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We have fabricated a three-contact photoconductive antenna for the polarization-sensitive detection of terahertz electromagnetic radiation. Taking into account all three photoconductive signal current components, this three-contact photoconductive antenna can measure the polarization state of pulsed THz radiation at an accuracy comparable to that achieved using the conventional method which employs a set of wire-grid polarizers. The three-contact photoconductive receiver may be useful for polarization-sensitive spectroscopy such as vibrational circular dichroism spectroscopy and ellipsometry in the THz frequency region.
©2007 Optical Society of America
1. Introduction
For the polarization measurement of terahertz (THz) electromagnetic radiation we have been using the conventional method involving wire-grid polarizers. For THz time-domain spectroscopy (THz-TDS) measurements, such a method requires multiple time-delay scans, which is time-consuming and can result in a systematic error caused by the intensity fluctuation of a pump laser. In addition, the efficiency of a wire-grid polarizer decreases with frequency as the wavelength approaches the grid spacing [1]. One of the reasons why spectroscopy, which requires accurate polarization detection (such as vibrational circular dichroism (VCD) spectroscopy [2–4]), has rarely been employed in the THz region [5] is the lack of an accurate polarization detection method. Recently, Castro-Camus et al. used a multi-contact photoconductive (PC) receiver, fabricated on an Fe+-ion implanted-InP substrate, for vectorial THz field sampling, successfully detecting the polarization waveform of pulsed THz radiation [6]. They also demonstrated measurements of the birefringence of quartz and the polarization dependence of THz radiation generated by optical rectification in (110)-ZnTe using the same type of multi-contact PC receiver with the capability to resolve changes in the polarization angle as small as 0.34° [7]. The reported signal to noise ratio was 100:1 and the usable spectral bandwidth was up to 4 THz.
In addition to the polarization-sensitive detector, modulation of the polarization state of THz radiation is useful to increase the sensitivity of the polarization measurement of THz radiation. Such polarization modulation using a four-contact PC antenna was recently reported [8]. Polarization modulations of THz radiation has also been achieved using electro-optic [9] and interferometric [10] techniques.
In the present paper, we report a highly accurate measurement of the polarization state of pulsed THz radiation with a three-contact photoconductive receiver. In the antenna geometry reported by Castro-Camus et al. [6] the current flow to the two contacts for signal detection was restricted only from the third ground contact and the two orthogonal photoconductive current signals were measured. In this case each signal directly represents one of the THz radiation’s orthogonal polarization field components. On the other hand, for our PC receiver based on a triangle-gap design we need to consider all three signal current components, including the cross-component between the two contacts for signal detection, for the measurement of the polarization state of THz radiation. This introduces some complexity to the derivation of the polarization state. However, our approach is generally applicable to any type of three-contact PC receiver and is free of the geometrical, electrical imperfections of the antenna. It is also an advantage for our approach that the inhomogeneity of the probe beam intensity in the gap can be taken into account with ease.
Fig.1. . a). (Color online) Microscopic view of the three-contact PC antenna. (b) Equivalent circuit for the three-contact PC antenna.
Fig. 2. (Color online) Schematic diagram of the polarization detection system with the three-contact photoconductive receiver.
2. Procedure for experiment
We fabricated a PC receiver [shown in Fig. 1(a)] having the three gold contacts on a lowtemperature- grown GaAs (LT-GaAs) [11–12] substrate using a standard photolithographic and chemical etching method. The gap shape formed by the apexes of the three contacts is an equilateral triangle having a side length of approximately 20 µm. One of the electrodes of the three-contact PC receiver is connected to ground, while the other two electrodes are each connected to a lock-in amplifier, respectively, to measure the signal photocurrents I1 and I2 [Fig. 1(b)].
A schematic diagram of our detection system is shown in Fig. 2. We used a mode-locked Ti:sapphire laser as the light source, whose center wavelength and spectrum width was approximately 770 nm and 10 nm (FWHM), respectively. The repetition rate of the laser was 82 MHz. A polarization beam splitter splits the laser into a pump beam and a probe beam with their average powers controlled to 20 mW and 30 mW, respectively, by neutral density filters. The pump laser beam is focused by a lens on the PC gap of a dipole PC antenna to generate pulsed THz radiation, whose amplitude and polarization direction are controlled by a series of wire-grid polarizers (with a 10-µm diameter and 25-µm grid spacing) placed in the path of the THz beam. The first polarizer prepared THz radiation in a horizontally polarized state (parallel to the x-axis). The second polarizer set the polarization axis of THz radiation at +45° (for positive polarization angles) or -45° (for negative polarization angles) from the x-axis. The last polarizer controlled the polarization angle of THz radiation incident on the receiver. A 33-kHz square-wave bias voltage with a 40-V peak-to-peak amplitude was applied to the emitter PC antenna to detect the current signals (I1 and I2) in the three-contact PC receiver with the lock-in amplifiers. The probe laser beam was loosely focused on the three-contact PC gap by a lens. When the THz field is incident on the three-contact PC gap there are three photocurrent components, i1, i2, and i3, corresponding to the three paths between the contacts as illustrated in Fig. 1(b). It is sufficient to measure two terminal currents, I1=i1+i3 and I2=i2 - i3, to determine the in-plane electric field vector, E=(Ex, Ey), incident on the PC gap. By scanning the time delay, τ, we obtain the time-domain signal waveforms, I1(τ) and I2(τ), simultaneously.
To obtain the frequency-domain amplitude spectra of the x and y axis components, Ex(ω) and Ey(ω), from the signal waveforms, I1(τ) and I2(τ), we define the receiver response matrix R(ω) in frequency domain as follows:
Here, Ii(ω) (i=1, 2) is the Fourier-transformed spectrum of Ii(τ) (i=1, 2).
To determine experimentally the matrix components of R(ω), we can measure, for example, the current signals Ii(τ) (i=1, 2) for two linearly polarized THz radiations with the same amplitude but which are orthogonal to each other. For THz radiation with its polarization along the x-axis (Ex=E0(t), Ey=0), we denote the time-domain signal IHi(τ) (i=1, 2). For THz radiation with its polarization along the y-axis with the same amplitude (Ex=0, Ey=E0(t)), we denote the time-domain signal IVi(τ) (i=1, 2). Their Fourier-transformed spectra are denoted correspondingly as IHi(ω) (i=1, 2) and IVi(ω) (i=1, 2), with which we can express the receiver response matrix as follows:
Here, α(ω),β(ω), and γ (ω) are the normalized response spectra given by the following relation:
The proportion factor R 0 is left unknown. However, this would not pose a problem for spectroscopy since only the ratio of the sample spectrum to the reference one is important to derive the sample’s absorbance or dispersion. The time-domain waveforms, Ex(τ) and Ey(τ), are obtained by the inverse Fourier-transform of the amplitude spectrum of Ex(ω) and Ey(ω), which are derived by using Eq. (1).
The normalized response matrix r can be determined analytically under certain appropriate assumptions. Here, we assume a homogeneous probe beam intensity on the gap, and an equivalent response of the three PC gaps. We also assume that the current component ii(τ) (i=1, 2, 3) is proportional to the THz electric field components parallel to the direction of the corresponding side of the equilateral triangle formed by the apex of the three contacts, one of which is taken to be parallel to the y-axis. The analytical form of the normalized matrix r is then given as follows.
Fig. 3. (Color online) (a) The signal waveforms Ii(τ) (i=1,2) and (b) their Fourier-transformed power spectra Ii(ω) (i=1,2) for THz radiation with a polarization angle of 45°.
Fig. 4. (Color online) Experimentally determined normalized response matrix components (solid lines) and the analytical ones (dashed lines with the same color to the corresponding experimental ones).
Note that in the analytical form, the components of the normalized response matrix are constants although we allow them to have frequency dependences in the experimental form.
3. Results and discussion
Figure 3 shows (a) the signal waveforms Ii(τ) (i=1, 2) and (b) their Fourier-transformed power spectra for THz radiation with a polarization angle of 45° (the angle is taken from the positive direction of the x-axis in the counterclockwise direction). The dynamic range defined by the spectrum peak to the noise floor at the high-frequency limit was approximately 106 (in amplitude it was about 1,000) for I 1(τ). These values are comparable to those obtained using a typical dipole-type PC antenna with an LT-GaAs substrate. Therefore, the detection bandwidth is not degraded by antenna geometry.
The frequency dependence of the experimentally determined normalized matrix components rij(ω) (i=x, y, j=1, 2) are shown in Fig. 4. The amplitudes |rij(ω)| are shown in Fig. 4(a) and the phases θij=arg{rij(ω)} are shown in Fig. 4(b). The values of |rij(ω)| are normalized by that of r y2(ω) at ω=0.5 THz. Therefore, the analytically expected value for |r y1(ω)|=|r y2(ω)| is 1 and that for |r x1(ω)|=|r x2(ω)| is 3 (=1.73). However, the experimental values of |rij(ω)| deviate significantly from analytically expected ones and show some frequency dependences. On the other hand, the phases θij reasonably agree with the analytically expected value, 0 or π, although they show slight frequency dependences corresponding to those of |rij(ω)|. There are several reasons for the deviation of the experimentally determined |rij(ω)| from the analytical one:
(i) inhomogeneity of probe beam intensity,
(ii) inhomogeneity of the electrical property of the photoconductive substrate,
(iii) imperfect shape of the contacts and gap,
(iv) misalignment of the antenna orientation, and
(v) polarization-dependent resonances or reflections of THz radiation in the antenna structure (this will result in a frequency dependent response matrix).
The response of the multi-contact PC receiver (and thus the normalized response matrix) is influenced by these factors. The important thing, however, is that the response matrix is determined properly, taking into account all these influences, by means of the calibration measurements, rather than the agreement between the experimentally determined response matrix and the analytical one.
In Fig. 5 we show the projection of (Ex(τ), Ey(τ)) in the Ex-Ey plane (the “polarization trajectory”) for various polarization angles of THz radiation measured using the three-contact PC antenna and calculated using the receiver response matrix R (symbols with solid lines). The polarization angles defined by the transmission axis of the wire-grid polarizer are 90°, 60°, 45°, 30°, 0°, -30°, -45°, and -60° and are indicated by dashed lines in Fig. 5.
Each polarization trajectory shows the linearly polarized characteristics of THz radiation and very close agreement with the polarization axis as defined by the wire-grid polarizer. The maximum deviation of the measured polarization axis from that defined by the wire-grid polarizers is ±1.6° (typically less than 1°), which is comparable to the accuracy of the conventional polarization measurement obtained using wire-grid polarizers.
Fig. 5. (Color online) “Polarization trajectories” of THz radiations with measurement using the three-contact photoconductive receiver for the wire-grid polarizer angles -60°, -45°, -30°, 0°, 30°, 45°, 60°, and 90°.
Fig. 6. (Color online) Relative changes of the THz polarization angle measured with the three-contact PC receiver (open circles) for rotations of the wire grid polarizer by 0.1° steps from 0 to 1° (indicated by a straight line).
Fig. 7. (Color online) Ellipticity of THz radiations with measurement using the three-contact photoconductive receiver for the wire-grid polarizer angles -90°, -60°, -30°, 0°, 30°, 60°, and 90°.
The relative sensitivity of the receiver to the change of the THz polarization angle was estimated using the method described in Ref. [7]. We varied the angle of the wire grid polarizer by 0.1° steps from 0 to 1° and measured the relative change of the THz polarization angle with the three-contact PC receiver. The result is shown in Fig. 6. The maximum deviation of the measured change of the THz polarization angle from the change of polarizer angle was ± 0.18° (the average of the absolute values of the deviation was 0.09°). Therefore, the minimum detectable change of polarization angle is less than 0.2°.
We also calculated the ellipticity spectrum for THz radiation at various polarization angles. The results are shown in Fig. 7 for a frequency range 0.1–1.0 THz. As expected from the almost linear polarization characteristics shown in Fig. 5, the ellipticities are nearly zero. However, they deviate slightly from zero and the deviation increases with increasing frequency. The maximum ellipticity around 1 THz is approximately ± 0.07. We measured the ellipticity of THz radiation using the conventional method employing a two-contact (dipole) PC receiver and wire-grid polarizers under the same condition for the three-contact PC receiver, and found that the maximum ellipticity around 1 THz is about ± 0.05, almost the same as that obtained by the three-contact PC receiver. This indicates that the observed finite ellipticities were not artifacts but intrinsic to the measured THz radiation. The observed ellipticity is explained by the transmission property of the linearly polarized THz radiation through a wire-grid polarizer. For THz radiation transmitted through a wire-grid polarizer there is a small polarization component orthogonal to the transmission axis of the polarizer (the direction normal to the wire) and it increases with increasing frequency [13–14]. Therefore, THz radiation becomes elliptic and its ellipticity increases with frequency when THz radiation is transmitted through a wire-grid polarizer with its polarization axis tilted from the transmission axis of the polarizer.
4. Conclusion
In conclusion, we successfully measured the polarization state of pulsed THz radiation using a three-contact PC receiver taking into consideration the three signal current components in the receiver circuit. This method allows measurements of the polarization state of THz radiation in a single time-delay scan without using other polarization analyzing optics. The accuracy of our detection system was close to the accuracy of the conventional polarization measurement using wire-grid polarizers. The resolution of the polarization angle was approximately 0.2°, which was comparable to that obtained using the orthogonal multi-contact PC receiver reported by Castro-Camus et al. [7]. This polarization detection method is useful for polarization-sensitive spectroscopy such as VCD spectroscopy and ellipsometry in the THz frequency region.
Acknowledgments
We acknowledge the help of the staff of the Prof. Tonouchi’s group at the Institute of Laser Engineering in the fabrication of the three-contact PC antenna. This work was supported by a grant for Scientific Research (B) (subject # 17360030) from the Grant-in-Aid for Scientific Research program of the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT).
References and links
1. J. H. W. G. den Boer, G. M. W. Kroesen, W. de Zeeuw, and F. J. de Hoog, “Improved polarizer in the infrared: two wire-grid polarizers in tandem,” Opt. Lett. 20, 800–802 (1995). [CrossRef]
2. N. V. Cohan and H. F. Hameka, “Isotope effects in optical rotation,” J. Am. Chem. Soc. 88, 2136–2142 (1966). [CrossRef]
3. L. A. Nafie, “Infrared and raman vibrational optical activity: theoretical and experimental aspects,” Annu. Rev. Phys. Chem. 48, 357–386 (1997). [CrossRef] [PubMed]
4. P. L. Polavarapu and Z. Deng, “Measurement of vibrational circular dichroism below 600 cm-1: progress towards meeting the challenge,” Appl. Spectrosc. 50, 686–692 (1996). [CrossRef]
5. J. Xu, G. J. Ramian, J. F. Galan, P. G. Savvidis, A. M. Scopatz, R. R. Birge, S. J. Allen, and K. W. Plaxco, “Terahertz circular dichroism spectroscopy: a potential approach to the in situ detection of life’s metabolic and genetic machinery,” Astrobiology 3, 489–504 (2003). [CrossRef] [PubMed]
6. E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization-sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86, 254102 (2005). [CrossRef]
7. E. Castro-Camus, J. Lloyd-Hughes, L. Fu, H. H. Tan, C. Jagadish, and M. B. Johnston, “An ion-implanted InP receiver for polarization resolved terahertz spectroscopy,” Opt. Express 15, 7047–7057 (2007). [CrossRef] [PubMed]
8. Y. Hirota, R. Hattori, M. Tani, and M. Hangyo, “Polarization modulation of terahertz electromagnetic radiation by four-contact photoconductive antenna,” Opt. Express 14, 4486–4493 (2006). [CrossRef] [PubMed]
9. Q. Chen and X.-C. Zhang, “Polarization modulation in optoelectronic generation and detection of terahertz beams,” Appl. Phys. Lett. 74, 3435–3437 (1999). [CrossRef]
10. R. Shimano, H. Nishimura, and T. Sato, “Frequency tunable circular polarization control of terahertz radiation,” Jpn. J. Appl. Phys. 44, L676–L678 (2005). [CrossRef]
11. D. C. Look, “Molecular beam epitaxial GaAs grown at low temperatures,” Thin Solid Films 231, 61–73 (1993). [CrossRef]
12. M. Tani, K. Sakai, H. Abe, S. Nakashima, H. Harima, M. Hangyo, Y. Tokuda, K. Kanamoto, Y. Abe, and N. Tsukada, “Spectroscopic characterization of low-temperature grown GaAs epitaxial films,” Jpn. J. Appl. Phys. 33, 4807–4811 (1994). [CrossRef]
13. C. L. Mok, W. G. Chambers, T. J. Parker, and A. E. Costley, “The far-infrared performance and application of free-standing grids wound from 5µm diameter tungsten wire,” Infrared Phys. 19, 437–442 (1979). [CrossRef]
14. A. Filin, M. Stowe, and R. Kersting, “Time-domain differentiation of terahertz pulses,” Opt. Lett. 26, 2008–2010 (2001). [CrossRef]
