Abstract

Recently, Chumak et al. have demonstrated experimentally the time-reversal of microwave spin pulses based on non-adiabatically tuning the wave speed in a spatially-periodic manner [Nat. Comm. 1, 141 (2010)]. Here, we solve the associated wave equations analytically, and give an explicit formula for the reversal efficiency. We discuss the implementation for short optical electromagnetic pulses and show that the new scheme may lead to their accurate time-reversal with efficiency higher than before.

© 2011 OSA

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  1. M. Fink, “Time-reversed acoustics,” Scientific American 91, (November1999).
  2. M. Fink, “Acoustic time-reversal mirrors: Imaging of complex media with acoustic and seismic waves,” Topics in Applied Physics 84, 17–43 (2002).
    [CrossRef]
  3. J. Aullbach, B. Gjonaj, P. M. Johnson, A. M. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
    [CrossRef]
  4. O. Katz, Y. Bromberg, E. Small, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Phot. 5, 372–377 (2011).
    [CrossRef]
  5. D. M. Pepper, Laser handbook , Vol. 4, (North-Holland Physics, Amsterdam1988).
  6. J. B. Pendry, “Time-reversal and negative refraction,” Science 322, 71–73 (2008).
    [CrossRef] [PubMed]
  7. X. Li and M. I. Stockman, “Highly efficient spatio-temporal coherent control in nanoplasmonics on a nanometer-femtosecond scale by time-reversal,” Phys. Rev. B 77, 195109 (2008).
    [CrossRef]
  8. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Phot. 2, 110–115 (2008).
    [CrossRef]
  9. Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
    [CrossRef] [PubMed]
  10. F. M. Cucchietti, “Time-reversal in an optical lattice,” J. Opt. Soc. Am. B 27, 30–35 (2010).
    [CrossRef]
  11. A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Femtosecond spectral holography,” IEEE J. Qu. Electron. 28, 2251–2261 (1992).
    [CrossRef]
  12. D. Marom, D. Panasenko, R. Rokitski, P.-C. Sun, and Y. Fainman, “Time-reversal of ultrafast waveforms by wave mixing of spectrally decomposed waves,” Opt. Lett. 25, 132–134 (2000).
    [CrossRef]
  13. O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
    [CrossRef]
  14. M. F. Yanik and S. Fan, “Time-reversal of light with linear optics and modulators,” Phys. Rev. Lett. 93, 173903 (2004).
    [CrossRef] [PubMed]
  15. S. Longhi, “Stopping and time-reversal of light in dynamic photonic structures via Bloch oscillations,” Phys. Rev. E 75, 026606 (2007).
    [CrossRef]
  16. A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
    [CrossRef]
  17. D. A. B Miller, “Time reversal of optical pulses by four-wave mixing,” Opt. Lett. 5, 300–302 (1980).
    [CrossRef] [PubMed]
  18. M. Tsang and D. Psaltis, “Spectral phase conjugation with cross-phase modulation compensation,” Opt. Exp. 12, 2207–2219 (2004).
    [CrossRef]
  19. A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A 64, 043809 (2001).
    [CrossRef]
  20. G. A. Melkov, A. A. Serga, V. S. Tiberkevich, A. N. Oliynyk, and A. N. Slavin, “Wave Front Reversal of a Dipolar Spin Wave Pulse in a Non-Stationary Three-Wave Parametric Interaction,” Phys. Rev. Lett. 84, 3438–3441 (2000).
    [CrossRef] [PubMed]
  21. L. Tkeshelashvili and K. Busch, “Nonlinear three-wave interaction in photonic crystals,” Appl. Phys. B 81, 225–229 (2005).
    [CrossRef]
  22. Y. Sivan and J. B. Pendry, “Time-reversal in dynamically-tuned zero-gap periodic systems,” Phys. Rev. Lett. , 106, 193902 (2011).
    [CrossRef] [PubMed]
  23. Y. Sivan and J. B. Pendry, “Theory of wave-front reversal of short pulses in dynamically-tuned zero-gap periodic systems,” submitted; available on ArXiv at http://arxiv.org/abs/1105.5583 .
  24. C. M. de Sterke and J. E. Sipe, in Prog. in Opt. , Vol. XXXIV, (North-Holland, Amsterdam1994).
  25. C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
    [CrossRef]
  26. P. Yeh, Optical Waves in Layered Media , (Wiley-Interscience, 2nd edition2005).
  27. G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217, 31–57 (2006).
    [CrossRef]
  28. Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and bose-einstein condensates,” Phys. Rev. Lett. 97, 193902 (2006).
    [CrossRef] [PubMed]
  29. B. A. Malomed, Y. V. Kartashov, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–306 (2011).
    [CrossRef]

2011

J. Aullbach, B. Gjonaj, P. M. Johnson, A. M. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

O. Katz, Y. Bromberg, E. Small, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Phot. 5, 372–377 (2011).
[CrossRef]

Y. Sivan and J. B. Pendry, “Time-reversal in dynamically-tuned zero-gap periodic systems,” Phys. Rev. Lett. , 106, 193902 (2011).
[CrossRef] [PubMed]

B. A. Malomed, Y. V. Kartashov, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–306 (2011).
[CrossRef]

2010

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

F. M. Cucchietti, “Time-reversal in an optical lattice,” J. Opt. Soc. Am. B 27, 30–35 (2010).
[CrossRef]

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

2009

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

2008

J. B. Pendry, “Time-reversal and negative refraction,” Science 322, 71–73 (2008).
[CrossRef] [PubMed]

X. Li and M. I. Stockman, “Highly efficient spatio-temporal coherent control in nanoplasmonics on a nanometer-femtosecond scale by time-reversal,” Phys. Rev. B 77, 195109 (2008).
[CrossRef]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Phot. 2, 110–115 (2008).
[CrossRef]

2007

S. Longhi, “Stopping and time-reversal of light in dynamic photonic structures via Bloch oscillations,” Phys. Rev. E 75, 026606 (2007).
[CrossRef]

2006

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217, 31–57 (2006).
[CrossRef]

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and bose-einstein condensates,” Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

2005

P. Yeh, Optical Waves in Layered Media , (Wiley-Interscience, 2nd edition2005).

L. Tkeshelashvili and K. Busch, “Nonlinear three-wave interaction in photonic crystals,” Appl. Phys. B 81, 225–229 (2005).
[CrossRef]

2004

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

M. Tsang and D. Psaltis, “Spectral phase conjugation with cross-phase modulation compensation,” Opt. Exp. 12, 2207–2219 (2004).
[CrossRef]

2002

M. Fink, “Acoustic time-reversal mirrors: Imaging of complex media with acoustic and seismic waves,” Topics in Applied Physics 84, 17–43 (2002).
[CrossRef]

2001

A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A 64, 043809 (2001).
[CrossRef]

2000

G. A. Melkov, A. A. Serga, V. S. Tiberkevich, A. N. Oliynyk, and A. N. Slavin, “Wave Front Reversal of a Dipolar Spin Wave Pulse in a Non-Stationary Three-Wave Parametric Interaction,” Phys. Rev. Lett. 84, 3438–3441 (2000).
[CrossRef] [PubMed]

D. Marom, D. Panasenko, R. Rokitski, P.-C. Sun, and Y. Fainman, “Time-reversal of ultrafast waveforms by wave mixing of spectrally decomposed waves,” Opt. Lett. 25, 132–134 (2000).
[CrossRef]

1999

M. Fink, “Time-reversed acoustics,” Scientific American 91, (November1999).

1996

C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
[CrossRef]

1994

C. M. de Sterke and J. E. Sipe, in Prog. in Opt. , Vol. XXXIV, (North-Holland, Amsterdam1994).

1992

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Femtosecond spectral holography,” IEEE J. Qu. Electron. 28, 2251–2261 (1992).
[CrossRef]

1988

D. M. Pepper, Laser handbook , Vol. 4, (North-Holland Physics, Amsterdam1988).

1980

Ando, K.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Aullbach, J.

J. Aullbach, B. Gjonaj, P. M. Johnson, A. M. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Bromberg, Y.

O. Katz, Y. Bromberg, E. Small, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Phot. 5, 372–377 (2011).
[CrossRef]

Busch, K.

L. Tkeshelashvili and K. Busch, “Nonlinear three-wave interaction in photonic crystals,” Appl. Phys. B 81, 225–229 (2005).
[CrossRef]

Chumak, A. V.

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

Cucchietti, F. M.

F. M. Cucchietti, “Time-reversal in an optical lattice,” J. Opt. Soc. Am. B 27, 30–35 (2010).
[CrossRef]

de Sterke, C. M.

C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
[CrossRef]

C. M. de Sterke and J. E. Sipe, in Prog. in Opt. , Vol. XXXIV, (North-Holland, Amsterdam1994).

Fainman, Y.

Fan, S.

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

Feld, M. S.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Phot. 2, 110–115 (2008).
[CrossRef]

Fibich, G.

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217, 31–57 (2006).
[CrossRef]

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and bose-einstein condensates,” Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

Fink, M.

M. Fink, “Acoustic time-reversal mirrors: Imaging of complex media with acoustic and seismic waves,” Topics in Applied Physics 84, 17–43 (2002).
[CrossRef]

M. Fink, “Time-reversed acoustics,” Scientific American 91, (November1999).

Foster, M. A.

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

Gaeta, A. L.

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

Gjonaj, B.

J. Aullbach, B. Gjonaj, P. M. Johnson, A. M. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Gregg, J. F.

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

Harii, K.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Hillebrands, B.

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

Johnson, P. M.

J. Aullbach, B. Gjonaj, P. M. Johnson, A. M. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Kajiwara, Y.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Karenowska, A. D.

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

Kartashov, Y. V.

B. A. Malomed, Y. V. Kartashov, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–306 (2011).
[CrossRef]

Katz, O.

O. Katz, Y. Bromberg, E. Small, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Phot. 5, 372–377 (2011).
[CrossRef]

Kawai, H.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Kocharovskaya, O.

A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A 64, 043809 (2001).
[CrossRef]

Kuzucu, O.

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

Lagendijk, A.

J. Aullbach, B. Gjonaj, P. M. Johnson, A. M. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Leaird, D. E.

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Femtosecond spectral holography,” IEEE J. Qu. Electron. 28, 2251–2261 (1992).
[CrossRef]

Li, X.

X. Li and M. I. Stockman, “Highly efficient spatio-temporal coherent control in nanoplasmonics on a nanometer-femtosecond scale by time-reversal,” Phys. Rev. B 77, 195109 (2008).
[CrossRef]

Lipson, M.

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

Longhi, S.

S. Longhi, “Stopping and time-reversal of light in dynamic photonic structures via Bloch oscillations,” Phys. Rev. E 75, 026606 (2007).
[CrossRef]

Maekawa, S.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Malomed, B. A.

B. A. Malomed, Y. V. Kartashov, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–306 (2011).
[CrossRef]

Marom, D.

Matsko, A. B.

A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A 64, 043809 (2001).
[CrossRef]

Melkov, G. A.

G. A. Melkov, A. A. Serga, V. S. Tiberkevich, A. N. Oliynyk, and A. N. Slavin, “Wave Front Reversal of a Dipolar Spin Wave Pulse in a Non-Stationary Three-Wave Parametric Interaction,” Phys. Rev. Lett. 84, 3438–3441 (2000).
[CrossRef] [PubMed]

Miller, D. A. B

Mizuguchi, M.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Mosk, A. M.

J. Aullbach, B. Gjonaj, P. M. Johnson, A. M. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Ohe, J.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Okawachi, Y.

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

Oliynyk, A. N.

G. A. Melkov, A. A. Serga, V. S. Tiberkevich, A. N. Oliynyk, and A. N. Slavin, “Wave Front Reversal of a Dipolar Spin Wave Pulse in a Non-Stationary Three-Wave Parametric Interaction,” Phys. Rev. Lett. 84, 3438–3441 (2000).
[CrossRef] [PubMed]

Paek, E. G.

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Femtosecond spectral holography,” IEEE J. Qu. Electron. 28, 2251–2261 (1992).
[CrossRef]

Panasenko, D.

Pendry, J. B.

Y. Sivan and J. B. Pendry, “Time-reversal in dynamically-tuned zero-gap periodic systems,” Phys. Rev. Lett. , 106, 193902 (2011).
[CrossRef] [PubMed]

J. B. Pendry, “Time-reversal and negative refraction,” Science 322, 71–73 (2008).
[CrossRef] [PubMed]

Pepper, D. M.

D. M. Pepper, Laser handbook , Vol. 4, (North-Holland Physics, Amsterdam1988).

Psaltis, D.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Phot. 2, 110–115 (2008).
[CrossRef]

M. Tsang and D. Psaltis, “Spectral phase conjugation with cross-phase modulation compensation,” Opt. Exp. 12, 2207–2219 (2004).
[CrossRef]

Reitze, D. H.

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Femtosecond spectral holography,” IEEE J. Qu. Electron. 28, 2251–2261 (1992).
[CrossRef]

Rokitski, R.

Rostovtsev, Y. V.

A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A 64, 043809 (2001).
[CrossRef]

Saitoh, E.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Salem, R.

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

Salinas, D. G.

C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
[CrossRef]

Scully, M. O.

A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A 64, 043809 (2001).
[CrossRef]

Serga, A. A.

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

G. A. Melkov, A. A. Serga, V. S. Tiberkevich, A. N. Oliynyk, and A. N. Slavin, “Wave Front Reversal of a Dipolar Spin Wave Pulse in a Non-Stationary Three-Wave Parametric Interaction,” Phys. Rev. Lett. 84, 3438–3441 (2000).
[CrossRef] [PubMed]

Silberberg, Y.

O. Katz, Y. Bromberg, E. Small, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Phot. 5, 372–377 (2011).
[CrossRef]

Sipe, J. E.

C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
[CrossRef]

C. M. de Sterke and J. E. Sipe, in Prog. in Opt. , Vol. XXXIV, (North-Holland, Amsterdam1994).

Sivan, Y.

Y. Sivan and J. B. Pendry, “Time-reversal in dynamically-tuned zero-gap periodic systems,” Phys. Rev. Lett. , 106, 193902 (2011).
[CrossRef] [PubMed]

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and bose-einstein condensates,” Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217, 31–57 (2006).
[CrossRef]

Slavin, A. N.

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

G. A. Melkov, A. A. Serga, V. S. Tiberkevich, A. N. Oliynyk, and A. N. Slavin, “Wave Front Reversal of a Dipolar Spin Wave Pulse in a Non-Stationary Three-Wave Parametric Interaction,” Phys. Rev. Lett. 84, 3438–3441 (2000).
[CrossRef] [PubMed]

Small, E.

O. Katz, Y. Bromberg, E. Small, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Phot. 5, 372–377 (2011).
[CrossRef]

Stockman, M. I.

X. Li and M. I. Stockman, “Highly efficient spatio-temporal coherent control in nanoplasmonics on a nanometer-femtosecond scale by time-reversal,” Phys. Rev. B 77, 195109 (2008).
[CrossRef]

Sun, P.-C.

Takahashi, S.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Takanashi, K.

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Tiberkevich, V. S.

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

G. A. Melkov, A. A. Serga, V. S. Tiberkevich, A. N. Oliynyk, and A. N. Slavin, “Wave Front Reversal of a Dipolar Spin Wave Pulse in a Non-Stationary Three-Wave Parametric Interaction,” Phys. Rev. Lett. 84, 3438–3441 (2000).
[CrossRef] [PubMed]

Tkeshelashvili, L.

L. Tkeshelashvili and K. Busch, “Nonlinear three-wave interaction in photonic crystals,” Appl. Phys. B 81, 225–229 (2005).
[CrossRef]

Torner, L.

B. A. Malomed, Y. V. Kartashov, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–306 (2011).
[CrossRef]

Tsang, M.

M. Tsang and D. Psaltis, “Spectral phase conjugation with cross-phase modulation compensation,” Opt. Exp. 12, 2207–2219 (2004).
[CrossRef]

Turner-Foster, A. C.

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

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Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

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Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

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A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Femtosecond spectral holography,” IEEE J. Qu. Electron. 28, 2251–2261 (1992).
[CrossRef]

Weinstein, M. I.

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and bose-einstein condensates,” Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217, 31–57 (2006).
[CrossRef]

Yang, C.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Phot. 2, 110–115 (2008).
[CrossRef]

Yanik, M. F.

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

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Phot. 2, 110–115 (2008).
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Yeh, P.

P. Yeh, Optical Waves in Layered Media , (Wiley-Interscience, 2nd edition2005).

Zibrov, A. S.

A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A 64, 043809 (2001).
[CrossRef]

Appl. Phys. B

L. Tkeshelashvili and K. Busch, “Nonlinear three-wave interaction in photonic crystals,” Appl. Phys. B 81, 225–229 (2005).
[CrossRef]

IEEE J. Qu. Electron.

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Femtosecond spectral holography,” IEEE J. Qu. Electron. 28, 2251–2261 (1992).
[CrossRef]

J. Opt. Soc. Am. B

F. M. Cucchietti, “Time-reversal in an optical lattice,” J. Opt. Soc. Am. B 27, 30–35 (2010).
[CrossRef]

Nat. Comm.

A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, “All-linear time-reversal by a dynamic artificial crystal,” Nat. Comm. 1, 141 (2010).
[CrossRef]

Nat. Phot.

O. Katz, Y. Bromberg, E. Small, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Phot. 5, 372–377 (2011).
[CrossRef]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Phot. 2, 110–115 (2008).
[CrossRef]

Nature

Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, “Transmission of electrical signals by spin-wave interconversion in a magnetic insulator,” Nature 464, 262–266 (2010).
[CrossRef] [PubMed]

Opt. Exp.

M. Tsang and D. Psaltis, “Spectral phase conjugation with cross-phase modulation compensation,” Opt. Exp. 12, 2207–2219 (2004).
[CrossRef]

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Exp. 17, 20605–20614 (2009).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A 64, 043809 (2001).
[CrossRef]

Phys. Rev. B

X. Li and M. I. Stockman, “Highly efficient spatio-temporal coherent control in nanoplasmonics on a nanometer-femtosecond scale by time-reversal,” Phys. Rev. B 77, 195109 (2008).
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[CrossRef] [PubMed]

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and bose-einstein condensates,” Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

G. A. Melkov, A. A. Serga, V. S. Tiberkevich, A. N. Oliynyk, and A. N. Slavin, “Wave Front Reversal of a Dipolar Spin Wave Pulse in a Non-Stationary Three-Wave Parametric Interaction,” Phys. Rev. Lett. 84, 3438–3441 (2000).
[CrossRef] [PubMed]

Y. Sivan and J. B. Pendry, “Time-reversal in dynamically-tuned zero-gap periodic systems,” Phys. Rev. Lett. , 106, 193902 (2011).
[CrossRef] [PubMed]

J. Aullbach, B. Gjonaj, P. M. Johnson, A. M. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
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Physica D

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217, 31–57 (2006).
[CrossRef]

Rev. Mod. Phys.

B. A. Malomed, Y. V. Kartashov, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–306 (2011).
[CrossRef]

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J. B. Pendry, “Time-reversal and negative refraction,” Science 322, 71–73 (2008).
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Equations (16)

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ɛ ( x , t ) = n 0 2 + Δ ɛ m ( t t 0 ) ɛ m ( x ) .
ɛ m ( x ) = ɛ m ( x + d ) , 0 d ɛ m ( x ) d x = 0 , m a x [ ɛ m ( x ) ] = 1 ,
x x E ( x , t ) = 1 c 2 t t [ ɛ ( x , t ) E ( x , t ) ] .
E ( x , t ) = [ E + ( x , t ) e i k 0 x + E ( x , t ) e i k 0 x ] e i ω 0 t + c . c . ,
2 i k 0 x E + + 2 i ω 0 n 0 2 c 2 t E + = 2 i ( k 0 x E ω 0 n 0 2 c 2 t E ) e 2 i k 0 x + Δ ɛ ɛ m ( x ) c 2 [ 2 t m ( t E + i ω 0 E + ) m ( 2 i ω 0 t E + + ω 0 2 E + ) ] + Δ ɛ ɛ m ( x ) c 2 [ 2 t m ( t E i ω 0 E ) m ( 2 i ω 0 t E + ω 0 2 E ) ] e 2 i k 0 x .
ɛ m ( x ) = j = 1 ɛ m ( j ) e i 2 π j x d + c . c . , ɛ m ( j ) = 1 d 0 d ɛ m ( x ) e i 2 π j x d d x .
ɛ m ( x ) = 2 ɛ m ( 1 ) cos ( 2 π x d ) .
2 i k 0 x E + ( x , t ) + 2 ( i k 0 n 0 c ( t m i ω 0 m ) Δ ɛ ɛ m ( 1 ) c 2 e 2 i δ k x ) t E + = Δ ɛ ɛ m ( 1 ) c 2 e 2 i δ k x ω 0 ( ω 0 m + 2 i t m ) E ,
2 i k 0 x E ( x , t ) + 2 ( i k 0 n 0 c ( t m i ω 0 m ) Δ ɛ ɛ m ( 1 ) * c 2 e 2 i δ k x ) t E = Δ ɛ ɛ m ( 1 ) * c 2 e 2 i δ k x ω 0 ( ω 0 m + 2 i t m ) E + .
x E + ( x , t ) + n 0 c t E + = i κ e 2 i δ k x m ( t ) E ,
x E ( x , t ) n 0 c t E = i κ * e 2 i δ k x m ( t ) E + ,
κ Δ ɛ ɛ m ( 1 ) 2 c n 0 ω 0 ,
E + ( x ( f ) , t ) = E + ( x v t , 0 ) E 0 + ( t ) ,
E ( x ( b ) , t ) = i v κ * e 2 i δ k x ( b ) t e 2 i δ k v t m ( t t 0 ) E + ( x ( b ) 2 v t ) d t .
E 0 + ( x v T p ) = e x 2 v 2 T p 2 , m ( t t 0 ) = e ( t t 0 ) 2 T m o d 2 .
| E ( x + v t ) | = π Δ n n 0 ω 0 T m o d T p T p 2 + 4 T m o d 2 E 0 + ( x + v t v T p 2 + 4 T m o d 2 ) .

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