Abstract

We theoretically propose a procedure based on a cascading genetic algorithm for the design of aperiodically quasi-phase-matched gratings for frequency conversion of optical ultrafast pulses during difference-frequency generation. By designing the sequence of a domain inversion grating, different wavelengths at the output idler pulse almost have the same phase response, so femtosecond laser pulses at wavelength 800  nm can be shifted to other wavelengths without group-velocity mismatch.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. S. Ashihara, T. Shimura, and K. Kuroda, "Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings," J. Opt. Soc. Am. B 20, 853-856 (2003).
    [CrossRef]
  2. N. Fujioka, S. Ashihara, H. Ono, T. Shimura, and K. Kuroda, "Group-velocity-matched noncollinear second-harmonic generation in quasi-phase matching," J. Opt. Soc. Am. B 22, 1283-1289 (2005).
    [CrossRef]
  3. S.-M. Gao, C.-xi Yang, and G.-F. Jin, "Wavelength converter based on linearly chirped gratings in lithium niobate through cascaded second-order processes," Chin. Phys. Lett. 20, 1272-1274 (2003).
    [CrossRef]
  4. J.-y. Zhang, J. Y. Huang, H. Wang, K. S. Wong, and G. K. Wong, "Second-harmonic generation from regeneratively amplified femtosecond laser pulses in BBO and LBO crystals," J. Opt. Soc. Am. B 15, 200-209 (1998).
    [CrossRef]
  5. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, "Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate," Opt. Lett. 22, 1341-1343 (1997).
    [CrossRef]
  6. G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, "Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping," J. Opt. Soc. Am. B 17, 304-318 (2000).
    [CrossRef]
  7. G. Imeshev, M. A. Arbore, S. Kasriel, and M. M. Fejer, "Pulse shaping and compression by second-harmonic generation with quasi-phase-matching gratings in the presence of arbitrary dispersion," J. Opt. Soc. Am. B 17, 1420-1437 (2000).
    [CrossRef]
  8. P. Loza-Alvarez, M. Ebrahimzadeh, W. Sibbett, D. T. Reid, D. Artigas, and M. Missey, "Femtosecond second-harmonic pulse compression in aperiodically poled lithium niobate: a systematic comparison of experiment and theory," J. Opt. Soc. Am. B 18, 1212-1217 (2001).
    [CrossRef]
  9. U. Sapaev and D. T. Reid, "General second-harmonic pulse shaping in grating-engineered quasi-phase-matched nonlinear crystals," Opt. Express 13, 3264-3276 (2005).
    [CrossRef] [PubMed]
  10. P. Li, X. Chen, Y. Chen, and Y. Xia, "Pulse compression during second-harmonic generation in engineered aperodic quasi-phase-matching gratings," Opt. Express 13, 6807-6814 (2005).
    [CrossRef] [PubMed]
  11. X. Chen, F. Wu, X. Zeng, Y. Chen, Y. Xia, and Y. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
    [CrossRef]
  12. G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter, "Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings," J. Opt. Soc. Am. B 18, 534-539 (2001).
    [CrossRef]
  13. D. H. Jundt, "Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate," Opt. Lett. 22, 1553-1555 (1997).
    [CrossRef]

2005 (3)

2004 (1)

X. Chen, F. Wu, X. Zeng, Y. Chen, Y. Xia, and Y. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

2003 (2)

S.-M. Gao, C.-xi Yang, and G.-F. Jin, "Wavelength converter based on linearly chirped gratings in lithium niobate through cascaded second-order processes," Chin. Phys. Lett. 20, 1272-1274 (2003).
[CrossRef]

S. Ashihara, T. Shimura, and K. Kuroda, "Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings," J. Opt. Soc. Am. B 20, 853-856 (2003).
[CrossRef]

2001 (2)

2000 (2)

1998 (1)

1997 (2)

Chin. Phys. Lett. (1)

S.-M. Gao, C.-xi Yang, and G.-F. Jin, "Wavelength converter based on linearly chirped gratings in lithium niobate through cascaded second-order processes," Chin. Phys. Lett. 20, 1272-1274 (2003).
[CrossRef]

J. Opt. Soc. Am. B (7)

J.-y. Zhang, J. Y. Huang, H. Wang, K. S. Wong, and G. K. Wong, "Second-harmonic generation from regeneratively amplified femtosecond laser pulses in BBO and LBO crystals," J. Opt. Soc. Am. B 15, 200-209 (1998).
[CrossRef]

S. Ashihara, T. Shimura, and K. Kuroda, "Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings," J. Opt. Soc. Am. B 20, 853-856 (2003).
[CrossRef]

N. Fujioka, S. Ashihara, H. Ono, T. Shimura, and K. Kuroda, "Group-velocity-matched noncollinear second-harmonic generation in quasi-phase matching," J. Opt. Soc. Am. B 22, 1283-1289 (2005).
[CrossRef]

G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, "Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping," J. Opt. Soc. Am. B 17, 304-318 (2000).
[CrossRef]

G. Imeshev, M. A. Arbore, S. Kasriel, and M. M. Fejer, "Pulse shaping and compression by second-harmonic generation with quasi-phase-matching gratings in the presence of arbitrary dispersion," J. Opt. Soc. Am. B 17, 1420-1437 (2000).
[CrossRef]

P. Loza-Alvarez, M. Ebrahimzadeh, W. Sibbett, D. T. Reid, D. Artigas, and M. Missey, "Femtosecond second-harmonic pulse compression in aperiodically poled lithium niobate: a systematic comparison of experiment and theory," J. Opt. Soc. Am. B 18, 1212-1217 (2001).
[CrossRef]

G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter, "Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings," J. Opt. Soc. Am. B 18, 534-539 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

X. Chen, F. Wu, X. Zeng, Y. Chen, Y. Xia, and Y. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(Color online) Schematic of pulse compression by DFG in aperiodically poled lithium niobate.

Fig. 2
Fig. 2

(Color online) (a)–(c) Spectral amplitude (solid curve) and spectral phase (dotted curve) of the output idler pulse. The block lengths of the grating are 4, 5, and 8 μ m .

Fig. 3
Fig. 3

(a) Input of the linearly chirped pulse intensity; (b)–(d) intensity of the DFG and the transform-limited pulse. The block lengths of the grating are 4, 5, and 8 μ m . The pulse widths are 35.4, 36.0, and 36.3   fs .

Fig. 4
Fig. 4

Simulation result for the grating with overpoled domain errors of Δ l / l = 10 % (dash) and Δ l / l = 20 % (dot); the block length of the grating is 5 μ m .

Equations (16)

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

d ( z ) = m = + d m ( z ) = m = + | d m ( z ) | exp [ i K 0 m z + i φ m ( z ) ] .
E ^ m ( z , ω ) = A ^ m ( z , Ω m ) exp [ i k ( ω m + Ω m ) z ] ,
z A ^ i ( z , Ω i ) = i μ 0 ω i 2 2 k i P ^ N L ( z , Ω i ) exp [ i k ( ω i + Ω i ) ] z ,
z A ^ s ( z , Ω s ) = 0 ,
z A ^ p ( z , Ω p ) = 0.
P ^ N L ( z , Ω ) = 2 ε 0 d ( z ) + A ^ s * ( z , Ω + Ω ) A ^ p ( z , Ω ) × exp { i [ k ( ω s Ω + Ω ) k ( ω p + Ω ) ] z } d Ω ,
A ^ s ( z , Ω ) = A ^ s ( z = 0 , Ω ) = A ^ s ( Ω ) ,
A ^ p ( z , Ω ) = A ^ p ( z = 0 , Ω ) = A ^ p ( Ω ) ,
A ^ i ( L , Ω ) = i γ 0 L d ( z ) d z + d Ω A ^ s * ( Ω Ω ) A ^ p ( Ω ) × exp [ i Δ k ( Ω , Ω ) z ] ,
Δ k ( Ω , Ω ) = k ( ω p + Ω ) k ( ω i + Ω ) k ( ω s + Ω Ω ) .
A ^ p ( Ω ) = E p δ ( Ω = 0 ) ,
A ^ i ( L , Ω ) = i γ A ^ s * ( Ω ) E p + d ( z ) exp [ i Δ k ( Ω ) z ] d z ,
Δ k ( Ω ) = k ( ω p ) k ( ω i + Ω ) k ( ω s Ω ) .
B s ( 0 , t ) = E s τ 0 τ 0 2 + i C 1   exp [ t 2 2 ( τ 0 2 + i C 1 ) ] .
A ^ s ( Ω ) = 1 2 π E s τ 0   exp [ 1 / 2 ( τ 0 2 + i C 1 ) Ω 2 ] .
σ 2 = 1 n [ ( ϕ 1 ϕ ¯ ) 2 + ( ϕ 2 ϕ ¯ ) 2 + + ( ϕ n ϕ ¯ ) 2 ] .

Metrics