Abstract

Time grating, a temporal analogy of the diffraction grating, is proposed. In the time grating, a laser pulse is split into several embranchments, which are modulated in phase by the phase-modulation function and then combined into a short pulse train. The characteristics and dispersion of the time grating are studied theoretically. Its dispersion, similar to that of the diffraction grating, is time dependent. The characteristics of the output pulse train are controllable by the phase-modulated function. The time grating has several applications, such as in temporal spectrum measurement and in the generation of a short pulse train with arbitrary shape.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. T. Khayim and M. Yamauchi, “Femtosecond optical pulse generation from a CW laser using an electro-optic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  15. D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
    [CrossRef]

2011 (1)

2009 (1)

2008 (1)

D. Yang, S. Kumar, and H. Wang, “Temporal filtering using time lenses for optical transmission systems,” Opt. Commun. 281, 238–247 (2008).
[CrossRef]

2006 (1)

2005 (2)

2004 (1)

1999 (1)

T. Khayim and M. Yamauchi, “Femtosecond optical pulse generation from a CW laser using an electro-optic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[CrossRef]

1997 (1)

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

1994 (1)

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

1992 (1)

1989 (1)

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Chen, A.

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Chena, D.

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Dai, Y.

Dalton, L. R.

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Fetterman, H. R.

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Hansryd, J.

Khayim, T.

T. Khayim and M. Yamauchi, “Femtosecond optical pulse generation from a CW laser using an electro-optic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[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]

B. H. Kolner and M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14, 630–632 (1989).
[CrossRef]

Kumar, S.

D. Yang, S. Kumar, and H. Wang, “Temporal filtering using time lenses for optical transmission systems,” Opt. Commun. 281, 238–247 (2008).
[CrossRef]

Lohmann, A. W.

Mendlovic, D.

Mollenauer, L. F.

L. F. Mollenauer and C. Xu, “Time-lens timing-jitter compensator in ultra-long haul DWDM dispersion managed soliton transmissions,” in Lasers and Electro-Optics (CLEO ’02), Technical Digest(IEEE, 2002), paper CPDB1-1.

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Nazarathy, M.

Shi, Y.

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Steier, W. H.

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

van Howe, J.

Wang, H.

D. Yang, S. Kumar, and H. Wang, “Temporal filtering using time lenses for optical transmission systems,” Opt. Commun. 281, 238–247 (2008).
[CrossRef]

Wang, S. W.

S. W. Wang, J. Zheng, and J. Q. Xu, “Generation of arbitrary shape and repetition rate pulses with phase modulation combination,” Chin. Opt. Lett. (to be published).

Wang, W.

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Xin, R.

Xu, C.

Xu, J. Q.

S. W. Wang, J. Zheng, and J. Q. Xu, “Generation of arbitrary shape and repetition rate pulses with phase modulation combination,” Chin. Opt. Lett. (to be published).

Yamauchi, M.

T. Khayim and M. Yamauchi, “Femtosecond optical pulse generation from a CW laser using an electro-optic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[CrossRef]

Yang, D.

D. Yang, S. Kumar, and H. Wang, “Temporal filtering using time lenses for optical transmission systems,” Opt. Commun. 281, 238–247 (2008).
[CrossRef]

Zheng, J.

S. W. Wang, J. Zheng, and J. Q. Xu, “Generation of arbitrary shape and repetition rate pulses with phase modulation combination,” Chin. Opt. Lett. (to be published).

Zuegel, J. D.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. Chena, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

T. Khayim and M. Yamauchi, “Femtosecond optical pulse generation from a CW laser using an electro-optic phase modulator featuring lens modulation,” IEEE J. Quantum Electron. 35, 1412–1418 (1999).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (2)

D. Yang, S. Kumar, and H. Wang, “Temporal filtering using time lenses for optical transmission systems,” Opt. Commun. 281, 238–247 (2008).
[CrossRef]

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Other (2)

S. W. Wang, J. Zheng, and J. Q. Xu, “Generation of arbitrary shape and repetition rate pulses with phase modulation combination,” Chin. Opt. Lett. (to be published).

L. F. Mollenauer and C. Xu, “Time-lens timing-jitter compensator in ultra-long haul DWDM dispersion managed soliton transmissions,” in Lasers and Electro-Optics (CLEO ’02), Technical Digest(IEEE, 2002), paper CPDB1-1.

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Figures (10)

Fig. 1.
Fig. 1.

Schematic comparison between the spatial grating (a) and the time grating (b).

Fig. 2.
Fig. 2.

Experimental example of time grating. FA, fiber amplifier; PM, phase modulator.

Fig. 3.
Fig. 3.

Combination pulse trains from time grating with N=2 (blue dashed curve) and 8 (green solid curve).

Fig. 4.
Fig. 4.

Output pulse profile from the time grating (a) for linear chirped, exponential chirped, and sine FM input pulses (b), where N=8 and the voltage is set to a constant ΔV(t)=2n0c/κf0; f0 is the starting frequency.

Fig. 5.
Fig. 5.

(a) Typical pulse trains generated from time grating with linear (top), quadratic (middle), and sine (bottom) phase modulations. (b) Corresponding PMFs.

Fig. 6.
Fig. 6.

(a) Linear PMF (blue dotted line) with slope ϕk=12πGHz, sawing PMF (green curve), and triangular PMF (red dashed curve). (b) Pulse train with the three types of PMFs in (a). N=8.

Fig. 7.
Fig. 7.

(a) Triangular (blue curve), and sinusoidal (red curve) PMFs with the same modulation depth and frequency. (b) Pulses generated from the corresponding PMFs where N=8.

Fig. 8.
Fig. 8.

(a) Triangular (blue solid curve) and trapezoidal (green dashed curve) PMFs with the same modulation depth and frequency. (b) Pulses generated from the corresponding PMFs where N=8.

Fig. 9.
Fig. 9.

Temporal dispersion for chromatic pulse from the time grating. (a) Whole intensity and (b) intensities for three spectral components. N=8 and the linear voltage ΔV=Vkt is applied.

Fig. 10.
Fig. 10.

Chirped pulse from the time grating for the polychromatic input light. N=8. The PMF Δϕ(t) is a triangular period function that is changed from 06π0 in every period.

Equations (18)

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I0(t)=|E0(t)ej(ωtkz)|2,
Ei(t)=E0(t)NHi(t)ej(ωtkz)+jϕi(t),
EN(t)=i=1NE0(t)Hi(t)ej(ωtkz)Nejϕi(t).
EN(t)=E0(t)H(t)ej(ωtkz)N[1+ejΔϕ(t)+ej2Δϕ(t)++ej(N1)Δϕ(t)]=E0(t)H(t)Nej(ωtkz)+j2(N1)Δϕ(t)sin[NΔϕ(t)/2]sin[Δϕ(t)/2].
IN(t)=I0(t)|H(t)|2N(sin[NΔϕ(t)/2]sin[Δϕ(t)/2])2.
Δϕ(t)=m*2π,
WΔϕ1.8πN,
I(θ)=I0(θ)H(θ)(sin[NΔϕ/2]sin[Δϕ/2])2.
Δϕ(t)=κπΔV(t)λ(t),
dtdλ=2mΔV(t)κ.
r=1Δt.
Δϕ(t)={ϕktwhent<T/4D/2App/2whenT/4D/2t<T/4+D/2ϕk(tT/2)whenT/4+D/2t<3T/4D/2App/2ϕk(tT)when3T/4D/2t<3T/4+D/2when3T/4+D/2t<T,
ΔV=2mκλmin.
ΔV=2mκλmax.
WΔV1.8Nκλ0+2mκΔλ,
ΔV=2(mc+1/N)λmaxκ=2(mc+11/N)λminκ,
mc=N2Nλ0Δλ12,
Wmax_ΔV=1.8κλ0N+2κ(N2Nλ0Δλ2).

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