Femtosecond third-harmonic pulse generation by mixing of pulses with di erent duration

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1 1 December 2000 Optics Communications 186 (2000) 211±217 Femtosecond third-harmonic pulse generation by mixing of pulses with di erent duration Audrius Dubietis *, Gintaras Tamosauskas, Arunas Varanavicius Laser Research Center, Vilnius University, Saul_etekio Avenue 9, Building 3, LT-2040 Vilnius, Lithuania Received 21 June 2000; received in revised form 25 September 2000; accepted 28 September 2000 Abstract We demonstrate a simple and e cient method for frequency tripling of Nd:glass laser radiation by femtosecond nonlinearly compressed second-harmonic pulse upconversion in the eld of a picosecond fundamental pulse. A threewave interaction involving 200-fs pulses at 527 nm and 0.9-ps pulses at 1055 nm was accomplished with energy conversion e ciency of 30±40% in 2.5- and 3-mm-thick KDP crystals, yielding 200-fs pulses at 351 nm with milijoule energy. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: Re; Ky; Nv Keywords: Ultrafast nonlinear optics; Frequency conversion; Third-harmonic generation; Group-velocity matching; Femtosecond UV pulses 1. Introduction * Corresponding author. Tel.: ; fax: address: audrius.dubietis@.vu.lt (A. Dubietis). Harmonic generation in crystals with secondorder nonlinearity, in particular frequency tripling of neodymium lasers as an e cient method for generation of intense UV radiation, has been widely studied since the inception of nonlinear optics. The spectral bandwidth of frequency converters, which in the time domain is directly related to the pulse group velocity mismatch (GVM), is of high importance for frequency conversion of broadband ultrashort laser pulses. Reduction of spectral bandwidth results in a drop of conversion e ciency and an increase of pulse duration. Numerous methods overcoming the constraints imposed by dispersion characteristics of frequency triplers have been developed. A predelay of quickly separating picosecond pulses allows one to maximize the frequency tripling e ciency [1]. This approach has led to the development of the pulse temporal walk-o compensation method in crystal stacks with alternating signs of group velocity walk-o [2,3]. Recently, an increase in acceptance bandwidth of several times using the angledetuned multi-crystal design for conversion of 1054-nm radiation into 351 nm was reported [4]. To date, however, only very few works have been devoted to the generation of femtosecond UV pulses by frequency tripling of neodymium laser radiation. Adjustable GVM by means of pulsefront tilting has led to nonlinear compression of picosecond Nd:glass radiation yielding 160-fs pulses at 351 nm [5]. More recently, frequency /00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S (00)

2 212 A. Dubietis et al. / Optics Communications 186 (2000) 211±217 mixing of pulses with controlled phase modulation [6] has been shown to produce powerful femtosecond third-harmonic (TH) radiation [7]. However, the complexity of these proposed methods makes the generation of powerful femtosecond pulses at 351 nm a hard task. In this contribution we suggest a simple and e cient method for alleviating short-pulse GVM problems in the ultraviolet spectral region. The main limitation for frequency tripling of femtosecond Nd:glass laser pulses arises from the signi cant group-velocity di erence between IR and UV pulses. We show that femtosecond TH pulses can be e ciently generated by femtosecond secondharmonic (SH) pulse upconversion in the eld of a picosecond fundamental pump and that the pulsewidth of the TH pulse is close to that of the SH if the GVM for these two pulses is small. It is important to note that initial pulses of di erent durations are readily delivered by the picosecond CPA Nd:glass laser systems that utilize the nonlinear SH pulse compression e ect [8,9]. Recent advances in frequency doubling of Nd:glass laser radiation employing the nonlinear pulse compression (NPC) technique have constituted a successful step towards the conversion of picosecond and subpicosecond Nd:glass laser systems into femtosecond laser sources [10±12], emitting powerful femtosecond pulses at 527 nm with the shortest pulse width of 70 fs reported to date [13]. 2. Frequency tripling in terms of group-velocity mismatch Temporal walk-o of pulses that move with di erent group velocities u j can be characterized by the GVM length L jk ˆ s= 1=u j 1=u k, where indexes j; k ˆ 1; 2; 3 correspond to fundamental, SH and TH pulses, respectively. Frequency tripling of Nd:glass fs fundamental pulses in most nonlinear crystals becomes ine cient at crystal lengths above 1 mm because the GVM-imposed pulse separation exceeds the duration of the interacting pulses. In order to improve the e ciency of the frequency mixing process in short interaction lengths one should increase the intensity of the pump pulses. However, with the increase of pulse intensity, the third-order nonlinear e ects start manifesting themselves, leading to usually undesirable spatial and temporal modulation of the output radiation. Note that these e ects scale up with the intensity of the pump pulse I p, whereas the e ciency of frequency conversion based on the second-order nonlinearity scales with I p 1=2. In this work we consider the case of short pulse upconversion in the eld of a long pump pulse as a possibility to circumvent the GVM imposed limitations. The numerical modeling of the sum-frequency generation process has showed that in the case when ju 1 jju 2 j, but u 2 u 3, the energy of the input pulses is e ciently transferred to the sum-frequency pulse (namely TH, in our case) if the condition s 1 s 2 is satis ed. Moreover, the duration of the generated sum-frequency pulse is close to the pulse width of the short input pulse s 2. Recently, a similar approach has been applied for the generation of femtosecond fth-harmonic pulses of the Nd:glass laser. Frequency upconversion of a 200-fs fourth-harmonic pulse [14] under the envelope of a 0.9-ps-long fundamental has led to the generation of 250-fs pulses at 211 nm with energy more than 100 lj [15]. Frequency tripling in general can be performed using two di erent phase-matching con gurations: type I (oo-e) and type II (eo-e). These two di erent con gurations o er di erent group-velocity relationships between the interacting pulses. For type I interactions the GVM lengths L 23 and L 13 di er by approximately a factor of 2 for a number of nonlinear crystals. Supposing femtosecond SH pulse upconversion in the eld of a picosecond fundamental pump, the fundamental pulse is rapidly depleted in the area of pulse temporal overlap, but due to the relatively small group velocity di erence it cannot e ciently supply fresh energy into the interaction zone. The energy reconversion process starts rather early resulting in reduced energy conversion, and the large amount of fundamental pulse energy remains unused. The di erence between L 23 and L 13 in the type II interaction is larger, giving an average ratio of 4 for popular nonlinear crystals, as listed in Table 1. The operating conditions ju 1 jju 2 j, u 2 u 3 are satis ed in type II phase-matching KDP, ADP, BBO and CLBO crystals. Values of L 13 and L 23

3 A. Dubietis et al. / Optics Communications 186 (2000) 211± Table 1 Parameters of nonlinear crystals for type II (eo-e) frequency tripling Crystal u 1 (mm/ps) u 2 (mm/ps) u 3 (mm/ps) L 13 (mm) L 23 (mm) d eff (pm/v) h (deg) KDP ADP BBO CLBO d eff is the e ective nonlinearity, h is the phase-matching angle. were calculated for s 1 ˆ s 2 ˆ 1-ps pulses. Assuming s 2 ˆ 200 fs, the real value of L 23 is ve times smaller, thus L 23 s 2 ˆ 200 fs; s 3 ˆ 200 fs L 13 s 1 ˆ 1ps; s 3 ˆ 200 fs. Such equality means that the temporal overlap area of the interacting pulses is extended due to the longer fastest pulse (fundamental) duration. 3. Numerical model and simulations In Fig. 1 an example of the evolution of temporal envelopes of interacting pulses during the frequency tripling in a KDP crystal is presented. As seen from the picture, the TH pulse e ciently extracts the energy of the pump pulses, preserving its 200-fs duration at interaction lengths up to 3 mm. At longer propagation distances the TH pulse tends to split or broaden (depending on the initial conditions) due to the parametric reconversion process. The computer simulations were performed using a plane-wave model by solving the set of equations [16] numerically: oa 1 oz 1 oa 1 i u 1 ot 2 g o 2 A 1 1 ˆ ir ot 2 1 A 2 A 3 exp idkz ic 1 ja 1 j 2 2jA 2 j 2 2jA 3 j 2 A 1 ; oa 2 oz 1 oa 2 i u 2 ot 2 g o 2 A 2 2 ˆ ir ot 2 2 A 1 A 3 exp idkz ic 2 2jA 1 j 2 ja 2 j 2 2jA 3 j 2 A 2 ; oa 3 oz 1 oa 3 i u 3 ot 2 g o 2 A 3 3 ˆ ir ot 2 3 A 1 A 2 exp idkz ic 3 2jA 1 j 2 2jA 2 j 2 ja 3 j 2 A 3 ; 1 where z and t are propagation and time coordinates, respectively, u j is the group velocity, Fig. 1. Femtosecond pulse frequency upconversion in the eld of a picosecond pump. Evolution of temporal envelopes of interacting pulses. TH generation in KDP type II phase-matching crystal. ju 1 jju 2 j, u 2 u 3, s 1 ˆ 1 ps, I 1 ˆ 10 GW/cm 2, s 2 ˆ 200 fs, I 2 ˆ 40 GW/cm 2. Frame of reference moves with TH pulse. g j ˆ d 2 k j =dx 2 is the group velocity dispersion coe cient, r j ˆ 4pk j =n 2 j d eff is the coupling coe cient, k j ˆ 2pn j =k j is the wave number, and Dk is the phase mismatch (in our case Dk ˆ 0). Subscript j ˆ 1; 2; 3 refers to fundamental, SH and TH waves, respectively. Coe cients c j are expressed through the third-order nonlinearity v 3 : c j ˆ 3pv 3 k j : 2 2n 2 j

4 214 A. Dubietis et al. / Optics Communications 186 (2000) 211±217 The relationship between v 3 and the nonlinear refractive index n 2 is given by n 2 ˆ 3p=n 0 v 3. The boundary conditions for Eq. (1) are A 1 t j zˆ0 ˆ A 10 t Dt ; A 3 t j zˆ0 ˆ 0; A 2 t j zˆ0 ˆ A 20 t ; 3 where Dt denotes the predelay between pump pulses. Pulse temporal pro les were assumed to be Gaussian: A j ˆ a j0 exp 2ln2t2 ; 4 s j0 where A j denotes the pulse complex amplitude and s j0 is the pulse width, de ned at the FWHM. The intensity and predelay of the input pulses were optimized for maximum energy conversion into the TH radiation. Fig. 2 illustrates output characteristics of the third-harmonic generator (THG) as a function of KDP crystal length. All other parameters were chosen close to experimental conditions: s 10 ˆ 1 ps, s 20 ˆ 200 fs, predelay of Dt ˆ 400 fs and input intensity I 2 ˆ 40 GW/cm 2. The intensity ratio of pump pulses M ˆ I 2 =I 1 was varied from 3 to 10, and the results are presented in Fig. 2. Some characteristic features under the aforementioned operating conditions must be noted. Pulse width behavior inside the nonlinear crystal is similar in all presented cases, and TH pulses with s 3 shorter than 200 fs are expected. The increase of the crystal length leads to either broadening of the TH pulse width (see Fig. 2(a)) or to pulse splitting due to the parametric reconversion process (Fig. 2(b), (c)), depending on the value of M. Energy conversion, de ned as g ˆ E 3 = E 1 E 2, is close to or higher than 50% (for the plane wave model used here). Analysis of numerical data shows that the optimum crystal length and value of M can be found when the maximum energy conversion is obtained at the shortest output pulse width. The TH pulse duration is rather insensitive to most of the initial conditions at the optimal crystal length. Neither the detuning from the optimum predelay between the fundamental and SH pulses, nor the deviation from the optimum intensity ratio has much in uence on the temporal envelope of the TH pulse. Also, the overall pump intensity can Fig. 2. Frequency tripling e ciency () and TH pulse width (± ± ±, Ð) versus the KDP crystal length. Solid curve shows TH pulse width with third-order nonlinearity and two-photon absorption e ects taken into account. (a) M ˆ 10, (b) M ˆ 5, (c) M ˆ 3. I 2 ˆ 40 GW/cm 2 and Dt ˆ 400 fs for all plots. be varied in a broad range, since it is below pulse self-action e ects. Third-order nonlinearity n 2 ˆ 2: m 2 =W and two-photon absorption

5 A. Dubietis et al. / Optics Communications 186 (2000) 211± b ˆ 0: m=w [17] resulted only in a weak contribution to the main trends as shown by the solid curves in Fig. 2. We have used the same n 2 ˆ 2: m 2 =W for all the interacting wavelengths, as there is no experimental data for 351 nm, and the measured n 2 values for 1064 and 532 nm are in the range of 2:0±2: m 2 =W. For many applications the intensity contrast is an important parameter that characterizes the pulse quality. The basic feature of the proposed TH generation scheme is that the TH pulse intensity contrast is set solely by the intensity contrast of the SH pulse, as the pulsefronts of the fundamental pulse do not interact with the SH pulse. Fig. 3 depicts the logarithmic plot of the TH pulse envelope, obtained in two cases: (a) input SH pulse is an ideal Gaussian function, and (b) input SH pulse has an intensity contrast of 50:1, which is typically obtainable at SH pulse compression rates of 4±5 [18]. The TH pulse envelopes were obtained under operating conditions that refer to that presented in Fig. 2(b) and the KDP crystal length of 3 mm. 4. Experiment A schematic of the experimental setup is shown in Fig. 4. We employed a commercial picosecond Nd:glass laser system, operating at a 20 Hz repetition rate (TWINKLE, Light Conversion Ltd.), which delivered 0.9-ps pulses with energy up to 5.5 mj at 1055 nm. The laser output was divided into two parts by means of a beamsplitter BS. The re- ected pulse (1.8 mj) served as a picosecond pump for the THG. The transmitted pulse (3.2 mj) was frequency doubled in the NPC, consisting of a half-wave plate and two 15-mm-long KDP type II phase-matching crystals. The rst crystal introduced a predelay between the o and e polarized fundamental pulses, and the second one served for frequency doubling. The NPC yielded 1.1-mJ, 190- fs pulses at 527 nm. The TH pulse was generated in a type II phase-matching KDP crystal (h ˆ 59, L ˆ 2:5 mm). Pairs of dichroic mirrors DM1, DM2 and DM3 were set as wavelength separators, transmitting remnants of the depleted radiation. DM1 was mounted on a ne mechanical delay line for pulse timing adjustment. The collinear coupling Fig. 3. Calculated temporal pro les of input SH (- - -) and output TH (Ð) pulses: (a) SH pulse has Gaussian shape, (b) SH pulse has an intensity contrast of 50:1. Fig. 4. Experimental setup for frequency tripling. BS is the beamsplitter, NPC is the nonlinear SH pulse compressor, THG is the frequency tripler, DM1±DM3 are the pairs of dichroic mirrors.

6 216 A. Dubietis et al. / Optics Communications 186 (2000) 211±217 of pump beams into THG was provided by means of DM2. The peak intensity was I 2 ˆ 40 GW/cm 2 for the SH pulse and I 1 ˆ 8 GW/cm 2 for the fundamental one. The intensity ratio of pump pulses M at the input face of the THG crystal was 5. It must be noted that proper intensity ratio could not be derived directly as M ˆ 1 j =j, where j ˆ x 2 =x 3 is the degeneracy parameter. The case when M ˆ 2 corresponds to the group-velocity matched interaction and equal input pulse widths. To some extent, the formula has been modi ed to M ˆ 1 j =j L 23 =L 13 [19] and gives a consistent result with the experiment in the presence of GVM, but again for equal input pulse widths. For nonequal pulse widths there is no simple empirical expression, hence the intensity ratio M ˆ 5usedin our experiment, was found numerically. The energy dependence of the TH pulse generated in a 2.5-mm-thick KDP crystal versus the predelay Dt between pump pulses is presented in Fig. 5(a). At optimum timing the TH pulse energy of E 3 ˆ 0:85 mj was measured. Energy conversion into the TH radiation was 29%, as measured in the whole beam (note the nearly Gaussian spatial pro le). The duration of the TH pulse was measured by the noncollinear degenerate four-wave mixing (self-di raction) technique with a scanning autocorrelator utilizing the third-order nonlinearity of a thin (0.2 mm) KDP crystal plate. The TH pulse width dependence on the predelay is shown in Fig. 5(b). The shortest pulses were measured at the optimum predelay between the pump pulses, as expected. No considerable TH pulse lengthening has been detected at even large (close to the fundamental pulse width) detuning from the optimum delay value. A third-order autocorrelation trace of the shortest TH pulse is shown in Fig. 6(a). Assuming Fig. 5. TH pulse energy (a) and pulse width (b) versus the predelay Dt between the pump pulses. Negative values denote that the SH pulse is advanced with respect to the fundamental one, and positive values denote that the SH pulse is delayed. Fig. 6. (a) Third-order autocorrelation function and (b) spectrum of the TH pulse, generated in a 2.5-mm-thick KDP crystal.

7 A. Dubietis et al. / Optics Communications 186 (2000) 211± a Gaussian shape, the TH pulse duration s 3 ˆ 180 fs from the autocorrelation data was retrieved. The corresponding spectrum is presented in Fig. 6(b). The time±bandwidth product DmDs ˆ 0:45 indicates an almost transform-limited TH pulse. With a 3-mm-thick KDP crystal, the energy conversion into TH radiation increased up to 36% yielding 1-mJ femtosecond pulses at 351 nm. However, we note that in this case the somewhat longer UV pulses of 210 fs were measured. We have not measured the TH beam pro le nevertheless some remarks are worth to be mentioned. The laser system produces beam at 1055 nm with spatial pro le close to ideal Gaussian intensity distribution. There could be a slight onset of self-focusing in the SH pulse compressor. In our experiment the pump intensity for the SH pulse compressor was chosen in such a way that the SH beam size reduction was less than 10% after the propagation of 5 m distance. For what concerns the spatial pro le of the TH beam, it should recall the features of the SH beam. 5. Conclusions The proposed method promises a simple and e cient means for femtosecond TH pulse generation in terawatt-power Nd:glass laser systems. The operating conditions ensuring short output pulse duration can be achieved in a number of nonlinear crystals and applied to other sum-frequency mixing setups. Under the optimized conditions nearly transform limited femtosecond pulses can be generated with energy conversion e ciency close to 40%. Acknowledgements The authors highly appreciate the help of Dr. G. Valiulis in preparing the software for the numerical simulations. The authors also would like to thank the reviewers for their constructive suggestions that helped to improve the paper. References [1] T. Zhang, Y. Kato, H. Daido, IEEE J. Quant. Electron. 32 (1996) 127±136. [2] A.V. Smith, D.J. Armstrong, W.J. Alford, J. Opt. Soc. Am. B 15 (1998) 122±141. [3] D. Eimerl, J.M. Auerbach, C.E. Barker, D. Milam, P.W. Milonni, Opt. Lett. 22 (1997) 1208±1210. [4] A. Babushkin, R.S. Craxton, S. Oskoui, M.J. Guardalben, R.L. Keck, W. Seka, Opt. Lett. 23 (1998) 927±929. [5] A. Dubietis, G. Valiulis, G. Tamosauskas, R. Danielius, A. Piskarskas, Opt. Commun. 144 (1997) 55±59. [6] A.C.L. Boscheron, C.J. Sauteret, A. Migus, J. Opt. Soc. Am. B 13 (1996) 818±826. [7] F. Raoult, A.C.L. Boscheron, D. Husson, C. Rouyer, C. Sauteret, A. Migus, Opt. Lett. 24 (1999) 354±356. [8] Y. Wang, R. Dragila, Phys. Rev. A 41 (1990) 5645± [9] A. Stabinis, G. Valiulis, E.A. Ibragimov, Opt. Commun. 86 (1991) 301±306. [10] Y. Wang, B. Luther-Davies, Opt. Lett. 17 (1992) 1459± [11] C.Y. Chien, G. Korn, J.S. Coe, J. Squier, G. Mourou, R.S. Craxton, Opt. Lett. 20 (1995) 353±355. [12] R. Danielius, A. Dubietis, G. Valiulis, A. Piskarskas, Opt. Lett. 20 (1995) 2225±2227. [13] A. Maksimchuk, J. Queneuille, G. Cheriaux, G. Mourou, R.S. Craxton, Conference of Lasers and Electrooptics, 1999 OSA Technical Digest Series, Optical Society of America, paper CTuD6, Washington DC, [14] G. Veitas, A. Dubietis, G. Valiulis, D. Podenas, G. Tamosauskas, Opt. Commun. 138 (1997) 333±336. [15] A. Dubietis, G. Tamosauskas, A. Varanavicius, G. Valiulis, R. Danielius, Opt. Lett. 25 (2000) 1116±1118. [16] T. Zhang, M. Yonemura, Jpn. J. Appl. Phys. 38 (1999) 6351±6358. [17] D.N. Nikogosyan, Properties of Optical and Laser Related Materials, Wiley, Chichester, [18] R. Danielius, A. Dubietis, A. Piskarskas, G. Valiulis, A. Varanavicius, Lithuan. J. Phys. 36 (1996) 329±332. [19] R. Danielius, A. Dubietis, A. Piskarskas, G. Valiulis, A. Varanavicius, Opt. Lett. 21 (1996) 216±218.