Abstract

We demonstrate the simultaneous generation and internal interference of two second-order parametric processes in a single nonlinear quadratic crystal. The two-frequency doubling processes are Type 0 (two extraordinary fundamental waves generate an extraordinary secondharmonic wave) and Type I (two ordinary fundamental waves generate an extraordinary second-harmonic wave) parametric interactions. The phasematching conditions for both processes are satisfied in a single periodically poled grating in LiNbO3 using quasi-phase-matching (QPM) vectors with different orders. We observe an interference of two processes, and compare the results with the theoretical analysis. We suggest several applications of this effect such as polarization-independent frequency doubling and a method for stabilizing the level of the generated second-harmonic signal.

© 2006 Optical Society of America

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  1. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, "Self-focusing and self-defocusing by cascaded 2nd-order effects in KTP," Opt. Lett. 17, 28 - 30 (1992).
    [CrossRef] [PubMed]
  2. S. M. Saltiel, A. A. Sukhorukov, and Yu. S. Kivshar, "Multistep parametric processes in nonlinear optics," in Progress in Optics, E. Wolf, ed., 47, 1-73 (2005). (Elsevier, Amsterdam, 2005), pp. 1-73.
    [CrossRef]
  3. V. Pasiskevicius, S. J. Holmgren, S. Wang, and F. Laurell, "Simultaneous second-harmonic generation with two orthogonal polarization states in periodically poled KTP," Opt. Lett. 27, 1628-1630 (2002).
    [CrossRef]
  4. C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
    [CrossRef]
  5. G. I. Petrov, O. Albert, J. Etchepare, and S. M. Saltiel, "Cross-polarized wave generation by effective cubic nonlinear optical interaction," Opt. Lett. 26,355 - 357 (2001).
    [CrossRef]
  6. S. Saltiel, and Y. Deyanova, "Polarization switching as a result of cascading of two simultaneously phase-matched quadratic processes," Opt. Lett. 24, 1296 - 1298 (1999).
    [CrossRef]
  7. A. DeRossi, C. Conti, and G. Assanto, "Mode interplay via quadratic cascading in a lithium niobate waveguide for all-optical processing," Opt. Quantum Electron. 29, 53 - 63 (1997).
    [CrossRef]
  8. G. Assanto, I. Torelli, and S. Trillo, "All-optical processing by means of vectorial interactions in 2nd-order cascading -novel approaches," Opt. Lett. 19, 1720-1722. (1994).
    [CrossRef] [PubMed]
  9. Yu. S Kivshar, A. A. Sukhorukov, and S. M. Saltiel, "Two-color multistep cascading and parametric soliton-induced waveguides," Phys. Rev. E 60, R5056 - R5059. (1999).
    [CrossRef]
  10. S. G Grechin, V. G. Dmitriev, and Yu. V. Yur’ev, "Second-harmonic generation under conditions of simultaneous phase-matched and quasi-phase-matched interactions in nonlinear crystals with a regular domain structure," Kvant. Elektron. 26, 155 - 157 (1999) in Russian [English translation: Quantum Electron. 29, 155 - 157 (1999)].
    [CrossRef]
  11. Y. Chen, R. Wu, X. Zeng, Y. Xia, and X. Chen, "Type I quasi-phase-matched blue second-harmonic generation with different polarizations in periodically poled LiNbO3," Opt. Laser Technol. 38, 19 - 22 (2006).
    [CrossRef]
  12. G. G. Gurzadian, V. G. Dmitriev, and D. N. Nikogosian, "Handbook of Nonlinear Optical Crystals," 3rd ed., Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).
  13. B. F. Johnston and M. J. Withford, "Dynamics of domain inversion in LiNbO3 poled using topographic electrode geometries," Appl. Phys. Lett. 86, 262901 (2005).
    [CrossRef]
  14. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, "Absolute scale of second-order nonlinear-optical coefficients," J. Opt. Soc. Am. B 14, 2268-2294 (1997).
    [CrossRef]
  15. M. Reich, F. Korte, C. Fallnich, H. Welling, and A. Tunnermann, "Electrode geometries for periodic poling of ferroelectric materials," Opt. Lett. 23, 1817-1819 (1998).
    [CrossRef]
  16. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631 - 2654 (1992).
    [CrossRef]

2006 (1)

Y. Chen, R. Wu, X. Zeng, Y. Xia, and X. Chen, "Type I quasi-phase-matched blue second-harmonic generation with different polarizations in periodically poled LiNbO3," Opt. Laser Technol. 38, 19 - 22 (2006).
[CrossRef]

2005 (1)

B. F. Johnston and M. J. Withford, "Dynamics of domain inversion in LiNbO3 poled using topographic electrode geometries," Appl. Phys. Lett. 86, 262901 (2005).
[CrossRef]

2002 (1)

2001 (1)

1999 (2)

S. Saltiel, and Y. Deyanova, "Polarization switching as a result of cascading of two simultaneously phase-matched quadratic processes," Opt. Lett. 24, 1296 - 1298 (1999).
[CrossRef]

Yu. S Kivshar, A. A. Sukhorukov, and S. M. Saltiel, "Two-color multistep cascading and parametric soliton-induced waveguides," Phys. Rev. E 60, R5056 - R5059. (1999).
[CrossRef]

1998 (1)

1997 (2)

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, "Absolute scale of second-order nonlinear-optical coefficients," J. Opt. Soc. Am. B 14, 2268-2294 (1997).
[CrossRef]

A. DeRossi, C. Conti, and G. Assanto, "Mode interplay via quadratic cascading in a lithium niobate waveguide for all-optical processing," Opt. Quantum Electron. 29, 53 - 63 (1997).
[CrossRef]

1995 (1)

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

1994 (1)

1992 (2)

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, "Self-focusing and self-defocusing by cascaded 2nd-order effects in KTP," Opt. Lett. 17, 28 - 30 (1992).
[CrossRef] [PubMed]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631 - 2654 (1992).
[CrossRef]

Albert, O.

Assanto, G.

A. DeRossi, C. Conti, and G. Assanto, "Mode interplay via quadratic cascading in a lithium niobate waveguide for all-optical processing," Opt. Quantum Electron. 29, 53 - 63 (1997).
[CrossRef]

G. Assanto, I. Torelli, and S. Trillo, "All-optical processing by means of vectorial interactions in 2nd-order cascading -novel approaches," Opt. Lett. 19, 1720-1722. (1994).
[CrossRef] [PubMed]

Baldi, P.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631 - 2654 (1992).
[CrossRef]

Chen, X.

Y. Chen, R. Wu, X. Zeng, Y. Xia, and X. Chen, "Type I quasi-phase-matched blue second-harmonic generation with different polarizations in periodically poled LiNbO3," Opt. Laser Technol. 38, 19 - 22 (2006).
[CrossRef]

Chen, Y.

Y. Chen, R. Wu, X. Zeng, Y. Xia, and X. Chen, "Type I quasi-phase-matched blue second-harmonic generation with different polarizations in periodically poled LiNbO3," Opt. Laser Technol. 38, 19 - 22 (2006).
[CrossRef]

Conti, C.

A. DeRossi, C. Conti, and G. Assanto, "Mode interplay via quadratic cascading in a lithium niobate waveguide for all-optical processing," Opt. Quantum Electron. 29, 53 - 63 (1997).
[CrossRef]

Delacourt, D.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

Demicheli, M. P.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

DeRossi, A.

A. DeRossi, C. Conti, and G. Assanto, "Mode interplay via quadratic cascading in a lithium niobate waveguide for all-optical processing," Opt. Quantum Electron. 29, 53 - 63 (1997).
[CrossRef]

DeSalvo, R.

Deyanova, Y.

Etchepare, J.

Fallnich, C.

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631 - 2654 (1992).
[CrossRef]

Hagan, D. J.

Holmgren, S. J.

Ito, R.

Johnston, B. F.

B. F. Johnston and M. J. Withford, "Dynamics of domain inversion in LiNbO3 poled using topographic electrode geometries," Appl. Phys. Lett. 86, 262901 (2005).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631 - 2654 (1992).
[CrossRef]

Kitamoto, A.

Kivshar, Yu. S

Yu. S Kivshar, A. A. Sukhorukov, and S. M. Saltiel, "Two-color multistep cascading and parametric soliton-induced waveguides," Phys. Rev. E 60, R5056 - R5059. (1999).
[CrossRef]

Kondo, T.

Korte, F.

Laurell, F.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631 - 2654 (1992).
[CrossRef]

Nouh, S.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

Ostrowsky, D. B.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

Papuchon, M.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

Pasiskevicius, V.

Petrov, G. I.

Reich, M.

Saltiel, S.

Saltiel, S. M.

G. I. Petrov, O. Albert, J. Etchepare, and S. M. Saltiel, "Cross-polarized wave generation by effective cubic nonlinear optical interaction," Opt. Lett. 26,355 - 357 (2001).
[CrossRef]

Yu. S Kivshar, A. A. Sukhorukov, and S. M. Saltiel, "Two-color multistep cascading and parametric soliton-induced waveguides," Phys. Rev. E 60, R5056 - R5059. (1999).
[CrossRef]

Sheik-Bahae, M.

Shirane, M.

Shoji, I.

Stegeman, G.

Stegeman, G. I.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

Sukhorukov, A. A.

Yu. S Kivshar, A. A. Sukhorukov, and S. M. Saltiel, "Two-color multistep cascading and parametric soliton-induced waveguides," Phys. Rev. E 60, R5056 - R5059. (1999).
[CrossRef]

Torelli, I.

Trevino-Palacios, C. G.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

Trillo, S.

Tunnermann, A.

Van Stryland, E. W.

Vanherzeele, H.

Wang, S.

Welling, H.

Withford, M. J.

B. F. Johnston and M. J. Withford, "Dynamics of domain inversion in LiNbO3 poled using topographic electrode geometries," Appl. Phys. Lett. 86, 262901 (2005).
[CrossRef]

Wu, R.

Y. Chen, R. Wu, X. Zeng, Y. Xia, and X. Chen, "Type I quasi-phase-matched blue second-harmonic generation with different polarizations in periodically poled LiNbO3," Opt. Laser Technol. 38, 19 - 22 (2006).
[CrossRef]

Xia, Y.

Y. Chen, R. Wu, X. Zeng, Y. Xia, and X. Chen, "Type I quasi-phase-matched blue second-harmonic generation with different polarizations in periodically poled LiNbO3," Opt. Laser Technol. 38, 19 - 22 (2006).
[CrossRef]

Zeng, X.

Y. Chen, R. Wu, X. Zeng, Y. Xia, and X. Chen, "Type I quasi-phase-matched blue second-harmonic generation with different polarizations in periodically poled LiNbO3," Opt. Laser Technol. 38, 19 - 22 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

C. G. Trevino-Palacios, G. I. Stegeman, M. P. Demicheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Intensity-dependent mode competition in 2nd-harmonic generation in multimode wave-guides," Appl. Phys. Lett. 67, 170 - 172 (1995).
[CrossRef]

B. F. Johnston and M. J. Withford, "Dynamics of domain inversion in LiNbO3 poled using topographic electrode geometries," Appl. Phys. Lett. 86, 262901 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631 - 2654 (1992).
[CrossRef]

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

Opt. Laser Technol. (1)

Y. Chen, R. Wu, X. Zeng, Y. Xia, and X. Chen, "Type I quasi-phase-matched blue second-harmonic generation with different polarizations in periodically poled LiNbO3," Opt. Laser Technol. 38, 19 - 22 (2006).
[CrossRef]

Opt. Lett. (6)

Opt. Quantum Electron. (1)

A. DeRossi, C. Conti, and G. Assanto, "Mode interplay via quadratic cascading in a lithium niobate waveguide for all-optical processing," Opt. Quantum Electron. 29, 53 - 63 (1997).
[CrossRef]

Phys. Rev. E (1)

Yu. S Kivshar, A. A. Sukhorukov, and S. M. Saltiel, "Two-color multistep cascading and parametric soliton-induced waveguides," Phys. Rev. E 60, R5056 - R5059. (1999).
[CrossRef]

Other (3)

S. G Grechin, V. G. Dmitriev, and Yu. V. Yur’ev, "Second-harmonic generation under conditions of simultaneous phase-matched and quasi-phase-matched interactions in nonlinear crystals with a regular domain structure," Kvant. Elektron. 26, 155 - 157 (1999) in Russian [English translation: Quantum Electron. 29, 155 - 157 (1999)].
[CrossRef]

S. M. Saltiel, A. A. Sukhorukov, and Yu. S. Kivshar, "Multistep parametric processes in nonlinear optics," in Progress in Optics, E. Wolf, ed., 47, 1-73 (2005). (Elsevier, Amsterdam, 2005), pp. 1-73.
[CrossRef]

G. G. Gurzadian, V. G. Dmitriev, and D. N. Nikogosian, "Handbook of Nonlinear Optical Crystals," 3rd ed., Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).

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Figures (7)

Fig. 1.
Fig. 1.

Simulations of the generated the second-harmonic output for Y1Y1-Z2: Z1Z1-Z2 double phase matching in LiNbO3 for the two different ratios of effective nonlinearities d33/7d31 =0.5 (top) and d33/7d31 =0.9 (bottom). The second-harmonic output is plotted against: (a) HWP angle which changes a ratio between the amplitudes of two fundamental components; (b) temperature detuning near the exact phase-matching temperature for the frequency-doubling processes (179.53°C). The cases when two fundamental waves are in phase (g=+1) or shifted out-of phase (g=- 1) are shown by blue-dash or red-solid lines, respectively.

Fig. 2.
Fig. 2.

Normalized intensity of the two fundamental waves, A and B, and the SH signal intensity for the AA-S:BB-S double phase matched frequency doubling process as a function of the normalized crystal length L/Lnl (with Lnl =1/(σ 1 A 0)). The ratio of the effective second order nonlinearities is d eff,A /d eff,B =3 and there is initially equal intensity in the fundamentals A and B. 2a) A and B are launched π/2 out of phase 2b) A and B are launched in phase.

Fig. 3.
Fig. 3.

Experimental set up for investigation of Y1Y1-Z2 (1st order) : Z1Z1-Z2 (7th order) double phase matched frequency doubling in periodically poled LiNbO3.

Fig. 4.
Fig. 4.

Experimental (dots) and theoretical (lines) temperature phase-matching curves for SHG Type I (blue) and SHG Type 0 (red) in the 45.75 µm and 45.79 µm period gratings. 4(a) 45.79 µm grating with ~ 6 nm deviation from the ideal calculated grating for DPM of the two processes. 4(b) 45.75 µm grating with ~50 nm deviation from the ideal calculated grating for DPM of the two processes.

Fig. 5.
Fig. 5.

Theoretical (lines) and experimental (dots) relationship between the SH power and the HWP angle which is controlling the input polarization, such that both the Y1Y1-Z2 and Z1Z1-Z2 processes are present. Blue traces indicate linear polarizations where only the HWP is in use. Red traces indicate elliptical/circular polarizations where a QWP is used in tandem with the HWP. 5(a) for QPM grating with 6 nm deviation from the ideal calculated grating for DPM of the two processes. 5(b) for QPM grating with 50 nm deviation from the ideal calculated grating for DPM of the two processes.

Fig. 6.
Fig. 6.

(a). Experimental and (b) theoretical temperature dependences for simultaneous processes Y1Y1-Z2(1st order) : Z1Z1-Z2(7th order) in the 45.79 µm grating. The HWP is set so that the fundamental components (Y and Z) are equal. Blue-dash curves show SHG from fundamental waves which are in phase (HWP only), red-solid curves show SHG from fundamental waves which are π/2 out of phase (QWP inline).

Fig. 7.
Fig. 7.

Proposal for a nonlinear optical device, a stabilized SH generator, based on Y1Y1Z2: Z1Z1Z2 double phase matched frequency doubling in single grating periodically poled LiNbO3 with phase dependent power control (see text).

Equations (8)

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

d A d x = i σ 1 S A * exp ( i Δ k 1 x )
d S d x = i σ 2 A 2 exp ( i Δ k 1 x ) i σ 4 B 2 exp ( i Δ k 0 x )
d B d x = i σ 3 S B * exp ( i Δ k 0 x )
S 2 = A 2 sinc ( Δ k 1 L 2 ) exp ( i ϕ L 2 ) + g m 1 d 33 m 2 d 31 B 2 sinc ( Δ k 0 L 2 ) 2 ( 4 d 31 λ n 2 L ) 2
B ( L ) = Re [ B ( 0 ) ] exp ( 1 2 σ 3 σ 2 A 2 L 2 ) + i lm [ B ( 0 ) ] exp ( 1 2 σ 3 σ 2 A 2 L 2 )
B ( L ) = B o + σ 3 σ 2 B o * A A L 2
sin ( m 2 D π ) sin ( m 1 D π ) = d 31 m 2 d 33 m 1
S 2 A 2 exp [ i φ ( V ) ] + g d 33 m 2 d 31 B 2 2

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