We uncover that thin (of few tens of μm thickness) BBO crystal exhibits reasonable transmittance and phase matching in the 3 − 5.2 μm range. We also provide refined dispersion equations of the ordinary and extraordinary refractive indexes for the 0.188 − 5.2 μm wavelength range, which were derived using an extended set of the refractive index values from direct measurements available in the literature and from indirect refractive index evaluation based on large collection of tuning curves provided by Light Conversion Ltd., and our own measurements of the sum-frequency mixing between the fundamental wavelength of Ti:sapphire laser and wavelength-tunable mid-infrared pulses. In particular, the uncovered mid-infrared features of BBO were exploited for the characterization of the ultrashort laser pulses at 4 μm and over an ultrabroad wavelength range, demonstrating simultaneous sum-frequency generation-based frequency-resolved optical gating of the signal and idler pulses from an optical parametric amplifier, and difference frequency pulse with central wavelengths of 1.3, 2.1 and 3.5 μm, respectively, using BBO crystal of 20 μm thickness.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Owing to its excellent optical properties (broad transparency range, high nonlinear optical coefficients, high damage threshold), beta barium borate (β-BaB2O4, BBO) is one of the most popular nonlinear crystals [1–4]. BBO is a negative uniaxial crystal, which provides phase-matching for various second-order interactions almost over its entire transparency range (from 185 nm to 3.3 μm, as deduced from the transmittance measurements using crystal samples of several mm thickness [1,4]), making it a widely used crystal for nonlinear frequency conversion in the ultraviolet, visible and near-infrared. In particular, BBO crystal serves as indispensable nonlinear medium that is used in various designs of the optical parametric amplifiers, see e.g.  and references therein, and in a variety of frequency up-conversion schemes, see e.g. . Due to favorable dispersive characteristics, BBO provides broad phase matching bandwidth, which supports the amplification of ultrabroadband, few-optical cycle pulses in the noncollinear geometry, see e.g. [7, 8]. In that regard, BBO is the most important nonlinear crystal for near-infrared optical parametric chirped pulse amplifiers , which currently deliver few optical cycle pulses with high average [10, 11] and ultrahigh peak [12–14] powers.
Broad phase matching bandwidth of BBO is also of importance for characterization of the shortest, few optical cycle pulses using many variants of frequency resolved optical gating (FROG) , spectral phase interferometry for direct electric field reconstruction (SPIDER) , and more recently developed techniques, such as dispersion scan  and chirp scan , which all typically employ very thin BBO crystals. In particular, characterization of nearly single optical cycle pulses [19, 20] and simultaneous measurements of the pulses with different carrier wavelengths and pulse trains [21, 22] was demonstrated using variants of FROG technique based on either second-harmonic or sum-frequency generation in BBO crystals of 5 – 20 μm thickness.
However, so far the applications of BBO crystal have been generally limited to wavelengths shorter than 3 μm, above which the crystal absorption becomes very significant. In this paper we demonstrate that thin (few tens of μm) BBO crystal still exhibits a reasonable transparency and phase matching in the 3 – 5.2 μm range that could be readily exploited for characterization of ultrashort mid-infrared laser pulses. Moreover, combining available refractive index data from the literature with refractive index values indirectly evaluated from large database of the phase matching curves collected by Light Conversion Ltd., who is an established world leader in commercial ultrafast optical parametric amplifiers, and our own measurements in the mid-infrared, we derived refined dispersion equations, which are valid for the entire transparency range (0.188 – 5.2 μm) of the BBO crystal.
2. Transmittance and phase matching in the mid-infrared
It is generally assumed that BBO crystal is transparent from 185 nm to 3.3 μm, and this assumption is based on the transmittance measurements in few mm-thick samples [1, 4]. These measurements demonstrate that BBO exhibits a steep drop of the ultraviolet transmittance for wavelengths below 200 nm, while in the infrared the decrease of the transmittance is relatively slow: the crystal starts absorbing at wavelengths greater than 2.1 μm, but still exhibits a reasonable (≥50%) infrared transparency up to 3 μm.
In the present study, we performed measurements of the transmittance in a much thinner crystal sample, which revealed a number of interesting features regarding the crystal transparency in the mid-infrared. Figure 1 presents the infrared transmittance of 200 μm-thick BBO crystal in the 2.5 – 6.5 μm wavelength range as measured by two different methods. The red solid curve presents the transmittance as recorded by means of FTIR spectrometer (Vertex 70, Bruker Corp.). The blue solid curve shows the transmittance measured by a home-built scanning prism spectrometer with PbSe detector and using femtosecond supercontinuum as a probe, which was generated by filamentation of 60 fs pulses with carrier wavelength of 3.5 μm in 4 mm-thick BaF2 plate, see  for details. These measurements revealed that 200 μm-thick BBO sample is still transparent up to 6.2 μm showing distinct transparency bands around 3.75 μm and 4.6 μm, and a more structured band in the 5.0 − 6.2 μm range. Since 20 μm crystal is attached by the optical contact on fused silica substrate, the direct measurement of its transmittance was not possible due to absorption in the substrate itself. Therefore the transmittance of 20 μm crystal was scaled using the absorption data of 200 μm-thick sample. The calculated transmittance is shown by a green dashed curve and demonstrates reasonably high (> 60%) transparency well above the alleged cut-off at 3.3 μm, which was determined for thick crystal samples and commonly regarded as the infrared transparency edge of BBO. The absence of data in the calculated transmittance around 4.9 μm and 5.75 μm originated from the uncertainty of the zero transmittance level as retrieved by the Fourier transform of 200 μm-thick sample transmittance data.
In what follows, we verified that BBO crystal provides phase matching for both type I and type II interactions in that wavelength range. For this purpose we performed the sum-frequency generation in the collinear geometry using two 200 μm-thick BBO crystals cut at θ = 29.2°, ϕ = 90° and θ = 30°, ϕ = 0°, which provided type I and type II phase matching, respectively. The sum-frequency was generated by mixing the fundamental harmonic (800 nm) pulses from the Ti:sapphire laser (Spitfire-PRO, Newport-Spectra Physics) with wavelength-tunable (in the 2.8–5.2 μm range) mid-infrared pulses as obtained by the difference frequency generation (DFG) between the signal and idler outputs of the fundamental harmonic-pumped optical parametric amplifier (Topas-Prime, Light Conversion Ltd.) in a 1-mm thick potassium titanyl arsenate (KTA) crystal cut for type II phase matching, see  for details. In the case of type I phase matching interaction, we used the o-polarized pulse at 800 nm and the o-polarized mid-infrared pulse, so generating the e-polarized sum-frequency pulse. In the case of type II phase matching, the e-polarized sum-frequency pulse was generated by mixing the o-polarized pulse at 800 nm and the e-polarized mid-infrared pulse. The crystals were mounted on a computer-controlled rotation stage, and the phase matching angles were found from the measurements of the sum frequency spectrum, as recorded with fiber spectrometer (Avaspec 3648-USB2-UA, Avantes). Phase matching angles for type I and type II second harmonic generation of the Ti:sapphire laser at 800 nm served as references to calibrate the absolute orientation of the crystals.
Figure 2 shows the phase matching angles for type I [Fig. 2(a)] and type II [Fig. 2(b)] sum-frequency generation in the 0.8 – 5.2 μm range, where circles depict the phase matching angles versus wavelength of the difference-frequency pulse, as measured in the present study. Crosses mark the mean values of the experimental phase matching angles in the near-infrared as taken from the database of Light Conversion Ltd., which contains more than 600 individual phase matching curves; the number of data points is intentionally reduced for illustrative purposes. These phase matching angles were measured by mixing 800 nm pulses with wavelength-tunable output from the optical parametric amplifier, in the 1.142 – 2.412 μm range for type I phase matching and in the 1.140 – 1.571 μm range for type II phase matching.
The experimental data are compared with the phase matching angles calculated using the dispersion equations from , which are considered as the most accurate for BBO crystal , the dispersion equations from , whose validity was justified experimentally over a wider wavelength range  and more recent equations provided by , where solid lines depict the phase matching curves in their validity ranges, which are limited to approximately 3.0 μm, whereas dashed lines show their extrapolations toward longer wavelengths. Notice an almost perfect coincidence between the measured phase matching angles and those calculated from  in the 0.8 – 3.0 μm range, while noticeable differences between the experimental points and phase matching curves calculated from  and  start emerging for wavelengths longer than ~ 2 μm. However, large discrepancies between the experimental and any of the extrapolated phase matching curves occur for wavelengths greater than 3 μm.
3. Revisit of the dispersion equations
Therefore, in what follows we revisited the dispersion equations of BBO with an account of the above experimental data. In doing so, the measured phase matching angles served to derive the values of the ordinary (no) and extraordinary (ne) refractive indexes. More specifically, the experimental phase matching angles for type I interaction allowed the calculation of no values in the 0.8 – 5.2 μm wavelength range. Accordingly, the experimental phase matching angles for type II interaction served to calculate the values of ne. In addition, the refractive index data range was extended by including experimentally measured refractive index values in the wavelength interval of 0.25365 – 2.3253 μm . The refractive index values down to 204.8 nm were obtained from the fitting rule of , which gives correct (well verified experimentally) phase matching angles for second harmonic generation in the ultraviolet. The refractive index values in the ultraviolet down to 188 nm were derived using the phase matching curves of sum-frequency mixing from the database of Light Conversion Ltd.
The best fit for the constructed refractive index dataset was obtained with Sellmeier equation assuming three idealized oscillators, a priori locating one oscillator in the mid-infrared and the other two in the ultraviolet, and yielded the following refined dispersion equations of no and ne over the full transparency range (0.188 – 5.2 μm) of BBO crystal:
Figure 3(a) shows the dispersion curves of the ordinary and extraordinary refractive indexes over the entire transparency range of BBO, as calculated using Eq.(1) and compares them with the refractive index curves calculated from the dispersion equations of ,  and . Almost perfect coincidence between the refined dispersion curves from Eq.(1) and those from the literature [1,4,24] is obtained in the ultraviolet, visible and near infrared. It is important to note that the refined dispersion curves fit the directly measured ordinary and extraordinary refractive index values in the 0.25365 – 2.3253 μm range, as tabulated in , with a remarkable accuracy better than 4 × 10−5. However, large discrepancies between the revisited dispersion curves and those provided in the literature [1, 4, 24] (and among these as well) occur for wavelengths greater than 3 μm, as highlighted in Fig. 3(b), which presents the dispersion of refractive indexes in the reduced, 0.5 – 5.5 μm range. The largest mismatch is observed between the revisited and extrapolated dispersion curves of , which used a modified dispersion equation of  assuming almost constant birefringence in the 0.5 – 3.17 μm range, thus yielding systematically underestimated values of ne. Extrapolation of the dispersion curves of  and , which were based on direct measurements of the refractive indexes in the 0.404 – 1.014 μm and 0.25365 – 2.3253 μm ranges, respectively, yield somewhat better agreement, in particular for the extraordinary refractive index.
It is interesting to note that the revisited dispersion equations expressed by Eq.(1), give the intersection point of no and ne dispersion curves at 4.62 μm, as indicated by the bold dot in Fig. 3(b). Such specific wavelength indicates the absence of birefringence (no = ne) and suggests that for longer wavelengths BBO becomes a positive uniaxial crystal, still possessing phase matching, as evident from Fig. 2. For a comparison, extrapolation of the dispersion equations of  and  predict the intersections at 5.75 μm and 5.66 μm, respectively, which are located outside the plot. Therefore the intersection wavelength may serve as an important checkpoint for justification of validity of the dispersion curves. In order to examine this interesting situation, we performed a complimentary experiment where we placed BBO crystal between two crossed polarizers (YVO4 Glan prisms) and measured the transmittance of the linearly polarized broadband DFG pulse by independently rotating the crystal in both, θ and ϕ planes. Regardless of the crystal orientation, no transmittance was observed at the proximity of 4.62 μm, as shown in Fig. 4, thereby justifying the absence of polarization rotation (i.e. the absence of birefringence) at this wavelength, exactly as predicted by revisited dispersion equations obtained in the present study.
Finally, Eq.(1) was used to calculate the phase matching curves for type I and type II sum frequency mixing, which are illustrated by red solid lines in Figs. 2(a) and 2(b), respectively. The evaluated differences between the calculated and measured phase matching angles do not exceed 0.2° in the 0.8 – 1.74 μm range and 0.4° for the rest of the wavelengths up to 5.2 μm for both types of phase matching.
4. Applications for the diagnostics of mid-infrared laser pulses
In this section we demonstrate that the uncovered features of transmittance and phase matching make the BBO crystal suitable to characterize the ultrashort pulses in the mid-infrared, where the choice of suitable nonlinear crystals is limited by their transparency range and acceptance bandwidth . As the first example, we demonstrate characterization of the difference frequency pulse with a central wavelength of 4 μm by means of cross-correlation frequency-resolved optical gating (XFROG). XFROG measurements were performed by the collinear sum-frequency generation in a thin (20 μm thickness) type I phase matching BBO crystal using a 24 fs reference pulse with a central wavelength of 0.72 μm, as delivered by the second harmonic-pumped non-collinear optical parametric amplifier (Topas-White, Light Conversion Ltd.). A clear advantage of using BBO crystal in the sum-frequency generation scheme is that the signal is converted into the range of Si detectors, enabling the use of standard spectrometers, which provide high spectral resolution, high sensitivity and hence the signal to noise ratio, making the measurements a lot easier. Figure 5 shows the measured and reconstructed XFROG traces, the measured and retrieved spectra, and the retrieved intensity profile, spectral and temporal phases of the pulse. A slight, but noticeable difference between the measured and retrieved spectral shapes is attributed to the absorption of atmospheric CO2, which produces a steep decrease of the measured spectral intensity at the vicinity of 4.25 μm. The pulse duration of 106 fs was retrieved within a grid size of 256 × 256 pixels and a reconstruction error of 1.2%.
As the second example, we demonstrate simultaneous diagnostics of several ultrashort pulses with very different carrier wavelengths. More precisely, we simultaneously characterized the signal, idler and difference frequency pulses with central wavelengths of 1.3, 2.1 and 3.5 μm, respectively, as they exit the DFG crystal. Such ultrabroadband characterization was made possible due to extremely broad acceptance bandwidth, which in the present configuration was estimated to be greater than 4300 nm.
The pulses of interest were polarized with respect to the optical table as follows: the signal and reference pulses were polarized horizontally, while the difference frequency and idler pulses were polarized vertically, as schematically illustrated in Fig. 6(a). The incident beams were collinearly combined through a wedged sapphire plate. The crystal was rotated at 45° with respect to the phase matching plane, so as to split the polarizations of the incident pulses into the o-polarized and e-polarized components, hence allowing simultaneous type I phase matching between the pulses of interest and the reference pulse. The sum-frequency signals were then coupled into a fiber spectrometer. The measured XFROG traces are presented in Fig. 6(b). Figure 6(c) shows the retrieved temporal profiles of the pulses. Notice that the pulses are shifted in time due to the group velocity mismatch in the DFG crystal, and how the temporal shapes of the signal and idler pulses are deteriorated because of their depletion during the DFG process.
Finally, it is worth mentioning that BBO crystal also provides phase matching for type I second harmonic generation with incident wavelengths up to 4.4 μm, and very broad acceptance bandwidth (e.g. > 3800 nm at 3.2 μm calculated for the crystal of 20 μm thickness) as could be easily verified from the refined dispersion equations, suggesting the suitability of BBO crystal for pulse characterization in the mid-infrared employing self-referenced diagnostic methods.
In conclusion, we uncovered that thin BBO crystal exhibits reasonable transparency and phase matching well beyond its alleged infrared absorption edge at 3.3 μm, as demonstrated by the measurements of transmittance and by sum-frequency generation experiments which involve the fundamental harmonics of Ti:sapphire laser at 800 nm and mid-infrared pulses whose wavelength was tuned in the 2.8 – 5.2 μm range. We revisited the dispersion equations of BBO crystal which are currently in use and which provide large discrepancies of the ordinary and extraordinary refractive index values and hence the phase matching angles in the mid-infrared. Based on indirect evaluation of the refractive index values from the phase matching angles as performed in the present study and directly measured refractive index data from the literature, we derived refined dispersion equations of BBO crystal, which are valid over its entire transparency range, from 188 nm to 5.2 μm.
The uncovered features of thin BBO crystal: mid-infrared transparency, phase matching and broad acceptance bandwidth, were demonstrated to be particularly useful for diagnostics of the ultrashort laser pulses over significantly wider wavelength range, as was considered before. To this end, we experimentally performed characterization of the pulses at 4 μm and simultaneous diagnostics of the pulses with distinctly different carrier wavelengths (1.3, 2.1 and 3.5 μm) by cross-correlation frequency resolved optical gating. Finally, the refined dispersion equations yield the phase matching for the second harmonic generation with incident wavelengths up to 4.4 μm, suggesting the possibility to characterize the mid-infrared laser pulses by means of self-referenced methods, such as spectral phase interferometry, chirp and dispersion scans, which typically employ very thin BBO crystals for broadband frequency doubling.
We acknowledge fruitful discussions with R. Grigonis form Light Conversion Ltd., and R. Valauskas and D. Kuzma from Eksma Optics, to whom we are also grateful for donating the crystals used in the experiments. We thank J. Čeponkus for the help with FTIR measurements, and J. Lukošiūnas and A. Marcinkevičiūte for their assistance in performing FROG diagnostics.
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