. Liu, T. Hong, K. Vahala, and A. Scherer, "Visible submicron microdisk lasers," Appl. Phys. Lett. 90, 111119 (2007).
[CrossRef]

Electron. Lett. (1)

T. Krauss, P. J. R. Laybourn, and J. Roberts, "CW operation of semiconductor ring lasers," Electron. Lett. 26, 2095-2097 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. B. Matsko, and V. S. Ilchenko, "Optical Resonators With Whispering-Gallery Modes Part I: Basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

J. Mod. Opt. (1)

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma enhanced chemical-vapour deposition grown Silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

J. Nanomater (1)

L. Ferraioli, M. Wang, G. Puker, D. Navarro-Urrios, N. Daldosso, C. Kompocholis, and L. Pavesi, "Photoluminescence of silicon nanocrystals in silicon oxide," J. Nanomater 2007, 43491 (2007).

Nat. Photonics (1)

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, "Trapping, corralling and spectral bonding of optical resonances through optically induced potentials," Nat. Photonics 1, 658-665 (2007).
[CrossRef]

Nature (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Philos. Mag. (1)

L. Rayleigh, "Further applications of Bessel’s functions of high order to the whispering gallery and allied problems," Philos. Mag. 27, 100-109 (1914).

Science (2)

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, "A Photon Turnstile Dynamically Regulated by One Atom," Science 319, 1062-1065 (2008).
[CrossRef] [PubMed]

Other (4)

V. A. Mandelshtam and H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys. 107, 6756-6769(1997). Erratum, ibid. 109, 4128 (1998).
[CrossRef]

L. Pavesi and D. Lockwood, Silicon Photonics. Topics in Applied Physics (Springer-Verlag, Berlin, 2004) Vol. 94.

A. Anopchenko, N. Daldosso, R. Guider, D. Navarro-Urrios, A. Pitanti, R. Spano, and L. Pavesi, in Silicon Nanocrystals: Fundamentals, Synthesis and Applications (eds., L. Pavesi and R. Turan), (Wiley-VCH Verlag GmbH, Berlin, 2009)

image source http://it.wikipedia.org/wiki/Kylix.

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Figures (5)

Fig. 1.
Fig. 1.

The micro-kylix resonator. (a) Cross-sectional scanning electron micrograph (SEM) of a micro-kylix resonator. Inset: The Greek wine-drinking cup - κυλιξ, with a broad relatively shallow body raised on a stem from a foot [12]. (b) Three-dimensional view of an analytically calculated bent-up resonator using experimental dimensions (experimental bending radius of 47 μm). The extremes of the scale-bar represent the height difference between the edge and the center of a 200 nm-thick disk. (c) Electrical field distribution of the TM-polarized whispering-gallery mode shows a rather good confinement within the core of the μ-kylix resonator

Fig. 2.
Fig. 2.

WGM emission from μ-kylix and μ-disk resonators. (a) An SEM image of the μ-kylix array with a cross-sectioned μ-kylix resonator on the sample edge. The inset shows an optical image of μ-kylix array, with the bright spot corresponding to the Si-nc emission from a single device. (b) Micro-photoluminescence (PL) setup used for testing single devices. (c)Measured emission spectrum of the μ-kylix resonator, showing sharp whispering-gallery resonances of the lowest-order family raising out from the broad PL band of Si-nc. (d)Measured emission spectrum of the μ-disk resonator. The 2nd-order family modes manifest as broad and damped peaks next to intense 1st-order family resonances.

Fig. 3.
Fig. 3.

Tuning of quality factors in μ-kylix resonators. Scanning electron micrographs and corresponding shape sketches for (a) μ-kylix, (b) μ-disk and (c) inverse μ-kylix resonators, respectively. (d) Measured Q-factor bands for differently shaped resonators.

Fig. 4.
Fig. 4.

Out-of-plane radiative losses and modified Q-dispersions. (a) Small reduction of the disk diameter by only 0.4%(from 10 μm to 9.96 μm) induces negligible change in radiative Q for μ-disks (• and ▴, respectively). Instead, bending the originally flat disk to an effective diameter of 9.96 μm (thus forming a μ-kylix) a tenfold attenuation of quality factor is observed. (b) Confinement factor dispersions, calculated for different resonator configurations. (c) (top panel) Numerical simulations of a non-absorbing μ-kylix show that due to a weaker mode confinement only 1st-order radial family manifests. Bottom panel shows that μ-disks support quite intense 2nd-order families. (d) Numerically calculated dispersions of radiative, material and total quality factors in a μ-disk and a μ-kylix according to Eq. (1).

Fig. 5.
Fig. 5.

Q-band shift in smaller flat disks. A 60 nm spectral shift of the Q-band is measured for twice smaller (5 μm) μ-disks, while the same shift can be achieved with a μ-kylix of only 0.4% smaller effective diameter.

Equations (2)

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Qtotal1(λ)Qrad1(λ)+Qmat1(λ)+Qi1,
Qrad1(R,z)=Qrad1(R)+Qbend1(z),

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