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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 24468–24474
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Design of thin infrared quarter-wave and half-wave plates using antenna-array sheets

Yuchu He and George V. Eleftheriades  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 24468-24474 (2013)
http://dx.doi.org/10.1364/OE.21.024468


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Abstract

A thin quarter-wave plate and a half-wave plate are designed based on multiple antenna-array sheets (AAS). For transmission through cascaded antenna-array sheets, an equivalent transmission-line model is used. The interspacing dielectric is modeled as a transmission line with each AAS treated as a loaded shunt admittance. By utilizing this transmission-line model to treat the plates as a differential phase shifter between two orthogonal polarizations, a quarter-wave plate can be designed with two AAS and a half-wave plate can be designed with three AAS. Both wave plates can achieve high transmission with the desired 90° and 180° phase difference between two orthogonal polarizations.

© 2013 Optical Society of America

1. Introduction

A wave-plate is an essential part of modern optics and photonics applications. In the long wavelength infrared (LWIR) regime, a quarter-wave plate (QWP) and a half-wave plate (HWP) can find applications in industrial CO2-laser machining to control the polarization state for offering more uniform and efficient cutting [1

1. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys. 32, 1455–1461 (1999). [CrossRef]

]. A HWP can also be found in beam splitters for polarization-sensitive imaging applications [2

2. J. Scott Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006). [CrossRef] [PubMed]

, 3

3. C. A. Farlow, D. B. Chenault, J. L. Pezzaniti, K. D. Spradley, and M. G. Gulley, “Imaging polarimeter development and applications,” in Polarization Analysis and Measurement IV, Proc. SPIE 4481, 118 (2002). [CrossRef]

]. A conventional LWIR wave-plate is usually made by polished anisotropic dielectric materials such as Cadmium Thiogallate with thicknesses in the millimeter range including the mount [4

4. J. D. Beasley and P. D. Marlowe, “Achromatic wave plates for the mid-infrared,” in Polarization: Measurement, Analysis, and Remote Sensing X, Proc. SPIE 8364,83640I (2012). [CrossRef]

]. The miniaturization of photonic devices and sensors has generated an interest for wave-plate integration which requires the development of thin wave-plates. In this regard, recent research in nano-metallic structures has provided a low cost method to fabricate thin wave-plates. Reflective QWPs and HWPs have been introduced in [5

5. A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett. 83, 513–515 (2013). [CrossRef]

8

8. A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, “Fabrication and characterization of a large-area metal nano-grid wave plate,” Appl. Phys. Lett. 103, 033111 (2013). [CrossRef]

]; however, a QWP or a HWP working in the transmission mode can be more desirable. A classical transmitting single-layer meanderline QWP operating in the range 8μm –12μm has been reported in [9

9. J. S. Tharp, B. A. Lail, B. A. Munk, and G. D. Boreman, “Design and demonstration of an Infrared meanderline phase retarder,” IEEE Trans. Antennas Propag. 55, 2983–2988 (2007). [CrossRef]

], but the transmitted power is rather low at 23%.

In this paper, we propose thin multilayer designs of a QWP and a HWP that are compatible with existing fabrication technology. The wave plates are designed based on microwave phase-shifter theory [10

10. R. V. Garver, “Broad-band diode phase shifters,” IEEE Trans. Microwave Theory Tech. 20, 314–323 (1972). [CrossRef]

]. They operate in the long wavelength infrared (LWIR) region in the transmission mode with a design frequency of 30THz. High transmission and low reflection can be achieved over a reasonable bandwidth. One advantage of the proposed designs is that they are readily scalable to any frequency as long as the metal remains reasonably opaque. Moreover, the materials used in the QWP and the HWP designs are common dielectrics of ZnSe and YbF3, and metallic layers made of gold. The QWP and the HWP designs with such materials have high laser-induced damage threshold (LIDT) [11

11. R. M. Wood, Laser-Induced Damage of Optical Materials (Institute of Physics2003). [CrossRef]

] and may be used with high power CO2 lasers at 10.6μm.

2. Theory and design

In [12

12. Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011). [CrossRef]

], the 90° phase difference required for a QWP is achieved by using two perpendicular detuned dipoles in a periodic fashion. The longer dipole acts as an inductor and introduces a phase delay in the transmitted field, whereas the shorter dipole acts as a capacitor and introduces a phase advance. By adjusting the lengths of the two perpendicular dipoles, a 90° phase difference is achieved between two orthogonal polarizations. Some other wave-plate designs working in the optical regime, based on single layer nano-metallic structures utilizing strips, slits and corrugated gratings are demonstrated in [12

12. Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011). [CrossRef]

17

17. A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101, 043902 (2008) [CrossRef] [PubMed]

]. To scale those single layer metallic periodic structures into the LWIR regime, we can treat the layers as frequency selective surfaces (FSS). A FSS is equivalent to a filter and the transmission through it can be described by a corresponding transfer function H(s) [18

18. B. A. Munk, Frequency Selective Surfaces (Wiley2000). [CrossRef]

]. Such an AAS of detuned dipoles has a transfer function equivalent to a FSS modeled as a series resistor-inductor-capacitor (RLC) band-reject filter. An AAS with two perpendicular detuned dipoles arranged in a cross can be modeled with two separate transfer functions, one for each polarization. To introduce a 90° phase difference between two polarizations, transfer function Hx(s) for the X-polarization has to introduce a +45° degree phase shift and transfer function Hy(s) for the Y-polarization has to introduce a −45° phase shift, as shown in Fig. 1(a). Hx(s) and Hy(s) are band-reject filters with different rejection frequencies. The magnitudes of Hx(s) and Hy(s) are exactly 1/2 when the corresponding phases are ±45° [19

19. J. W. Nilsson, Electric Circuits (Prentice Hall2010).

], indicating a total 50% of transmitted power which constitutes the upper bound for this type of single-layer AAS based QWP. Similarly, for a HWP, a ±90° phase shift is required for the two transfer functions, as shown in Fig. 1(b). However, as the phase difference approaches 180°, the magnitudes of both transfer functions approach zero. In fact, it is not possible to achieve exactly 180° phase difference with a thin single layer AAS made of cross dipoles. A similar statement also applies to single layer cross-slot designs which can be modeled as band-pass filters. The transmission limitation of a single layer QWP or HWP can be overcame by using multilayer designs [18

18. B. A. Munk, Frequency Selective Surfaces (Wiley2000). [CrossRef]

]. This multilayer concept has recently been employed in [20

20. F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013). [CrossRef]

] to overcome this transmission limitation in the optical regime.

Fig. 1 Magnitude and phase of the transmitted fields of a QWP and a HWP made from single layer AAS of cross dipoles. The intersection of the magnitude curves determines the ideal operating frequency since the same power is transmitted for both polarizations. (a) For a QWP, to achieve a 90° phase difference at the operating frequency, at most 50% power is transmitted for both polarizations. (b) For a HWP, as the phase difference approaches 180°, the transmission magnitudes approach zero.

2.1. Design and results of a quarter-wave plate

The transmission through a two-layer AAS from the input to the output plane can be modeled as a transmission line loaded with lumped reactances as shown in Fig. 2, where the dielectric is modeled as a transmission line having an impedance of Z0 and the AAS are modeled as shunt reactances. A single AAS layer provides a reactance jBx for the X-polarized field and a reactance jBy for the Y-polarized field. It should be pointed out that in the model of Fig. 2, the corresponding transmission-line impedances should be adjusted according to the angle of incidence and polarization state. For simplicity, we only consider here the case of normal incidence. For unity transmission, the phase difference Δϕ between the transmitted Ex and Ey fields can be computed by Eq. (1) [10

10. R. V. Garver, “Broad-band diode phase shifters,” IEEE Trans. Microwave Theory Tech. 20, 314–323 (1972). [CrossRef]

], with Bx and By normalized with respect to Z0.
Δϕ=tan1[Bx+(112Bx2)1Bx]tan1[By+(112By2)1By]
(1)

By assuming that reactance Bx gives a +45° phase shift and reactance By gives a −45° phase shift, the normalized values of Bx and By are calculated to be +4 and −4. In free space, Bx is 1500Ω and By is −1500Ω. We can relate Bx and By to the self-reactance of a dipole and approximate the corresponding dipole lengths from [21

21. C. A. Balanis, Antenna Theory: Analysis and Design (Wiley2005).

]. The dipole lengths needed are approximated to be 0.75λ and 0.25λ respectively. Therefore, by using an array of cross dipoles of lengths 0.75λ and 0.25λ for each layer, a QWP with transmission close to unity can be implemented.

Fig. 2 The circuit model for a normally incident field E0 containing both X and Y polarizations with equal magnitude passing through a 2-layer AAS. The dielectric is modeled as a transmission line with impedance Z0 and the AAS layers are modeled as shunt reactances. The AAS layer has an admittance jBx for the X-polarized field and jBy for the Y-polarized field. Depending on the values of jBx and jBy, a 90° differential phase shift can be achieved with a combined transmission magnitude of unity.

Fig. 3 A unit cell design of the proposed QWP using double layer elliptical patches made of gold with dielectrics of ZnSe with ε1 = 5.8 and YbF3 with ε2 = 2.3.

The simulated result of the transmitted field for each polarization is shown in Fig. 4. The transmission magnitudes of both the X and Y components are about 0.95, leading to 90% transmitted power. The axial ratio (AR) and phase difference between the two polarizations are shown in Fig. 5. The bandwidth of the QWP can be defined by satisfying both the AR limit and the phase difference limit which are 0.8 – 1.2 and 80° – 100° respectively. This bandwidth of the QWP is 8.6μm – 10.4μm, or 19% of the design frequency.

Fig. 4 Magnitude and phase of the transmitted fields in the X and Y polarizations.
Fig. 5 The axial ratio and phase difference between the X and Y polarizations. The bandwidth of the QWP is 8.6μm–10.4μm, which is the frequency range where both AR and phase difference curves stay within the gray region.

2.2. Design and results of a half-wave plate

For a HWP design, the required phase difference Δϕ is π in Eq. (1). However, the arctan function has a periodicity of π, which leads to the same value for jBx and jBy. As a result, it is not possible to design a HWP of unity transmission using 2 layers. This problem can be solved by cascading one more layer [20

20. F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013). [CrossRef]

,26

26. J. Y. Lau and S. V. Hum, “Analysis and characterization of a multipole reconfigurable transmitarray element,” IEEE Trans. Antennas Propag. 59, 70–79 (2011). [CrossRef]

]. By adding one more quarter-wavelength dielectric layer and gold elliptical patches, the HWP can be designed with good transmission.

Figure 6 shows a triple layer AAS design with elliptical patches. The major axis Lx of the elliptical patch remains 3.3μm but the minor axis Ly is changed slightly to 1.45μm for the required 180° phase difference. The total thickness of the HWP is 3.8μm. The transmission of each polarization is shown in Fig. 7. The transmission magnitudes at the operating frequency are about 0.9 leading to 80% of transmitted power. The phase difference is 180° as desired. We can define the bandwidth of this HWP by satisfying both the AR and the phase difference limits which are 0.8 – 1.2 and 160° – 200° respectively. As shown in Fig. 8, this bandwidth of the HWP is from 9.2μm – 11μm.

Fig. 6 A unit cell design of a HWP using three layers of gold elliptical patches.
Fig. 7 Magnitude and phase of the transmitted fields in the X and Y polarizations.
Fig. 8 The axial ratio and phase difference between the X and Y polarizations. The bandwidth of this HWP is 9.2μm – 11μm, or 17% of the operating frequency.

Both the QWP and the HWP designs presented utilize gold layers with the same patterning (homogenous loading) and fixed interlayer spacing of λ/4. The specific choice of λ/4 is to achieve the widest bandwidth possible, since in this case the incident and reflected waves are out of phase and cancel each together. This is consistent with [10

10. R. V. Garver, “Broad-band diode phase shifters,” IEEE Trans. Microwave Theory Tech. 20, 314–323 (1972). [CrossRef]

] which shows that indeed the bandwidth is widest when the interspacing is λ/4 between the loading elements. As the QWP or the HWP is sandwiched between a glass substrate and air with different impedances, a quarter-wave transformer is required to achieve good matching. It may be possible that with inhomogeneous loading (different metallization patterning) and different dielectric interspace materials the quarter-wave matching could be eliminated. This is even more likely for more broadband designs that contain more layers, as it is well known from microwave filter theory. However, in this example of only having 2 or 3 layers, we used a homogenous loading for simplicity and ease of fabrication.

3. Conclusion

In this paper, we have presented a thin quarter-wave plate and a half-wave plate design based on microwave phase-shifter theory. Both wave-plates operate in the long wavelength infrared region at 30THz with 90% and 80% transmitted power respectively. Good axial ratios and phase differences can be maintained over bandwidths of 19% and 17% for the QWP and HWP respectively. The advantages of the proposed plates are that (a) they are compatible with current planar fabrication technology and potentially are scalable up to the near IR regime where metal remains reasonably opaque (b) they are typically less than one wavelength thick (c) they offer high transmission since they are well matched due to their multilayers structure (d) they exhibit a good bandwidth and (e) gold layers with ZnSe and YbF3 dielectrics have low absorption in the far infrared region which leads to high laser-induced damage threshold. Hence QWP and HWP designs with such materials can be potentially used with high power CO2 lasers. In addition, it should be pointed out that larger bandwidths can be achieved by cascading more layers. Finally, one could envision 2D inhomogeneous metallization of elliptical patches in the transverse plane for general wavefront manipulation [27

27. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011). [CrossRef] [PubMed]

].

References and links

1.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys. 32, 1455–1461 (1999). [CrossRef]

2.

J. Scott Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006). [CrossRef] [PubMed]

3.

C. A. Farlow, D. B. Chenault, J. L. Pezzaniti, K. D. Spradley, and M. G. Gulley, “Imaging polarimeter development and applications,” in Polarization Analysis and Measurement IV, Proc. SPIE 4481, 118 (2002). [CrossRef]

4.

J. D. Beasley and P. D. Marlowe, “Achromatic wave plates for the mid-infrared,” in Polarization: Measurement, Analysis, and Remote Sensing X, Proc. SPIE 8364,83640I (2012). [CrossRef]

5.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett. 83, 513–515 (2013). [CrossRef]

6.

S. L. Wadsworth and G. D. Boreman, “Broadband infrared meanderline reflective quarter-wave plate,” Opt. Express 19, 10604–10612 (2011). [CrossRef] [PubMed]

7.

Y. Pang and R. Gordon, “Metal nano-grid reflective wave plate,” Opt. Express 17, 2871–2879 (2009). [CrossRef] [PubMed]

8.

A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, “Fabrication and characterization of a large-area metal nano-grid wave plate,” Appl. Phys. Lett. 103, 033111 (2013). [CrossRef]

9.

J. S. Tharp, B. A. Lail, B. A. Munk, and G. D. Boreman, “Design and demonstration of an Infrared meanderline phase retarder,” IEEE Trans. Antennas Propag. 55, 2983–2988 (2007). [CrossRef]

10.

R. V. Garver, “Broad-band diode phase shifters,” IEEE Trans. Microwave Theory Tech. 20, 314–323 (1972). [CrossRef]

11.

R. M. Wood, Laser-Induced Damage of Optical Materials (Institute of Physics2003). [CrossRef]

12.

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011). [CrossRef]

13.

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009). [CrossRef] [PubMed]

14.

B. Yang, W. Ye, X. Yuan, Z. Zhu, and C. Zeng, “Design of ultrathin plasmonic quarter-wave plate based on period coupling,” Opt. Lett. 38, 679–681 (2013). [CrossRef] [PubMed]

15.

A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37, 1820–1822 (2012). [CrossRef] [PubMed]

16.

A. Pors, M. G. Nielsen, G. D. Valle, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles,” Opt. Lett. 36, 1626–1628 (2011). [CrossRef] [PubMed]

17.

A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101, 043902 (2008) [CrossRef] [PubMed]

18.

B. A. Munk, Frequency Selective Surfaces (Wiley2000). [CrossRef]

19.

J. W. Nilsson, Electric Circuits (Prentice Hall2010).

20.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013). [CrossRef]

21.

C. A. Balanis, Antenna Theory: Analysis and Design (Wiley2005).

22.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

23.

H. H. Li, “Refractive index of ZnSe, ZnS and ZnTe and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 13, 103 (1984). [CrossRef]

24.

P. J. Wright and B. Cockayne, “The organometallic chemical vapour deposition of ZnS and ZnSe at atmospheric pressure,” J.Cryst. Growth 59, 148–154 (1982). [CrossRef]

25.

M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser-induced damage threshold measurements of antireflective-coated ZnSe and metal mirrors at 10.6μm,” in Laser-Induced Damage in Optical Materials, Proc. SPIE 1441, 113 (1991). [CrossRef]

26.

J. Y. Lau and S. V. Hum, “Analysis and characterization of a multipole reconfigurable transmitarray element,” IEEE Trans. Antennas Propag. 59, 70–79 (2011). [CrossRef]

27.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011). [CrossRef] [PubMed]

OCIS Codes
(260.3090) Physical optics : Infrared, far
(260.3910) Physical optics : Metal optics
(260.5430) Physical optics : Polarization

ToC Category:
Optical Devices

History
Original Manuscript: July 22, 2013
Revised Manuscript: September 23, 2013
Manuscript Accepted: September 25, 2013
Published: October 7, 2013

Citation
Yuchu He and George V. Eleftheriades, "Design of thin infrared quarter-wave and half-wave plates using antenna-array sheets," Opt. Express 21, 24468-24474 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-24468


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References

  1. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys.32, 1455–1461 (1999). [CrossRef]
  2. J. Scott Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt.45, 5453–5469 (2006). [CrossRef] [PubMed]
  3. C. A. Farlow, D. B. Chenault, J. L. Pezzaniti, K. D. Spradley, and M. G. Gulley, “Imaging polarimeter development and applications,” in Polarization Analysis and Measurement IV, Proc. SPIE4481, 118 (2002). [CrossRef]
  4. J. D. Beasley and P. D. Marlowe, “Achromatic wave plates for the mid-infrared,” in Polarization: Measurement, Analysis, and Remote Sensing X, Proc. SPIE8364,83640I (2012). [CrossRef]
  5. A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett.83, 513–515 (2013). [CrossRef]
  6. S. L. Wadsworth and G. D. Boreman, “Broadband infrared meanderline reflective quarter-wave plate,” Opt. Express19, 10604–10612 (2011). [CrossRef] [PubMed]
  7. Y. Pang and R. Gordon, “Metal nano-grid reflective wave plate,” Opt. Express17, 2871–2879 (2009). [CrossRef] [PubMed]
  8. A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, “Fabrication and characterization of a large-area metal nano-grid wave plate,” Appl. Phys. Lett.103, 033111 (2013). [CrossRef]
  9. J. S. Tharp, B. A. Lail, B. A. Munk, and G. D. Boreman, “Design and demonstration of an Infrared meanderline phase retarder,” IEEE Trans. Antennas Propag.55, 2983–2988 (2007). [CrossRef]
  10. R. V. Garver, “Broad-band diode phase shifters,” IEEE Trans. Microwave Theory Tech.20, 314–323 (1972). [CrossRef]
  11. R. M. Wood, Laser-Induced Damage of Optical Materials (Institute of Physics2003). [CrossRef]
  12. Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B84, 205428 (2011). [CrossRef]
  13. P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett.102, 256801 (2009). [CrossRef] [PubMed]
  14. B. Yang, W. Ye, X. Yuan, Z. Zhu, and C. Zeng, “Design of ultrathin plasmonic quarter-wave plate based on period coupling,” Opt. Lett.38, 679–681 (2013). [CrossRef] [PubMed]
  15. A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett.37, 1820–1822 (2012). [CrossRef] [PubMed]
  16. A. Pors, M. G. Nielsen, G. D. Valle, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles,” Opt. Lett.36, 1626–1628 (2011). [CrossRef] [PubMed]
  17. A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett.101, 043902 (2008) [CrossRef] [PubMed]
  18. B. A. Munk, Frequency Selective Surfaces (Wiley2000). [CrossRef]
  19. J. W. Nilsson, Electric Circuits (Prentice Hall2010).
  20. F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett.110, 203903 (2013). [CrossRef]
  21. C. A. Balanis, Antenna Theory: Analysis and Design (Wiley2005).
  22. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972). [CrossRef]
  23. H. H. Li, “Refractive index of ZnSe, ZnS and ZnTe and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data13, 103 (1984). [CrossRef]
  24. P. J. Wright and B. Cockayne, “The organometallic chemical vapour deposition of ZnS and ZnSe at atmospheric pressure,” J.Cryst. Growth59, 148–154 (1982). [CrossRef]
  25. M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser-induced damage threshold measurements of antireflective-coated ZnSe and metal mirrors at 10.6μm,” in Laser-Induced Damage in Optical Materials, Proc. SPIE1441, 113 (1991). [CrossRef]
  26. J. Y. Lau and S. V. Hum, “Analysis and characterization of a multipole reconfigurable transmitarray element,” IEEE Trans. Antennas Propag.59, 70–79 (2011). [CrossRef]
  27. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011). [CrossRef] [PubMed]

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