1. Introduction

The development of terahertz (THz) technologies has attracted considerable interest in recent years because of the need for electromagnetic waves in the THz region (0.1–10 THz) for such applications as spectroscopy, medical diagnosis, and security inspection. Optical components for this frequency region are therefore also in demand. Dichroic filters, metallic hole arrays that use nematic liquid crystals, and photonic band gap materials have been proposed for band-pass filters [1–3]. Plasmonic materials have been used to design THz high pass filters while a mixed type-I/type-II GaAs/AlAs multiple-quantum-well sample has been constructed for use as an optically controllable THz filter and a phase shifter [4,5]. Notch filters in this frequency region are relatively less developed. Skierbiszewski et al. have demonstrated a tunable notch filter based on cyclotron resonance for far-infrared spectroscopy [6]. In this paper, we introduce a notch filter that uses the strong absorption of intermolecular hydrogen bonds in a molecular crystal.

Intermolecular hydrogen bonds play a crucial role in, for example, crystal formation and protein conformation. The energy of a long hydrogen bond is weak, (meV order). These bonds can be investigated by Fourier transform infrared spectroscopy and THz time-domain spectroscopy (THz-TDS) [7,8]. THz-TDS is a powerful tool for observing such weak hydrogen bonds and low-frequency vibrational modes because of its high signal to noise ratio compared with other methods [9]. Intermolecular hydrogen bonds can be assigned by many methods such as by substituting a hydrogen atom with deuterium, observing the temperature dependence of the absorption line positions, or comparing the crystalline and amorphous phases [10,11]. A higher molecular weight in a deuterated sample results in weaker intermolecular hydrogen, leading to a red shift. The shift of hydrogen bonding bands to higher frequencies with decreasing temperature is associated with lattice shrinkage. The intermolecular hydrogen bond disappears in the amorphous phase because of the low order molecular arrangement.

Sucrose consists of disaccharide molecules composed of glucose and fructose. Hydrogen bonds form inside the molecule and with other molecules as O-H⋯O. The molecular structure of sucrose crystals has been studied by neutron and X-ray diffraction techniques [12,13]. Walther et al. studied the temperature dependence of the intermolecular interactions in polycrystalline sucrose and other saccharides using THz spectroscopy [11]. The intermolecular hydrogen absorption around 1.4 and 1.6 THz is shifted and sharpened with decreasing temperature. The THz absorption spectra of sucrose single crystals at low temperature and the mapping of dipole vibration modes to some crystal faces have been reported [14].

In this paper, we report the orientation dependent absorption of sucrose crystals in the 0.3–3.0 THz range. It has sharp, strong absorption at room temperature that is attributed to intermolecular hydrogen bond resonance. The two longest hydrogen bonds found at 1.45 and 1.64 THz were orthogonal. We propose the use of the notch-like absorption feature of the intermolecular hydrogen bond in a molecular crystal for filtering THz waves. Using the rotation dependent absorption properties of sucrose crystals, we obtain filtered images of continuous THz waves and compare their transmission features with spectroscopic results obtained by THz-TDS.

2. Material and sample preparation

Sucrose, C₁₂H₂₂O₁₁, was obtained from Wako Pure Chemical Industries, Ltd. Two crystals with approximate sizes of 0.95 mm×1.88 mm×2.79 mm and 0.99 mm×1.86 mm×2.52 mm, and called S1 and S2, respectively, were used for rotation measurements. Sucrose crystals belong to the monoclinic sphenoidal class whose cleavage is parallel to the (100) face [15], namely a 1.88 mm×2.79 mm face for S1 and a 1.86 mm×2.52 mm face for S2. The powder sample was prepared by crushing sucrose crystals. 30 mg of sucrose powder was mixed with polyethylene powder at a ratio of 1:5 and pressed into a 14 mm-diameter pellet that was 1.92 mm thick. To obtain a practical sucrose filter, we used a large sucrose crystal approximately 23 mm x 16 mm x 11 mm in size purchased from Nakanippon Hyoto Co., Ltd. [16]. The sucrose filter was fabricated by reducing the thickness along the crystallographic a-axis, normal to the cleavage, from 11 to 1.33 mm.

3. Experimental methods

3.1 Spectroscopy

Terahertz spectroscopy was performed using a commercially available THz spectrometer (THz-TDS2004, Aispec) and a 10 fs duration pulse of 800 mm light from a femtosecond laser (Integral, Femtolasers). The spectrometer includes photoconductive antennas for the generation and detection of THz pulses. The emitted THz radiation was focused and collected at the detector by using gold-coated parabolic mirrors. We adopted a rotation stage with a 1.0 mm-diameter aperture at the center of an aluminum plate as a sample holder for the crystal measurements. The sample holder was installed at the focal planes of the mirrors so that the center of the THz beam passed through the aperture. This meant that rotating the aperture had no significant effect on the waveforms of the THz pulses. The rotation angle of the stage was accurate to 2 degrees. Long wavelengths were blocked by the metal aperture. As a result, there was a sharp dip in the THz spectrum at 137.43 GHz. We avoided this dip and accompanying side effects by considering the THz spectrum from 0.3 THz. The sample crystal was attached centrally on the rear of the holder. In other words, the THz beam passed through the aperture before reaching the sample. The experiments were performed under a pressure of 50 Pa to avoid water vapor absorption.

3.2 Imaging

We used continuous THz waves from a tunable gas laser (SIFIR-50, Coherent) with a linewidth of approximately 50 kHz in our imaging experiment. A 7 mm-diameter laser beam was focused onto a thermal imaging pyroelectric CCD camera (Pyrocam III, Spiricon) by using a 30 mm-diameter plano-convex Tsurupica lens (Broadband, Inc.). The focal length of the lens was 100 mm. The camera was operated with a chopper frequency of 24 Hz. The spatial resolution of the image was 1 mm. The sucrose filter was inserted in the beam path between the laser output window and the lens. We used THz waves at 1.40 and 1.63 THz, corresponding to the intermolecular hydrogen bonding absorption and available with CH₂F₂ gas, to realize the sucrose filter. The output laser power was approximately 50 mW for a 1.40 THz wave and 40 mW for a 1.63 THz wave.

We observed the effect of strong absorption due to an intermolecular hydrogen bond at a particular sucrose orientation by detecting the surface temperature of the crystal using an infrared thermal detector (IT2-50, Keyence). In this experiment, the THz laser beam was focused onto the (100) sugar plate using a 100 mm-focal length Tsurupica lens. The thermal detector was placed outside the THz beam path to transmit an infrared laser light with a wavelength of 6-10 µm into the center of the THz spot on the sugar surface. The detection area, namely the infrared spot size, was 1.2 mm in diameter. The thermal resolution was 0.1°C.

4. Spectroscopic results

Reference THz pulses (empty aperture) and sample THz pulses were recorded for 32 scans each and averaged for data extraction. The Fourier amplitudes of the average THz pulses that passed through a 1 mm empty aperture, E _r, and the sucrose crystal S1, E _s, are shown in Fig. 1. The absorption of water vapor under a pressure of 50 Pa appeared as shallow depletions at the same positions in each spectrum. The sample spectrum has a notch at 1.45 THz (Band I) when the b-axis of the crystal and the THz polarization are parallel to each other and at 1.64 THz (Band II) for perpendicular configurations. The electric field strengths in Bands I and II decrease 99.75 % and 98.92 %, respectively, with respect to the reference value. A broad absorption band exists after the notch in the sample spectra.

 

Fig. 1. Fourier amplitudes of THz pulses that passed through a 1 mm aperture (reference) and the sucrose crystal, S1, when its b-axis was parallel (red line) and perpendicular (blue line) to the THz electric field. The arrows indicate sharp depletions at 1.45 THz (Band I) and at 1.64 THz (Band II).

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Figure 2 compares the absorption coefficient α(ν) of a sucrose single crystal for different angles between its b-axis and THz polarization and randomly orientated polycrystals, where ν is frequency. The absorption coefficient was calculated by using the amplitude and phase ratio of reference and sample pulses given by E _s/E _r=exp(-αd/2+inωd/c). Here, d is the thickness of the sample, n is the index of refraction given by

n=1+cΔφ/ωd, c is the velocity of light in a vacuum, Δφ is phase difference, and ω is the angular frequency. The crystal spectra reveal the development of absorption peaks in 10 degree steps. The absorption peak positions in the powder spectrum are shown in the figure with dashed lines as a guide for the eye. Interestingly, weak absorption bands in the powder spectrum exist explicitly in the crystal spectrum at certain angles such as those at 1.45, 1.65, and 1.95 THz. The powder peak at 1.82 THz is high and clear but broad in the crystal spectra at 0-30 degrees. Most of the crystal peaks shifted when the crystal was rotated while some were not observable in this measurement such as those at 2.24 and 2.84 THz. The absorption spectrum of another sucrose crystal, called S2, was measured to confirm that the peak shift was not the result of sample holder misalignment. Definable peak positions near Bands I and II of two crystals are plotted in Fig. 3. The peak shift was well reproduced in crystal S2. Inconsistent positions are of the order of the frequency resolution, i.e., 7.2 GHz.

 

Fig. 2. Absorption coefficients of the sucrose crystal, S1, at various angles between the b-axis and the THz polarization (colored lines) and sucrose powder 20 %. The spectra at 0 degrees (baxis//E _THz) and 90 degrees (b-axis⊥E _THz) were calculated from the data shown in Fig. 1. The sucrose crystal spectra were shifted vertically with a multiple number of 50. The powder spectrum is multiplied by a factor of 3 for clarity. The vertical dashed guidelines show observable absorption peaks in the powder spectrum.

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Fig. 3. Peak positions of Band I (1.45 THz) and Band II (1.64 THz) in the absorption spectra of crystals S1 and S2.

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5. Images of filtered THz beams

The intensity profiles of continuous THz waves filtered by the sugar plate were captured with a pyroelectric camera, and are shown in Fig. 4(a) for 1.40 THz and in Fig. 4(b) for 1.63 THz. The laser beam was set to pass through the sugar plate and focus on the CCD chip. The exposure time of the camera was set at 83 ms, namely two frames per image. Real-time images were recorded every 10 degrees of rotation. The 1.40 THz wave was strongly absorbed at 0 degrees while the 1.63 THz wave was strongly absorbed at greater degrees of rotation. These tendencies agree well with the spectroscopic results in Fig. 1. There are two reasons for the difference in intensity of the two wavelengths. One is that the output power of the gas laser at 1.40 THz was higher than that at 1.63 THz. The frequency of 1.4 THz is out of the 3 dB frequency range (45 GHz) of Band I whereas the frequency of 1.63 THz falls in the 3 dB frequency range of Band II (75 GHz). Therefore, the residue at 0 degrees of 1.4 THz is observable while that at 90 degrees of 1.63 THz is comparable to the noise level.

 

Fig. 4. Intensity profiles of a focused 1.40-THz wave (a) and 1.63-THz wave (b) transmitted through the sucrose filter. The orientation of the sugar crystal was rotated from 0 (b-axis//E _THz) degrees to 90 degrees in 10 degree steps whose number is shown in each image. The image size is 7.6 mm×7.6 mm. The color bars show intensity scale.

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6. Discussion

The spectroscopic results in Fig. 2 show that the absorption band and its intensity depend on crystal orientation. A strong absorption peak indicates good coupling of the THz polarization with the hydrogen bond direction or with the oscillating dipole of a molecular vibrational mode. In a sucrose crystal, the longest hydrogen bond resonance, corresponding to Band I (6 meV) observed by THz-TDS at room temperature, is nearly parallel to the crystallography baxis. For example, the absorption at Bands I and II shows that the hydrogen bond in the <010> direction is looser than the bond in the <-1/2,0,1> direction. It should be noted that the angle between the a-and b-axes is 102.956 degrees [13].

A THz wave with its electric field vector parallel to the b-axis of the sucrose crystal is absorbed, but the crystal is transparent to the orthogonal wave polarization. We conducted another experiment to show this feature in which we measured the change in the surface temperature caused by THz wave absorption by the crystal. Figure 5(a) shows the surface temperature of a sugar crystal irradiated by a focused 1.40 THz wave. A metal shutter was inserted in the THz beam path. When the shutter was open the surface temperature with both configurations, b-axis//E _THz and b-axis ⊥ to E _THz, increased exponentially with increasing time as shown in Fig. 5(a). However, the temperature of the parallel configuration rose faster and the steady temperature was approximately one degree higher than with the other configuration. The temperature decay times were almost the same with both configurations. In another experiment, the sugar plate was swapped for the two configurations every 80 seconds. The result plotted in Fig. 5(b) indicates the temperature difference between the two orthogonal configurations, which is in good agreement with the absorption feature in Fig. 5(a).

 

Fig. 5. Temperature change on the sucrose filter irradiated by a focused 1.40-THz wave. (a) The temperature was measured when the b-axis of the sucrose crystal was parallel (black circles) and perpendicular (red circles) to the THz polarization. The first and second guidelines show the times when the THz radiation was on and off, respectively. (b) The sucrose plate was rotated between parallel (//) and perpendicular (⊥) configurations every 80 seconds. The guidelines between the first and last dashed lines indicate rotating positions. Switching between two configurations took approximately 5 seconds.

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Fig. 6. (a) Angular dependence of power spectral density at 1.40 THz (red symbols) and at 1.63 THz (blue symbols) calculated from spectroscopic results and (b) angular dependence of cw THz intensity at the same frequencies extracted from averaged 3×3 pixels near the middle of the image data in Fig. 4. Traces represent fitting curves using a sine function.

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The intermolecular hydrogen bond absorption in a single sucrose crystal enables the crystal to be employed as a notch filter for linearly polarized THz radiation. A sucrose crystal can provide two notch filters, i.e., for 1.45 THz and 1.64 THz, if we change the orthogonal orientation of the crystal. As seen in Fig. 1, there are other absorption bands in addition to the above two frequencies. We can define the applicable range for the 1.45 and 1.64 THz notch filters as 0.1–1.7 THz and 0.1–1.8 THz, respectively. The upper limit of the filter range is determined at the 0.1 % transmitted power spectral density. The optical densities of the sucrose filter at the center wavelength of 1.45 THz and the 1.64 THz filter are 5.22 and 3.93, respectively. The imaging results in Fig. 4 show that the sucrose crystal functioned as an intensity filter for particular frequencies. The development of the intensity for 1.40 and 1.63 THz waves reversed when the crystal was rotated from 0 to 90 degrees, which is consistent with the spectroscopic result shown in Fig. 6. Figure 6(a) shows the intensity filter characteristic with power spectra obtained from spectroscopic results at 1.40 and 1.63 THz versus rotation angle in 10 degrees increments. The experimental data were well fitted with sine functions. The intensities of the imaging results in Fig. 6(b) were extracted from the average for 9 pixels near the center of the laser beam. A fluctuation in laser intensity and the imperfection of the sucrose filter caused the highest intensity for the 1.40 THz wave that deviated from 90 degrees and for the 1.63-THz wave that deviated from 0 degrees. For practical use, it should be noted that even at the highest transmission angle, the transmittance is approximately half of the incoming light intensity shown in Fig. 1. The central frequency can be slightly tuned by changing the temperature of the crystal. We observed the behavior of the temperature dependent absorption of the single crystal and found that the peak shift occurred when the sample was cooled, as in the polycrystalline spectra [11]. For example, Bands I and II exhibit a blue shift with decreasing temperature from room temperature to 173 K of about 20 and 36 GHz, respectively. Since sucrose is susceptible to humidity, the background absorption may increase in a humid environment. However, other humidity dependent substrates such as NaCl or KBr have been carefully used as infrared spectrometer windows. Compared with the THz notch filter using cyclotron resonance [6], the sucrose filter has a wider bandwidth, less tunability and poor transmission outside the bands. Nevertheless, the filter is user-friendly because unlike the cyclotron resonance filter it does not need to be immersed in a helium bath or placed in a magnetic field.

7. Conclusion

We demonstrated that a single sucrose crystal can be used as a notch filter that employs an intermolecular hydrogen bond for a particular frequency range in the THz region. The absorption characteristics of the crystal in the far-infrared region were observed with THz-TDS and compared with the macroscopic features of the sucrose powder. Certain weak absorption peaks in the crystal power dominate the crystal spectrum at particular crystal orientations. This reflects the hydrogen bond strength with which molecules are packed in a crystal and it corresponds to the direction and oscillating dipole of low-frequency vibration modes. Intermolecular hydrogen bond absorption in a sucrose single crystal is strong and sharp. Therefore, a crystal that has such a strong absorption can be used to filter out specific components. The notch filter may be employed for measuring the wavelength of the continuous THz wave radiation of gas lasers, for example, by using the advantage of its narrow linewidth. It is also useful for engineered far-infrared emission devices such as GaAs/AlGaAs multi-quantum wells. However, the stop band depends on the substrate signature. Finding other strong, sharp absorption bands in a molecular crystal remains a great challenge.