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Paper terahertz wave plates

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Abstract

We present a low-cost terahertz wave plate based on form birefringence fabricated using ordinary paper. Measurements of the transfer function of the wave plate between polarizers closely agree with predictions based on the measured complex indices of refraction of the effective medium. For the design frequency, the dependence on wave plate angle also agrees with theory.

©2011 Optical Society of America

1. Introduction

The terahertz region of the electromagnetic spectrum has seen significant technological advances during the last few decades [1]. These advances have mainly been driven by applications in sensing [2], although this frequency range is also very useful for fundamental science [36]. The development of generation and detection methods based on ultrafast lasers, including photoconductive switches [7] and nonlinear crystals [8], have been key to the rapid advances. However, one technological area has been lagging, namely the development of components for manipulating polarization, for example wave plates, at these frequencies. The challenge of fabricating wave plates that work in this frequency range has been recognized since before the development of terahertz technology based on ultrafast lasers [9]. Methods used in the optical regions of the spectrum, such as, birefringence in crystalline material [10] or liquid crystals [11], can be adapted to terahertz frequencies. Alternatively, materials that are not usable in the optical regions of the spectrum, for instance wood [12], can be used to construct wave plates at THz frequencies. However, the dramatic difference in length scales between the optical and terahertz regions of the spectrum can dramatically change the evaluation of various technologies. One example of this is the concept of form birefringence. Form birefringence results from an anisotropic periodic structure, such as a grating. However, the grating period needs to be subwavelength [13], which makes fabrication at optical frequencies very difficult, whereas it is as not difficult at terahertz frequencies.

The use of form birefringence to fabricate phase retarders was first demonstrated in the optical region of the spectrum by etching sub-wavelength gratings into dielectrics [14,15]. However the fabrication of these devices with subwavelength length scales and either high dielectric contrast or high aspect ratio is challenging and costly. Recently, efforts have been made towards low cost, but laborious, fabrication of form birefringent quarter-wave plates [16]. Form birefringence has been demonstrated at terahertz frequencies by etching gratings in silicon [17] and stacked polymer layers [18].

Another approach to fabricating wave plates is based on the birefringence provided by metamaterials [19,20]. However, this approach is more complex and difficult compared to the approach described below.

In this paper, we describe the fabrication and characterization of wave plates for terahertz frequencies that are fabricated out of ordinary paper. As compared to our previous work [18], this approach is very low cost and simple to implement. In particular no sophisticated raw materials such as TiO2 doped polyethylene are needed. Moreover, we perform a detailed investigation of the angular dependent transmission and discuss the polarization dependent attenuation, which modifies the optimum angle for the half-wave plates. Furthermore, the paper based wave plates have a reduced reflection coefficient in comparison to the structure in [18]. The demonstrated performance of the wave plate exceeds more expensive approaches and agrees with theoretical predictions based on the measured properties of the materials.

2. Fabrication of device

The paper terahertz wave plates are fabricated by simply cutting strips of standard office paper (for all measurements shown in this paper, we use Xerox Business TCF 80 g/m2, thickness 120 µm) of appropriate dimension and then stacking them so that air gaps between the individual layers result. A guillotine cutter was used to cut the sheets to the width matching the desired wave plate thickness. Some of the resulting sheets are cut to a shorter length to be used as spacers. As shown in Fig. 1(b) , the shorter spacer sheets are placed at each end of the wave plate to create the appropriate air gaps between the longer sheets. The wave plates produced consisted of 150 to 200 paper/air pairs. Once stacked, the paper was held in place using standard binder clips or rubber bands.

 figure: Fig. 1

Fig. 1 (a) Schematic drawing of the wave plate. The x- and y-axes define the TM or p-polarization and TE or s-polarization directions, respectively. The THz wave propagates in z-direction. α denotes the angle between the y-axis and the polarization of the THz electric field. (b) Photograph of the form-birefringent quarter-wave plate fabricated from paper.

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Measurements on wave plates, built from different paper types with different quality have shown that the paper quality slightly affects the properties of the wave plates. However, wave plates made from different paper brands with comparable quality show very similar results.

For a half wave plate, the width of the paper strips d (see Fig. 1(a)) for a desired design frequency is d=c/(2fΔn)where f is the design frequency of the wave plate, c is the speed of light and Δn is the birefringence. We found that 0.15 is a reasonable first estimate for the birefringence of our wave plates. This value agrees well with the experiments in the next section. We estimate that the upper limit on the half wave frequency is around 450 GHz for manually fabricated paper wave plates. This value is determined by two factors. The first is the constraint that the stacking period has to be smaller than the wavelength [13]. Secondly, manual fabrication of the wave plates by cutting and stacking sets a mechanical limit to the range of operation.

3. Measured indices of refraction

The indices of refraction and absorption coefficients of the wave plate were measured as a function of frequency for both polarizations using a conventional terahertz time domain spectrometer [21]. The results are shown in Fig. 2 .

 figure: Fig. 2

Fig. 2 Frequency dependence of (a) indices of refraction and (b) absorption coefficients for a 4.2 mm paper wave plate for s and p-polarization (green and red symbols respectively). The solid lines in (a) represent the theoretical expectation according to [18]. The solid lines in (b) are curves obtained with the SVMAF filter as described in [22].

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Figure 2(a) shows the indices of refraction for the two polarizations. The p-polarized THz wave experiences a higher effective refractive index than an s-polarized wave. The birefringence of the wave plate is relatively constant over the measured frequency range. We determine the exact value at the half wave frequency of the 4.2 mm thick wave plate to be Δn0.244THz = 0.146. This value is determined by the filling factor of the paper-air-composite and applies for all wave plates that we produced and measured regardless of their thickness d. The graph in Fig. 2(b) shows the absorption coefficient, calculated with the method described in [22,23]. We find that it is higher for p-polarization than for s-polarization.

The measurements of the indices of refraction were compared to the theoretical expressions given by Scheller et al. [18], which are shown as solid lines in Fig. 2(a). For the theory, the index of refraction for the air gaps was assumed to be 1 and that of the paper to be 1.6, while their respective thicknesses were q = 180 µm and p = 120 µm. We attribute the variance between the thickness of the air gap and the thickness of the spacer layer to the stack not being completely pressed together. However, these thickness values are consistent with the total measured thickness of the stack. These values yield good agreement between the measurements and theory.

4. Transfer function

To characterize the performance of the paper wave plates, the same terahertz time domain spectrometer was used with wire grid polarizers inserted to obtain clean polarization states for the generated terahertz radiation and the detected radiation. The paper wave plate was inserted between the polarizers. Using this system, the frequency dependence of the transfer function of parallel polarizations was measured with the wave plate adjust to rotate the polarization by 90° at the half-wave frequency. The dependence of the transfer function on the wave plate angle was measured for generation and detection co- and cross-polarized.

4.1 Frequency dependence

A half-wave plate set with its principal axes at 45°with respect to the polarization direction of an incident linearly polarized field will rotate the polarization by 90°. However, the presence of polarization dependent loss, as displayed in Fig. 2(b), causes the wave-plate angle required for a 90° polarization rotation to deviate from 45°. The wave plate angle was optimized by adjusting the azimuthal angle to minimize the transfer function at the designed half-wave frequency. The detailed angle dependence is presented and discussed for the 4.2 mm wave plate in the next section. For the 4.2 mm, 5 mm and 7.08 mm wave plates, the optimum angles were found to be 53°, 52° and 53°, respectively. These values are consistent with simulations taking into account the measured absorption coefficients. For frequencies around 0.25 THz the overall transmission losses due to absorption are less than 5 dB. The measured frequency dependence of the transfer functions for wave plates of the 3 different thicknesses are shown in Fig. 3 . The transfer function is defined as H(ω)=Eα(ω)/Ey(ω), where Eα is the electric field polarized with an angle α as defined in Fig. 1(a) and Ey is the reference electric field polarized along the y-axis which means that it is s-polarized. The cusps correspond to the half wave frequencies of the wave plates so that the transmitted terahertz radiation is cross polarized with respect to the detection polarizer.

 figure: Fig. 3

Fig. 3 Frequency dependent transfer function of three paper wave plates of different thicknesses. Symbols are measurements, lines are simulations.

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Using the measured indices of refraction and absorption coefficient, the the transfer functions of the three wave plates were calculated and are plotted in Fig. 3 as lines. The calculated transfer functions agree quite well with the measured ones. The contrast ratio is limited by the dynamic range of the measurement system, nevertheless, the 40 dB contrast ratio shown in these measurements demonstrates that the wave plates are producing a pure polarization state and a depolarizing is negligible.

4.2 Angular dependence

To further characterize the performance of the 4.2 mm thick paper wave plate, the transfer function at the half wave frequency of 0.244 THz was measured as function of the azimuthal angle α (see Fig. 1(a)) of the wave plate for the detector polarizer parallel (Fig. 4(a) ) and perpendicular (Fig. 4(b)) to the source polarizer. As expected, nulls are observed when the wave plate rotates the polarization of the transmitted terahertz radiation to be cross-polarized with respect to the detection polarizer. The observed pattern (symbols) agrees with the calculated pattern (lines) and confirms that the wave plate can be used to rotate a linearly polarized state while preserving the purity of the polarization.

 figure: Fig. 4

Fig. 4 Angular dependence of the transfer function for the half-wave frequency of the 4.2 mm thick wave plate for analyzer polarizer (a) parallel and (b) crossed to the source polarizer. Symbols are measurements, lines are simulations.

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4.3 Beam profile

We investigate to what degree the wave plate affects the beam spatial profile. To this end, we determined the profile of the beam when propagating through air and through the wave plate, respectively, by x-y-scanning of the detector (see [24] for a description of the apparatus). In this experiment the wave plate was positioned at α = 52°, i.e., the wave plate rotates the polarization by 90°. The results are shown in Fig. 5 . For the measurement with the wave plate, the detector and source polarizer are oriented perpendicular to each other. For the reference measurement, they are oriented parallel to each other. In this figure, we plot the intensity of the Fourier transformed time domain signal, integrated between 200 GHz and 300 GHz, i.e. in the frequency window for which the paper stack acts as a half wave plate. One can see that the beam quality is only weakly affected by the wave plate as the beam profile still exhibits a Gaussian shape.

 figure: Fig. 5

Fig. 5 Beam profiles of the THz beam at the detector with (b) and without (a) a wave plate inserted into the beam path. Plotted is the integrated intensity from 200 to 300 GHz.

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5. Summary

We have described wave plates for terahertz frequency radiation that are fabricated from ordinary office paper. The indices of refractions and absorption coefficients of the wave plates were measured. To characterize their performance as wave plates, the frequency and angular dependence of their transfer functions when inserted between polarizers was measured. The measured transfer functions agree well with calculations based on the measured indices of refraction and absorption coefficients. The large contrast ratio confirms that the wave plates are not depolarizing the transmitted terahertz radiation.

These wave plates have the advantage of being extremely inexpensive and easy to fabricate. They show excellent performance at their design frequency. Of course, terahertz radiation often has extremely large fractional bandwidth, which presents a challenge for polarization control based on phase shifts from propagation in birefringent material. Achromatic wave plates consisting of multiple plates of varying thickness can be constructed and have been demonstrated at terahertz frequencies [10]. Constructing a paper achromatic wave plate is clearly the next step.

Acknowledgments

B. S. acknowledges financial support from the Friedrich Ebert Stiftung. S. T. C. would like to acknowledge funding from the Alexander von Humboldt Stiftung.

References and links

1. P. U. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011). [CrossRef]  

2. D. M. Mittleman, Sensing with Terahertz Radiation (Springer, 2003).

3. R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011). [CrossRef]  

4. S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009). [CrossRef]  

5. R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001). [CrossRef]   [PubMed]  

6. N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010). [CrossRef]  

7. D. Grischkowsky, S. R. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semicondcutors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990). [CrossRef]  

8. Q. Wu and X. C. Zhang, “Ultrafast electo-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996). [CrossRef]  

9. A. H. F. van Vliet and Th. de Graauw, “Quarter wave plates for submillimeter wavelengths,” Int. J. Infrared Millim. Waves 2(3), 465–477 (1981). [CrossRef]  

10. J.-B. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. 31(2), 265–267 (2006). [CrossRef]   [PubMed]  

11. 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(8), 1112–1114 (2006). [CrossRef]   [PubMed]  

12. M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45(12), 2766–2772 (2006). [CrossRef]   [PubMed]  

13. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983). [CrossRef]  

14. R. C. Enger and S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22(20), 3220–3228 (1983). [CrossRef]   [PubMed]  

15. L. H. Cescato, E. Gluch, and N. Streibl, “Holographic quarterwave plates,” Appl. Opt. 29(22), 3286–3290 (1990). [CrossRef]   [PubMed]  

16. B. Päivänranta, N. Passilly, J. Pietarinen, P. Laakkonen, M. Kuittinen, and J. Tervo, “Low-cost fabrication of form-birefringent quarter-wave plates,” Opt. Express 16(21), 16334–16342 (2008). [CrossRef]   [PubMed]  

17. S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010). [CrossRef]  

18. M. Scheller, C. Jördens, and M. Koch, “Terahertz form birefringence,” Opt. Express 18(10), 10137–10142 (2010). [CrossRef]   [PubMed]  

19. A. C. Strikwerda, K. Fan, H. Tao, D. V. Pilon, X. Zhang, and R. D. Averitt, “Comparison of birefringent electric split-ring resonator and meanderline structures as quarter-wave plates at terahertz frequencies,” Opt. Express 17(1), 136–149 (2009). [CrossRef]   [PubMed]  

20. P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009). [CrossRef]  

21. C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010). [CrossRef]  

22. I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15(7), 4335–4350 (2007). [CrossRef]   [PubMed]  

23. M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009). [CrossRef]  

24. B. Scherger, C. Jördens, and M. Koch, “Variable-focus terahertz lens,” Opt. Express 19(5), 4528–4535 (2011). [CrossRef]   [PubMed]  

References

  • View by:

  1. P. U. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
    [Crossref]
  2. D. M. Mittleman, Sensing with Terahertz Radiation (Springer, 2003).
  3. R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
    [Crossref]
  4. S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
    [Crossref]
  5. R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
    [Crossref] [PubMed]
  6. N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010).
    [Crossref]
  7. D. Grischkowsky, S. R. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semicondcutors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990).
    [Crossref]
  8. Q. Wu and X. C. Zhang, “Ultrafast electo-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
    [Crossref]
  9. A. H. F. van Vliet and Th. de Graauw, “Quarter wave plates for submillimeter wavelengths,” Int. J. Infrared Millim. Waves 2(3), 465–477 (1981).
    [Crossref]
  10. J.-B. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. 31(2), 265–267 (2006).
    [Crossref] [PubMed]
  11. 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(8), 1112–1114 (2006).
    [Crossref] [PubMed]
  12. M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45(12), 2766–2772 (2006).
    [Crossref] [PubMed]
  13. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983).
    [Crossref]
  14. R. C. Enger and S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22(20), 3220–3228 (1983).
    [Crossref] [PubMed]
  15. L. H. Cescato, E. Gluch, and N. Streibl, “Holographic quarterwave plates,” Appl. Opt. 29(22), 3286–3290 (1990).
    [Crossref] [PubMed]
  16. B. Päivänranta, N. Passilly, J. Pietarinen, P. Laakkonen, M. Kuittinen, and J. Tervo, “Low-cost fabrication of form-birefringent quarter-wave plates,” Opt. Express 16(21), 16334–16342 (2008).
    [Crossref] [PubMed]
  17. S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010).
    [Crossref]
  18. M. Scheller, C. Jördens, and M. Koch, “Terahertz form birefringence,” Opt. Express 18(10), 10137–10142 (2010).
    [Crossref] [PubMed]
  19. A. C. Strikwerda, K. Fan, H. Tao, D. V. Pilon, X. Zhang, and R. D. Averitt, “Comparison of birefringent electric split-ring resonator and meanderline structures as quarter-wave plates at terahertz frequencies,” Opt. Express 17(1), 136–149 (2009).
    [Crossref] [PubMed]
  20. P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009).
    [Crossref]
  21. C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
    [Crossref]
  22. I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15(7), 4335–4350 (2007).
    [Crossref] [PubMed]
  23. M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
    [Crossref]
  24. B. Scherger, C. Jördens, and M. Koch, “Variable-focus terahertz lens,” Opt. Express 19(5), 4528–4535 (2011).
    [Crossref] [PubMed]

2011 (3)

P. U. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

B. Scherger, C. Jördens, and M. Koch, “Variable-focus terahertz lens,” Opt. Express 19(5), 4528–4535 (2011).
[Crossref] [PubMed]

2010 (4)

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010).
[Crossref]

S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010).
[Crossref]

M. Scheller, C. Jördens, and M. Koch, “Terahertz form birefringence,” Opt. Express 18(10), 10137–10142 (2010).
[Crossref] [PubMed]

2009 (4)

A. C. Strikwerda, K. Fan, H. Tao, D. V. Pilon, X. Zhang, and R. D. Averitt, “Comparison of birefringent electric split-ring resonator and meanderline structures as quarter-wave plates at terahertz frequencies,” Opt. Express 17(1), 136–149 (2009).
[Crossref] [PubMed]

P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009).
[Crossref]

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (3)

2001 (1)

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[Crossref] [PubMed]

1996 (1)

Q. Wu and X. C. Zhang, “Ultrafast electo-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[Crossref]

1990 (2)

1983 (2)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983).
[Crossref]

R. C. Enger and S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22(20), 3220–3228 (1983).
[Crossref] [PubMed]

1981 (1)

A. H. F. van Vliet and Th. de Graauw, “Quarter wave plates for submillimeter wavelengths,” Int. J. Infrared Millim. Waves 2(3), 465–477 (1981).
[Crossref]

Abstreiter, G.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[Crossref] [PubMed]

Averitt, R. D.

Beigang, R.

P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009).
[Crossref]

Bichler, M.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[Crossref] [PubMed]

Bonn, M.

R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Brodschelm, A.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[Crossref] [PubMed]

Case, S. K.

Cescato, L. H.

Chatterjee, S.

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

Chen, H.-L.

Cooke, D.

P. U. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Cumming, D. R. S.

S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010).
[Crossref]

de Graauw, Th.

A. H. F. van Vliet and Th. de Graauw, “Quarter wave plates for submillimeter wavelengths,” Int. J. Infrared Millim. Waves 2(3), 465–477 (1981).
[Crossref]

Enger, R. C.

Fan, K.

Fattinger, C.

Fedosejevs, R.

Flanders, D. C.

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983).
[Crossref]

Gallot, G.

Gluch, E.

Golde, D.

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

Grant, J. P.

S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010).
[Crossref]

Grischkowsky, D.

Grunwald, T.

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

Heinz, T. F.

R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Henry, E.

R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Hsieh, C.-F.

Huber, R.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[Crossref] [PubMed]

Imhof, C.

P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009).
[Crossref]

Jansen, C.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

Jepsen, P. U.

P. U. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Jördens, C.

B. Scherger, C. Jördens, and M. Koch, “Variable-focus terahertz lens,” Opt. Express 19(5), 4528–4535 (2011).
[Crossref] [PubMed]

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

M. Scheller, C. Jördens, and M. Koch, “Terahertz form birefringence,” Opt. Express 18(10), 10137–10142 (2010).
[Crossref] [PubMed]

Keiding, S. R.

Khalid, A.

S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010).
[Crossref]

Kira, M.

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

Koch, M.

P. U. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

B. Scherger, C. Jördens, and M. Koch, “Variable-focus terahertz lens,” Opt. Express 19(5), 4528–4535 (2011).
[Crossref] [PubMed]

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010).
[Crossref]

M. Scheller, C. Jördens, and M. Koch, “Terahertz form birefringence,” Opt. Express 18(10), 10137–10142 (2010).
[Crossref] [PubMed]

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15(7), 4335–4350 (2007).
[Crossref] [PubMed]

Koch, S. W.

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

Köhler, D.

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

Kuittinen, M.

Laakkonen, P.

Leitenstorfer, A.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[Crossref] [PubMed]

Ma, Y.

S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010).
[Crossref]

Masson, J.-B.

Mikulics, M.

N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010).
[Crossref]

Päivänranta, B.

Pan, C.-L.

Pan, R.-P.

Passilly, N.

Paul, O.

P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009).
[Crossref]

Pierz, K.

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

Pietarinen, J.

Pilon, D. V.

Pupeza, I.

Rahm, M.

P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009).
[Crossref]

Reid, M.

Romeike, D.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

Saha, S. C.

S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010).
[Crossref]

Scheller, M.

M. Scheller, C. Jördens, and M. Koch, “Terahertz form birefringence,” Opt. Express 18(10), 10137–10142 (2010).
[Crossref] [PubMed]

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

Scherger, B.

B. Scherger, C. Jördens, and M. Koch, “Variable-focus terahertz lens,” Opt. Express 19(5), 4528–4535 (2011).
[Crossref] [PubMed]

N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010).
[Crossref]

Shakfa, M. K.

N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010).
[Crossref]

Shan, J.

R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Streibl, N.

Strikwerda, A. C.

Tang, T.-T.

Tao, H.

Tauser, F.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[Crossref] [PubMed]

Tervo, J.

Ulbricht, R.

R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

van Exter, M.

van Vliet, A. H. F.

A. H. F. van Vliet and Th. de Graauw, “Quarter wave plates for submillimeter wavelengths,” Int. J. Infrared Millim. Waves 2(3), 465–477 (1981).
[Crossref]

Vieweg, N.

N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010).
[Crossref]

Weis, P.

P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009).
[Crossref]

Wiesauer, K.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

Wietzke, S.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

Wilk, R.

Wu, Q.

Q. Wu and X. C. Zhang, “Ultrafast electo-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[Crossref]

Zentgraf, T.

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

Zhang, X.

Zhang, X. C.

Q. Wu and X. C. Zhang, “Ultrafast electo-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (3)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42(6), 492–494 (1983).
[Crossref]

Q. Wu and X. C. Zhang, “Ultrafast electo-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[Crossref]

P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009).
[Crossref]

Compos. Sci. Technol. (1)

C. Jördens, M. Scheller, S. Wietzke, D. Romeike, C. Jansen, T. Zentgraf, K. Wiesauer, and M. Koch, “Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics,” Compos. Sci. Technol. 70(3), 472–477 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (1)

S. C. Saha, Y. Ma, J. P. Grant, A. Khalid, and D. R. S. Cumming, “Low-loss terahertz artificial dielectric birefringent quarter-wave plates,” IEEE Photon. Technol. Lett. 22(2), 79–81 (2010).
[Crossref]

Int. J. Infrared Millim. Waves (1)

A. H. F. van Vliet and Th. de Graauw, “Quarter wave plates for submillimeter wavelengths,” Int. J. Infrared Millim. Waves 2(3), 465–477 (1981).
[Crossref]

J. Infrared Milli Terahz Waves (1)

N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, “THz Properties of Nematic Liquid Crystals,” J. Infrared Milli Terahz Waves 31(11), 1312–1320 (2010).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

P. U. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Nature (1)

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[Crossref] [PubMed]

Opt. Commun. (1)

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Phys. Stat. Solidi C (1)

S. Chatterjee, T. Grunwald, D. Köhler, K. Pierz, D. Golde, M. Kira, and S. W. Koch, “THz measurements of the optical response in a two-dimensional electron gas,” Phys. Stat. Solidi C 6(2), 453–456 (2009).
[Crossref]

Rev. Mod. Phys. (1)

R. Ulbricht, E. Henry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011).
[Crossref]

Other (1)

D. M. Mittleman, Sensing with Terahertz Radiation (Springer, 2003).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic drawing of the wave plate. The x- and y-axes define the TM or p-polarization and TE or s-polarization directions, respectively. The THz wave propagates in z-direction. α denotes the angle between the y-axis and the polarization of the THz electric field. (b) Photograph of the form-birefringent quarter-wave plate fabricated from paper.
Fig. 2
Fig. 2 Frequency dependence of (a) indices of refraction and (b) absorption coefficients for a 4.2 mm paper wave plate for s and p-polarization (green and red symbols respectively). The solid lines in (a) represent the theoretical expectation according to [18]. The solid lines in (b) are curves obtained with the SVMAF filter as described in [22].
Fig. 3
Fig. 3 Frequency dependent transfer function of three paper wave plates of different thicknesses. Symbols are measurements, lines are simulations.
Fig. 4
Fig. 4 Angular dependence of the transfer function for the half-wave frequency of the 4.2 mm thick wave plate for analyzer polarizer (a) parallel and (b) crossed to the source polarizer. Symbols are measurements, lines are simulations.
Fig. 5
Fig. 5 Beam profiles of the THz beam at the detector with (b) and without (a) a wave plate inserted into the beam path. Plotted is the integrated intensity from 200 to 300 GHz.

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