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Optical parametric properties of 532-nm-pumped beta-barium-borate near the infrared absorption edge
15 October 2000
Optics Communications 184 (2000) 485±491
www.elsevier.com/locate/optcom
Optical parametric properties of 532-nm-pumped beta-bariumborate near the infrared absorption edge Dongxiang Zhang, Yufei Kong, Jing-yuan Zhang * Department of Physics, Georgia Southern University, Statesboro, GA 30460, USA Received 3 August 2000; received in revised form 18 August 2000; accepted 21 August 2000
Abstract We report some new experimental results on optical parametric properties in the near-IR absorption edge of a type-I phase-matched BBO-OPG/OPA (beta-barium-borate, BBO; optical parametric generation/ampli®cation, OPG/OPA) pumped at 532 nm. It was found that at the edges of the tuning curve, both the experimental tuning curve and the bandwidth are signi®cantly dierent from the calculated result based on the Sellmeier equations proposed by Kato. It is found that the bandwidth of OPG in above-mentioned region is near transform-limited without using dispersion element. The results are attributed to the signi®cant decrease of refractive index near the absorption edge of BBO and the retracing behavior of 532-nm-pumped BBO crystal. The retracing occurs at 665 nm and 2.66 lm, respectively. The modi®ed Sellmeier equations are given based on our experimental tuning curve. The theoretical calculation of the bandwidth of OPG using the modi®ed Sellmeier equations agrees very well with our experimental measurement. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Beta-barium-borate (BBO) crystal has been commonly used in the nonlinear frequency conversion. It has been demonstrated to be one of the best candidates in nanosecond [1], picosecond [2], and femtosecond [3] optical parametric devices. Actually, optical parametric devices have been widely developed and represent one of the most successful ways to obtain a widely tunable laser source. Over the past several years, there has been tremendous progress in nonlinear optical parametric devices. Currently, it has become very popular in the scienti®c research laboratories.
*
Corresponding author. Fax: +1-912-681-5703. E-mail address: [email protected] (J.-y. Zhang).
In this paper, we report some new results on the parametric properties of a type-I phase-matched BBO optical parametric generation/ampli®cation (OPG/OPA) system pumped at 532 nm in the wavelength range near the infrared absorption edge of BBO. Experimentally, it was found that there is a retracing behavior in the tuning curve (wavelength versus angle of the crystal) at the wavelength around 665 nm and 2.66 lm. Most importantly, the retracing behavior of the tuning curve signi®cantly diers from the theoretical calculation using the Sellmeier equation that has been commonly quoted in the literature [4] especially near the ends of the tuning curve. It was also found that the tuning of the 532-nm-pumped BBO OPG/OPA can cover a wider range from 637 nm to 3.2 lm, compared with the tuning range from 650 nm to 2.5 lm as reported in the literature [5].
0030-4018/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 0 ) 0 0 9 6 8 - 8
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D. Zhang et al. / Optics Communications 184 (2000) 485±491
The results are attributed to a rapid decrease in the refractive index caused by the contribution of phonon-related excitations as the idler wavelength approaches the absorption bands. Modi®ed Sellmeier equations are given based on our experimental data. It was also found that that the bandwidth of OPG at the end of the tuning curve, where the wavelength of the idler branch of OPG approaches the infrared absorption edge of BBO, is signi®cantly narrower than that at other parts of the tuning curve. Without using any dispersion element the bandwidth of OPG generated near the end of the tuning curve is nearly transform-limited. The mechanisms for bandwidth narrowing are discussed and are attributed to the signi®cant changes of the factors in that region, which include the slope of the refractive index of crystal for the extra-ordinary wave versus the angle, the dierence of refractive index between the signal and the o idler n o s h ÿ ni h, and the dierence of dispersion of the crystal between the signal and the o idler on o s h=oxxs ÿ oni h=oxxi . The theoretical calculation of the bandwidth using the modi®ed Sellmeier equations agrees well with the experimental data.
2. Experimental setup The experimental setup for conducting the measurements is brie¯y described as the following: the pumping source used in our OPG/OPA is a modi®ed commercial actively and passively modelocked Nd:YAG laser. The pulse duration of the YAG at 1.064 lm is compressed from 40 to 12 ps using a combined eect of negative feedback and self-defocusing with a 0.6-mm thick GaAs plate inserted in the cavity [6]. The output of the laser at 1.064 lm is about 20 mJ per pulse. The pulse duration of the laser is then further compressed by a photon-collision technique with a type-II phasematched second harmonic generator using a 5-cm long KDP crystal [7]. After the pulse compression, the laser energy at 532 nm is about 3 mJ per pulse, and the pulse duration is about 2 ps. The pumping scheme is essentially the same as our previous work on 355-nm pumped BBO-OPA
[3] except that there is only one BBO crystal used in the OPG stage in our experiment. The pumping beam is split into two parts by a beam splitter. 30% of the output energy of the lasers is used to pump the OPG stage to generate a seed beam, the pump beam is telescoped down to 2.5 mm in diameter to reach a pump intensity of 14 GW/cm2 . A 5 mm H 7 mm W 12 mm L BBO crystal cut at 22.5° is used in the OPG in a double-pass scheme without using any dispersion element. The tunable seed beam is then ampli®ed in a second 12-mm long BBO crystal in the OPA stage, which is pumped by the residual 70% of the pump energy. The pumping intensity can be adjusted to optimize the optical conversion eciency. The two BBO crystals are rotated synchronously by a mechanical device. The output of the OPG/OPA system, after removing the residual pump beam by a CaF2 dichroic mirror, which is highly re¯ective R 99% at 532 nm, is measured by a power meter (Molectron Max-400), whose spectral response is ¯at from the UV to the far-IR. The use of CaF2 substrate for the dichroic mirror allows effective transmission of the idler output. A Ge-®lter is used to block the idler output shorter than 2 lm and make the study of the output around 3 lm, which is near the IR absorption band of BBO, possible. Part of the output is picked up by a piece of glass and imaged onto the entrance slit of a 0.5m spectrometer for analysis of the spectrum. The spectrum of the OPG is recorded either by a CCD camera for the wavelength of the signal branch or by an IR detector for the idler branch. 3. Experimental result and discussion By careful spectral and temporal overlapping between the seed beam and the pump beam in the OPA stage and rotating two BBO crystals synchronously, the output of the angle-tuned OPG/ OPA system is continuously tunable from 637 nm to 3.2 lm, except three gaps near the degenerate points at 665, 1064 nm, and 2.66 lm, respectively. The above tuning range is broader than that reported in the literature. The wavelength range from 2.6 to 3.2 lm is already at the infrared absorption edge of BBO. The highest energy con-
D. Zhang et al. / Optics Communications 184 (2000) 485±491
version eciency of the system is more than 20%, which occurs at the signal wavelength of around 900 nm. In addition, we observed some new parametric properties: (1) there are retracing phenomena occurred at 665 nm and 2.66 lm, respectively; (2) the experimental tuning curve signi®cantly diers from the theoretical calculation based on the Sellmeier equations proposed by Kato [4]; and (3) the bandwidth of the OPG become nearly transform-limited when the signal wavelength is tuned to the blue side of the retracing point at 665 nm, especially near the end of the tuning curve. The new results on the parametric properties of the 532-nm-pumped BBOOPG/OPA are presented and discussed below. 3.1. Retracing behavior and discrepancy between the experimental and theoretical tuning curve By measuring the generated wavelength of the OPG while rotating the angle of the crystal step by step, we were able to construct a tuning curve of wavelength versus crystal angle. By using the 0.5m CCD spectrometer, we were able to record the spectra of the signal wave at various crystal angles with the wavelength ranging from the visible to the near IR around 1.0 lm. It is interesting to see that at a given crystal angle between 20.9° and 21.5°, there are two components in the signal branch. Besides the expected signal branch ranging from 666 to 724 nm, the output of the OPG/OPA contains an additional component at the short wavelength. Fig. 1 presents the spectra measured at various crystal angles. As can be seen that when the signal wavelength is tuned from 665 to 723 nm, there is an additional component, which is continuously tunable from 665 to 637 nm, accordingly. The later corresponds to a tuning range from 2.66 to 3.23 lm in the idler branch. The signal output cuts o sharply at 637 nm, which corresponds the idler wavelength of 3.23 lm, at which the infrared absorption of BBO crystal increases sharply. The constructed tuning curve indicates a retracing behavior of the 532-nm-pumped BBO OPG/OPA occurred at 665 nm and 2.66 lm, respectively.
487
Fig. 1. Spectra of OPG measured at various crystal angles h showing the additional frequency component due to retracing behavior of the 532-nm-pumped BBO-OPG: (a) h 21:39°, (b) h 21:23°, (c) h 21:12°, (d) h 21:01°, (e) h 20:95°, (f) h 20:91°, and (g) h 20:80°.
The retracing behavior was ®rst observed in LBO crystal when it is pumped at 532 nm [8,9]. Later, it was found that the retracing behavior of LBO could also be observed when the pumping wavelength is between 520 and 540 nm [10]. However, to our knowledge, for the 532-nmpumped BBO parametric devices, not retracing behavior has been reported in the previous work. 3.2. Discrepancy between the experimental and the theoretical tuning curve Comparing the measured data with the theoretical tuning curve, it is found that the experimental retracing behavior has signi®cant dierence from the theoretical data calculated based on the following Sellmeier equations of BBO crystal [4]: 0:01878 ÿ 0:01354k2 ; k ÿ 0:01822 0:01224 ÿ 0:01516k2 ; n2e k 2:3753 2 k ÿ 0:01667 n2o k 2:7359
2
1
where the unit of wavelength is in micrometer. Fig. 2 shows the experimentally measured tuning curve of our OPG/OPA system and the theoretically calculated tuning curve of the 532-nmpumped BBO-OPG based on the Sellmeier equations proposed by Kato as shown in Eq. (1). The experimental data exhibits a retracing behavior at
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D. Zhang et al. / Optics Communications 184 (2000) 485±491
Fig. 2. Comparison between the tuning curves calculated using Sellmeier equations proposed by Kato as shown in Eq. (1) (- - -) and the experimental data (). The solid line is data ®tting of experimental results.
around 2.66 lm in the idler branch and 665 nm in the signal branch, respectively. On the other hand, the theoretical calculation based on the Sellmeier equations shows the retracing would occur at 3.26 lm and 630 nm, respectively, and it is beyond the tuning range of BBO. The signi®cant dierence between the experimental data and the theoretical calculation indicates that the Sellmeier equations of BBO crystal given in the literatures are inaccurate and need to be modi®ed. Note that the original Sellmeier equations proposed by Kato were derived from the measurements of refractive index from 200 nm to 1.0 lm. Therefore, for wavelength longer than 1.0 lm, the predicted refractive index should be less accurate [11]. This is particularly true when the signal wavelength is shorter than 680 nm, the corresponding wavelength of the idler branch is longer than 2.2 lm, where the infrared absorption edge of BBO is approached. As can be seen in Fig. 2, there are signi®cant dierence between the experimental and theoretical tuning curve when the idler wavelength is longer than 2.2 lm. Study of infrared absorption spectrum of BBO shows that the absorption starts at 2.2 lm and increases signi®cantly with wavelength. At 3.2 lm, the transmission of a 3.72 mm thick BBO is less
than 20% [11]. Since the idler wavelength longer than 2.2 lm is close to the overtone of lattice vibrations, it is possible that the change of refractive index could be attributed to the phonon-related excitation. As a result, according to Kramer± Kronig relations, the index of refraction should decrease signi®cantly in this region. Similar discrepancy between the calculated results based on Eq. (1) and the measured tuning curves also occurs in the short wavelength side of the tuning curve at the corresponding signal wavelength from 665 to 637 nm. This is due to the fact that the signal and the idler photons are always generated in pair and they must both satisfy the phase-matching condition. The details for the retracing in the signal branch are shown in the inset of Fig. 2. Using the measured data and a nonlinear least square routine, modi®ed Sellmeier equations can be obtained. The resulted modi®ed Sellmeier equations are given as the following: 0:01878 ÿ 0:01471k2 k ÿ 0:01822 0:0006081k4 ÿ 0:00006740k6 ; 0:01224 ÿ 0:01627k2 n2e k 2:3753 2 k ÿ 0:01667 0:0005716k4 ÿ 0:00006305k6 ;
n2o k 2:7359
2
2
where the unit of wavelength is in micrometer. For comparison, we plot in Fig. 3 the refractive index of BBO as a function of wavelength based on Eq. (1) (dashed line) and Eq. (2) (solid line). It is seen that as the wavelength approaches the infrared absorption edge of BBO (>2.2 lm), the refractive index based on the modi®ed Sellmeier equations becomes signi®cantly lower than that from the original ones. The results match the discrepancies between two tuning curves shown in Fig. 2. 3.3. Bandwidth narrowing at the edge of the tuning curve It is also interesting to point out that, as can be seen from Fig. 1, the bandwidth of OPG in the blue side of the turning point of the retracing region around 660 nm is much narrower than that in the red side. As the wavelength approaches the
D. Zhang et al. / Optics Communications 184 (2000) 485±491
Fig. 3. Comparison between the calculated refractive index of BBO for ordinary wave, no , and extraordinary wave, ne , as a function of wavelength using the Sellmeier equations given by Kato (- - -) and the modi®ed Sellmeier equations (Ð). Insert shows the details for the dierence at long wavelength, where the absorption becomes signi®cant.
blue end of the tuning curve, the bandwidth become very narrow. Fig. 4 shows the spectrum of OPG/OPA around 637 nm taking by the 0.5-m CCD spectrometer. For comparison, the spectrum of a He±Ne laser at 632.8 is also showed in Fig. 4. The bandwidth of the OPG at 637 nm is measured to be about 1.3 nm (32 cmÿ1 ). After taking into account the resolution of the spectrometer, the bandwidth is found to be less than 30 cmÿ1 . Considering the pulse duration of the generated OPG, which is no more than 1.5 ps, a near transform-limited bandwidth is achieved without using any dispersion element in the OPG/OPA system. Compared with the bandwidth of OPG around 727 nm, the former is only about 1/8 width of the latter. The bandwidth of an OPG/OPA is determined through the energy conservation and phasematching conditions primarily by the bandwidth of the pump laser, the angular divergence of the pump, and the crystal length. For a double-pass OPG or an OPA stage, the bandwidth also depends on the distance that the seed beam traveled before it hits the crystal and gets ampli®ed again.
489
Fig. 4. Spectrum of the narrow band OPG at 637.1 nm (the peak on the right). For calibration and comparison, the spectrum of He±Ne laser is also shown (the peak on the left).
With a ®nite beam size of the pump, the ampli®er acts as a spatial ®lter. Consider a type-I phase-match optical parametric device using a negative uniaxial crystal, such as the case of our BBO-OPG, the ®nite beam divergence Dhp will in general lead to a range of values, Dkp , of the magnitude of the propagation vector of the pump beam which will, in turn, lead to a spread of values of the sum of the propagation vectors of the signal and idler waves D ks kp . Therefore, when the propagation direction of the interacting waves is not along a principal axis of the crystal such as the case of angle-tuned OPG, the bandwidth of the signal wave of the single-pass traveling wave OPG is dominantly limited by the ®nite beam divergence Dhp of the pump beam. The bandwidth of our BBO-OPG can be calculated by using the following equation [12]: Dx xp on e p h=ohp Dhp ; o o o o ns h ÿ ni h ons h=oxxs ÿ oni h=oxxi 3
where Dhp is the ®nite beam divergence of the pump. At a given wavelength, the bandwidth is
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D. Zhang et al. / Optics Communications 184 (2000) 485±491
proportional to the beam divergence of the pump Dhp , the slope of the refractive index of crystal of the extra-ordinary wave versus the angle of the crystal on e p h=ohp , which is a value related to the angular dispersion of the crystal. In addition, it is also related to the dierence of refractive index o between the signal and the idler n o s h ÿ ni h, and the dispersion of the crystal on o s h=oxxs ÿ o oni h=oxxi . A similar relation can also be found for the idler since the signal and the idler are generated in pair. We calculated the bandwidth of OPG at various wavelengths using about bandwidth equation (3) and used the Sellmeier equations proposed by Kato (Eq. (1)) and the modi®ed equations given by our work (Eq. (2)), respectively. The calculated results and the experimental data are shown in Fig. 5. The doted line in Fig. 5 is the calculation based on the original Sellmeier equations given by Kato, the solid line is based on the modi®ed equations, and the circles are the experimental data. The
Fig. 5. Bandwidth of the signal branch of 532-nm-pumped BBO-OPG as a function of wavelength obtained from the theoretical calculation based on the Sellmeier equations given by Kato (Eq. (1)) and the bandwidth equation (3) ( ), the calculation based on the modi®ed Sellmeier equations (2) and (3) (Ð), and the experimental data (s). The beam divergence of the pump used in the calculations is based on the experimental value of 1.5 mrad.
beam divergence of the pump beam Dhp used in our calculation is 1.5 mrad, which was measured experimentally. It can be seen that the calculated results using the modi®ed equations agree very well with our experimental data or the results using the original equations do not. The narrowed bandwidth towards the short wavelength side of the tuning curve is due to the fact that all three above-mentioned factors, which aect the bandwidth of OPG, are in favor of reducing the bandwidth of OPG as the wavelength moves towards the edge of the tuning curve. The details can be discussed as the following: ®rst, due to the retracing around 665 nm, at the wavelength shorter than the turning point, as the wavelength becomes shorter, the crystal angle hp becomes larger. The larger the angle is, the smaller the value of onp e h=ohp will be. Such a trend leads further reduction of the bandwidth. Secondly, as the wavelength tuned toward the edge of the tuning curve, the signi®cant change of the dierence of refractive index between the signal and the idler increases signi®cantly since the refractive index of the idler decreases rapidly as it approaches the absorption band from 2.6 to 3.2 lm. The o factor [n o s h ÿ ni h] makes positive contribution to the reduction of the bandwidth. Finally, the contribution of dispersion factor o on o s h=oxxs ÿ oni h=oxxi in the denominator of Eq. (3) is also favorable of reducing the bandwidth as the wavelength turned to the blue edge since the dierence of their values between the signal and the idler becomes larger at shorter wavelengths. We were unable to measured the bandwidth of the idler because our CCD camera is only sensitive from the UV to the near IR, however, the bandwidth of the OPG towards the tuning edge of the idler is also expected to be narrower since the signal and the idler are generated in pair. The calculation also shows a signi®cant bandwidth reduction as the idler wavelength longer than the turning point of the retracing around 2.66 lm. The good agreement between the experimental bandwidth and the theoretical calculation based on the modi®ed Sellmeier equations also indicates the modi®ed equations are closed to the true value of the refractive index of BBO.
D. Zhang et al. / Optics Communications 184 (2000) 485±491
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4. Conclusion
Acknowledgements
In conclusion, we have reported some new results on the phase matching optical parametric generation near the infrared absorption edge of the nonlinear medium. Due to the contribution of phonon-related excitation the refractive index of the NLO medium as a function of the wavelength is expected to change more rapidly. This causes the discrepancy between the experimental tuning curve and the calculated results based on the Sellmeier equations proposed by Kato. Modi®ed Sellmeier equations are presented based on our experimental measurements. A near transformlimited pulse can be achieved without using any dispersion element in our OPG/OPA system and it agrees well with the theoretical calculation based on the bandwidth equation and the modi®ed Sellmeier equations. The bandwidth narrowing was attributed to the angular dispersion of BBO for the pump, the dierence of the refractive index between the signal and the idler, and the dierence of the dispersion of BBO between the signal and the idler. All these three factors that determine the bandwidth of OPG are in favor of reduction of the bandwidth when the wavelength is shorter than the turning point of the retracing behavior of BBO at 665 nm.
This work was supported by National Science Foundation grant PHY9601922. The authors thank Dr. Jung Y. Huang for his valuable input in preparing the manuscript.
References [1] W.R. Bosenberg, L.K. Cheng, C.L. Tang, Appl. Phys. Lett. 54 (1989) 13. [2] J.Y. Huang, J.Y. Zhang, Y.R. Shen, C. Chen, B. Wu, Appl. Phys. Lett. 57 (1990) 1963. [3] D.C. Edelstein, E.S. Wachman, C.L. Tang, Appl. Phys. Lett. 54 (1989) 1730. [4] K. Kato, IEEE J. Quant. Electron. QE-22 (1986) 1013. [5] X.D. Zhu, L. Deng, Appl. Phys. Lett. 61 (1992) 1490. [6] A.V. Babushkin, N.S. Vorobev, A.M. Prokhorov, M.Ya. Shchelev, Sov. J. Quant. Electron. 19 (1989) 1310. [7] A. Umbrasas, J.-C. Diels, J. Jacob, G. Valiulis, A. Piskarskas, Opt. Lett. 20 (1995) 2228. [8] S.J. Lin, B.C. Wu, F. Xie, C.T. Chen, Appl. Phys. Lett. 59 (1991) 1541. [9] S.J. Lin, J.Y. Huang, J.W. Ling, C.T. Chen, Y.R. Shen, Appl. Phys. Lett. 59 (1991) 2805. [10] Z. Xu, X. Liu, D. Deng, Q. Wu, L. Wu, B. Wu, S. Lin, B. Lin, C. Chen, J. Opt. Soc. Am. B 12 (1995) 2222. [11] C.T. Chen, private communication. [12] Y.R. Shen, The Principles of Nonlinear Optics, Wiley, New York, 1984, p. 128.
Optics Communications 184 (2000) 485±491
www.elsevier.com/locate/optcom
Optical parametric properties of 532-nm-pumped beta-bariumborate near the infrared absorption edge Dongxiang Zhang, Yufei Kong, Jing-yuan Zhang * Department of Physics, Georgia Southern University, Statesboro, GA 30460, USA Received 3 August 2000; received in revised form 18 August 2000; accepted 21 August 2000
Abstract We report some new experimental results on optical parametric properties in the near-IR absorption edge of a type-I phase-matched BBO-OPG/OPA (beta-barium-borate, BBO; optical parametric generation/ampli®cation, OPG/OPA) pumped at 532 nm. It was found that at the edges of the tuning curve, both the experimental tuning curve and the bandwidth are signi®cantly dierent from the calculated result based on the Sellmeier equations proposed by Kato. It is found that the bandwidth of OPG in above-mentioned region is near transform-limited without using dispersion element. The results are attributed to the signi®cant decrease of refractive index near the absorption edge of BBO and the retracing behavior of 532-nm-pumped BBO crystal. The retracing occurs at 665 nm and 2.66 lm, respectively. The modi®ed Sellmeier equations are given based on our experimental tuning curve. The theoretical calculation of the bandwidth of OPG using the modi®ed Sellmeier equations agrees very well with our experimental measurement. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Beta-barium-borate (BBO) crystal has been commonly used in the nonlinear frequency conversion. It has been demonstrated to be one of the best candidates in nanosecond [1], picosecond [2], and femtosecond [3] optical parametric devices. Actually, optical parametric devices have been widely developed and represent one of the most successful ways to obtain a widely tunable laser source. Over the past several years, there has been tremendous progress in nonlinear optical parametric devices. Currently, it has become very popular in the scienti®c research laboratories.
*
Corresponding author. Fax: +1-912-681-5703. E-mail address: [email protected] (J.-y. Zhang).
In this paper, we report some new results on the parametric properties of a type-I phase-matched BBO optical parametric generation/ampli®cation (OPG/OPA) system pumped at 532 nm in the wavelength range near the infrared absorption edge of BBO. Experimentally, it was found that there is a retracing behavior in the tuning curve (wavelength versus angle of the crystal) at the wavelength around 665 nm and 2.66 lm. Most importantly, the retracing behavior of the tuning curve signi®cantly diers from the theoretical calculation using the Sellmeier equation that has been commonly quoted in the literature [4] especially near the ends of the tuning curve. It was also found that the tuning of the 532-nm-pumped BBO OPG/OPA can cover a wider range from 637 nm to 3.2 lm, compared with the tuning range from 650 nm to 2.5 lm as reported in the literature [5].
0030-4018/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 0 ) 0 0 9 6 8 - 8
486
D. Zhang et al. / Optics Communications 184 (2000) 485±491
The results are attributed to a rapid decrease in the refractive index caused by the contribution of phonon-related excitations as the idler wavelength approaches the absorption bands. Modi®ed Sellmeier equations are given based on our experimental data. It was also found that that the bandwidth of OPG at the end of the tuning curve, where the wavelength of the idler branch of OPG approaches the infrared absorption edge of BBO, is signi®cantly narrower than that at other parts of the tuning curve. Without using any dispersion element the bandwidth of OPG generated near the end of the tuning curve is nearly transform-limited. The mechanisms for bandwidth narrowing are discussed and are attributed to the signi®cant changes of the factors in that region, which include the slope of the refractive index of crystal for the extra-ordinary wave versus the angle, the dierence of refractive index between the signal and the o idler n o s h ÿ ni h, and the dierence of dispersion of the crystal between the signal and the o idler on o s h=oxxs ÿ oni h=oxxi . The theoretical calculation of the bandwidth using the modi®ed Sellmeier equations agrees well with the experimental data.
2. Experimental setup The experimental setup for conducting the measurements is brie¯y described as the following: the pumping source used in our OPG/OPA is a modi®ed commercial actively and passively modelocked Nd:YAG laser. The pulse duration of the YAG at 1.064 lm is compressed from 40 to 12 ps using a combined eect of negative feedback and self-defocusing with a 0.6-mm thick GaAs plate inserted in the cavity [6]. The output of the laser at 1.064 lm is about 20 mJ per pulse. The pulse duration of the laser is then further compressed by a photon-collision technique with a type-II phasematched second harmonic generator using a 5-cm long KDP crystal [7]. After the pulse compression, the laser energy at 532 nm is about 3 mJ per pulse, and the pulse duration is about 2 ps. The pumping scheme is essentially the same as our previous work on 355-nm pumped BBO-OPA
[3] except that there is only one BBO crystal used in the OPG stage in our experiment. The pumping beam is split into two parts by a beam splitter. 30% of the output energy of the lasers is used to pump the OPG stage to generate a seed beam, the pump beam is telescoped down to 2.5 mm in diameter to reach a pump intensity of 14 GW/cm2 . A 5 mm H 7 mm W 12 mm L BBO crystal cut at 22.5° is used in the OPG in a double-pass scheme without using any dispersion element. The tunable seed beam is then ampli®ed in a second 12-mm long BBO crystal in the OPA stage, which is pumped by the residual 70% of the pump energy. The pumping intensity can be adjusted to optimize the optical conversion eciency. The two BBO crystals are rotated synchronously by a mechanical device. The output of the OPG/OPA system, after removing the residual pump beam by a CaF2 dichroic mirror, which is highly re¯ective R 99% at 532 nm, is measured by a power meter (Molectron Max-400), whose spectral response is ¯at from the UV to the far-IR. The use of CaF2 substrate for the dichroic mirror allows effective transmission of the idler output. A Ge-®lter is used to block the idler output shorter than 2 lm and make the study of the output around 3 lm, which is near the IR absorption band of BBO, possible. Part of the output is picked up by a piece of glass and imaged onto the entrance slit of a 0.5m spectrometer for analysis of the spectrum. The spectrum of the OPG is recorded either by a CCD camera for the wavelength of the signal branch or by an IR detector for the idler branch. 3. Experimental result and discussion By careful spectral and temporal overlapping between the seed beam and the pump beam in the OPA stage and rotating two BBO crystals synchronously, the output of the angle-tuned OPG/ OPA system is continuously tunable from 637 nm to 3.2 lm, except three gaps near the degenerate points at 665, 1064 nm, and 2.66 lm, respectively. The above tuning range is broader than that reported in the literature. The wavelength range from 2.6 to 3.2 lm is already at the infrared absorption edge of BBO. The highest energy con-
D. Zhang et al. / Optics Communications 184 (2000) 485±491
version eciency of the system is more than 20%, which occurs at the signal wavelength of around 900 nm. In addition, we observed some new parametric properties: (1) there are retracing phenomena occurred at 665 nm and 2.66 lm, respectively; (2) the experimental tuning curve signi®cantly diers from the theoretical calculation based on the Sellmeier equations proposed by Kato [4]; and (3) the bandwidth of the OPG become nearly transform-limited when the signal wavelength is tuned to the blue side of the retracing point at 665 nm, especially near the end of the tuning curve. The new results on the parametric properties of the 532-nm-pumped BBOOPG/OPA are presented and discussed below. 3.1. Retracing behavior and discrepancy between the experimental and theoretical tuning curve By measuring the generated wavelength of the OPG while rotating the angle of the crystal step by step, we were able to construct a tuning curve of wavelength versus crystal angle. By using the 0.5m CCD spectrometer, we were able to record the spectra of the signal wave at various crystal angles with the wavelength ranging from the visible to the near IR around 1.0 lm. It is interesting to see that at a given crystal angle between 20.9° and 21.5°, there are two components in the signal branch. Besides the expected signal branch ranging from 666 to 724 nm, the output of the OPG/OPA contains an additional component at the short wavelength. Fig. 1 presents the spectra measured at various crystal angles. As can be seen that when the signal wavelength is tuned from 665 to 723 nm, there is an additional component, which is continuously tunable from 665 to 637 nm, accordingly. The later corresponds to a tuning range from 2.66 to 3.23 lm in the idler branch. The signal output cuts o sharply at 637 nm, which corresponds the idler wavelength of 3.23 lm, at which the infrared absorption of BBO crystal increases sharply. The constructed tuning curve indicates a retracing behavior of the 532-nm-pumped BBO OPG/OPA occurred at 665 nm and 2.66 lm, respectively.
487
Fig. 1. Spectra of OPG measured at various crystal angles h showing the additional frequency component due to retracing behavior of the 532-nm-pumped BBO-OPG: (a) h 21:39°, (b) h 21:23°, (c) h 21:12°, (d) h 21:01°, (e) h 20:95°, (f) h 20:91°, and (g) h 20:80°.
The retracing behavior was ®rst observed in LBO crystal when it is pumped at 532 nm [8,9]. Later, it was found that the retracing behavior of LBO could also be observed when the pumping wavelength is between 520 and 540 nm [10]. However, to our knowledge, for the 532-nmpumped BBO parametric devices, not retracing behavior has been reported in the previous work. 3.2. Discrepancy between the experimental and the theoretical tuning curve Comparing the measured data with the theoretical tuning curve, it is found that the experimental retracing behavior has signi®cant dierence from the theoretical data calculated based on the following Sellmeier equations of BBO crystal [4]: 0:01878 ÿ 0:01354k2 ; k ÿ 0:01822 0:01224 ÿ 0:01516k2 ; n2e k 2:3753 2 k ÿ 0:01667 n2o k 2:7359
2
1
where the unit of wavelength is in micrometer. Fig. 2 shows the experimentally measured tuning curve of our OPG/OPA system and the theoretically calculated tuning curve of the 532-nmpumped BBO-OPG based on the Sellmeier equations proposed by Kato as shown in Eq. (1). The experimental data exhibits a retracing behavior at
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Fig. 2. Comparison between the tuning curves calculated using Sellmeier equations proposed by Kato as shown in Eq. (1) (- - -) and the experimental data (). The solid line is data ®tting of experimental results.
around 2.66 lm in the idler branch and 665 nm in the signal branch, respectively. On the other hand, the theoretical calculation based on the Sellmeier equations shows the retracing would occur at 3.26 lm and 630 nm, respectively, and it is beyond the tuning range of BBO. The signi®cant dierence between the experimental data and the theoretical calculation indicates that the Sellmeier equations of BBO crystal given in the literatures are inaccurate and need to be modi®ed. Note that the original Sellmeier equations proposed by Kato were derived from the measurements of refractive index from 200 nm to 1.0 lm. Therefore, for wavelength longer than 1.0 lm, the predicted refractive index should be less accurate [11]. This is particularly true when the signal wavelength is shorter than 680 nm, the corresponding wavelength of the idler branch is longer than 2.2 lm, where the infrared absorption edge of BBO is approached. As can be seen in Fig. 2, there are signi®cant dierence between the experimental and theoretical tuning curve when the idler wavelength is longer than 2.2 lm. Study of infrared absorption spectrum of BBO shows that the absorption starts at 2.2 lm and increases signi®cantly with wavelength. At 3.2 lm, the transmission of a 3.72 mm thick BBO is less
than 20% [11]. Since the idler wavelength longer than 2.2 lm is close to the overtone of lattice vibrations, it is possible that the change of refractive index could be attributed to the phonon-related excitation. As a result, according to Kramer± Kronig relations, the index of refraction should decrease signi®cantly in this region. Similar discrepancy between the calculated results based on Eq. (1) and the measured tuning curves also occurs in the short wavelength side of the tuning curve at the corresponding signal wavelength from 665 to 637 nm. This is due to the fact that the signal and the idler photons are always generated in pair and they must both satisfy the phase-matching condition. The details for the retracing in the signal branch are shown in the inset of Fig. 2. Using the measured data and a nonlinear least square routine, modi®ed Sellmeier equations can be obtained. The resulted modi®ed Sellmeier equations are given as the following: 0:01878 ÿ 0:01471k2 k ÿ 0:01822 0:0006081k4 ÿ 0:00006740k6 ; 0:01224 ÿ 0:01627k2 n2e k 2:3753 2 k ÿ 0:01667 0:0005716k4 ÿ 0:00006305k6 ;
n2o k 2:7359
2
2
where the unit of wavelength is in micrometer. For comparison, we plot in Fig. 3 the refractive index of BBO as a function of wavelength based on Eq. (1) (dashed line) and Eq. (2) (solid line). It is seen that as the wavelength approaches the infrared absorption edge of BBO (>2.2 lm), the refractive index based on the modi®ed Sellmeier equations becomes signi®cantly lower than that from the original ones. The results match the discrepancies between two tuning curves shown in Fig. 2. 3.3. Bandwidth narrowing at the edge of the tuning curve It is also interesting to point out that, as can be seen from Fig. 1, the bandwidth of OPG in the blue side of the turning point of the retracing region around 660 nm is much narrower than that in the red side. As the wavelength approaches the
D. Zhang et al. / Optics Communications 184 (2000) 485±491
Fig. 3. Comparison between the calculated refractive index of BBO for ordinary wave, no , and extraordinary wave, ne , as a function of wavelength using the Sellmeier equations given by Kato (- - -) and the modi®ed Sellmeier equations (Ð). Insert shows the details for the dierence at long wavelength, where the absorption becomes signi®cant.
blue end of the tuning curve, the bandwidth become very narrow. Fig. 4 shows the spectrum of OPG/OPA around 637 nm taking by the 0.5-m CCD spectrometer. For comparison, the spectrum of a He±Ne laser at 632.8 is also showed in Fig. 4. The bandwidth of the OPG at 637 nm is measured to be about 1.3 nm (32 cmÿ1 ). After taking into account the resolution of the spectrometer, the bandwidth is found to be less than 30 cmÿ1 . Considering the pulse duration of the generated OPG, which is no more than 1.5 ps, a near transform-limited bandwidth is achieved without using any dispersion element in the OPG/OPA system. Compared with the bandwidth of OPG around 727 nm, the former is only about 1/8 width of the latter. The bandwidth of an OPG/OPA is determined through the energy conservation and phasematching conditions primarily by the bandwidth of the pump laser, the angular divergence of the pump, and the crystal length. For a double-pass OPG or an OPA stage, the bandwidth also depends on the distance that the seed beam traveled before it hits the crystal and gets ampli®ed again.
489
Fig. 4. Spectrum of the narrow band OPG at 637.1 nm (the peak on the right). For calibration and comparison, the spectrum of He±Ne laser is also shown (the peak on the left).
With a ®nite beam size of the pump, the ampli®er acts as a spatial ®lter. Consider a type-I phase-match optical parametric device using a negative uniaxial crystal, such as the case of our BBO-OPG, the ®nite beam divergence Dhp will in general lead to a range of values, Dkp , of the magnitude of the propagation vector of the pump beam which will, in turn, lead to a spread of values of the sum of the propagation vectors of the signal and idler waves D ks kp . Therefore, when the propagation direction of the interacting waves is not along a principal axis of the crystal such as the case of angle-tuned OPG, the bandwidth of the signal wave of the single-pass traveling wave OPG is dominantly limited by the ®nite beam divergence Dhp of the pump beam. The bandwidth of our BBO-OPG can be calculated by using the following equation [12]: Dx xp on e p h=ohp Dhp ; o o o o ns h ÿ ni h ons h=oxxs ÿ oni h=oxxi 3
where Dhp is the ®nite beam divergence of the pump. At a given wavelength, the bandwidth is
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proportional to the beam divergence of the pump Dhp , the slope of the refractive index of crystal of the extra-ordinary wave versus the angle of the crystal on e p h=ohp , which is a value related to the angular dispersion of the crystal. In addition, it is also related to the dierence of refractive index o between the signal and the idler n o s h ÿ ni h, and the dispersion of the crystal on o s h=oxxs ÿ o oni h=oxxi . A similar relation can also be found for the idler since the signal and the idler are generated in pair. We calculated the bandwidth of OPG at various wavelengths using about bandwidth equation (3) and used the Sellmeier equations proposed by Kato (Eq. (1)) and the modi®ed equations given by our work (Eq. (2)), respectively. The calculated results and the experimental data are shown in Fig. 5. The doted line in Fig. 5 is the calculation based on the original Sellmeier equations given by Kato, the solid line is based on the modi®ed equations, and the circles are the experimental data. The
Fig. 5. Bandwidth of the signal branch of 532-nm-pumped BBO-OPG as a function of wavelength obtained from the theoretical calculation based on the Sellmeier equations given by Kato (Eq. (1)) and the bandwidth equation (3) ( ), the calculation based on the modi®ed Sellmeier equations (2) and (3) (Ð), and the experimental data (s). The beam divergence of the pump used in the calculations is based on the experimental value of 1.5 mrad.
beam divergence of the pump beam Dhp used in our calculation is 1.5 mrad, which was measured experimentally. It can be seen that the calculated results using the modi®ed equations agree very well with our experimental data or the results using the original equations do not. The narrowed bandwidth towards the short wavelength side of the tuning curve is due to the fact that all three above-mentioned factors, which aect the bandwidth of OPG, are in favor of reducing the bandwidth of OPG as the wavelength moves towards the edge of the tuning curve. The details can be discussed as the following: ®rst, due to the retracing around 665 nm, at the wavelength shorter than the turning point, as the wavelength becomes shorter, the crystal angle hp becomes larger. The larger the angle is, the smaller the value of onp e h=ohp will be. Such a trend leads further reduction of the bandwidth. Secondly, as the wavelength tuned toward the edge of the tuning curve, the signi®cant change of the dierence of refractive index between the signal and the idler increases signi®cantly since the refractive index of the idler decreases rapidly as it approaches the absorption band from 2.6 to 3.2 lm. The o factor [n o s h ÿ ni h] makes positive contribution to the reduction of the bandwidth. Finally, the contribution of dispersion factor o on o s h=oxxs ÿ oni h=oxxi in the denominator of Eq. (3) is also favorable of reducing the bandwidth as the wavelength turned to the blue edge since the dierence of their values between the signal and the idler becomes larger at shorter wavelengths. We were unable to measured the bandwidth of the idler because our CCD camera is only sensitive from the UV to the near IR, however, the bandwidth of the OPG towards the tuning edge of the idler is also expected to be narrower since the signal and the idler are generated in pair. The calculation also shows a signi®cant bandwidth reduction as the idler wavelength longer than the turning point of the retracing around 2.66 lm. The good agreement between the experimental bandwidth and the theoretical calculation based on the modi®ed Sellmeier equations also indicates the modi®ed equations are closed to the true value of the refractive index of BBO.
D. Zhang et al. / Optics Communications 184 (2000) 485±491
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4. Conclusion
Acknowledgements
In conclusion, we have reported some new results on the phase matching optical parametric generation near the infrared absorption edge of the nonlinear medium. Due to the contribution of phonon-related excitation the refractive index of the NLO medium as a function of the wavelength is expected to change more rapidly. This causes the discrepancy between the experimental tuning curve and the calculated results based on the Sellmeier equations proposed by Kato. Modi®ed Sellmeier equations are presented based on our experimental measurements. A near transformlimited pulse can be achieved without using any dispersion element in our OPG/OPA system and it agrees well with the theoretical calculation based on the bandwidth equation and the modi®ed Sellmeier equations. The bandwidth narrowing was attributed to the angular dispersion of BBO for the pump, the dierence of the refractive index between the signal and the idler, and the dierence of the dispersion of BBO between the signal and the idler. All these three factors that determine the bandwidth of OPG are in favor of reduction of the bandwidth when the wavelength is shorter than the turning point of the retracing behavior of BBO at 665 nm.
This work was supported by National Science Foundation grant PHY9601922. The authors thank Dr. Jung Y. Huang for his valuable input in preparing the manuscript.
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