Abstract

The effect that geometrical resonances of orbiting internally reflecting rays have on the morphology-dependent resonances of microspheres is investigated heuristically and numerically using generalized Lorenz–Mie theory. Angularly resolved off-axis Gaussian beam elastic scattering spectra are presented. The results obtained show that the elastic scattering intensity of morphology-dependent resonances is noticeably enhanced in the vicinity of the geometrical resonance scattering angles.

© 2011 Optical Society of America

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  14. A. Serpengüzel and A. Demir, “Silicon microspheres for near-IR communication applications,” Semicond. Sci. Technol. 23, 064009 (2008).
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  15. E. Yüce, O. Gürlü, and A. Serpengüzel, “Optical modulation with silicon microspheres,” IEEE Photon. Technol. Lett. 21, 1481–1483 (2009).
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2011 (1)

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

2010 (1)

2009 (4)

G. Gilardi, D. Donisi, A. Serpengüzel, and R. Beccherelli, “Liquid-crystal tunable filter based on sapphire microspheres,” Opt. Lett. 34, 3253–3255 (2009).
[CrossRef]

G. Gouesbet, “Generalized Lorenz–Mie theories, the third decade: a perspective,” J. Quant. Spectrosc. Radiat. Transfer 110, 1223–1238 (2009).
[CrossRef]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009).
[CrossRef]

E. Yüce, O. Gürlü, and A. Serpengüzel, “Optical modulation with silicon microspheres,” IEEE Photon. Technol. Lett. 21, 1481–1483 (2009).
[CrossRef]

2008 (3)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

A. Serpengüzel, A. Kurt, and U. K. Ayaz, “Silicon microspheres for electronic and photonic integration,” Photon. Nanostr. Fundam. Appl. 6, 179–182 (2008).
[CrossRef]

A. Serpengüzel and A. Demir, “Silicon microspheres for near-IR communication applications,” Semicond. Sci. Technol. 23, 064009 (2008).
[CrossRef]

2007 (1)

2006 (2)

J. A. Lock, S. Y. Wrbanek, and K. E. Weiland, “Scattering of a tightly focused beam by optically trapped particle,” Appl. Opt. 45, 3634–3645 (2006).
[CrossRef]

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, “Enhancing sensitivity of a whispering gallery mode biosensor by subwavelength confinement,” Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

2005 (3)

A. Braun, C. Kornmessser, and V. Beushausen, “Simultaneous spatial and spectral imaging of lasing droplets,” J. Opt. Soc. Am. A 22, 1772–1779 (2005).
[CrossRef]

Y. O. Yilmaz, A. Demir, A. Kurt, and A. Serpengüzel, “Optical channel dropping with a silicon microsphere,” IEEE Photon. Technol. Lett. 17, 1662–1664 (2005).
[CrossRef]

A. Demir and A. Serpengüzel, “Silica microspheres for biomolecular detection applications,” IEE Proc. Nanobiotechnol. 152, 105–108 (2005).
[CrossRef]

2004 (3)

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804(R) (2004).
[CrossRef]

T. Bilici, S. Işçi, A. Kurt, and A. Serpengüzel, “Microsphere-based channel dropping filter with an integrated photodetector,” IEEE Photon. Technol. Lett. 16, 476–478 (2004).
[CrossRef]

2003 (2)

2002 (2)

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14, 1118–1120 (2002).
[CrossRef]

S. M. Spillane, J. T. Kippenberg, and K. J. Vahala, “Ultralow threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef]

2001 (1)

G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, “Periodic orbits in Hamiltonian chaos of the annular billiard,” Phys. Rev. E 65, 016212 (2001).
[CrossRef]

2000 (1)

1999 (1)

1998 (2)

1996 (1)

1995 (1)

1993 (1)

1992 (1)

1979 (1)

1969 (1)

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. II. Theory of the rainbow and the glory,” J. Math. Phys. 10, 125–176 (1969).
[CrossRef]

Arnold, S.

Ayaz, U. K.

A. Serpengüzel, A. Kurt, and U. K. Ayaz, “Silicon microspheres for electronic and photonic integration,” Photon. Nanostr. Fundam. Appl. 6, 179–182 (2008).
[CrossRef]

Barton, J. P.

Beccherelli, R.

Beushausen, V.

Bilici, T.

T. Bilici, S. Işçi, A. Kurt, and A. Serpengüzel, “Microsphere-based channel dropping filter with an integrated photodetector,” IEEE Photon. Technol. Lett. 16, 476–478 (2004).
[CrossRef]

Braun, A.

Cai, M.

Campillo, A. J.

Connolly, J.

Culic-Viskota, J.

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, “Enhancing sensitivity of a whispering gallery mode biosensor by subwavelength confinement,” Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

Demir, A.

A. Serpengüzel and A. Demir, “Silicon microspheres for near-IR communication applications,” Semicond. Sci. Technol. 23, 064009 (2008).
[CrossRef]

A. Demir and A. Serpengüzel, “Silica microspheres for biomolecular detection applications,” IEE Proc. Nanobiotechnol. 152, 105–108 (2005).
[CrossRef]

Y. O. Yilmaz, A. Demir, A. Kurt, and A. Serpengüzel, “Optical channel dropping with a silicon microsphere,” IEEE Photon. Technol. Lett. 17, 1662–1664 (2005).
[CrossRef]

Donisi, D.

Eversole, J. D.

Gaathon, O.

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, “Enhancing sensitivity of a whispering gallery mode biosensor by subwavelength confinement,” Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

Gilardi, G.

Gouesbet, G.

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

G. Gouesbet, “Generalized Lorenz–Mie theories, the third decade: a perspective,” J. Quant. Spectrosc. Radiat. Transfer 110, 1223–1238 (2009).
[CrossRef]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009).
[CrossRef]

G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, “Periodic orbits in Hamiltonian chaos of the annular billiard,” Phys. Rev. E 65, 016212 (2001).
[CrossRef]

Gréhan, G.

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, “Periodic orbits in Hamiltonian chaos of the annular billiard,” Phys. Rev. E 65, 016212 (2001).
[CrossRef]

Griffel, G.

Gürlü, O.

E. Yüce, O. Gürlü, and A. Serpengüzel, “Optical modulation with silicon microspheres,” IEEE Photon. Technol. Lett. 21, 1481–1483 (2009).
[CrossRef]

Holler, S.

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804(R) (2004).
[CrossRef]

Isçi, S.

T. Bilici, S. Işçi, A. Kurt, and A. Serpengüzel, “Microsphere-based channel dropping filter with an integrated photodetector,” IEEE Photon. Technol. Lett. 16, 476–478 (2004).
[CrossRef]

Jiang, L.

Khoshsima, M.

Kippenberg, J. T.

S. M. Spillane, J. T. Kippenberg, and K. J. Vahala, “Ultralow threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef]

Kornmessser, C.

Kurt, A.

A. Serpengüzel, A. Kurt, and U. K. Ayaz, “Silicon microspheres for electronic and photonic integration,” Photon. Nanostr. Fundam. Appl. 6, 179–182 (2008).
[CrossRef]

Y. O. Yilmaz, A. Demir, A. Kurt, and A. Serpengüzel, “Optical channel dropping with a silicon microsphere,” IEEE Photon. Technol. Lett. 17, 1662–1664 (2005).
[CrossRef]

T. Bilici, S. Işçi, A. Kurt, and A. Serpengüzel, “Microsphere-based channel dropping filter with an integrated photodetector,” IEEE Photon. Technol. Lett. 16, 476–478 (2004).
[CrossRef]

Laine, J. P.

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14, 1118–1120 (2002).
[CrossRef]

Lam, C. C.

Lane, P. A.

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14, 1118–1120 (2002).
[CrossRef]

Leung, P. T.

Libchaber, A.

Lin, H.-B.

Lin, N.

Lock, J. A.

Lu, Y.

Maleki, L.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804(R) (2004).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[CrossRef]

Matsko, A. B.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804(R) (2004).
[CrossRef]

Meunier-Guttin-Cluzel, S.

G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, “Periodic orbits in Hamiltonian chaos of the annular billiard,” Phys. Rev. E 65, 016212 (2001).
[CrossRef]

Mihnev, M.

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, “Enhancing sensitivity of a whispering gallery mode biosensor by subwavelength confinement,” Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

Morris, N.

Nöckel, J. U.

J. U. Nöckel and A. D. Stone, “Chaotic light: a theory of asymmetric resonant cavities,” in Optical Processes in Microcavities, R. K. Chang and A. J. Campillo, eds. (World Scientific, 1996), pp. 389–426.

Nussenzveig, H. M.

H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
[CrossRef]

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. II. Theory of the rainbow and the glory,” J. Math. Phys. 10, 125–176 (1969).
[CrossRef]

Painter, O.

Ren, H. C.

Savchenkov, A. A.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804(R) (2004).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[CrossRef]

Serpengüzel, A.

G. Gilardi, D. Donisi, A. Serpengüzel, and R. Beccherelli, “Liquid-crystal tunable filter based on sapphire microspheres,” Opt. Lett. 34, 3253–3255 (2009).
[CrossRef]

E. Yüce, O. Gürlü, and A. Serpengüzel, “Optical modulation with silicon microspheres,” IEEE Photon. Technol. Lett. 21, 1481–1483 (2009).
[CrossRef]

A. Serpengüzel, A. Kurt, and U. K. Ayaz, “Silicon microspheres for electronic and photonic integration,” Photon. Nanostr. Fundam. Appl. 6, 179–182 (2008).
[CrossRef]

A. Serpengüzel and A. Demir, “Silicon microspheres for near-IR communication applications,” Semicond. Sci. Technol. 23, 064009 (2008).
[CrossRef]

Y. O. Yilmaz, A. Demir, A. Kurt, and A. Serpengüzel, “Optical channel dropping with a silicon microsphere,” IEEE Photon. Technol. Lett. 17, 1662–1664 (2005).
[CrossRef]

A. Demir and A. Serpengüzel, “Silica microspheres for biomolecular detection applications,” IEE Proc. Nanobiotechnol. 152, 105–108 (2005).
[CrossRef]

T. Bilici, S. Işçi, A. Kurt, and A. Serpengüzel, “Microsphere-based channel dropping filter with an integrated photodetector,” IEEE Photon. Technol. Lett. 16, 476–478 (2004).
[CrossRef]

G. Griffel, S. Arnold, D. Taskent, A. Serpengüzel, J. Connolly, and N. Morris, “Morphology-dependent resonances of a microsphere-optical fiber system,” Opt. Lett. 21, 695–697 (1996).
[CrossRef]

Spillane, S. M.

S. M. Spillane, J. T. Kippenberg, and K. J. Vahala, “Ultralow threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef]

Stone, A. D.

J. U. Nöckel and A. D. Stone, “Chaotic light: a theory of asymmetric resonant cavities,” in Optical Processes in Microcavities, R. K. Chang and A. J. Campillo, eds. (World Scientific, 1996), pp. 389–426.

Tapalian, H. C.

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14, 1118–1120 (2002).
[CrossRef]

Taskent, D.

Teraoka, I.

Tsai, H.

Vahala, K. J.

S. M. Spillane, J. T. Kippenberg, and K. J. Vahala, “Ultralow threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, “Fiber-coupled microsphere laser,” Opt. Lett. 25, 1430–1432 (2000).
[CrossRef]

Vollmer, F.

Wang, S.

Weiland, K. E.

Wrbanek, S. Y.

Xiao, H.

Yilmaz, Y. O.

Y. O. Yilmaz, A. Demir, A. Kurt, and A. Serpengüzel, “Optical channel dropping with a silicon microsphere,” IEEE Photon. Technol. Lett. 17, 1662–1664 (2005).
[CrossRef]

Young, K.

Yuan, L.

Yüce, E.

E. Yüce, O. Gürlü, and A. Serpengüzel, “Optical modulation with silicon microspheres,” IEEE Photon. Technol. Lett. 21, 1481–1483 (2009).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, “Enhancing sensitivity of a whispering gallery mode biosensor by subwavelength confinement,” Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

IEE Proc. Nanobiotechnol. (1)

A. Demir and A. Serpengüzel, “Silica microspheres for biomolecular detection applications,” IEE Proc. Nanobiotechnol. 152, 105–108 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

Y. O. Yilmaz, A. Demir, A. Kurt, and A. Serpengüzel, “Optical channel dropping with a silicon microsphere,” IEEE Photon. Technol. Lett. 17, 1662–1664 (2005).
[CrossRef]

T. Bilici, S. Işçi, A. Kurt, and A. Serpengüzel, “Microsphere-based channel dropping filter with an integrated photodetector,” IEEE Photon. Technol. Lett. 16, 476–478 (2004).
[CrossRef]

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14, 1118–1120 (2002).
[CrossRef]

E. Yüce, O. Gürlü, and A. Serpengüzel, “Optical modulation with silicon microspheres,” IEEE Photon. Technol. Lett. 21, 1481–1483 (2009).
[CrossRef]

J. Math. Phys. (1)

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. II. Theory of the rainbow and the glory,” J. Math. Phys. 10, 125–176 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (2)

J. Quant. Spectrosc. Radiat. Transfer (3)

G. Gouesbet, “Generalized Lorenz–Mie theories, the third decade: a perspective,” J. Quant. Spectrosc. Radiat. Transfer 110, 1223–1238 (2009).
[CrossRef]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

Nature (1)

S. M. Spillane, J. T. Kippenberg, and K. J. Vahala, “Ultralow threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef]

Opt. Commun. (1)

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Photon. Nanostr. Fundam. Appl. (1)

A. Serpengüzel, A. Kurt, and U. K. Ayaz, “Silicon microspheres for electronic and photonic integration,” Photon. Nanostr. Fundam. Appl. 6, 179–182 (2008).
[CrossRef]

Phys. Rev. A (1)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804(R) (2004).
[CrossRef]

Phys. Rev. E (1)

G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, “Periodic orbits in Hamiltonian chaos of the annular billiard,” Phys. Rev. E 65, 016212 (2001).
[CrossRef]

Semicond. Sci. Technol. (1)

A. Serpengüzel and A. Demir, “Silicon microspheres for near-IR communication applications,” Semicond. Sci. Technol. 23, 064009 (2008).
[CrossRef]

Other (3)

R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, 1996).

A. Serpengüzel and A. W. Poon, eds., Optical Processes in Microparticles and Nanostructures (World Scientific, 2011).

J. U. Nöckel and A. D. Stone, “Chaotic light: a theory of asymmetric resonant cavities,” in Optical Processes in Microcavities, R. K. Chang and A. J. Campillo, eds. (World Scientific, 1996), pp. 389–426.

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Figures (5)

Fig. 1.
Fig. 1.

Geometrical resonance formation geometries for p=3, 4, 5 and N=1. The black arrows outside the sphere denote the scattering angles of the geometrically resonant ray for 0qp1.

Fig. 2.
Fig. 2.

Relative refractive index of the sphere for a geometrical resonance as a function of p for N=1.

Fig. 3.
Fig. 3.

Expected spectral and scattering angle intensity distribution for p=3 and m=2.

Fig. 4.
Fig. 4.

TM elastic light scattering intensity in decibels as (a) a false color image, (b) at scattering angles of 47° and 110°, and (c) at wavelengths of 1312 and 1318nm.

Fig. 5.
Fig. 5.

TE elastic light scattering intensity in decibels as (a) a false color image (b) at scattering angles of 47° and 96°, and (c) at wavelengths of 1320 and 1326nm.

Equations (3)

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θc=π2(12p).
m=1cos(πp).
λ=2paMtan(πp),

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