We present a polarization-controlled terahertz(THz) spectroscopy method to characterize the birefringent materials. The polarization of THz wave was controlled by changing the relative phase of the fundamental and second-harmonic waves in the two-color laser-induced air plasma THz generation configuration. The optical axis orientation was investigated through detecting one component of the transmitted THz electric field by continuously changing the electric field direction of the linearly polarized incident THz wave. This work demonstrates that the polarization-controlled THz spectroscopy can be used to study the anisotropy of the inner structure for birefringent materials.
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Recently, with the rapid development of terahertz (THz) technology, some birefringent materials are utilized for THz domain applications. For example, liquid crystals have been employed as frequency modulated THz waveplates; artificial metamaterials are considered promising candidates for THz polarization modulation [1–4]. Biological tissues such as murine livers have been reported to exhibit THz birefringence . In order to investigate the THz properties involved with the intrinsic anisotropy of these materials, it is essential to perform orientation analysis on these samples within THz spectral domain. Conventionally, crystal orientation analyses are performed using X-ray diffraction or optical scattering methods. However, due to the large-scale inner structures of THz materials, and the invasiveness of X-ray to some biological tissues, X-ray diffraction is not applicable in characterizing THz domain birefringence. On the other hand, as most of the THz materials are not transparent for optical beams, the optical scattering method cannot be employed, either. In Matthew Reid’s work, an approach for lens paper’s fiber-orientation analysis was presented by extracting the time delay of the THz time-domain signal as a function of the azimuthal angle . However, it is unable to work for thicker samples with a larger birefringence, where double-pulse signals are observed when the optical path lengths difference for the ordinary (o) and extraordinary (e) rays is larger than the THz pulse width. A numerical optimization process was developed to map the optical axis orientation of birefringent samples by THz time-domain measurements . In their simulation, a transfer function which is derived from the material parameters has to be known prior to the measurement, which may not be applicable in some situations.
Precise control of THz polarization has gradually identified its importance in a number of applications, such as THz communications, nondestructive industrial evaluation, biomedical sensing and imaging, and novel polarimetric THz devices, by means of revealing more information related to the intrinsic properties of the target [8–11]. Studies have shown that the polarization of THz radiations generated from two-color laser-induced air plasma can be continuously controlled by changing the relative phase between the fundamental and second-harmonic waves. The phase adjustment can be conveniently achieved by varying the axial position of beta-barium borate (BBO) crystal or using a phase compensator [12–15].
In this study, we present an anisotropic inner structure characterization method for birefringent materials by using a polarization-controlled spectroscopic system based on the THz radiation generated from a two-color laser-induced air plasma.
2. Theoretical background
When a THz pulse is measured using the electro-optical sampling method, assuming the (001) axis of a (110)-oriented ZnTe is fixed at the vertical direction and the polarization of the probe beam is horizontal, the detected current intensity difference is proportional to the horizontal component of the electric field amplitude of the THz wave ,
When a linearly polarized THz wave transmits through a birefringent crystal with a thickness of d, the phase delay between the orthogonal components (vertical or parallel to the optical axis) is given byEq. (1), it is further noted that the minimal signal intensity is detected when the polarization of the incident wave is ; likewise, it can also be concluded that when , the birefringent crystal behaves like a half waveplate and the electric field of the transmitted wave is rotated by twice the angle between the incident polarization and the optical axis of the crystal. Consequently, from Eq. (1), the minimal signal intensity is detected when the polarization of the incident wave is (θ is the optical axis orientation respect to the horizontal direction).
The above deductions imply that, if the electric field direction of the incident THz wave (linearly polarized) continuously rotates, given the frequencies at which reaches extreme values and the angle α, we can determine the optical axis orientation of the birefringent material without any knowledge of the material’s optical properties.
3. Experimental results and discussion
The fundamental and second harmonic optical fields were created by focusing a laser pulse with 50 fs pulse width, 1 mJ power and 800 nm wavelength through a 100 μm type-I BBO crystal (Fig. 1 ). The THz emission was collected and then focused by two pairs of off-axis parabolic mirrors. A piece of 2 mm thick (110)-oriented ZnTe crystal was used as the sensor for electro-optical sampling detection with its (001) axis fixed at the vertical direction. The horizontally polarized probe pulse was focused onto the ZnTe crystal and overlapping with the THz beam. Therefore only the horizontal component of the THz electric field was detected. In the two-color laser-induced air plasma THz generation configuration, the superposed fundamental and second harmonic optical fields tunnel-ionize the air and drive a time-dependent current, leading to THz emission in the forward direction [17–19]. It has been demonstrated that the generated THz wave is linearly polarized and the polarization undergoes a continuous rotation through radians which is proportional to the relative phase of the two-color fields [13,14].
By placing the BBO crystal on a one-dimensional linear stage and scanning the BBO relative position from −13 mm to 26 mm at a stepsize of 0.2 mm, the measured THz amplitude versus the relative position is a cosine function (Fig. 2 , black dots). The polarization angle of the emitted THz wave changed continuously. Knowing (), when the THz polarization rotates at least half circle, the polarization angle can be calculated by (Fig. 2, white dots). Specifically, it was found that a horizontally polarized THz field became vertically polarized with comparable intensity when the BBO crystal was moved from 0 mm to 10 mm.
Although theoretically the orientation of the optical axis can be extracted without any knowledge of the material’s optical properties, in order to demonstrate the concept and validity of this method, in this work, a 10 × 10 × 5mm3 thick 0°-cut quartz crystal with a known crystal axis and refractive index was employed as the sample. Through measuring the ellipticity of the transmitted wave within the effective frequency band, it was found that the waves at the frequencies of 0.66, 1.29 and 1.87 THz are linearly polarized (Fig. 3 , black dots). The abrupt increase at 1.7 THz is caused by strong water vapor absorption in the ambient air. It is noteworthy that for a material with absorption lines in the measured frequency region, similar discontinuities will also be observed on the curve. To prove the validity of this method, given the refractive indices of the 5 mm quartz crystal, the phase retardation between the two principle axes of the quartz crystal is also calculated and plotted as a reference (Fig. 3, white dots). Not surprisingly, it confirms that the phase retardations (δ) are π, and at 0.66, 1.29 and 1.87 THz, respectively.
In the next step, we investigated the optical axis orientation of the sample and compared the measured results with the known orientation directions. The crystal was mounted on a rotation stage and its known orientation of axis was placed at 0°, 60°, 40°and 130°respect to the horizontal direction. The measured THz amplitudes transmitted through the quartz crystal at 0.66, 1.29 and 1.87 THz versus BBO scanning position are plotted for each orientation angle (Fig. 4 ). At 0°orientation [Fig. 4(a)], the minimal amplitudes at the three frequencies are almost zero where the relative position of the BBO is 10 mm. It is noted that the THz signal without passing through the quartz crystal also reaches zero at 10 mm (Fig. 2, black dot). This means the polarization of the transmitted THz wave maintains the same direction as the incident wave and confirms that the optical axis orientation is 0°. At 60° [Fig. 4(b)], the minimum amplitudes for the three specific frequencies are observed at different BBO positions. For 1.29 THz, the output THz wave maintains the same direction as the incident wave at a relative BBO position of 10 mm, as a consequence of its 2 π phase retardation. However, for 0.66 and 1.87 THz the minimal amplitudes sit at 5 mm, where the polarization angle of the incident wave α is 33°. Therefore, it is calculated that the orientation of the crystal axis is with respect to the horizontal direction. The discrepancy between the calculated result (61.6°) and the known orientation (60°) is attributable to the inaccuracy involved with the linear stage stepsize, and is also possibly due to an uncertainty in the angular orientation of the crystal with respect to the incident light.
The equation indicates that and θ correspond to the same α. To verify this, the crystal axis was adjusted at 40°and 130°orientations [Fig. 1(c) and 1(d)]. Similar curves of THz amplitude versus BBO relative position are observed. The minimal intensities are both found at 20 mm, which corresponds to the 170°polarization of the incident THz wave. Following the above process, at both positions, the calculations yield two crystal orientations or . This 90°ambiguity can be eliminated by comparing their time-domain waveforms. Figure 5 illustrates the measured time-domain waveform at the two orientations. It is known that when the difference in the optical path lengths for the o and e rays is larger than the THz pulse width, the THz pulse passing through a birefringent crystal is split into two parts: the first peak (indicated by the dashed line on the left in Fig. 5) corresponds to o ray and the second one (indicated by the dashed line on the right in Fig. 5) is e ray. Because the measured THz peak magnitude is its projection onto the horizontal axis, the intensities of the two peaks are and . Therefore, when, the orientation angle θ satisfies or ; when , θ satisfies . This assertion is verified by the two waveforms presented in Fig. 5, in which the THz waveform of 40° shows a smaller leading peak and 130°has a taller one.
In this work, by using the proposed method to characterize the quartz crystal and comparing the measured results with its known crystal orientations, the calculated angles match with the real crystal orientations well. It has to be pointed out that the investigated crystal must be thick enough or has moderate birefringence to ensure a phase retardation between o and e rays greater than π. The minimum thickness of the sample being investigated is also limited by the effective frequency range of the spectrometer. The broader the bandwidth is, the smaller the minimum thickness of the sample will be. The resolution of the angle measurement is determined by the scan stepsize of the BBO position: in general, a finer resolution will improve the accuracy of the angle measurement but also increase the scan time. In real applications, a balance between the data acquisition time and desired precision has to be considered. It is also noteworthy that at this moment the characterization method presented in this work only applies to a sample with two faces parallel to its optical axis. A more adaptive version of the polarization controlled method, which is able to characterize birefringent materials with more random shape, will be investigated in the future work.
In conclusion, we developed a polarization-controlled THz spectroscopic method to determine the optical axis orientation of birefringent materials without knowing the material parameters prior to the measurement. A good agreement between the values of the real and calculated orientation angles is achieved, providing enough evidence to support its validity in characterization of THz birefringent material, that are not able to be measured by using traditional methods. The convenient and effective orientation analyzing technology also opens pathways to study the inner anisotropic structures of biological materials.
This work was funded by the National Keystone Basic Research Program (973 Program) under Grant No. 2007CB310408 and 2006CB302901, the National Natural Science Foundation of China under Grant No. 10804077. It is also supported by the State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences.
References and links
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