Abstract

We propose several applications of graded-index (GRIN) time lenses including time–frequency conversion (time-to-frequency conversion and frequency-to-time conversion simultaneously), temporal filtering, and temporal imaging. The evolution of the signal pulses in these systems is demonstrated. As two important parameters, the focal length and the time–frequency conversion factors of time–frequency conversion based on GRIN time lenses are evaluated.

© 2012 Optical Society of America

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References

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2008

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef]

2006

2004

1999

M. D. Pelusi, Y. Matsui, and A. Suzuki, IEEE Photon. Technol. Lett. 11, 1461 (1999).
[CrossRef]

1994

B. H. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

1993

1992

Arai, J.

Azaña, J.

Banyai, W.

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Berger, N. K.

Bernardo, L. M.

Bloom, D.

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Fischer, B.

Foster, M. A.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef]

Gaeta, A. L.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef]

Geraghty, D. F.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef]

Godil, A.

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Kauffman, M.

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Kolner, B. H.

B. H. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

Levit, B.

Lipson, M.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef]

Lohmann, A. W.

Marinho, F. J.

Matsui, Y.

M. D. Pelusi, Y. Matsui, and A. Suzuki, IEEE Photon. Technol. Lett. 11, 1461 (1999).
[CrossRef]

Mendlovic, D.

Okano, F.

Okui, M.

Ozaktas, H. M.

Pelusi, M. D.

M. D. Pelusi, Y. Matsui, and A. Suzuki, IEEE Photon. Technol. Lett. 11, 1461 (1999).
[CrossRef]

Salem, R.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef]

Suzuki, A.

M. D. Pelusi, Y. Matsui, and A. Suzuki, IEEE Photon. Technol. Lett. 11, 1461 (1999).
[CrossRef]

Turner-Foster, A. C.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

IEEE J. Quantum Electron.

B. H. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

M. D. Pelusi, Y. Matsui, and A. Suzuki, IEEE Photon. Technol. Lett. 11, 1461 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Nature

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef]

Opt. Lett.

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Figures (8)

Fig. 1.
Fig. 1.

Temporal Fourier transform (time–frequency conversion) configuration.

Fig. 2.
Fig. 2.

Evolution of the signal pulses along the GRIN time lens in which L is the focal length. (a) Temporal shape evolution and (b) spectrum evolution.

Fig. 3.
Fig. 3.

Phase modulation amplitudes calculated in the simulation (circles) and those analyzed according to Eq. (6) (solid curve) versus focal length.

Fig. 4.
Fig. 4.

Output (circles) at the focal length of a GRIN time lens and scaled input (solid curve) according to Eq. (9). (a) The output temporal shape and scaled input spectrum and (b) the output spectrum and scaled input temporal shape.

Fig. 5.
Fig. 5.

Temporal filtering configuration.

Fig. 6.
Fig. 6.

Evolution of the signal pulses along the temporal filtering system. (a) Temporal shape evolution and (b) spectrum evolution.

Fig. 7.
Fig. 7.

Temporal imaging configuration.

Fig. 8.
Fig. 8.

Evolution of the signal pulses along the temporal imaging system. (a) Temporal shape evolution and (b) spectrum evolution.

Equations (12)

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iA(ξ,τ)ξ+β222A(ξ,τ)τ2+ϕ(ξ,τ)ξA(ξ,τ)=0,
A(0,τ)=l=0alφl(τ),
al=+A(0,τ)φl(τ)dτ,
φl(τ)=(2ll!π)1/2Hl(τ/στ)exp(τ2/2στ2).
A(ξ,τ)=exp(iΓ0)l=0alφl(τ)×exp[i(ωm2Γ0β2/ξ)1/2(l+1/2)ξ].
F[A(0,τ)]=l=0alφl(στ2ω)2πστexp(ilπ/2).
L=π2/(4ωm2Γ0β2).
L=1/(ωm2Γ0β2),
Δt/Δω=2β2L/π.
Δt/Δω=β2L,
iAξ+β222Aτ2+γ|Ap|2A=0,
M=πβ2L/(2β2L),

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