Abstract

The propagation of a laser pulse in a graded-index (GRIN) space lens and in an electro-optic crystal with an appropriate refractive index modulation is studied. It is shown that the crystal functions as a GRIN time lens if the propagation’s second-order dispersion is included and if the phase velocity of the modulating wave equals the group velocity of the laser pulse.

© 2006 Optical Society of America

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References

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  1. S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, Sov. Phys. JETP 28, 748 (1969).
  2. B. H. Kolner and M. Nazarathy, Opt. Lett. 14, 630 (1989).
    [Crossref] [PubMed]
  3. B. H. Kolner, IEEE J. Quantum Electron. 34, 1951 (1994).
    [Crossref]
  4. B. H. Kolner, Appl. Phys. Lett. 52, 1122 (1988).
    [Crossref]
  5. C. V. Bennett and B. H. Kolner, IEEE J. Quantum Electron. 36, 430 (2000).
    [Crossref]
  6. G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
    [Crossref] [PubMed]
  7. S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
    [Crossref]
  8. A. Yariv, Quantum Electronics (Wiley, 1988).
  9. S. Mookherjea and A. Yariv, Opt. Lett. 26, 1323 (2001).
    [Crossref]
  10. A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).
  11. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).
  12. L. M. Bernardo, Opt. Eng. 35, 732 (1996).
    [Crossref]

2001 (2)

S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
[Crossref]

S. Mookherjea and A. Yariv, Opt. Lett. 26, 1323 (2001).
[Crossref]

2000 (1)

C. V. Bennett and B. H. Kolner, IEEE J. Quantum Electron. 36, 430 (2000).
[Crossref]

1996 (1)

L. M. Bernardo, Opt. Eng. 35, 732 (1996).
[Crossref]

1994 (1)

B. H. Kolner, IEEE J. Quantum Electron. 34, 1951 (1994).
[Crossref]

1989 (2)

B. H. Kolner and M. Nazarathy, Opt. Lett. 14, 630 (1989).
[Crossref] [PubMed]

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[Crossref] [PubMed]

1988 (1)

B. H. Kolner, Appl. Phys. Lett. 52, 1122 (1988).
[Crossref]

1969 (1)

S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, Sov. Phys. JETP 28, 748 (1969).

Agrawal, G. P.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[Crossref] [PubMed]

Akhmanov, S. A.

S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, Sov. Phys. JETP 28, 748 (1969).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Alfano, R. R.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[Crossref] [PubMed]

Baldeck, P. L.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[Crossref] [PubMed]

Bennett, C. V.

C. V. Bennett and B. H. Kolner, IEEE J. Quantum Electron. 36, 430 (2000).
[Crossref]

Bernardo, L. M.

L. M. Bernardo, Opt. Eng. 35, 732 (1996).
[Crossref]

Chirkin, A. S.

S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, Sov. Phys. JETP 28, 748 (1969).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Kolner, B. H.

C. V. Bennett and B. H. Kolner, IEEE J. Quantum Electron. 36, 430 (2000).
[Crossref]

B. H. Kolner, IEEE J. Quantum Electron. 34, 1951 (1994).
[Crossref]

B. H. Kolner and M. Nazarathy, Opt. Lett. 14, 630 (1989).
[Crossref] [PubMed]

B. H. Kolner, Appl. Phys. Lett. 52, 1122 (1988).
[Crossref]

Mookherjea, S.

S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
[Crossref]

S. Mookherjea and A. Yariv, Opt. Lett. 26, 1323 (2001).
[Crossref]

Nazarathy, M.

Sukhorukov, A. P.

S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, Sov. Phys. JETP 28, 748 (1969).

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Yariv, A.

S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
[Crossref]

S. Mookherjea and A. Yariv, Opt. Lett. 26, 1323 (2001).
[Crossref]

A. Yariv, Quantum Electronics (Wiley, 1988).

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

Appl. Phys. Lett. (1)

B. H. Kolner, Appl. Phys. Lett. 52, 1122 (1988).
[Crossref]

IEEE J. Quantum Electron. (2)

C. V. Bennett and B. H. Kolner, IEEE J. Quantum Electron. 36, 430 (2000).
[Crossref]

B. H. Kolner, IEEE J. Quantum Electron. 34, 1951 (1994).
[Crossref]

Opt. Eng. (1)

L. M. Bernardo, Opt. Eng. 35, 732 (1996).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 40, 5063 (1989).
[Crossref] [PubMed]

Phys. Rev. E (1)

S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
[Crossref]

Sov. Phys. JETP (1)

S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, Sov. Phys. JETP 28, 748 (1969).

Other (3)

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

A. Yariv, Quantum Electronics (Wiley, 1988).

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Tables (1)

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Table 1 Translation between GRIN Time Lens and GRIN Space Lens

Equations (21)

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n 2 ( ρ ) = n 0 2 [ 1 ( n 2 n 0 ) ρ 2 ] ,
2 E ( ρ , z ) + k 0 2 [ 1 ( n 2 n 0 ) ρ 2 ] E ( ρ , z ) = 0 ,
φ l ( x ) = C l H l ( x σ x ) exp ( x 2 2 σ x 2 ) ,
β l m = k 0 [ 1 ( 2 k 0 ) n 2 n 0 ( l + m + 1 ) ] 1 2 ,
β l m k 0 n 2 n 0 ( l + m + 1 ) .
2 i k 0 A ( ρ , z ) z + 2 A ( ρ , z ) k 0 2 n 2 n 0 A ( ρ , z ) = 0 .
A ( x ) = l = 0 a l φ l ( x ) ,
a l = + A ( x ) φ l ( x ) d x .
A ( x , z ) = l = 0 a l φ l ( x ) exp [ i n 2 n 0 ( l + 1 2 ) z ] ,
E ( x , z ) = exp ( i k 0 z ) l = 0 a l φ l ( x ) exp [ i n 2 n 0 ( l + 1 2 ) z ] .
2 E ( r , t ) μ 0 ϵ 0 2 E ( r , t ) t 2 = μ 0 2 P ( r , t ) t 2 ,
Δ P ( r , t ) = ϵ 0 n 0 4 r eff E m ( r , t ) E ( r , t ) .
E m ( r , t ) = E m 0 cos ( ω m t k m z ) .
[ A ( z , t ) z + β 1 A ( z , t ) t i β 2 2 2 A ( z , t ) t 2 ] exp [ i ( ω 0 t β 0 z ) ] = i μ 0 2 β 0 2 Δ P ( z , t ) t 2 ,
i μ 0 2 β 0 2 Δ P ( z , t ) t 2 i μ 0 ω 0 2 2 β 0 Δ P ( z , t ) = i ω 0 2 c n 0 3 r eff A ( z , t ) E m 0 cos [ i ( ω m t k m z ) ] exp [ i ( ω 0 t β 0 z ) ] ,
A ( ξ , τ ) ξ i β 2 2 2 A ( ξ , τ ) τ 2 = i ω 0 2 c n 0 3 r eff E m 0 cos ( ω m τ Δ ϕ ) A ( ξ , τ ) ,
1 i A ( ξ , τ ) ξ β 2 2 2 A ( ξ , τ ) τ 2 ω 0 2 c n 0 3 r eff E m 0 ( 1 ω m 2 τ 2 2 ) A ( ξ , τ ) = 0 .
2 A ( τ ) τ 2 + β 0 β 2 ( 2 β β 0 + 2 Δ n 0 n 0 Δ n 0 n 0 ω m 2 τ 2 ) A ( τ ) = 0 ,
φ l ( τ ) = C l H l ( τ σ τ ) exp ( τ 2 2 σ τ 2 ) ,
β l = β 0 [ Δ n 0 n 0 ω m ( β 2 β 0 Δ n 0 n 0 ) 1 2 ( l + 1 2 ) ] .
A ( ξ , τ ) = exp ( i Δ n 0 n 0 β 0 ξ ) l = 0 a l φ l ( τ ) exp [ i ω m β 0 ( β 2 β 0 Δ n 0 n 0 ) 1 2 ( l + 1 2 ) ξ ] ,

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