Abstract

This paper discusses a theoretical approach towards synthesizing broadband circularly polarizing reflectors. The broadband polarizing reflectors consist of birefringent metallo-dielectric metasurfaces which are described by the Jones matrices and verified via full-wave simulations. Specifically, full-wave simulations for candidate designs are presented that target operation in the near infrared band. In addition, reconfigurability is introduced and demonstrated for candidate designs at the long wave infrared band through the inclusion of a bistable phase change chalcogenide glass substrate.

© 2013 OSA

1. Introduction

Electromagnetic metamaterials are engineered structures that utilize periodic sub-wavelength patterning to create an effective macroscopic response. The engineered resonances and symmetries of the metamaterial can mimic or facilitate behavior not found in naturally occurring materials [1,2]. Each unit cell is most commonly comprised of a planarized metallic inductor - capacitor (LC) resonant circuit along with a supporting low loss dielectric substrate. This approach, with the appropriate geometry scaling, allows metamaterials to be applied to radio waves, microwaves, terahertz waves, and even into the infrared and optical ranges where fabrication constraints and ohmic losses can become a limiting factor. The metamaterial unit cell geometry is generally treated as a flat (d = λ), two-dimensional periodic surface with a sub-wavelength unit cell width (w ˂ λ). As a result, propagation distance through the dielectric can generally be ignored, and diffraction is eliminated at normal incidence in addition to a considerable range of oblique angles. Metamaterials can be considered to be weakly spatially dispersive, due to the small periodicity of the unit cells compared to the characteristic wavelength. Thus, due to a reduced field interaction, the sub-wavelength design requires that an efficient, and in turn high Q-factor, LC-type resonator be employed, the most familiar of which is the split ring resonator (SRR) [3].

Recently, interest is transitioning from the inherent narrowband behavior of LC resonators to metamaterials that exhibit broadband behavior. Broadband metamaterial design methodologies represent an emerging technology with a wide range of potential applications [48]. For example, they can be utilized in conjunction with existing communication bands or designed to coincide with atmospheric transmission windows. In this paper, a theoretical analysis is presented on the synthesis of broadband circularly polarizing mirrors. Full wave simulations are performed on candidate designs with traditional dielectric substrates in addition to designs which incorporate bistable phase changing substrates, facilitating broadband polarization reconfigurability.

2. Scattering from a two dimensional infinitely periodic metamaterial

Let us assume that a planar metamaterial is infinitely periodic along the X - Y plane. A forward traveling plane wave propagates along a vector at an angle, θ, off surface normal and subsequently interacts with the metamaterial. This interaction, or more specifically the linear, lossless scattering of polarized light, can be described in a manner similar to Jones matrix calculus [913] as described elsewhere [14]. The forward propagating transmission matrix is given as:

t(θ)=(a+1bcd+1)
and the corresponding reflection matrix:
r(θ)=(cdab)
For convenience, these two lossless scattering relations are collected into the forward propagating scattering matrix [14]:
s(θ)=(abcd).
With this information in hand, the scattering for additional incident directions on both sides of the metamaterial can be understood through the application of two electromagnetic principles. First, planar metamaterials can only couple to tangential electric fields and normal magnetic fields; thus, two electromagnetic waves that are described by the same field components must interact with the metamaterial in the same way [14]. Therefore, if the incident vector is rotated 180° around the Y axis, the resultant scattering matrix, as a function of the original scattering parameters, is given by the backwards scattering matrix:
s(θ)=(dcba).
In the context of a circularly polarized (CP) wave, Eq. (4) results in [14],
s++(θ)=s(θ) and s(θ)=s++(θ),
s+(θ)=s+(θ) and s+(θ)=s+(θ),
where the ( + ) corresponds to right handed circular polarization (RHCP) and the (–) corresponds to left handed circular polarization (LHCP). These relationships state that a forward propagating wave incident on the front of the metamaterial with a specific polarization handedness will experience the same scattering matrix as a backwards propagating wave of the opposite handedness incident on the reverse side of the metamaterial.

Next, in the absence of any static magnetic fields, we can apply the Lorentz reciprocity theorem [15]. When applied to oppositely propagating vectors the Lorentz reciprocity theorem results in the following scattering relationship:

sij=sji,
where the subscripts i and j designate the scattering matrix indices. In the context of a polarized wave, Eq. (7) results in [14],
s++(θ)=s++(θ) and s(θ)=s(θ),
s+(θ)=s+(θ) and s+(θ)=s+(θ),
Isotropic media is always reciprocal. The Lorentz reciprocity theorem also holds for anisotropic media given symmetrical permittivity and permeability tensors:
ε¯¯=ε¯¯T,
μ¯¯=μ¯¯T.
For bianisotropic media, reciprocity exists if Eqs. (10-11) hold in addition to:
ξ¯¯=ζ¯¯T.
which exists when ξ¯¯ and ζ¯¯ are purely imaginary matrices. In general ξ¯¯ and ζ¯¯ can be expressed in terms of the Tellegen parameter, χ¯¯, and the chirality parameter, κ¯¯, as [16]:
ξ¯¯=(χ¯¯jκ¯¯)μ0ε0,
ζ¯¯=(χ¯¯+jκ¯¯)μ0ε0.
Yet, birefringence only requires that achiral anisotropic media be considered. Reciprocity is enforced via proper geometry symmetries; thus, by combining Eq. (4) and Eq. (7), we can understand the scattering properties of a planar reciprocal metamaterial for a single plane of incidence and three related directions. Their relationships are summarized in Fig. 1 .

 

Fig. 1 Scattering matrices for opposite angles and directions of incidence.

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Solving for the scattering matrix coefficients, the forward and backward scattering eigenvalues,λ1,2s, are determined as follows:

det(aλsbcdλs)=(aλs)(dλs)bc=0
resulting in,
λ1,2s=a+d2±(ad2)2+bc.
In the context of a lossless birefringent planar metamaterial, further constraints can be imposed on the scattering matrix coefficients. An achiral birefringent metamaterial can be created by utilizing a geometry with two-fold mirror symmetry, where a=d and |b|=|c| [14]. As a result, the eigenvalues reduce to:
λ1,2s=a±|b|eiθ.
The phase difference between the eigenvalues is given as,
ρs=2tan1|ba|,
where circular polarization (CP) is achieved forρs=π/2. In turn, the power fraction of the scattered wave, S, can be expressed as [17]:
S=a=cos2(ρs2),
resulting ina=1/2for the desired CP condition - a transmitted CP wave and a reflected CP wave of opposite handedness and equal amplitude. Energy conservation dictates that [14]:
|a+12|=|d+12|12,
|b|=|c|12,
|a+12|2+|b|2=(12)2.
Therefore, applying a=1/2 to Eq. (22) implies that |b|=1/2. Returning to Eq. (17), we have:
λ1,2s=12(1±eiθ).
The eigenvalues for forward and reverse propagation must be orthogonal; thus, θ=π/2. This gives:
b=c*.
The scattering matrix for Eq. (1) can now be expressed as,
s(θ)=12(1eiδe±iδ1).
Since the metamaterial is birefringent, Eq. (25) is satisfied for azimuthal rotations measured between the incident field and the metamaterial line of symmetry which satisfyφ=π/4+nπ/2. Therefore, Eq. (25) can be expressed in terms of φ under these bounds as,

s(θ,φ)=12(1ei2φe±i2φ1).

To demonstrate the polarization conversion of the birefringent metamaterial, a normally incident plane wave,

Einc=E0(cosφxsinφx)ei(kzωt),
is assumed to be horizontally polarized (i.e. φx=0), and in phase at the metamaterial’s interface, simplifying to,
Einc=(10).
The resultant interactions with the reflection and transmission matrices are:
Er=12(e±iπ211eiπ2)(10)=12(±i1)=22E
and
Et=12(1eiπ2e±iπ21)(10)=12(1±i)=22E.
The metamaterial scattering consists of a purely circularly polarized reflected wave and a purely circularly polarized transmitted wave of opposite handedness and equivalent magnitude (see Fig. 2 ).

 

Fig. 2 Birefringent metamaterial scattered field handedness, amplitude, and propagation direction with a linearly polarized incident field for the condition of circular polarization.

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With an additional φ=±π/4 azimuthal rotation, the reflection can be considered as maximized or minimized respectively. In other words, the metamaterial does not couple with the electric field for φ=0; but, it becomes resonantly excited for φ=π/4. Thus, a planar electrically resonant anisotropic metamaterial can be represented as:

ε¯¯=ε0(1001).
In the context of surface impedance, this electrically resonant behavior centered at ω0 gives:
η¯¯(ω0±Δ)=η0(i001).
It has been shown in Eqs. (19), (29) that the maximum circularly polarized reflection which can occur with a birefringent metamaterial structure is 50% of the incident field power. Yet, intuition applied to the equivalent surface impedance (Eq. (32)) provides a solution for 100% CP reflection. Specifically, creating a composite structure by backing it with a metallic ground plane such that:
η¯¯(ω0±Δ)=η0(i000).
resulting in a birefringent impedance surface [18].

Alternatively, this can be explained by first recognizing that the incident linearly polarized plane wave can be decomposed into two co-propagating CP waves of opposite handedness. Next, the result of Eq. (30) reveals that the transmission eigenstate for the metamaterial is E±. Applying Eq. (4), the transmission eigenstate for reverse propagation is E which also happens to represent the transmitted field after reflection from the ground plane. In such a configuration, where the field transmits through the metamaterial and reflects off a ground plane, the field propagates through the dielectric substrate with negligible net phase advancement and retransmits through the now transparent metamaterial, resulting in the following transmission matrix:

Et=14(1e±i(π2+π)ei(π2+π)1)(1i)=12(1i)=22E.
This retransmitted field sums with the reflected field to form a purely CP backwards propagating wave of equivalent amplitude to the incident field (see Fig. 3 ),

 

Fig. 3 Birefringent metasurface scattered field handedness, amplitude, and propagation direction with a linearly polarized incident field for the condition of circular polarization.

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Er=12(±i1)+12(1i)=22(e±i3π2e±i5π2)=22(1±i)=E.

The propagation is phase-delayed due to the inductance attributed to the finite (d<λ/4) substrate transmission line length, wherein a properly tuned structure will have a total phase advancement of zero degrees for the round-trip wave propagation through the dielectric [19,20].

The reflection of the composite metasurface can alternatively be described for all azimuthal angles through the use of Jones calculus applied to rotational polarization elements [913]. Where, at normal incidence, the metasurface reflection matrix is:

rm(φ)=R(φ)NR(φ).
The clockwise rotation matrix, R, is given as,
R(φ)=(cosφsinφsinφcosφ).
The N matrix corresponds to the axial reflection coefficients of the birefringent metamaterial at normal incidence:
N=(rx00ry).
A solution for CP reflection is given by:
N=(i001).
The y-axis reflection coefficient corresponds to that given by a perfect electrical conductor (PEC); whereas, the x-axis reflection coefficient is purely imaginary corresponding to the surface impedance given by Eq. (33). As demonstrated with the matrices given by Eqs. (1-3), the metasurface reflection matrix is extended to oblique angles of incidence where reasonable agreement is assumed for a considerable field of view (FOV),

rm(θ,φ)=R(φ)(i001)R(φ).

At this juncture, several assumptions have been utilized in order to simplify the analysis. For example, a 2D infinite periodic structure has been assumed for simulation purposes. Such an assumption is commonly expected to agree with physical measurements if the metamaterial structure has an overall dimension of several wavelengths in both directions. Additionally, the assumption of a negligible substrate thickness has been refined to be that of insignificant electrical distance. However, the assumption of low loss needs further consideration. For example, Eq. (31) is only partially valid since loss is not taken into account. The well-known Kramers-Kronig relations,

εr'(ω)=1+2π0ω'εr"(ω')(ω')2ω2dω',
εr"(ω)=2ωπ01εr'(ω')(ω')2ω2dω',
describe the coupling between the real and imaginary parts of the permittivity. We can observe from these relations that negative permittivity requires loss due to causality. Physically, the imaginary permittivity is attributed to radiation, dielectric and resistive losses [21]. Fortunately, this loss is generally much smaller than the reactance slightly off resonance; thus, a simple solution for metamaterial design is to work in this lower loss frequency region. Nevertheless, Eq. (40) is essentially valid for a solitary frequency point since negative permittivity is a resonance induced phenomenon and in turn highly dispersive. As a result, broadband planar metamaterials are inherently challenging.

3. Broadband circularly polarizing metasurfaces

As previously discussed, the desire for broadband metamaterials is primarily driven by existing communication bands and atmospheric transmission windows. Revisiting Eq. (40), it will now be shown that this condition can exist in between two resonances if the resonances are sufficiently separated in frequency and occur along orthogonal axes. In turn, the resulting dispersive N matrix supporting broadband CP reflection is given by:

N(ω)=(ei(5π4+δ1(ω))00ei(3π4+δ2(ω))).
The bandwidth is defined by ω1<ω<ω2; where, ω1 represents the lower resonance frequency bound and ω2 represents the upper resonance frequency bound. At the center frequency,ω0,the following condition holds:
δ1,2(ω0)=0
At the bandwidth bounds,
δ1(ω1)π4,
δ2(ω2)π4.
Thus, the metasurface reflection matrix, Eq. (40), can still be utilized when ω1<ω<ω2,
rm(θ,φ,ω)=R(φ)(i001)R(φ).
Assuming φ=π/4+nπ/2, and applying Eq. (28) to Eq. (47), the reflected wave may be expressed in the form:
Er(θ,ω)=(ei3π4ei(π4+nπ2)ei(π4+nπ2)ei3π4)(10)=(ieinπ)=E(θ,ω).
While seemingly restrictive, Eq. (48) is readily achieved over a considerable bandwidth when the two frequency offset orthogonal resonances are low loss and have comparable Q factors.

3.1 Broadband infrared circularly polarizing metasurface simulation and performance metrics

To validate Eq. (48) and emphasize the advantages of metamaterials, two examples are presented for the short wave infrared band, using full wave simulations with dispersive material parameters measured via ellipsometry. To simultaneously convey the reflected wave intensity, bandwidth and polarization, the Stokes parameters are utilized [22]. The Stokes vector is represented by the I (intensity), Q (linear polarization), U (45 degree rotated linear polarization) and V (circular) parameters. In Cartesian coordinates, the Stokes parameters are calculated as follows:

I=|Ex|2+|Ey|2,
Q=|Ex|2|Ey|2,
U=2Re(ExEy*),
V=2Im(ExEy*),

The first metallo-dielectric structure is a 2D infinitely periodic metasurface that consists of capacitively end-loaded dipole elements. The unit cell is 480 nm x 480 nm and the dipole is comprised of 75 nm thick Au, supported by a 75 nm polyimide substrate, and backed by a 200 nm Au ground plane. The lower resonance, ω1, caused by the decomposition of an incident linear wave parallel to the dipole axis falls into the realm of metamaterial (i.e. sub-wavelength) behavior due to the size reduction caused by the capacitive end-loading of adjacent unit cells. However, the orthogonal resonance, ω2, does not occur at a sufficiently large wavelength because it is attributed to the formation of a dependent grating which is in turn highly angularly dependent [23]. Consequently, a very broadband CP design is achieved at normal incidence but performance degrades rapidly for increasing oblique angles (Fig. 4(a) ), limiting the utility of the design.

 

Fig. 4 Full wave simulation of periodic and grounded metallo-dielectric structures with response represented in the I and V Stokes parameter for normal incidence and oblique angles. (a) 2D periodic capacitively end-loaded dipole. (b) 2D periodic split ring.

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The second metallo-dielectric structure is a 2D infinitely periodic metasurface that consists of split ring (SR) elements. The unit cell is 380 nm x 380 nm and the SR is comprised of 75 nm thick Au, supported by a 50 nm Polyimide substrate, and backed by a 200 nm Au ground plane. The lower resonance, ω1, is caused by the decomposition of an incident linear wave perpendicular to the SR gap. The upper orthogonal resonance is a caused by the decomposition of an incident linear wave parallel to the SR gap. Both resonances fall within the realm of metamaterial behavior due to the retention of a sufficiently sub wavelength geometry at both frequencies. This directly results in a broadband CP reflector with a wide field of view (FOV). Referencing Fig. 4(b), a low loss, wide FOV, wide CP band centered at λ = 1.55 µm is evident.

For added clarity the SR metasurface polarization response for a horizontally polarized wave normally incident upon a φ=π/4 rotated SR metasurface is represented by additional metrics in Fig. 5 The metrics utilized are axial ratio and polarization conversion ratio (PCR) respectively. These metrics are useful in comparing the published performance for metamaterial based polarizers presented elsewhere across various spectrum [2434] in addition to conventional dielectric quarter wave plates. Figure 6(a) depicts the complete Stokes parameters at normal incidence and Fig. 6(b) depicts the complete Stokes parameters for λ=1.55 µm as a function of a normally incident field’s azimuthal rotation.

 

Fig. 5 Full wave simulations depicted by different metrics for the periodic SR structure depicted in Fig. 4(b). (a-d) Horizontally polarized incident wave reflection expressed in terms of phase axial ratio and polarization conversion ratio respectively.

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Fig. 6 Full wave simulations depicted by different metrics for the periodic SR structure depicted in Fig. 4(b). (a) Horizontally polarized incident wave reflection expressed in terms of the complete Stokes parameters. (b) The Stokes parameters for reflection of 45° rotated SR geometry as a function of incident linearly polarized wave azimuthal rotation.

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3.2 Broadband reconfigurable circularly polarizing metasurface using phase change materials

The utility of the circularly polarizing metasurface can be increased if reconfigurability is introduced since polarization sensing can offer a lower signal to noise ratio than amplitude modulation. Some examples of reconfigurable metamaterials include the incorporation of a semiconducting substrate [35] or inclusion of a semiconducting device [36,37], the incorporation of cantilevers [38,39] or MEMs [21], and the incorporation of phase change materials (PCM) [3942]. Chalcogenide glass (ChG) PCMs have gained considerable interest due to their reversible, thermally-induced phase transition between amorphous and crystalline states with a large associated change in electrical and optical properties [43].

To demonstrate the effect of upper and lower resonance Q factor symmetry and unit cell size, three examples are presented for the long wave infrared band. Each design incorporates a Ge2Sb2Te5 (GST) ChG PCM substrate and functions as a circular polarizer when the GST is in the amorphous state. In the crystalline state the substrate becomes lossy, resulting in a mirror like reflection with no polarization conversion. The measured values utilized for GST at λ = 10µm are n = 4.2, k = 0.01 in the amorphous state and n = 8, k = 4.8 in the crystalline state. As with the near IR designs, full wave simulations consider all losses using material parameters measured via ellipsometry.

The first metallo-dielectric structure is a 2D infinitely periodic metasurface that consists of end-loaded dipole elements. The unit cell is 700 nm x 700 nm and the dipole is comprised of 150 nm thick Au, supported by a 430 nm GST substrate, and backed by a 150 nm Au ground plane. The lower resonance, ω1, is caused by the decomposition of an incident linear wave parallel to the dipole axis. The orthogonal resonance, ω2, is attributed to the higher Q end load resonance. Since the structure is sufficiently sub-wavelength, good angular performance is exhibited (Fig. 7(a) ); but, the asymmetrical Q factors result in a reduced region of high CP.

 

Fig. 7 Full wave simulation of periodic and grounded metallo-dielectric structures with response represented in the I and V Stokes parameters for normal incidence and oblique angles. (a) 2D periodic end-loaded dipole. (b) 2D periodic meander line. (c) 2D periodic split ring. (d) Reconfigurable polarization response of the split ring design as a function of the GST substrate material phase.

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The second metallo-dielectric structure is a 2D infinitely periodic metasurface that consists of meander line elements. The unit cell is 900 nm x 1800 nm and the meander line is comprised of 150 nm thick Au, supported by a 400 nm GST substrate, and backed by a 150 nm Au ground plane. While exhibiting a broad bandwidth and reasonably comparable Q factors for the lower and upper resonances (Fig. 7(b)), the large unit cell length results in a deterioration of angular performance. This is exhibited by the emergence of an in-band resonance at larger oblique angles.

The third metallo-dielectric structure is the familiar SR design with appropriate geometry scaling. The unit cell is 975 nm x 975 nm and the SR is comprised of 150 nm thick Au, supported by a 465 nm GST substrate, and backed by a 150 nm Au ground plane. Since the structure is sufficiently sub-wavelength and exhibits highly symmetric Q factors, broad bandwidth and good angular performance is exhibited (Fig. 7(c)). Furthermore, when the GST substrate phase is changed to the crystalline state the structure no longer behaves as a broadband birefringent surface but rather as a metallic mirror (Fig. 7(d)).

4. Conclusion

A theoretical analysis utilizing Jones matrices is presented, enabling the synthesis of broadband circularly polarizing mirrors. The theoretical analysis and the validity of the associated assumptions are confirmed through full wave simulations performed on candidate designs with traditional dielectric substrates in addition to designs which incorporate the bistable phase changing substrate GST, facilitating broadband polarization reconfigurability.

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  20. N. Behdad, M. Al-Joumayly, and M. Salehi, “A low-profile third-order bandpass frequency selective surface,” IEEE Trans. Antenn. Propag. 57(2), 460–466 (2009).
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  26. J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).
  27. J. M. Hao, and Lei Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: Generalized 4x4 transfer-matrix method,” Phys. Rev. B 77, 094201, 1–12 (2008).
  28. J. Y. Chin, J. N. Gollub, J. J. Mock, R. P. Liu, C. Harrison, D. R. Smith, and T. J. Cui, “An efficient broadband metamaterial wave retarder,” Opt. Express 17(9), 7640–7647 (2009).
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  30. J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
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  31. M. Liu, Y. Zhang, X. Wang, and C. Jin, “Incident-angle-insensitive and polarization independent polarization rotator,” Opt. Express 18(11), 11990–12001 (2010).
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  32. M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization converter,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
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  33. W. Sun, Q. He, J. Hao, and L. Zhou, “A transparent metamaterial to manipulate electromagnetic wave polarizations,” Opt. Lett. 36(6), 927–929 (2011).
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  34. E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
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  35. A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
    [Crossref]
  36. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
    [Crossref] [PubMed]
  37. H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
    [Crossref]
  38. B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
    [Crossref]
  39. W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
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  40. H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
    [Crossref] [PubMed]
  41. J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011).
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  42. M. J. Dicken, K. Aydin, I. M. Pryce, L. A. Sweatlock, E. M. Boyd, S. Walavalkar, J. Ma, and H. A. Atwater, “Frequency tunable near-infrared metamaterials based on VO2 phase transition,” Opt. Express 17(20), 18330–18339 (2009).
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  43. D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
    [Crossref]

2012 (4)

Z. H. Jiang, Q. Wu, and D. H. Werner, “Demonstration of enhanced broadband unidirectional electromagnetic radiation enabled by a subwavelength profile leaky anisotropic zero-index metamaterial coating,” Phys. Rev. B 86(12), 125131 (2012).
[Crossref]

Q. Wu, C. P. Scarborough, D. H. Werner, E. Lier, and X. Wang, “Design synthesis of metasurfaces for broadband hybrid-mode horn antennas with enhanced radiation pattern and polarization characteristics,” IEEE Trans. Antenn. Propag. 60(8), 3594–3604 (2012).
[Crossref]

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

2011 (7)

W. Sun, Q. He, J. Hao, and L. Zhou, “A transparent metamaterial to manipulate electromagnetic wave polarizations,” Opt. Lett. 36(6), 927–929 (2011).
[Crossref] [PubMed]

W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
[Crossref]

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011).
[Crossref] [PubMed]

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radiofrequency metamaterial,” Nat. Mater. 10(3), 216–222 (2011).
[Crossref] [PubMed]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “A broadband monopole antenna enabled by an ultra-thin anisotropic metamaterial coating,” IEEE Antennas Wirel. Propag. Lett. 10, 1543–1546 (2011).
[Crossref]

2010 (4)

F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultra thin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. Antenn. Propag. 58(5), 1551–1558 (2010).
[Crossref]

M. Liu, Y. Zhang, X. Wang, and C. Jin, “Incident-angle-insensitive and polarization independent polarization rotator,” Opt. Express 18(11), 11990–12001 (2010).
[Crossref] [PubMed]

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization converter,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

2009 (6)

2008 (2)

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

J. M. Hao, and Lei Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: Generalized 4x4 transfer-matrix method,” Phys. Rev. B 77, 094201, 1–12 (2008).

2007 (1)

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

2006 (1)

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

2002 (1)

K. Karkkainen and M. Stuchly, “Frequency selective surface as a polarization transformer,” Proc. Inst. Elect Eng. Microw. Antennas Propag. 149(5-6), 248–252 (2002).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

1965 (1)

D. S. Lerner, “A wave polarization converter for circular polarization,” IEEE Trans. Antenn. Propag. 13(1), 3–7 (1965).
[Crossref]

1956 (1)

1948 (1)

1947 (1)

1941 (1)

Abbott, D.

W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
[Crossref]

Alici, K. B.

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Al-Joumayly, M.

N. Behdad, M. Al-Joumayly, and M. Salehi, “A low-profile third-order bandpass frequency selective surface,” IEEE Trans. Antenn. Propag. 57(2), 460–466 (2009).
[Crossref]

An, Z.

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
[Crossref]

Atwater, H. A.

Averitt, R. D.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

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]

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Aydin, K.

Azad, A. K.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

Behdad, N.

N. Behdad, M. Al-Joumayly, and M. Salehi, “A low-profile third-order bandpass frequency selective surface,” IEEE Trans. Antenn. Propag. 57(2), 460–466 (2009).
[Crossref]

Bossard, J. A.

E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radiofrequency metamaterial,” Nat. Mater. 10(3), 216–222 (2011).
[Crossref] [PubMed]

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Boyd, E. M.

Cahill, R.

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization converter,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

Chan, C. T.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

Chen, H.-T.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Chen, Z.

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
[Crossref]

Chin, J. Y.

Costa, F.

F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultra thin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. Antenn. Propag. 58(5), 1551–1558 (2010).
[Crossref]

Cui, T. J.

Dabidian, N.

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Dicken, M. J.

Dickie, R.

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization converter,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

Doumanis, E.

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

Euler, M.

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization converter,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

Fan, K.

Feng, Y.

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

Fumeaux, C.

W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
[Crossref]

Fusco, V.

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization converter,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

Gollub, J. N.

Gomez-Tornero, J. L.

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

Gossard, A. C.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Goussetis, G.

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

Gregory, M. D.

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “A broadband monopole antenna enabled by an ultra-thin anisotropic metamaterial coating,” IEEE Antennas Wirel. Propag. Lett. 10, 1543–1546 (2011).
[Crossref]

Hao, J.

W. Sun, Q. He, J. Hao, and L. Zhou, “A transparent metamaterial to manipulate electromagnetic wave polarizations,” Opt. Lett. 36(6), 927–929 (2011).
[Crossref] [PubMed]

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
[Crossref]

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

Hao, J. M.

J. M. Hao, and Lei Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: Generalized 4x4 transfer-matrix method,” Phys. Rev. B 77, 094201, 1–12 (2008).

Harrison, C.

He, Q.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Huang, C.

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

Huang, X.

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
[Crossref]

Jiang, L.

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011).
[Crossref] [PubMed]

Jiang, T.

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

Jiang, Z. H.

Z. H. Jiang, Q. Wu, and D. H. Werner, “Demonstration of enhanced broadband unidirectional electromagnetic radiation enabled by a subwavelength profile leaky anisotropic zero-index metamaterial coating,” Phys. Rev. B 86(12), 125131 (2012).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “A broadband monopole antenna enabled by an ultra-thin anisotropic metamaterial coating,” IEEE Antennas Wirel. Propag. Lett. 10, 1543–1546 (2011).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

Jin, C.

Johnson, J. D.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Jones, C. R.

Karkkainen, K.

K. Karkkainen and M. Stuchly, “Frequency selective surface as a polarization transformer,” Proc. Inst. Elect Eng. Microw. Antennas Propag. 149(5-6), 248–252 (2002).
[Crossref]

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Kong, J. A.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

Lerner, D. S.

D. S. Lerner, “A wave polarization converter for circular polarization,” IEEE Trans. Antenn. Propag. 13(1), 3–7 (1965).
[Crossref]

Lier, E.

Q. Wu, C. P. Scarborough, D. H. Werner, E. Lier, and X. Wang, “Design synthesis of metasurfaces for broadband hybrid-mode horn antennas with enhanced radiation pattern and polarization characteristics,” IEEE Trans. Antenn. Propag. 60(8), 3594–3604 (2012).
[Crossref]

E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radiofrequency metamaterial,” Nat. Mater. 10(3), 216–222 (2011).
[Crossref] [PubMed]

Liu, M.

Liu, R. P.

Ma, J.

Manara, G.

F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultra thin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. Antenn. Propag. 58(5), 1551–1558 (2010).
[Crossref]

Mayer, T. S.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Mock, J. J.

Monorchio, A.

F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultra thin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. Antenn. Propag. 58(5), 1551–1558 (2010).
[Crossref]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Muise, R.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Musgraves, J. D.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

O'Hara, J. F.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

Ou, J. Y.

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011).
[Crossref] [PubMed]

Padilla, W. J.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Pilon, D. V.

Plum, E.

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011).
[Crossref] [PubMed]

Podraza, N.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Pogrebnyakov, A.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Pryce, I. M.

Qiu, M.

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
[Crossref]

Ran, L.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

Ren, Q.

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
[Crossref]

Richardson, K.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Rivero-Baleine, C.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Rogers, S.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Salehi, M.

N. Behdad, M. Al-Joumayly, and M. Salehi, “A low-profile third-order bandpass frequency selective surface,” IEEE Trans. Antenn. Propag. 57(2), 460–466 (2009).
[Crossref]

Scarborough, C. P.

Q. Wu, C. P. Scarborough, D. H. Werner, E. Lier, and X. Wang, “Design synthesis of metasurfaces for broadband hybrid-mode horn antennas with enhanced radiation pattern and polarization characteristics,” IEEE Trans. Antenn. Propag. 60(8), 3594–3604 (2012).
[Crossref]

E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radiofrequency metamaterial,” Nat. Mater. 10(3), 216–222 (2011).
[Crossref] [PubMed]

Shin, H. J.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Shrekenhamer, D. B.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Smith, D. R.

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Strikwerda, A. C.

Stuchly, M.

K. Karkkainen and M. Stuchly, “Frequency selective surface as a polarization transformer,” Proc. Inst. Elect Eng. Microw. Antennas Propag. 149(5-6), 248–252 (2002).
[Crossref]

Sun, W.

Sweatlock, L. A.

Tao, H.

Taylor, A. J.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Turpin, J.

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Walavalkar, S.

Wang, X.

Q. Wu, C. P. Scarborough, D. H. Werner, E. Lier, and X. Wang, “Design synthesis of metasurfaces for broadband hybrid-mode horn antennas with enhanced radiation pattern and polarization characteristics,” IEEE Trans. Antenn. Propag. 60(8), 3594–3604 (2012).
[Crossref]

M. Liu, Y. Zhang, X. Wang, and C. Jin, “Incident-angle-insensitive and polarization independent polarization rotator,” Opt. Express 18(11), 11990–12001 (2010).
[Crossref] [PubMed]

Werner, D. H.

Q. Wu, C. P. Scarborough, D. H. Werner, E. Lier, and X. Wang, “Design synthesis of metasurfaces for broadband hybrid-mode horn antennas with enhanced radiation pattern and polarization characteristics,” IEEE Trans. Antenn. Propag. 60(8), 3594–3604 (2012).
[Crossref]

Z. H. Jiang, Q. Wu, and D. H. Werner, “Demonstration of enhanced broadband unidirectional electromagnetic radiation enabled by a subwavelength profile leaky anisotropic zero-index metamaterial coating,” Phys. Rev. B 86(12), 125131 (2012).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “A broadband monopole antenna enabled by an ultra-thin anisotropic metamaterial coating,” IEEE Antennas Wirel. Propag. Lett. 10, 1543–1546 (2011).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radiofrequency metamaterial,” Nat. Mater. 10(3), 216–222 (2011).
[Crossref] [PubMed]

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Withayachumnankul, W.

W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
[Crossref]

Wu, C.

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Wu, Q.

Q. Wu, C. P. Scarborough, D. H. Werner, E. Lier, and X. Wang, “Design synthesis of metasurfaces for broadband hybrid-mode horn antennas with enhanced radiation pattern and polarization characteristics,” IEEE Trans. Antenn. Propag. 60(8), 3594–3604 (2012).
[Crossref]

Z. H. Jiang, Q. Wu, and D. H. Werner, “Demonstration of enhanced broadband unidirectional electromagnetic radiation enabled by a subwavelength profile leaky anisotropic zero-index metamaterial coating,” Phys. Rev. B 86(12), 125131 (2012).
[Crossref]

E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radiofrequency metamaterial,” Nat. Mater. 10(3), 216–222 (2011).
[Crossref] [PubMed]

Yuan, Y.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

Zhang, X.

Zhang, Y.

Zhao, J.

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

Zheludev, N. I.

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011).
[Crossref] [PubMed]

Zhou, L.

W. Sun, Q. He, J. Hao, and L. Zhou, “A transparent metamaterial to manipulate electromagnetic wave polarizations,” Opt. Lett. 36(6), 927–929 (2011).
[Crossref] [PubMed]

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
[Crossref]

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

Zhu, B.

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

Zide, J. M. O.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

IEEE Antennas Wirel. Propag. Lett. (2)

W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “A broadband monopole antenna enabled by an ultra-thin anisotropic metamaterial coating,” IEEE Antennas Wirel. Propag. Lett. 10, 1543–1546 (2011).
[Crossref]

IEEE Trans. Antenn. Propag. (6)

D. S. Lerner, “A wave polarization converter for circular polarization,” IEEE Trans. Antenn. Propag. 13(1), 3–7 (1965).
[Crossref]

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization converter,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

Q. Wu, C. P. Scarborough, D. H. Werner, E. Lier, and X. Wang, “Design synthesis of metasurfaces for broadband hybrid-mode horn antennas with enhanced radiation pattern and polarization characteristics,” IEEE Trans. Antenn. Propag. 60(8), 3594–3604 (2012).
[Crossref]

F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultra thin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. Antenn. Propag. 58(5), 1551–1558 (2010).
[Crossref]

N. Behdad, M. Al-Joumayly, and M. Salehi, “A low-profile third-order bandpass frequency selective surface,” IEEE Trans. Antenn. Propag. 57(2), 460–466 (2009).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

J. Opt. Soc. Am. (4)

Nano Lett. (1)

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011).
[Crossref] [PubMed]

Nat. Mater. (1)

E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radiofrequency metamaterial,” Nat. Mater. 10(3), 216–222 (2011).
[Crossref] [PubMed]

Nat. Photonics (1)

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

Nature (1)

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Opt. Commun. (1)

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (1)

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80(2), 023807 (2009).
[Crossref]

Phys. Rev. B (3)

J. M. Hao, and Lei Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: Generalized 4x4 transfer-matrix method,” Phys. Rev. B 77, 094201, 1–12 (2008).

Z. H. Jiang, Q. Wu, and D. H. Werner, “Demonstration of enhanced broadband unidirectional electromagnetic radiation enabled by a subwavelength profile leaky anisotropic zero-index metamaterial coating,” Phys. Rev. B 86(12), 125131 (2012).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

Phys. Rev. Lett (1)

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.  99, 063908, 1–4 (2007).

Phys. Rev. Lett. (2)

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Proc. Inst. Elect Eng. Microw. Antennas Propag. (1)

K. Karkkainen and M. Stuchly, “Frequency selective surface as a polarization transformer,” Proc. Inst. Elect Eng. Microw. Antennas Propag. 149(5-6), 248–252 (2002).
[Crossref]

Proc. SPIE (1)

D. H. Werner, T. S. Mayer, C. Rivero-Baleine, N. Podraza, K. Richardson, J. Turpin, A. Pogrebnyakov, J. D. Musgraves, J. A. Bossard, H. J. Shin, R. Muise, S. Rogers, and J. D. Johnson, “Adaptive phase change metamaterials for infrared aperture control,” Proc. SPIE 8165, 1–9 (2011).
[Crossref]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Other (9)

T. H. Hand, Design and Applications of Frequency Tunable and Reconfigurable Metamaterials. (Ph.D. Thesis, Duke University, 2009).

C. H. Papas, Theory of Electromagnetic Wave Propagation (McGraw-Hill, 1965).

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

E. Collett, “Field guide to polarization,” in SPIE Field Guides, J.E. Greivenkamp, ed. (SPIE, 2005), Vol. FG05.

A. A. Maradudin, Structured Surfaces as Optical Metamaterials (Cambridge University Press, 2011).

J. Kong, Electromagnetic Wave Theory (Wiley, 1986).

V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

E. Plum, Chirality and Metamaterials (Ph.D. Thesis, University of Southampton, 2010).

P. E. Sieber and D. H. Werner, “A reconfigurable near-infrared circularly polarizing reflector based on phase changing anisotropic metamaterials,” Proceedings of the International Symposium on Antennas and Propagation and USNC/URSI National Radio Science Meeting (IEEE, 2012), IF54.2.

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Figures (7)

Fig. 1
Fig. 1

Scattering matrices for opposite angles and directions of incidence.

Fig. 2
Fig. 2

Birefringent metamaterial scattered field handedness, amplitude, and propagation direction with a linearly polarized incident field for the condition of circular polarization.

Fig. 3
Fig. 3

Birefringent metasurface scattered field handedness, amplitude, and propagation direction with a linearly polarized incident field for the condition of circular polarization.

Fig. 4
Fig. 4

Full wave simulation of periodic and grounded metallo-dielectric structures with response represented in the I and V Stokes parameter for normal incidence and oblique angles. (a) 2D periodic capacitively end-loaded dipole. (b) 2D periodic split ring.

Fig. 5
Fig. 5

Full wave simulations depicted by different metrics for the periodic SR structure depicted in Fig. 4(b). (a-d) Horizontally polarized incident wave reflection expressed in terms of phase axial ratio and polarization conversion ratio respectively.

Fig. 6
Fig. 6

Full wave simulations depicted by different metrics for the periodic SR structure depicted in Fig. 4(b). (a) Horizontally polarized incident wave reflection expressed in terms of the complete Stokes parameters. (b) The Stokes parameters for reflection of 45° rotated SR geometry as a function of incident linearly polarized wave azimuthal rotation.

Fig. 7
Fig. 7

Full wave simulation of periodic and grounded metallo-dielectric structures with response represented in the I and V Stokes parameters for normal incidence and oblique angles. (a) 2D periodic end-loaded dipole. (b) 2D periodic meander line. (c) 2D periodic split ring. (d) Reconfigurable polarization response of the split ring design as a function of the GST substrate material phase.

Equations (52)

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t ( θ )=( a+1 b c d+1 )
r ( θ )=( c d a b )
s ( θ )=( a b c d ).
s ( θ )=( d c b a ).
s ++ ( θ )= s ( θ ) and  s ( θ )= s ++ ( θ ),
s + ( θ )= s + ( θ ) and  s + ( θ )= s + ( θ ),
s ij = s ji ,
s ++ ( θ )= s ++ ( θ ) and  s ( θ )= s ( θ ),
s + ( θ )= s + ( θ ) and  s + ( θ )= s + ( θ ),
ε ¯ ¯ = ε ¯ ¯ T ,
μ ¯ ¯ = μ ¯ ¯ T .
ξ ¯ ¯ = ζ ¯ ¯ T .
ξ ¯ ¯ =( χ ¯ ¯ j κ ¯ ¯ ) μ 0 ε 0 ,
ζ ¯ ¯ =( χ ¯ ¯ +j κ ¯ ¯ ) μ 0 ε 0 .
det( a λ s b c d λ s )=( a λ s )( d λ s )bc=0
λ 1,2 s = a+d 2 ± ( ad 2 ) 2 +bc.
λ 1,2 s =a±| b | e iθ .
ρ s =2 tan 1 | b a |,
S=a= cos 2 ( ρ s 2 ),
| a+ 1 2 |=| d+ 1 2 | 1 2 ,
| b |=| c | 1 2 ,
| a+ 1 2 | 2 + | b | 2 = ( 1 2 ) 2 .
λ 1,2 s = 1 2 ( 1± e iθ ).
b= c * .
s ( θ )= 1 2 ( 1 e iδ e ±iδ 1 ).
s ( θ,φ )= 1 2 ( 1 e i2φ e ±i2φ 1 ).
E inc = E 0 ( cos φ x sin φ x ) e i( kzωt ) ,
E inc =( 1 0 ).
E r = 1 2 ( e ±i π 2 1 1 e i π 2 )( 1 0 )= 1 2 ( ±i 1 )= 2 2 E
E t = 1 2 ( 1 e i π 2 e ±i π 2 1 )( 1 0 )= 1 2 ( 1 ±i )= 2 2 E .
ε ¯ ¯ = ε 0 ( 1 0 0 1 ).
η ¯ ¯ ( ω 0 ±Δ )= η 0 ( i 0 0 1 ).
η ¯ ¯ ( ω 0 ±Δ )= η 0 ( i 0 0 0 ).
E t = 1 4 ( 1 e ±i( π 2 +π ) e i( π 2 +π ) 1 )( 1 i )= 1 2 ( 1 i )= 2 2 E .
E r = 1 2 ( ±i 1 )+ 1 2 ( 1 i )= 2 2 ( e ±i 3π 2 e ±i 5π 2 )= 2 2 ( 1 ±i )= E .
r m ( φ )=R( φ )NR( φ ).
R( φ )=( cosφ sinφ sinφ cosφ ).
N=( r x 0 0 r y ).
N=( i 0 0 1 ).
r m ( θ,φ )=R( φ )( i 0 0 1 )R( φ ).
ε r ' ( ω )=1+ 2 π 0 ω ' ε r " ( ω ' ) ( ω ' ) 2 ω 2 d ω ' ,
ε r " ( ω )= 2ω π 0 1 ε r ' ( ω ' ) ( ω ' ) 2 ω 2 d ω ' ,
N( ω )=( e i( 5π 4 + δ 1 ( ω ) ) 0 0 e i( 3π 4 + δ 2 ( ω ) ) ).
δ 1,2 ( ω 0 )=0
δ 1 ( ω 1 ) π 4 ,
δ 2 ( ω 2 ) π 4 .
r m ( θ,φ,ω )=R( φ )( i 0 0 1 )R( φ ).
E r ( θ,ω )=( e i 3π 4 e i( π 4 +n π 2 ) e i( π 4 +n π 2 ) e i 3π 4 )( 1 0 )=( i e inπ )= E ( θ,ω ).
I= | E x | 2 + | E y | 2 ,
Q= | E x | 2 | E y | 2 ,
U=2Re( E x E y * ),
V=2Im( E x E y * ),

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