A method for simultaneously measuring the refractive index and absorption coefficient of nonlinear optical crystals in the ultra-wideband terahertz (THz) region is described. This method is based on the analysis of a collinear difference frequency generation (DFG) process using a tunable, dual-wavelength, optical parametric oscillator. The refractive index and the absorption coefficient in the organic nonlinear crystal DAST were experimentally determined in the frequency range 2.5–26.2 THz by measuring the THz-wave output using DFG. The resultant refractive index in the x-direction was ~2.3, while the absorption spectrum was in good agreement with FT-IR measurements. The output of the DAST-DFG THz-wave source was optimized to the phase-matching condition using the measured refractive index spectrum in THz region, which resulted in an improvement in the output power of up to a factor of nine.
© 2010 OSA
THz-wave radiation has been used in several fields of science, including physics, chemistry, biology, medicine, and environmental science. In THz technology, a monochromatic source is an extremely important device and has enabled many applications. Ito et al. have developed tunable monochromatic THz-wave sources based on nonlinear optical processes. These systems use optical parametric oscillations (OPO) [1,2] and difference-frequency generation (DFG) [3,4]. They have achieved THz-wave sources that are widely tunable and frequency agile by using organic nonlinear crystals for the DFG process.
In these nonlinear processes, high output power THz radiation is expected when the phase-matching condition is met and the THz-wave gain is higher than the loss. Therefore, the refractive index and absorption coefficient in the THz region, which are related to the phase-matching condition and losses in a nonlinear material, are very important. These optical properties provide us the information not only to optimize the pump wavelength and the suitable crystal thickness for THz generation , but also to assign the inter- and intramolecular vibration modes in organics .
Optical crystals of 4-dimethylamino-N-methyl-4-stilbazolium-tosylate (DAST)  are remarkable in their ability to generate THz waves due to the high optical nonlinearity  and low refractive index dispersion in the THz and near-infrared regions [9–11]. Moreover, wideband THz-wave generation has been reported [12,13]. The refractive index of DAST has been studied in the near-infrared region , and the refractive index and absorption in the region 0–3 THz using a terahertz time-domain spectroscopy . Directly measuring the reflective index in the wideband from the THz-region to the mid-infrared region is difficult because of the large absorption coefficient in DAST, and the absence of a tunable source or detector in this frequency region. In this paper, we report the development of a simultaneous method to obtain both the refractive index and the absorption coefficient in a nonlinear optical crystal in the ultra-wideband THz region using a collinear DFG process. Our method is based on the fact that the output power from the collinear DFG processes depends strongly on the refractive index, absorption, and the wavelengths of the input and output electromagnetic waves.
Consider the situation where two pump beams with wavelengths λ1 and λ2, where λ1 < λ2, are collinearly incident on a nonlinear crystal of thickness L. The THz-wave radiation with wavelength λTHz is generated in the crystal by a DFG process. The functional form of the output power from the process is given by [11,12]
Here, we consider the case of THz-wave generation using a DAST crystal as reported in Ref. 3. In the optical region, the refractive index, n, of DAST has been established by F. Pan et al.  Therefore, n λ1 and n λ2 are known in this case. Because the absorption coefficient in THz frequency region is very large (α > 100 cm−1, as shown in FT-IR measurement in experimental section), we assume that the absorption in the optical region can be ignored in Eq. (3), yielding . So, in the DAST case, one can obtain n THz and αTHz from the two-dimensional measurement of S(λ1, λ2). Since we are considering a nonlinear process in which three wavelengths are coupling with the component, d 111, in the nonlinear coefficient tensor of the DAST, n λ1 and n λ2 in the x-direction were used for the calculation and n THz and αTHz in the same direction were obtained.
Note that, with a traditional method (e.g., THz-TDS) one must prepare thin samples to measure the refractive index and the absorption in opaque materials; however, with this method, controlling the sample thickness is not necessary because these are given within the functional form factor of the peak shift and line width of S(λ1, λ2). Furthermore, one need not consider the Fresnel loss at the sample surfaces to obtain the absorption coefficient. This method can be applied not only to DFG processes, but also to other nonlinear processes including sum frequency generation and higher order processes.
The collinear DFG and detection experimental setup is shown in Fig. 1 . It was similar to that of the broad tunable THz-wave source reported earlier by Ito et al.  λ1 and λ2 are generated in a dual-wavelength source (KTP-OPO), which was pumped by pulsed 532-nm radiation from a frequency-doubled Nd:YAG laser (8 ns, 100 pps, 95 mJ/pulse). KTP-OPO is based on a single resonance-type OPO in which the signal wave (762–921 nm) is confined by mirrors M1 and M2. M1 is coated for high reflectivity of the signal waves and high transmittance of the 532 nm and idler waves (1260–1760 nm), M2 is a broadband mirror, and M3 is coated for high reflection of idler waves but high transmittance at 532 nm. Since the two KTP crystals (a) and (b) are mounted on galvano scanners in one cavity, one can independently select a pair of wavelengths λa and λb from 1260 to 1760 nm by setting the incident angles for the pump beam of each crystal. The shorter of the wavelengths λa and λb is designated λ1 and the longer λ2.
The two waves from the KTP-OPO propagate onto the c-axis of a 1-mm-thick DAST crystal. In the DAST crystal, the THz wave is generated by a type-zero DFG process in which the polarization direction of every wave is along to the a-axis of the DAST crystal. The THz waves pass though the low-pass filter to clip λ1 and λ2 and are then collimated and focused onto a 4 K Si bolometer by a pair of off-axis parabolic mirrors. Note that the maximum measurable frequency was limited to 30 THz due to the sensitivity of the bolometer; other types of detectors (e.g., pyro-detector) could potentially improve the range.
4. Results and discussion
The DFG output power was measured while varying λa and λb independently from 1260 to 1760 nm. Figure 2 (a) shows a two-dimensional mapping of the output power. The output power was normalized to the maximum at each frequency difference, and the frequency dependence comes from the dispersion of the refractive index in the THz region. The width of the absorption band also depends on the THz frequency. The measured area in Fig. 2 was limited by both the range in rotation angle of the KTP crystals in the OPO cavity and the frequency sensitivity of the bolometer used as a detector. The output spectra were measured with good signal-to-noise ratios in the frequency regions of 2.5–20 THz and 22.5–26.2 THz. The horizontal fine structure in Fig. 2(a) results from the power fluctuation of the KTP-OPO, and is a consequence of optical cavity modes of the crystal. Figure 2(b) shows the spectral mapping with this fine structure removed by applying a low intensity threshold to the data.
To obtain the refractive index and absorption coefficient as a function of the THz frequency, the cross sections at each frequency difference on the mapping were analyzed by applying a least square fit to Eq. (1). For the fitting, the refractive indices n λ1 and n λ2 in the x-direction were given by the Sellmeier formula using parameters from Ref. 8 and L = 1 mm was substituted into Eq. (1) and A, n THz and α THz were adjustable. Figure 3 shows an example of this fitting; the spectral shift and line width were replicated by the fitting function. The refractive index and absorption coefficient at 18.9 THz were n THz = 2.295 ± 0.001 and α THz = 125 ± 10 cm−1, respectively. Since the accuracy of refractive index has influence to the spectral shift, it was depended on the accuracy of n λ1 and n λ2, which were given to four significant figures in Ref. 8, the wavelength determination accuracy of the KTP-OPO and the uncertainty of the fitting. The accuracy of absorption coefficient is linked to the spectral line width of the output function and is limited by the accuracy of L and the broadband flatness of the KTP-OPO output power in addition to the factors for refractive index. In our case, the uncertainty of the fitting was the most dominant in these limiting factors. Thus, the error was estimated from the statistical uncertainty of the least square fit in which we took the confidence interval to 95%. The same fitting process was performed at all frequencies.
Figure 4(a) shows the results for the refractive index as best-fit coefficients for all frequencies. The positive and negative difference frequency points both oscillated around n = 2.3, and the functional form follows that of the absorption coefficient. The refractive index obtained using the new method is in satisfactory agreement with the data from Ref. 14, which was measured using a THz time-domain spectroscopic method. Figure 4(b) shows results for the absorption coefficient, together with the absorption coefficient spectrum along the x-axis of the DAST crystal measured using an FT-IR spectrometer. Because of the large absorption of a DAST in the THz region, for the FT-IR measurement we thinned the DAST crystal to 0.25 mm using a special turning lathe . The Fresnel losses at the surfaces of the DAST crystal were considered due to the refractive index of 2.3. The absorption spectra were in good agreement, both in terms of functional form and magnitude. The absorption coefficient at around 15 THz was too large to measure using FT-IR, however, could be measured using the present method. We also took into account that the spectral resolution of the refractive index and the absorption coefficient were reduced by the 180-GHz spectral line width of the KTP-OPO output. The discrepancy of absorption coefficient between the present method and the FT-IR measurement was rather large in between from 10 to 20 THz. We consider that this is due to the assumptions that we neglected the absorption of λ1 and λ2 in the DAST for the present method and that we also neglected the dispersion of the refractive index to obtain the Fresnel losses for the FT-IR measurement. In the range, 20–23 THz the absorption coefficient is large, and the signal-to-noise ratio is too low to make reliable measurements. For this reason, there is a gap in the data in Fig. 4. The shaded region in Fig. 4(a) shows the frequency range where we cannot determine the refractive index using the difference frequency system. However, the refractive index is within these limits for almost all frequencies. Following the publication of this work, the numerical data will become available on the THz-database .
The refractive index spectra of nonlinear crystals in the THz region make it possible to optimize the phase matching condition at all frequencies5. This can be achieved by controlling the phase mis-match, Δk, which appears in Eq. (2) and which depends on n THz. Figure 5 shows a comparison of the normalized THz output power spectrum with and without the optimized phase matching. The latter in which one wavelength was fixed to 1.3 μm as provided in Ref. 3 was useful for achieving the wide tunability and easy controlling of KTP-OPO, but had disadvantage in the high power output. An increase in the output power of up to a factor of nine was observed.
We have developed a method to measure the refractive index and absorption coefficient of nonlinear crystals in the THz frequency range. Using this technique, we measured a DAST crystal, and characterized n and α in the range 2.5–26 THz. The frequency-dependent refractive index data was used in improve the phase matching condition for DFG, and an improvement in the output power of up to a factor of nine was observed. This method is, in principle, applicable to all nonlinear crystals that can be used for DFG of THz-wave radiation.
The authors thank A. Nawahara for his valued assistance in the experimental procedures. We also thank C. Takyu, T. Shoji, and Y. Konno, who respectively performed the dielectric and metal coating, the polishing of the various optical components, and the turning of the DAST crystals. This work was partly supported by a Grant-in-Aid for Scientific Research (A) from the Japan Society for the Promotion of Science (JSPS) (No. 19206009) and a Research for Promoting Technological Seeds for 2008 from the Japan Science and Technology Agency (JST) (No. 03-036).
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