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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 2853–2859
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Tunable millimeter and sub-millimeter spectral response of textile metamaterial via resonant states

Michael Ghebrebrhan, Francisco J. Aranda, David P. Ziegler, Joel B. Carlson, Jeffrey Perry, Deana M. Archambault, David A. DiGiovanni, Andrew J. Gatesman, Robert H. Giles, Weidong Zhang, Elliott R. Brown, and Brian R. Kimball  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 2853-2859 (2014)
http://dx.doi.org/10.1364/OE.22.002853


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Abstract

We report on a new textile metamaterial created by adding metal wires directly into the polymer yarn. Split-ring resonator-like extended states are created. Simulations revealed that the extended states can be easily tuned via the geometry. Measurements of the transmittance spectrum as a function of the polarization angle in the low terahertz range were also performed and these peaks were ascribed to a polarization-dependent resonator model. The fabrics are viable candidates for flexible and deformable gigahertz and terahertz-enabled metamaterials.

© 2014 Optical Society of America

1. Introduction

2. Methods

The textile samples were from a composite yarn consisting of an iCon fiber twisted with a 72-filament polypropylene fiber at a rate of 0.5 twists per inch. The resulting composite yarn had a bulk density more suitable for producing woven and knitted fabrics. The 75 µm-diameter iCon fiber, consisting of a 46 µm-diameter indium core and a PETG cladding, was obtained from EY Technologies under the trademark iCon-75TM [25

25. Specialty Product: ICON-75,” http://www.eytechnologies.com/icon-75.html.

]. The iCon fiber had a resistance per unit length of 130 Ω/m. The woven sample for this study was produced on a Harrisville Design 22” floor loom. The fabric was constructed using a balanced plain weave design, of 12 ends per inch in the warp direction by 12 picks per inch in the filling (weft) direction. The knitted fabric sample for this study was produced on a Lawson Hemphill Fiber Analysis Knitter Sampler (FAK-S). The knitted fabric sample was constructed as a single jersey circular weft knit. Conductivity and index values for the materials are presented in Table 1

Table 1. Conductivity and Refractive Indices of Materials Used

table-icon
View This Table
; it was assumed that the index values change very little over the frequencies considered.

Measurements of the reflection and transmission spectra at normal incidence for both polarizations from 10 to 110 GHz were carried out using an Agilent Professional Network Analyzer in three disjoint bands: 3.6-18 GHz, 27.8-40 GHz, and 67-111 GHz. Next, transmission measurements were conducted for various polarization states in the range 0.2 to 1.6 THz using a coherent photomixing spectrometer.

Finite-element simulations with COMSOL were used for both fabric samples to fill in the gaps in the measured gigahertz spectra and to provide additional physical insight of the observed response [28

28. COMSOL,” http://www.comsol.com/.

]. To reduce the size of the simulation, periodic boundary conditions are assumed. The iCon fiber topology can be determined by visual inspection of the fabric and taking measurements of relative positions of certain points within a unit cell. Because the optical thickness of the PETG sheath was much smaller than the wavelengths used, it was not included in simulations. This also allowed fewer elements to be used. To further facilitate simulations we note that the wavelengths of interest are larger than the periods and homogenize the polypropylene fibers with an isotropic, volume-weighted average dielectric constant. The volume fractions were estimated by calculating the volume occupied by a polypropylene yarn tracing the path of the iCon fiber and normalizing with a volume with dimensions given by periods in both directions and the crimp height.

3. Results

The fabrics’ electromagnetic response originates with the iCon fibers. The spacing of the iCon fibers is different in the warp (vertically oriented) and weft (horizontally oriented) directions; the spectra will be polarization dependent. For the woven fabric, the distance between the warp and weft iCon fibers is roughly 1.90 and 0.45 mm, respectively. The warp iCon fibers run straight while the weft iCon fibers are woven over and under the much thicker warp polypropylene fibers giving the textile crimp (Fig. 1, bottom left). The metal content of the fabrics is less than 1% by volume so the shielding effectiveness will be significantly reduced for gigahertz frequencies. However, split-ring resonator extended states are created and are weakly confined to the fabric and allow us to tailor the spectra. The polarization is with respect to directions A (y) and B (x) in Fig. 1, top left and top right. The reflection and transmission spectra for y-polarized normally incident waves are plotted in Fig. 2(a)
Fig. 2 (a) Measured and simulated reflection (left) and transmission spectra (right) of the woven fabric for the y-polarization. (b) Measured and simulated reflection (left) and transmission spectra (right) for x- polarization. (c) Induced charges and current in a unit cell of the woven fabric for the x-polarization at the first resonant peak. Positive and negative surface charge red and blue, respectively. Current flows in a clockwise fashion. Incident plane wave wavevector and E-field indicated.
. For the y-polarization the woven fabric behaved like an inductive mesh with a cutoff frequency around 10 GHz. Around 95 GHz the reflection is at its minimum; this is due to a Fabry-Perot resonance created by the polypropylene layer. Simulations, plotted as circled lines in Fig. 2(a), follow the measurements; differences occur because of the variation of the unit cell dimensions and estimates used for the polypropylene yarn effective index. The effective index depends on the estimates for the fabric thickness, the relative fraction of fiber and air, and the degree of twisting in an individual yarn.

For the other polarization, measurements suggest the existence of resonant peaks at 40 GHz and 110 GHz, in Fig. 2(b). Simulations confirm the presence of resonance peaks at 37 GHz and 110 GHz. Note that R+T<1 because the other polarization channel carries away some of the energy. To better understand the resonant peaks, the field patterns were examined both on- and off-resonance. On-resonance, the incident field induces circular current flow and charge separation as illustrated in Fig. 2(c). The induced current, dark blue arrows, at the top of the fabric creates an induced H-field that creates via Faraday’s law a counter-flow current in the lower half of the warp iCon fibers. (Note that the two halves are not part of the same fiber and do not touch.) Net charge is concentrated at the closest point between neighboring parallel iCon wires. There the fabric has a large capacitance. An estimate of the resonant frequency of a double-split ring resonator, assuming a uniform current distribution in a circular loop with only the gaps contributing to the capacitance, yields roughly 40 GHz. At off-resonance the current in the top half and bottom half both flow in the same direction, so the fabric responds simply as an inductive mesh.

We can tune the location of the resonance by varying the geometric parameters. Increasing the crimp height should increase the inductance since the loop area increases. Indeed, the resonant frequency, given by (LC)1/2 where L and C are the circuit inductance and capacitance, varies as the inverse of the crimp height. The period of the weft fibers gives the most direct control over the capacitance. By increasing the weft period the capacitance should decrease which would increase the resonant frequency. Simulations show that the resonant frequency varies as p0.4 where p is the weft period.

For the knitted fabric, measurements of the reflection and transmission spectra were performed for the two different polarizations, Figs. 3(a)
Fig. 3 (a) Measured and simulated reflection (left) and transmission spectra (right) of the knitted fabric for the x-polarization. Tuning the effective index of the polypropylene layer can improve the match in the low frequency region. (b) Measured and simulated reflection (left) and transmission spectra (right) for the y-polarization.
and 3(b). Simulations agree reasonably well though diverge at frequencies above 60 GHz presumably because of the index and geometric parameters used. Given the lack of rotational symmetry, the low frequency (< 1 GHz) response is expected to be polarization dependent. The x-polarized response is inductive-like due to the continuous iCon fiber path while the y-polarized response is capacitive-like as the current can only move as far as a single row. The iCon fibers can be seen to lie mostly in a plane forming interlocking loops; changing the crimp height yields less variation than in the woven sample. However, varying the warp or weft period produces larger shifts in the spectrum. The peak in the reflection spectrum at 60 GHz for the x-polarization appears to be a low-Q circuit resonance. Separation of charge and current flow can be seen when examining the fields. The field energy is concentrated around where iCon fibers from interlocking rows run in the same direction. Thus tuning the resonant frequency can be accomplished by varying the spacing between the parallel portions of the iCon fibers. For the y-polarization spectra, a resonance appears somewhere beyond 40 GHz which causes the reflection spectrum to drop.

For both fabrics real-time active tuning around the resonant frequencies is a possibility. For instance, for the knitted fabric tuning could be accomplished by applying a force in the warp direction. A stress-strain curve exists for the fabric that is dependent on the type of knit, the size of the yarns, the periods, and the direction of the applied force. Beyond the initial stress needed to overcome friction between the yarns, the stress-strain curve is linear. i.e., the elastic regime [29

29. J. W. S. Hearle, P. Grosberg, and S. Backer, Structural Mechanics of Fibers, Yarns, and Fabrics (John Wiley, 1969).

]. Recoverable strains on the order of 10-40% are typical and since this fabric displays a positive Poisson ratio, the resonant frequency shift will be proportional to the applied stress [30

30. M. Matsuo and T. Yamada, “Hysteresis of tensile load–strain route of knitted fabrics under extension and recovery processes estimated by strain history,” Text. Res. J. 79(3), 275–284 (2009). [CrossRef]

].

At frequencies beyond 200 GHz, the fabrics’ response can be attributed to resonances created by the iCon fiber. Interestingly, the peaks in the woven fabric correlate well with high density of states of a rectangular waveguide (not pictured). In Fig. 4
Fig. 4 (Left) Linear polarized normal incidence specular transmission spectrum in dB for the woven fabric at various polarization angles, (right) for the knitted fabric.
, left, and 4, right, the specular transmission of a linearly polarized beam is measured for various polarization angles with respect to direction B in Fig. 1. Given that the polypropylene fiber diameter is around 0.4 mm and the periods are roughly 0.5-1.5 mm, at these shorter wavelengths scattering is inevitable. With linearly polarized radiation we see strong polarization dependence. The polarization angle was stepped in 15° increments from 0 to 90°.For the woven fabric, when the incident radiation is polarized along the warp fibers, strong oscillations are seen, while for the orthogonal polarization, much weaker oscillations are observed after smoothing the data. Oscillations in the 0° polarization spectrum are a result of coupling to resonant modes that resemble rectangular waveguide states. For the orthogonal polarization (90°) the faint oscillations can be Fourier transformed to reveal a periodicity determined by the fabric thickness and index. This behavior is present in the knitted fabric as well.

In conclusion, we report on resonant fabrics co-woven with metallic wires. They are light, flexible, and potentially inexpensive. Other weaves and topologies may yield resonant states. It is possible to push the split-ring resonator-like resonances to higher frequencies, including the sub-millimeter regime, by using thinner yarns with fewer filaments. A reduction of the number of filaments by a factor of 3 or 4 would be possible and still allow weaving or knitting. In addition, thinner yarns could be made by using denser filaments with lower denier values, such as polyester or silk. The resonant states would allow high, narrow-band absorption with weak absorbers, i.e., resonant absorption. However, the iCon fibers conductance and polypropylene yarn absorption coefficient (< 0.5 cm−1) are much too low to have high absorption [31

31. J. R. Birch, “The far-infrared optical constants of polypropylene, PTFE, and polystyrene,” Infrared Phys. 33(1), 33–38 (1992). [CrossRef]

]. If we could match the absorption rate to the radiative rate satisfying the Q-matching condition, resonant absorption could be maximized to 50% [32

32. H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1983).

, 33

33. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef]

]. This could be achieved by adding certain compounds in the polypropylene fibers such as carbonyl iron or replacing the iCon fiber with a more resistive wire, such as carbon fiber.

Acknowledgments

The authors would like to thank Richard Osgood III for useful discussions. This research was supported in part by an appointment to the Postgraduate Research Participation Program at the U.S. Army Natick Soldier Research Engineering and Development Center administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the U.S. Department of Energy and NSRDEC. This material is based upon work supported by, or in part by, the U. S. Army Research Laboratory and the U. S. Army Research Office under contract number W911NF-11-1-0024.

References and links

1.

B. A. Munk, Frequency Selective Surfaces: Theory and Design, (John Wiley, 2000).

2.

D. Sievenpepper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47(11), 2059–2074 (1999). [CrossRef]

3.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

4.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

5.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

6.

W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23(3), 404–414 (2006). [CrossRef]

7.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, “Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial,” Phys. Rev. Lett. 94(6), 063901 (2005). [CrossRef] [PubMed]

8.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006). [CrossRef]

9.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]

10.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]

11.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

12.

P. F. Goldsmith, C. T. Hsieh, G. Huguenin, J. Kapitzky, and E. Moore, “Focal plane image systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41(10), 1664–1675 (1993). [CrossRef]

13.

R. Appleby, “Passive millimetre-wave imaging and how it differs from terahertz imaging,” Philos. Trans. R. Soc. London, Ser. A 362, 379–393 (2004).

14.

J. E. Bjarnason, J. T. L. Chan, M. A. W. Lee, A. M. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85(4), 519–521 (2004). [CrossRef]

15.

E. N. Grossman, A. K. Bhupathiraju, A. J. Miller, and C. D. Reintsema, “Concealed weapons detection using an uncooled millimeter-wave microbolometer system,” Proc. SPIE 4719, 364–369 (2002). [CrossRef]

16.

M. N. Asfar, “Precision millimeter-wave measurements of complex refractive index, complex dielectric permittivity, and loss tangent of common polymers,” IEEE Trans. Instrum. Meas. 36(2), 530–536 (1987).

17.

I. Dunayevskiy, B. Bortnik, K. Geary, R. Lombardo, M. Jack, and H. Fetterman, “Millimeter- and submillimeter-wave characterization of various fabrics,” Appl. Opt. 46(24), 6161–6165 (2007). [CrossRef] [PubMed]

18.

G. Pastorelli, T. Trafela, P. F. Taday, A. Portieri, D. Lowe, K. Fukunaga, and M. Strlič, “Characterisation of historic plastics using terahertz time-domain spectroscopy and pulsed imaging,” Anal. Bioanal. Chem. 403(5), 1405–1414 (2012). [CrossRef] [PubMed]

19.

S. Maity, K. Singha, P. Debnath, and M. Singha, “Textiles in electromagnetic radiation protection,” J. Safety Eng. 2(2), 11–19 (2013).

20.

D. Soyaslan, S. Comlekci, and O. Goktepe, “Determination of electromagnetic shielding performance of plain knitting and 1X1 rib structures with coaxial test fixture relating to ASTM D4935,” J. Text. Inst. 101(10), 890–897 (2010). [CrossRef]

21.

R. Perumalraj, B. S. Dasaradan, R. Anbarasu, P. Arokiaraj, and S. L. Harish, “Electromagnetic shielding effectiveness of copper,” J. Text. Inst. 100(6), 512–524 (2009). [CrossRef]

22.

A. Tennant, W. Hurley, and T. Dias, “Experimental knitted, textile frequency selective surfaces,” IEEE Electron. Lett. 48(22), 1386–1388 (2012). [CrossRef]

23.

M. S. Mirotznik, S. Yarlagadda, R. McCauley, and P. Pa, “Broadband electromagnetic modeling of woven fabric composites,” IEEE Trans. Microwave Theory Tech. 60(1), 158–169 (2012). [CrossRef]

24.

M. Michalak, V. Kazakevicius, S. Dudzinska, I. Krucinska, and R. Brazis, “Textiles embroidered with split-rings as barriers against microwave radiation,” Fibres Textiles E. Eur. 17(1), 66–70 (2009).

25.

Specialty Product: ICON-75,” http://www.eytechnologies.com/icon-75.html.

26.

D. DiGiovanni and A. Gatesman, personal communication.

27.

J. W. Lamb, “Miscellaneous data on materials for millimetre and submillimetre optics,” J. Infrared Millimeter Terahertz Waves 17(12), 1997–2034 (1996). [CrossRef]

28.

COMSOL,” http://www.comsol.com/.

29.

J. W. S. Hearle, P. Grosberg, and S. Backer, Structural Mechanics of Fibers, Yarns, and Fabrics (John Wiley, 1969).

30.

M. Matsuo and T. Yamada, “Hysteresis of tensile load–strain route of knitted fabrics under extension and recovery processes estimated by strain history,” Text. Res. J. 79(3), 275–284 (2009). [CrossRef]

31.

J. R. Birch, “The far-infrared optical constants of polypropylene, PTFE, and polystyrene,” Infrared Phys. 33(1), 33–38 (1992). [CrossRef]

32.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1983).

33.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef]

OCIS Codes
(350.4010) Other areas of optics : Microwaves
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: October 23, 2013
Revised Manuscript: November 29, 2013
Manuscript Accepted: December 2, 2013
Published: January 31, 2014

Citation
Michael Ghebrebrhan, Francisco J. Aranda, David P. Ziegler, Joel B. Carlson, Jeffrey Perry, Deana M. Archambault, David A. DiGiovanni, Andrew J. Gatesman, Robert H. Giles, Weidong Zhang, Elliott R. Brown, and Brian R. Kimball, "Tunable millimeter and sub-millimeter spectral response of textile metamaterial via resonant states," Opt. Express 22, 2853-2859 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2853


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References

  1. B. A. Munk, Frequency Selective Surfaces: Theory and Design, (John Wiley, 2000).
  2. D. Sievenpepper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47(11), 2059–2074 (1999). [CrossRef]
  3. J. B. Pendry, L. Martín-Moreno, F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]
  4. J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]
  5. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]
  6. W. J. Padilla, D. R. Smith, D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23(3), 404–414 (2006). [CrossRef]
  7. H. O. Moser, B. D. F. Casse, O. Wilhelmi, B. T. Saw, “Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial,” Phys. Rev. Lett. 94(6), 063901 (2005). [CrossRef] [PubMed]
  8. D. Schurig, J. J. Mock, D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006). [CrossRef]
  9. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]
  10. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]
  11. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).
  12. P. F. Goldsmith, C. T. Hsieh, G. Huguenin, J. Kapitzky, E. Moore, “Focal plane image systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41(10), 1664–1675 (1993). [CrossRef]
  13. R. Appleby, “Passive millimetre-wave imaging and how it differs from terahertz imaging,” Philos. Trans. R. Soc. London, Ser. A 362, 379–393 (2004).
  14. J. E. Bjarnason, J. T. L. Chan, M. A. W. Lee, A. M. Celis, E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85(4), 519–521 (2004). [CrossRef]
  15. E. N. Grossman, A. K. Bhupathiraju, A. J. Miller, C. D. Reintsema, “Concealed weapons detection using an uncooled millimeter-wave microbolometer system,” Proc. SPIE 4719, 364–369 (2002). [CrossRef]
  16. M. N. Asfar, “Precision millimeter-wave measurements of complex refractive index, complex dielectric permittivity, and loss tangent of common polymers,” IEEE Trans. Instrum. Meas. 36(2), 530–536 (1987).
  17. I. Dunayevskiy, B. Bortnik, K. Geary, R. Lombardo, M. Jack, H. Fetterman, “Millimeter- and submillimeter-wave characterization of various fabrics,” Appl. Opt. 46(24), 6161–6165 (2007). [CrossRef] [PubMed]
  18. G. Pastorelli, T. Trafela, P. F. Taday, A. Portieri, D. Lowe, K. Fukunaga, M. Strlič, “Characterisation of historic plastics using terahertz time-domain spectroscopy and pulsed imaging,” Anal. Bioanal. Chem. 403(5), 1405–1414 (2012). [CrossRef] [PubMed]
  19. S. Maity, K. Singha, P. Debnath, M. Singha, “Textiles in electromagnetic radiation protection,” J. Safety Eng. 2(2), 11–19 (2013).
  20. D. Soyaslan, S. Comlekci, O. Goktepe, “Determination of electromagnetic shielding performance of plain knitting and 1X1 rib structures with coaxial test fixture relating to ASTM D4935,” J. Text. Inst. 101(10), 890–897 (2010). [CrossRef]
  21. R. Perumalraj, B. S. Dasaradan, R. Anbarasu, P. Arokiaraj, S. L. Harish, “Electromagnetic shielding effectiveness of copper,” J. Text. Inst. 100(6), 512–524 (2009). [CrossRef]
  22. A. Tennant, W. Hurley, T. Dias, “Experimental knitted, textile frequency selective surfaces,” IEEE Electron. Lett. 48(22), 1386–1388 (2012). [CrossRef]
  23. M. S. Mirotznik, S. Yarlagadda, R. McCauley, P. Pa, “Broadband electromagnetic modeling of woven fabric composites,” IEEE Trans. Microwave Theory Tech. 60(1), 158–169 (2012). [CrossRef]
  24. M. Michalak, V. Kazakevicius, S. Dudzinska, I. Krucinska, R. Brazis, “Textiles embroidered with split-rings as barriers against microwave radiation,” Fibres Textiles E. Eur. 17(1), 66–70 (2009).
  25. Specialty Product: ICON-75,” http://www.eytechnologies.com/icon-75.html .
  26. D. DiGiovanni and A. Gatesman, personal communication.
  27. J. W. Lamb, “Miscellaneous data on materials for millimetre and submillimetre optics,” J. Infrared Millimeter Terahertz Waves 17(12), 1997–2034 (1996). [CrossRef]
  28. COMSOL,” http://www.comsol.com/ .
  29. J. W. S. Hearle, P. Grosberg, and S. Backer, Structural Mechanics of Fibers, Yarns, and Fabrics (John Wiley, 1969).
  30. M. Matsuo, T. Yamada, “Hysteresis of tensile load–strain route of knitted fabrics under extension and recovery processes estimated by strain history,” Text. Res. J. 79(3), 275–284 (2009). [CrossRef]
  31. J. R. Birch, “The far-infrared optical constants of polypropylene, PTFE, and polystyrene,” Infrared Phys. 33(1), 33–38 (1992). [CrossRef]
  32. H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1983).
  33. S. Fan, W. Suh, J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef]

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