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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 11763–11768
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Phase-matching spectral phase measurement and domain period reconstruction of aperiodic quasi-phase matched gratings by nonlinear spectral interferometry

Chia-Lun Tsai, Ming-Chi Chen, Jui-Yu Lai, Dong-Yi Wu, and Shang-Da Yang  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 11763-11768 (2013)
http://dx.doi.org/10.1364/OE.21.011763


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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.

© 2013 OSA

1. Introduction

Designs and applications of aperiodic quasi-phase matched (QPM) gratings have been intensively explored during the past two decades [1

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(11), 2631–2654 (1992). [CrossRef]

7

7. G. H. C. New, “Theory of pulse compression using aperiodic quasi-phase-matched gratings,” J. Opt. Soc. Am. B 24(5), 1144–1149 (2007). [CrossRef]

]. For example, an arbitrary nonlinear conversion efficiency spectrum can be achieved by optimizing the domain orientation distribution g(x) (defined in [1

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(11), 2631–2654 (1992). [CrossRef]

]) and has been applied to the detection of multiple hydrocarbon gases [2

2. M. Asobe, O. Tadanaga, T. Umeki, T. Yanagawa, Y. Nishida, K. Magari, and H. Suzuki, “Unequally spaced multiple mid-infrared wavelength generation using an engineered quasi-phase-matching device,” Opt. Lett. 32(23), 3388–3390 (2007). [CrossRef] [PubMed]

,3

3. J.-Y. Lai, C.-W. Hsu, N. Hsu, Y.-H. Chen, and S.-D. Yang, “Hyperfine aperiodic optical superlattice optimized by iterative domino algorithm for phase-matching engineering,” Opt. Lett. 37(7), 1184–1186 (2012). [CrossRef] [PubMed]

]. Chirped QPM gratings with broadened and tailored complex phase-matching (PM) responses H(Ω) [defined in Eq. (1)] were used in parametric amplification of few-cycle mid-infrared pulse [5

5. C. Heese, C. R. Phillips, L. Gallmann, M. M. Fejer, and U. Keller, “Ultrabroadband, highly flexible amplifier for ultrashort midinfrared laser pulses based on a periodically poled Mg:LiNbO3,” Opt. Lett. 35(14), 2340–2342 (2010). [CrossRef] [PubMed]

] and second-harmonic pulse shaping [6

6. U. Kornaszewski, M. Kohler, U. K. Sapaev, and D. T. Reid, “Designer femtosecond pulse shaping using grating-engineered quasi-phase-matching in lithium niobate,” Opt. Lett. 33(4), 378–380 (2008). [CrossRef] [PubMed]

,7

7. G. H. C. New, “Theory of pulse compression using aperiodic quasi-phase-matched gratings,” J. Opt. Soc. Am. B 24(5), 1144–1149 (2007). [CrossRef]

], respectively. Applications of aperiodic QPM can be facilitated by the ability to measure H(Ω) experimentally for two reasons. First, the temporal shaping of the nonlinear signal depends on H(Ω), which could deviate from the design due to the increased poling error in the presence of different domain sizes [6

6. U. Kornaszewski, M. Kohler, U. K. Sapaev, and D. T. Reid, “Designer femtosecond pulse shaping using grating-engineered quasi-phase-matching in lithium niobate,” Opt. Lett. 33(4), 378–380 (2008). [CrossRef] [PubMed]

]. Second, the domain period function Λ(x), or even the domain orientation distribution g(x), can be reconstructed if H(Ω) and the dispersion relation are known. In contrast to measuring the statistical information (e.g. random duty cycle error) of periodic QPM gratings by analyzing the PM efficiency pedestal [8

8. J. S. Pelc, C. R. Phillips, D. Chang, C. Langrock, and M. M. Fejer, “Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors,” Opt. Lett. 36(6), 864–866 (2011). [CrossRef] [PubMed]

] or Maker fringes [9

9. W. H. Peeters and M. P. van Exter, “Optical characterization of periodically-poled KTiOPO4.,” Opt. Express 16(10), 7344–7360 (2008). [CrossRef] [PubMed]

], this approach would allow the convenient determination of the slowly-varying Λ(x) or deformations of aperiodic QPM structures arising from lithographic patterning error in the presence of uneven substrates [10

10. C. Langrock, private communication (2012).

]. There exist some methods able to measure H(Ω) or g(x) experimentally. (1) Under the assumptions of plane waves, non-depleted pump, and negligible group velocity dispersion, the second-harmonic spectral envelope is given by a transfer function relation [1

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(11), 2631–2654 (1992). [CrossRef]

]:
A2ω(Ω)=PNL(Ω)×H(Ω),
(1)
where PNL(Ω) = AωAω is the nonlinear polarization spectrum of the fundamental spectral envelope Aω(ω). As a result, H(Ω) can be determined by simultaneously measuring the fundamental and second-harmonic fields Aω(ω) and A2ω(Ω). However, measuring A2ω(Ω) typically requires another nonlinear conversion process [e.g. second-harmonic generation (SHG) or parametric amplification] [11

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

], which is subject to worse sensitivity, accumulated error, and higher risk that the converted wavelengths become absorptive in the nonlinear medium. (2) A double-pass SHG scheme was proposed to measure g(x) of arbitrary QPM gratings nondestructively [12

12. S. K. Johansen and P. Baldi, “Characterization of quasi-phase-matching gratings in quadratic media through double-pass second-harmonic power measurements,” J. Opt. Soc. Am. B 21(6), 1137–1145 (2004). [CrossRef]

], but has not been experimentally verified. (3) Taking local microscopic images of the etched surface of a QPM grating, and concatenating them to obtain the global g(x). In addition to the enormous time and effort required in sample preparation, image taking, and signal processing, this method suffers from errors due to image concatenation (artificial random duty period error) and non-uniformly poled cross-section that could be substantial for short-period or thick QPM gratings (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.
).

In this paper, we propose a scheme based on nonlinear spectral interferometry (NLSI) to measure the phase of H(Ω) and reconstruct the domain period function Λ(x). The functions of H(Ω) and Λ(x) of aperiodically poled MgO-doped lithium niobate (A-PPMgLN) samples were experimentally measured by NLSI and microscopic images (of the HF-etched surfaces), respectively. They were analyzed and compared with those defined by the lithographic masks. NLSI is nondestructive, fast, sensitive, accurate, and applicable to different nonlinear materials. It is free of the artificial random duty period error, and can directly measure the domain period distribution in the crystal interior (where optical beam normally accesses).

2. Theory

Spectral interferometry is a linear technique used in measuring the spectral phase difference between two optical waves of the same carrier frequency [13

13. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]

]. In NLSI, the signal and reference waves come from SHG of a common fundamental field of carrier frequency ω0 and spectral envelope Aω(ω) passing through a test QPM grating and a reference thin nonlinear crystal with complex PM responses H(Ω) = |H(Ω)| × exp[(Ω)] and Hr(Ω) = |Hr(Ω)| × exp[r(Ω)] (Ω denotes the angular frequency detuning from 2ω0), respectively. According to Eq. (1), the spectral envelopes of the (second-harmonic) signal and reference waves are As(Ω) = PNL(Ω) × H(Ω) and Ar(Ω) = PNL(Ω) × Hr(Ω), respectively. If the two waves are temporally separated by a delay τ, the resulting power spectrum (interferogram) becomes
S(Ω)=|As(Ω)|2+|Ar(Ω)|2+2|As(Ω)×Ar(Ω)|×cos[τΩAs(Ω)+Ar(Ω)+2ω0τ],
(2)
where the symbol ∠Z means the phase of Z. Equation (2) shows that the spectral phase difference function Δψ(Ω) = ∠As(Ω)−∠Ar(Ω) can be retrieved by Fourier analysis of S(Ω) [13

13. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]

]. Since ∠As(Ω) = ∠PNL(Ω) + ψ(Ω), ∠Ar(Ω) = ∠PNL(Ω) + ψr(Ω), the phase difference Δψ(Ω) = ψ(Ω)−ψr(Ω) is independent of the phase of PNL(Ω). This means that the fundamental spectral phase ∠Aω(ω) is unimportant, and a broadband light source (regardless of its chirp) is sufficient for NLSI. Besides, Δψ(Ω) will be equal to the desired PM spectral phase ψ(Ω) if the reference crystal is sufficiently thin such that ψr(Ω) is nearly constant within the spectral range of interest. By measuring SHG yield as a function of input wavelength, one can independently determine the PM spectral intensity |H(Ω)|2 and thus the complex H(Ω).

3. Experimental results

Figure 3(a)
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.
shows the experimental setup of NLSI. A mode-locked fiber laser produces 50 MHz, 300 fs pulses at 1560 nm. The −10 dB bandwidth is broadened from 24 nm to 79 nm [dotted and solid curves, Fig. 3(b)] by passing the pulse through a 15-m-long highly nonlinear fiber. The p-wave and s-wave components are separated by a polarization beamsplitter, focused into a 1-mm-long Type-I BBO reference crystal and a 49.5-mm-long A-PPMgLN with different types of QPM gratings (HC Photonics) to generate the second-harmonic reference and signal pulses, respectively. The mask-defined domain period distributions Λ(x) of QPM1 and QPM2 are linear and quadratic functions monotonically decreasing from 20.4 µm to 19.9 µm, corresponding to phase-matched fundamental wavelengths of 1566-1586 nm [shaded, Fig. 3(b)]. A polarization controller is used to maximize the fringe contrast of the interferogram S(Ω) by controlling the power ratio of the two arms. The two s-polarized second-harmonic pulses are delayed with each other, recombined by a beamsplitter, focused into a spectrograph, and recorded by an un-cooled CCD array to get the interferogram S(Ω). In our experiment, 12-μW average fundamental power and 100-ms CCD integration time would be sufficient for accurate measurements. The broad input spectral width and the short BBO crystal (phase-matched wavelengths are beyond 1520-1630 nm) ensure that the fringes of S(Ω) exist for the entire spectral range of H(Ω) of each QPM grating [a prerequisite of measuring ψ(Ω)].

Figure 4(a)
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.
shows a sample microscopic image of the QPM1 surface, from which we can measure the local domain lengths. The global domain length distributions [Fig. 4(b)] of QPM1, QPM2 were obtained by combining the results of ~620 images taken from each of the two QPM gratings. In addition to the majority lengths around 10 μm, there are 30 and 40 “long domains” (~30 μm) out of the total 4925 and 4948 “mask-defined” domains in QPM1 and QPM2, respectively. This is attributed to the domain inversion failure such that three neighboring mask-defined domains merge into a 3-time-longer domain.

Figures 5(a)
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.
and 5(d) illustrate the second-harmonic power spectra of the reference pulse (solid), the signal pulse (dashed), and their interferogram S(Ω) (shaded) due to QPM1 and QPM2, respectively. The fringe density of either S(Ω) increases with wavelength, consistent with a down-chirped second-harmonic signal pulse caused by a QPM grating with monotonically decreasing domain period function Λ(x). Figures 5(b) and 5(e) show the PM power spectra of QPM1 and QPM2 obtained by three methods: (1) wavelength-scanning SHG experiment (solid and shaded), (2) FT of the mask-defined g(x) (dashed), (3) FT of the microscopically imaged g(x) (dashed dotted), respectively. It is evident that the artificial random duty period error due to concatenating a large number of microscopic images may result in seriously distorted PM power spectra. The curves in Figs. 5(c) and 5(f) represent the PM spectral phases of QPM1 and QPM2 obtained by NLSI experiment ψexp (solid), mask function ψm (dashed), and microscopic images ψμ (dashed-dotted), respectively. The accuracy of PM spectral phase measurement can be quantitatively estimated by the intensity-weighted root-mean-square (rms) phase error
εrmsi=1N[ψexp(λi)ψ(λi)]2×|H(λi)|2/i=1N|H(λi)|2,
(4)
where |H(λi)|2 is the phase-matching power spectrum, and λi (i = 1-N) indicates the ith sampling wavelength. The rms phase errors between ψexp and ψm are 0.36π (QPM1) and 0.31π (QPM2), better than 1.46π (QPM1) and 0.32π (QPM2) between ψμ and ψm. Since these εrms values are much smaller than the overall phase range (~40π), our method is reasonably accurate.

4. Conclusions

We experimentally retrieved the phase-matching spectral phases of aperiodic QPM gratings for the first time (to the best of our knowledge) by using nonlinear spectral interferometry. The complex phase-matching responses and domain period distributions of aperiodic QPM gratings measured by NLSI and microscopic images are in good agreement with those defined by the lithographic masks. Our method is nondestructive, fast (only acquiring one power spectrum and using non-iterative phase retrieval), sensitive (using only one nonlinear conversion process), accurate, applicable to different nonlinear materials, and independent of the chirp of the fundamental light source. Compared to taking microscopic images of the etched crystal surface, our method can directly measure the domain period distribution in the crystal interior (normally accessed by the optical beams) and is free of the artificial random duty period error due to image concatenation.

Acknowledgment

This material is based on research supported by the National Science Council of Taiwan under grants NSC-99-2120-M-007-010, and NSC-100-2221-E-007-093-MY3 and by the National Tsing Hua University under grant 101N2081E1.

References and links

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(11), 2631–2654 (1992). [CrossRef]

2.

M. Asobe, O. Tadanaga, T. Umeki, T. Yanagawa, Y. Nishida, K. Magari, and H. Suzuki, “Unequally spaced multiple mid-infrared wavelength generation using an engineered quasi-phase-matching device,” Opt. Lett. 32(23), 3388–3390 (2007). [CrossRef] [PubMed]

3.

J.-Y. Lai, C.-W. Hsu, N. Hsu, Y.-H. Chen, and S.-D. Yang, “Hyperfine aperiodic optical superlattice optimized by iterative domino algorithm for phase-matching engineering,” Opt. Lett. 37(7), 1184–1186 (2012). [CrossRef] [PubMed]

4.

J.-Y. Lai, C.-W. Hsu, D.-Y. Wu, S.-B. Hung, M.-H. Chou, and S.-D. Yang, “Healing block-assisted quasi-phase matching,” Opt. Lett. 38(7), 1176–1178 (2013). [CrossRef] [PubMed]

5.

C. Heese, C. R. Phillips, L. Gallmann, M. M. Fejer, and U. Keller, “Ultrabroadband, highly flexible amplifier for ultrashort midinfrared laser pulses based on a periodically poled Mg:LiNbO3,” Opt. Lett. 35(14), 2340–2342 (2010). [CrossRef] [PubMed]

6.

U. Kornaszewski, M. Kohler, U. K. Sapaev, and D. T. Reid, “Designer femtosecond pulse shaping using grating-engineered quasi-phase-matching in lithium niobate,” Opt. Lett. 33(4), 378–380 (2008). [CrossRef] [PubMed]

7.

G. H. C. New, “Theory of pulse compression using aperiodic quasi-phase-matched gratings,” J. Opt. Soc. Am. B 24(5), 1144–1149 (2007). [CrossRef]

8.

J. S. Pelc, C. R. Phillips, D. Chang, C. Langrock, and M. M. Fejer, “Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors,” Opt. Lett. 36(6), 864–866 (2011). [CrossRef] [PubMed]

9.

W. H. Peeters and M. P. van Exter, “Optical characterization of periodically-poled KTiOPO4.,” Opt. Express 16(10), 7344–7360 (2008). [CrossRef] [PubMed]

10.

C. Langrock, private communication (2012).

11.

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

12.

S. K. Johansen and P. Baldi, “Characterization of quasi-phase-matching gratings in quadratic media through double-pass second-harmonic power measurements,” J. Opt. Soc. Am. B 21(6), 1137–1145 (2004). [CrossRef]

13.

L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]

14.

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. B 91(2), 343–348 (2008). [CrossRef]

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(230.4320) Optical devices : Nonlinear optical devices

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: March 14, 2013
Revised Manuscript: May 1, 2013
Manuscript Accepted: May 2, 2013
Published: May 7, 2013

Citation
Chia-Lun Tsai, Ming-Chi Chen, Jui-Yu Lai, Dong-Yi Wu, and Shang-Da Yang, "Phase-matching spectral phase measurement and domain period reconstruction of aperiodic quasi-phase matched gratings by nonlinear spectral interferometry," Opt. Express 21, 11763-11768 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-11763


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References

  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(11), 2631–2654 (1992). [CrossRef]
  2. M. Asobe, O. Tadanaga, T. Umeki, T. Yanagawa, Y. Nishida, K. Magari, and H. Suzuki, “Unequally spaced multiple mid-infrared wavelength generation using an engineered quasi-phase-matching device,” Opt. Lett.32(23), 3388–3390 (2007). [CrossRef] [PubMed]
  3. J.-Y. Lai, C.-W. Hsu, N. Hsu, Y.-H. Chen, and S.-D. Yang, “Hyperfine aperiodic optical superlattice optimized by iterative domino algorithm for phase-matching engineering,” Opt. Lett.37(7), 1184–1186 (2012). [CrossRef] [PubMed]
  4. J.-Y. Lai, C.-W. Hsu, D.-Y. Wu, S.-B. Hung, M.-H. Chou, and S.-D. Yang, “Healing block-assisted quasi-phase matching,” Opt. Lett.38(7), 1176–1178 (2013). [CrossRef] [PubMed]
  5. C. Heese, C. R. Phillips, L. Gallmann, M. M. Fejer, and U. Keller, “Ultrabroadband, highly flexible amplifier for ultrashort midinfrared laser pulses based on a periodically poled Mg:LiNbO3,” Opt. Lett.35(14), 2340–2342 (2010). [CrossRef] [PubMed]
  6. U. Kornaszewski, M. Kohler, U. K. Sapaev, and D. T. Reid, “Designer femtosecond pulse shaping using grating-engineered quasi-phase-matching in lithium niobate,” Opt. Lett.33(4), 378–380 (2008). [CrossRef] [PubMed]
  7. G. H. C. New, “Theory of pulse compression using aperiodic quasi-phase-matched gratings,” J. Opt. Soc. Am. B24(5), 1144–1149 (2007). [CrossRef]
  8. J. S. Pelc, C. R. Phillips, D. Chang, C. Langrock, and M. M. Fejer, “Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors,” Opt. Lett.36(6), 864–866 (2011). [CrossRef] [PubMed]
  9. W. H. Peeters and M. P. van Exter, “Optical characterization of periodically-poled KTiOPO4.,” Opt. Express16(10), 7344–7360 (2008). [CrossRef] [PubMed]
  10. C. Langrock, private communication (2012).
  11. R. Trebino, in Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, 2000).
  12. S. K. Johansen and P. Baldi, “Characterization of quasi-phase-matching gratings in quadratic media through double-pass second-harmonic power measurements,” J. Opt. Soc. Am. B21(6), 1137–1145 (2004). [CrossRef]
  13. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B12(12), 2467–2474 (1995). [CrossRef]
  14. 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]

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