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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 22 — Oct. 26, 2009
  • pp: 20266–20271
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Terahertz wave polarization analyzer using birefringent materials

Liangliang Zhang, Hua Zhong, Chao Deng, Cunlin Zhang, and Yuejin Zhao  »View Author Affiliations


Optics Express, Vol. 17, Issue 22, pp. 20266-20271 (2009)
http://dx.doi.org/10.1364/OE.17.020266


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Abstract

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

1. Introduction

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

1. B. B. Hu and M. C. Nuss, “Imaging with Terahertz Waves,” Opt. Lett. 20, 1716 (1995). [CrossRef] [PubMed]

3

3. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22, 904 (1997). [CrossRef] [PubMed]

]. In most cases, the information carried by THz pulse amplitude, timing and spectrum are evaluated and interpreted [1

1. B. B. Hu and M. C. Nuss, “Imaging with Terahertz Waves,” Opt. Lett. 20, 1716 (1995). [CrossRef] [PubMed]

,2

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]

]. Recent advances have shown that polarization of the THz radiation is also critical in understanding wave properties, generation mechanism, and information extraction [4

4. C. Jordens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, “Terahertz birefringence for orientation analysis,” Appl. Opt. 48, 2037 (2009). [CrossRef] [PubMed]

7

7. J.-B. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. 31, 265 (2006). [CrossRef] [PubMed]

]. 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

8. H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009). [CrossRef] [PubMed]

,9

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]

]. Polarization change of THz wave reflected from rugged surface is also used to reconstruct the fine surface structure of the target [10

10. R. Zhang, Y. Cui, W. Sun, and Y. Zhang, “Polarization information for terahertz imaging,” Appl. Opt. 47, 6422 (2008). [CrossRef] [PubMed]

12

12. N. C. J. van der Valk, A. M. Van der Marel, and P. C. M. Planken, “Terahertz polarization imaging,” Opt. Lett. 30, 2802 (2005). [CrossRef] [PubMed]

]. 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 [13

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]

].

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 [14

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]

],

ΔI(α)=Ipωn3êTHzr41Lccosα
(1)

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:

α=arccos(ΔI(α)ΔImax)
(2)

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:

êouto(t)=êin(t)sin(45°θ)cos(45°)
(3a)
êoute(t)=êin(t)cos(45°θ)cos(135°)
(3b)

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:

θ=45°arctan(êoutoêoute)
(4)
Fig. 1. (a). Orientation illustration of incoming THz field, quartz crystal and transmitted THz field. (b) THz time-domain waveform transmitted through the birefringent material with the optical axis oriented at 45°. The inset shows the reference THz waveform without passing through the birefringent material.

3. Experimental results

Fig. 2. Schematic diagram of the experimental setup. L1-3: Lenses; P1-4: parabolic mirrors; QWP: quarter-wave plate; WP: polarizing beam splitter (wollaston prism).

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

17. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210 (2000). [CrossRef]

20

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]

]. 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

8. H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009). [CrossRef] [PubMed]

,9

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]

]. 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 2ωd/c, where nω and n 2ω are the refractive indices of the fundamental and the second harmonic field in the air [8

8. H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009). [CrossRef] [PubMed]

].

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.

Fig. 3. THz wave peak amplitude versus relative phase of the two-color field: directly measured THz peak without passing through quartz (open dots); the first THz peak after passing through quartz (solid black); the second THz peak after passing through quartz (solid gray). The dash line indicated zero 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.

Fig. 4. THz polarization rotation angle with respect to the horizontal direction versus relative phase of the two-color field, calculated using Eq. (4) (open dots) and (2) (solid dots). The dash line indicated 90° rotation angle.

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 [4

4. C. Jordens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, “Terahertz birefringence for orientation analysis,” Appl. Opt. 48, 2037 (2009). [CrossRef] [PubMed]

]. 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.

Acknowledgements

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

1.

B. B. Hu and M. C. Nuss, “Imaging with Terahertz Waves,” Opt. Lett. 20, 1716 (1995). [CrossRef] [PubMed]

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]

3.

D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22, 904 (1997). [CrossRef] [PubMed]

4.

C. Jordens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, “Terahertz birefringence for orientation analysis,” Appl. Opt. 48, 2037 (2009). [CrossRef] [PubMed]

5.

M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45, 2766 (2006). [CrossRef] [PubMed]

6.

C.-F. Hsieh, R.-P. Pan, T.-T Tang, H.-L. Chen, and C. -L. Pan, “Voltage-controlled liquid-crystal terahertz phase shifter and quarter-wave plate,” Opt. Lett. 31, 1112 (2006). [CrossRef] [PubMed]

7.

J.-B. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. 31, 265 (2006). [CrossRef] [PubMed]

8.

H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009). [CrossRef] [PubMed]

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]

10.

R. Zhang, Y. Cui, W. Sun, and Y. Zhang, “Polarization information for terahertz imaging,” Appl. Opt. 47, 6422 (2008). [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]

12.

N. C. J. van der Valk, A. M. Van der Marel, and P. C. M. Planken, “Terahertz polarization imaging,” Opt. Lett. 30, 2802 (2005). [CrossRef] [PubMed]

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]

18.

X. Xie, J. Dai, and X. -C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006). [CrossRef] [PubMed]

19.

J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97, 103903 (2006). [CrossRef] [PubMed]

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]

OCIS Codes
(260.1440) Physical optics : Birefringence
(260.5430) Physical optics : Polarization

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: September 14, 2009
Revised Manuscript: October 20, 2009
Manuscript Accepted: October 20, 2009
Published: October 22, 2009

Citation
Liangliang Zhang, Hua Zhong, Chao Deng, Cunlin Zhang, and Yuejin Zhao, "Terahertz wave polarization analyzer using birefringent materials," Opt. Express 17, 20266-20271 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-20266


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References

  1. B. B. Hu and M. C. Nuss, "Imaging with Terahertz Waves," Opt. Lett. 20, 1716 (1995). [CrossRef] [PubMed]
  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]
  3. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, "T-ray tomography," Opt. Lett. 22, 904 (1997). [CrossRef] [PubMed]
  4. C. Jordens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, "Terahertz birefringence for orientation analysis," Appl. Opt. 48, 2037 (2009). [CrossRef] [PubMed]
  5. M. Reid and R. Fedosejevs, "Terahertz birefringence and attenuation properties of wood and paper," Appl. Opt. 45, 2766 (2006). [CrossRef] [PubMed]
  6. C.-F. Hsieh, R.-P. Pan, T.-T Tang, H.-L. Chen, and C. -L. Pan, "Voltage-controlled liquid-crystal terahertz phase shifter and quarter-wave plate," Opt. Lett. 31, 1112 (2006). [CrossRef] [PubMed]
  7. J.-B. Masson, and G. Gallot, "Terahertz achromatic quarter-wave plate," Opt. Lett. 31, 265 (2006). [CrossRef] [PubMed]
  8. H. Wen and A. M. Lindenberg, "Coherent terahertz polarization control through manipulation of electron trajectories," Phys. Rev. Lett. 103, 023902 (2009). [CrossRef] [PubMed]
  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]
  10. R. Zhang, Y. Cui, W. Sun, and Y. Zhang, "Polarization information for terahertz imaging," Appl. Opt. 47, 6422 (2008). [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]
  12. N. C. J. van der Valk, A. M. Van der Marel, and P. C. M. Planken, "Terahertz polarization imaging," Opt. Lett. 30, 2802 (2005). [CrossRef] [PubMed]
  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]
  18. X. Xie, J. Dai, and X. -C. Zhang, "Coherent control of THz wave generation in ambient air," Phys. Rev. Lett. 96, 075005 (2006). [CrossRef] [PubMed]
  19. J. Dai, X. Xie, and X.-C. Zhang, "Detection of broadband terahertz waves with a laser-induced plasma in gases," Phys. Rev. Lett. 97, 103903 (2006). [CrossRef] [PubMed]
  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]

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