Journal of Infrared, Millimeter, and Terahertz Waves

, Volume 38, Issue 9, pp 1047–1066 | Cite as

Review on Polarization Selective Terahertz Metamaterials: from Chiral Metamaterials to Stereometamaterials

  • Elizabath Philip
  • M. Zeki Güngördü
  • Sharmistha Pal
  • Patrick Kung
  • Seongsin Margaret Kim


In this article, recent progress and development of terahertz chiral metamaterials including stereometamaterials are thoroughly reviewed. This review mainly focuses on the fundamental principles of design and arrangement of meta-atoms in metamaterials exhibiting chirality with various asymmetry and symmetry and 2D and 3D configuration. Related optical and propagation properties in chiral metamaterials, such as optical activity, circular dichroism, and negative refraction for each different chiral metamaterials, are compared and investigated. Finally, comparison between chiral metamaterials with stereometamaterials in terms of the polarization selective operation along with the similarity and the distinction is addressed as well.


THz metamaterials Polarization selective Chiral metamaterials Stereometamaterials Optical activity 

1 Introduction

Metamaterials, a new class of engineered materials consisting of arrays of subwavelength scale resonant building blocks, i.e., meta-atoms, have been the focus of growing interest for both fundamental research and practical applications since they were first predicted by Vesalago and realized by Pendry and Smith [1, 2, 3, 4, 5, 6, 7, 8, 9]. Through proper arrangement of these meta-atoms and related structures, metamaterials can be engineered to exhibit negative index of refraction (n < 0) that does not occur in nature. By manipulating both the electric permittivity, ε(ω) = ε(ω) + iε(ω), and the magnetic permeability, μ(ω) = μ(ω) + (ω), the electric and magnetic responses of metamaterials can be independently adjusted, which can provide a convenient method to realize a wide range of devices. This ability of independent adjustment also provides a significant advantage over conventional materials which, generally, do not support this capability. So far, the most conventional metamaterial structure consists of two parts: one is metal wire which provides negative permittivity, and the other consists of split ring resonators (SRRs) to achieve negative permeability, resulting in a combination that exhibits a negative refractive index at certain resonant frequencies. Another important advantage of metamaterials is that they can be geometrically scaled in order to operate in any desired frequency regime since the fundamental properties of subwavelength structures can be applied to any frequency and wavelength spectrum. These electromagnetically active structures are very promising in the development of low cost, ultrasensitive, and easy-to-use room-temperature devices, especially those operating at terahertz (THz) frequencies to fully exploit the wide range applications of this scientifically rich spectrum [10, 11, 12, 13].

THz waves, spanning from 0.1 to 10 THz, have not been fully utilized mainly due to the lack of high-performance sources, detectors, and availability of other passive components, but are considered one of the most intriguing frequency ranges of electromagnetic (EM) waves that can be used from fundamental physical sciences to biomedical imaging [10, 12, 14, 15, 16, 17, 18]. Meta-atoms have been developed in various types, such as spiral [19], fishnet [20], labyrinth [21], and electric field coupled (ELC) [22] resonators and could lead to various applications such as image compression, superlenses, subwavelength imaging, cloaking, perfect absorption, and black holes [23, 24, 25, 26].

Following the rapid progress in the development and demonstration of THz metamaterials for various applications during the last few decades, achieving polarization selection and control of propagation wave through metamaterial media became extremely important. With more sophisticated structures, the manipulation of polarization using metamaterials in general becomes more effective as well. Furthermore, chiral metamaterials and stereometamaterials have gained great attention for their unique and exotic propagation properties in terms of polarization.

Chiral metamaterials are based on arrangement of meta-atoms that exhibit polarization properties like left handedness (LH) and right handedness (RH). It is common for most optical systems to exhibit such polarization dependence when they are subjected to circularly polarized light. Chirality, a word that originated from Greek, meaning “hand,” can be found in objects with no internal mirror symmetry in their structures. In fact, a hand is the most easily understood example to explain chirality. The left hand can never be superimposed on the right hand no matter how it is rotated. Chirality is most commonly found in many biomolecules which directly impacts important functions in chemistry, biology, and pharmaceuticals. Like sugar (glucose), many biologically active molecules such as amino acids and enzymes are chiral and lack internal mirror symmetry. Such biomolecules’ chirality has been probed with circularly polarized light, since the polarization dependence is the major distinction between chiral and non-chiral molecules. Furthermore, like the left and right hand, which are mirror images of each other, enantiomers are two stereoisomers that are related to each other by reflection, i.e., mirror images of each other that cannot be superimposed. Therefore, chiral molecules naturally fit into the part of stereoisomers.

Stereoisomers have the same molecular formula and same sequence of molecular bonding, but differ in their spatial orientation and/or rotational symmetry. Stereometamaterials stem from the same conceptual structure of stereoisomers, in which their optical and propagation properties differ by spatial constitution rather than the distinction of meta-atoms’ properties. Since some stereoisomers exhibit their chirality, it becomes interesting how polarization sensitivity is revealed in stereometamaterials as well.

In this review, we will focus on recent development of chiral and stereometamaterials in terms of the design of meta-atoms and the optical and propagation properties reported. In the selection of the references, we decided to focus on chiral and stereometamaterials operating at only THz frequencies; therefore, infrared, visible, and microwave chiral and/or stereometamaterials were not included as references. There have been a few review articles on chiral metamaterials so far which included other operating frequencies and wavelength regime [27, 28, 29]. The polarization selective transmission and reflection properties became critical measure of determining the chirality of the reported structures and are compared in some of the reported structures reviewed here. After that, we will compare the polarization properties of stereometamaterials, and finally, the prospective applications will be discussed.

2 Structural Analysis of Chiral THz Metamaterials

2.1 Types of Structures

There are a wide variety of chiral metamaterials that successfully show various chiral optical properties in the THz regime. Although their structures range from simple single-layer metamaterials to complex multilayer ones, we categorize them here based on a few basic principles. First, we look into the overall structure of the device: they can be multilayered or non-planar 3D structures, or more simplified, single-layered 2D structures. Then, we will look specifically into the geometrical patterns used in the devices and categorize them based on their symmetry.

Among 3D structures, the most common type seen is the stacked layers of 2D planar structures, sometimes with a dielectric spacer between the layers [30, 31, 32, 33, 34, 35, 36, 37, 38]. The spirals used by He et al. [38] use up to eight layers. Then, there are single-layered but non-planar structures that also fall under 3D structures such as the 3D microcoils by Waselikowski et al. [39]. Most of the single-layer non-planar 3D structures are studied only using simulations without experimental tests due to the complexity in fabricating them. The conjugated rosettes and the microcoils [39, 40] are exceptions, where they have successfully been fabricated into devices. The 3D or bulk structure fabricated by Wu et al. [40] called a chiral metafoil (CMF) is an all-metal, self-supported, freestanding, flexible chiral metamaterial, with properties that are solely determined by the geometric structure and the metallic characteristics, since there are no dielectric materials involved. The CMF consist of square arrays of conjugated rosettes interconnected with metallic wires and pillars between rosettes as shown in Fig. 1a, and they can be considered as a composite chiral metamaterial. It reveals interesting properties such as strong optical activity, circular dichroism, and negative refractive index with a high figure of merit (FOM), which will be later discussed in more detail. Whereas, Wu et al. [41] reached 3D chirality by using specific rotation between neighboring layers in these fractional-screw-like structures. Fractional-screw-like structures consist of stacking and connecting three of such planar non-chiral rods with a rotation angle of 90° between them. It is the basic building block of chiral metafoils. The architecture principle of gold chiral metafoil is shown in Fig. 1b, c. The design features a simple rod, with a length of l = 90 μm, width of w = 30 μm, and thickness of t = 17 μm. While each element is strictly non-chiral, the structure generates a strong, resonant anisotropy within the plane.
Fig. 1

a 3D schematics of the conjugated rosette CMF; reprinted from [40] with the permission of AIP Publishing. The configuration of right-handed b and left-handed c chiral metafoils as discussed in Wu et al. Actual values of parameters are l = 90 μm, w = 30 μm, and t = 17 μm; reprinted with permission from [41], copyright (2014) by the American Physical Society. d Planar chiral terahertz metamaterials based on adjoined orthogonally oriented SRRs; reprinted with permission from [42], copyright (2009) by the American Physical Society. e Other planar CMM structure based on Y shaped without symmetry [43]

In contrast to 3D and freestanding design, the conventional 2D planar design of chiral metamaterials (CMMs) appears less frequently [42, 43, 44]. Singh et al. [42] reported 2D chiral pattern based on pairs of split ring resonators adjoined together with orthogonal orientation. The planar chiral metamaterials are made of 200-nm-thick aluminum on a 640-μm-thick silicon substrate as shown in Fig. 1d. The asymmetric transmission was observed from the structure by changing the incident wave direction; it is right-handed when observed from the front and left-handed when observed from the back. Wongkasem et al. [43] presented a planar metamaterial based on the Y structure as shown in Fig. 1e. In this design, co-polarized and cross-polarized transmission coefficients were successfully measured in the THz regime. This Y-shaped planar CMM demonstrates negative refraction index metamaterial.

2.2 Symmetries in Designing of Chiral Metamaterials

Apart from the overall structure being either 2D or 3D, another interesting feature is the type of symmetry observed in the geometrical designs of these THz chiral metamaterial structures. Ideally, chiral molecules should not have any in-plane mirror symmetry in order for it to display optical activity. However, with metamaterials, we see that this definition does not always hold. Although most geometrical shapes used in chiral metamaterials have no in-plane symmetry, more and more devices with one or more forms of symmetry are now being made that still show optical or extrinsic chirality.

2.2.1 Chiral Structures Without In-Plane Mirror Symmetry

First, we will discuss the most popular case: pure chiral structures. These are geometries without any in-plane mirror symmetry. However, most of them have some form of rotational symmetry. Several of them [30, 31, 35, 36, 37, 40, 45] show fourfold rotational symmetry. Most of these fall within these three common shapes—the rosette, gammadion, and cross-wires.


This design appears many times in various references. The chiral metamaterials used by Zhou et al. [36] are bilayer, purely chiral metamaterials made of planar, conjugated gammadion metal structures as shown in Fig. 2a, b. The gammadions are made of 200-nm gold separated by a low-loss polyimide (PI) spacer, which is 10 μm thick. The bottom-layer resonators sit on 600-nm-thick square intrinsic silicon islands patterned from a silicon-on sapphire substrate. This metamaterial showed strong chirality which also resulted in a negative refractive index. Unlike the usual twisted conjugated gammadion, Xu et al. [31] simulates a composite chiral structure made by combining the twisted conjugated gammadion with four L-shaped resonator pairs and a layer of dielectric in between as shown in the Fig. 2c, d. The metal patterns are 6-μm-thick gold layers, and the dielectric used is silica. This bilayer metamaterial showed giant and non-resonant optical activity with very low dispersion.
Fig. 2

Purely chiral metamaterials made of planar, conjugated gammadion metal structures. a Design schematic of the unit cell of the dynamic chiral metamaterials and b large area of fabricated sample; reprinted with permission from [36], copyright (2012) by the American Physical Society. c Unit cell of combined twisted conjugated gammadion THz chiral metamaterials and d its multilayered structure with dielectric in between; reprinted with permission from [31], © Springer Science+Business Media New York 2016. e Schematic diagram of a unit cell of the CCMM. The EM wave is normal incident along the z-axis when the structure is viewed from the front (left). The twisted angle φ is fixed at 30° along the x-axis and is tunable [37], © IOP Publishing. Reproduced with permission. All rights reserved. f Samples of constructed Fermat’s spiral quadfiler chiral THz metamaterials for circular polarizer and filter [46]. g, h Additional THz CMM based on the spiral unit cell; reprinted with permission from [47], © Springer Science+Business Media New York 2016; reprinted from [38], copyright (2011), with permission from Elsevier, respectively

Cross-Wires and Spirals

Ding et al. [37] uses cross-wires in their complementary chiral MMs (CCMMs) as shown in Fig. 2e. The various parameters for the structure are tm = 0.2 μm, t = 2 μm, p = 20 μm, w = 2 μm, l = 18 μm, and the twist angle ϕ is 30°. The metal used for the resonators is gold due to its very low loss in the terahertz and higher frequency regions, and benzocyclobutene (BCB) as the dielectric spacer. They numerically studied its optical activity, negative refractive index, and also the influence of the twist angle, dielectric layer thickness, width, and length of the complementary cross-wire pairs on the optical activity. Yogesh et al. [46] reported bilayer-twisted Fermat’s spiral chiral metamaterials as a circular polarizer and a polarization filter. A quadfilar system has four Fermat’s spiral (FS) arms with 90° rotational arrangements, and each spiral consists of a spiral turn of 2п as shown in Fig. 2f. The chiral metamaterials’ design consists of the spiraling constant of A = 4.8 μm/(rad)1/2. This design is based on mutually conjugated quadfilar system, in which the configuration breaks the mirror symmetry throughout the aspect of propagation of light. It successfully demonstrated higher optical isolation, wide-angle operation, and large bandwidth. Tang et al. [47] recently suggested a new planar spiral chiral structure having the fourfold rotational symmetry. This design has two spiral metallic silver layers on both sides of a dielectric substrate as shown in Fig. 2g. The unit cell’s parameters are a = 31 μm, d2 = 3.7 μm, l = 12 μm, and w = 2 μm. The rotation of angle between front and back metallic layer θ is 45°. Such structure reveals the cross-polarization conversion (CPC) and strong optical activity in THz frequency. Finally, He et al. [38] also uses a spiral structure of up to six layers as part of their device as shown in Fig. 2h. A single-layer array of metallic spirals, with the helix diameter R = 36 μm and width of 4 μm, arranged to constitute CMM. A BCB dielectric spacer of thickness d = 18 μm and aluminum metal spiral of 200-nm thickness was used. A mutual twist angle θ is maintained between the multiple metal resonator layers. Parameters such as the number of layers and the twist angle θ are varied to study their influence in producing strong chirality and, in turn, achieve a negative refractive index.

Other Exotic Designs of THz Chiral Metamaterials

While most structures with symmetry fall within twofold or fourfold symmetry, Sonsilphong et al. [32] uses a C8 (eightfold) symmetry structure. This flexible, conjugated bilayer chiral metamaterial uses PI as its substrate and SU-8 resist as the spacer between the bilayers as shown in Fig. 3a, b. The bilayers can either be right-handed or left-handed as can be seen in the figure, and their transmission coefficients, refractive indices, and chirality are investigated for right circular polarization (RCP) and left circular polarization (LCP) waves. It is very rare to find a structure without any rotational symmetry like the V-shaped babinet dimers [44] and the planar spirals in [38]. Zalkovskij et al.’s work based on the babinet dimmers [44] further stands out in their approach, where instead of using arrays of metallic rods on the metamaterial, they use its complement, which are arrays of hollow slots on metal sheet. Their babinet planar metamaterial structures, referred as the babinet asymmetric dimer, were designed to mimic the asymmetric split ring geometry, but with straightened segments. Their structure consists of nanorod dimers with straight, non-parallel elements of different sizes. By using a babinet structure, they can create a freestanding metamaterial of metal only, in this case Ni, without any dielectric. The spectral properties of the babinet structure is expected to be similar to that of an array of metallic rods, but inverted, as per the babinet principle. All these structures mentioned so far maintain their geometrical chirality even when considering their 3D layers. One last exotic structure is the Tai Chi chiral metamaterial structure reported by Huang et al. [48]. Of the two CMMs, one is a mirror symmetric structure, while the other is a complementary one. Each unit cell comprises of three layers, and both the mirror symmetric and complementary structures have two metallic layers separated by 10-μm-thick polymer, and the dimensions are shown in Fig. 3c, d. The length of unit cell is l = 60 μm, the radius of two semi-circle r1 = 24 μm and r2 =12 μm, and the radius of the smallest circle r3 = 2 μm, respectively. While the mirror symmetric structure showed circular dichroism and strong optical activity, the complementary structure shows no polarization dependence.
Fig. 3

Unit cells of conjugated bilayer structures. a RH and b LH C8 structures, H1 = 75 μm, H2 = 30.04 μm, ax = ay = 185 μm, w = 18 μm, t = 25 μm, tc = 0.2 μm, and d = 2.5 μm. ϕ = 22.5° and θ = 22.5° [32], © IOP Publishing. Reproduced with permission. All rights reserved. Schematic of Tai Chi patterned CMM, c mirror symmetric Tai Chi structure, and d complementary Tai Chi structure. Geometrical parameters of two structures: w = 60 μm, r1 = 24 μm, r2 = 12 μm, and r3 = 2 μm. The thickness d of metallic layers and td of dielectric layers are 0.2 and 10 μm, respectively; reprinted with permission from [48], © Springer Science+Business Media New York 2015

2.2.2 Chiral Structures with In-Plane Mirror Symmetry

Some structures have both rotational symmetry and in-plane mirror symmetry, which technically makes it achiral. However, when you look through both the layers comprising its 3D structure, the in-plane symmetry is broken, thereby making it a chiral structure after all. Ozer et al. [33] proposed one such chiral metamaterial device with resonator metallic parts made of 0.2-μm-thick silver placed to the front and back of a 450-μm-thick quartz dielectric substrate. The structure provides asymmetric transmission for linearly polarized EM waves. Here, silver was chosen for its low resistivity.

3 Polarization Selectivity and Other Optical Properties of Chiral THz Metamaterials

Now that we have looked into the various chiral metamaterial structures used in the THz regime, here we will review in detail each of the EM properties successfully displayed by these devices. The theoretical principles behind several of these properties were discussed in previous review paper [28]. The devices are measured in the transmission mode using terahertz spectroscopy, to determine the four linear co-polarization and cross-polarization states Txx, Txy, Tyx, and Tyy. The x and y imply the two linearly polarized waves with the electric field polarized along the two orthogonal directions, while the first and second lower indices indicate the transmitted and incident signal polarizations, respectively. For example, Tij = Eitran / Ejinc, where Ejinc is the incident y-polarized electric field and Eitran is the transmitted x-polarized electric field. The devices are usually measured for normal incidence except the achiral structure by Cao et al. [49] where it is incident at an angle. The results from the four measurements are then used to calculate the four circular polarization states T++, T+−, T−+, and T−− using the equation below.
$$ \left(\begin{array}{cc}\hfill {T}_{++}\hfill & \hfill {T}_{+-}\hfill \\ {}\hfill {T}_{-+}\hfill & \hfill {T}_{--}\hfill \end{array}\right)=\frac{1}{2}\left[\begin{array}{cc}\hfill \left({T}_{xx}+{T}_{yy}\right)+ i\left({T}_{xy}-{T}_{yx}\right)\hfill & \hfill \left({T}_{xx}-{T}_{yy}\right)- i\left({T}_{xy}+{T}_{yx}\right)\hfill \\ {}\hfill \left({T}_{xx}-{T}_{yy}\right)+ i\left({T}_{xy}+{T}_{yx}\right)\hfill & \hfill \left({T}_{xx}+{T}_{yy}\right)- i\left({T}_{xy}-{T}_{yx}\right)\hfill \end{array}\right] $$
Here, + implies RCP, and – implies LCP, and similar to the linear polarization, the first and second lower indices indicate the transmitted and incident signal polarizations, respectively. It is using these values for T++, T+−, T−+, and T−− that several of the optical properties below are calculated and plotted. The transmission graphs for V-shaped babinet dimers [44] are shown in Fig. 4. The device shows up to 65% conversion between the left-to-right (T−+) and right-to-left (T+−) circular polarizations in the 0.49 to 0.52 THz region. However, in most other devices, the cross-polarization terms are neglected due to the fourfold rotational symmetry of the structure and only the co-polarization terms are analyzed [31, 33, 36, 40].
Fig. 4

a Relative transmission (T++, T) and circular polarization conversion (T+−, T−+) in terms of power for V-shaped slot planar metamaterial. b Optical activity for V-shaped antirod slot metamaterial. c Image of the V-shaped sample [44], © 2013 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

3.1 Optical Activity

Optical activity is one of the most common properties displayed in chiral metamaterials. It is measured by the rotation angle of the plane of a plane-polarized light that is passed through the chiral material. With the proper design of meta-atoms in chiral metamaterials, it is possible to achieve extremely strong (or giant) optical activity, in other words, extremely large rotation angles. Several structures surveyed and discussed in the previous sections exhibit strong optical activities [31, 36, 37, 39, 44, 45]. The composite twisted conjugate gammadion with L-shaped resonators by Xu et al. [31] was optimized by varying the dielectric thickness to produce giant and dispersionless optical activity. Though twisted conjugated gammadions by themselves (without the L resonators) showed giant optical activity from 1.97 to 2.078 THz, the CMM structure had a higher dispersion with an ellipticity of 13.5° at the resonant frequency f = 1.95 THz. But by utilizing the composite structure, it was possible to reduce the dispersion, while maintaining a giant optical activity as shown in Fig. 5. After calculating the polarization rotation angle and the ellipticity of the composite metamaterial shown in Fig. 2d, it is seen, from 2.37 to 2.691 THz, that there is giant optical activity with the polarization rotation angle reaching an extremely high 90.3° across this frequency ranges. Meanwhile, an extremely low ellipticity is maintained across this range, with a maximum of 0.46° seen only at the resonant frequency in Fig. 5. The optimal thickness of the dielectric was determined by first studying the results for varying thicknesses.
Fig. 5

Examples of transmission properties measured from chiral metamaterials. a The transmission coefficient of left and right hand circularly polarized, respectively, b phase angle, and c ellipticity (red) and optical activity (blue) for circularly polarized waves of CCM; reprinted with permission from [31], © Springer Science+Business Media New York 2016

Another case of dispersionless and giant optical activity is reported by Wu et al. [40]. Here, in between the two resonant frequencies, they see a polarization rotation of 10° while the ellipticity reaches zero. However, Zhou et al. [36] at zero ellipticity achieve a rotation angle slightly greater than 12° in the off-resonance region. They also dynamically controlled the chirality of the sample by changing the conductivity of the silicon substrate. The conductivity was experimentally varied by using near-infrared femtosecond laser to excite the photo-carriers in the intrinsic silicon. Zalkovskij et al. [44] was able to show optical activity reaching up to a polarization plane rotation rate of 500°/λ for their V-shaped Babinet asymmetric dimer as shown in Fig. 4a–c. This result clearly shows that a single layer of planar babinet structures is comparable to that of other more complicated, multilayered structures. Also, the results of the V-shaped babinet are compared to the results of the corresponding parallel-shaped babinet metamaterial. The parallel ones exhibit no optical activity, proving that the asymmetric design of the V-shaped slot dimers greatly contributed in the anisotropic transmission behavior. Kanda et al. [50, 51] explains that relatively thin structured samples with a step of only 100 nm cause strong polarization effects for the THz wave. This will open new techniques to control the polarization of THz wave by classic microprinting techniques. Additionally, it may be possible to achieve a THz polarization modulator in combination with MEMS technology as well. The chiral samples indicate that marked orthogonal components of the electric fields and the sign of the electric fields are opposite for right-twisted and left-twisted gammadion. The amplitude of frequency domain spectra, Ex(ω), is almost the same for right-twisted and left-twisted patterns, and much larger than that of the cross pattern. In addition to the mechanical tuning of the optical activity of the THz CMM, photo-control of optical activity has been studied as well by the same group [51] and another group [36]. The measured transmission spectra and polarization-rotation spectra of chiral and achiral structures concluded that an increase of the pump power prevented the transmittance. The induced optical activity was not linked to the pump beam’s polarization direction.

Kenanakis et al. [52] studied numerically the dynamical tuning capabilities of different THz chiral metamaterial structures with specific metallic parts replaced by photo-conductive silicon. The response of the structure analysis depends on the calculation of the transmission spectrum for linearly polarized incident wave. The structures show regions with giant tunable optical activity and impressive dynamical tuning of the ellipticity of the transmitted wave. It demonstrates the notable switchable polarizer capabilities of reported structures in various frequency regimes: regarding the cross-wire structure around 5.5 THz, it can be easily switched from circular to linear polarizer by changing the flux of the excitation power. Similar switchable response is observed also at ~10 THz for the cross-structure and at ~8.8 THz for the second cross-structure.

3.2 Circular Dichroism

Another very prominent property of chiral metamaterials is circular dichroism (CD). It is measured by the difference in transmission (or reflection) of left and right circular polarized light through the chiral medium. A strong CD can also imply that one of circular polarizations passes through the medium by a larger amount than the other, and as a result enables the medium to be polarization selective. There are several chiral metamaterials that exhibit strong CD [33, 37, 40, 41, 46, 52].

The complementary cross-wires by Ding et al. [37] calculated a change of about 2.5 dB between LCP and RCP waves from their simulations; when they further tested their device by changing some of the device parameters, they detected CD to reach −21 dB when the dielectric thickness was set to 1 μm. Similarly, the CMFs by Wu et al. [40] showed a difference of 62% between the LCP and RCP transmission at one of its resonant frequencies. Furthermore, Wu et al. [41] was able to achieve a high-contrast broadband circular polarization selectivity using their chiral metafoil. The dichroic response had a bandwidth of about one octave at a center frequency of 2.4 THz, with the maximum transmittance of approximately 70%. Lastly, the bilayer-twisted Fermat’s spiral chiral metamaterial (FSCMM) proposed by Yogesh et al. [46] also displays strong circular dichroism at around 2.5 THz as shown in Fig. 6. As a result, the device is selective to circular polarized light, where it filters out either right-handed or left-handed CP light and can function for oblique incidences up to 20°.
Fig. 6

Strong optical activity from measurements of Fermet’s spiral chiral metamaterials. a, b Corresponding to the amplitude and phase spectrum of cross-polarized and co-polarized transmission levels of the Fermet’s spiral chiral metamaterials (FSCMM), respectively. c Circular polarization transmission plot for x-polarized and y-polarized normal incident light and d the corresponding ellipticity spectrum [46]

3.3 Negative Refractive Index

Theoretically, chirality was originally proposed by several research groups as an alternative route to obtain negative refractive index [53, 54, 55, 56]. Pendry proposed a 3D spiral (helical) structure that can realize negative refractive index in the given medium, which turned out to be a chiral metamaterial [53]. Tretyakov et al. theoretically calculated a negative refraction in chiral composites consisting of chiral and dipole particles. With the theoretical support of realizing negative refraction, most chiral metamaterials reported here actively measured negative refractive index. Negative refraction is one of the most desirable properties to attain from the chiral metamaterials.

The 3D, conjugated rosettes explained in Wu et al.’s work [40] show strong chirality at two resonant frequencies and cause the refractive index of the RCP/LCP light to be negative from 1.23 to 1.31 THz for n+ and from 1.42 to 1.49 THz for n− as shown by the shaded regions in Fig. 7a, b. They were able to achieve an amplitude of 0.3 for the chirality at off-resonance frequency, which is much higher in comparison to values close to 10−5 for natural materials such as sugar and quartz. The efficiency of the corresponding change in the negative refractive index is quantified using the figure of merit (FOM) = −Re(n) / Im(n), which gets as high as 4.2 for LCP light. The conjugated gammadions by Zhou et al. [36] were numerically simulated for two different silicon conductivities of σ = 0 and 5 × 104 S/m. For σ = 0, they achieved large chirality around the resonance frequencies f1 = 0.7 THz and f2 = 1.1 THz, which, in turn, lead to negative refractive index n for LCP and RCP lights shown in the green and yellow-shaded regions, respectively, in Fig. 7c–e. At off-resonance frequency, they attained a chirality of 1.5 which is even higher than that obtained for the previously mentioned chiral structures. Furthermore, as the silicon conductivity is increased to 5 × 104 S/m, the chirality strength decreased causing refractive index values to become positive as shown by the blue (dashed) curves in Fig. 7c–e. The complementary twisted cross [37] exhibits negative refractive index around the resonant frequency points of 6.9 and 10.9 THz. Similarly, the multilayer spiral structure by He et al. [38] also demonstrated strong chirality and negative refractive index at the resonant transmission frequency of the LCP (t) and RCP (t+) waves as shown in Fig. 8a–c [38]. They further investigate how the refractive index changes from positive to negative as the design configurations such as the twist angle between the layers and the number of layers are changed.
Fig. 7

Retrieved effective parameters of the CMF based on the simulation data. a Real parts of the refractive index n and chirality k. b Real parts of the refractive indices for the LCP and RCP waves; reprinted from [40] with the permission of AIP Publishing. ce Another example of achieving negative refractive index from Zhou et al., dynamically controlled chirality structure based on conjugated gammadions. Refractive index for c LCP and d RCP obtained from numerical simulations with silicon island conductivity σ = 0 (red solid lines) and 5 × 104 S/m (blue dashed lines), which corresponds to laser fluence of 0 and 40 μJ/mm2 in experiments. Green (left) and yellow (right) shaded regions highlight negative values of refractive index and nLCP and nRCP, respectively. e Real part of the chirality parameter κ; reprinted with permission from [36], copyright (2012) by the American Physical Society

Fig. 8

a The transmission amplitudes of t1 and t2. b The transmission amplitudes for RCP (t+) and LCP (t) waves. c The retrieved real part of refractive index for RCP and LCP waves; reprinted from [38], copyright (2011), with permission from Elsevier

4 Polarization Controlled THz Stereometamaterials

As a broader and less investigated class of metamaterials, THz stereometamaterials designate structures that are realized using the same building blocks or meta-atoms but arranged differently in space and exhibiting distinct responses to THz waves as a direct result [57, 58, 59]. Stereometamaterial is still in its infancy, and tremendous fundamental knowledge can be gained through a correlated theoretical and experimental investigation.

This can be illustrated in one of our recent studies of perfect absorber structure consisting of two non-concentric copper rings, which showed rotationally asymmetric THz absorption and reflection properties at resonant frequencies depending on the polarization of the incident wave [59]. The investigation showed that such a THz device had a rotationally asymmetric absorption and reflection characteristics at resonant frequencies, i.e., dependent on the polarization of the incident wave.

More specifically, several devices were designed as arrays of unit cells, each of which consisting of a pair of non-concentric, slightly translated, and non-coplanar copper rings that still remain electromagnetically coupled by being separated only by a thin dielectric layer. The Cu rings had different diameters and were further separated from a Cu backplane by another dielectric spacer layer. This basic frequency selective stereometamaterial (FSS) is illustrated in Fig. 9. Devices were first modeled using multiphysics 3D finite element simulation as a function of the specific geometry and spatial arrangement of rings in order to determine expected spectral absorption responses in the THz [60, 61]. By utilizing simulation, we were thus able to investigate a large number of structures prior to carrying out actual fabrication, including, for example, getting better understanding of the effects of the center-to-center translation distances between the two constituent rings in both x and y in-plane directions. Selected structures were then lithographically fabricated, and THz time domain spectroscopy was used to experimentally measure the absorption of an incoming wave at normal incidence with different linear polarization angles, in the range 0.3–3.0 THz [61, 62].
Fig. 9

a Illustration of the unit cell of a THz stereometamaterial absorber showing the incident wave polarization of 0° (E field horizontal) and 90° (E field vertical). b Microscope image of a fabricated unit cell stereometamaterial. c Cross-sectional illustration showing the stacking of the rings and backplane

The simulated absorption spectra from a typical THz stereometamaterial are shown in Fig. 10a, as a function of incident wave polarization. Two absorption resonance frequencies can be distinguished at 0.725 and 0.790 THz. However, both resonances do not occur under the same conditions or strength. Instead, when the polarization changes from 90° (vertical) to 0° (horizontal), the absorption at higher frequency 0.790 THz strengthens, while the absorption at lower frequency 0.725 THz weakens, as indicated by the arrows. The two resonance peaks originate from different rings, as demonstrated in Fig. 10d, in which one can see that the absorption resonance at 0.725 THz in red is slightly red-shifted from the one associated with the front or larger ring when taken individually, while the resonance at 0.790 THz in black is slightly red-shifted from that associated with the back or smaller ring when taken individually. Experimental measurement results (dashed lines) were in good agreement with the predicted absorption curves (solid lines), both in frequency and strength, as shown in Fig. 10b. Figure 10c is a color map representation of the measured absorption spectrum as a function of incident wave polarization, illustrating the shifting nature of the absorption with polarization in the stereometamaterial device.
Fig. 10

a Simulated absorption spectra for different incident wave polarizations (colored) with the polarization angle indicated. b Comparison between simulated (solid lines) and experimentally measured (dashed lines) absorption spectra as a function of polarization. c Strength map of experimentally measured absorption versus frequency and polarization. d Comparison of the absorption spectra between single-ring absorbers (dashed curves) and stereometamaterial absorber in 0° and 90° polarizations (solid curves)

Strengthened by the good agreement between the experimental and simulation results, we were able to gain deeper fundamental insight into the physical mechanisms at the origin(s) of the absorption features, including the shifting of the peak as a function of polarization. Specifically, using the multiphysics finite element simulation, we were able to quantitatively evaluate (i) the electric field of the electromagnetic wave within the stereometamaterial structure in the vicinity of the rings and backplane and (ii) the electric current densities on the rings and backplane, as a function of incident wave polarization angles. For example, in the case of a 90° incident wave polarization, i.e., when the resonance occurs at 0.725 THz, Fig. 11a, c, e shows the magnitude of the electric field on the front larger ring, the back smaller ring, and the backplane, respectively, while Fig. 11b, d, f shows the x-component of the current density in those same respective planes with the curved arrows showing the directions of current flow. Analysis of these features revealed the emergence of electric dipoles on the rings. Additionally, we found that (i) the dipole/currents in the front ring (which is the ring resonating at 0.725 THz) induced a matching dipole/currents in the backplane and that (ii) it was the dipole/currents in the backplane that were at the origin of the dipole/currents in the back ring. In other words, the features in the back ring were not directly induced from the front ring dipole/currents, which was in direct contrast to the case when the rings were concentric (i.e., symmetric structure). As a result, and because the polarization is in the direction along which the rings are translated, the dipole on the back ring was not symmetric and the top pole is stronger than the bottom pole, as confirmed in Fig. 11c, while the dipole on the front ring remained symmetric at resonance (Fig. 11a).
Fig. 11

Electric field intensity and x-component of the current density when incident wave is polarized vertically (90°), at resonance at 0.725 THz. a, b In the plane of the front larger ring. c, d In the plane of the back smaller ring. e, f In the backplane

Similarly, in the case of a 0° incident wave polarization, i.e., when the resonance occurs at 0.790 THz, Fig. 12a, c, e shows the magnitude of the electric field on the front larger ring, the back smaller ring, and the backplane, respectively, while Fig. 12b, d, f shows the y-component of the current density in those same respective planes with the curved arrows showing the directions of current flow. Similar to the previous case, the back ring (which is the ring resonating at 0.790 THz) induced image poles on the backplane, which, in turn, induced a dipole and associated currents in the front ring. However, unlike the previous case, the poles on both the front ring and the back ring had similar strengths, i.e., the dipole on the front ring was symmetric and the dipole on the back ring was symmetric as well at resonance. This can be confirmed by looking at Fig. 12a, c and is a consequence of the polarization of the incident wave being perpendicular to the direction along which the rings are translated.
Fig. 12

Electric field intensity and y-component of the current density when incident wave is polarized horizontally (0°), at resonance at 0.790 THz. a, b In the plane of the front larger ring. c, d In the plane of the back smaller ring. e, f In the backplane

Based on these findings, the absorption spectra at 90° and 0° incident wave polarization can be interpreted as a wave interaction phenomenon between two waves. The first one originated from the reflection from the overall effective dipole on the stereometamaterial FSS. The other wave arose from the mirror image dipole to that of the FSS with respect to the backplane, after undergoing multiple internal reflections through a cavity, formed by the FSS and the metal backplane, as it propagates. At resonance, a perfect absorption occurred because of the destructive interference between these two waves.

In the particular case of a 45° incident wave polarization, a similar analysis revealed that at 0.725 THz, the polarization of the reflected wave was actually still nearly vertical, while at 0.790 THz, the reflected wave was still nearly horizontal, a direct result of the formed dipoles P1 and P2 at those respective frequencies, as shown in Fig. 13f, g. The reason why dipoles formed on the rings was not in the same directions as the incident wave polarization could be interpreted by the phenomenon of optical forces arising from dipole-dipole interactions [58, 63, 64, 65, 66]. Because of the non-concentric ring geometry of the stereometamaterial structure investigated here, the optical forces created between the dipoles led to tangential forces on the electrons along the rings, the movement of electrons, and their possible redistribution. In the case of a 0° and 90° incident wave polarization, the tangential component of the forces canceled each other and there was no charge redistribution. Therefore, the reflected wave has the same polarization as the incident wave. But for a 45° polarization, as a direct consequence of the peculiar geometrical arrangement of the rings with respect to the polarization, charges are redistributed to result in either a nearly vertical or horizontal effective dipole instead, at 0.725 and 0.790 THz, respectively.
Fig. 13

Visualizations of the electric field intensity maps in different planes within the stereometamaterial and a 0.725 and 0.790 THz, when incident wave has a 45° polarization. a, b The map in the plane of the front larger ring, while c, d are for the plane of the back smaller ring. a, c At 0.725 THz, while b, d At 0.790 THz. f, g The corresponding intensity maps of the reflected electric field in a plane located 50 μm away from the absorber at the indicated frequencies, respectively

5 Remark and Conclusion

In this review, we surveyed and thoroughly reviewed recent development of more sophisticated metamaterial structures called chiral metamaterials and stereometamaterials in the THz frequency region and their ability to perform as polarization waveplates, filters, modulators, etc. More and more new and developed concepts of chiral and stereometamaterials have appeared since the last few review articles [27, 28, 29, 67]. THz frequency is critically important and has become the center of research as it has the potential to find and reveal unknown nature of the fingerprints of many naturally occurring molecules. It is reasonable why THz chiral metamaterials and stereometamaterials have become so exciting. The interest in chirality and stereoisomers can be related to naturally occurring molecules and materials that we would like to explore. Using such artificially engineered meta-atoms which constitute metamaterials, we can mimic some of these exotic properties and hope to unveil some of the natural phenomena associated with it. Such new development can bring THz metamaterials to a new horizon of applications. The exploration of such exquisite metamaterials will continue and contribute to the rapidly developing new technologies.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Elizabath Philip
    • 1
  • M. Zeki Güngördü
    • 1
  • Sharmistha Pal
    • 1
  • Patrick Kung
    • 1
  • Seongsin Margaret Kim
    • 1
  1. 1.Electrical and Computer Engineering DepartmentUniversity of AlabamaTuscaloosaUSA

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