Abstract

We describe pulse propagation through a slab with periodic dielectric function ε(t), thus extending our previous investigation for monochromatic incidence [Phys. Rev. A 79, 053821 (2009)]. Based on the concepts of phase and group delays, we prove that, for an incident quasi-monochromatic pulse, the transmitted pulse can be expressed as a superposition of partial pulses that are exact replicas of the incident pulse and that exit the slab with a time delay. These partial pulses have harmonic carrier frequencies ωcnΩ (n is an integer, ωc is the carrier frequency of the incident pulse, and Ω = 2π/T is the slab modulation frequency). We find numerically that these partial pulses can be fast (peak velocity vn > c or vn < 0) or slow (vnc). Further, we investigate the peak velocity vp of the outcoming pulse for several cases. We find that this peak velocity vp and the partial peak velocities vn do not diverge —as occurs to the group velocity vg of the bulk dynamic-periodic medium when ωc = Ω/2. We expect that these results could be verified in the microwave regime [see Halevi et al., Proc. SPIE 8095, 80950I (2011)].

© 2012 OSA

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  1. C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
    [CrossRef]
  2. S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
    [CrossRef]
  3. S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811–1814 (1986).
    [CrossRef] [PubMed]
  4. S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
    [CrossRef] [PubMed]
  5. M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
    [CrossRef] [PubMed]
  6. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
    [CrossRef]
  7. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
    [CrossRef] [PubMed]
  8. A. Dogariu, A. Kuzmich, H. Cao, and L. J. Wang, “Superluminal light pulse propagation via rephasing in a transparent anomalously dispersive medium,” Opt. Express 8, 344–350 (2001).
    [CrossRef] [PubMed]
  9. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
    [CrossRef] [PubMed]
  10. K. Y. Song, M. G. Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated brillouin scattering,” Opt. Express 13, 82–88 (2005).
    [CrossRef] [PubMed]
  11. R. W. Boyd and D. J. Gauthier, “Slow and Fast Light,” in Progress in Optics, Vol. 43, E. Wolf, ed. (Elsevier, Amsterdam, 2002), pp. 497–530.
    [CrossRef]
  12. J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79, 053821 (2009).
    [CrossRef]
  13. J. R. Zurita-Sánchez and P. Halevi, “Resonances in the optical response of a slab with time-periodic dielectric function ε(t),” Phys. Rev. A 81, 053834 (2010).
    [CrossRef]
  14. F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, “Dynamics of light propagation in spatiotemporal dielectric structures,” Phys. Rev. E 75, 046607 (2007).
    [CrossRef]
  15. Y. Xiao, G. P. Agrawal, and D. N. Maywar, “Spectral and temporal changes of optical pulses propagating through time-varying linear media,” Opt. Lett. 36, 505–507 (2011).
    [CrossRef] [PubMed]
  16. S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293–296 (2007).
    [CrossRef]
  17. M. W. McCutcheon, A. G. Pattantyus-Abraham, G. W. Rieger, and J. F. Young, “Emission spectrum of electromagnetic energy stored in a dynamically perturbed optical microcavity,” Opt. Express 15, 11472–11480 (2007).
    [CrossRef] [PubMed]
  18. T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102, 043907 (2009).
    [CrossRef] [PubMed]
  19. T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
    [CrossRef]
  20. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
    [CrossRef] [PubMed]
  21. V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
    [CrossRef]
  22. E. Poutrina, S. Larouche, and D. R. Smith, “Parametric oscillator based on a single-layer resonant metamaterial,” Opt. Comm. 283, 1640–1646 (2010).
    [CrossRef]
  23. A. R. Katko, S. Gu, J. P. Barret, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905 (2010).
    [CrossRef] [PubMed]
  24. P. Halevi, U. Algredo-Badillo, and J. R. Zurita-Sánchez, “Optical response of a slab with time-periodic dielectric function ε(t): towards a dynamic metamaterial,” in Active Photonic Materials IV, G. S. Subramania and S. Foteinopoulou, eds., Proc. SPIE8095, 80950I (2011).
  25. A. Papoulis, Signal Analysis (McGraw-Hill, Tokio, 1977).
  26. P. Halevi, “Transit velocity of a pulse through a transparent plate,” Opt. Lett. 11, 759–760 (1986).
    [CrossRef] [PubMed]
  27. P. Halevi and L. D. Valenzuela, “Propagation of a broad light pulse through a plate,” J. Opt. Soc. Am. B 8, 1512–1515 (1991).
    [CrossRef]

2011

2010

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
[CrossRef]

J. R. Zurita-Sánchez and P. Halevi, “Resonances in the optical response of a slab with time-periodic dielectric function ε(t),” Phys. Rev. A 81, 053834 (2010).
[CrossRef]

E. Poutrina, S. Larouche, and D. R. Smith, “Parametric oscillator based on a single-layer resonant metamaterial,” Opt. Comm. 283, 1640–1646 (2010).
[CrossRef]

A. R. Katko, S. Gu, J. P. Barret, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905 (2010).
[CrossRef] [PubMed]

2009

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102, 043907 (2009).
[CrossRef] [PubMed]

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79, 053821 (2009).
[CrossRef]

2007

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293–296 (2007).
[CrossRef]

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, “Dynamics of light propagation in spatiotemporal dielectric structures,” Phys. Rev. E 75, 046607 (2007).
[CrossRef]

V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

M. W. McCutcheon, A. G. Pattantyus-Abraham, G. W. Rieger, and J. F. Young, “Emission spectrum of electromagnetic energy stored in a dynamically perturbed optical microcavity,” Opt. Express 15, 11472–11480 (2007).
[CrossRef] [PubMed]

2006

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

2005

2003

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

2001

2000

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[CrossRef] [PubMed]

1999

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

1995

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

1991

1990

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

1986

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811–1814 (1986).
[CrossRef] [PubMed]

P. Halevi, “Transit velocity of a pulse through a transparent plate,” Opt. Lett. 11, 759–760 (1986).
[CrossRef] [PubMed]

1982

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[CrossRef]

1970

C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[CrossRef]

Agarwal, G. S.

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811–1814 (1986).
[CrossRef] [PubMed]

Agrawal, G. P.

Algredo-Badillo, U.

P. Halevi, U. Algredo-Badillo, and J. R. Zurita-Sánchez, “Optical response of a slab with time-periodic dielectric function ε(t): towards a dynamic metamaterial,” in Active Photonic Materials IV, G. S. Subramania and S. Foteinopoulou, eds., Proc. SPIE8095, 80950I (2011).

Amann, A.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, “Dynamics of light propagation in spatiotemporal dielectric structures,” Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Averitt, R. D.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Barret, J. P.

A. R. Katko, S. Gu, J. P. Barret, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905 (2010).
[CrossRef] [PubMed]

Beggs, D. M.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Biancalana, F.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, “Dynamics of light propagation in spatiotemporal dielectric structures,” Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “Slow and Fast Light,” in Progress in Optics, Vol. 43, E. Wolf, ed. (Elsevier, Amsterdam, 2002), pp. 497–530.
[CrossRef]

Bratkovsky, A. M.

V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

Cao, H.

Cervantes-González, J. C.

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79, 053821 (2009).
[CrossRef]

Chu, S.

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[CrossRef]

Cummer, S. A.

A. R. Katko, S. Gu, J. P. Barret, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905 (2010).
[CrossRef] [PubMed]

Dogariu, A.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

Garrett, C. G. B.

C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[CrossRef]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “Slow and Fast Light,” in Progress in Optics, Vol. 43, E. Wolf, ed. (Elsevier, Amsterdam, 2002), pp. 497–530.
[CrossRef]

Gea-Banacloche, J.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

Gu, S.

A. R. Katko, S. Gu, J. P. Barret, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905 (2010).
[CrossRef] [PubMed]

Halevi, P.

J. R. Zurita-Sánchez and P. Halevi, “Resonances in the optical response of a slab with time-periodic dielectric function ε(t),” Phys. Rev. A 81, 053834 (2010).
[CrossRef]

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79, 053821 (2009).
[CrossRef]

P. Halevi and L. D. Valenzuela, “Propagation of a broad light pulse through a plate,” J. Opt. Soc. Am. B 8, 1512–1515 (1991).
[CrossRef]

P. Halevi, “Transit velocity of a pulse through a transparent plate,” Opt. Lett. 11, 759–760 (1986).
[CrossRef] [PubMed]

P. Halevi, U. Algredo-Badillo, and J. R. Zurita-Sánchez, “Optical response of a slab with time-periodic dielectric function ε(t): towards a dynamic metamaterial,” in Active Photonic Materials IV, G. S. Subramania and S. Foteinopoulou, eds., Proc. SPIE8095, 80950I (2011).

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Herráez, M. G.

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Imamoglu, A.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

Islam, M. S.

V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

Jin, S.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

Kampfrath, T.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Katko, A. R.

A. R. Katko, S. Gu, J. P. Barret, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905 (2010).
[CrossRef] [PubMed]

Krauss, T. F.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Kuekes, P. J.

V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

Kuipers, L.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Kuramochi, E.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102, 043907 (2009).
[CrossRef] [PubMed]

Kuzmich, A.

Larouche, S.

E. Poutrina, S. Larouche, and D. R. Smith, “Parametric oscillator based on a single-layer resonant metamaterial,” Opt. Comm. 283, 1640–1646 (2010).
[CrossRef]

Lee, M.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Li, Y.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

Lipson, M.

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293–296 (2007).
[CrossRef]

Logeeswaran, V. J.

V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

Maywar, D. N.

McCumber, D. E.

C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[CrossRef]

McCutcheon, M. W.

Melloni, A.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Notomi, M.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102, 043907 (2009).
[CrossRef] [PubMed]

O’Reilly, E. P.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, “Dynamics of light propagation in spatiotemporal dielectric structures,” Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Padilla, W. J.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Papoulis, A.

A. Papoulis, Signal Analysis (McGraw-Hill, Tokio, 1977).

Pattantyus-Abraham, A. G.

Popa, B.-I.

A. R. Katko, S. Gu, J. P. Barret, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905 (2010).
[CrossRef] [PubMed]

Poutrina, E.

E. Poutrina, S. Larouche, and D. R. Smith, “Parametric oscillator based on a single-layer resonant metamaterial,” Opt. Comm. 283, 1640–1646 (2010).
[CrossRef]

Preble, S. F.

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293–296 (2007).
[CrossRef]

Rieger, G. W.

Shvets, G.

A. R. Katko, S. Gu, J. P. Barret, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905 (2010).
[CrossRef] [PubMed]

Smith, D. R.

E. Poutrina, S. Larouche, and D. R. Smith, “Parametric oscillator based on a single-layer resonant metamaterial,” Opt. Comm. 283, 1640–1646 (2010).
[CrossRef]

Song, K. Y.

Stameroff, A. N.

V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

Tanabe, T.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102, 043907 (2009).
[CrossRef] [PubMed]

Taniyama, H.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102, 043907 (2009).
[CrossRef] [PubMed]

Taylor, A. J.

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V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

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T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
[CrossRef]

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V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

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[CrossRef]

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V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

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[CrossRef]

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[CrossRef]

P. Halevi, U. Algredo-Badillo, and J. R. Zurita-Sánchez, “Optical response of a slab with time-periodic dielectric function ε(t): towards a dynamic metamaterial,” in Active Photonic Materials IV, G. S. Subramania and S. Foteinopoulou, eds., Proc. SPIE8095, 80950I (2011).

Appl. Phys. A

V. J. Logeeswaran, A. N. Stameroff, M. S. Islam, W. Wu, A. M. Bratkovsky, P. J. Kuekes, S. Y. Wang, and R. S. Williams, “Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation,” Appl. Phys. A 87, 209–216 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293–296 (2007).
[CrossRef]

Nature

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[CrossRef]

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[CrossRef]

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Opt. Lett.

Phys. Rev. A

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, “Ultrafast adiabatic manipulation of slow light in a photonic crystal,” Phys. Rev. A 81, 043837 (2010).
[CrossRef]

C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[CrossRef]

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79, 053821 (2009).
[CrossRef]

J. R. Zurita-Sánchez and P. Halevi, “Resonances in the optical response of a slab with time-periodic dielectric function ε(t),” Phys. Rev. A 81, 053834 (2010).
[CrossRef]

Phys. Rev. E

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, “Dynamics of light propagation in spatiotemporal dielectric structures,” Phys. Rev. E 75, 046607 (2007).
[CrossRef]

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[CrossRef] [PubMed]

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[CrossRef]

S. P. Tewari and G. S. Agarwal, “Control of phase matching and nonlinear generation in dense media by resonant fields,” Phys. Rev. Lett. 56, 1811–1814 (1986).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef] [PubMed]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Incident and transmitted pulses as a function of the normalized time for a slab with normalized modulation frequency Ω̃ = 2. (a) The incident electric pulse Ei with carrier frequency ωc/Ω = 0.5 and spectral bandwidth Δω/Ω = 0.1. (b) The transmitted pulse for a modulation strength M = 0.162. (c) The transmitted pulse for a modulation strength M = 0.648. Here ωcτ = 10 and ts Δω = 0.2.

Fig. 2
Fig. 2

Incident and transmitted pulses as a function of the normalized time for a slab with normalized modulation frequency Ω̃ = 8 and modulation strength M = 0.648. (a) The incident electric pulse Ei with carrier frequency ωc/Ω = 0.67 and spectral bandwidth Δω/Ω = 0.1. (b) The transmitted pulse. Here ωcτ = 13.4 and ts Δω = 0.8.

Fig. 3
Fig. 3

Incident and transmitted pulses as a function of the normalized time for a slab with normalized modulation frequency Ω̃ = 8 and modulation strength M = 0.648. (a) The incident electric pulse Ei with carrier frequency ωc/Ω = 0.67 and spectral bandwidth Δω/Ω = 0.01. (b) The transmitted pulse (inset shows the whole pulse). Here ωcτ = 134 and ts Δω = 0.08.

Fig. 4
Fig. 4

Incident and transmitted pulses vs. the normalized time for M = 0.162 (moderate modulation) and M = 0.648 (strong modulation). The incident Gaussian pulse has a large bandwidth Δω/Ω = 5 and carrier frequency ωc/Ω = 5, and the normalized time is taken with respect to Ω̃ = 2. (a) Ω̃ = 2 and ts Δω = 10. (b) Ω̃ = 8 and ts Δω = 40 (the inset is a closeup of the second pulse). Here ωcτ = 2.

Fig. 5
Fig. 5

Peak velocity of a Gaussian pulse with carrier frequency ωc/Ω = 0.5, as a function of the normalized thickness ( Ω ε ¯ / c)D for weak (M = 0.016) and strong (M = 0.648) modulations with Δω/Ω = 0.1, strong modulation with reduced spectral width Δω/Ω = 0.1, and a static case. For the static case M = 0 we consider a wide pulse in time with τD/vs. The inset is the bulk dispersion relation [normalized frequency ω/Ω vs. normalized wavevector k c / ( Ω ε ¯ )] for the strong modulation as in Ref. [12].

Tables (3)

Tables Icon

Table 1 The characteristics of the outcoming partial Gaussian pulses [Eq. (24)] for the harmonic n and modulation strength M = 0.648 (strong). Incident Gaussian pulse with carrier frequency ωc/Ω = 0.5 and spectral width Δω/Ω = 0.1; slab with normalized modulation frequency Ω̃ = 2. Here ωcτ = 10 and ts Δω = 0.2.

Tables Icon

Table 2 The characteristics of the outcoming partial Gaussian pulses [Eq. (24)] for the harmonic n and modulation strength M = 0.648 (strong). Incident Gaussian pulse with carrier frequency ωc/Ω = 0.67 and spectral width Δω/Ω = 0.01; slab with normalized modulation frequency Ω̃ = 8. Here ωcτ = 134 and ts Δω = 0.08.

Tables Icon

Table 3 Sum of the reflectance and transmittance (�� + ��) for incident Gaussian pulses with carrier frequency ωc/Ω = 0.5 and 1 and spectral width Δω/Ω = 0.1; a normalized modulation frequency Ω̃ = 2, and modulation strengths M = 0.016 (weak), 0.162 (moderate), and 0.648 (strong).

Equations (27)

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E i ( y , t ) = E o ( ω ) exp [ i ω ( y / c t ) ] d ω ,
E o ( ω ) = 1 2 π E i ( 0 , t ) exp ( i ω t ) d ω .
E s ( y , t ) = p = 1 n = { A p ( ω ) exp [ i k p ( ω ) y ] + B p ( ω ) exp [ i k p ( ω ) y ] } × e p n ( ω ) exp [ i ( ω n Ω ) t ] d ω ,
E r ( y , t ) = n = E n r ( ω ) exp [ i ( ω n Ω ) ( y / c + t ) ] d ω ,
E t ( y , t ) = n = E n t ( ω ) exp { i ( ω n Ω ) [ ( y D ) / c t ] } d ω .
E r ( 0 , t ) = n = r n ( ω ) E o ( ω ) exp [ i ( ω n Ω ) t ] d ω ,
E t ( D , t ) = n = t n ( ω ) E o ( ω ) exp [ i ( ω n Ω ) t ] d ω ,
E i ( y = 0 , t ) = 𝒠 ( t ) exp ( i ω c t ) .
E o ( α + ω c ) = 𝒠 ˜ ( α ) ,
𝒠 ˜ ( α ) = 1 2 π 𝒠 ( t ) exp ( i α t ) d t .
E t ( y = D , t ) = n = exp [ i ( ω c n Ω ) t ] t n ( ω c + α ) 𝒠 ˜ ( α ) exp [ i α t ] d α .
t n ( ω ) = A n ( ω ) exp [ i ϕ n ( ω ) ] ,
| α | = | ω ω c | ω c .
t n ( ω c + α ) A n ( ω c ) exp [ i ϕ n ( ω c ) ] + [ A n ( ω c ) + i ϕ n ( ω c ) A n ( ω c ) ] exp [ i ϕ n ( ω c ) ] α .
| A n ( ω c ) A n ( ω c ) | | ϕ n ( ω c ) | .
t n ( ω c + α ) A n ( ω c ) exp [ i ϕ ( ω c ) ] [ 1 + i ϕ n ( ω c ) α ] t n ( ω c ) exp [ i ϕ n ( ω c ) α ] .
E t ( y = D , t ) = n = A n ( ω c ) exp { i [ ( ω c n Ω ) t ϕ n ( ω c ) ] } × 𝒠 ˜ ( α ) exp { i α [ t ϕ n ( ω c ) ] } d α , = n = t n ( ω c ) exp [ i ( ω c n Ω ) t ] 𝒠 [ t ϕ n ( ω c ) ] .
v n = D / ϕ n ( ω c ) .
E i ( y , t ) = exp [ ( y c t ) 2 / ( c 2 τ 2 ) ] cos [ ω c ( y / c t ) ] ,
E o ( ω ) = τ 4 π { exp [ τ 2 ( ω ω c ) 2 / 4 ] + exp [ τ 2 ( ω + ω c ) 2 / 4 ] } ,
ε ( t ) = ε ¯ [ 1 + M sin ( Ω t ) ] ,
Ω ˜ = Ω t s = Ω ε ¯ D / c
t ˜ = t / t s = t c / ( ε ¯ D ) ,
E n t ( D , t ˜ ) = A n ( ω ^ c ) exp [ t s 2 ( t ˜ Δ τ ˜ n ) 2 / τ 2 ] cos [ ( ω ^ c n ) Ω ˜ t ˜ ϕ n ( ω ^ c ) ] ,
v p = v s [ 2 ε ¯ 1 + ε ¯ cos 2 ( ω c ε ¯ D / c ) + 1 + ε ¯ 2 ε ¯ sin 2 ( ω c ε ¯ D / c ) ] .
( 𝒯 ) = | A r ( t ) ( ω ) | 2 d ω / | E o ( ω ) | 2 d ω .
A r ( ω ) = n = r n ( ω + n Ω ) E o ( ω + n Ω ) , A t ( ω ) = n = t n ( ω + n Ω ) E o ( ω + n Ω ) .

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