Abstract

The analogy between free-space propagation of optical beams and light-pulse reflection from linearly chirped fiber gratings is used to analyze the Lau effect in the temporal domain. The coherence conditions that are satisfied in the spatial domain for obtaining, at certain fixed locations, periodic fringes patterns are reformulated for guided light propagation. In this analogy, spatial periodic irradiance distributions are transformed in periodic sequences of light pulses. An optical setup is proposed to produce sharp pulse trains, with minimal distortion effects, that have repetition frequencies that are different from those associated with the input periodic optical signal. Some numerical results are given to illustrate this approach.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. M. Kempe, W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. R. Piestun, D. A. B. Miller, “Spatiotemporal control of ultrashort optical pulses by refractive-diffractive-dispersive structured optical elements,” Opt. Lett. 26, 1373–1375 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
    [CrossRef]
  11. Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).
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    [CrossRef]
  13. J. Azaña, M. A. Muriel, “Temporal Talbot effect in fiber gratings and its applications,” Appl. Opt. 38, 6700–6704 (1999).
    [CrossRef]
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    [CrossRef]
  15. J. Azaña, M. A. Muriel, “Technique for multiplying the repetition rates at periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings,” Opt. Lett. 24, 1672–1674 (1999).
    [CrossRef]
  16. E. Lau, “Beugungserscheinungen an Doppelrastern,” Ann. Phys. (Leipzig) 6, 417–423 (1948).
  17. G. J. Swanson, E. N. Leith, “Lau effect and grating imaging,” J. Opt. Soc. Am. 72, 552–555 (1982).
    [CrossRef]
  18. J. Ojeda-Castañeda, P. Andrés, J. Ibarra, “Lensless theta decoder with high light throughput,” Opt. Commun. 67, 256–260 (1988).
    [CrossRef]

2003 (1)

2001 (2)

R. Piestun, D. A. B. Miller, “Spatiotemporal control of ultrashort optical pulses by refractive-diffractive-dispersive structured optical elements,” Opt. Lett. 26, 1373–1375 (2001).
[CrossRef]

J. Azaña, M. A. Muriel, “Temporal self-imaging effects: theory and applications for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7, 728–744 (2001).
[CrossRef]

1999 (2)

1995 (1)

1994 (2)

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

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

1993 (1)

M. Kempe, W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

1992 (2)

M. Kempe, U. Stamm, B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[CrossRef]

Z. Bor, Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

1988 (1)

J. Ojeda-Castañeda, P. Andrés, J. Ibarra, “Lensless theta decoder with high light throughput,” Opt. Commun. 67, 256–260 (1988).
[CrossRef]

1987 (1)

1982 (1)

1965 (1)

J. T. Winthrop, C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. A 55, 373–381 (1965).
[CrossRef]

1948 (1)

E. Lau, “Beugungserscheinungen an Doppelrastern,” Ann. Phys. (Leipzig) 6, 417–423 (1948).

1881 (1)

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).

Andrés, P.

J. Ojeda-Castañeda, P. Andrés, J. Ibarra, “Lensless theta decoder with high light throughput,” Opt. Commun. 67, 256–260 (1988).
[CrossRef]

Azaña, J.

Bor, Z.

Z. Bor, Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

Horváth, Z. L.

Z. Bor, Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

Ibarra, J.

J. Ojeda-Castañeda, P. Andrés, J. Ibarra, “Lensless theta decoder with high light throughput,” Opt. Commun. 67, 256–260 (1988).
[CrossRef]

Kempe, M.

M. Kempe, W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

M. Kempe, U. Stamm, B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[CrossRef]

Kolner, B. H.

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

Lau, E.

E. Lau, “Beugungserscheinungen an Doppelrastern,” Ann. Phys. (Leipzig) 6, 417–423 (1948).

Leith, E. N.

Migus, A.

Miller, D. A. B.

Muriel, M. A.

Ojeda-Castañeda, J.

J. Ojeda-Castañeda, P. Andrés, J. Ibarra, “Lensless theta decoder with high light throughput,” Opt. Commun. 67, 256–260 (1988).
[CrossRef]

Ouellette, F.

Papoulis, A.

Paye, J.

Piestun, R.

Rayleigh, Lord

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).

Rudolph, W.

M. Kempe, W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

Stamm, U.

M. Kempe, U. Stamm, B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[CrossRef]

Swanson, G. J.

Wilhelmi, B.

M. Kempe, U. Stamm, B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[CrossRef]

Winthrop, J. T.

J. T. Winthrop, C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. A 55, 373–381 (1965).
[CrossRef]

Worthington, C. R.

J. T. Winthrop, C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. A 55, 373–381 (1965).
[CrossRef]

Zalvidea, D.

Ann. Phys. (Leipzig) (1)

E. Lau, “Beugungserscheinungen an Doppelrastern,” Ann. Phys. (Leipzig) 6, 417–423 (1948).

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

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

IEEE J. Sel. Top. Quantum Electron. (1)

J. Azaña, M. A. Muriel, “Temporal self-imaging effects: theory and applications for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7, 728–744 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Opt. Commun. (3)

J. Ojeda-Castañeda, P. Andrés, J. Ibarra, “Lensless theta decoder with high light throughput,” Opt. Commun. 67, 256–260 (1988).
[CrossRef]

M. Kempe, U. Stamm, B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[CrossRef]

Z. Bor, Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

Opt. Lett. (3)

Philos. Mag. (1)

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).

Phys. Rev. A (1)

M. Kempe, W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the optical device proposed for implementing the temporal Lau effect: LCFG1, LCFG2, linearly chirped fiber gratings; OC1, OC2, optical circulators. (a) The output periodic signal is undistorted if the Lau conditions are met. (b) The output signal becomes distorted when the Lau conditions are not satisfied.

Fig. 2
Fig. 2

Optical power temporal distributions from the setup of Fig. 1. (a) Temporal Lau conditions are satisfied, with n = 3 and m = 1. The output signal is practically a distortionless version of the input signal, with a repetition frequency that is half that of the original signal. (b) Temporal Lau conditions are satisfied, with n = -2, and m = 1. The output signal shows very low distortion, and it has an associated repetition frequency that is twice that of the original signal.

Fig. 3
Fig. 3

Optical power temporal distributions from the setup of Fig. 1. The temporal Lau conditions are not satisfied. The output signal undergoes a strong distortion.

Equations (12)

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

hx; z=h0 exp-i πλz x2,
rΔω=r0 exp-iΦ1,0Δωexp-i Φ2,02Δω2,
ĥrΔt=h0 expi 12Φ2,0Δt2,
x  Δt, λz  -2πΦ2,0.
1z+1z0=1nd2/λ,
z0=ndd0/mλ
d=d z+z0z0.
TM=2πmn|Φ2,01|T,
2π|Φ2,02|=nTM21-nTM2/2π|Φ2,01|,
T=TMΦ2,02+Φ2,01Φ2,01.
P˜1refω=ϰ1ωP˜1inω,
ϰ1ω=r1ωr1ω,

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