Abstract

The theory of periodic walk-off compensation in monolithic structures is tested with type II second-harmonic generation experiments in the YZ plane of KTiOPO4 by use of 2N optically contacted, walk-off-compensating (OCWOC) structures with numbers of plates 2N=10 and 2N=4. The results confirm the theoretical prediction that such structures behave as harmonic birefringence filters whose N-dependent transfer functions select ranges of wavelengths for maximum conversion at normal incidence and extinguish others within the tuning bandwidth curve of nominal birefringence phase matching. The residual plate orientation mismatches that alter the periodicity of the phase-mismatch gratings were found to be responsible both for the reduced second-harmonic enhancement compared with that of a reference bulk crystal of the same total length and for broadening of the tuning bandwidth. The shapes of the tuning curves depend critically on the pump wavelength, displaying a variety of modulated patterns that were previously attributed to plate orientation mismatches. The tuning filter response was found to change with periodicity defects. An enhancement factor of 15 (scalable to 22) compared with a reference bulk crystal was measured with a 10-OCWOC structure of length LC=10 mm.

© 2003 Optical Society of America

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  1. J.-J. Zondy, Ch. Bonnin, and D. Lupinski, “Second-harmonic generation with monolithic walk-off-compensating periodic structures. I. Theory,” J. Opt. Soc. Am. B 20, 1675–1694 (2003).
    [CrossRef]
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    [CrossRef]
  3. A. V. Smith, D. J. Armstrong and W. J. Alford, “Increased acceptance bandwidths in optical frequency conversion by use of multiple walk-off-compensating nonlinear crystals,” J. Opt. Soc. Am. B 15, 122–141 (1998).
    [CrossRef]
  4. J.-J. Zondy, “Comparative theory of walkoff-limited type-IIversus type-I second-harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991). Erratum: inEq. (3.1a) of this reference exp(−x2) should read as exp(−x2/2).
    [CrossRef]
  5. J.-J. Zondy, D. Touahri, and O. Acef, “Absolute value of the d36 nonlinear coefficient of AgGaS2: prospect for a low-threshold doubly resonant oscillator-based 3:1 frequency divider,” J. Opt. Soc. Am. B 14, 2481–2497 (1997).
    [CrossRef]
  6. K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
    [CrossRef]
  7. R. L. Sutherland, Handbook of Nonlinear Optics, Vol. 52 of Marcel Dekker Optical Engineering Series (Marcel Dekker, New York, 1996), Chap. 2, p. 67.
  8. J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
    [CrossRef]
  9. J.-J. Zondy and Cristal-Laser SA, “Structure monolithique obtenue par contact optique de cristaux non lineaires en compensation de walk-off,” French patent (brevet d’invention 96 01 197, April 2, 1999).
  10. Custom KTiOPO4 (KTP)/RbTiOAsO4 (RTA) OCWOC and diffusion-bonded WOC structures are commercially available at http://www.cristal-laser.fr.
  11. J.-J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walkoff-compensated type-II second-harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11, 2368–2379 (1994).
    [CrossRef]
  12. D. J. Armstrong, W. J. Alford, T. D. Raymond, and A. V. Smith, “Parametric amplification and oscillation with walkoff-compensating crystals,” J. Opt. Soc. Am. B 14, 460–474 (1997).
    [CrossRef]
  13. Y. Hadjar, F. Ducos, and O. Acef, “Stable 120-mW green output tunable over 2 THz by a second-harmonic generation process in a KTP crystal at room temperature,” Opt. Lett. 25, 1367–1369 (2000).
    [CrossRef]
  14. R. F. Wu, P. B. Phua, K. S. Lai, Y. L. Lim, E. Lau, A. Chang, C. Bonnin, and D. Lupinski, “Compact 21-W 2-μm intracavity optical parametric oscillator,” Opt. Lett. 25, 1460–1462 (2000).
    [CrossRef]
  15. B. Boulanger, J. P. Fève, G. Marnier, C. Bonnin, P. Villeval, and J. J. Zondy, “Absolute measurement of quadratic nonlinearities from phase-matched second-harmonic generation in a single KTP crystal cut as a sphere,” J. Opt. Soc. Am. B 14, 1380–1386 (1997).
    [CrossRef]

2003 (1)

2000 (2)

1998 (2)

1997 (3)

1996 (1)

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

1994 (1)

1991 (2)

K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
[CrossRef]

J.-J. Zondy, “Comparative theory of walkoff-limited type-IIversus type-I second-harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991). Erratum: inEq. (3.1a) of this reference exp(−x2) should read as exp(−x2/2).
[CrossRef]

Abed, M.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

J.-J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walkoff-compensated type-II second-harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11, 2368–2379 (1994).
[CrossRef]

Acef, O.

Albrecht, H.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

Alford, W. J.

Armstrong, D. J.

Bonnin, C.

Bonnin, Ch.

Boulanger, B.

Brown, M.

Chang, A.

Ducos, F.

Fève, J. P.

Hadjar, Y.

Kato, K.

K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
[CrossRef]

Khodja, S.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

J.-J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walkoff-compensated type-II second-harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11, 2368–2379 (1994).
[CrossRef]

Lai, K. S.

Lau, E.

Lim, Y. L.

Lupinski, D.

J.-J. Zondy, Ch. Bonnin, and D. Lupinski, “Second-harmonic generation with monolithic walk-off-compensating periodic structures. I. Theory,” J. Opt. Soc. Am. B 20, 1675–1694 (2003).
[CrossRef]

R. F. Wu, P. B. Phua, K. S. Lai, Y. L. Lim, E. Lau, A. Chang, C. Bonnin, and D. Lupinski, “Compact 21-W 2-μm intracavity optical parametric oscillator,” Opt. Lett. 25, 1460–1462 (2000).
[CrossRef]

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

Marnier, G.

Phua, P. B.

Rainaud, B.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

Raymond, T. D.

Smith, A. V.

Touahri, D.

Villeval, P.

Wu, R. F.

Zondy, J. J.

Zondy, J.-J.

J.-J. Zondy, Ch. Bonnin, and D. Lupinski, “Second-harmonic generation with monolithic walk-off-compensating periodic structures. I. Theory,” J. Opt. Soc. Am. B 20, 1675–1694 (2003).
[CrossRef]

J.-J. Zondy, D. Touahri, and O. Acef, “Absolute value of the d36 nonlinear coefficient of AgGaS2: prospect for a low-threshold doubly resonant oscillator-based 3:1 frequency divider,” J. Opt. Soc. Am. B 14, 2481–2497 (1997).
[CrossRef]

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

J.-J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walkoff-compensated type-II second-harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11, 2368–2379 (1994).
[CrossRef]

J.-J. Zondy, “Comparative theory of walkoff-limited type-IIversus type-I second-harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991). Erratum: inEq. (3.1a) of this reference exp(−x2) should read as exp(−x2/2).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
[CrossRef]

J. Opt. Soc. Am. B (6)

Opt. Commun. (1)

J.-J. Zondy, “Comparative theory of walkoff-limited type-IIversus type-I second-harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991). Erratum: inEq. (3.1a) of this reference exp(−x2) should read as exp(−x2/2).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (1)

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

Other (3)

J.-J. Zondy and Cristal-Laser SA, “Structure monolithique obtenue par contact optique de cristaux non lineaires en compensation de walk-off,” French patent (brevet d’invention 96 01 197, April 2, 1999).

Custom KTiOPO4 (KTP)/RbTiOAsO4 (RTA) OCWOC and diffusion-bonded WOC structures are commercially available at http://www.cristal-laser.fr.

R. L. Sutherland, Handbook of Nonlinear Optics, Vol. 52 of Marcel Dekker Optical Engineering Series (Marcel Dekker, New York, 1996), Chap. 2, p. 67.

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Figures (21)

Fig. 1
Fig. 1

Plane-wave theoretical (a) angular and (b) spectral tuning curves for the SHG of a 1064.5-nm laser in the YZ plane of KTP for an ideal 10-OCWOC structure, computed from Eqs. (1)–(4), (6), and (7). The indices of refraction used are nω,o=1.7399, nω,e=1.8181, and n2ω,o=1.7790, with LC=10 mm. Insets in (a) and (b) show periodic filter transfer function FN(Φ). The dashed curves correspond to the sinc2(Φ/2N) function for one platelet; dotted curves about the main lobe correspond to the sinc2(Φ) function for a bulk crystal with LC=10 mm.

Fig. 2
Fig. 2

Effect of residual plate orientation mismatches in a 10-OCWOC structure computed by the split-step beam propagation method (LC=10 mm, w0=60 μm, d=1.35 pm/V, Pω=100 mW). P, maximum theoretical SH power. Mismatches δθj, (j=1,, 10) are expressed in degrees. (a) Ideal structure (δθj=0). (b) Periodic sequence with δθ2n+1=0 and δθ2n=-0.04. (c) Periodicity defects at the second unit cell: δθj=[0, -0.04; 0, 0; 0, -0.04; 0, -0.04; 0, -0.04]. (d) Periodicity defects at the last unit cell: δθj=[0, -0.04; 0, -0.04; 0,-0.04;0, -0.04;0, 0]. (e) Periodicity defects at the third unit cell: δθj=[0, -0.04; 0, -0.04; 0, 0; 0, -0.04; 0, -0.04].

Fig. 3
Fig. 3

(a) Fabrication of 2N OCWOC structures, showing the geometrical walk-off-compensation effect on an e-ray path (N=3 unit cells). (b) Left, 10-OCWOC structure; and right, witness bulk crystal. The (X) principal axis of KTP points in the vertical direction.

Fig. 4
Fig. 4

Experimental setup for SH detection: HWP, half-wave plate; GF, colored glass filter; Osc., analog oscilloscope; OP, operational amplifier. The YZ plane of KTP lies in the plane of the figure.

Fig. 5
Fig. 5

Experimental (normalized) angular tuning curves of the bulk witness sample (LC=10 mm; symbols) and their fit (solid curves) to focusing parameter L=LC/zR with the focusing function h(σ, L) [Eq. (2)] as a function of incidence angle (i=0 corresponds to the normal incidence).

Fig. 6
Fig. 6

Spectral tuning curves of the 10-OCWOC structures compared with the bulk (N=0) tuning curves at w0=250 μm and w0=50 μm. The incidence angle is i=0. In (a) the vertical scale is absolute power, whereas in (b) a normalized unit is used because of the large SH level difference. The extinction wavelengths occur in the ranges (a) λnull1064.351064.4 nm and (b) λnull10664.41064.5 nm.

Fig. 7
Fig. 7

Angular tuning in the azimuthal ϕ direction of the bulk reference sample and of the 10-OCWOC structure at fixed θ=68.7° and at one extinction wavelength of Fig. 6(b), demonstrating the change in the filter function phase parameter caused by the ϕ dependence of the indices of refraction. Inset, angular tuning in the YZ plane at fixed ϕ=90°, showing a maximum at nonnormal incidence.

Fig. 8
Fig. 8

Spectral tuning curves of the 4-OCWOC structures at w0=50 μm and w0=20 μm compared with the theoretical bulk (N=0) tuning curve computed with h(σ, L) (w0=20 μm). The extinction wavelength occurs at λnull1064.9 nm.

Fig. 9
Fig. 9

Conversion efficiencies of the 10-mm bulk sample (P2ω=15.6 nW at w0=50 μm), the 10-OCWOC structure (P2ω=198 nW at w0=50 μm), and the 4-OCWOC structure (P2ω=24.5 nW at w0=20 μm). The upper solid curve is proportional to h5(B=5.2, L); the lower solid curve to h2(B=3.28, L); the dashed curve, to h(B=5.2, L).

Fig. 10
Fig. 10

Plane-wave angular tuning curves of the 10-OCWOC structure: (a) at optimal normal-incidence wavelength and (b), (c) at slightly lower wavelengths. The bulk sample is 10 mm long, and the sinc2(Φ/2N) tuning curve shown is that of a single plate.

Fig. 11
Fig. 11

Angular tuning curves of the 10-OCWOC structure for w0=250 μm: (a) at the optimal value of λ0 [in boldface; near the peak of the spectral tuning curve of Fig. 6(a)] and (b) at a wavelength located near the extinction wavelength of Fig. 6(a).

Fig. 12
Fig. 12

Angular tuning curves of the 10-OCWOC structure for w0=120 μm: (a) at the optimal value of [in boldface; near the peak of the spectral tuning curve of Fig. 6(a)] and (b)–(d) other values of λ.

Fig. 13
Fig. 13

Angular tuning curves of the 10-OCWOC structure at the focusing corresponding to the maximum observed SH power, w0=50 μm: (a) at λ0 located near the top of the main lobe of the spectral tuning curve of Fig. 6(b); (b) at λ located at the right-hand end of this spectral tuning curve; (c) at λ located at the left-hand end of the spectral tuning curve.

Fig. 14
Fig. 14

Angular tuning curves of the 10-OCWOC structure at the strongest focusing, w0=20 μm: (a), (c) at λ0 located near the top of the main lobe of the spectral tuning curve of Fig. 6(b); (b) at λ located at the right-hand end of this spectral tuning curve; (d) at λ located at the left-hand end of the spectral tuning curve.

Fig. 15
Fig. 15

(b) New 10-APWOC structure obtained from (a) the 10-OCWOC structure by a π rotation of the subblock formed by the five last plates about the propagation axis. For plates j=5 and j=6, walk-off angles β are identical, as are the wave-vector mismatches σ. In addition, the nonlinear coefficient of the inverted subblock changes from d to -d following the inappropriate relative orientation.

Fig. 16
Fig. 16

Angular tuning curve of the 10-APWOC structure for (a) wavelength λ (within the optimal wavelength range λ1065 nm of the 10-OCWOC structure) and (b) wavelength λ detuned at as shown.

Fig. 17
Fig. 17

Comparison of the spectral acceptance curves of the 10-APWOC, 10-OCWOC, and bulk reference samples at w0=120 μm, showing the filter transfer functions that are due to the periodicity defects sketched in Fig. 15. The maximum SH power is P2ω=12.6 nW for the 10-APWOC sample, P2ω=19.8 nW for the 10-OCWOC sample, and P2ω=6.8 nW for the bulk sample.

Fig. 18
Fig. 18

Comparison of the spectral tuning curves of the 10-APWOC and the 10-OCWOC structures at optimal wavelength λ0=1064.513 nm for w0=250 μm and w0=120 μm.

Fig. 19
Fig. 19

Ideal 4-OCWOC plane-wave theoretical tuning curve, with LC=4 mm (solid curve). The main lobe of the sinc2(Φ/2) envelope function comprises a three-peak fine structure.

Fig. 20
Fig. 20

Angular tuning curves of the 4-OCWOC structure for w0=250 μm and w0=120 μm at three FF wavelengths. The underlined wavelengths correspond to the optimal wavelengths that yield maximum SH power at normal incidence. The sinc2(Φ/2) envelope functions are also shown.

Fig. 21
Fig. 21

Angular tuning curves of the 4-OCWOC structure at strong focusing: w0=50 μm and w0=20 μm at two FF wavelengths. The strong-focusing h(σ, l) envelope function for a single plate is also shown.

Equations (8)

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ΓN=KLCkωhN(σ, L)=K(LC/w0)2GN(σ, L),
h(σ, L)=12L-fL-fdτdτexp{-1/4β2(τ-τ)2-1/2β2[(τ+f )2+(τ+f )2]}(1+iτ)(1-iτ)exp[-iσ(τ-τ)],
ΓNPW=KLCw02sinc2Φ2Ncos2(Φ)FN(Φ),
FN(Φ)=1N2sin[(N+1)(Φ/2N)]+sin[(N-1)(Φ/2N)]sin(Φ/N)2Nodd4N2cos(Φ/2N)sin(Φ/2)sin(Φ/N)2Neven,
Φ=πLCn2ω(λω, θ, ϕ)λ2ω-2 nω(λω, θ, ϕ)λω;
γθ=Δkθθ=68.7°=+0.33382[μm-1rad-1].
γλ=Δkλλ=1064nm=+7.6006×10-2[μm-2].
Γ2PW=K(LC/w0)2cos2 Φ sinc2(Φ/2);

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