Chun Wang(王春) Bo Wang(王博) Gaoshuai Wei(魏高帅)Jianing Chen(陈佳宁) and Li Wang(汪力)

1Beijing National Laboratory for Condensed Matter Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China

2School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

Keywords: circular dichroism,terahertz,α-lactose

1. Introduction

Circular dichroism(CD),defined by different absorptions of circularly polarized light with opposite chirality,[1,2]has been an attractive topic for a long time. One origin of this fascinating physical phenomenon is the interaction between light and chiral molecules,which can not be transformed into their images by rotation operations in three-dimensional(3D)space.[1,2]The CD spectroscopy technique is advantageous in studying biomolecules because many of them, such as sugars,DNA,and proteins,are chiral.[2–4]These chiral molecules are building blocks of life. The ability to distinguish the chirality that contributes to the characterization of the secondary structure[2–5]is essential, representing proteins’ folding and binding properties and even monitoring the conformational changes of the structures.[2,6,7]

Electronic and vibration transitions lead to CD signals,but the corresponding frequency regions are different: electronic CD is usually in the visible or ultraviolet region,while vibration CD is usually in the infrared or terahertz region.Many biomolecules vibrate at the terahertz frequencies. The terahertz CD spectra related to these vibration modes are excellent to probe biomolecules’ soft oscillatory motions.[8–10]Measuring the CD signals requires accurate polarimetry of electromagnetic waves.[11,12]However,in the terahertz region,this kind of technique is still rare because of lacking devices that can modulate the polarization states of terahertz waves.Exceptionally a few works have reported measurement of the terahertz CD spectra of natural material even though it is considered as a prospective tool. Another factor hindering measuring terahertz CD spectra of natural materials is that the CD signal is about three-order weaker at terahertz frequencies than in the invisible or UV region. Some terahertz CD experiments have been conducted on chiral meta-materials to enhance electromagnetic response at resonances.[13–17]

In this paper, we report the experimental study on terahertz CD spectra ofα-lactose molecules by carefully measuring the polarization states of the transmitted terahertz waveforms with terahertz time-domain spectroscopy(TDS).While the measured CD signal is weak, it has enough dynamic range compared to a polyethylene (PE) sample. Our work demonstrates a typical application of terahertz CD spectra on biomolecules.

2. Experiment

2.1. Sample preparation

Saccharide is an very important organic compound widely distributed in nature. Sucrose in daily consumption,starch in grain,cellulose in plant body,glucose in human blood and so on all belong to saccharide.It plays an important role in the process of life activities,and it is the main source of energy required by all living things to maintain life activities. Therefore,we choose theα-lactose(0-β-d-galactopyranosyl-(1-4)-α-d-glucopyranose)molecule,which is a disaccharide that has been found in milk of most mammals,[18]to measure terahertz CD spectra.It has a chiral molecular structure.Figure 1 shows the structural formula ofα-lactose.[19]The specific rotation ofα-lactose solution at 20°is reported to be +89.4°at wavelength 589 nm.[18,19]Moreover,α-lactose molecules have many vibration modes in the terahertz region.[20–22]These properties ofα-lactose provide conditions for measuring terahertz vibration CD spectra. It is not easy to measure a single molecule because the absorption difference for left-handed circularly and right-handed circularly polarized light is less than 1/1000.[23]Moreover, the absorption of terahertz in an aqueous solution is substantial. Hence,we prepared the samples by pressing theα-lactose polycrystal power into tablets with a pressure of 26 MPa. Table 1 shows that differentαlactose samples with four thicknesses of 0.990 mm,1.740 mm,2.305 mm, 2.565 mm are pressed and almost isotropic, but we will show later that they present slightly spatial anisotropy,which will affect the CD signal and need to be considered in data procession.The polyethylene(PE)tablet with a thickness of 2.28 mm is used as the control sample. We also measured the terahertz CD spectra of a D-glucose tablet with thickness of 1.28 mm,which also belongs to saccharide.

Table 1. Materials.

Fig.1. The structural formula of α-lactose.[19]

2.2. Experimental setup

To measure terahertz CD spectra, one critical thing is to track the variation of the polarization states when the terahertz waves transmit through the sample. Our home-built terahertz TDS has the ability to characterize the polarization state of terahertz waves. The experimental setup is shown in Fig. 2. A ZnTe crystal generates terahertz pulses under the excitation of femtosecond laser pulses(repetition frequency 80 MHz, central wavelength 800 nm,duration 70 fs)delivered from a commercial Ti:sapphire oscillator. The terahertz polarization detection system consists of three terahertz wire-grid polarizers(P1, P2 and P3). The first polarizer P1 is used to ensure the incident wave(E0)to be vertically polarized.Behind the sample, the polarizer P2 is mounted on a precise and electrically controlled rotation stage(newport),allowing polarization projections of the transmitted terahertz electric fields to be+45°(p+)or-45°(p-)with respect to the incident terahertz pulse.The two projected components are written asE1andE2.

Fig. 2. Schematic of the experimental setup for polarization-sensitive terahertz TDS.

The polarizer P3 projectsE1andE2into vertical polarization to maintain the same response function of electric-optic sampling detector. All the terahertz optics are sealed in a vacuum chamber to prevent vapor absorption of terahertz waves.The experiments are conducted at room temperature. The signal-to-noise ratio of our Terahertz TDS system is 1000:1.

The transmittance of anistropic or chiral media can be fully described by the Jones matrix

Here, the coordinate systemxyzis defined on the sample and terahertz wave propagates along thez-axis. To measuretxxandtyx,we rotate the sample so that the incident electric fieldE0is parallel with thex-axis. Then,txx=(E1+E2)/E0andtyx=(E1-E2)/E0. Rotate the sample around thezaxis by 90°so thatE0is parallel with theyaxis,tyyandtxycan be obtained in the same way. The Jones matrix between 0.3 THz and 2.5 THz can be obtained with enough dynamic range with our home-made THz-TDS. We will show in the next section how to extract CD signals from the measured Jones matrix.

2.3. Data analysis

Theα-lactose tablet may process some spatial anisotropy caused by the polycrystal structure.The birefringence induced by spatial anisotropy should be eliminated from the measured Jones matrix to extract the CD signal. Every Jones matrix can be decomposed into a symmetric matrix:

We can obtain two electromagnetic eigenmodes by diagonalizing the Jones matrix. As shown in Fig.3,the two eigenmodes are generally elliptically polarized. The two eigenmode ellipses of bothTSandTAhave the same ellipticity, and their principal axes are orthogonal with each other. However, the two eigenmodes ofTShave the same chirality while those ofTAhave opposite chirality. These properties indicate that the transmission resulting from the chirality is represented byTAand that resulting from spatial anisotropy is represented byTS.

Then, in a circular base, the symmetric Jones matrix can be calculated byTSC=A-1R(θ)-1TSR(θ)Aand the anti-symmetric one is calculated byTAC=A-1R(θ)-1TAR(θ)A. The results are

This CD signal eliminates the effects caused by the spatial anisotropy of the sample and is independent of the sample azimuth angle.

Fig. 3. Eigenmodes of symmetric Jones matrix (left) and anti-symmetric Jones matrix(right). The ellipses represent the trajectories of electric fields.

3. Results and discussion

First, we measure the Jones matrixTM[Eq. (1)] of the sameα-lactose2 tablet at an azimuth of 0°,10°,20°,30°,40°,50°,60°. Transforming theTMto circular base with the equationTMC=A-1TMA,we can obtain CD signal[Eq.(8)]at the seven sample azimuth angles,as shown in Fig.4. We can find that both the shapes and values of the CD signal almost remain unchanged when rotating the sample,which is consistent with the theoretical prediction given by Eq. (8) and confirms the validity of the CD signal measurement.

Fig. 4. CD signals at different sample azimuths with the thickness of α-lactose tablet being 1.74 mm.

Fig.5. Transmittance of the lactose tablets with different thicknesses.

Fig.6. CD signals of the lactose tablets with different thicknesses.

Other sugar molecules such as D-glucose also have chiral structures. To demonstrate that our method can be used in glucose molecules, we measured the Jones matrix of D-glucose tablet at an azimuth of 0°, 10°, 20°, 30°. The CD signals are shown in Fig. 7. Similar to the CD signal of theα-lactose molecules, the shapes and values of the CD signal almost remain unchanged at all the azimuth angles.

Fig. 7. CD signals at different sample azimuths with the thickness of D-glucose tablet being 1.280 mm.

4. Conclusion and perspectives

We have demonstrated an experimental observation on the terahertz CD spectra ofα-lactose.A polarization-sensitive terahertz TDS is built to measure the transmission Jones matrix,from which the CD signal defined by Eq.(8)is obtained.The CD signal of lactose has enough dynamic range compared to PE. We have shown that the obtained CD signal does not contain the birefringence caused by spatial anisotropy. Although we have captured the terahertz CD signal,the intensity is not strong enough to directly extract the difference of the refractive index of two circular modes with opposite chirality from the experimental data. Nevertheless, our terahertz CD spectra demonstrate the related advances in terahertz CD techniques and typical applying scenarios in investigating vibrational motion in biochemical compounds that are instructive to biosensing in the terahertz frequency region.

Acknowledgement

Project supported by the National Natural Science Foundation of China(Grant No.61775233).