Abstract

We have developed low-loss polymer artificial dielectric quarter wave plates (QWP) operating at 2.6, 3.2 and 3.8 THz. The QWPs are imprinted on high density polyethylene (HDPE) using silicon masters. The grating period for the quarter wave plates is 60 µm. 330 µm, 280 μm and 230 μm deep gratings are used to obtain a π/2 phase retardance between TE and TM polarization propagating through the QWPs. High frequency structure simulator (HFSS) was used to optimize the grating depth. Since the required grating depth is high, two plates, fixed in a back-to-back configuration were used for each QWP. A maximum aspect ratio (grating height/grating width) of 6.6 was used.

©2010 Optical Society of America

1. Introduction

Terahertz (THz) systems have recently received significant attention for applications in material inspection, security imaging, short range and high bandwidth communications [1,2]. There is currently a great deal of interest in developing systems for large standoff distance imaging to detect concealed weapons and explosives. These systems have applications in continuous monitoring of airport and public places. In order to build such a system there is a requirement to realize a wide range of terahertz sources, detectors and components. Several components have already been demonstrated including a variable polarization compensator [3], diffractive optics [4], filters [5], sources and detectors [6,7]. In this paper, we present the design and characterization of quarter wave plates (QWPs) fabricated in high density polyethylene (HDPE) using an imprinting technology. The design of a QWP is based on the theory of birefringence in an artificial dielectric [8]. The birefringence of the material is obtained by imprinting vertical grooves in the dielectric substrate [3,9]. The operating frequency of the QWP is dominated by the groove depth and the fill-factor that is given by a/Λ, where a is the line width and Λ is the grating period, as shown in Fig. 1 .

 figure: Fig. 1

Fig. 1 A cross-sectional view of a quarter wave plate (two plates fixed back-to-back). The device is made of a vertical grating with alternate refractive index ηh (HDPE) and ηa=1 (air). The grating vector is k.

Download Full Size | PPT Slide | PDF

Non-artificial dielectric based QWPs have been demonstrated at 1 THz. Multiple quartz layers were required and the device was relatively thick [10]. The absorption coefficient beyond 1 THz for many materials significantly increases thus making thick QWPs inefficient [11]. By contrast, the absorption coefficient of HDPE is reasonably small, lying in the range 0.5 - 1 cm−1 between 1 - 4 THz [12,13]. Furthermore, the refractive index of the HDPE is 1.55, which is not large with respect to that of air (1.0), thus the index mismatch is relatively small hence the component surface will have a low reflection coefficient (< 0.05), reducing insertion loss. The loss due to surface reflection will also be reduced due to the matching properties of artificial dielectrics [14], albeit the pattern is not optimized as an antireflection layer in the present case. The advantages accruing by using a low refractive index polymer are, however, offset by additional fabrication difficulty. Because of the low refractive index of HDPE, the grating grooves required to produce the birefringence will need to be suitably deep in order to achieve a quarter-wave polarization rotation. It is therefore necessary to make high aspect ratio structures.

A high aspect ratio imprint method has previously been reported [15]. The procedure required a combination of imprint lithography and photolithography, and an aspect ratio (e.g. d 1/(Λ-a) in Fig. 1) of 3 was obtained. Artificial dielectric QWPs working in the visible frequency range have been reported using a combination of electron beam lithography and nano-imprint [9]. The fabrication method was complex, requiring several etch steps to produce the masters. The imprint was performed on a liquid ultra violet (UV) curable prepolymer. This required a UV replication step, and a large aspect ratio of 6 was obtained. However, nano-imprint lithography is not appropriate for micron scale THz devices.

In this paper, we report on artificial dielectric QWPs produced by imprinting on HDPE substrates from silicon masters. The silicon masters were produced using photolithography and an inductively coupled plasma (ICP) etch process. A combination of heat and pressure were used for imprinting using an Obducat imprinting tool. Three QWPs were demonstrated to work at three discrete frequencies.

2. Design and simulation

In micro-imprinting, the maximum achievable grating depth is limited by the grating period. The grating depth and period of a QWP is inversely proportional to the operating frequency. For a low refractive index polymer, the required grating depth might be too large to achieve in a single imprint step. Therefore, multiple plates may be required to obtain the desired phase retardance for a QWP. With a dielectric constant of 2.4, HDPE polarization retarders require a relatively deep grating depth (>200 μm) to make a QWP at terahertz frequencies. Because the required depth cannot be achieved in a single grating we have used two imprinted plates fixed back-to-back for each QWP. A cross-sectional view of the HDPE QWP with the main geometrical parameters is shown in Fig. 1. The grating period Λ of the QWP is 60 μm. Assuming Λ = 2a [8], the calculated effective refractive index in the grating for transverse electric (TE) and transverse magnetic (TM) incident beam are ny = 1.30 and nx = 1.19 respectively. In Fig. 1 TM waves have an electric field component parallel to the grating vector k. Based on the above parameters, the calculated total grating depth d = (d1+d2) should be 300 μm, 235 μm and 200 μm for 2.2, 2.8 and 3.3 THz QWPs respectively. These frequencies were studied since source technologies such as quantum cascade lasers are now becoming available, opening up opportunities to develop new terahertz products and systems [16].

It is preferred to have Λ = 2a as this will maximize the phase difference between the TM and TE waves for a given grating depth. In practice (see Section 3), the exact ratio Λ/a = 2 is hard to achieve due to fabrication constraints. Initial fabrication parameters for a 115 µm deep grating produced devices with a = 35 μm instead of 30 μm. This gives a fill factor of 0.6 instead of 0.5, modifying the required grating depth for the desired operating frequency. Rather than invest heavily in re-optimizing the process to achieve Λ/a = 2, we have chosen the cheaper and quicker option of using high frequency structure simulator (HFSS) from Ansoft to optimize the grating parameters [17]. After simulation, the total grating depth, from combination of two plates was optimized to 330 μm, 280 μm and 230 μm for the required polarization at 2.2, 2.8 and 3.3 THz respectively. The simulated phase and transmission of TE and TM wave for QWPs with a 330 μm deep grating are shown in Figs. 2(a) and 2(b) respectively.

 figure: Fig. 2

Fig. 2 (a) The simulated phase and the phase difference (PD) and (b) transmission amplitude of the TE and TM waves for the HDPE QWP with total grating depth (d1 + d2) of 330 μm. (Λ = 60 μm and a = 35 μm).

Download Full Size | PPT Slide | PDF

The phase of the TE and TM waves both follow a sawtooth repeating profile and the phase difference or retardation between the TE and TM waves increases gradually with frequency, with a small sinusoidal variation superimposed upon it. From Fig. 2(a), it can be easily seen that the retardation between TE and TM wave is 90° (π/2) at 2.2 THz. From the Fig. 2(b) it is also seen that both TE and TM wave transmission of the QWPs, which follows an oscillatory behavior, is greater than 85% at the operating frequency. The transmission coefficient decreases to some extent with increasing frequency. The oscillation in phase difference and transmission is due to the Fabry-Perot reflections from two sides of the HDPE plates.

3. Fabrication of silicon masters and imprinting into HDPE

The fabrication was performed in two sequences. First, a silicon master was fabricated and then the QWP was printed on HDPE using the silicon master. A single mask process was used to fabricate the silicon masters, using a 1000 μm thick silicon wafer, polished on one side. The sample was cleaned and spin coated with 6.1 μm thick AZ 4562 positive tone photo resist and soft baked at 90 °C for 30 mins in a convection oven. The wafer was then exposed using a mask plate in a Suss MicroTec MA6 aligner for 23 seconds at 7.2 mW/cm2 power and developed in 4:1 reverse osmosis (RO) water:AZ400K developer for 3 minutes. After development, the wafer was hard baked at 120 °C for 30 mins in a convection oven. The device was etched by deep reactive ion etching using SF6 (130 SCCM), and C4F8 (85 SCCM) gases with a pressure of 25 mTorr [4]. The coil and platen power was 593 W and 4.2 W respectively. Using two samples that were lithographically the same, two silicon masters were produced using the ICP etching process for 45 min (sample A) and 30 min (sample B) respectively at an etch rate of ~3.7 μm/minute. For both samples the photoresist mask was stripped and cleaned using hot acetone, iso-propanol and RO water. Scanning electron microscopy (SEM) was used to check the quality of the masters. A SEM image of master B is shown in Fig. 3(a) . From the SEM images, it can be seen that the etch depth of sample B is 115 μm. The silicon width, a’, that complements a in the final HPDE structure was found to be 25 µm for both samples A and B, so that the fill-factor for the master was 0.4. After imprint, this will correspond to a fill-factor of 0.6 in the final devices. The master fill-factor should ideally be 0.5, and we attribute the difference to a dry etch under cut leading to wider than anticipated grooves. As described in Section 2 the difference between the actual and the original design choice for the fill-factor has an impact on the operating frequency for a QWP that we compensate for by modifying the etch depth.

 figure: Fig. 3

Fig. 3 The SEM images of (a) the 115 μm deep silicon master and (b) corresponding imprinted HDPE plate.

Download Full Size | PPT Slide | PDF

After fabrication of the masters, the gratings were printed on to 1 mm thick HDPE using the imprinting tool. In order to reduce the surface tension and make the sample hydrophobic prior to imprinting, the masters were treated in a mixture of 97% triclorosilane (C8H4Cl3F13Sl) and RO water for 10 minutes. This process facilitates the separation of the imprinted grating from the master after the imprint process. During imprinting, the temperature was increased to 140 °C, then 5 bar pressure was applied for 5 min. The pressure and temperature were reduced gradually to 3 bar and 60 °C respectively, and held at these conditions for 3 min. Next, the pressure was fully released and the sample allowed to cool to room temperature. Finally the imprinted gratings were separated from the masters. A SEM image of an imprinted sample from master B is shown in Fig. 3(b). By examining several imprinted devices made from imprint masters A and B we find the groove width is 25 µm, indicating a faithfully, complementary, copy of the master has been made in each instance.

4. Result and discussion

The QWP samples were measured in a Bruker IFS 66v/S Fourier Transform Infrared (FTIR) spectrometer using a broadband globar source. The experimental set up is shown in Fig. 4(a) and is similar to the setup presented in [18]. Two sets of samples made from masters A and B with groove depths 165 µm and 115 µm respectively were used. Pairs of samples were fixed back-to-back to give the combinations A+A, A+B and B+B. In this way the two samples with different groove depths were used to obtain the required π/2 polarization retardation at three different frequencies. In the FTIR specimen chamber the incident beam is linearly polarized using a polarizer that was made by making a fine pitch aluminum grating on HPDE [5]. A second, identically made, analyzing polarizer is mounted on a rotation stage.

 figure: Fig. 4

Fig. 4 (a) a sketch of the experimental set up used to characterize the QWP and (b) the transmission of the QWP (A+A) for several different analyzer angles. The plotted P(f) is calculated from this data using the minimum and maximum transmission curves.

Download Full Size | PPT Slide | PDF

The QWPs were placed in the FTIR at so that their grating angle was set at 45° with respect to the fixed polarizer. At the optimum frequency for any of the QWPs the output beam will be circularly polarized – i.e. it will have equal TE and TM components. Measurements are made by rotating the analyzer from 0° to 90° in 15° increments. A transmission spectra is collected for each rotation of the analyzer. Typical data for the sample combination A+A is shown in Fig. 4(b). The operating frequency for a QWP is identified as being the position in the spectra where rotation of the analyzer (0° to 90°) gives rise to the smallest (ideally zero) variation in transmission. In order to quantify the performance of the QWP the parameter polarizing factor P(f) for the QWP is introduced as:

P(f)=Tmax(f)Tmin(f)Tmax(f)+Tmin(f)
where T max (f) and T min(f) are the curves that show the maximum and minimum transmission coefficients as a function of the frequency, f, chosen from among the spectra at different analyzer angles, as shown in Fig. 4(b). The polarizing factor P(f) is also shown in Fig. 4(b) for the specific sample combination. The minima in P(f) correspond to the frequencies where the phase retardance is an odd multiple of π/2. Figure 5(a) shows the polarization factor P(f) as a function of frequency for all the QWPs. From Fig. 5(a) it can be seen that the operating frequencies of the QWPs are 2.6 THz (A+A), 3.2 THz (A+B) and 3.8 THz (B+B) respectively. The polarizing factors are 0.05, 0.04 and 0.10 at the operating frequency of respective QWPs. These are slightly greater than the ideal value (P(f) = 0). We attribute this non-ideality to the known properties of grating artificial dielectrics [3]. For comparison, the polarizing factor calculated from the simulated phase and transmission is shown in Fig. 5(b) for the same configurations. A moving average function is used to eliminate the ripple caused by the Fabry-Perot effect. The measured optimum frequency for each of the QWPs is greater than the simulated value. There are several reasons for this. Although a = 35 μm, the exact value may vary along the structure due to expansion of HDPE after imprinting. In addition, when two plates are fixed back-to-back for measurement, ideally the grating direction of both plates will exactly align to each other. In reality, there may be a small rotational misalignment that will reduce the overall phase difference to some extent. Both of these factors will reduce the phase difference at any specific frequency and shift the QWP operating frequency to a higher value.

 figure: Fig. 5

Fig. 5 (a) The measured polarizing factor P(f) of the QWPs for three device configurations, and (b) the simulated polarizing factor for the same configurations. Note the scale difference in x and y axis.

Download Full Size | PPT Slide | PDF

The transmission of the TE and TM wave for a single plate (A) and the combination of two plates (A+A) fixed back-to-back are shown in Fig. 6 . The transmission of the QWP is around 65% when two plates are used back-to-back. From Fig. 6, it is also seen that the transmission can be increased up to 85%, for a device made using only a single plate. The backsides of the imprinted HDPE plates are not perfectly polished, so there will be small air pockets at the interface when two samples are fixed back-to-back. When the terahertz beam passes through them, the beam experiences a change in media i.e. HDPE-air-HDPE. This introduces a reflection coefficient due to the index mismatch between HDPE and air. The loss would therefore be reduced if the two plates were printed on two sides of a single HDPE sheet. Alternatively, the total grating depth could be imprinted on one side of HDPE, but this would be beyond the capability of the present master technology. From Fig. 6, it is also seen that the transmission coefficient of TE and TM wave differ to some extent. This is due to the difference in nx and ny as presented in Section 2.

 figure: Fig. 6

Fig. 6 The transmission of plates A and A+A in TE and TM mode.

Download Full Size | PPT Slide | PDF

5. Conclusions

We have imprinted terahertz quarter wave plates in a high density polyethylene substrate. The operating frequencies of the three configurations are 2.6, 3.2 and 3.8 THz. The polarizing factor P(f) of the QWPs is below 0.05 at 2.6 and 3.2 THz and approximately 0.10 at 3.8 THz. A transmission coefficient of up to 85% could in principle be achieved if the QWPs were printed on a single sheet. A maximum aspect ratio of 6.6 was obtained using the imprint technology. The method of imprinting is simple, cheap and elegant. The resulting components can be made to a quality that is superior to the prior art.

References

1. D. T. Petkie, C. Casto, F. C. De Lucia, S. R. Murrill, B. Redman, R. L. Espinola, C. C. Franck, E. L. Jacobs, S. T. Griffin, C. E. Halford, J. Reynolds, S. O’Brien, and D. Tofsted, “Active and Passive imaging in the THz spectral region: phenomenonlogy, dynamic range, modes and illumination,” J. Opt. Soc. Am. B 25(9), 1523–1531 (2008). [CrossRef]  

2. R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multi-gigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron. 14(2), 421–430 (2008). [CrossRef]  

3. T. D. Drysdale, R. J. Blaikie, H. M. Chong, and D. R. S. Cumming, “Artificial dielectric devices for variable polarization compensation at millimeter and submillimeter wavelengths,” IEEE Trans. Antenn. Propag. 51(11), 3072–3079 (2003). [CrossRef]  

4. E. D. Walsby, J. Alton, C. Worrall, H. E. Beere, D. A. Ritchie, and D. R. S. Cumming, “Imprinted diffractive optics for terahertz radiation,” Opt. Lett. 32(9), 1141–1143 (2007). [CrossRef]   [PubMed]  

5. Y. Ma, A. Khalid, T. D. Drysdale, and D. R. S. Cumming, “Direct fabrication of terahertz optical devices on low-absorption polymer substrates,” Opt. Lett. 34(10), 1555–1557 (2009). [CrossRef]   [PubMed]  

6. A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009). [CrossRef]  

7. M. J. Khan, J. C. Chen, and S. Kaushik, “Optical detection of terahertz using nonlinear parametric upconversion,” Opt. Lett. 33(23), 2725–2727 (2008). [CrossRef]   [PubMed]  

8. A. H. F. van Vliet and T. de Graauw, “Quarter wave plate for sub-millimetre wavelengths,” Int. J. Infrared Millim. Waves 2(3), 465–477 (1981). [CrossRef]  

9. 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]  

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

11. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy: A new tool for the study of glasses in the far infrared,” J. Non-Cryst. Solids 351(40-42), 3341–3346 (2005). [CrossRef]  

12. W. Frank, “Far-infrared spectrum of irradiated polyethylene,” Polymer. Letters. Edition. 15(11), 679–682 (1977). [CrossRef]  

13. G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971). [CrossRef]  

14. D. Raguin and G. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32(14), 2582–2598 (1993). [CrossRef]   [PubMed]  

15. W. Liao and S. Hsu, “High aspect ratio pattern transfer in imprint lithography using a hybrid mold,” J. Vac. Sci. Technol. B 22(6), 2764–2767 (2004). [CrossRef]  

16. B. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007). [CrossRef]  

17. H. F. S. S. Ansoft, v11 from Ansys Inc (www.ansoft.com, 10.08.2009).

18. S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. D. T. Petkie, C. Casto, F. C. De Lucia, S. R. Murrill, B. Redman, R. L. Espinola, C. C. Franck, E. L. Jacobs, S. T. Griffin, C. E. Halford, J. Reynolds, S. O’Brien, and D. Tofsted, “Active and Passive imaging in the THz spectral region: phenomenonlogy, dynamic range, modes and illumination,” J. Opt. Soc. Am. B 25(9), 1523–1531 (2008).
    [Crossref]
  2. R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multi-gigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron. 14(2), 421–430 (2008).
    [Crossref]
  3. T. D. Drysdale, R. J. Blaikie, H. M. Chong, and D. R. S. Cumming, “Artificial dielectric devices for variable polarization compensation at millimeter and submillimeter wavelengths,” IEEE Trans. Antenn. Propag. 51(11), 3072–3079 (2003).
    [Crossref]
  4. E. D. Walsby, J. Alton, C. Worrall, H. E. Beere, D. A. Ritchie, and D. R. S. Cumming, “Imprinted diffractive optics for terahertz radiation,” Opt. Lett. 32(9), 1141–1143 (2007).
    [Crossref] [PubMed]
  5. Y. Ma, A. Khalid, T. D. Drysdale, and D. R. S. Cumming, “Direct fabrication of terahertz optical devices on low-absorption polymer substrates,” Opt. Lett. 34(10), 1555–1557 (2009).
    [Crossref] [PubMed]
  6. A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
    [Crossref]
  7. M. J. Khan, J. C. Chen, and S. Kaushik, “Optical detection of terahertz using nonlinear parametric upconversion,” Opt. Lett. 33(23), 2725–2727 (2008).
    [Crossref] [PubMed]
  8. A. H. F. van Vliet and T. de Graauw, “Quarter wave plate for sub-millimetre wavelengths,” Int. J. Infrared Millim. Waves 2(3), 465–477 (1981).
    [Crossref]
  9. 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]
  10. J. B. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. 31(2), 265–267 (2006).
    [Crossref] [PubMed]
  11. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy: A new tool for the study of glasses in the far infrared,” J. Non-Cryst. Solids 351(40-42), 3341–3346 (2005).
    [Crossref]
  12. W. Frank, “Far-infrared spectrum of irradiated polyethylene,” Polymer. Letters. Edition. 15(11), 679–682 (1977).
    [Crossref]
  13. G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971).
    [Crossref]
  14. D. Raguin and G. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32(14), 2582–2598 (1993).
    [Crossref] [PubMed]
  15. W. Liao and S. Hsu, “High aspect ratio pattern transfer in imprint lithography using a hybrid mold,” J. Vac. Sci. Technol. B 22(6), 2764–2767 (2004).
    [Crossref]
  16. B. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
    [Crossref]
  17. H. F. S. S. Ansoft, v11 from Ansys Inc ( www.ansoft.com , 10.08.2009).
  18. S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010).
    [Crossref]

2010 (1)

S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010).
[Crossref]

2009 (2)

Y. Ma, A. Khalid, T. D. Drysdale, and D. R. S. Cumming, “Direct fabrication of terahertz optical devices on low-absorption polymer substrates,” Opt. Lett. 34(10), 1555–1557 (2009).
[Crossref] [PubMed]

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

2008 (4)

2007 (2)

2006 (1)

2005 (1)

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy: A new tool for the study of glasses in the far infrared,” J. Non-Cryst. Solids 351(40-42), 3341–3346 (2005).
[Crossref]

2004 (1)

W. Liao and S. Hsu, “High aspect ratio pattern transfer in imprint lithography using a hybrid mold,” J. Vac. Sci. Technol. B 22(6), 2764–2767 (2004).
[Crossref]

2003 (1)

T. D. Drysdale, R. J. Blaikie, H. M. Chong, and D. R. S. Cumming, “Artificial dielectric devices for variable polarization compensation at millimeter and submillimeter wavelengths,” IEEE Trans. Antenn. Propag. 51(11), 3072–3079 (2003).
[Crossref]

1993 (1)

1981 (1)

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

1977 (1)

W. Frank, “Far-infrared spectrum of irradiated polyethylene,” Polymer. Letters. Edition. 15(11), 679–682 (1977).
[Crossref]

1971 (1)

G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971).
[Crossref]

Alton, J.

Beere, H. E.

Blaikie, R. J.

T. D. Drysdale, R. J. Blaikie, H. M. Chong, and D. R. S. Cumming, “Artificial dielectric devices for variable polarization compensation at millimeter and submillimeter wavelengths,” IEEE Trans. Antenn. Propag. 51(11), 3072–3079 (2003).
[Crossref]

Casto, C.

Chantry, G.

G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971).
[Crossref]

Chen, J. C.

Chong, H. M.

T. D. Drysdale, R. J. Blaikie, H. M. Chong, and D. R. S. Cumming, “Artificial dielectric devices for variable polarization compensation at millimeter and submillimeter wavelengths,” IEEE Trans. Antenn. Propag. 51(11), 3072–3079 (2003).
[Crossref]

Cudby, M.

G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971).
[Crossref]

Cumming, D.

S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010).
[Crossref]

Cumming, D. R. S.

de Graauw, T.

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

De Lucia, F. C.

Drysdale, T. D.

Y. Ma, A. Khalid, T. D. Drysdale, and D. R. S. Cumming, “Direct fabrication of terahertz optical devices on low-absorption polymer substrates,” Opt. Lett. 34(10), 1555–1557 (2009).
[Crossref] [PubMed]

T. D. Drysdale, R. J. Blaikie, H. M. Chong, and D. R. S. Cumming, “Artificial dielectric devices for variable polarization compensation at millimeter and submillimeter wavelengths,” IEEE Trans. Antenn. Propag. 51(11), 3072–3079 (2003).
[Crossref]

Espinola, R. L.

Fedorov, G.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

Fleming, J.

G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971).
[Crossref]

Franck, C. C.

Frank, W.

W. Frank, “Far-infrared spectrum of irradiated polyethylene,” Polymer. Letters. Edition. 15(11), 679–682 (1977).
[Crossref]

Gallot, G.

Grant, J.

S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010).
[Crossref]

Griffin, S. T.

Halford, C. E.

Hsu, S.

W. Liao and S. Hsu, “High aspect ratio pattern transfer in imprint lithography using a hybrid mold,” J. Vac. Sci. Technol. B 22(6), 2764–2767 (2004).
[Crossref]

Hu, Q.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

Jacob, M.

R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multi-gigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron. 14(2), 421–430 (2008).
[Crossref]

Jacobs, E. L.

Kaushik, S.

Khalid, A.

S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010).
[Crossref]

Y. Ma, A. Khalid, T. D. Drysdale, and D. R. S. Cumming, “Direct fabrication of terahertz optical devices on low-absorption polymer substrates,” Opt. Lett. 34(10), 1555–1557 (2009).
[Crossref] [PubMed]

Khan, M. J.

Koch, M.

R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multi-gigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron. 14(2), 421–430 (2008).
[Crossref]

Kuittinen, M.

Kumar, S.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

Kürner, T.

R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multi-gigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron. 14(2), 421–430 (2008).
[Crossref]

Laakkonen, P.

Liao, W.

W. Liao and S. Hsu, “High aspect ratio pattern transfer in imprint lithography using a hybrid mold,” J. Vac. Sci. Technol. B 22(6), 2764–2767 (2004).
[Crossref]

Ma, Y.

S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010).
[Crossref]

Y. Ma, A. Khalid, T. D. Drysdale, and D. R. S. Cumming, “Direct fabrication of terahertz optical devices on low-absorption polymer substrates,” Opt. Lett. 34(10), 1555–1557 (2009).
[Crossref] [PubMed]

Masson, J. B.

Miles, R. E.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy: A new tool for the study of glasses in the far infrared,” J. Non-Cryst. Solids 351(40-42), 3341–3346 (2005).
[Crossref]

Morris, G.

Murrill, S. R.

Naftaly, M.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy: A new tool for the study of glasses in the far infrared,” J. Non-Cryst. Solids 351(40-42), 3341–3346 (2005).
[Crossref]

O’Brien, S.

Päivänranta, B.

Passilly, N.

Petkie, D. T.

Piesiewicz, R.

R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multi-gigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron. 14(2), 421–430 (2008).
[Crossref]

Pietarinen, J.

Raguin, D.

Redman, B.

Reno, J. L.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

Reynolds, J.

Ritchie, D. A.

Saha, S.

S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010).
[Crossref]

Schoebel, J.

R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multi-gigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron. 14(2), 421–430 (2008).
[Crossref]

Smirnov, D.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

Smith, P.

G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971).
[Crossref]

Tervo, J.

Tofsted, D.

van Vliet, A. H. F.

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

Wade, A.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

Walsby, E. D.

Williams, B.

B. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

Williams, B. S.

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

Willis, H.

G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971).
[Crossref]

Worrall, C.

Appl. Opt. (1)

Chem. Phys. Lett. (1)

G. Chantry, J. Fleming, P. Smith, M. Cudby, and H. Willis, “Far infrared and millimeter-wave absorption spectra of some low-loss polymers,” Chem. Phys. Lett. 10(4), 473–477 (1971).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multi-gigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron. 14(2), 421–430 (2008).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

T. D. Drysdale, R. J. Blaikie, H. M. Chong, and D. R. S. Cumming, “Artificial dielectric devices for variable polarization compensation at millimeter and submillimeter wavelengths,” IEEE Trans. Antenn. Propag. 51(11), 3072–3079 (2003).
[Crossref]

Int. J. Infrared Millim. Waves (1)

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

J. IEEE PTL (1)

S. Saha, Y. Ma, J. Grant, A. Khalid, and D. Cumming, “Low-Loss Terahertz Artificial Dielectric Birefringent Quarter-Wave Plates,” J. IEEE PTL 22(2), 79–81 (2010).
[Crossref]

J. Non-Cryst. Solids (1)

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy: A new tool for the study of glasses in the far infrared,” J. Non-Cryst. Solids 351(40-42), 3341–3346 (2005).
[Crossref]

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

J. Vac. Sci. Technol. B (1)

W. Liao and S. Hsu, “High aspect ratio pattern transfer in imprint lithography using a hybrid mold,” J. Vac. Sci. Technol. B 22(6), 2764–2767 (2004).
[Crossref]

Nat. Photonics (2)

B. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K,” Nat. Photonics 3(1), 41–45 (2009).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Polymer. Letters. Edition. (1)

W. Frank, “Far-infrared spectrum of irradiated polyethylene,” Polymer. Letters. Edition. 15(11), 679–682 (1977).
[Crossref]

Other (1)

H. F. S. S. Ansoft, v11 from Ansys Inc ( www.ansoft.com , 10.08.2009).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 A cross-sectional view of a quarter wave plate (two plates fixed back-to-back). The device is made of a vertical grating with alternate refractive index ηh (HDPE) and ηa=1 (air). The grating vector is k .
Fig. 2
Fig. 2 (a) The simulated phase and the phase difference (PD) and (b) transmission amplitude of the TE and TM waves for the HDPE QWP with total grating depth (d1 + d2 ) of 330 μm. (Λ = 60 μm and a = 35 μm).
Fig. 3
Fig. 3 The SEM images of (a) the 115 μm deep silicon master and (b) corresponding imprinted HDPE plate.
Fig. 4
Fig. 4 (a) a sketch of the experimental set up used to characterize the QWP and (b) the transmission of the QWP (A+A) for several different analyzer angles. The plotted P(f) is calculated from this data using the minimum and maximum transmission curves.
Fig. 5
Fig. 5 (a) The measured polarizing factor P(f) of the QWPs for three device configurations, and (b) the simulated polarizing factor for the same configurations. Note the scale difference in x and y axis.
Fig. 6
Fig. 6 The transmission of plates A and A+A in TE and TM mode.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

P ( f ) = T max ( f ) T min ( f ) T max ( f ) + T min ( f )

Metrics