When a sample being tested is optically opaque or has a high absorption coefficient, a reflective measurement is often more suitable than a transmission measurement. We report the design and evaluation of a reflective terahertz time-domain spectroscopy (R-THz-TDS), using air as THz wave emitter and sensor, together with air-biased-coherent-detection (ABCD) method for the first time. With an 85 fs pulse amplified laser, we demonstrate a usable bandwidth from 0.5 THz to 12 THz, together with a peak dynamic range (DR) better than 2000:1 and a peak THz electrical field greater than 30 kV/cm. With a 32 fs pulse amplified laser, the usable bandwidth is remarkably expanded to a continuous 35 THz. Several far-infrared optical properties in various samples are reported. Furthermore, the time-resolved optical pump-THz probe experiment is performed. Finally, the uniqueness and advantage of this spectrometer are comprehensively compared with traditional THz-TDS and Fourier transform infrared (FTIR) spectroscopy.
©2010 Optical Society of America
Over the last decade, terahertz time-domain spectroscopy (THz-TDS) has undergone powerful development within various regions: THz imaging, bio-sensing, non-explosive testing, as well as linear and non-linear optics studying [1–5]. However, the high power and broad bandwidth THz field is still much less developed. Although several groups have developed a strong THz source via LiNbO3 crystal in a table top system [6,7], the bandwidth is limited below 3 THz. On the other hand, a wideband THz response using organic, electro-optic polymer emitter-sensor pairs was recently reported . The polymer material with electro-optic coefficient >300 pm/V provides brighter THz generation and more sensitive THz detection. However, the intense THz waves generated from laser-induced plasma in gaseous media provide a promising broadband THz source [9–14]. We apply dry air (or selected gases) as the emitter and detection medium [15,16] and furthermore integrate the THz air-biased-coherent-detection (THz-ABCD) mechanism. Gap-free emission and detection with higher signal-to-noise ratio (SNR), compared to other methods, have been obtained. The useable bandwidth is laser pulse duration limited. Pulse duration of 85 fs and 32 fs (FWHM) are two examples. In this study, we demonstrate a prototype, broadband, reflective THz spectrometer for the first time. Operating with a pulse amplified laser (85 fs or 32 fs), it provides a usable bandwidth from 0.5 THz to 12 THz (or remarkably 35 THz) continuously. A peak dynamic range (DR) better than 2000:1 and a peak-THz electrical field greater than 30 kV/cm have been obtained with the 85 fs laser source.
The reflective spectroscopy is usually performed in opaque materials. Compared to the commonly used transmission spectroscopy, the reflective geometry comes with the added difficulty of great sensitivity of the incident angle and the sample position. A normal incident angle with a long focal length might reduce the incident angle issue. However, the precise determination of the sample position is difficult, but essential, to properly determine the phase spectra. Several experimental methods to correct the phase errors have been proposed [17–24]. Rønne et al. make use of specific sample properties to avoid the position error between the sample and the reference ; Khazan et al. extract the complex function from the s-and p-polarized THz signals reflected from the sample [20,21]. These methods are realized in particular cases. On the other hand, Nashima et al. attach a slab in front of the sample surface, which comes with the problem of contact between two samples . Regarding the temporal stability of the whole setup, including the beam-pointing stability of the laser source and repeatability of the delay stage, the limit factor results not only from precise positioning of the sample but the temporal stability. To achieve our best fits the relative positions were theoretically adjusted by typically ± 5 um. This is similar to the problem in transmission THz-TDS, involving the precision of the sample thickness . The details to decide sample position are depicted in the section 3.1 sample measurement.
In this letter, we demonstrate the prototype of reflective THz-TDS (R-THz-TDS) and compare the uniqueness and advantage of this spectrometer with traditional THz-TDS and Fourier transform infrared (FTIR) spectroscopy . Several optical properties such as phonon resonance and plasma resonance in various samples under reflection and transmission geometries are reported. Furthermore, the time-resolved optical pump-THz probe experiment for a GaAs sample is performed. By integrating the dual chopping frequencies, the differential THz spectroscopy provides better contrast ratio. The broadband plasma dynamics by optical excitation is demonstrated. In addition, a fast data acquisition system introduced provides an alternative method to reach shorter scan time in THz-TDS.
2. Design and experimental setup
The broadband reflective THz-ABCD (R-THz-ABCD) spectrometer is schematically shown in Fig. 1 . A Ti-sapphire amplified laser (Spectra-Physics Hurricane) with a central wavelength of 800 nm, 85 fs (FWHM) pulse duration, 750 μJ pulse energy, and 1 kHz repetition rate is used as the optical source. The laser beam is separated into two beams by an optical beam splitter: one beam with 75% energy passing through a motorized delay line and a 100 μm thick type-I beta BBO crystal, by which the 400 nm second harmonic (SH) is produced. The fundamental (ω) and SH (2ω) beam are focused in dry nitrogen with an effective focal length 150 mm lens. The pre-dominantly p-polarized broadband THz emission from the laser-induced plasma is collimated and refocused by a pair of parabolic mirrors P1 (4” focal length) and P2 (6” focal length), and then reflected back by the sample surface located at the focal point of the parabolic mirror P2. The reflected beam is collimated again by P2. A high resistivity silicon beam splitter steers the backward THz beam by 90° to the detection part. The residual 25% optical energy is guided through the hole of the parabolic mirror P3 (2” focal length) as the probe beam.
Both the THz and probe beams are focused between two needle-shaped electrodes with 1 mm separation distance. SH generation is generated through the nonlinear interaction of the probe beam, the THz beam and the bias electric field, and its intensity is proportional to THz electrical field strength and local bias field strength. A laser-synchronized alternating bias ± 20 kV/cm at 500 Hz was applied by a high voltage (HV) modulator. It introduces an AC external bias to the optical focus point between two needle-shaped electrodes, where a bias-field-induced second harmonic pulse is generated to improve the DR and ensure coherent detection . The coherent field-induced SH generation is selected by several band pass filters and detected by a photomultiplier tube (PMT) (Hamamatsu H7732-10). Figure 2 (a) is the time-domain waveform and Fig. 2 (b) is the Fourier transform spectrum. The DR in Fig. 2 (a) is better than 2000:1, according to the definition in . About 54% of the backward THz electrical field strength was lost after the reflection on the silicon beam splitter surface. However, this design enables the normal reflection measurement and the THz electric field at the sample position is greater than 30 kV/cm. The entire THz beam path is purged with dry nitrogen to eliminate absorption lines of water vapor.
We apply air photonics based on the third order nonlinear process for THz wave generation and detection. Regarding the generation part, Cook et al. , Bartel et at . and Xu et al.  have experimentally demonstrated THz wave generation in air and initially treated it through perturbation as four-wave mixing (FWM). The THz field has the form:13] came up with semi-classical picture to explain the THz wave generation. Recently, Karpowicz et al.  applied quantum mechanics models to provide a unique look at emitted THz waves. In his model, the THz generation process takes place in two steps. First, the atoms or molecules are asymmetrically ionized within a fraction of the optical pulses, resulting in a broadband THz transient. Second, the released electron wave packets interact with the surrounding medium, resulting in the loss of their coherent motion, which produces a lower-frequency echo with frequency components below the inverse of the scattering time.
In the detection part, Dai et al.  reported broadband THz detection via THz-field-induced second-harmonic (TFISH) generation in laser-induced plasma. In the reciprocal process of FWM, TFISH in third-order nonlinearity can be expressed as:
Again, a shorter probe pulse produces a broader detected bandwidth, which is the similar mechanism as with the generation part.
In order to reach a broader THz bandwidth, instead of applying the 85 fs Ti-sapphire amplified laser, we used a 32 fs (FWHM) Ti-sapphire amplified laser (Coherent Legend Elite Duo USP) as the optical source. Figure 2 (c) and (d) show the THz waveform and spectrum generated through the 32 fs amplified laser with 700 mW input power by the R-THz-ABCD spectrometer. The phonon resonances of a silicon beam splitter at 15 THz, 18 THz and 22 THz [28,29] are clearly shown in Fig. 2 (d). The spectrum covers the region from 0.5 to 20 THz with 10% or greater of the maximum amplitude at 4.4 THz, and meets the noise floor of the measurement at approximately 35 THz.
3. System performance
3.1 Sample measurement
The THz range of water vapor absorption, reflective features of several dielectric materials and semiconductors are measured through the R-THz-ABCD spectrometer. An aluminum (Al) mirror is used as a reference due to its uniform and high reflectivity (over 98%) in the THz range. We fix the front surface of the sample position where sample is mounted vertically and mechanically held on the backside of the sample target with an open window of 3 mm diameter. This makes us easy to switch the reference mirror and samples during the measurement. With special attention, the position error is less than 5 um.
Figure 3 shows the water vapor absorption spectrum via the R-THz-ABCD, compared with the result of FTIR spectroscopy, in 15% relative humidity. The two spectra are in good agreement. The magnification of Fig. 3 reveals water absorptions between 2 THz ~2.5 THz and these absorptions correspond to previous reports [30,31].
With regards to dielectric materials, we measured optical phonon resonances of CaCO3 and α-BBO crystals along with reference measurements through the R-THz-ABCD. The reference curves are taken from reflection signals of the Al mirror. Figure 4 (a) shows spectra of a CaCO3 sample in the solid lines, which is an X-cut crystal with 2.8 mm thickness and an optical quality area of 15 × 18 mm without coating. It clearly shows the different optical properties between e and o axes when we rotate the sample corresponding to the pre-dominated p-polarization of the THz field. The dash curves shows the phase responses corresponding to the spectra. Figure 4 (b) is the transmission spectra of the same crystal measured through a transmission THz-ABCD system. No features can be resolved from these data due to large absorption and the spectra above 1.8 THz are merged at the noise floor. The R-THz-ABCD spectrometer provides a unique advantage in the measurement of high-absorption materials. The phonon resonances at 3.06 THz and 6.61 THz of o axis are shown in Fig. 4 (c) while one phonon resonance at 2.82 THz of e axis is shown in Fig. 4 (d), which is in agreement with . Here, we re-plot the reflective indices (real part: n and imaginary part: k) based on  with scatters.
Here, we demonstrate an animation of phonon resonances of a 90° cut α-BBO crystal shifting when the optical axis of the α-BBO crystal rotates along the plane perpendicular to the THz beam path. Figure 5 (a) shows the waveforms change with different angles, and Fig. 5 (b) is related spectra. As the angle is 0 degree, the major phonons modes shows at 3.0 and 6.8 THz while major phonon modes shows at 3.5, 4.1, 4.4, and 6.2 THz for 90 degree in the R-THz-ABCD system .
Regarding optical properties of semiconductors, we measured the reflective spectroscopy of several THz emitters such as n-type InAs, p-type InAs, GaAs, and GaP samples with an 85 fs amplified laser. Figure 6 (a) shows the spectrum of an n-type InAs sample with 1.4 × 1017 cm−3 dopant concentration. The plasma resonance appears around 3THz, which results in the large reflection below 3 THz and the phonon resonance around 7.2 THz related to previous publication . Figure 6 (b) shows the spectrum of a p-type InAs sample and the phonon resonance is around 7.2 THz.
Although operating with an 85 fs amplified laser, integrating a pulse steepening unit into the probe beam path, as shown in Fig. 7 (a) , provides an alternative method to obtain shorter pulse duration and broader detection bandwidth. The beam steepening unit, which consists of two convex lenses with the focal length of 8.8 cm and 7.6 cm respectively, pre-focuses the probe beam to generate air plasma and then collimates the beam. The optical pulses shrink and bandwidth broaden after passing through the air plasma . Figure 7 (b) shows the usable bandwidth of the R-THz-ABCD spectrometer continuous from 0.5 THz to 20 THz. This method expands the detected THz bandwidth to more than 20 THz while the spectrum has dips at 18 THz, which are caused by the phonon resonance of the silicon beam splitter. Figure 7 (c) shows the reflectance of a GaAs sample with the phonon resonance around 8.8 THz . Figure 7 (d) shows the reflectance of a GaP sample with the phonon resonance around 11 THz .
3.2 Pump-probe experiment
R-THz-ABCD spectroscopy provides the feasibility to investigate carrier dynamics of semiconductors, vibration relaxation in large molecules and biological complexes and so on. We demonstrate an optical pump-THz probe experiment of a GaAs sample as an example. The other optical pump pulse (800 nm) is integrated into the R-THz-ABCD spectrometer with 4 mm diameter spot size and around 20° incident angle as shown in Fig. 8 (a) . To provide better contrast ratio, we combine the dual chopping frequencies to get the differential signals with the differential frequency (Δω(166.7 Hz) = ω1(500 Hz)-ω2(333.3 Hz)) read by Lock-in amplifier. The differential reflective amplitudes (Δr) of the peak THz probe pulses are plotted as a function of pump-probe delay (tD) for optical pump pulse energies from 107.9 µJ to 1.9 µJ, as shown in Fig. 8 (b). The broaden plasma appears around 8 THz and shifts to lower frequency around 7 THz when the pump pulse energy decreases which is shown in Fig. 8 (c). The normalized differential amplitude (Δr/r) below the dash line shows the negative numbers which are due to the plasma resonance.
3.3 Fast scan system
To get one single waveform, the step scan, which is usually preferred in THz-TDS, takes one to several minutes. In real world applications, it is desired to get the whole picture of the signal within a short time. However, it is difficult for a THz-ABCD system because the repetition rate of amplified lasers is usually one to several kHz. The repetition rate limits the modulation frequency which means the lock-in amplifier time constant can’t be too short. A piezo stage (Nanomotion FB050-200) is used to perform the fast delay. This stage, powered by a piezo-ceramic linear motor, provides a maximum continuous moving speed of 1 m/s, which is more than enough for our application. A servo controller (Allmotion EZSV17) is installed to convert the command from the computer to the stage and to feed back the position reading. The minimum lock-in amplifier time constant available is 3 ms, according to the 1 kHz laser repetition rate. With this time constant, the maximum scan speed without distorting the waveform is around 1 mm/s. It takes about 2 s with the DR of ~80 to finish a single waveform, as demonstrated in Fig. 9 .
R-THz-ABCD spectroscopy, traditional THz-TDS, FTIR spectroscopy
According to the above results, we comprehensively compare the uniqueness and advantages among the R-THz-ABCD spectroscopy, traditional THz-TDS, and FTIR spectroscopy from far infrared to mid infrared range. THz-TDS with high SNR has been developed over the last decade by Wu et at . However, the useful bandwidth in the THz range is limited (<3 THz) and the peak THz electric field is weak (< several kV/cm). On the other hand, FTIR spectroscopy has been a commercial product for some time, providing a useful bandwidth from far infrared to visible range. However, the peak electric field is much weaker than THz-TDS and it is hard to realize time-resolved experiments . Operating in an 85 fs pulse amplified laser, the R-THz-ABCD system provides the broad bandwidth (0.5~10 THz with 10% or greater of the maximum amplitude at 1.72 THz referred to Fig. 7 (b)), high peak THz field (>30 kV/cm) as well as time-resolved experiments. Table 1 lists a series of comparisons including radiation source, detector, DR, bandwidth, resolution, peak power, and data acquisition time. In terms of SNR according to the definition of , we provide the SNR variation with frequency in both the R-THz-TDS and FTIR spectroscopy as shown in Fig. 10 . In this paper, we utilize the performance of a Bruker IFS 66v/S spectrometer for comparison in which we choose mercury as the source and DTGS as the detector. In a nine time scan average, several parameters are selected, such as 0.6 cm−1 resolution, T222 beam splitter, 6 mm aperture setting, single-sided acquisition mode. For the R-THz-ABCD spectrometer, we set resolution at 1.6 cm−1 and a 100 ms Lock-in amplifier time constant in a nine time scan average. Figure 10 clearly shows the R-THz-ABCD with higher SNR below 5.4 THz compared to FTIR. Even though the SNR of the R-THz-ABCD decays with frequency after 3 THz, it still has good SNR until 16 THz.
Broad bandwidth (0.5~35 THz in 32 fs laser), high peak electrical field (>30 kV/cm), high peak DR (>2000), time-resolved feasibility, absorption-free material measurement, and table-top R-THz-ABCD spectrometer have been realized. We report several sample measurements and demonstrate the carrier dynamics by an optical pump-THz probe experiment. By integrating a pulse steepening unit, THz bandwidth covers the entire THz gap and enters the middle infrared with an 85 fs laser pulse. Finally, we comprehensively perform a comparison among R-THz-ABCD spectroscopy, traditional THz-TDS and FTIR spectroscopy. Compared to transitional THz-TDS, R-THz-ABCD has unprecedented bandwidth as well as at least one order larger peak THz field. Compared to FTIR spectroscopy, it provides time-resolved optical gating and several orders larger peak electric field.
We acknowledge valuable discussion with Dr. Nick Karpowicz and technical support from Dr. Jianming Dai. We also gratefully acknowledge support from the Office of Naval Research, the National Science Foundation, DTRA, and the Department of Homeland Security through the DHS-ALERT Center under Award No. 2008-ST-061-ED0001. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security.
References and links
1. M. C. Nuss, D. H. Auston, and F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58(22), 2355–2358 (1987). [CrossRef] [PubMed]
2. D. Grischkowsky, S. Keiding, M. V. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990). [CrossRef]
4. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2(3), 679–692 (1996). [CrossRef]
5. T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, “Terahertz time-domain spectroscopy studies of the optical constants of the nematic liquid crystal 5CB,” Appl. Opt. 42(13), 2372–2376 (2003). [CrossRef] [PubMed]
6. A. G. Stepanov, J. Hebling, and J. Kuhl, “Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. Lett. 83(15), 3000–3002 (2003). [CrossRef]
7. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]
8. C. V. McLaughlin, L. M. Hayden, B. Polishak, S. Huang, J. Luo, T.-D. Kim, and A. K.-Y. Jen, “Wideband 15 THz response using organic electro-optic polymer emitter-sensor pairs at telecommunication wavelengths,” Appl. Phys. Lett. 92(15), 151107 (2008). [CrossRef]
9. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71(17), 2725–2728 (1993). [CrossRef] [PubMed]
10. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25(16), 1210–1212 (2000). [CrossRef]
11. T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30(20), 2805–2807 (2005). [CrossRef] [PubMed]
13. K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15(8), 4577–4584 (2007). [CrossRef] [PubMed]
16. X. Lu, N. Karpowicz, and X.-C. Zhang, “Broadband terahertz detection with selected gases,” J. Opt. Soc. Am. B 26(9), A66–A73 (2009). [CrossRef]
17. C. Rønne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107(14), 5319–5331 (1997). [CrossRef]
18. D. Hashimshony, I. Geltner, G. Cohen, Y. Avitzour, A. Zigler, and C. Smith, “Characterization of the electrical properties and thickness of thin epitaxial semiconductor layers by THz reflection spectroscopy,” J. Appl. Phys. 90(11), 5778–5781 (2001). [CrossRef]
19. C.-H. Shon, W.-Y. Chong, S.-G. Jeon, G.-J. Kim, J.-I. Kim, and Y.-S. Jin, “High Speed Terahertz Pulse Imaging in the Reflection Geometry and Image Quality Enhancement by Digital Image Processing,” Int. J. Infrared Millim. Waves 29(1), 79–88 (2008). [CrossRef]
20. M. Khazan, R. Meissner, and I. Wilke, “Convertible transmission-reflection time-domain terahertz spectrometer,” Rev. Sci. Instrum. 72(8), 3427–3430 (2001). [CrossRef]
21. A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, “Phase-sensitive time-domain terahertz reflection spectroscopy,” Rev. Sci. Instrum. 74(11), 4711–4717 (2003). [CrossRef]
22. S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. 79(24), 3923–3925 (2001). [CrossRef]
23. T.-I. Jeon and D. Grischkowsky, “Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy,” Appl. Phys. Lett. 72(23), 3032–3034 (1998). [CrossRef]
24. S. Watanabe, R. Kondo, S. Kagoshima, and R. Shimano, “Spin-density-wave gap in (TMTSF)2PF6 probed by reflection-type terahertz time-domain spectroscopy,” Phys. Stat. Sol. (b) 245(12), 2688–2691 (2008). [CrossRef]
26. N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire “terahertz gap”,” Appl. Phys. Lett. 92(1), 011131 (2008). [CrossRef]
27. M. Naftaly and R. Dudley, “Methodologies for determining the dynamic ranges and signal-to-noise ratios of terahertz time-domain spectrometers,” Opt. Lett. 34(8), 1213–1215 (2009). [CrossRef] [PubMed]
28. D. Edward, Palik, “Silicon (Si),” “Calcium Carbonate, Calcite (CaCO3),” “Indium Arsenide (InAs),” in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Elsevier, 1998).
30. V. B. Podobedov, D. F. Plusquellica, K. E. Siegrist, G. T. Fraser, Q. Ma, and R. H. Tipping, “New measurements of the water vapor continuum in the region from 0.3 to 2.7 THz,” JQSRT 109, 458–467 (2008).
32. J. Liu and X. C. Zhang, “Birefringence and absorption coefficients of alpha barium borate in terahertz range,” J. Appl. Phys. 106(2), 023107 (2009). [CrossRef]
33. S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16(22), 17626–17636 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-17626. [CrossRef] [PubMed]
34. L. J. Bignell and R. A. Lewis, “Reflectance studies of candidate THz emitters,” J. Mater. Sci. Mater. Electron. 20(S1), S326–S331 (2009). [CrossRef]
35. Q. Wu, F. G. Sun, P. Campbell, and X.-C. Zhang, “Dynamic range of an electro-optic field sensor and its imaging applications,” Appl. Phys. Lett. 68(23), 3224–3226 (1996). [CrossRef]
36. P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, “A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy,” J. Appl. Phys. 89(4), 2357–2359 (2001). [CrossRef]