Abstract

We investigate theoretically the switching effects for the whispering gallery modes in a spherical dielectric resonator when its material is subject to abrupt time change in permittivity. A rigorous analytical approach is used to study the transformation process. Details of both the transient response and the steady-state regime are described.

© 2012 Optical Society of America

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  9. E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Color of shock waves in photonic crystals,” Phys. Rev. Lett. 90, 203904(2003).
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    [CrossRef]
  25. N. K. Sakhnenko, A. G. Nerukh, T. M. Benson, and P. Sewell, “Whispering Gallery Mode transformation in a switched micro-cavity with concentric ring geometry,” Opt. Quantum Electron. 40, 818–820 (2008).
    [CrossRef]
  26. N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Near field pattern images in 2D circular resonator with time varying plasma,” IEEE Trans. Plasma Sci. 36, 1222–1223 (2008).
    [CrossRef]
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  29. F. R. Morgenthaler, “Velocity modulation of electromagnetic waves,” IRE Trans. Microwave Theory Tech. 6, 167–172(1958).
    [CrossRef]
  30. A. Nerukh, T. Remaeva, and N. Sakhnenko, “Frequency change of partial spherical waves indused by time change of medium permittivity,” Opt. Quantum Electron. 41, 327–335 (2009).
    [CrossRef]

2009 (2)

A. G. Nerukh and N. K. Sakhnenko, “Formation of point source image by time change of the medium,” IEEE J. Sel. Top. Quantum Electron. 15, 1368–1373 (2009).
[CrossRef]

A. Nerukh, T. Remaeva, and N. Sakhnenko, “Frequency change of partial spherical waves indused by time change of medium permittivity,” Opt. Quantum Electron. 41, 327–335 (2009).
[CrossRef]

2008 (4)

N. K. Sakhnenko, A. G. Nerukh, T. M. Benson, and P. Sewell, “Whispering Gallery Mode transformation in a switched micro-cavity with concentric ring geometry,” Opt. Quantum Electron. 40, 818–820 (2008).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Near field pattern images in 2D circular resonator with time varying plasma,” IEEE Trans. Plasma Sci. 36, 1222–1223 (2008).
[CrossRef]

A. V. Boriskin, S. V. Boriskina, A. Rolland, R. Sauleau, and A. I. Nosich, “Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder,” J. Opt. Soc. Am. A 25, 1169–1173 (2008).
[CrossRef]

M. Benyoucef, S. Kiravittaya, Y. Mei, A. Rastelli, and O. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

2007 (2)

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Frequency conversion and field pattern rotation in WGM resonator with transient inclusion,” Opt. Quantum Electron. 39, 761–771 (2007).
[CrossRef]

E. V. Bekker, A. Vukovic, P. Sewell, T. M. Benson, N. K. Sakhnenko, and A. G. Nerukh, “An assessment of coherent coupling through radiation fields in time varying slab waveguides,” Opt. Quantum Electron. 39, 533–551 (2007).
[CrossRef]

2006 (2)

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
[CrossRef]

N. K. Sakhnenko, T. M. Benson, P. Sewell, and A. G. Nerukh, “Transient transformation of whispering gallery resonator modes due to time variations in dielectric permittivity,” Opt. Quantum Electron. 38, 71–81 (2006).
[CrossRef]

2005 (1)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “High-order tunable filters on a chain of coupled crystalline whispering-gallery-mode resonators,” IEEE Photon. Technol. Lett. 17, 136–138 (2005).
[CrossRef]

2004 (4)

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

M. Yanic and S. Fan, “Time reversal of light with linear optics and modulators,” Phys. Rev. Lett. 93, 173903 (2004).
[CrossRef]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, M. A. Foster, D. G. Ouzounov, and A. L. Gaeta, “All-optical switching on a silicon chip,” Opt. Lett. 29, 2867–2869 (2004).
[CrossRef]

2003 (2)

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Color of shock waves in photonic crystals,” Phys. Rev. Lett. 90, 203904(2003).
[CrossRef] [PubMed]

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901(2003).
[CrossRef] [PubMed]

2002 (4)

A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic bandgap,” Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

K. Djordjev, S. J. Choi, S. J. Choi, and R. Dapkus, “Microdisk tunable resonant filters and switches,” IEEE Photon. Technol. Lett. 14, 823–830 (2002).
[CrossRef]

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonant-array waveguide,” Phys. Rev. E 65, 036619 (2002).
[CrossRef]

A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron. 32, 377–400 (2002).
[CrossRef]

2001 (3)

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

1997 (2)

F. Blom, D. Dijk, H. Hoekstra, M. Driessen, and A. Popma, “Experimental study of integrated-optics microcavity resonators,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

1990 (1)

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990).
[CrossRef]

1958 (1)

F. R. Morgenthaler, “Velocity modulation of electromagnetic waves,” IRE Trans. Microwave Theory Tech. 6, 167–172(1958).
[CrossRef]

Almeida, V. R.

Andre, A.

A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic bandgap,” Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Barrios, C. A.

Bekker, E. V.

E. V. Bekker, A. Vukovic, P. Sewell, T. M. Benson, N. K. Sakhnenko, and A. G. Nerukh, “An assessment of coherent coupling through radiation fields in time varying slab waveguides,” Opt. Quantum Electron. 39, 533–551 (2007).
[CrossRef]

Bennett, B. R.

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990).
[CrossRef]

Benson, T.

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Near field pattern images in 2D circular resonator with time varying plasma,” IEEE Trans. Plasma Sci. 36, 1222–1223 (2008).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Frequency conversion and field pattern rotation in WGM resonator with transient inclusion,” Opt. Quantum Electron. 39, 761–771 (2007).
[CrossRef]

Benson, T. M.

N. K. Sakhnenko, A. G. Nerukh, T. M. Benson, and P. Sewell, “Whispering Gallery Mode transformation in a switched micro-cavity with concentric ring geometry,” Opt. Quantum Electron. 40, 818–820 (2008).
[CrossRef]

E. V. Bekker, A. Vukovic, P. Sewell, T. M. Benson, N. K. Sakhnenko, and A. G. Nerukh, “An assessment of coherent coupling through radiation fields in time varying slab waveguides,” Opt. Quantum Electron. 39, 533–551 (2007).
[CrossRef]

N. K. Sakhnenko, T. M. Benson, P. Sewell, and A. G. Nerukh, “Transient transformation of whispering gallery resonator modes due to time variations in dielectric permittivity,” Opt. Quantum Electron. 38, 71–81 (2006).
[CrossRef]

Benyoucef, M.

M. Benyoucef, S. Kiravittaya, Y. Mei, A. Rastelli, and O. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Blair, S.

Blom, F.

F. Blom, D. Dijk, H. Hoekstra, M. Driessen, and A. Popma, “Experimental study of integrated-optics microcavity resonators,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Boriskin, A. V.

Boriskina, S. V.

Boyd, R. W.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonant-array waveguide,” Phys. Rev. E 65, 036619 (2002).
[CrossRef]

R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742–5747 (2001).
[CrossRef]

Cai, M.

Chang, H.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Chen, Y.

Choi, S. J.

K. Djordjev, S. J. Choi, S. J. Choi, and R. Dapkus, “Microdisk tunable resonant filters and switches,” IEEE Photon. Technol. Lett. 14, 823–830 (2002).
[CrossRef]

K. Djordjev, S. J. Choi, S. J. Choi, and R. Dapkus, “Microdisk tunable resonant filters and switches,” IEEE Photon. Technol. Lett. 14, 823–830 (2002).
[CrossRef]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Cohen, O.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Dapkus, R.

K. Djordjev, S. J. Choi, S. J. Choi, and R. Dapkus, “Microdisk tunable resonant filters and switches,” IEEE Photon. Technol. Lett. 14, 823–830 (2002).
[CrossRef]

Del Alamo, J. A.

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990).
[CrossRef]

Dijk, D.

F. Blom, D. Dijk, H. Hoekstra, M. Driessen, and A. Popma, “Experimental study of integrated-optics microcavity resonators,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Djordjev, K.

K. Djordjev, S. J. Choi, S. J. Choi, and R. Dapkus, “Microdisk tunable resonant filters and switches,” IEEE Photon. Technol. Lett. 14, 823–830 (2002).
[CrossRef]

Driessen, M.

F. Blom, D. Dijk, H. Hoekstra, M. Driessen, and A. Popma, “Experimental study of integrated-optics microcavity resonators,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Fan, S.

M. Yanic and S. Fan, “Time reversal of light with linear optics and modulators,” Phys. Rev. Lett. 93, 173903 (2004).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Foster, M. A.

Fuller, K. A.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Gaeta, A. L.

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Heebner, J. E.

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonant-array waveguide,” Phys. Rev. E 65, 036619 (2002).
[CrossRef]

R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742–5747 (2001).
[CrossRef]

Hoekstra, H.

F. Blom, D. Dijk, H. Hoekstra, M. Driessen, and A. Popma, “Experimental study of integrated-optics microcavity resonators,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Ilchenko, V. S.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “High-order tunable filters on a chain of coupled crystalline whispering-gallery-mode resonators,” IEEE Photon. Technol. Lett. 17, 136–138 (2005).
[CrossRef]

Joannopoulos, J. D.

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Color of shock waves in photonic crystals,” Phys. Rev. Lett. 90, 203904(2003).
[CrossRef] [PubMed]

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901(2003).
[CrossRef] [PubMed]

Jones, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Kiravittaya, S.

M. Benyoucef, S. Kiravittaya, Y. Mei, A. Rastelli, and O. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Liao, L.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Lipson, M.

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Liu, A.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Lukin, M. D.

A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic bandgap,” Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Maleki, L.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “High-order tunable filters on a chain of coupled crystalline whispering-gallery-mode resonators,” IEEE Photon. Technol. Lett. 17, 136–138 (2005).
[CrossRef]

Matsko, A. B.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “High-order tunable filters on a chain of coupled crystalline whispering-gallery-mode resonators,” IEEE Photon. Technol. Lett. 17, 136–138 (2005).
[CrossRef]

Mei, Y.

M. Benyoucef, S. Kiravittaya, Y. Mei, A. Rastelli, and O. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Mitsugi, S.

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
[CrossRef]

Morgenthaler, F. R.

F. R. Morgenthaler, “Velocity modulation of electromagnetic waves,” IRE Trans. Microwave Theory Tech. 6, 167–172(1958).
[CrossRef]

Nerukh, A.

A. Nerukh, T. Remaeva, and N. Sakhnenko, “Frequency change of partial spherical waves indused by time change of medium permittivity,” Opt. Quantum Electron. 41, 327–335 (2009).
[CrossRef]

Nerukh, A. G.

A. G. Nerukh and N. K. Sakhnenko, “Formation of point source image by time change of the medium,” IEEE J. Sel. Top. Quantum Electron. 15, 1368–1373 (2009).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. M. Benson, and P. Sewell, “Whispering Gallery Mode transformation in a switched micro-cavity with concentric ring geometry,” Opt. Quantum Electron. 40, 818–820 (2008).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Near field pattern images in 2D circular resonator with time varying plasma,” IEEE Trans. Plasma Sci. 36, 1222–1223 (2008).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Frequency conversion and field pattern rotation in WGM resonator with transient inclusion,” Opt. Quantum Electron. 39, 761–771 (2007).
[CrossRef]

E. V. Bekker, A. Vukovic, P. Sewell, T. M. Benson, N. K. Sakhnenko, and A. G. Nerukh, “An assessment of coherent coupling through radiation fields in time varying slab waveguides,” Opt. Quantum Electron. 39, 533–551 (2007).
[CrossRef]

N. K. Sakhnenko, T. M. Benson, P. Sewell, and A. G. Nerukh, “Transient transformation of whispering gallery resonator modes due to time variations in dielectric permittivity,” Opt. Quantum Electron. 38, 71–81 (2006).
[CrossRef]

Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Nosich, A. I.

Notomi, M.

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
[CrossRef]

Oraevsky, A. N.

A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron. 32, 377–400 (2002).
[CrossRef]

Ouzounov, D. G.

Panepucci, R. R.

Paniccia, M.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Park, Q.-H.

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonant-array waveguide,” Phys. Rev. E 65, 036619 (2002).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Popma, A.

F. Blom, D. Dijk, H. Hoekstra, M. Driessen, and A. Popma, “Experimental study of integrated-optics microcavity resonators,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Rastelli, A.

M. Benyoucef, S. Kiravittaya, Y. Mei, A. Rastelli, and O. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Reed, E. J.

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Color of shock waves in photonic crystals,” Phys. Rev. Lett. 90, 203904(2003).
[CrossRef] [PubMed]

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901(2003).
[CrossRef] [PubMed]

Remaeva, T.

A. Nerukh, T. Remaeva, and N. Sakhnenko, “Frequency change of partial spherical waves indused by time change of medium permittivity,” Opt. Quantum Electron. 41, 327–335 (2009).
[CrossRef]

Rolland, A.

Rosenberger, A. T.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Rubin, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Sakhnenko, N.

A. Nerukh, T. Remaeva, and N. Sakhnenko, “Frequency change of partial spherical waves indused by time change of medium permittivity,” Opt. Quantum Electron. 41, 327–335 (2009).
[CrossRef]

Sakhnenko, N. K.

A. G. Nerukh and N. K. Sakhnenko, “Formation of point source image by time change of the medium,” IEEE J. Sel. Top. Quantum Electron. 15, 1368–1373 (2009).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. M. Benson, and P. Sewell, “Whispering Gallery Mode transformation in a switched micro-cavity with concentric ring geometry,” Opt. Quantum Electron. 40, 818–820 (2008).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Near field pattern images in 2D circular resonator with time varying plasma,” IEEE Trans. Plasma Sci. 36, 1222–1223 (2008).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Frequency conversion and field pattern rotation in WGM resonator with transient inclusion,” Opt. Quantum Electron. 39, 761–771 (2007).
[CrossRef]

E. V. Bekker, A. Vukovic, P. Sewell, T. M. Benson, N. K. Sakhnenko, and A. G. Nerukh, “An assessment of coherent coupling through radiation fields in time varying slab waveguides,” Opt. Quantum Electron. 39, 533–551 (2007).
[CrossRef]

N. K. Sakhnenko, T. M. Benson, P. Sewell, and A. G. Nerukh, “Transient transformation of whispering gallery resonator modes due to time variations in dielectric permittivity,” Opt. Quantum Electron. 38, 71–81 (2006).
[CrossRef]

Samara-Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Sauleau, R.

Savchenkov, A. A.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “High-order tunable filters on a chain of coupled crystalline whispering-gallery-mode resonators,” IEEE Photon. Technol. Lett. 17, 136–138 (2005).
[CrossRef]

Schmidt, O.

M. Benyoucef, S. Kiravittaya, Y. Mei, A. Rastelli, and O. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Sewell, P.

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Near field pattern images in 2D circular resonator with time varying plasma,” IEEE Trans. Plasma Sci. 36, 1222–1223 (2008).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. M. Benson, and P. Sewell, “Whispering Gallery Mode transformation in a switched micro-cavity with concentric ring geometry,” Opt. Quantum Electron. 40, 818–820 (2008).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Frequency conversion and field pattern rotation in WGM resonator with transient inclusion,” Opt. Quantum Electron. 39, 761–771 (2007).
[CrossRef]

E. V. Bekker, A. Vukovic, P. Sewell, T. M. Benson, N. K. Sakhnenko, and A. G. Nerukh, “An assessment of coherent coupling through radiation fields in time varying slab waveguides,” Opt. Quantum Electron. 39, 533–551 (2007).
[CrossRef]

N. K. Sakhnenko, T. M. Benson, P. Sewell, and A. G. Nerukh, “Transient transformation of whispering gallery resonator modes due to time variations in dielectric permittivity,” Opt. Quantum Electron. 38, 71–81 (2006).
[CrossRef]

Smith, D. D.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Soljacic, M.

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901(2003).
[CrossRef] [PubMed]

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Color of shock waves in photonic crystals,” Phys. Rev. Lett. 90, 203904(2003).
[CrossRef] [PubMed]

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E. V. Bekker, A. Vukovic, P. Sewell, T. M. Benson, N. K. Sakhnenko, and A. G. Nerukh, “An assessment of coherent coupling through radiation fields in time varying slab waveguides,” Opt. Quantum Electron. 39, 533–551 (2007).
[CrossRef]

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M. Yanic and S. Fan, “Time reversal of light with linear optics and modulators,” Phys. Rev. Lett. 93, 173903 (2004).
[CrossRef]

Appl. Opt. (2)

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[CrossRef]

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

A. G. Nerukh and N. K. Sakhnenko, “Formation of point source image by time change of the medium,” IEEE J. Sel. Top. Quantum Electron. 15, 1368–1373 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

K. Djordjev, S. J. Choi, S. J. Choi, and R. Dapkus, “Microdisk tunable resonant filters and switches,” IEEE Photon. Technol. Lett. 14, 823–830 (2002).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “High-order tunable filters on a chain of coupled crystalline whispering-gallery-mode resonators,” IEEE Photon. Technol. Lett. 17, 136–138 (2005).
[CrossRef]

IEEE Trans. Plasma Sci. (1)

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Near field pattern images in 2D circular resonator with time varying plasma,” IEEE Trans. Plasma Sci. 36, 1222–1223 (2008).
[CrossRef]

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[CrossRef]

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Nature (1)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Opt. Lett. (2)

Opt. Quantum Electron. (5)

A. Nerukh, T. Remaeva, and N. Sakhnenko, “Frequency change of partial spherical waves indused by time change of medium permittivity,” Opt. Quantum Electron. 41, 327–335 (2009).
[CrossRef]

E. V. Bekker, A. Vukovic, P. Sewell, T. M. Benson, N. K. Sakhnenko, and A. G. Nerukh, “An assessment of coherent coupling through radiation fields in time varying slab waveguides,” Opt. Quantum Electron. 39, 533–551 (2007).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. M. Benson, and P. Sewell, “Whispering Gallery Mode transformation in a switched micro-cavity with concentric ring geometry,” Opt. Quantum Electron. 40, 818–820 (2008).
[CrossRef]

N. K. Sakhnenko, T. M. Benson, P. Sewell, and A. G. Nerukh, “Transient transformation of whispering gallery resonator modes due to time variations in dielectric permittivity,” Opt. Quantum Electron. 38, 71–81 (2006).
[CrossRef]

N. K. Sakhnenko, A. G. Nerukh, T. Benson, and P. Sewell, “Frequency conversion and field pattern rotation in WGM resonator with transient inclusion,” Opt. Quantum Electron. 39, 761–771 (2007).
[CrossRef]

Phys. Rev. A (2)

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
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M. Benyoucef, S. Kiravittaya, Y. Mei, A. Rastelli, and O. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
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M. Yanic and S. Fan, “Time reversal of light with linear optics and modulators,” Phys. Rev. Lett. 93, 173903 (2004).
[CrossRef]

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Color of shock waves in photonic crystals,” Phys. Rev. Lett. 90, 203904(2003).
[CrossRef] [PubMed]

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901(2003).
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Figures (3)

Fig. 1
Fig. 1

Spectrum of the internal field before and after index turning. WGH-mode ( s = 1 , m = n = 7 , k a = 3.38 + 1.46 · 10 5 i ) is considered as initial one. Refractive index is tuned from the value n 1 = 3.4 to the value n 2 = 3.35 . After tuning, the red-shifting of the frequency corresponds to the excited WGH-mode ( s = 1 , m = n = 7 , k a = 3.43 + 1.85 · 10 5 i ). Zoom (bottom) indicates excitation of higher modes with negligible amplitudes.

Fig. 2
Fig. 2

Real part of the magnetic field of TM-polarized mode versus the normalized time ( t c / a ).WGH-mode ( s = 1 , m = n = 7 , k a = 3.38 + 1.46 · 10 5 i ) is considered as initial one. Refractive index is tuned from the value n 1 = 3.4 to the value n 2 = 3.35 .

Fig. 3
Fig. 3

The normalized frequency shift ( Re ( k 1 a k 2 a ) ) versus the angular number of WG mode for different values of Δ n = n 2 n 1 .

Equations (26)

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U r = 0 ; U θ = i ω α Y m n φ W ; U φ = i ω α Y m n θ W ;
W = { A j n ( k 1 r ) / sin θ , ( r < a ) B h n ( 2 ) ( k 0 r ) / sin θ , ( r > a ) ,
α = { ε 0 , TM   mode μ 0 , TE   mode ,
A = h n ( 2 ) ( k a ) / j n ( k 1 a ) B .
TM : [ ( k 1 a ) · j n ( k 1 a ) ] · h n ( 2 ) ( k a ) = [ ( k a ) · h n ( 2 ) ( k a ) ] · ε 1 j n ( k 1 a ) ,
TE : [ ( k 1 a ) · j n ( k 1 a ) ] · h n ( 2 ) ( k a ) = [ ( k a ) · h n ( 2 ) ( k a ) ] · j n ( k 1 a ) .
× × U + 1 v 2 2 2 t 2 U = 0 , ( r < a ) ,
× × U + 1 c 2 2 t 2 U = 0 , ( r > a ) .
E ( t = 0 + ) = ε 1 / ε 2 E ( t = 0 ) , E ( t = 0 + ) = ε 1 / ε 2 E ( t = 0 ) , ( r < a ) ,
H ( t = 0 + ) = H ( t = 0 ) , H ( t = 0 + ) = ε 1 / ε 2 H ( t = 0 ) , ( r < a ) .
E ( t = 0 + ) = E ( t = 0 ) , E ( t = 0 + ) = E ( t = 0 ) , ( r > a ) ,
H ( t = 0 + ) = H ( t = 0 ) , H ( t = 0 + ) = H ( t = 0 ) , ( r > a ) .
U t = U i + U b .
U r i = 0 ; U θ i = i ω α Y m n φ W i ; U φ i = i ω α Y m n θ W i ;
W i = { A M ( p ) j n ( k 1 r ) / sin θ ( r < a ) B N ( p ) h n ( 2 ) ( k 0 r ) / sin θ ( r > a ) .
M ( p ) = { p v 1 2 + i ω v 2 2 p 2 v 1 2 + ω 2 v 2 2 e i ω t , TM   mode v 2 2 ( p + i ω 0 ) p 2 v 1 2 + ω 0 2 v 2 2 e i ω t , TE   mode
N ( p ) = e i ω t p i ω 0 .
U r b = 0 ; U θ b = i ω α Y m n φ W b ; U φ b = i ω α Y m n θ W b ,
W b = { A C ( p ) j n ( ε 2 q r ) / sin θ ( r < a ) B D ( p ) h n ( 2 ) ( q r ) / sin θ ( r > a ) .
C TE = p 2 ( v 1 2 v 2 2 ) e i ω t ( p i ω 0 ) ( p 2 v 1 2 + ω 0 2 v 2 2 ) [ ( k 1 a ) · j n ( k 1 a ) ] h n ( 2 ) ( q a ) [ ( q a ) h n ( 2 ) ( q a ) ] j n ( k 1 a ) [ ( ε 2 q a ) · j n ( ε 2 q a ) ] h n ( 2 ) ( q a ) [ ( q a ) h n ( 2 ) ( q a ) ] j n ( ε 2 q a ) ,
D TE = p 2 ( v 1 2 v 2 2 ) e i ω t ( p i ω 0 ) ( p 2 v 1 2 + ω 0 2 v 2 2 ) · [ ( k 1 a ) · j n ( k 1 a ) ] j n ( ε 2 q a ) [ ( ε 2 q a ) · j n ( ε 2 q a ) ] j n ( k 1 a ) [ ( ε 2 q a ) · j n ( ε 2 q a ) ] h n ( 2 ) ( q a ) [ ( q a ) h n ( 2 ) ( q a ) ] j n ( ε 2 q a ) ,
C TM = ε 2 p ( v 1 2 v 2 2 ) e i ω t ( p i ω 0 ) ( p 2 v 1 2 + ω 0 2 v 2 2 ) p 2 [ ( k 1 a ) · j n ( k 1 a ) ] h n ( 2 ) ( q a ) + ε 1 ω 0 2 [ ( q a ) h n ( 2 ) ( q a ) ] j n ( k 1 a ) [ ( ε 2 q a ) · j n ( ε 2 q a ) ] h n ( 2 ) ( q a ) ε 2 [ ( q a ) h n ( 2 ) ( q a ) ] j n ( ε 2 q a ) ,
D TM = p ( v 1 2 v 2 2 ) e i ω t ( p i ω 0 ) ( p 2 v 1 2 + ω 0 2 v 2 2 ) ε 2 p 2 [ ( k 1 a ) · j n ( k 1 a ) ] j n ( ε 2 q a ) + ε 1 ω 0 2 [ ( ε 2 q a ) · j n ( ε 2 q a ) ] j n ( k 1 a ) [ ( ε 2 q a ) · j n ( ε 2 q a ) ] h n ( 2 ) ( q a ) ε 2 [ ( q a ) h n ( 2 ) ( q a ) ] j n ( ε 2 q a ) .
ω 1 ω 0 ω 0 = v 2 / v 1 ω 0 ω 0 ω 0 = ε 1 ε 2 1 .
ω n TE c ε a ( n + 1.8557 n 3 1 ε ε ε 1 ) ,
ω n TM c ε a ( n + 1.8557 n 3 ε ε 1 ) .

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