## Phase-matching spectral phase measurement and domain period reconstruction of aperiodic quasi-phase matched gratings by nonlinear spectral interferometry |

Optics Express, Vol. 21, Issue 10, pp. 11763-11768 (2013)

http://dx.doi.org/10.1364/OE.21.011763

Acrobat PDF (1475 KB)

### 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

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. 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]

*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]

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]

*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:LiNbO_{3},” 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]

*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]

*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]

9. W. H. Peeters and M. P. van Exter, “Optical characterization of periodically-poled KTiOPO_{4.},” Opt. Express **16**(10), 7344–7360 (2008). [CrossRef] [PubMed]

*x*) or deformations of aperiodic QPM structures arising from lithographic patterning error in the presence of uneven substrates [10]. 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]

*P*(Ω) =

_{NL}*A*⊗

_{ω}*A*is the nonlinear polarization spectrum of the fundamental spectral envelope

_{ω}*A*(

_{ω}*ω*). As a result,

*H*(Ω) can be determined by simultaneously measuring the fundamental and second-harmonic fields

*A*(

_{ω}*ω*) and

*A*

_{2}

*(Ω). However, measuring*

_{ω}*A*

_{2}

*(Ω) typically requires another nonlinear conversion process [e.g. second-harmonic generation (SHG) or parametric amplification] [11], 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*

_{ω}*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]

*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 ).

*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

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]

*ω*

_{0}and spectral envelope

*A*(

_{ω}*ω*) passing through a test QPM grating and a reference thin nonlinear crystal with complex PM responses

*H*(Ω) = |

*H*(Ω)| × exp[

*jψ*(Ω)] and

*H*(Ω) = |

_{r}*H*(Ω)| × exp[

_{r}*jψ*(Ω)] (Ω denotes the angular frequency detuning from 2

_{r}*ω*

_{0}), respectively. According to Eq. (1), the spectral envelopes of the (second-harmonic) signal and reference waves are

*A*(Ω) =

_{s}*P*(Ω) ×

_{NL}*H*(Ω) and

*A*(Ω) =

_{r}*P*(Ω) ×

_{NL}*H*(Ω), respectively. If the two waves are temporally separated by a delay

_{r}*τ*, the resulting power spectrum (interferogram) becomeswhere the symbol ∠

*Z*means the phase of

*Z*. Equation (2) shows that the spectral phase difference function Δ

*ψ*(Ω) = ∠

*A*(Ω)−∠

_{s}*A*(Ω) can be retrieved by Fourier analysis of

_{r}*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]

*A*(Ω) = ∠

_{s}*P*(Ω) +

_{NL}*ψ*(Ω), ∠

*A*(Ω) = ∠

_{r}*P*(Ω) +

_{NL}*ψ*(Ω), the phase difference Δ

_{r}*ψ*(Ω) =

*ψ*(Ω)−

*ψ*(Ω) is independent of the phase of

_{r}*P*(Ω). This means that the fundamental spectral phase ∠

_{NL}*A*(

_{ω}*ω*) is unimportant, and a broadband light source (regardless of its chirp) is sufficient for NLSI. Besides, Δ

*ψ*(Ω) will be equal to the desired PM spectral phase

*ψ*(Ω) if the reference crystal is sufficiently thin such that

*ψ*(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 |

_{r}*H*(Ω)|

^{2}and thus the complex

*H*(Ω).

## 3. Experimental results

*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)].

*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

*ψ*

_{exp}(solid), mask function

*ψ*

_{m}(dashed), and microscopic images

*ψ*

_{μ}(dashed-dotted), respectively. The accuracy of PM spectral phase measurement can be quantitatively estimated by the intensity-weighted root-mean-square (rms) phase errorwhere |

*H*(

*λ*)|

_{i}^{2}is the phase-matching power spectrum, and

*λ*(

_{i}*i*= 1-

*N*) indicates the

*i*th sampling wavelength. The rms phase errors between

*ψ*

_{exp}and

*ψ*

_{m}are 0.36π (QPM1) and 0.31π (QPM2), better than 1.46π (QPM1) and 0.32π (QPM2) between

*ψ*

_{μ}and

*ψ*

_{m}. Since these

*ε*

_{rms}values are much smaller than the overall phase range (~40π), our method is reasonably accurate.

_{exp}(

*x*) and Λ

_{μ}(

*x*) measured by (NLSI and wavelength-scanning SHG) experiments and microscopic images, respectively. Simulation [Fig. 2(b)] shows that the spectral window (783-792 nm) of the interferogram enables a spatial resolution of 810 μm. As a result, we reduced the spatial resolution of the raw domain period functions to ~800 μm by piecewise average. This resolution can reveal the slowly-varying domain periods due to mask design or undesired lithographic patterning error [10], but is insufficient to identify the ~30-μm “long domains”. As shown in Figs. 6(a) and 6(b), Λ

_{exp}(

*x*) and Λ

_{μ}(

*x*) of QPM1 and QPM2 indeed resolve the linear and quadratic trends of Λ

_{m}(

*x*) defined by the lithographic masks. The bumpy Λ

_{μ}(

*x*) curves are primarily due to the uncertainty (~0.2 μm) in positioning the domain boundaries of microscopic images. The mean and standard deviation of the period difference ΔΛ(

*x*) = |Λ

_{exp}(

*x*)-Λ

_{μ}(

*x*)| are 41 nm and 58 nm for QPM1, or 31 nm and 39 nm for QPM2, respectively.

## 4. Conclusions

## Acknowledgment

## 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. |

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. |

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. |

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. |

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:LiNbO |

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. |

7. | G. H. C. New, “Theory of pulse compression using aperiodic quasi-phase-matched gratings,” J. Opt. Soc. Am. B |

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. |

9. | W. H. Peeters and M. P. van Exter, “Optical characterization of periodically-poled KTiOPO |

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

11. | R. Trebino, in |

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 |

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 |

14. | O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO |

**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

Sort: Year | Journal | Reset

### References

- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. H. C. New, “Theory of pulse compression using aperiodic quasi-phase-matched gratings,” J. Opt. Soc. Am. B24(5), 1144–1149 (2007). [CrossRef]
- 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]
- W. H. Peeters and M. P. van Exter, “Optical characterization of periodically-poled KTiOPO4.,” Opt. Express16(10), 7344–7360 (2008). [CrossRef] [PubMed]
- C. Langrock, private communication (2012).
- R. Trebino, in Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, 2000).
- 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]
- 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]
- 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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.