Abstract

Cross-phase modulation (XPM) of a frequency comb (finite-duration optical pulse sequence) by an intense, long Gaussian pump pulse is theoretically investigated, and new effects, namely, frequency-domain self-imaging phenomena (integer and fractional Talbot effects), are reported. The conditions favorable for observing spectral self-imaging phenomena by XPM are derived and numerically confirmed. The effects of nonidealities in a practical experiment (e.g., group-delay walk-off and dispersion) are also evaluated. One can use spectral self-imaging to tune the free spectral range of a frequency comb (without affecting the shape and bandwidth of the individual passbands) simply by adjusting the pump power in a fiber XPM scheme.

© 2005 Optical Society of America

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References

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2004

C. Wang, J. Azaña, and L. R. Chen, Opt. Lett. 29, 1591 (2004).

2002

V. E. Perlin and H. G. Winful, IEEE Photon. Technol. Lett. 14, 176 (2002).
[CrossRef]

2000

1999

1993

A. D. Ellis and D. M. Patrick, Electron. Lett. 29, 149 (1993).
[CrossRef]

1990

1989

P. A. Bélanger, IEEE Photon. Technol. Lett. 1, 71 (1989).
[CrossRef]

1981

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001), Chap. 7.

Atkins, S.

Azaña, J.

C. Wang, J. Azaña, and L. R. Chen, Opt. Lett. 29, 1591 (2004).

J. Azaña and M. A. Muriel, Opt. Lett. 24, 1672 (1999).
[CrossRef]

Bekker, A.

Bélanger, P. A.

P. A. Bélanger, IEEE Photon. Technol. Lett. 1, 71 (1989).
[CrossRef]

Blow, K. J.

Chen, L. R.

C. Wang, J. Azaña, and L. R. Chen, Opt. Lett. 29, 1591 (2004).

Doran, N. J.

Ellis, A. D.

A. D. Ellis and D. M. Patrick, Electron. Lett. 29, 149 (1993).
[CrossRef]

Fischer, B.

Indebetouw, G.

G. Indebetouw, J. Mod. Opt. 37, 1439 (1990).
[CrossRef]

Jannson, J.

Jannson, T.

Muriel, M. A.

Nayar, B. K.

Nelson, B. P.

Patorski, K.

K. Patorski, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1989), Vol. 27, pp. 1–108.
[CrossRef]

Patrick, D. M.

A. D. Ellis and D. M. Patrick, Electron. Lett. 29, 149 (1993).
[CrossRef]

Perlin, V. E.

V. E. Perlin and H. G. Winful, IEEE Photon. Technol. Lett. 14, 176 (2002).
[CrossRef]

Vodonos, B.

Wang, C.

C. Wang, J. Azaña, and L. R. Chen, Opt. Lett. 29, 1591 (2004).

Winful, H. G.

V. E. Perlin and H. G. Winful, IEEE Photon. Technol. Lett. 14, 176 (2002).
[CrossRef]

Electron. Lett.

A. D. Ellis and D. M. Patrick, Electron. Lett. 29, 149 (1993).
[CrossRef]

IEEE Photon. Technol. Lett.

V. E. Perlin and H. G. Winful, IEEE Photon. Technol. Lett. 14, 176 (2002).
[CrossRef]

P. A. Bélanger, IEEE Photon. Technol. Lett. 1, 71 (1989).
[CrossRef]

J. Mod. Opt.

G. Indebetouw, J. Mod. Opt. 37, 1439 (1990).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001), Chap. 7.

K. Patorski, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1989), Vol. 27, pp. 1–108.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Temporal waveform and (b) energy spectrum of the frequency comb used as the input probe signal in our numerical simulations (n.u., normalized units). Here are shown the energy spectra of the output probe signal after XPM by a Gaussian pump pulse when the pump power is fixed (c) to an arbitrary value sufficiently strong to induce interband interference, (d) such that reversed integer spectral Talbot phenomena can be observed, and (e) such that direct fractional spectral Talbot phenomena (m=2) can be observed. For comparison, the input probe spectrum is represented in (d) and (e) by dashed curves.

Fig. 2
Fig. 2

Energy spectrum of the output probe signal after XPM when the nominal pump power is fixed such that fractional spectral Talbot phenomena with m=2 [same as in Fig. 1(e)] can be observed for (a) a 5% pump power variation with respect to the nominal value and (b) initial pump–probe desynchronization of 5 ps (50% of the repetition period of the probe sequence) and group-delay mismatch such that L=75LW.

Equations (5)

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AprobeL,τ=Aprobe0,τexpjϕNLτ,
ϕNLτ=2γLApump0,τ2,
AprobeL,τ=Gτp=- expjϕNLpTRxτ-pTR.
ϕNLτ2γLPpump-Ppump/τpump2τ2.
2γLPpump=τpumpTR2smπ,

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