We present a terahertz wave polarization analysis method to extract the polarization rotation angle with respect to the horizontal direction. A quartz crystal is used as the polarization analyzer with the optical axis of the crystal fixed at 45° orientation. The polarization angle of the terahertz waves generated from two-color laser-induced gas plasma is extracted by measuring the transmitted ordinary and extraordinary beams. This work demonstrates that low-absorbance birefringent materials are good candidates for terahertz polarization analysis.
©2009 Optical Society of America
Terahertz (THz) radiations have attracted people’s attention for many years. Their distinct characteristics, such as non-invasiveness to human body, high penetration through many daily materials and the broadband ability of spectral fingerprint identification, favor a number of applications in industry and national security, including nondestructive evaluation, biomedical characterization, standoff inspection, etc [1–3]. In most cases, the information carried by THz pulse amplitude, timing and spectrum are evaluated and interpreted [1,2]. Recent advances have shown that polarization of the THz radiation is also critical in understanding wave properties, generation mechanism, and information extraction [4–7]. For example, by studying the polarization of THz radiations produced from two-color laser-induced air plasma, one is able to derive that changing the relative phase of the fundamental and second-harmonic waves effectively controls THz wave polarization [8,9]. Polarization change of THz wave reflected from rugged surface is also used to reconstruct the fine surface structure of the target [10–12]. Relying on rotating wire-grid polarizers for maxima transmittance or electro-optic sensors, the available THz wave polarization measurements requires at least semi circle rotation to estimate the linear polarization direction, with its accuracy limited by the rotation stepsize .
In this letter, we developed a convenient THz wave polarization analysis method using birefringent materials by extracting the polarization angle of the linearly polarized wave through a single measurement of the ordinary (o) and extraordinary (e) rays.
2. Theoretical analysis
When the THz pulse is measured using electro-optic sampling, assuming the (001) axis of (110)-oriented ZnTe is fixed at vertical direction and the polarization of the probe beam is horizontal, then only the horizontally polarized THz electric field component is detected. The measured current intensity difference is proportional to the electric field amplitude of the THz wave êTHz ,
Where α is the angle of the THz polarization directions with respect to the horizontal direction. Ip is the probe intensity, ω is the angular frequency of the probe pulse, n and r 41 are the refractive index and only nonzero coefficient of the electro-optic tensor of ZnTe crystal, respectively. L is the thickness of the ZnTe crystal and c is the velocity of light. On the other hand, knowing the maximum intensity difference ΔI max by rotating the THz polarization for at least half circle, which means cos α=1, the arbitrary polarization angle can be found by:
When a linearly polarized THz pulse êin(t) oriented under an angle θ with respect to the horizontal direction passes through a birefringent crystal oriented at 45° with negligible absorptions, it decomposes into two vector components with the polarizations parallel (êin(t) cos(45°-θ)) and perpendicular (êin(t)sin(45°-θ)) to the optical axis of the analyzer (Fig. 1(a)). Each part travels through the birefringent crystal, producing o or e rays with similar shape to the reference beam. Since the detector is only sensitive to the horizontal polarization, the detected signal is proportional to the projection of the outgoing field on the horizontal axis. Specifically, ignoring the attenuation and reflection loss, the output signal contributed from o and e rays are:
When the incident terahertz wave is horizontally polarized, the pulse splits into two parts with comparable magnitude. If the difference of the optical path lengths for o and e rays is larger than the THz pulse width, the detected signal is superposed by êouto and êoute, appearing to be a pulse train with two distinct peaks (Fig. 1(b)). When the polarization of the incident beam rotates, the orientation angle θ with respect to the horizontal direction can be extracted by the ratio of the amplitudes of the first maximum êouto and the second maximum êoute of the transmitted THz signal:
3. Experimental results
In this work, a 4-mm-thick quartz crystal was used as polarization analyzer. Our previous work has shown that the absorption coefficients of quartz for both the o (αo) and e (αe) rays are similar and lower than 0.5 cm-1 in the THz frequency range . The refractive indices of o (no) and e (ne) rays increase with frequency and both values are below 2.1 . Its medium birefringence and relative small absorption loss ensured that the attenuation caused by the different absorption and reflection losses for both axes can be neglected [15,16]. The thickness of the crystal slab was chosen to cause sufficient walk-off between the o and e rays assuring distinguishable split of the two pulses in the time-domain. To demonstrate this method, THz wave generated from two-color laser-induced gas plasma was employed (Fig. 2). Its polarization change was examined using the quartz analyzer and in the meantime, compared with that measured by conventional polarization sensitive detection method [14,15]. A superposition of the fundamental and the second harmonic optical fields was created by focusing a 50 fs, 1 mJ and 800 nm laser pulse through a 100 µ m type-I beta-barium borate (BBO) crystal. The THz emission was collected by two pairs of off-axis parabolic mirrors and traveled through the quartz polarization analyzer at its focus with normal incidence. 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 overlapping with the THz beam. After the sensor, the probe beam passed through a quarter-wave plate and then a Wollaston prism, which separated the two orthogonally polarized beams.
In two-color laser-induced air plasma THz generation configuration, the superposed fundamental and the second harmonic optical fields tunnel-ionize the air and drive a time-dependent current, leading to THz emission in the forward direction [17–20]. It has been found that the generated THz wave is linearly polarized when the fundamental laser is linear. The polarization of the radiated THz field undergoes a continuous rotation through 2π radians as a function of the relative phase of the two-color field [8,9]. In this work, the BBO-to-plasma distance was varied to tune the relative phase of the fundamental and the second harmonic field. The relative phase change Δφ is proportional to the change of the BBO position Δd, by Δφ=ω(nω-n 2ω)Δd/c, where nω and n 2ω are the refractive indices of the fundamental and the second harmonic field in the air .
The position of BBO was scanned at a stepsize of 0.5 mm. The measured electro-optic sampling signal fell from maximum to zero when the BBO-to-plasma distance changed from 42 mm to 56 mm, indicating 90° polarization rotation of the THz wave. The curve of the directly detected THz peak amplitude without quartz plate versus BBO position is given in Fig. 3 (open dot). The peak amplitudes of the two split THz pulses are also plotted (solid black and gray lines). It is noted that when the THz polarization rotated 90°, the directly detected signal was almost zero while each peak still retained large amplitude.
Figure 4 gives the retrieved THz wave polarization angles respect to the horizontal direction using Eq. (4). As a comparison, the angle was also calculated using (2). The good agreement between the two curves indicates the validity of this method. In addition, this method is more convenient and time-efficient by requiring only one-time measurement. Meanwhile, it is also more reliable by measuring the amplitude difference between the two peaks, each remaining sufficient signal-to-noise ratio during one rotation cycle, enabling its higher sensitivity in detecting subtle polarization variations.
4. Discussion and conclusion
It has to be pointed out that the angle retrieving algorithm employed in this paper is an approximation, which only fits to those materials with medium birefringence and relatively low absorption in THz region. The ringing effect of either o or e ray, which is mainly resulted from atmospheric absorption in THz region, also affects the accuracy of the calculation by superposing on the signal of the other one. However, by using an analyzer thick enough to separate o and e rays beyond one cycle THz pulse and eliminate the water rings by nitrogen purge, the method can attain higher accuracy by sacrificing delay stage scan time. A more rigorous deduction applicable to any type of birefringent material can be obtained with a numerical optimization process by knowing a priori knowledge of each pulse . In addition, in this experiment only linearly polarized THz source was considered, while most THz generations are inherently elliptical. Nevertheless, it is believed that the ellipticity of the THz pulses produced from laser-inducer air plasma is small and didn’t introduce significant deviation when using Eq. (4). Finally, even with the above limitations, this method is still regarded more reliable and sensitive in picking up subtle variations of polarization change.
In conclusion, by using a 4-mm-thick quartz crystal as polarization analyzer, the polarization angles of THz radiation generated from two-color laser-induced air plasma were measured. Good agreement between this method and the conventional angle-retrieval measurement manifests that low-absorption and medium birefringent materials can be made into convenient and reliable THz polarization analyzer.
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, and Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality.
References and links
2. 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, 3224 (1996). [CrossRef]
9. J. Dai, N. Karpowicz, and X. -C. Zhang, “Coherent polarization control of terahertz waves generated from two-color laser-induced gas plasma,” Phys. Rev. Lett. 103, 023001 (2009). [CrossRef] [PubMed]
11. J. Pearce, Z. Jian, and D. M. Mittleman, “Spectral shifts as a signature of the onset of diffusion of broadband terahertz pulses,” Opt. Lett. 29, 2926 (2004). [CrossRef]
13. A. E. Costley, K. H. Hursey, G. F. Neill, and J. M. Wald, “Free-standing fine-wire grids: Their manufacture, performance, and use at millimeter and submillimeter wavelengths,” J. Opt. Soc. Am. 67, 979 (1977). [CrossRef]
14. P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313 (2001). [CrossRef]
15. L. Zhang, H. Zhong, C. Deng, C. Zhang, and Y. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94, 211106 (2009). [CrossRef]
16. D. Grischkowsky, S. Keiding, M. Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006 (1990). [CrossRef]
17. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210 (2000). [CrossRef]
20. J. Dai, X. Xie, and X.-C. Zhang, “Terahertz wave amplification in gases with the excitation of femtosecond laser pulses,” Appl. Phys. Lett. 91, 211102 (2007). [CrossRef]