Abstract

The time-reversal (TR) protocol we implement in an erbium-doped YSO crystal is based on photon echoes but avoids the storage of the signal to be processed. Unlike other approaches implying digitizing or highly dispersive optical fibers, the proposed scheme reaches the μs range and potentially offers high bandwidth, both required for RADAR applications. In this Letter, we demonstrate faithful reversal of arbitrary pulse sequences with 6 μs duration and 10 MHz bandwidth. To the best of our knowledge, this is the first demonstration of TR via linear filtering in a programmable material.

© 2013 Optical Society of America

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2010

M. Bonarota, J. Ruggiero, J.-L. Le Gouët, and T. Chanelière, Phys. Rev. A 81, 033803 (2010).
[CrossRef]

2009

M. Foster, R. Salem, Y. Okawachi, A. Turner-Foster, M. Lipson, and A. Gaeta, Nat. Photonics 3, 581 (2009).
[CrossRef]

T. Böttger, C. Thiel, R. Cone, and Y. Sun, Phys. Rev. B 79, 115104 (2009).
[CrossRef]

2006

T. Böttger, C. Thiel, Y. Sun, and R. Cone, Phys. Rev. B 73, 075101 (2006).
[CrossRef]

2005

J. Azaña, N. Berger, B. Levit, and B. Fischer, IEEE Photon. Technol. Lett. 17, 94 (2005).
[CrossRef]

2004

G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).
[CrossRef]

2000

1999

F. Coppinger, A. Bhushan, and B. Jalali, Electron. Lett. 35, 1230 (1999).
[CrossRef]

1997

M. Fink, Phys. Today 50(3), 34 (1997).
[CrossRef]

1995

1994

C. Bennett, R. Scott, and B. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

1990

G. Liu and R. Cone, Phys. Rev. B 41, 6193 (1990).
[CrossRef]

1982

Azaña, J.

J. Azaña, N. Berger, B. Levit, and B. Fischer, IEEE Photon. Technol. Lett. 17, 94 (2005).
[CrossRef]

Bennett, C.

C. Bennett, R. Scott, and B. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

Berger, N.

J. Azaña, N. Berger, B. Levit, and B. Fischer, IEEE Photon. Technol. Lett. 17, 94 (2005).
[CrossRef]

Bhushan, A.

F. Coppinger, A. Bhushan, and B. Jalali, Electron. Lett. 35, 1230 (1999).
[CrossRef]

Bonarota, M.

M. Bonarota, J. Ruggiero, J.-L. Le Gouët, and T. Chanelière, Phys. Rev. A 81, 033803 (2010).
[CrossRef]

Böttger, T.

T. Böttger, C. Thiel, R. Cone, and Y. Sun, Phys. Rev. B 79, 115104 (2009).
[CrossRef]

T. Böttger, C. Thiel, Y. Sun, and R. Cone, Phys. Rev. B 73, 075101 (2006).
[CrossRef]

Cabaret, L.

Chanelière, T.

M. Bonarota, J. Ruggiero, J.-L. Le Gouët, and T. Chanelière, Phys. Rev. A 81, 033803 (2010).
[CrossRef]

Cone, R.

T. Böttger, C. Thiel, R. Cone, and Y. Sun, Phys. Rev. B 79, 115104 (2009).
[CrossRef]

T. Böttger, C. Thiel, Y. Sun, and R. Cone, Phys. Rev. B 73, 075101 (2006).
[CrossRef]

G. Liu and R. Cone, Phys. Rev. B 41, 6193 (1990).
[CrossRef]

Coppinger, F.

F. Coppinger, A. Bhushan, and B. Jalali, Electron. Lett. 35, 1230 (1999).
[CrossRef]

De Rosny, J.

G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).
[CrossRef]

Derode, A.

G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).
[CrossRef]

Fink, M.

G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).
[CrossRef]

M. Fink, Phys. Today 50(3), 34 (1997).
[CrossRef]

Fischer, B.

J. Azaña, N. Berger, B. Levit, and B. Fischer, IEEE Photon. Technol. Lett. 17, 94 (2005).
[CrossRef]

Foster, M.

M. Foster, R. Salem, Y. Okawachi, A. Turner-Foster, M. Lipson, and A. Gaeta, Nat. Photonics 3, 581 (2009).
[CrossRef]

Gaeta, A.

M. Foster, R. Salem, Y. Okawachi, A. Turner-Foster, M. Lipson, and A. Gaeta, Nat. Photonics 3, 581 (2009).
[CrossRef]

Jalali, B.

F. Coppinger, A. Bhushan, and B. Jalali, Electron. Lett. 35, 1230 (1999).
[CrossRef]

Kemp, M.

M. Kemp, in Inside the Camera Obscura: Optics and Art under the Spell of the Projected Image (Max-Planck Institute für Wissenschaftsgeschichte, 2007), pp. 243–264.

Kolner, B.

C. Bennett, R. Scott, and B. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

Le Gouët, J.-L.

M. Bonarota, J. Ruggiero, J.-L. Le Gouët, and T. Chanelière, Phys. Rev. A 81, 033803 (2010).
[CrossRef]

L. Ménager, L. Cabaret, I. Lorgeré, and J.-L. Le Gouët, Opt. Lett. 25, 1246 (2000).
[CrossRef]

Lerosey, G.

G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).
[CrossRef]

Levit, B.

J. Azaña, N. Berger, B. Levit, and B. Fischer, IEEE Photon. Technol. Lett. 17, 94 (2005).
[CrossRef]

Lin, H.

Lipson, M.

M. Foster, R. Salem, Y. Okawachi, A. Turner-Foster, M. Lipson, and A. Gaeta, Nat. Photonics 3, 581 (2009).
[CrossRef]

Liu, G.

G. Liu and R. Cone, Phys. Rev. B 41, 6193 (1990).
[CrossRef]

Lorgeré, I.

Ménager, L.

Montaldo, G.

G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).
[CrossRef]

Mossberg, T.

Okawachi, Y.

M. Foster, R. Salem, Y. Okawachi, A. Turner-Foster, M. Lipson, and A. Gaeta, Nat. Photonics 3, 581 (2009).
[CrossRef]

Ruggiero, J.

M. Bonarota, J. Ruggiero, J.-L. Le Gouët, and T. Chanelière, Phys. Rev. A 81, 033803 (2010).
[CrossRef]

Salem, R.

M. Foster, R. Salem, Y. Okawachi, A. Turner-Foster, M. Lipson, and A. Gaeta, Nat. Photonics 3, 581 (2009).
[CrossRef]

Scott, R.

C. Bennett, R. Scott, and B. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

Sun, Y.

T. Böttger, C. Thiel, R. Cone, and Y. Sun, Phys. Rev. B 79, 115104 (2009).
[CrossRef]

T. Böttger, C. Thiel, Y. Sun, and R. Cone, Phys. Rev. B 73, 075101 (2006).
[CrossRef]

Thiel, C.

T. Böttger, C. Thiel, R. Cone, and Y. Sun, Phys. Rev. B 79, 115104 (2009).
[CrossRef]

T. Böttger, C. Thiel, Y. Sun, and R. Cone, Phys. Rev. B 73, 075101 (2006).
[CrossRef]

Tourin, A.

G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).
[CrossRef]

Turner-Foster, A.

M. Foster, R. Salem, Y. Okawachi, A. Turner-Foster, M. Lipson, and A. Gaeta, Nat. Photonics 3, 581 (2009).
[CrossRef]

Wang, T.

Appl. Phys. Lett.

C. Bennett, R. Scott, and B. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

Electron. Lett.

F. Coppinger, A. Bhushan, and B. Jalali, Electron. Lett. 35, 1230 (1999).
[CrossRef]

IEEE Photon. Technol. Lett.

J. Azaña, N. Berger, B. Levit, and B. Fischer, IEEE Photon. Technol. Lett. 17, 94 (2005).
[CrossRef]

Nat. Photonics

M. Foster, R. Salem, Y. Okawachi, A. Turner-Foster, M. Lipson, and A. Gaeta, Nat. Photonics 3, 581 (2009).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Bonarota, J. Ruggiero, J.-L. Le Gouët, and T. Chanelière, Phys. Rev. A 81, 033803 (2010).
[CrossRef]

Phys. Rev. B

T. Böttger, C. Thiel, R. Cone, and Y. Sun, Phys. Rev. B 79, 115104 (2009).
[CrossRef]

G. Liu and R. Cone, Phys. Rev. B 41, 6193 (1990).
[CrossRef]

T. Böttger, C. Thiel, Y. Sun, and R. Cone, Phys. Rev. B 73, 075101 (2006).
[CrossRef]

Phys. Rev. Lett.

G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).
[CrossRef]

Phys. Today

M. Fink, Phys. Today 50(3), 34 (1997).
[CrossRef]

Other

M. Kemp, in Inside the Camera Obscura: Optics and Art under the Spell of the Projected Image (Max-Planck Institute für Wissenschaftsgeschichte, 2007), pp. 243–264.

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Figures (4)

Fig. 1.
Fig. 1.

3PE-scheme: (a) laser pulse (solid line) and echo (dashed line) chirped frequency, (b) 3PEs at four different frequency addresses, and (c) TR protocol: continuous engraving is achieved by pulses 1 and 2. The waveform, carried by pulse 3, is time reversed in the echo.

Fig. 2.
Fig. 2.

(a) frequency chirps during engraving; (b) schematic absorption profile, dashed and solid line: without and with engraving; (i)–(iii) normalized experimental transmission spectra and sinusoidal fit. The maximum contrast reaches 15%.

Fig. 3.
Fig. 3.

Input and output pulses: (a) input and perfectly time-reversed output; (b) single-shot experimental transmission, dashed line: effect of interaction of Er3+ with fluctuating environment, solid line: effect of optical depth variation over Δνoptic; and (c) output corrected for the two previously cited effects.

Fig. 4.
Fig. 4.

(a) Normalized input and output pulses for several Gaussian pulse durations tgauss. Output corrected for interaction with environment and αL-variation, (i) tgauss=95ns, (ii) tgauss=46ns, (iii) tgauss=39ns. (b) Bode diagram representing normalized cross correlation between input pulse and time-reversed output pulse versus input spectral bandwidth ΔνRF. Input intensity envelope modulations are due to αL variation over the scanned range Δνoptic.

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