Abstract

We demonstrate a method that enables in situ modification of the spectral shape of the parametric-gain profile in quasi-phase-matching crystals. In our experiment we used the electro-optic effect to modify the phase-matching profile for second-harmonic generation in a 57-mm-long nonuniformly poled LiNbO3 crystal. In the direction of beam propagation the crystal is divided into three segments, where the first and the third segments have an equal length of 17 mm. Both segments are periodically poled with the same period of 21.6 µm, in order to obtain quasi phase matching for frequency doubling a fundamental wavelength of 1653 nm. The center segment is single-domain LiNbO3 whose index of refraction is changed by the electro-optic effect by applying a voltage. Using a continuously tunable, single-frequency, single-stripe, distributed-feedback diode laser as the fundamental source, we recorded the parametric phase-matching profile for second-harmonic generation as a function of the laser wavelength and investigated the modification of the profile in dependence of the voltage applied to the crystal center segment. The measured phase-matching spectra are in excellent agreement with the theoretical prediction. The demonstrated method opens the possibility of rapidly changing the parametric-gain profile for all types of χ(2) nonlinear conversion processes.

© 2002 Optical Society of America

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References

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  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. QE-28, 2631–2654 (1992).
    [CrossRef]
  2. M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFG)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999).
    [CrossRef]
  3. K. Mizuuchi and K. Yamamoto, “Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts,” Opt. Lett. 23, 1880–1882 (1998).
    [CrossRef]
  4. T. Beddard, M. Ebrahimzadeh, T. D. Reid, and W. Sibbett, “Five-optical cycle pulse generation in the mid infrared from an optical parametric oscillator based on periodically poled lithium niobate,” Opt. Lett. 25, 1052–1054 (2000).
    [CrossRef]
  5. N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett. 24, 1750–1752 (1999).
    [CrossRef]
  6. M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
    [CrossRef]
  7. A. Yariv, Quantum Electronics (Wiley, New York, 1988).
  8. J. F. Nye, Physical Properties of Crystals (Oxford University, London, 1957).
  9. D. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
    [CrossRef]
  10. T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
    [CrossRef]
  11. L. E. Myers, R. C. Eckhardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
    [CrossRef]

2000 (1)

1999 (4)

M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
[CrossRef]

N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett. 24, 1750–1752 (1999).
[CrossRef]

M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFG)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999).
[CrossRef]

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

1992 (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. QE-28, 2631–2654 (1992).
[CrossRef]

Beddard, T.

Brener, I.

M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFG)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999).
[CrossRef]

Byer, R. L.

L. E. Myers, R. C. Eckhardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

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. QE-28, 2631–2654 (1992).
[CrossRef]

Chou, M. H.

M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFG)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999).
[CrossRef]

M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
[CrossRef]

Dominic, V.

Ebrahimzadeh, M.

Eckhardt, R. C.

Fejer, M. M.

M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
[CrossRef]

M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFG)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999).
[CrossRef]

L. E. Myers, R. C. Eckhardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

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. QE-28, 2631–2654 (1992).
[CrossRef]

Fujiwara, T.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Furukawa, Y.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Ikushima, A. J.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Jundt, D.

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. QE-28, 2631–2654 (1992).
[CrossRef]

Kitamura, K.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

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. QE-28, 2631–2654 (1992).
[CrossRef]

Missey, M.

Mizuuchi, K.

Myers, L. E.

O’Brien, N.

Ohama, M.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Parameswaran, K. R.

M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFG)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999).
[CrossRef]

M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
[CrossRef]

Powers, P.

Reid, T. D.

Schepler, K. L.

Sibbett, W.

Takahashi, M.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Yamamoto, K.

Electron. Lett. (2)

M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFG)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999).
[CrossRef]

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[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. QE-28, 2631–2654 (1992).
[CrossRef]

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

Opt. Lett. (5)

Other (2)

A. Yariv, Quantum Electronics (Wiley, New York, 1988).

J. F. Nye, Physical Properties of Crystals (Oxford University, London, 1957).

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Figures (8)

Fig. 1
Fig. 1

General layout of segmented quasi-phase-matching crystals utilizing the electro-optic effect. Segments with suitably designed domain structures are separated by single-domain segments that are provided with electrodes. The parametric-gain profile of such crystals can be modified in a predictable manner during the experiment, simply by applying appropriate voltages to the electrodes.

Fig. 2
Fig. 2

(A) Layout of the three-segment LiNbO3 crystal used in the experiment. The first and third segments have equal lengths L1,3 and are periodically poled with the same grating period Λ. The refractive index in the single-domain center segment of the crystal (length L2) can be adjusted by the electro-optic effect. (B) Modulation of the nonlinear coefficient (normalized) along the crystal. In segments 1 and 3 the coefficient changes its sign with a rectangular function, which has a spatial period of Λ. In segment 2 the nonlinear coefficient is constant.

Fig. 3
Fig. 3

Solid curves: second-harmonic intensity generated in a symetric three-segment crystal as a function of the phase mismatch in the periodically poled segments, for different phase shifts Ψ in the center segment. (A) Ψ=-π, (B) Ψ=-π/2, (C) Ψ=0, (D) Ψ=+π/2, (E) Ψ=+π. The intensity peaks are labeled to facilitate tracking of their movement from right to left as Ψ increases. Dashed curves: sinc2 envelopes of the parametric-gain profile, given by the phase matching in the periodically poled outer segments of the crystal.

Fig. 4
Fig. 4

Experimental setup for measuring the second-harmonic phase-matching profiles of the three-segment crystal for different voltages U applied to the center segment. The fundamental-wave source is a distributed-feedback (DFB) single-frequency diode laser, which is continuously tunable near 1653 nm. The second-harmonic wave is generated in a single pass through the segmented LiNbO3 crystal and detected with a photomultiplier tube, PMT.

Fig. 5
Fig. 5

Dots: measured second-harmonic intensity generated in the three-segment LiNbO3 crystal, as a function of the fundamental wavelength, when no voltage is applied to the center segment. Solid curve: theoretical-fit curve of the phase-matching profile to the experimental values. The fit yields a phase difference of Ψ=1.1×π. Dashed curve: sinc2 shaped envelope of the theoretical-gain profile. The full width at half-maximum of the sinc2 function is 0.86 nm, in very good agreement with theory.

Fig. 6
Fig. 6

Second-harmonic intensity as a function of the fundamental wavelength for three selected voltages applied to the crystal center segment. (A) U=-730 V, (B) U=0 V, (C) U=+730 V. The solid curves are theoretical fits of the phase-matching profile to the experimental values (dots), yielding phase differences of Ψ=0, +/-π, and 0 for A, B, and C, respectively.

Fig. 7
Fig. 7

Measured second-harmonic power at fundamental wavelengths of λF,1=1653.1 nm (squares) and λF,2=1652.5 nm (triangles), as a function of the voltage applied to the crystal center segment. Solid curves: sine-shape fit curves to the experimental values. Both curves exhibit the same period of 1460 V, in very good agreement with the theoretical value of 1445 V, calculated for this crystal configuration.

Fig. 8
Fig. 8

(A) Measured second-harmonic intensity as a function of the fundamental wavelength and of the applied voltage. High intensities are represented by dark areas, low intensities by light areas. (B) Calculated second-harmonic intensity as a function of the phase mismatch ΔkL1,3/2 and of the phase difference Ψ. The comparison of both figure parts illustrates the good agreement of experiment and theory for a wide field of parameters.

Equations (25)

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dESHdz=Γdeff(z)exp[-iΔΦ(z)],
Γ=23LCiω EF2nSHc
ΔΦ(z)=ΦSH(z)-2ΦF(z).
ΔΦ(z)=Δkz=2ωzc(nSH-nF),
ESH(LC)=Γ0LCdeff(z)exp(-iΔkz)dz.
I(LC)|ESH(LC)|2=|ΓdeffLC|2sinc2ΔkLC2.
Δkn=kSH,n-2kF,n
deff(z)=0z<L1,3d/2×exp(i2πz/Λ+iψ1)+c.c.L1,3z<L1,3+L2dL1,3+L2z<LCd/2×exp(i2πz/Λ+iψ3)+c.c..
ΔΦ(z)=0zL1,3Δk1,3zL1,3<zL1,3+L2Δk1,3L1,3+Δk2(z-L1,3)L1,3+L2<zLCΔk1,3L1,3+Δk2L2+Δk1,3(z-L1,3-L2).
ESH(LC)=ESH,1+ESH,2+ESH,3,
 ESH,1=Γ0L1,312d exp(i2πz/Λ+iψ1)+c.c.×exp(-iΔk1,3z)dz,
ESH,2=Γ0L2 12d exp(-iΔk1,3L1,3-iΔk2z)dz,
ESH,3=Γ0L1,312d exp[i2π(z+L1,3+L2)/Λ+iψ3]+c.c.exp(-iΔk1,3L1,3-iΔk2L2-iΔk1,3z)dz.
ESH,112Γd exp(iΨ1)0L1,3 exp(-iΔk1,3¯z)dz,
ESH,20,
ESH,312Γd exp[iψ3-iΔk1,3¯L1,3-i(Δk2-2π/Λ)L2]0L1,3 exp(-iΔk1,3¯z)dz,
ESH(LC)=Γd2iΔk1,3¯[exp(iΔk1,3¯L1,3)-1]×{exp(iψ1)+exp[iψ3-iΔk1,3¯L1,3-i(Δk2-2π/Λ)L2]}.
Ψ=ψ3-ψ1-Δk1,3¯L1,3-(Δk2-2π/Λ)L2
ESH(LC)=iΓd exp(iψ1)2Δk1,3¯[exp(-iΔk1,3¯L1,3)-1]×[exp(iΨ)+1].
ISH(LC)|ΓdL1,3|2sinc2Δk1,3¯L1,32cos2Ψ2.
Ψ=0-Δk1,3¯(L1,3+L2)-(Δk2-Δk1,3)L2.
Δk2-Δk1,3=2ωc[nSH(U)-nF(U)-nSH(0)+nF(0)]=2ωc[ΔnSH(U)-ΔnF(U)],
ΔnF,SH(U)=-12nF,SH3rF,SH UB,
12Ψ(U)=-Δk1,3¯ L1,3+L22+ωL22c(nSH3rSH-nF3rF) UB.
UP=λFBL2(nSH3rSH-nF3rF)-1,

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