Backward frequency doubling of near infrared picosecond pulses Alessandro C. Busacca,1,* Salvatore Stivala,1 Luciano Curcio,1 Alessandro Tomasino1 and Gaetano Assanto2 2
1 Laboratory of Optics and OptoelectroniX (LOOX), DEIM, University of Palermo, 90128 Palermo, Italy Nonlinear Optics and OptoElectronics Lab (NooEL), University of Rome “Roma Tre”, 00146 Rome, Italy * [email protected]
Abstract: We report on backward second-harmonic generation using ps laser pulses in congruent lithium niobate with 3.2 µm periodic poling. Three resonant peaks were measured between 1530 and 1730 nm, corresponding to 16th, 17th and 18th quasi-phase-matching orders in the backward configuration, with a conversion efficiency of 4.75 x 10-5%/W for the 16th order. We could also discriminate the contributions from inverted domains randomized in duty-cycle. ©2014 Optical Society of America OCIS codes: (190.4410) Nonlinear optics, parametric processes; (190.2620) Harmonic generation and mixing; (320.5390) Picosecond phenomena.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
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). A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First order quasi-phase matched blue light generation in surface poled Ti-indiffused lithium niobate waveguide,” Appl. Phys. Lett. 84(22), 4430–4432 (2004). S. Stivala, A. Pasquazi, L. Colace, G. Assanto, A. C. Busacca, M. Cherchi, S. Riva-Sanseverino, A. C. Cino, and A. Parisi, “Guided-wave frequency doubling in surface periodically poled lithium niobate: competing effects,” J. Opt. Soc. Am. B 24(7), 1564–1570 (2007). Y. J. Ding, J. U. Kang, and J. B. Khurgin, “Theory of backward second-harmonic generation using laser pulses in quasi-phase-matched second-order nonlinear media,” IEEE J. Quantum Electron. 34(6), 966–974 (1998). X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, “Backward second-harmonic and third-harmonic generation in a periodically poled potassium titanyl phosphate waveguide,” Opt. Lett. 24(3), 127–129 (1999). X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, “Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide,” Opt. Commun. 181(1-3), 153–159 (2000). C. Canalias, V. Pasiskevicius, M. Fokine, and F. Laurell, “Backward quasi-phase-matched second-harmonic generation in submicrometer periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 86(18), 181105 (2005). S. Stivala, A. C. Busacca, L. Curcio, R. L. Oliveri, S. Riva-Sanseverino, and G. Assanto, “Continuous-wave backward frequency doubling in periodically poled lithium niobate,” Appl. Phys. Lett. 96(11), 111110 (2010). S. Janz, C. Fernando, H. Dai, F. Chatenoud, M. Dion, and R. Normandin, “Quasi-phase-matched secondharmonic generation in reflection from AlxGa1-xAs heterostructures,” Opt. Lett. 18(8), 589–591 (1993). J. U. Kang, Y. J. Ding, W. K. Burns, and J. S. Melinger, “Backward second-harmonic generation in periodically poled bulk LiNbO3.,” Opt. Lett. 22(12), 862–864 (1997). X. Gu, R. Y. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, “Backward second-harmonic generation in periodically poled lithium niobate,” J. Opt. Soc. Am. B 15(5), 1561–1566 (1998). G. D. Landry and T. A. Maldonado, “Counterpropagating quasi-phase matching: a generalized analysis,” J. Opt. Soc. Am. B 21(8), 1509–1521 (2004). M. Clerici, L. Caspani, E. Rubino, M. Peccianti, M. Cassataro, A. Busacca, T. Ozaki, D. Faccio, and R. Morandotti, “Counterpropagating frequency mixing with terahertz waves in diamond,” Opt. Lett. 38(2), 178–180 (2013). M. Peccianti, M. Clerici, A. Pasquazi, L. Caspani, S. P. Ho, F. Buccheri, J. Ali, A. Busacca, T. Ozaki, and R. Morandotti, “Exact reconstruction of THz sub-λ source features in knife-edge measurements,” IEEE J. Sel. Top. Quantum Electron. 19(1), 8401211 (2013). A. Tomasino, A. Parisi, S. Stivala, P. Livreri, A. C. Cino, A. C. Busacca, M. Peccianti, and R. Morandotti, “Wideband THz Time Domain Spectroscopy based on Optical Rectification and Electro-Optic sampling,” Sci Rep 3, 3116 (2013). C. Conti, S. Trillo, and G. Assanto, “Energy localization in photonic crystals of a purely nonlinear origin,” Phys. Rev. Lett. 85(12), 2502–2505 (2000).
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7544
17. C. Canalias and V. Pasiskevicius, “Mirrorless optical parametric oscillator,” Nat. Photonics 1(8), 459–462 (2007). 18. M. Conforti, C. de Angelis, U. K. Sapaev, and G. Assanto, “Pulse shaping via backward second harmonic generation,” Opt. Express 16(3), 2115–2121 (2008). 19. Y. J. Ding, “Phase conjugation based on single backward second-order nonlinear parametric process,” Opt. Lett. 37(22), 4792–4794 (2012). 20. R. Iliew, C. Etrich, T. Pertsch, F. Lederer, and Y. S. Kivshar, “Huge enhancement of backward second-harmonic generation with slow light in photonic crystals,” Phys. Rev. A 81(2), 023820 (2010). 21. M. Lauritano, A. Parini, G. Bellanca, S. Trillo, M. Conforti, A. Locatelli, and C. De Angelis, “Bistability, limiting, and self-pulsing in backward second-harmonic generation: a time-domain approach,” J. Opt. A 8(7), S494–S501 (2006). 22. A. C. Busacca, C. Sones, V. Apostopoulos, R. Eason, and S. Mailis, “Surface domain engineering in congruent lithium niobate single crystals: A route to submicron periodic poling,” Appl. Phys. Lett. 81(26), 4946–4948 (2002). 23. A. C. Busacca, A. C. Cino, S. Riva Sanseverino, M. Ravaro, and G. Assanto, “Silica masks for improved surface poling of lithium niobate,” Electron. Lett. 41(2), 92–94 (2005). 24. E. Glavas, J. M. Cabrera, and P. D. Townsend, “A comparison of optical damage in different types of LiNbO3 waveguides,” J. Phys. D 22(5), 611–616 (1989). 25. S. Stivala, A. C. Busacca, A. Pasquazi, R. L. Oliveri, R. Morandotti, and G. Assanto, “Random quasi-phasematched second-harmonic generation in periodically poled lithium tantalate,” Opt. Lett. 35(3), 363–365 (2010). 26. C. Conti, E. D’Asaro, S. Stivala, A. Busacca, and G. Assanto, “Parametric self-trapping in the presence of randomized quasi phase matching,” Opt. Lett. 35(22), 3760–3762 (2010). 27. A. Pasquazi, A. C. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010). 28. S. Stivala, F. Buccheri, L. Curcio, R. L. Oliveri, A. C. Busacca, and G. Assanto, “Features of randomized electric-field assisted domain inversion in lithium tantalate,” Opt. Express 19(25), 25780–25785 (2011). 29. R. W. Boyd, Nonlinear Optics (Academic Press, 2008). 30. http://www.goochandhousego.com/products//technical-info-ln/LNmatProperties.pdf 31. J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, “Light absorption in undoped congruent and magnesium-doped lithium niobate crystals in the visible wavelength range,” Appl. Phys. B 100(1), 109–115 (2010). 32. C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, J. Jiang, M. E. Fermann, and I. Hartl, “Supercontinuum generation in quasi-phase-matched LiNbO3 waveguide pumped by a Tm-doped fiber laser system,” Opt. Lett. 36(19), 3912–3914 (2011). 33. M. Bache and F. W. Wise, “Type-I cascaded quadratic soliton compression in lithium niobate: Compressing femtosecond pulses from high-power fiber lasers,” Phys. Rev. A 81(5), 053815 (2010).
1. Introduction Optical parametric interactions including second-harmonic generation (SHG) are well established in non-centrosymmetric ferroelectric crystals subjected to periodic electric-field poling in order to achieve quasi-phase-matching (QPM) [1–3]. If the poling period is short enough, QPM SHG can occur between fundamental frequency (FF) and SH waves traveling in opposite directions, yielding backward-SHG (BSHG) [4–8]. Since BSHG conversion depends on the QPM-order yielding phase matching, higher conversion efficiencies require lower QPM-orders and, consequently, short subwavelength periods. QPM-BSHG was first demonstrated in multilayer semiconductor heterostructures [9] and in periodically poled lithium niobate (PPLN) crystals [10, 11]. Since then, counter-propagating geometries were analyzed and, in a few cases, demonstrated towards various second order nonlinear optical effects, including gap solitons, mirrorless parametric oscillators, pulse shaping and phase conjugation [12–19]. Theoretical and numerical studies on BSHG enhancement, bistability and self-pulsing were carried out in recent years [20, 21]. BSHG experiments were reported with continuous waves (cw) [7, 8] and either ns or fs pulses [5, 6, 10, 11]. In this paper we present what we believe are the first results on picosecond backward frequency doubling of near infrared laser pulses in a 3.2 µm PPLN crystal, 3 mm in length. By
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7545
Fig. 1. (a) Scanning electron microphotograph of the 3.2 µm periodically poled sample as it appears after chemical etching in hydrofluoric acid. (b) Experimental setup for BSHG measurements. HWP: half-wave-plate; BS: beam splitter; PD: photodetector, PPLN: periodically poled lithium niobate sample.
tuning both the pump wavelength and the sample temperature, we observed three BSHG resonant peaks in the range 1530-1730 nm, corresponding to 16th, 17th and 18th QPM orders, respectively. A maximum conversion efficiency of 0.475% was achieved at the 16th order with a 10kW peak pump power, i.e., 4.75 × 10-5%/W. The latter is the highest BSHG conversion reported in bulk to date, with an improvement >50% with respect to those previously achieved with ns pulses for the same order of resonance [11]. The use of ps excitation allows keeping the average power low, thus reducing the chance of photorefractive damage while avoiding dispersive effects. 2. Sample fabrication The samples were prepared in Z-cut 500µm-thick congruent lithium niobate crystals (Crystal TechnologyTM). Standard photolithography was used to define a grating of period Λ = 3.2 µm over a length L = 3 mm on a 2-µm-thick film of positive photoresist (ShipleyTM S1813) previously spin-coated on the -Z facet. After photoresist development, the pattern was softbaked overnight at 90 °C and then hard-baked for 3 hours at 130°C. The curing temperature was gradually raised in order to avoid failures due to the pyroelectric effect. This thermal process ensured a better adhesion of the photoresist on the crystal substrate whilst enhancing insulation during the poling, when samples were contacted by using gel-electrolyte layers and then subjected to high voltage pulses from an amplified waveform generator (AgilentTM). In order to exceed the coercive field and obtain a charge-controlled domain inversion in lithium niobate, we applied single 1.3 kV pulses over a 10 kV offset for appropriate time intervals. This approach allowed the inverted domains to enucleate from the -Z facet in the region under the electrodes and extend towards the + Z facet before eventually coalescing [22, 23]. Finally, the end-facets (FF input and output) of the chips were polished for optical coupling and characterization. An image of the grating -obtained by means of a SEM- is shown in Fig. 1(a). 3. Nonlinear characterization and data analysis For our measurements, we employed the set-up sketched in Fig. 1(b). The source was an optical parametric amplifier/oscillator (OPA/OPO) pumped by frequency-doubled pulse trains and single (cavity dumped) pulses from a picosecond Nd:YAG pump at 1.064 µm. The OPA/OPO provides 25 ps pulses at 10 Hz rep-rate, tunable in the range 0.72-2.1 µm with a linewidth of about 1.2 cm−1 in the near-infrared between 1.1 and 2.1 µm. Such pulse duration and repetition rate helped minimize the detrimental effects of photorefractive damage [24]. After spatial filtering to yield a TEM00 mode, the laser beam was gently focused by a 10x
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7546
Fig. 2. (a) FF wavelength scan showing three QPM peaks in BSHG conversion efficiency: the solid lines from the model [4] are in good agreement with the experimental data (circles). FF peak power were 10 kW, 8 kW and 15 kW for 16th, 17th and 18th orders, respectively. (b) Calculated BSHG conversion efficiency versus duty cycle for m = 16 (blue), 17 (red) and 18 (black), respectively. Each efficiency curve is normalized to its own maximum. Panels (c), (d) and (e) detail the tuning curves for 18th, 17th and 16th resonant orders, respectively.
microscope objective at the input of the periodically poled region to a waist (1/e2 radius) of about 20 µm, as evaluated by the knife-edge method. A Peltier cell and a temperature controller were employed to either keep the crystal at a constant temperature during wavelength tuning or perform temperature tuning during measurements at fixed wavelengths. An output microscope objective was not required in the BSHG set-up and a dichroic mirror helped separating the back-reflected FF pump from the generated backward-propagating SH. The output facet of the sample was slightly tilted in order to separate BSHG from the forward-SH emission due to randomized domain QPM and back-reflected. A randomized domain distribution, in fact, can yield broadband frequency doubling [8, 25, 26]. The input FF energy per pulse was measured with a pyroelectric detector. The energy of BSHG pulses was measured with a Si photodiode and a boxcar averager, whereas the BSHG intensity profile was imaged by a Si-CCD camera. Figure 2(a) and Figs. 2(c)-2(e) graphs the measured BSHG conversion efficiency versus FF wavelength (λFF): three resonant peaks are visible at 1535.1, 1623.9 and 1722.0 nm, corresponding to the 18th, 17th and 16th QPM orders for the backward configuration, respectively. The different SH offsets for various QPM orders can be ascribed to the random domain contributions, due to domain nucleation and spreading which lead to unequal conversion efficiencies [27, 28]. The generation of frequency-doubled light for both odd and even resonant QPM orders (m) stems from the unbalanced duty-cycle D of the nonlinear grating. Indeed, for D = 0.50 the effective quadratic nonlinearity d eff = 2 / (mπ ) sin(mπ D)d33 (with d33 the largest diagonal element of the second-order nonlinear susceptibility tensor) is zero for even QPM orders [1, 11]. However, the duty-cycle tends to slightly deviate from 50% in non-optimized cases and varies along the sample, with a substantial impact on BSHG efficiency for high QPM orders [8]. Figure 2(b) shows the dependence of the conversion efficiency on the duty-cycle: the value D = 53.13% (52.78%) maximizes the BSHG efficiency for the 16th (18th) resonant order, while the odd (17th) order yields the maximum conversion for D = 50.00%. The data presented in Fig. 2 for each
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7547
Fig. 3. BSHG conversion efficiency for the (a) 16th, (b) 17th and (c) 18th QPM order versus temperature. FF wavelength and peak power were 1722.0nm and 10 kW in (a); 1623.9nm and 8 kW in (b); 1535.1nm and 12 kW in (c), respectively.
Fig. 4. (a) Measured (circles) and calculated (solid line) BSHG energy vs input FF energy per pulse for the 16th resonant order. (b) Comparison between BSHG for m = 16 (blue circles) and the forward random-QPM SHG (red diamonds), the latter measured at the (FF) output.
resonance were acquired by slightly adjusting the sample position and orientation (with respect to the input pump beam) in order to maximize BSHG. Otherwise stated, each peak in conversion efficiency corresponds to a poled region where the duty-cycle distribution maximizes deff for each resonance [11]. The BSHG resonance for mth-order QPM is given by: ΔkQPM =
4π
λFF
(nFF + nSH ) −
2mπ = 0, Λ
(1)
where ΔkQPM is the wavevector mismatch, nFF and nSH are the extraordinary refractive indices [29] at FF and SH, respectively; the latter can be evaluated using the temperature-dependent Sellmeier equations (provided by the crystal supplier [30]). Equation (1) is satisfied for m = 16, 17, 18 at the experimentally observed resonant wavelengths when the QPM grating has periods Λ16 = 3.20053, Λ17 = 3.20128 and Λ18 = 3.19851 µm, respectively. These values are remarkably close to the nominal poling period, especially when considering that, as noted above, the three BSHG maxima correspond to distinct regions of the sample. The linewidth of our pump laser is between 230 and 290 pm in the range 1530-1725 nm. Using the experimental data in Fig. 2, we estimated the spectral bandwidth of each resonance; for the three orders the full width at half maximum (FWHM) are FWHM16 = 1233, FWHM17 = 520, and FWHM18 = 1860 pm, respectively. These values are about one order of magnitude larger than those calculated from Sellmeier equations according to [1]: 0.4429λm nSH − nFF ∂nFF 1 ∂nSH FWHM th = + − L λm ∂λ 2 ∂λ
−1
(2)
Equation (2) provides FWHMth(16) = 105, FWHMth(17) = 93 and FWHMth(18) = 83 pm, respectively. The discrepancy between measured and predicted bandwidths is ascribed to spatial non-uniformity of the domain distribution in both transverse (i.e. across the laser beam profile) and longitudinal coordinates [11]. We stress that group velocity dispersion plays no role in our measurements, as the dispersion length exceeds the sample length by orders of magnitude.
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7548
BSHG efficiency results versus temperature at fixed FF wavelengths, corresponding to the three BSHG resonances in Figs. 2(b)-2(d), are presented in Figs. 3(a)-3(c). For each resonant order, the BSHG signal exhibited a quadratic dependence on the FF pump. Figure 4(a) details the most efficient case (m = 16), whereas Fig. 4(b) compares BSHG via the 16th order (circles) and the forward SHG via randomized QPM in the range 1685-1740 nm (diamonds). The latter was measured at the FF (forward) output, on the opposite side of the sample with respect to the input facet. The data pinpoint the presence of frequency-doubled contributions with two distinct origins; hence, it was essential to separate backward propagating signals from those generated forward and reflected back by the output facet. The data in Fig. 4(b) provide further evidence that, although the acquired BSHG signal can be added to the reflected random-QPM SHG (as observed in the offsets in Fig. 2), we did not measure a spectral replica of the forward signal and could therefore discriminate the sought BSHG resonance. Finally, we compared measured and predicted BSHG conversion efficiency. Since we could not use the simplified expressions for quasi-cw or fs excitations [4], we considered Gaussian FF pulses of duration τ; the second harmonic pulses generated in a sample of length L then have the form: H (t ) = [ P ( 2 M b − 2T ) + P ( 2T ) − 1]2
(3)
with P(x) the integration of the normalized Gaussian probability function, Mb = L(nSH + nFF)/(τc) with c the speed of light in vacuum and T = t/τ a normalized time coordinate. In our work, for τ = 25 ps and L = 3 mm, we obtain M b ≈ 1.7 for the three BSHG resonances. By defining JH as the integral of H, i.e., J H =
+∞
−∞
H (T )dT , the SH conversion efficiency
can be expressed in terms of energy density per pulse as:
η=
+∞
−∞
I SH dt
I FFτ
=
2 η0 d332 I FF τ 2c2 J H
2nSH n (nSH + nFF ) Λ 2 FF
4
2
sin c 2 (
ΔkQPM L 2
)
(4)
with IFF and ISH the peak intensities at FF and SH, respectively. Equation (4) does not account for optical losses, as they are negligible for LN in the explored wavelength interval [30, 31]. We computed the conversion efficiency η from Eq. (4) using the material Sellmeier equations for the refractive indices and the actual values for sample length, pulse duration, FF peak intensity; d33 was the only fit parameter. The best fits of our data are shown as solid lines in Figs. 2(a) and 4(a), with d33 equal to 29.03, 27.32 and 25.13 pm/V, for m = 16, 17 and 18, respectively. These d33 values are in close agreement with those calculated from the nonlinearity d33 = 33 pm/V (provided by the crystal supplier [30]) around 1064 nm using the constant-Miller-delta scaling [29, 32, 33]. This confirms that the crystal nonlinearity was unaffected by the poling process, with an effectively optimized BSHG at the three resonant orders. 4. Conclusions
In conclusion, using 3.2 µm periodically poled crystals, we have observed - for the first time in the picosecond regime - BSHG in congruent Lithium Niobate at three near-infrared wavelengths corresponding to 16th, 17th and 18th QPM resonances, with a conversion efficiency as high as 0.475% for the lowest order, despite its parity. Our measurements discriminated the contributions from randomized duty-cycle QPM domains, with experimental data in agreement with a simple model for ps pulsed BSHG. Acknowledgments
We gratefully acknowledge E. D’Asaro for contributing to the experimental work.
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7549
1 Laboratory of Optics and OptoelectroniX (LOOX), DEIM, University of Palermo, 90128 Palermo, Italy Nonlinear Optics and OptoElectronics Lab (NooEL), University of Rome “Roma Tre”, 00146 Rome, Italy * [email protected]
Abstract: We report on backward second-harmonic generation using ps laser pulses in congruent lithium niobate with 3.2 µm periodic poling. Three resonant peaks were measured between 1530 and 1730 nm, corresponding to 16th, 17th and 18th quasi-phase-matching orders in the backward configuration, with a conversion efficiency of 4.75 x 10-5%/W for the 16th order. We could also discriminate the contributions from inverted domains randomized in duty-cycle. ©2014 Optical Society of America OCIS codes: (190.4410) Nonlinear optics, parametric processes; (190.2620) Harmonic generation and mixing; (320.5390) Picosecond phenomena.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
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). A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First order quasi-phase matched blue light generation in surface poled Ti-indiffused lithium niobate waveguide,” Appl. Phys. Lett. 84(22), 4430–4432 (2004). S. Stivala, A. Pasquazi, L. Colace, G. Assanto, A. C. Busacca, M. Cherchi, S. Riva-Sanseverino, A. C. Cino, and A. Parisi, “Guided-wave frequency doubling in surface periodically poled lithium niobate: competing effects,” J. Opt. Soc. Am. B 24(7), 1564–1570 (2007). Y. J. Ding, J. U. Kang, and J. B. Khurgin, “Theory of backward second-harmonic generation using laser pulses in quasi-phase-matched second-order nonlinear media,” IEEE J. Quantum Electron. 34(6), 966–974 (1998). X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, “Backward second-harmonic and third-harmonic generation in a periodically poled potassium titanyl phosphate waveguide,” Opt. Lett. 24(3), 127–129 (1999). X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, “Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide,” Opt. Commun. 181(1-3), 153–159 (2000). C. Canalias, V. Pasiskevicius, M. Fokine, and F. Laurell, “Backward quasi-phase-matched second-harmonic generation in submicrometer periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 86(18), 181105 (2005). S. Stivala, A. C. Busacca, L. Curcio, R. L. Oliveri, S. Riva-Sanseverino, and G. Assanto, “Continuous-wave backward frequency doubling in periodically poled lithium niobate,” Appl. Phys. Lett. 96(11), 111110 (2010). S. Janz, C. Fernando, H. Dai, F. Chatenoud, M. Dion, and R. Normandin, “Quasi-phase-matched secondharmonic generation in reflection from AlxGa1-xAs heterostructures,” Opt. Lett. 18(8), 589–591 (1993). J. U. Kang, Y. J. Ding, W. K. Burns, and J. S. Melinger, “Backward second-harmonic generation in periodically poled bulk LiNbO3.,” Opt. Lett. 22(12), 862–864 (1997). X. Gu, R. Y. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, “Backward second-harmonic generation in periodically poled lithium niobate,” J. Opt. Soc. Am. B 15(5), 1561–1566 (1998). G. D. Landry and T. A. Maldonado, “Counterpropagating quasi-phase matching: a generalized analysis,” J. Opt. Soc. Am. B 21(8), 1509–1521 (2004). M. Clerici, L. Caspani, E. Rubino, M. Peccianti, M. Cassataro, A. Busacca, T. Ozaki, D. Faccio, and R. Morandotti, “Counterpropagating frequency mixing with terahertz waves in diamond,” Opt. Lett. 38(2), 178–180 (2013). M. Peccianti, M. Clerici, A. Pasquazi, L. Caspani, S. P. Ho, F. Buccheri, J. Ali, A. Busacca, T. Ozaki, and R. Morandotti, “Exact reconstruction of THz sub-λ source features in knife-edge measurements,” IEEE J. Sel. Top. Quantum Electron. 19(1), 8401211 (2013). A. Tomasino, A. Parisi, S. Stivala, P. Livreri, A. C. Cino, A. C. Busacca, M. Peccianti, and R. Morandotti, “Wideband THz Time Domain Spectroscopy based on Optical Rectification and Electro-Optic sampling,” Sci Rep 3, 3116 (2013). C. Conti, S. Trillo, and G. Assanto, “Energy localization in photonic crystals of a purely nonlinear origin,” Phys. Rev. Lett. 85(12), 2502–2505 (2000).
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7544
17. C. Canalias and V. Pasiskevicius, “Mirrorless optical parametric oscillator,” Nat. Photonics 1(8), 459–462 (2007). 18. M. Conforti, C. de Angelis, U. K. Sapaev, and G. Assanto, “Pulse shaping via backward second harmonic generation,” Opt. Express 16(3), 2115–2121 (2008). 19. Y. J. Ding, “Phase conjugation based on single backward second-order nonlinear parametric process,” Opt. Lett. 37(22), 4792–4794 (2012). 20. R. Iliew, C. Etrich, T. Pertsch, F. Lederer, and Y. S. Kivshar, “Huge enhancement of backward second-harmonic generation with slow light in photonic crystals,” Phys. Rev. A 81(2), 023820 (2010). 21. M. Lauritano, A. Parini, G. Bellanca, S. Trillo, M. Conforti, A. Locatelli, and C. De Angelis, “Bistability, limiting, and self-pulsing in backward second-harmonic generation: a time-domain approach,” J. Opt. A 8(7), S494–S501 (2006). 22. A. C. Busacca, C. Sones, V. Apostopoulos, R. Eason, and S. Mailis, “Surface domain engineering in congruent lithium niobate single crystals: A route to submicron periodic poling,” Appl. Phys. Lett. 81(26), 4946–4948 (2002). 23. A. C. Busacca, A. C. Cino, S. Riva Sanseverino, M. Ravaro, and G. Assanto, “Silica masks for improved surface poling of lithium niobate,” Electron. Lett. 41(2), 92–94 (2005). 24. E. Glavas, J. M. Cabrera, and P. D. Townsend, “A comparison of optical damage in different types of LiNbO3 waveguides,” J. Phys. D 22(5), 611–616 (1989). 25. S. Stivala, A. C. Busacca, A. Pasquazi, R. L. Oliveri, R. Morandotti, and G. Assanto, “Random quasi-phasematched second-harmonic generation in periodically poled lithium tantalate,” Opt. Lett. 35(3), 363–365 (2010). 26. C. Conti, E. D’Asaro, S. Stivala, A. Busacca, and G. Assanto, “Parametric self-trapping in the presence of randomized quasi phase matching,” Opt. Lett. 35(22), 3760–3762 (2010). 27. A. Pasquazi, A. C. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010). 28. S. Stivala, F. Buccheri, L. Curcio, R. L. Oliveri, A. C. Busacca, and G. Assanto, “Features of randomized electric-field assisted domain inversion in lithium tantalate,” Opt. Express 19(25), 25780–25785 (2011). 29. R. W. Boyd, Nonlinear Optics (Academic Press, 2008). 30. http://www.goochandhousego.com/products//technical-info-ln/LNmatProperties.pdf 31. J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, “Light absorption in undoped congruent and magnesium-doped lithium niobate crystals in the visible wavelength range,” Appl. Phys. B 100(1), 109–115 (2010). 32. C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, J. Jiang, M. E. Fermann, and I. Hartl, “Supercontinuum generation in quasi-phase-matched LiNbO3 waveguide pumped by a Tm-doped fiber laser system,” Opt. Lett. 36(19), 3912–3914 (2011). 33. M. Bache and F. W. Wise, “Type-I cascaded quadratic soliton compression in lithium niobate: Compressing femtosecond pulses from high-power fiber lasers,” Phys. Rev. A 81(5), 053815 (2010).
1. Introduction Optical parametric interactions including second-harmonic generation (SHG) are well established in non-centrosymmetric ferroelectric crystals subjected to periodic electric-field poling in order to achieve quasi-phase-matching (QPM) [1–3]. If the poling period is short enough, QPM SHG can occur between fundamental frequency (FF) and SH waves traveling in opposite directions, yielding backward-SHG (BSHG) [4–8]. Since BSHG conversion depends on the QPM-order yielding phase matching, higher conversion efficiencies require lower QPM-orders and, consequently, short subwavelength periods. QPM-BSHG was first demonstrated in multilayer semiconductor heterostructures [9] and in periodically poled lithium niobate (PPLN) crystals [10, 11]. Since then, counter-propagating geometries were analyzed and, in a few cases, demonstrated towards various second order nonlinear optical effects, including gap solitons, mirrorless parametric oscillators, pulse shaping and phase conjugation [12–19]. Theoretical and numerical studies on BSHG enhancement, bistability and self-pulsing were carried out in recent years [20, 21]. BSHG experiments were reported with continuous waves (cw) [7, 8] and either ns or fs pulses [5, 6, 10, 11]. In this paper we present what we believe are the first results on picosecond backward frequency doubling of near infrared laser pulses in a 3.2 µm PPLN crystal, 3 mm in length. By
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7545
Fig. 1. (a) Scanning electron microphotograph of the 3.2 µm periodically poled sample as it appears after chemical etching in hydrofluoric acid. (b) Experimental setup for BSHG measurements. HWP: half-wave-plate; BS: beam splitter; PD: photodetector, PPLN: periodically poled lithium niobate sample.
tuning both the pump wavelength and the sample temperature, we observed three BSHG resonant peaks in the range 1530-1730 nm, corresponding to 16th, 17th and 18th QPM orders, respectively. A maximum conversion efficiency of 0.475% was achieved at the 16th order with a 10kW peak pump power, i.e., 4.75 × 10-5%/W. The latter is the highest BSHG conversion reported in bulk to date, with an improvement >50% with respect to those previously achieved with ns pulses for the same order of resonance [11]. The use of ps excitation allows keeping the average power low, thus reducing the chance of photorefractive damage while avoiding dispersive effects. 2. Sample fabrication The samples were prepared in Z-cut 500µm-thick congruent lithium niobate crystals (Crystal TechnologyTM). Standard photolithography was used to define a grating of period Λ = 3.2 µm over a length L = 3 mm on a 2-µm-thick film of positive photoresist (ShipleyTM S1813) previously spin-coated on the -Z facet. After photoresist development, the pattern was softbaked overnight at 90 °C and then hard-baked for 3 hours at 130°C. The curing temperature was gradually raised in order to avoid failures due to the pyroelectric effect. This thermal process ensured a better adhesion of the photoresist on the crystal substrate whilst enhancing insulation during the poling, when samples were contacted by using gel-electrolyte layers and then subjected to high voltage pulses from an amplified waveform generator (AgilentTM). In order to exceed the coercive field and obtain a charge-controlled domain inversion in lithium niobate, we applied single 1.3 kV pulses over a 10 kV offset for appropriate time intervals. This approach allowed the inverted domains to enucleate from the -Z facet in the region under the electrodes and extend towards the + Z facet before eventually coalescing [22, 23]. Finally, the end-facets (FF input and output) of the chips were polished for optical coupling and characterization. An image of the grating -obtained by means of a SEM- is shown in Fig. 1(a). 3. Nonlinear characterization and data analysis For our measurements, we employed the set-up sketched in Fig. 1(b). The source was an optical parametric amplifier/oscillator (OPA/OPO) pumped by frequency-doubled pulse trains and single (cavity dumped) pulses from a picosecond Nd:YAG pump at 1.064 µm. The OPA/OPO provides 25 ps pulses at 10 Hz rep-rate, tunable in the range 0.72-2.1 µm with a linewidth of about 1.2 cm−1 in the near-infrared between 1.1 and 2.1 µm. Such pulse duration and repetition rate helped minimize the detrimental effects of photorefractive damage [24]. After spatial filtering to yield a TEM00 mode, the laser beam was gently focused by a 10x
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7546
Fig. 2. (a) FF wavelength scan showing three QPM peaks in BSHG conversion efficiency: the solid lines from the model [4] are in good agreement with the experimental data (circles). FF peak power were 10 kW, 8 kW and 15 kW for 16th, 17th and 18th orders, respectively. (b) Calculated BSHG conversion efficiency versus duty cycle for m = 16 (blue), 17 (red) and 18 (black), respectively. Each efficiency curve is normalized to its own maximum. Panels (c), (d) and (e) detail the tuning curves for 18th, 17th and 16th resonant orders, respectively.
microscope objective at the input of the periodically poled region to a waist (1/e2 radius) of about 20 µm, as evaluated by the knife-edge method. A Peltier cell and a temperature controller were employed to either keep the crystal at a constant temperature during wavelength tuning or perform temperature tuning during measurements at fixed wavelengths. An output microscope objective was not required in the BSHG set-up and a dichroic mirror helped separating the back-reflected FF pump from the generated backward-propagating SH. The output facet of the sample was slightly tilted in order to separate BSHG from the forward-SH emission due to randomized domain QPM and back-reflected. A randomized domain distribution, in fact, can yield broadband frequency doubling [8, 25, 26]. The input FF energy per pulse was measured with a pyroelectric detector. The energy of BSHG pulses was measured with a Si photodiode and a boxcar averager, whereas the BSHG intensity profile was imaged by a Si-CCD camera. Figure 2(a) and Figs. 2(c)-2(e) graphs the measured BSHG conversion efficiency versus FF wavelength (λFF): three resonant peaks are visible at 1535.1, 1623.9 and 1722.0 nm, corresponding to the 18th, 17th and 16th QPM orders for the backward configuration, respectively. The different SH offsets for various QPM orders can be ascribed to the random domain contributions, due to domain nucleation and spreading which lead to unequal conversion efficiencies [27, 28]. The generation of frequency-doubled light for both odd and even resonant QPM orders (m) stems from the unbalanced duty-cycle D of the nonlinear grating. Indeed, for D = 0.50 the effective quadratic nonlinearity d eff = 2 / (mπ ) sin(mπ D)d33 (with d33 the largest diagonal element of the second-order nonlinear susceptibility tensor) is zero for even QPM orders [1, 11]. However, the duty-cycle tends to slightly deviate from 50% in non-optimized cases and varies along the sample, with a substantial impact on BSHG efficiency for high QPM orders [8]. Figure 2(b) shows the dependence of the conversion efficiency on the duty-cycle: the value D = 53.13% (52.78%) maximizes the BSHG efficiency for the 16th (18th) resonant order, while the odd (17th) order yields the maximum conversion for D = 50.00%. The data presented in Fig. 2 for each
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7547
Fig. 3. BSHG conversion efficiency for the (a) 16th, (b) 17th and (c) 18th QPM order versus temperature. FF wavelength and peak power were 1722.0nm and 10 kW in (a); 1623.9nm and 8 kW in (b); 1535.1nm and 12 kW in (c), respectively.
Fig. 4. (a) Measured (circles) and calculated (solid line) BSHG energy vs input FF energy per pulse for the 16th resonant order. (b) Comparison between BSHG for m = 16 (blue circles) and the forward random-QPM SHG (red diamonds), the latter measured at the (FF) output.
resonance were acquired by slightly adjusting the sample position and orientation (with respect to the input pump beam) in order to maximize BSHG. Otherwise stated, each peak in conversion efficiency corresponds to a poled region where the duty-cycle distribution maximizes deff for each resonance [11]. The BSHG resonance for mth-order QPM is given by: ΔkQPM =
4π
λFF
(nFF + nSH ) −
2mπ = 0, Λ
(1)
where ΔkQPM is the wavevector mismatch, nFF and nSH are the extraordinary refractive indices [29] at FF and SH, respectively; the latter can be evaluated using the temperature-dependent Sellmeier equations (provided by the crystal supplier [30]). Equation (1) is satisfied for m = 16, 17, 18 at the experimentally observed resonant wavelengths when the QPM grating has periods Λ16 = 3.20053, Λ17 = 3.20128 and Λ18 = 3.19851 µm, respectively. These values are remarkably close to the nominal poling period, especially when considering that, as noted above, the three BSHG maxima correspond to distinct regions of the sample. The linewidth of our pump laser is between 230 and 290 pm in the range 1530-1725 nm. Using the experimental data in Fig. 2, we estimated the spectral bandwidth of each resonance; for the three orders the full width at half maximum (FWHM) are FWHM16 = 1233, FWHM17 = 520, and FWHM18 = 1860 pm, respectively. These values are about one order of magnitude larger than those calculated from Sellmeier equations according to [1]: 0.4429λm nSH − nFF ∂nFF 1 ∂nSH FWHM th = + − L λm ∂λ 2 ∂λ
−1
(2)
Equation (2) provides FWHMth(16) = 105, FWHMth(17) = 93 and FWHMth(18) = 83 pm, respectively. The discrepancy between measured and predicted bandwidths is ascribed to spatial non-uniformity of the domain distribution in both transverse (i.e. across the laser beam profile) and longitudinal coordinates [11]. We stress that group velocity dispersion plays no role in our measurements, as the dispersion length exceeds the sample length by orders of magnitude.
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7548
BSHG efficiency results versus temperature at fixed FF wavelengths, corresponding to the three BSHG resonances in Figs. 2(b)-2(d), are presented in Figs. 3(a)-3(c). For each resonant order, the BSHG signal exhibited a quadratic dependence on the FF pump. Figure 4(a) details the most efficient case (m = 16), whereas Fig. 4(b) compares BSHG via the 16th order (circles) and the forward SHG via randomized QPM in the range 1685-1740 nm (diamonds). The latter was measured at the FF (forward) output, on the opposite side of the sample with respect to the input facet. The data pinpoint the presence of frequency-doubled contributions with two distinct origins; hence, it was essential to separate backward propagating signals from those generated forward and reflected back by the output facet. The data in Fig. 4(b) provide further evidence that, although the acquired BSHG signal can be added to the reflected random-QPM SHG (as observed in the offsets in Fig. 2), we did not measure a spectral replica of the forward signal and could therefore discriminate the sought BSHG resonance. Finally, we compared measured and predicted BSHG conversion efficiency. Since we could not use the simplified expressions for quasi-cw or fs excitations [4], we considered Gaussian FF pulses of duration τ; the second harmonic pulses generated in a sample of length L then have the form: H (t ) = [ P ( 2 M b − 2T ) + P ( 2T ) − 1]2
(3)
with P(x) the integration of the normalized Gaussian probability function, Mb = L(nSH + nFF)/(τc) with c the speed of light in vacuum and T = t/τ a normalized time coordinate. In our work, for τ = 25 ps and L = 3 mm, we obtain M b ≈ 1.7 for the three BSHG resonances. By defining JH as the integral of H, i.e., J H =
+∞
−∞
H (T )dT , the SH conversion efficiency
can be expressed in terms of energy density per pulse as:
η=
+∞
−∞
I SH dt
I FFτ
=
2 η0 d332 I FF τ 2c2 J H
2nSH n (nSH + nFF ) Λ 2 FF
4
2
sin c 2 (
ΔkQPM L 2
)
(4)
with IFF and ISH the peak intensities at FF and SH, respectively. Equation (4) does not account for optical losses, as they are negligible for LN in the explored wavelength interval [30, 31]. We computed the conversion efficiency η from Eq. (4) using the material Sellmeier equations for the refractive indices and the actual values for sample length, pulse duration, FF peak intensity; d33 was the only fit parameter. The best fits of our data are shown as solid lines in Figs. 2(a) and 4(a), with d33 equal to 29.03, 27.32 and 25.13 pm/V, for m = 16, 17 and 18, respectively. These d33 values are in close agreement with those calculated from the nonlinearity d33 = 33 pm/V (provided by the crystal supplier [30]) around 1064 nm using the constant-Miller-delta scaling [29, 32, 33]. This confirms that the crystal nonlinearity was unaffected by the poling process, with an effectively optimized BSHG at the three resonant orders. 4. Conclusions
In conclusion, using 3.2 µm periodically poled crystals, we have observed - for the first time in the picosecond regime - BSHG in congruent Lithium Niobate at three near-infrared wavelengths corresponding to 16th, 17th and 18th QPM resonances, with a conversion efficiency as high as 0.475% for the lowest order, despite its parity. Our measurements discriminated the contributions from randomized duty-cycle QPM domains, with experimental data in agreement with a simple model for ps pulsed BSHG. Acknowledgments
We gratefully acknowledge E. D’Asaro for contributing to the experimental work.
#202106 - $15.00 USD (C) 2014 OSA
Received 29 Nov 2013; revised 24 Jan 2014; accepted 27 Jan 2014; published 25 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007544 | OPTICS EXPRESS 7549
