Abstract

An achromatic phase-matching scheme is reported for an optical parametric oscillator in tilted quasi-phase-matched gratings. The spectral angular dispersion is introduced in interaction waves such that each wave component satisfies the two-dimensional (noncollinear) quasi-phase matching. This is equivalent to simultaneous quasi-phase matching and group-velocity matching for ultrashort pulses. The phase-matching bandwidth for 10 mm periodically poled KTP increases by a factor of 12 at λs=1.7 μm compared with one-dimensional quasi-phase matching. The effective interaction length will increase as a result of the matching.

© 2006 Optical Society of America

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References

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  1. W. Q. Zhang, "Group-velocity matching in mixing of three noncollinear phase matched waves for biaxial crystal," Opt. Commun. 221, 191-197 (2003).
    [CrossRef]
  2. W. Q. Zhang, "Femtosecond optical parametric generation of noncollinear phase matching for a biaxial crystal," Appl. Opt. 42, 5596-5601 (2003).
    [CrossRef] [PubMed]
  3. W. Q. Zhang, "Optimum operation of femtosecond parametric oscillation of a noncollinear phase match in KTP," Appl. Opt. 44, 2431-2437 (2005).
    [CrossRef] [PubMed]
  4. J. Hellström and V. Pasiskevicius, "High-power parametric oscillation in large-aperture periodically poled KTiOPO4," Opt. Lett. 25, 174-176 (2000).
    [CrossRef]
  5. M. J. Missey, V. Dominic, and P. E. Power, "Periodically poled lithium niobate nanosecond optical parametric oscillators and generator," Opt. Lett. 24, 1227-1229 (1999).
    [CrossRef]
  6. V. Smilgevicius, A. Stabinis, and A. Piskarskas, "A noncollinear optical parametric oscillator with periodically poled KTP," Opt. Commun. 173, 365-369 (2000).
    [CrossRef]
  7. C. W. Hsu and C. C. Yang, "Broadband infrared generation with noncollinear optical parametric processes on periodically poled LiNbO3," Opt. Lett. 26, 1412-1414 (2001).
    [CrossRef]
  8. B. Zhao, X. Liang, Y. Leng, C. Wang, and Z. Xu, "Investigation of noncollinear QPM optical parametric amplification based on periodically poled KTP," Opt. Commun. 248, 394-397 (2005).
  9. A. M. Schober, M. Charbonneau-Lefort, and M. M. Fejer, "Broadband quasi-phase-matched second-harmonic generation of ultrashort optical pulses with spectral angular dispersion," J. Opt. Soc. Am. B 22, 1699-1713 (2005).
    [CrossRef]
  10. W. Q. Zhang, "Optical parametric generation for biaxial crystal," Opt. Commun. 105, 226-232 (1994).
    [CrossRef]
  11. K. Kato and E. Takaoka, "Sellmeier and thermo-optic dispersion formulas for KTP," Appl. Opt. 41, 5040-5044 (2002).
    [CrossRef] [PubMed]
  12. W. Q. Zhang, "Femtosecond second and third harmonic light generation in biaxial crystal," Optik (Stuttgart) 104, 87-91 (1997).

2005 (3)

2003 (2)

W. Q. Zhang, "Group-velocity matching in mixing of three noncollinear phase matched waves for biaxial crystal," Opt. Commun. 221, 191-197 (2003).
[CrossRef]

W. Q. Zhang, "Femtosecond optical parametric generation of noncollinear phase matching for a biaxial crystal," Appl. Opt. 42, 5596-5601 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

2000 (2)

V. Smilgevicius, A. Stabinis, and A. Piskarskas, "A noncollinear optical parametric oscillator with periodically poled KTP," Opt. Commun. 173, 365-369 (2000).
[CrossRef]

J. Hellström and V. Pasiskevicius, "High-power parametric oscillation in large-aperture periodically poled KTiOPO4," Opt. Lett. 25, 174-176 (2000).
[CrossRef]

1999 (1)

1997 (1)

W. Q. Zhang, "Femtosecond second and third harmonic light generation in biaxial crystal," Optik (Stuttgart) 104, 87-91 (1997).

1994 (1)

W. Q. Zhang, "Optical parametric generation for biaxial crystal," Opt. Commun. 105, 226-232 (1994).
[CrossRef]

Charbonneau-Lefort, M.

Dominic, V.

Fejer, M. M.

Hellström, J.

Hsu, C. W.

Kato, K.

Leng, Y.

B. Zhao, X. Liang, Y. Leng, C. Wang, and Z. Xu, "Investigation of noncollinear QPM optical parametric amplification based on periodically poled KTP," Opt. Commun. 248, 394-397 (2005).

Liang, X.

B. Zhao, X. Liang, Y. Leng, C. Wang, and Z. Xu, "Investigation of noncollinear QPM optical parametric amplification based on periodically poled KTP," Opt. Commun. 248, 394-397 (2005).

Missey, M. J.

Pasiskevicius, V.

Piskarskas, A.

V. Smilgevicius, A. Stabinis, and A. Piskarskas, "A noncollinear optical parametric oscillator with periodically poled KTP," Opt. Commun. 173, 365-369 (2000).
[CrossRef]

Power, P. E.

Schober, A. M.

Smilgevicius, V.

V. Smilgevicius, A. Stabinis, and A. Piskarskas, "A noncollinear optical parametric oscillator with periodically poled KTP," Opt. Commun. 173, 365-369 (2000).
[CrossRef]

Stabinis, A.

V. Smilgevicius, A. Stabinis, and A. Piskarskas, "A noncollinear optical parametric oscillator with periodically poled KTP," Opt. Commun. 173, 365-369 (2000).
[CrossRef]

Takaoka, E.

Wang, C.

B. Zhao, X. Liang, Y. Leng, C. Wang, and Z. Xu, "Investigation of noncollinear QPM optical parametric amplification based on periodically poled KTP," Opt. Commun. 248, 394-397 (2005).

Xu, Z.

B. Zhao, X. Liang, Y. Leng, C. Wang, and Z. Xu, "Investigation of noncollinear QPM optical parametric amplification based on periodically poled KTP," Opt. Commun. 248, 394-397 (2005).

Yang, C. C.

Zhang, W. Q.

W. Q. Zhang, "Optimum operation of femtosecond parametric oscillation of a noncollinear phase match in KTP," Appl. Opt. 44, 2431-2437 (2005).
[CrossRef] [PubMed]

W. Q. Zhang, "Femtosecond optical parametric generation of noncollinear phase matching for a biaxial crystal," Appl. Opt. 42, 5596-5601 (2003).
[CrossRef] [PubMed]

W. Q. Zhang, "Group-velocity matching in mixing of three noncollinear phase matched waves for biaxial crystal," Opt. Commun. 221, 191-197 (2003).
[CrossRef]

W. Q. Zhang, "Femtosecond second and third harmonic light generation in biaxial crystal," Optik (Stuttgart) 104, 87-91 (1997).

W. Q. Zhang, "Optical parametric generation for biaxial crystal," Opt. Commun. 105, 226-232 (1994).
[CrossRef]

Zhao, B.

B. Zhao, X. Liang, Y. Leng, C. Wang, and Z. Xu, "Investigation of noncollinear QPM optical parametric amplification based on periodically poled KTP," Opt. Commun. 248, 394-397 (2005).

Appl. Opt. (3)

J. Opt. Soc. Am. B (1)

Opt. Commun. (4)

W. Q. Zhang, "Optical parametric generation for biaxial crystal," Opt. Commun. 105, 226-232 (1994).
[CrossRef]

V. Smilgevicius, A. Stabinis, and A. Piskarskas, "A noncollinear optical parametric oscillator with periodically poled KTP," Opt. Commun. 173, 365-369 (2000).
[CrossRef]

W. Q. Zhang, "Group-velocity matching in mixing of three noncollinear phase matched waves for biaxial crystal," Opt. Commun. 221, 191-197 (2003).
[CrossRef]

B. Zhao, X. Liang, Y. Leng, C. Wang, and Z. Xu, "Investigation of noncollinear QPM optical parametric amplification based on periodically poled KTP," Opt. Commun. 248, 394-397 (2005).

Opt. Lett. (3)

Optik (1)

W. Q. Zhang, "Femtosecond second and third harmonic light generation in biaxial crystal," Optik (Stuttgart) 104, 87-91 (1997).

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Figures (5)

Fig. 1
Fig. 1

Schematic of a noncollinear OPO in tilted QPM structures: (a) wave-vector diagram for θ s = θ p − β and (b) wave-vector diagram for θ s = θ p + β in the yz plane.

Fig. 2
Fig. 2

Tuning curves: (a) γ angle as a function of signal wavelength λ s ; (b) β angle as a function of signal wavelength λ s . Solid curves, Λ = 15 μm and θ s = θ p − β, ξ = 31.3°. Dashed curves, Λ = 10 μm and θ s = θ p + β, ξ = 49.4°. Dashed–dotted curves, Λ = 10 μm and θ s = θ p − β, ξ = 56.7°.

Fig. 3
Fig. 3

Calculated values of the spectral angular dispersion (a) ε′ = dα∕dλ p and (b) ε = dγ∕dλ p plotted as a function of signal wavelength λ s . The solid, dashed, and dashed–dotted curves are the same as in Fig. 2.

Fig. 4
Fig. 4

Calculated values of (a) (Δλ p )L for 1D QPM and (b) (Δλ p )2 L for noncollinear QPM with the appropriate spectral angular dispersion plotted as a function of signal wavelength λ s , where (Δλ p ) is the phase-matching bandwidth of the pump wave for L = 10 mm. The solid, dashed, and dashed–dotted curves are the same as in Fig. 2.

Fig. 5
Fig. 5

Calculated values of the walk-off angle of Poynting vectors plotted as a function of signal wavelength λ s . The solid, dashed, and dashed–dotted curves are the same as in Fig. 2.

Tables (1)

Tables Icon

Table 1 Sellmeier Coefficients for KTP

Equations (17)

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k x = sin θ cos φ , k y = sin θ sin φ , k z = cos θ ,
n = 2 1 / 2 [ e + A ± ( b 2 2 B b + A 2 ) 1 / 2 ] 1 / 2 ,
n i 2 = A i + B i / ( λ 2 C i ) + D i / ( λ 2 E i ) ( i = x , y , z ) ,
Δ K = K p cos θ p ( K s + K i ) cos ( θ p β ) K cos ξ [ for Fig . 1 ( a ) ] ,
Δ K = K p cos θ p ( K s + K i ) cos ( θ p + β ) K cos ξ [ for Fig . 1 ( b ) ] ,
Δ K ( λ 0 + Δ λ p ) = Δ K ( λ 0 ) + d [ Δ K ( λ ) ] / d λ | λ 0 ( Δ λ p ) + 1 / 2 d 2 [ Δ K ( λ ) ] / d λ 2 | λ 0 ( Δ λ p ) 2 + .
( Δ K ) 2 = K 2 K p     2 + ( K s + K i ) 2 + 2 K ( K s + K i ) cos α = 0.
cos γ = [ K 2 + K p     2 ( K s + K i ) 2 ] / ( 2 K K p ) ,
cos β = [ K p     2 + ( K s + K i ) 2 K 2 ] / [ 2 ( K s + K i ) K p ] .
ε = / d λ p | λ i 0 = { ( K cos γ - K p ) d K p / d λ p | λ p 0 + ( K s + K i ) [ d K s / d λ s ( d λ s / d λ p ) | λ s 0 + d K i / d λ i ( d λ i / d λ p ) | λ i 0 ] } / ( K p K sin γ ) ,
ε = ( / d λ p λ 0 = [ ( K cos α + K s + K i ) [ d K s / d λ s ( d λ s / d λ p ) | λ s 0 + d K i / d λ i ( d λ i / d λ p ) λ i 0 ] K p d K p / d λ p λ p 0 ] / [ K ( K s + K i ) sin α ] ,
G R = sinc 2 { [ ( Δ K / 2 ) 2 Γ 2 ] 1 / 2 L } ,
Γ = 4 π | E p | 2 d eff / ( n s λ s ) / ( n i λ i ) .
( Δ K ) = 2 [ ( x / L ) 2 + Γ 2 ] 1 / 2 .
( Δ λ p ) L = 2 [ ( x ) 2 + Γ 2 L 2 ] 1 / 2 / d [ Δ K ( λ ) ] / d λ | λ 0 .
( Δ λ p ) 2 L = 4 [ ( x ) 2 + Γ 2 L 2 ] 1 / 2 / d 2 [ Δ K ( λ ) ] / d λ 2 | λ 0 .
θ p s = cos 1 ( S p x S s x + S p y S s y + S p z S s z ) ,

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