Abstract

We demonstrate energy exchange between two orthogonally polarized optical waves as a consequence of a two-color multistep parametric interaction. The energy exchange results from cascading of two quasi-phase-matched (QPM) second-harmonic parametric processes, and it is intrinsically instantaneous. The effect is observed when both the type-I (ooe) second-harmonic generation process and higher QPM order type-0 (eee) second-harmonic generation processes are phase-matched simultaneously in a congruent periodically-poled lithium niobate crystal. The two second-harmonic generation processes share a common second-harmonic wave which couple the two cross-polarized fundamental components and facilitate an energy flow between them. We demonstrate a good agreement between the experimental data and the results of numerical simulations.

© 2007 Optical Society of America

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  1. M. H. Chou, K. R. Parameswaran, and M. M. Fejer, "Multiple-channel wavelength conversion by use of engineered quasi-phase-matching," Opt. Lett. 24, 1157-1159 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2007 (1)

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

2006 (1)

2005 (2)

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]

S. M. Saltiel, A. A. Sukhorukov, and YuS Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

2004 (1)

2002 (1)

2001 (2)

1999 (2)

M. H. Chou, K. R. Parameswaran, and M. M. Fejer, "Multiple-channel wavelength conversion by use of engineered quasi-phase-matching," Opt. Lett. 24, 1157-1159 (1999).
[CrossRef]

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

1998 (1)

1997 (2)

P. Vidakovic, D. J. Lovering, J. A. Levenson, J. Webjrn, and P. S. J. Russell, "Large nonlinear phase shift owing to cascaded ?(2) in quasi-phase-matched bulk LiNbO3," Opt. Lett. 22, 277-279 (1997).
[CrossRef]

S. Zhu, Y. Zhu, and N. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, "All optical switching devices based on large nonlinear phase-shifts from second harmonic generation," App. Phys. Lett. 62, 1324-1326 (1993).
[CrossRef]

1992 (1)

1987 (1)

Albert, O.

Assanto, G.

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]

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, "All optical switching devices based on large nonlinear phase-shifts from second harmonic generation," App. Phys. Lett. 62, 1324-1326 (1993).
[CrossRef]

Boland, B. F.

Bosenberg, W. R.

Bratfalean, R. T.

Broderick, N. G. R.

Byer, R. L.

Cheng, B.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Chou, M. H.

Chowdhury, A.

de Sterke, C. M.

Dekker, P.

DeSalvo, R.

Deyanova, Y.

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

Dou, J.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Eckardt, R. C.

Etchepare, J.

Fallnich, C.

Fejer, M. M.

Hagan, D. J.

Johnston, B. F.

B. F. Johnston, P. Dekker, S. M. Saltiel, M. J. Withford, and Yu. S. Kivshar, "Simultaneous phase matching and interference of two second order parametric processes," Opt. Express 14, 11756-11765 (2006).
[CrossRef] [PubMed]

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]

Kivshar, Yu. S.

Korte, F.

Kuech, T. F.

Levenson, J. A.

Lovering, D. J.

Ma, B.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

McCaughan, L.

Ming, N.

S. Zhu, Y. Zhu, and N. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

Monro, T. M.

Myers, L. E.

Norton, A. H.

Parameswaran, K. R.

Petrov, G. I.

Pierce, J. W.

Reich, M.

Richardson, D. J.

Russell, P. S. J.

Saltiel, S.

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

Saltiel, S. M.

Sheik-Bahae, M.

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, "All optical switching devices based on large nonlinear phase-shifts from second harmonic generation," App. Phys. Lett. 62, 1324-1326 (1993).
[CrossRef]

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]

Sheng, Y.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Staus, C.

Stegeman, G.

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, "All optical switching devices based on large nonlinear phase-shifts from second harmonic generation," App. Phys. Lett. 62, 1324-1326 (1993).
[CrossRef]

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]

Sukhorukov, A. A.

S. M. Saltiel, A. A. Sukhorukov, and YuS Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

Torelli, I.

Trillo, S.

Tunnermann, A.

Van Stryland, E.

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, "All optical switching devices based on large nonlinear phase-shifts from second harmonic generation," App. Phys. Lett. 62, 1324-1326 (1993).
[CrossRef]

Van Stryland, E. W.

Vanherzeele, H.

Vidakovic, P.

Webjrn, J.

Welling, H.

Withford, M. J.

B. F. Johnston, P. Dekker, S. M. Saltiel, M. J. Withford, and Yu. S. Kivshar, "Simultaneous phase matching and interference of two second order parametric processes," Opt. Express 14, 11756-11765 (2006).
[CrossRef] [PubMed]

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]

Yeh, P.

Yu, A. A.

S. M. Saltiel, A. A. Sukhorukov, and YuS Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

Zhang, D.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Zhu, S.

S. Zhu, Y. Zhu, and N. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

Zhu, Y.

S. Zhu, Y. Zhu, and N. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

App. Phys. Lett. (1)

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, "All optical switching devices based on large nonlinear phase-shifts from second harmonic generation," App. Phys. Lett. 62, 1324-1326 (1993).
[CrossRef]

Appl. Phys. Lett. (2)

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]

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Express (2)

Opt. Lett (1)

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

Opt. Lett. (7)

Prog. Opt. (1)

S. M. Saltiel, A. A. Sukhorukov, and YuS Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

Science (1)

S. Zhu, Y. Zhu, and N. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

Other (1)

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 (10)

Fig. 1.
Fig. 1.

QPM periods for 1st order type-I and 5th and 7th order type-0 SHG for a 1064 nm fundamental wavelength in lithium niobate as a function of crystal temperature.

Fig. 2.
Fig. 2.

Domains on the -z face of a 45.75 μm period PPLN crystals, revealed by polishing and phase-contrast microscopy.

Fig. 3.
Fig. 3.

Temperature detuning curves for SHG, and nonlinear phase-shifts of fundamentals for simultaneously phase-matched type-0 and type-I SHG in 4.5 mm long lithium niobate. Plots a) and b) show the calculated SHG detuning curves for fundamentals launched in-phase and with a π/2 phase shift respectively. Plots c) and d) show the calculated nonlinear phase shift of the fundamental fields fundamentals launched in-phase and with a π/2 phase shift respectively.

Fig. 4.
Fig. 4.

Left: cascading of energy from a dominant e-wave fundamental field to a weaker o-wave fundamental field when the two fundaments are launched with π/2 phase shift. Inset shows rescaled plot for o-component demonstrating parametric gain at zero detuning. Right: relative parametric gains of the o-polarized component (involved in type-I SHG) in relation to the ratio of o-e polarizations plotted for various efficiencies of the parent SHG processes.

Fig. 5.
Fig. 5.

Experimental layout for investigating simultaneous phase-matching and χ(2)(2) cascading in single period PPLN using a Nd:Gd:YVO4 as the source. (WP’ - waveplate.)

Fig. 6.
Fig. 6.

Temperature detuning curves for type-I (1st order QPM on d31 ) and type-0 (7th order QPM on d33 ) SHG of a 1064.5 nm laser in 45.75 μm period PPLN. Each curve is measured separately with either a pure type-0 or type-I polarization being set as the input. Irradiance has been normalized to peak SH irradiance of the type I process.

Fig. 7.
Fig. 7.

Temperature detuning curves for simultaneous type-I and type-0 SHG from equally intensive and in-phase fundamentals. Left: measured and calculated detuning curve for the SH. Right measured and calculated detuning curves for the o-wave fundamental and e-wave fundamental.

Fig. 8.
Fig. 8.

Temperature detuning curves for simultaneous type-I and type-0 SHG processes. The two o- and e- fundamentals are with equal intensities and π/2 phase shifted. Left: measured and calculated detuning curve for the second-harmonic wave. Right: measured and calculated detuning curves for the o- and e- fundamental waves.

Fig. 9.
Fig. 9.

Left: detuning curve for the weaker type-I (o-polarized) fundamental component when the ratio is 3:7 (o:e) and it is phase shifted with respect to the other type-0 (e-polarized) fundamental. Left: relative parametric gain of the type-I (o-polarized) fundamental in relation to the ratio of the magnitudes of the fundamental components.

Fig. 10.
Fig. 10.

Left: Net fractional gains in relation to signal magnitudes for a variety of pump levels with shown SH efficiency. Right: Transfer function of signals for a variety of pump intensities with shown SH efficiency.

Equations (6)

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d 33 7 d 31 = 27 pm V 1 7 × 4.7 pm V 1 = 0.91 .
dA dx = i σ 1 SA * exp ( i Δ k 1 x ) ,
dB dx = i σ 2 SB * exp ( i Δ k 0 x ) ,
dS dx = i σ 3 AA exp ( i Δ k 1 x ) i σ 4 BB exp ( i Δ k 0 x ) ,
Δ k 1 ( T ) = Δ k ooe ( T ) G 1 ,
Δ k 0 ( T ) = Δ k eee ( T ) G 7 .

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