Evaluation of domain randomness in periodically poled lithium niobate by diffraction noise measurement Prashant Povel Dwivedi, Hee Joo Choi, Byoung Joo Kim, and Myoungsik Cha* Department of Physics, Pusan National University, Busan 609-735, South Korea * [email protected]
Abstract: Random duty-cycle errors (RDE) in ferroelectric quasi-phasematching (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 OCIS codes: (190.4360) Nonlinear optics, devices; (160.2260) Ferroelectrics; (050.1950) Diffraction gratings; (160.3730) Lithium niobate.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
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). 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). J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, “Influence of domain disorder on parametric noise in quasiphase-matched quantum frequency converters,” Opt. Lett. 35(16), 2804–2806 (2010). C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient singlephoton detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30(13), 1725–1727 (2005). 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). 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). 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). V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B 78(3–4), 363–366 (2004). 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). 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). 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). 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). Manuscript in preparation by the authors.
#197705 - $15.00 USD Received 13 Sep 2013; revised 2 Nov 2013; accepted 12 Nov 2013; published 2 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.030221 | OPTICS EXPRESS 30221
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 [2– 5]. 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, 6–9]. 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 ‘preaveraging’ 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
#197705 - $15.00 USD Received 13 Sep 2013; revised 2 Nov 2013; accepted 12 Nov 2013; published 2 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.030221 | OPTICS EXPRESS 30222
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 / 2 and xkl = ck − wkl / 2 are the coordinates of the right and the left boundaries of the poled domain, respectively.
x rk
x kl
1 2
w kl
1 2
w rk
Fig. 1. Schematic diagram of random domain model. (Ps: spontaneous polarization)
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: x r + xkl x− k N x t ( x ) = rect( ) + Q rect[ r 2 l ] (1) L k =1 xk − xk where L = NΛ is the length of the grating under uniform illumination, Q = eiφ − 1 , 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 ) = A t ( x )e −2iπξ x dx
(2)
−∞
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: 2
BQ 1 sin(πΛN ξ ) 2 I (ξ ) = [ (1 − f (ξ )) + f (ξ ) sin 2 (πξΛR )( ) ] 2 ( Λξ ) 2 N N sin(πΛξ )
(3)
2
where B is a constant, the function f (ξ ) = e − (πσξ ) contains 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 (X ≡ Λξ = 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
#197705 - $15.00 USD Received 13 Sep 2013; revised 2 Nov 2013; accepted 12 Nov 2013; published 2 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.030221 | OPTICS EXPRESS 30223
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 (ε ≡ σ/Λ
Abstract: Random duty-cycle errors (RDE) in ferroelectric quasi-phasematching (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 OCIS codes: (190.4360) Nonlinear optics, devices; (160.2260) Ferroelectrics; (050.1950) Diffraction gratings; (160.3730) Lithium niobate.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
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). 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). J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, “Influence of domain disorder on parametric noise in quasiphase-matched quantum frequency converters,” Opt. Lett. 35(16), 2804–2806 (2010). C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient singlephoton detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30(13), 1725–1727 (2005). 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). 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). 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). V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B 78(3–4), 363–366 (2004). 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). 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). 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). 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). Manuscript in preparation by the authors.
#197705 - $15.00 USD Received 13 Sep 2013; revised 2 Nov 2013; accepted 12 Nov 2013; published 2 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.030221 | OPTICS EXPRESS 30221
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 [2– 5]. 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, 6–9]. 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 ‘preaveraging’ 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
#197705 - $15.00 USD Received 13 Sep 2013; revised 2 Nov 2013; accepted 12 Nov 2013; published 2 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.030221 | OPTICS EXPRESS 30222
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 / 2 and xkl = ck − wkl / 2 are the coordinates of the right and the left boundaries of the poled domain, respectively.
x rk
x kl
1 2
w kl
1 2
w rk
Fig. 1. Schematic diagram of random domain model. (Ps: spontaneous polarization)
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: x r + xkl x− k N x t ( x ) = rect( ) + Q rect[ r 2 l ] (1) L k =1 xk − xk where L = NΛ is the length of the grating under uniform illumination, Q = eiφ − 1 , 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 ) = A t ( x )e −2iπξ x dx
(2)
−∞
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: 2
BQ 1 sin(πΛN ξ ) 2 I (ξ ) = [ (1 − f (ξ )) + f (ξ ) sin 2 (πξΛR )( ) ] 2 ( Λξ ) 2 N N sin(πΛξ )
(3)
2
where B is a constant, the function f (ξ ) = e − (πσξ ) contains 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 (X ≡ Λξ = 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
#197705 - $15.00 USD Received 13 Sep 2013; revised 2 Nov 2013; accepted 12 Nov 2013; published 2 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.030221 | OPTICS EXPRESS 30223
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 (ε ≡ σ/Λ
