Abstract

We theoretically discuss the use of holography to achieve the phase conjugation of temporal signals. The reversal of a particular asymmetric pulse envelope is experimentally demonstrated. The holographic material is a photorefractive crystal used in a four-wave mixing configuration.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. L. Roblin, F. Gires, R. Grousson, P. Lavallard, “Enregistrement par holographie de volume d'une loi de phase spectrale. Application à la compression d'impulsions picoseconde,” Opt. Commun. 62, 209–214 (1987).
    [CrossRef]
  2. J. H. Marburger, “Optical Pulse Integration and Chirp Reversal in Degenerate Four Wave Mixing,” Appl. Phys. Lett. 32, 372–374 (1978).
    [CrossRef]
  3. A. Yariv, D. Fekete, D. M. Pepper, “Compensation for Channel Dispersion by Nonlinear Optical Phase Conjugation,” Opt. Lett. 4, 52–54 (1979).
    [CrossRef] [PubMed]
  4. D. A. B. Miller, “Time Reversal of Optical Pulses by Four-Wave Mixing,” Opt. Lett. 5, 300–302 (1980).
    [CrossRef] [PubMed]
  5. P. M. Saari, R. K. Kaarli, A. K. Rebane, “Holography of Space-Time Events,” Sov. J. Quantum Electron, 15, 443–449 (1985).
    [CrossRef]
  6. A. Yariv, “Phase Conjugate Optics and Real Time Holography,” IEEE J. Quantum Electron. QE-14, 650–000 (1978).
    [CrossRef]
  7. D. M. Bloom, P. F. Liao, N. P. Economou, “Observation of Amplified Reflection by Degenerate Four-Wave Mixing in Atomic Sodium Vapor,” Opt. Lett. 2, 58–60 (1978).
    [CrossRef] [PubMed]
  8. F. Gires, P. Tournois, “Interferometre utilisable pour la compression d'impulsions lumineuses modulées en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).
  9. R. Grousson, M. L. Roblin, F. Gires, “Miroir à conjugaison de phase temporel,” in Proceedings, Fourteenth Congress of the International Commission for Optics, Quebec, 24–28 Aug. 1987 (1987), p. 26.
  10. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1987 (1)

M. L. Roblin, F. Gires, R. Grousson, P. Lavallard, “Enregistrement par holographie de volume d'une loi de phase spectrale. Application à la compression d'impulsions picoseconde,” Opt. Commun. 62, 209–214 (1987).
[CrossRef]

1985 (1)

P. M. Saari, R. K. Kaarli, A. K. Rebane, “Holography of Space-Time Events,” Sov. J. Quantum Electron, 15, 443–449 (1985).
[CrossRef]

1980 (1)

1979 (1)

1978 (3)

J. H. Marburger, “Optical Pulse Integration and Chirp Reversal in Degenerate Four Wave Mixing,” Appl. Phys. Lett. 32, 372–374 (1978).
[CrossRef]

A. Yariv, “Phase Conjugate Optics and Real Time Holography,” IEEE J. Quantum Electron. QE-14, 650–000 (1978).
[CrossRef]

D. M. Bloom, P. F. Liao, N. P. Economou, “Observation of Amplified Reflection by Degenerate Four-Wave Mixing in Atomic Sodium Vapor,” Opt. Lett. 2, 58–60 (1978).
[CrossRef] [PubMed]

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1964 (1)

F. Gires, P. Tournois, “Interferometre utilisable pour la compression d'impulsions lumineuses modulées en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

Bloom, D. M.

Economou, N. P.

Fekete, D.

Gires, F.

M. L. Roblin, F. Gires, R. Grousson, P. Lavallard, “Enregistrement par holographie de volume d'une loi de phase spectrale. Application à la compression d'impulsions picoseconde,” Opt. Commun. 62, 209–214 (1987).
[CrossRef]

F. Gires, P. Tournois, “Interferometre utilisable pour la compression d'impulsions lumineuses modulées en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

R. Grousson, M. L. Roblin, F. Gires, “Miroir à conjugaison de phase temporel,” in Proceedings, Fourteenth Congress of the International Commission for Optics, Quebec, 24–28 Aug. 1987 (1987), p. 26.

Grousson, R.

M. L. Roblin, F. Gires, R. Grousson, P. Lavallard, “Enregistrement par holographie de volume d'une loi de phase spectrale. Application à la compression d'impulsions picoseconde,” Opt. Commun. 62, 209–214 (1987).
[CrossRef]

R. Grousson, M. L. Roblin, F. Gires, “Miroir à conjugaison de phase temporel,” in Proceedings, Fourteenth Congress of the International Commission for Optics, Quebec, 24–28 Aug. 1987 (1987), p. 26.

Kaarli, R. K.

P. M. Saari, R. K. Kaarli, A. K. Rebane, “Holography of Space-Time Events,” Sov. J. Quantum Electron, 15, 443–449 (1985).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Lavallard, P.

M. L. Roblin, F. Gires, R. Grousson, P. Lavallard, “Enregistrement par holographie de volume d'une loi de phase spectrale. Application à la compression d'impulsions picoseconde,” Opt. Commun. 62, 209–214 (1987).
[CrossRef]

Liao, P. F.

Marburger, J. H.

J. H. Marburger, “Optical Pulse Integration and Chirp Reversal in Degenerate Four Wave Mixing,” Appl. Phys. Lett. 32, 372–374 (1978).
[CrossRef]

Miller, D. A. B.

Pepper, D. M.

Rebane, A. K.

P. M. Saari, R. K. Kaarli, A. K. Rebane, “Holography of Space-Time Events,” Sov. J. Quantum Electron, 15, 443–449 (1985).
[CrossRef]

Roblin, M. L.

M. L. Roblin, F. Gires, R. Grousson, P. Lavallard, “Enregistrement par holographie de volume d'une loi de phase spectrale. Application à la compression d'impulsions picoseconde,” Opt. Commun. 62, 209–214 (1987).
[CrossRef]

R. Grousson, M. L. Roblin, F. Gires, “Miroir à conjugaison de phase temporel,” in Proceedings, Fourteenth Congress of the International Commission for Optics, Quebec, 24–28 Aug. 1987 (1987), p. 26.

Saari, P. M.

P. M. Saari, R. K. Kaarli, A. K. Rebane, “Holography of Space-Time Events,” Sov. J. Quantum Electron, 15, 443–449 (1985).
[CrossRef]

Tournois, P.

F. Gires, P. Tournois, “Interferometre utilisable pour la compression d'impulsions lumineuses modulées en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

Yariv, A.

A. Yariv, D. Fekete, D. M. Pepper, “Compensation for Channel Dispersion by Nonlinear Optical Phase Conjugation,” Opt. Lett. 4, 52–54 (1979).
[CrossRef] [PubMed]

A. Yariv, “Phase Conjugate Optics and Real Time Holography,” IEEE J. Quantum Electron. QE-14, 650–000 (1978).
[CrossRef]

Appl. Phys. Lett. (1)

J. H. Marburger, “Optical Pulse Integration and Chirp Reversal in Degenerate Four Wave Mixing,” Appl. Phys. Lett. 32, 372–374 (1978).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

C. R. Acad. Sci. Paris (1)

F. Gires, P. Tournois, “Interferometre utilisable pour la compression d'impulsions lumineuses modulées en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

IEEE J. Quantum Electron. (1)

A. Yariv, “Phase Conjugate Optics and Real Time Holography,” IEEE J. Quantum Electron. QE-14, 650–000 (1978).
[CrossRef]

Opt. Commun. (1)

M. L. Roblin, F. Gires, R. Grousson, P. Lavallard, “Enregistrement par holographie de volume d'une loi de phase spectrale. Application à la compression d'impulsions picoseconde,” Opt. Commun. 62, 209–214 (1987).
[CrossRef]

Opt. Lett. (3)

Sov. J. Quantum Electron (1)

P. M. Saari, R. K. Kaarli, A. K. Rebane, “Holography of Space-Time Events,” Sov. J. Quantum Electron, 15, 443–449 (1985).
[CrossRef]

Other (1)

R. Grousson, M. L. Roblin, F. Gires, “Miroir à conjugaison de phase temporel,” in Proceedings, Fourteenth Congress of the International Commission for Optics, Quebec, 24–28 Aug. 1987 (1987), p. 26.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Plane wave 1) incident on a distorting medium and emerging with a phase distortion ψ(r) 2). The wave reflected by the conjugation mirror 3) traverses the medium in reverse. The wave obtained at the exit of the medium 4) is identical to the incident wave 1).

Fig. 2
Fig. 2

Pulse E0(t) 1) incident on a spectral phase distorting medium and emerging with a spectral phase distortion Φ(ν) 2). The pulse reflected by the spectral phase conjugation mirror 3) has a spectral phase Φ(ν) and traverses the medium in reverse. The pulse obtained at the exit of the medium is identical to the incident pulse 1).

Fig. 3
Fig. 3

Holographic setup identical to a four-wave mixing configuration. The object pulse E1(t) (probe) interferes with the reference pulse E0(t) (pump1). The hologram is read out by the reference pulse propagating in reverse (pump2) and reconstructs the conjugate pulse E2(t).

Fig. 4
Fig. 4

Visibility curve V(x) corresponding to the spatial index modulation Δn(x) recorded in the photorefractive crystal by the interference of two pulses.

Fig. 5
Fig. 5

Analysis device performing amplitude correlation.

Fig. 6
Fig. 6

Principle of the GTI.

Fig. 7
Fig. 7

(a) Derivative of the GTI phase law and (b) frequency spectrum of the pulse.

Fig. 8
Fig. 8

Theoretical and experimental correlation of the (a) incident, (b) GTI reflected, (c) inversed, (d) healed pulse.

Fig. 9
Fig. 9

General experimental apparatus. B0 splits the incident beam. The part sent to the moving mirror M0 is the reference beam for pulse analysis and is directed to D by means of B1. B2 extracts the reading beam which is directed to H by M1 and M2. B3 separates the reference beam for hologram recording which is directed to H by M3. B4 splits the incident (or reconstructed) beam. After collimation on M4 (or G) the reflected beam can be directed either to H (for holographic recording) or D by B5 (for analysis purpose).

Fig. 10
Fig. 10

Input pulse analysis. I0 is the initial pulse reflected by M4, and h1 is the pulse spectrally dephased by reflection on G. They are directed to D by B5 and interfere with I0 coming from M0.

Fig. 11
Fig. 11

Hologram recording. I0 and h1 interfere at H.

Fig. 12
Fig. 12

Readout and reconstructed pulse analysis. I0 is the reading pulse, I2 is the reconstructed pulse. After collimation on M4, I2 is sent to D by B5. After reflection on B4 and collimation on G, I2 is healed and becomes I3, which is sent to D by B4 and B5. I2 and I3 interfere with I0 coming from M0.

Fig. 13
Fig. 13

(a) Experimental, (b) corrected efficiency curve, and (c) corresponding refractive index variations.

Equations (45)

Equations on this page are rendered with MathJax. Learn more.

E 0 ( r , t ) = ½ { exp [ i ( ω t k z ) ] + c . c . } ,
E 2 ( r , t ) = ½ { Ψ ( r ) exp [ i ( ω t k z ) ] + c . c . } = ½ [ A 1 ( r ) exp ( i ω t ) + c . c . ] ,
A 1 ( r ) = Ψ ( r ) exp ( i k z ) .
E 2 ( r , t ) = Re [ A 1 * ( r ) exp ( i ω t ) ] z < z 0 , = Re { Ψ * ( r ) exp [ i ( ω t + k z ) ] }
E 2 ( r , t ) = E 1 ( r , t ) .
E 0 ( t ) = ½ [ a ( ν ν 0 ) exp ( i 2 π ν t ) d ν + c . c . ] .
E 0 ( t ) = ½ [ exp ( i 2 π ν 0 t ) a ( μ ) exp ( i 2 π μ t ) d μ + c . c . ] , E 0 ( t ) = ½ [ exp ( i 2 π ν 0 t ) A 0 ( t ) + c . c . ] ,
E 1 ( t ) = ½ [ exp ( i 2 π ν 0 t ) A 1 ( t ) + exp ( i 2 π ν 0 t ) A 1 * ( t ) ] ,
E 2 ( t ) = ½ [ a ( ν ν 0 ) × exp [ i Φ ( ν ) ] exp ( i 2 π ν t ) d ν + c . c . ] for z < z 0 ,
E 2 ( t ) = ½ [ exp ( i 2 π ν 0 t ) A 1 * ( t ) + exp ( i 2 π ν 0 t ) A 1 ( t ) ] ,
E 0 ( t ) = F 0 ( ν ) exp ( i 2 π ν t ) d ν = A 0 ( t ) exp ( i 2 π ν 0 t ) , E 1 ( t ) = F 1 ( ν ) exp ( i 2 π ν t ) d ν = A 1 ( t ) exp ( i 2 π ν 0 t ) .
E ( t , r ) = E 0 ( t α ̂ 0 r υ ) + E 1 ( t α ̂ 1 r υ ) ,
Δ n ( r ) | E 0 + E 1 | 2 d t .
H ( r ) = F 0 ( ν 1 ) F 1 * ( ν 1 ) exp [ i 2 π ν 1 ( α ̂ 0 α ̂ 1 ) r υ ] d ν 1
H ( r ) = exp [ i 2 π ν 0 ( α ̂ 0 α ̂ 1 ) r υ ] × A 0 ( t α ̂ 0 r υ ) A 1 * ( t α ̂ 1 r υ ) d t .
V ( x ) = A 0 ( t x υ ) A 1 * ( t ) d t ,
V ( x ) = a 2 ( μ ) exp [ i Φ ( μ ) ] exp ( 2 i π μ x υ ) d μ .
E ( t α ̂ r υ ) = F ( ν ) exp [ 2 i π ν ( t α ̂ r υ ) ] d ν ,
E ( t , α ̂ ) = E ( t α ̂ r υ + α ̂ r υ ) H ( r ) d r .
F ( ν , α ̂ ) = E ( t , α ̂ ) exp ( i 2 π ν t ) d t = F ( ν ) H ( r ) exp [ i 2 π ν ( α ̂ α ̂ ) r υ ] d r .
F ( ν , α ̂ ) = F ( ν ) F 0 ( ν 1 ) F 1 * ( ν 1 ) δ [ ν ( α ̂ α ̂ ) + ν 1 ( α ̂ 0 α ̂ 1 ) ] d v 1 .
F 2 ( ν ) = F 0 ( ν ) F 0 ( ν ) F 1 * ( ν ) ,
F 2 ( ν ) = a 3 ( ν ν 0 ) exp [ i Φ ( ν ) ] ,
A ( t ) = F 2 ( ν ) exp ( i 2 π ν t ) d ν .
S ( t , δ ) = A ( t ) exp ( 2 i π ν 0 t ) + A 0 ( t δ C ) exp [ 2 i π ν 0 ( t δ C ) ] .
I M ( δ ) = V ( δ ) cos [ 2 π ν 0 δ + φ ( δ ) ] ,
A 1 ( t ) A 0 * ( t δ C ) d t ,
exp [ i Φ ( ν ) ] = r + t 2 exp ( i φ ) [ 1 + r exp ( i φ ) + r exp ( 2 i φ ) + ] ,
exp [ ( t Δ t ) 2 ]
exp [ ( t 2 Δ t ) 2 ]
Δ ν i Δ ν 0 = 2 τ π Δ t .
E 1 ( t ) = r E 0 ( t ) + t 2 exp ( i φ 0 ) E 0 ( t τ ) [ 1 + r exp ( i φ 0 ) E 0 ( t τ ) + r 2 exp ( 2 i φ 0 ) E 0 ( t 2 τ ) + ] ,
A 1 ( t ) = | r A 0 ( t ) + t 2 exp ( i φ 0 ) A 0 ( t τ ) × [ 1 + r exp ( i φ 0 ) A 0 ( t 2 τ ) + r 2 exp ( i 2 φ 0 ) A 0 ( t 3 τ ) + ] | .
exp [ ( t Δ t ) 2 ] .
exp [ ( t 2 Δ t ) 2 ] ,
exp [ ( t 2 Δ t ) 2 ] ,
exp [ ( t 2 Δ t ) 2 ]
η = t h 2 ( π Δ n Δ z λ ) ( π Δ n Δ z λ ) 2 .
Δ E = π Δ n ( x ) Δ x 2 λ exp ( 2 i π ν 0 x υ ) A 0 ( t + x υ ) exp [ 2 i π ν 0 ( t + x υ ) ] ,
E ( t ) = exp ( 2 i π ν 0 t ) π 2 λ Δ n ( x ) A 0 ( t + x υ ) d x .
Δ n ( x ) = Δ N V ( x υ ) ,
V ( x υ ) = A 0 ( t x υ ) A 0 * ( t ) d t | A 0 ( t ) | 2 d t .
η = | A ( t ) | 2 d t | A 0 ( t ) | 2 d t ,
A ( t ) = π 2 λ Δ N υ A 0 ( t + τ ) V ( τ ) d τ with τ = x υ .
η = ( π Δ N υ Δ t 2 λ ) 2 ( 2 π 3 3 ) .

Metrics