Abstract

We experimentally measured the phase-matching spectral phases of aperiodic quasi-phase matched gratings for the first time (to the best of our knowledge) by nonlinear spectral interferometry. The retrieved information is useful in determining the temporal shape of the nonlinearly converted ultrafast signal and reconstructing the slowly-varying domain period distribution. The method is nondestructive, fast, sensitive, accurate, and applicable to different nonlinear materials. Compared to taking microscopic images of the etched crystal surface, our method can directly measure the domain period distribution in the crystal interior and is free of the artificial random duty period error due to image concatenation.

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

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1992

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(11), 2631–2654 (1992).
[CrossRef]

Arie, A.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B91(2), 343–348 (2008).
[CrossRef]

Asobe, M.

Baldi, P.

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(11), 2631–2654 (1992).
[CrossRef]

Chang, D.

Chen, Y.-H.

Chériaux, G.

Chou, M.-H.

Fejer, M. M.

Gallmann, L.

Galun, E.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B91(2), 343–348 (2008).
[CrossRef]

Gayer, O.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B91(2), 343–348 (2008).
[CrossRef]

Heese, C.

Hsu, C.-W.

Hsu, N.

Hung, S.-B.

Joffre, M.

Johansen, S. K.

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(11), 2631–2654 (1992).
[CrossRef]

Keller, U.

Kohler, M.

Kornaszewski, U.

Lai, J.-Y.

Langrock, C.

Lepetit, L.

Magari, K.

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(11), 2631–2654 (1992).
[CrossRef]

New, G. H. C.

Nishida, Y.

Peeters, W. H.

Pelc, J. S.

Phillips, C. R.

Reid, D. T.

Sacks, Z.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B91(2), 343–348 (2008).
[CrossRef]

Sapaev, U. K.

Suzuki, H.

Tadanaga, O.

Umeki, T.

van Exter, M. P.

Wu, D.-Y.

Yanagawa, T.

Yang, S.-D.

Appl. Phys. B

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B91(2), 343–348 (2008).
[CrossRef]

IEEE J. Quantum Electron.

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(11), 2631–2654 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Other

C. Langrock, private communication (2012).

R. Trebino, in Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, 2000).

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Figures (6)

Fig. 1
Fig. 1

Microscopic side views of two z-cut periodically poled MgO-doped lithium niobate (PPMgLN) samples with (a) uniformly, and (b) non-uniformly poled cross-sections, respectively. Dark regions represent the inverted domains.

Fig. 2
Fig. 2

Dependence of spatial resolution on source bandwidth. (a) SHG wavenumber mismatch Δk of PPMgLN versus fundamental wavelength λ. (b) The fundamental frequency bandwidth (solid) and boundary wavelengths (dotted, dashed-dotted) versus the corresponding spatial resolution of the reconstructed g(x) of a PPMgLN with 1575-nm central PM wavelength. The maximum wavelength (dashed) is ceiled due to the increasing Δk for λ>2701 nm shown in (a).

Fig. 3
Fig. 3

(a) Experimental setup. HNLF: Highly nonlinear fiber. PC: Polarization controller. PBS: Polarization beamsplitter. L#: Lens. BS: Beamsplitter. (b) Power spectra before (dotted) and after (solid) the HNLF, respectively. The shaded area indicates the phase-matched spectral range of QPM1 and QPM2.

Fig. 4
Fig. 4

(a) A microscopic image of QPM1 with more than 8 domains. (b) The global domain length distributions of QPM1, QPM2 obtained by concatenating ~620 microscopic images.

Fig. 5
Fig. 5

Experiment results of (a-c) QPM1 and (d-f) QPM2. (a,c) Second-harmonic power spectra of the reference (solid), signal (dashed), and their interferogram (shaded). (b,c,e,f) PM spectral intensities and phases obtained by experiments (solid and shaded), lithographic mask function (dashed), and microscopic images (dashed-dotted), respectively.

Fig. 6
Fig. 6

Domain period distributions measured by experiments (solid) and microscopic images (dashed-dotted) for (a) QPM1, and (b) QPM2, respectively.

Equations (4)

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A 2ω (Ω)= P NL (Ω)×H(Ω),
S(Ω)= | A s (Ω) | 2 + | A r (Ω) | 2 +2| A s (Ω)× A r (Ω) |×cos[ τΩ A s (Ω)+ A r (Ω)+2 ω 0 τ ],
H(Ω) 0 L g(x) e iΔkx dx , Δk=( Ω/c )×[ n(Ω)n(Ω/2 ) ].
ε rms i=1 N [ ψ exp ( λ i )ψ( λ i ) ] 2 × | H( λ i ) | 2 / i=1 N | H( λ i ) | 2 ,

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