Abstract

Random duty-cycle errors (RDE) in ferroelectric quasi-phase-matching (QPM) devices not only affect the frequency conversion efficiency, but also generate non-phase-matched parasitic noise that can be detrimental to some applications. We demonstrate an accurate but simple method for measuring the RDE in periodically poled lithium niobate. Due to the equivalence between the undepleted harmonic generation spectrum and the diffraction pattern from the QPM grating, we employed linear diffraction measurement which is much simpler than tunable harmonic generation experiments [J. S. Pelc, et al., Opt. Lett. 36, 864–866 (2011)]. As a result, we could relate the RDE for the QPM device to the relative noise intensity between the diffraction orders.

© 2013 Optical Society of America

1. Introduction

Quasi-phase matching (QPM) devices based on ferroelectric crystals are widely used in applications such as highly efficient optical frequency converters and parametric optical amplifiers/oscillators. For the optimal performance of a QPM device, the poled domain structure must ensure good fidelity to the designed grating structure. In the standard electric field poling process using e-beam-defined photo-masks, high-quality QPM devices with sharp domain boundaries can be obtained from various ferroelectric crystals. Although such a photolithographic process assures stable periodicity in the QPM grating, randomness in the domain boundary locations is inevitable in ferroelectric QPM devices [1]. Such randomness, negligible in conventional gratings, does occur during high-voltage ferroelectric domain reversal, due to non-uniform expansion of the reversed ferroelectric domain regions. The statistical departure of the domain boundaries from the ideal locations, called the random duty-cycle error (RDE) by Pelc et al., can lead to decreased efficiency as well as undesired function of the devices such as parasitic harmonic generation [2]. In a reasonably good QPM device, the decrease in the conversion efficiency is not significant, but the non-phase-matched parasitic generation can be detrimental to photon-level frequency conversion applications [25].

Although the RDE of a QPM device can be directly evaluated by measuring the widths of poled and unpoled domains using a microscope, the measurement of an entire QPM channel (typically made of ~1,000 domains or more) is time consuming, which is not desirable for either device makers or users. Thus, several indirect methods for poling quality evaluation have been developed [2, 69]. Among them, wavelength-tunable second-harmonic generation (SHG) is representative, and gives a direct estimation of the performance as other types of frequency conversion devices do [1]. The relationship between the RDE and the efficiency of the SHG pedestal has been established in [2]. However, most of these methods are more sophisticated than the direct microscopic measurement, and sometimes not practical. The tunable SHG experiment is not easy either; it requires tunable narrow-linewidth sources, and the tuning range is significantly limited even with two tunable lasers in sequence [2]. Thus, it allows the measurement of the parasitic generation only near the first order QPM peak, but cannot give experimental estimation of the amount far from the QPM peaks.

In this work, instead of a tunable SHG experiment, we measured the far-field diffraction pattern from the QPM grating, which is mathematically equivalent to the SHG tuning curve. The mathematical equivalence results from the fact that both of them are Fourier transforms of the grating structure, when the SHG spectrum is calculated under the negligible depletion limit, and has been experimentally proven valid [10,11]. The same RDE information was obtained from a much simpler diffraction experiment with a low-power laser. Furthermore, the pure background noise far from the orders could be measured, overcoming the limited tunable range in the tunable SHG experiment.

In our previous works [10,11], a small beam (focused spot) was used to detect the first order and the second order diffraction intensities from a QPM grating, and their ratio gave the local duty ratio. Because the statistics of the duty ratio was obtained by scanning the spot throughout the QPM channel, the RDE was somewhat underestimated due to the averaging effect within the focused spot illuminating a few periods. In the present work, we used an expanded, collimated beam to cover the whole channel of the QPM channel. The RDE was obtained directly from the diffraction pattern without scanning a focused spot, and the ‘pre-averaging’ problem was also overcome.

2. Theory

Here, we introduce a realistic model for the random domain structure fabricated by the standard electric field poling method, and calculate the far-field diffraction pattern as a function of the standard deviation (STD) of the duty ratio. Since the standard electric field poling method employs a photo-mask, the QPM period is kept uniform throughout the channel. Our model is similar to the one described in [2], but different in that the average duty ratio is not necessarily 1/2, as explained below. First, we assumed that the electrode locations are perfectly periodic, and that the poled domain created under each electrode expands randomly to both right and left sides as schematically described in Fig. 1. We considered the random locations of the domain boundaries at both sides. In Fig. 1, ck = Λ (k−N/2) (k = 1, 2, …, N) represents the exact locations of the center of the k-th electrode, where Λ is the QPM period and N is the number of periods. wkl and wkr are the distances of the left and right domain boundaries from the center, respectively, whose distributions are assumed to be Gaussian with the same average and STD. Then, xkr=ck+wkr/2andxkl=ckwkl/2are the coordinates of the right and the left boundaries of the poled domain, respectively.

 figure: Fig. 1

Fig. 1 Schematic diagram of random domain model. (Ps: spontaneous polarization)

Download Full Size | PPT Slide | PDF

After poling, the top electrodes are removed, and the bottom surface is slightly etched to reveal a surface-relief phase grating structure. For a plane light wave illuminating the random phase grating at normal incidence, we can write the transmission function t(x) as follows:

t(x)=rect(xL)+k=1NQrect[xxkr+xkl2xkrxkl]
where L = NΛ is the length of the grating under uniform illumination,Q=eiϕ1, and ϕ is the phase depth which is constant throughout the grating. Then, the Fraunhofer diffraction pattern can be written as the Fourier transform of t(x),
E(ξ)=At(x)e2iπξxdx
where A is a constant and ξ = sinθ /λ is the spatial frequency (θ being the diffraction angle). From this, the ensemble-averaged intensity pattern is obtained by calculating EE*, and averaging it with the statistical distributions of wkl and wkr. The result is:
I(ξ)=B|Q|2(Λξ)2[12N(1f(ξ))+f(ξ)sin2(πξΛR¯)(sin(πΛNξ)Nsin(πΛξ))2]
where B is a constant, the function f(ξ)=e(πσξ)2contains the RDE information, σ is the STD of the poled domain width, and is the average duty ratio. Equation (3) agrees with the results of recent theoretical studies on such broad phase-matching Fourier spectra [12]. It should be noted that Eq. (3) has been obtained by transforming the second term of Eq. (1). The first term in Eq. (1) contributes to the Fourier transform only in the very narrow region around the origin (ξ = 0), and the small effect in the spatial frequency regions of our interest (XΛξ = Λ sinθ /λ = 1 ~2) can be measured easily by removing the grating (leaving a slit of width L), and subtracting from the measured intensity with the grating in place.

If the grating structure is ideal (σ = 0), f(ξ) = 1 and the first term of Eq. (3) vanishes. Then, the diffraction intensity pattern represented by the second term is that of a conventional binary phase grating exhibiting pronounced narrow orders (X = 1, 2, 3 …), and small tails around them. For a grating with disorder, however, the strength of each diffraction order is decreased by the factor f (ξ), and the first term adds a background noise to the tails of the second term. For a QPM device with small disorder (εσ/Λ << 1), f(ξ) ≈1 – (πξσ)2, the diffraction efficiency of each order is not significantly affected by σ, while the noise term is roughly proportional to ε2/N, exhibiting a flat background in the spatial frequency spectrum [12].

In practice, it is difficult to measure the absolute noise intensity for a given input intensity. Instead, it is much easier to measure the relative intensity of the noise with reference to one of the diffraction orders, within the same diffraction pattern. We measured the noise intensity (In) at the midpoint (X = 1.5) between the first order (X = 1) and the second order (X = 2), and compared it with the first order intensity (I1). For a grating with small disorder (σ/Λ << 1), the relative noise intensity is obtained directly from Eq. (3),

InI1=I(X=1.5)I(X=1)(πε)22Nsin2(πR¯)
where εσ/Λ is the relative STD with respect to the grating period. The above expression contains not only the RDE, but also the average duty ratio of the grating under test. It should be noted that the same factor |Q|2 is included in both In and I1, and cancelled in Eq. (4), conveniently making In/I1 independent of the phase depth ϕ.

We also point out that the SHG tuning curve is obtained through the same procedure simply by replacing Q = e 1 with Q = −2 in Eq. (3), showing the mathematical equivalence between the SHG tuning curve and the diffraction pattern.

3. Experiment

For the demonstration of our method, we periodically poled a z-cut congruent LiNbO3 crystal plate by the standard electric field poling method using a photo-mask. In order to produce a phase grating for the diffraction experiment, the original negative z-face of the periodically poled LiNbO3 (PPLN) sample was slightly etched with an acid solution, giving a uniform depth of 31 ± 2 nm throughout the channel. For our sample, we observed that the domain boundaries were almost parallel to the ferroelectric axis, confirming that the etched surface grating structure is an accurate projection of the QPM structure. The grating channel was about 10 mm long and 3 mm wide, with a period of 21.2 μm.

We used a He-Ne laser (633 nm, 2.5 mW) as a light source for the diffraction experiment. The laser beam was expanded and collimated by a pair of cylindrical lenses, illuminating the PPLN grating channel at normal incidence. The grating region of 10 mm was uniformly illuminated by limiting the input beam with a pair of blockers placed directly in front of the sample. We used a convex lens with a focal length of 1 m just behind the sample, in order to obtain the far-field diffraction pattern at the focal plane. A CCD-camera was used to record a rough diffraction pattern, shown as the inset of Fig. 2(a). For a quantitative measurement of the intensity, however, a Si-photodetector replaced the CCD-camera due to its poor linearity. The Si-photodetector with an attached slit was scanned along the diffraction pattern on the Fourier plane. A slit width of 0.05 mm was used to resolve the intensity profiles of the narrow orders, while it was increased to 3.0 mm in the noise region. A greater slit width not only smoothens the background noise, but also helps enhance detection sensitivity by increasing the amount of light received by the detector. For comparison, we performed the same experiment on a reference grating (period 26 μm), which was made on a glass plate as a thin photoresist grating. We took microscopic pictures of both the PPLN and the reference grating, and measured the domain widths for verifying the validity of the suggested diffraction method.

 figure: Fig. 2

Fig. 2 Far-field diffraction patterns for PPLN (a) and reference grating (b). Inset of (a) is a CCD-image. Two bright spots indicate the first and second orders (look larger due to saturation of CCD). The region between them was enhanced to show small diffraction noise. Solid curves were calculated by Eq. (3) with ε = 10% for PPLN (a) and ε = 1.7% for the reference (b).

Download Full Size | PPT Slide | PDF

4. Results and analysis

The far-field diffraction pattern from our PPLN sample is shown in Fig. 2 in comparison with that from the reference grating. The graphs were normalized to the first order intensity I1. For PPLN, the measured diffraction noise was In/I1 = 1.2 × 10−4, from which we could estimate the STD using Eq. (4), ε = 10% of the grating period. The average duty ratio R¯ could be estimated directly from the microscopic picture or from the ratio of the intensities of the two orders, I2/I1 [10]. The two methods gave R¯ = 0.46 and 0.41, respectively, for the PPLN. This difference puts 0.3% additional uncertainty in the estimation of ε. For the reference grating, R¯ = 0.49 and 0.45 from the direct microscopic observation and the measured I2/I1 value, respectively, and a small value of ε = 1.7% was obtained from the measured value of In/I1 = 4.1 × 10−6.

In the above evaluation using Eq. (4), we took the noise intensity averaged around X = 1.5 (midpoint between the first and the second orders). However, the choice of this specific spatial frequency is somewhat arbitrary, in the sense that the noise intensity is not minimal at this point, but continues to decrease slightly with spatial frequency. Taking the noise intensity at the real minimum would not give more valuable data, because small contributions from the tails of the strong orders cannot be separated anyway. These contributions can be significantly reduced by a Gaussian beam input that creates smaller tails than the rect-beam [13].

A broad shoulder is observed for PPLN in the spatial frequency range of 1< X <1.4, and is more significant than that for the reference grating. If we fit the noise data in this range instead of the noise value at X = 1.5, the STD would be 14.5%. Although further investigation is necessary to understand the sources of the additional noise, one of the causes could be the departure of the real PPLN grating from our simple one-dimensional model defined by Eq. (1). Microscopic observation revealed that the reference grating is almost uniform in the y-direction perpendicular to the grating vector, where the one-dimensional model can be ideally applied. However, the PPLN grating had disorder not only in the x-direction, but also in the y-direction. Direct measurement of the domain wall width was carried out along a single horizontal line parallel to the x-axis, while the diffraction measurement used a natural laser beam width of ~1 mm in the y-dimension, which contains additional disorder, and could produce more noise in some spatial frequency region. The shoulder could be reduced if one minimizes the y-dimension of the illuminated area by focusing the input beam in this direction.

In order to verify the validity of the suggested diffraction method, we statistically analyzed the microscopic image of the PPLN grating. Figure 3 shows the histograms representing the statistics of the poled and unpoled domain widths in the 10 mm-long grating. For the poled domains [Fig. 3(a)], the average domain width was 9.8 μm, and the STD was 2.0 μm (ε = 9.4%), supporting the results obtained from the diffraction experiment. For the unpoled domains [Fig. 3(b)], the average domain width was 11.4 μm, and the STD was the same, as expected. The same analysis has been carried out on the reference grating. We obtained a relative STD of 1.5%, which also confirms the value of 1.7% obtained by the diffraction method within the measurement uncertainty. The STD always tends to be overestimated due to the finite slit width used in the measurement of the first order peak intensity. More accurate STD values could have been obtained by using a narrower slit or a long focal length lens for Fourier transform.

 figure: Fig. 3

Fig. 3 Histograms showing statistics of the widths of poled (a) and unpoled (b) domains with corresponding Gaussian distributions.

Download Full Size | PPT Slide | PDF

The statistical RDE information obtained by the above diffraction noise method gives the equivalent information that could be acquired by the tunable SHG experiment, where the equivalence has been verified in [10]. Furthermore, we can predict the parasitic noise in any frequency conversion process based on the estimated STD, as long as the pump wave depletion is not significant.

The diffraction noise measurement provides a versatile method for quantifying the poling quality of QPM devices, as long as the surface-etched structure projects the (averaged) ferroelectric domain structure. This condition may not be satisfied if the domain boundaries are not parallel to the ferroelectric axis (“slant domains”). In this case, the domain widths vary along the axis, resulting in a distributed duty ratio. Then, the diffraction pattern would not give the same information as in the SHG spectrum, because SHG would average the effects within the beam area. However, the RDE information obtained on the surface can still provide an essential figure for the poling quality for the slant domains in the crystal plate.

Another important point in the diffraction experiment is that surface etching is not required for PPLNs made of congruent LiNbO3. Such PPLNs showed a diffraction pattern due to a small refractive index modulation between the poled and unpoled domains even without etching, resulting in the same quality estimation [10]. The index contrast was attributed to the stress field formed after the domain inversion. Further investigations are needed for other periodically poled ferroelectric crystals.

Finally, we should mention that a photodetector was scanned along the diffraction pattern in order to ensure linearity in this experiment. However, a CCD-camera with good linearity (or carefully calibrated CCD) can be used to obtain the diffraction pattern without scanning, shortening the measurement time dramatically.

5. Conclusion

We proposed diffraction noise measurement to evaluate the poling quality of PPLN. With this method, we quantified the statistical information about the duty-cycle error by analyzing the diffraction pattern. Our proposed method can provide a fast, low-cost, but accurate tool for evaluating the microscopic quality, and predicting the frequency conversion performance of QPM devices. Although random duty-cycle errors are inherent in the fabrication of ferroelectric QPM devices, our method can provide fast feedback to the poling process facilitating efficient quality control, for both users and manufacturers.

Acknowledgments

This work was supported by the Korea Research Institute of Standards and Science under the “Metrology Research Center” project. We appreciate M. M. Fejer for suggesting a key idea.

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. 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]  

3. J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, “Influence of domain disorder on parametric noise in quasi-phase-matched quantum frequency converters,” Opt. Lett. 35(16), 2804–2806 (2010). [CrossRef]   [PubMed]  

4. C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30(13), 1725–1727 (2005). [CrossRef]   [PubMed]  

5. M. A. Albota and F. N. Wong, “Efficient single-photon counting at 1.55 μm by means of frequency upconversion,” Opt. Lett. 29(13), 1449–1451 (2004). [CrossRef]   [PubMed]  

6. S. Kurimura and Y. Uesu, “Application of the second harmonic generation microscope to nondestructive observation of periodically poled ferroelectric domain in quasi-phase-matched wavelength converters,” J. Appl. Phys. 81(1), 369–375 (1997). [CrossRef]  

7. Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000). [CrossRef]  

8. V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B 78(3–4), 363–366 (2004). [CrossRef]  

9. G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005). [CrossRef]  

10. K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Nondestructive quality evaluation of periodically poled lithium niobate crystals by diffraction,” Opt. Express 17(20), 17862–17867 (2009). [CrossRef]   [PubMed]  

11. K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).

12. C. R. Phillips, J. S. Pelc, and M. M. Fejer, “Parametric processes in quasi-phasematching gratings with random duty cycle errors,” J. Opt. Soc. Am. B 30(4), 982–993 (2013). [CrossRef]  

13. Manuscript in preparation by the authors.

References

  • View by:

  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. 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]
  3. J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, “Influence of domain disorder on parametric noise in quasi-phase-matched quantum frequency converters,” Opt. Lett. 35(16), 2804–2806 (2010).
    [Crossref] [PubMed]
  4. C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30(13), 1725–1727 (2005).
    [Crossref] [PubMed]
  5. M. A. Albota and F. N. Wong, “Efficient single-photon counting at 1.55 μm by means of frequency upconversion,” Opt. Lett. 29(13), 1449–1451 (2004).
    [Crossref] [PubMed]
  6. S. Kurimura and Y. Uesu, “Application of the second harmonic generation microscope to nondestructive observation of periodically poled ferroelectric domain in quasi-phase-matched wavelength converters,” J. Appl. Phys. 81(1), 369–375 (1997).
    [Crossref]
  7. Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000).
    [Crossref]
  8. V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B 78(3–4), 363–366 (2004).
    [Crossref]
  9. G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
    [Crossref]
  10. K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Nondestructive quality evaluation of periodically poled lithium niobate crystals by diffraction,” Opt. Express 17(20), 17862–17867 (2009).
    [Crossref] [PubMed]
  11. K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).
  12. C. R. Phillips, J. S. Pelc, and M. M. Fejer, “Parametric processes in quasi-phasematching gratings with random duty cycle errors,” J. Opt. Soc. Am. B 30(4), 982–993 (2013).
    [Crossref]
  13. Manuscript in preparation by the authors.

2013 (1)

2011 (1)

2010 (1)

2009 (2)

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Nondestructive quality evaluation of periodically poled lithium niobate crystals by diffraction,” Opt. Express 17(20), 17862–17867 (2009).
[Crossref] [PubMed]

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).

2005 (2)

C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30(13), 1725–1727 (2005).
[Crossref] [PubMed]

G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
[Crossref]

2004 (2)

V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B 78(3–4), 363–366 (2004).
[Crossref]

M. A. Albota and F. N. Wong, “Efficient single-photon counting at 1.55 μm by means of frequency upconversion,” Opt. Lett. 29(13), 1449–1451 (2004).
[Crossref] [PubMed]

2000 (1)

Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000).
[Crossref]

1997 (1)

S. Kurimura and Y. Uesu, “Application of the second harmonic generation microscope to nondestructive observation of periodically poled ferroelectric domain in quasi-phase-matched wavelength converters,” J. Appl. Phys. 81(1), 369–375 (1997).
[Crossref]

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. 28(11), 2631–2654 (1992).
[Crossref]

Albota, M. A.

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]

Cha, M.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Nondestructive quality evaluation of periodically poled lithium niobate crystals by diffraction,” Opt. Express 17(20), 17862–17867 (2009).
[Crossref] [PubMed]

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).

Chang, D.

Diamanti, E.

Dierolf, V.

V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B 78(3–4), 363–366 (2004).
[Crossref]

Fejer, M. M.

Galvanauskas, A.

Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000).
[Crossref]

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]

Kang, C. H.

G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
[Crossref]

Kang, Y. S.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Nondestructive quality evaluation of periodically poled lithium niobate crystals by diffraction,” Opt. Express 17(20), 17862–17867 (2009).
[Crossref] [PubMed]

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).

Kim, B. J.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Nondestructive quality evaluation of periodically poled lithium niobate crystals by diffraction,” Opt. Express 17(20), 17862–17867 (2009).
[Crossref] [PubMed]

Kitaeva, G. K.

G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
[Crossref]

Kurimura, S.

S. Kurimura and Y. Uesu, “Application of the second harmonic generation microscope to nondestructive observation of periodically poled ferroelectric domain in quasi-phase-matched wavelength converters,” J. Appl. Phys. 81(1), 369–375 (1997).
[Crossref]

Langrock, C.

Lee, Y.-S.

Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000).
[Crossref]

Lim, H. H.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Nondestructive quality evaluation of periodically poled lithium niobate crystals by diffraction,” Opt. Express 17(20), 17862–17867 (2009).
[Crossref] [PubMed]

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).

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]

Meade, T.

Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000).
[Crossref]

Naudeau, M. L.

Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000).
[Crossref]

Naumova, I. I.

G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
[Crossref]

Norris, T. B.

Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000).
[Crossref]

Pandiyan, K.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Nondestructive quality evaluation of periodically poled lithium niobate crystals by diffraction,” Opt. Express 17(20), 17862–17867 (2009).
[Crossref] [PubMed]

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).

Pelc, J. S.

Penin, A. N.

G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
[Crossref]

Phillips, C. R.

Roussev, R. V.

Sandmann, C.

V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B 78(3–4), 363–366 (2004).
[Crossref]

Takesue, H.

Tang, S. H.

G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
[Crossref]

Tishkova, V. V.

G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
[Crossref]

Uesu, Y.

S. Kurimura and Y. Uesu, “Application of the second harmonic generation microscope to nondestructive observation of periodically poled ferroelectric domain in quasi-phase-matched wavelength converters,” J. Appl. Phys. 81(1), 369–375 (1997).
[Crossref]

Wong, F. N.

Yamamoto, Y.

Zhang, Q.

Appl. Phys. B (2)

V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B 78(3–4), 363–366 (2004).
[Crossref]

G. K. Kitaeva, V. V. Tishkova, I. I. Naumova, A. N. Penin, C. H. Kang, and S. H. Tang, “Mapping of periodically poled crystals via spontaneous parametric down-conversion,” Appl. Phys. B 81(5), 645–650 (2005).
[Crossref]

Appl. Phys. Lett. (1)

Y.-S. Lee, T. Meade, M. L. Naudeau, T. B. Norris, and A. Galvanauskas, “Domain mapping of periodically poled lithium niobate via terahertz wave form analysis,” Appl. Phys. Lett. 77(16), 2488–2490 (2000).
[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. 28(11), 2631–2654 (1992).
[Crossref]

J. Appl. Phys. (1)

S. Kurimura and Y. Uesu, “Application of the second harmonic generation microscope to nondestructive observation of periodically poled ferroelectric domain in quasi-phase-matched wavelength converters,” J. Appl. Phys. 81(1), 369–375 (1997).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (4)

Proc. SPIE (1)

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, and M. Cha, “Quality evaluation of quasi‐ phase‐ matched devices by far‐field diffraction pattern analysis,” Proc. SPIE 7197, 71970R (2009).

Other (1)

Manuscript in preparation by the authors.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1 Schematic diagram of random domain model. (Ps: spontaneous polarization)
Fig. 2
Fig. 2 Far-field diffraction patterns for PPLN (a) and reference grating (b). Inset of (a) is a CCD-image. Two bright spots indicate the first and second orders (look larger due to saturation of CCD). The region between them was enhanced to show small diffraction noise. Solid curves were calculated by Eq. (3) with ε = 10% for PPLN (a) and ε = 1.7% for the reference (b).
Fig. 3
Fig. 3 Histograms showing statistics of the widths of poled (a) and unpoled (b) domains with corresponding Gaussian distributions.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

t(x)=rect( x L )+ k=1 N Qrect[ x x k r + x k l 2 x k r x k l ]
E(ξ)=A t(x) e 2iπξx dx
I(ξ)= B | Q | 2 (Λξ) 2 [ 1 2N (1f(ξ))+f(ξ) sin 2 (πξΛ R ¯ ) ( sin(πΛNξ) Nsin(πΛξ) ) 2 ]
I n I 1 = I(X=1.5) I(X=1) (πε) 2 2N sin 2 (π R ¯ )

Metrics