Abstract

We present what we believe is a new method to introduce self-imaging properties under dispersive transmission of single or multiple light pulses with different temporal characteristics. By properly performing a temporal filtering into a given input signal it can produce an output signal having a spectral content satisfying the Montgomery condition, thereby allowing self-imaging of this signal under further dispersive transmission. An array of fiber loops performs the filtering operation on the input signal. We show some numerical simulations with a single light pulse as an input signal to verify the feasibility of the method and demonstrate the effects of the several involved parameters on both the pulse shape and the noise level.

© 2007 Optical Society of America

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  2. A. Papoulis, "Pulse compression, fiber communications, and diffraction: a unified approach," J. Opt. Soc. Am. A 11, 3-13 (1994).
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  3. P. Naulleau and E. Leith, "Stretch, time lenses, and incoherent time imaging," Appl. Opt. 34, 4119-4128 (1995).
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  10. C. Cuadrado-Laborde, P. A. Costanzo-Caso, R. Duchowicz, and E. E. Sicre, "Temporal Talbot effect applied to determine dispersion parameters," Opt. Commun. 260, 528-534 (2006).
    [CrossRef]
  11. L. Chantada, C. R. Fernández-Pousa, and C. Gómez-Reino, "Spectral analysis of the temporal self-imaging phenomenon in fiber dispersive lines," J. Lightwave Technol. 24, 2015-2025 (2006).
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  12. J. Jahns, H. Knuppertz, and A. W. Lohmann, "Montgomery self-imaging effect using computer-generated diffractive optical elements," Opt. Commun. 225, 13-17 (2003).
    [CrossRef]
  13. J. Jahns and A. W. Lohmann, "Temporal filtering by double diffraction," Appl. Opt. 43, 4339-4344 (2004).
    [CrossRef] [PubMed]
  14. G. Mínguez-Vega and J. Jahns, "Temporal processing with the Montgomery interferometer," Opt. Commun. 236, 45-52 (2004).
    [CrossRef]
  15. W. D. Montgomery, "Self-imaging objects of infinite apertures," J. Opt. Soc. Am. 57, 772-778 (1967).
    [CrossRef]
  16. G. Indebetouw, "Self-imaging through a Fabry-Perot interferometer," J. Mod. Opt. 30, 1463-1471 (1983).
    [CrossRef]
  17. G. Indebetouw, "Polychromatic self-imaging," J. Mod. Opt. 35, 243-252 (1988).
    [CrossRef]
  18. G. Indebetouw, "Necessary condition for temporal self-imaging in a linear dispersive medium," J. Mod. Opt. 37, 1439-1451 (1990).
    [CrossRef]
  19. G. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, 2001).

2006

2004

J. Jahns and A. W. Lohmann, "Temporal filtering by double diffraction," Appl. Opt. 43, 4339-4344 (2004).
[CrossRef] [PubMed]

G. Mínguez-Vega and J. Jahns, "Temporal processing with the Montgomery interferometer," Opt. Commun. 236, 45-52 (2004).
[CrossRef]

2003

2001

G. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, 2001).

1999

1995

1994

B. H. Kolner, "Spacer-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30, 1951-1963 (1994).
[CrossRef]

A. Papoulis, "Pulse compression, fiber communications, and diffraction: a unified approach," J. Opt. Soc. Am. A 11, 3-13 (1994).
[CrossRef]

1990

G. Indebetouw, "Necessary condition for temporal self-imaging in a linear dispersive medium," J. Mod. Opt. 37, 1439-1451 (1990).
[CrossRef]

1989

P. A. Belanger, "Periodic restoration of pulse trains in a linear dispersive medium," IEEE Photon. Technol. Lett. 1, 71-72 (1989).
[CrossRef]

1988

G. Indebetouw, "Polychromatic self-imaging," J. Mod. Opt. 35, 243-252 (1988).
[CrossRef]

1983

G. Indebetouw, "Self-imaging through a Fabry-Perot interferometer," J. Mod. Opt. 30, 1463-1471 (1983).
[CrossRef]

1981

1967

Agrawal, G.

G. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, 2001).

Azaña, J.

Belanger, P. A.

P. A. Belanger, "Periodic restoration of pulse trains in a linear dispersive medium," IEEE Photon. Technol. Lett. 1, 71-72 (1989).
[CrossRef]

Chantada, L.

Chen, L. R.

Costanzo-Caso, P. A.

C. Cuadrado-Laborde, P. A. Costanzo-Caso, R. Duchowicz, and E. E. Sicre, "Temporal Talbot effect applied to determine dispersion parameters," Opt. Commun. 260, 528-534 (2006).
[CrossRef]

Cuadrado-Laborde, C.

C. Cuadrado-Laborde, P. A. Costanzo-Caso, R. Duchowicz, and E. E. Sicre, "Temporal Talbot effect applied to determine dispersion parameters," Opt. Commun. 260, 528-534 (2006).
[CrossRef]

Duchowicz, R.

C. Cuadrado-Laborde, P. A. Costanzo-Caso, R. Duchowicz, and E. E. Sicre, "Temporal Talbot effect applied to determine dispersion parameters," Opt. Commun. 260, 528-534 (2006).
[CrossRef]

Fernández-Pousa, C. R.

Gómez-Reino, C.

Indebetouw, G.

G. Indebetouw, "Necessary condition for temporal self-imaging in a linear dispersive medium," J. Mod. Opt. 37, 1439-1451 (1990).
[CrossRef]

G. Indebetouw, "Polychromatic self-imaging," J. Mod. Opt. 35, 243-252 (1988).
[CrossRef]

G. Indebetouw, "Self-imaging through a Fabry-Perot interferometer," J. Mod. Opt. 30, 1463-1471 (1983).
[CrossRef]

Jahns, J.

G. Mínguez-Vega and J. Jahns, "Temporal processing with the Montgomery interferometer," Opt. Commun. 236, 45-52 (2004).
[CrossRef]

J. Jahns and A. W. Lohmann, "Temporal filtering by double diffraction," Appl. Opt. 43, 4339-4344 (2004).
[CrossRef] [PubMed]

J. Jahns, H. Knuppertz, and A. W. Lohmann, "Montgomery self-imaging effect using computer-generated diffractive optical elements," Opt. Commun. 225, 13-17 (2003).
[CrossRef]

Jannson, J.

Jannson, T.

Knuppertz, H.

J. Jahns, H. Knuppertz, and A. W. Lohmann, "Montgomery self-imaging effect using computer-generated diffractive optical elements," Opt. Commun. 225, 13-17 (2003).
[CrossRef]

Kolner, B. H.

B. H. Kolner, "Spacer-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30, 1951-1963 (1994).
[CrossRef]

Leith, E.

Lohmann, A. W.

J. Jahns and A. W. Lohmann, "Temporal filtering by double diffraction," Appl. Opt. 43, 4339-4344 (2004).
[CrossRef] [PubMed]

J. Jahns, H. Knuppertz, and A. W. Lohmann, "Montgomery self-imaging effect using computer-generated diffractive optical elements," Opt. Commun. 225, 13-17 (2003).
[CrossRef]

Mínguez-Vega, G.

G. Mínguez-Vega and J. Jahns, "Temporal processing with the Montgomery interferometer," Opt. Commun. 236, 45-52 (2004).
[CrossRef]

Montgomery, W. D.

Muriel, M. A.

Naulleau, P.

Papoulis, A.

Sicre, E. E.

C. Cuadrado-Laborde, P. A. Costanzo-Caso, R. Duchowicz, and E. E. Sicre, "Temporal Talbot effect applied to determine dispersion parameters," Opt. Commun. 260, 528-534 (2006).
[CrossRef]

van Howe, J.

Xu, C.

Appl. Opt.

IEEE J. Quantum Electron.

B. H. Kolner, "Spacer-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30, 1951-1963 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

P. A. Belanger, "Periodic restoration of pulse trains in a linear dispersive medium," IEEE Photon. Technol. Lett. 1, 71-72 (1989).
[CrossRef]

J. Lightwave Technol.

J. Mod. Opt.

G. Indebetouw, "Self-imaging through a Fabry-Perot interferometer," J. Mod. Opt. 30, 1463-1471 (1983).
[CrossRef]

G. Indebetouw, "Polychromatic self-imaging," J. Mod. Opt. 35, 243-252 (1988).
[CrossRef]

G. Indebetouw, "Necessary condition for temporal self-imaging in a linear dispersive medium," J. Mod. Opt. 37, 1439-1451 (1990).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

G. Mínguez-Vega and J. Jahns, "Temporal processing with the Montgomery interferometer," Opt. Commun. 236, 45-52 (2004).
[CrossRef]

C. Cuadrado-Laborde, P. A. Costanzo-Caso, R. Duchowicz, and E. E. Sicre, "Temporal Talbot effect applied to determine dispersion parameters," Opt. Commun. 260, 528-534 (2006).
[CrossRef]

J. Jahns, H. Knuppertz, and A. W. Lohmann, "Montgomery self-imaging effect using computer-generated diffractive optical elements," Opt. Commun. 225, 13-17 (2003).
[CrossRef]

Other

G. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, 2001).

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Figures (7)

Fig. 1
Fig. 1

Scheme of the proposed photonic device. The amplitude x F ( t ) can be considered as a filtered version of the aperiodic input signal x 0 ( t ) having Montgomery self-imaging properties. FL stands for fiber loop.

Fig. 2
Fig. 2

(a) Input optical power | x 0 ( t ) | 2 . (b) Output optical power | x F ( t ) | 2 of a single fiber loop ( T = 50   ps , R = 0.99 ) when a single Gaussian pulse is the input signal.

Fig. 3
Fig. 3

Influence of the fundamental round-trip time T f on the filtering action. Normalized output optical power of the filter | x F ( t ) | 2 for (a) T f = 25   ps , (b) 50   ps , and (c) 100   ps . Eight fiber loops were used with R = 0.99 each.

Fig. 4
Fig. 4

(a) Output optical power | x F ( t ) | 2 of the temporal filter when a single Gaussian pulse of T 0 = 2   ps is the input signal. (b) and (c) Output optical powers of the dispersion line corresponding to the first ( m = 1 ) and second ( m = 2 ) Montgomery self-images, respectively.

Fig. 5
Fig. 5

Cross-correlation parameter between | x F ( t ) | 2 and | x out ( t ) | 2 for a varying dispersion line Φ 20 . To better visualize the self-image conditions, the correlation is displayed against the variable m = π Φ 20 / T f 2 . The self-images are met for the integer values of m.

Fig. 6
Fig. 6

Influence of the fundamental round-trip time on the first self-image formation for (a) T f = 25   ps , (b) 50   ps , and (c) 100   ps . Eight fiber loops were used with R = 0.99 each.

Fig. 7
Fig. 7

Influence of the reflectivity on the first self-image formation. Normalized output optical power for: R = 0.95 (solid line), R = 0.97 (dashed line), and R = 0.995 (dotted line). Eight fiber loops were used with a fundamental round-trip time of 50   ps .

Equations (119)

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t ( x , y )
t ˜ ( u , v )
t ˜ ( u , v ) 0 u 2 + v 2 = ρ 0 n ,
ρ 0 = 2 / λ z 0
z 0
v = 0
ρ 0 = 1 / d
n = m 2
u m = m / d
x 0 ( t )
Δ t
x 0 ( t )
Δ t T A T ¯ 1
T ¯ 1
x 0 ( t )
F L j ( ν )
F L j ( ν ) = 1 R j 1 R j exp ( i 2 π ν / Δ ν j ) ,
R j
Δ ν j
Δ ν j = v g / L j = 1 / T j
v g
L j
T j
Δ ν f
L f
x 0 ( t )
Δ ν f < 1 / T ¯ 1
Δ ν j = j Δ ν f , j = 2 , 3 , … ,  n , …  .
δ ν j
δ ν j = 2 j π T 1 sin 1 ( 1 2 F j ) ,
F j = 4 R j / ( 1 R j ) 2
R j 1 , F j
x F ( t )
x F ( t ) = [ j = 1 n h j ( t ) ] x 0 ( t ) ,
h j ( t )
F L j
x 0 ( t )
x F ( t )
Φ 20
Φ 20 = 2 m T f 2 2 π , m = 1 , 2 , 3 , … , 
T f
j 15
x 0 ( t )
1 / e
T 0 = 2   ps
T = 50   ps
R = 0.99
| x F ( t ) | 2
( 1 R n )
n = 8
T j = T f / j
j = 2
j = 4
j = 9
j = 1
j = 1
R j = 0.99
T f
T f
Δ ν f
Δ ν f
Δ ν j < 1 / T ¯ 1
Δ ν j
R 0
R 1
x F ( t )
| x out ( t ) | 2
x F ( t )
Φ 20 = 7.96 × 10 2 ps 2 / rad
1.59 × 10 3 ps 2 / rad
m = 1
m = 2
| x F ( t ) | 2
| x F ( t ) | 2
| x out ( t ) | 2
x out ( t )
Δ m = 0.1
Φ 20
| x F ( t ) | 2
| x out ( t ) | 2
0 < Φ 20 < 1.67 × 10 3 ps 2 / rad
Φ 20
| x out ( t ) | 2
T f
Φ 20
T f
T f
Φ 20 = 1.98 × 10 2 ps 2 / rad
7.96 × 10 2 ps 2 / rad
3.18 × 10 3 ps 2 / rad
R = 0.95
x F ( t )
x 0 ( t )
| x 0 ( t ) | 2
| x F ( t ) | 2
T = 50   ps
R = 0.99
T f
| x F ( t ) | 2
T f = 25   ps
50   ps
100   ps
R = 0.99
| x F ( t ) | 2
T 0 = 2   ps
( m = 1 )
( m = 2 )
| x F ( t ) | 2
| x out ( t ) | 2
Φ 20
m = π Φ 20 / T f 2
T f = 25   ps
50   ps
100   ps
R = 0.99
R = 0.95
R = 0.97
R = 0.995
50   ps

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