Tunable and nonlinear metamaterials for controlling circular polarization

Circularly polarized light is used in many important applications, such as circular dichroism spectroscopy,¹ ultrafast magnetization control,^2,3 and manipulation of quantum states.⁴ In recent years, planar metamaterials comprising metallic or dielectric artificial structures with sizes smaller than the wavelength of light have been shown to perform various novel optical functions based on their shapes.^5,6 They particularly gained renewed attention for their potential to control the circular polarization state of light. The symmetry of the structure plays a particularly important role in controlling polarization-sensitive optical phenomena by using these artificial structures. For example, to control the anisotropy of linearly polarized light, a birefringent structure, in which each polarized light in the X or Y direction is an eigenstate and has a different refractive index, is used. On the other hand, to perform circular polarization control, it is important to design a metamaterial having appropriate symmetry and whose eigenstates are circularly polarized light. It is also possible to convert linearly polarized light to circularly polarized light by adjusting the anisotropy of the birefringent structure or the oblique incident angle. However, in these cases, circular polarization is not an eigenstate, and the optical response changes, depending on the direction of incident polarization. Therefore, this article will mainly focus on the metamaterials with isotropic linear response.

A circular polarization-sensitive linear optical response is an optical activity observed in a chiral metamaterial with no reflection symmetry. In recent years, tunable chiral metamaterials that can actively control the magnitude of the polarization effect have been actively studied from the terahertz to the optical frequency region. In nonlinear response, metamaterials with rotational symmetry enable circular polarization control. By designing the shape of these metamaterials, wavelength conversion and propagation control can be performed simultaneously, which are difficult to generate with nonlinear optical crystals in nature, and can be achieved in the vacuum ultraviolet (VUV) and extreme ultraviolet (EUV) regions. This article introduces recent studies for circular polarization control highlighting tunable chiral metamaterials (Secs. II and III) and nonlinear metamaterials with rotational symmetry (Sec. IV). Then, our perspective on future research directions is provided in Secs. V and VI.

Optical activity is a phenomenon in which the polarization state (azimuth angle and ellipticity angle) of transmitted light changes due to the difference in the complex refractive index of left- and right-handed circularly polarized light in a chiral material, which does not possess mirror symmetry.⁷ The sign of the polarization change depends on the handedness of the chirality. Thus, the shapes of the polarization rotation spectra of the enantiomers are identical, but their signs are opposite. Also, the sign of the polarization change does not depend on the direction of light incidence (reciprocity). Optical activity was discovered by Arago in 1811 and has been essential in the field of chemistry to detect the chirality of molecules.

The absolute values of the observed polarization rotation in the single-layer chiral metamaterials were too small for practical application to polarization control. Therefore, the researchers attempted to increase the polarization effect by enhancing the anisotropy in the propagating direction of light at normal incidence by making double-layered^21–24 and multi-layered²⁵ chiral metamaterials at various frequencies from visible light to microwave. Negative indices of refraction, theoretically predicted by Pendry,²⁶ have been also realized using such chiral metamaterials with large optical activity.^21,24,25,27 On the other hand, stacking achiral structures with different in-plane orientations have been demonstrated to achieve large chiral effect, and almost perfect circular polarization was realized at specific wavelengths.^23,28,29 Moreover, Yin et al. demonstrated that metallic nanorod systems function as the plasmonic analog of the Born–Kuhn model of chiral media.³⁰ One nanorod was regarded as one oscillator in the Born–Kuhn model, and two nanorods with a length of about 220 nm were displaced with 120 nm, with a 90° angle, as shown in Fig 1(c). As shown in Fig 1(d), when the quarter of the wavelength of the incident light is equal to the distance between the nanorods, the circularly polarized light resonates to the structure. Here, depending on the helicity of the incident circularly polarized light, the resonance wavelength is blueshifted in an antibonding mode because the charges with the same sign approach each other. Or it can shift to a bonding mode in which the resonance wavelength is redshifted because the charges with different signs approach each other are excited. Since the loss becomes large at the resonance wavelength, the transmittance of the non-resonant circularly polarized light becomes relatively large, resulting in circular dichroism. The observed polarization spectrum fits well in Eq. (17), indicating that the analogy of the Born–Kuhn model holds even in the plasmonic region.³⁰ 

Three-dimensional chiral structures are common in nature such as the double helix structure of DNA. Such a three-dimensional chiral structure has already been put into practical use as a helical antenna having circular polarization selectivity in the microwave region,³¹ but it has been difficult to create three-dimensional metamaterial in the optical frequency region. Wegener and his colleagues fabricated a spiral structure inside a photocurable resin by three-dimensional laser lithography and used it as a template to create a submicron-scale three-dimensional metal spiral structure.³² This structure has been shown to exhibit broadband and high circular polarization selectivity in the infrared region.^32,33 They have also developed a unique laser three-dimensional microstructure fabrication technology³⁴ inspired by the stimulated emission depletion microscopy (STED) known for realizing super-resolution microscopy. As a result, a finer three-dimensional helical array structure was formed.³⁵ On the other hand, Mark et al. produced a smaller metal 3D spiral structure by performing vapor deposition from an oblique direction while rotating the substrate and observed large optical activity in the visible region.³⁶ A chemical technique for producing an artificial three-dimensional metal chiral structure with large optical activity by spirally modifying metal nanoparticles using a biopolymer such as DNA as a template has also been developed.^37,38

Since the optical response of a metamaterial is determined by its shape, it is unfeasible to change the response once it is manufactured. Therefore, tunable magnitude and frequency of the optical response can be achieved by constructing the metamaterial with a substance whose shape and physical properties can be actively controlled by external stimuli, such as light, heat and electricity.³⁹ Various methods have been investigated to achieve tunability by which modulated polarization becomes viable. This is, in particular, essential for the terahertz region where the polarization modulation elements are insufficient.

Active control of chiral metamaterials was first demonstrated by photoexcitation of silicon in the terahertz frequency region. In this region, a high-resistance silicon substrate manufactured by the floating-zone method is transparent but carriers generated in silicon by optical excitation have a metallic response. Kanda et al. achieved optically pumped terahertz polarization modulation using a two-dimensional array of metallic gammadion structures fabricated on a high-resistance silicon substrate.⁴⁰ They fabricated a gammadion-shaped metal pattern with a 100-μm period on a high-resistivity silicon substrate, as shown in Fig. 2(a). Optical activity is not observed in a chiral metamaterial made of a single-layer metal thin film with a thickness of about 100 nm because the film thickness is too small for a terahertz wave, whose typical wavelength is of the order of several hundreds of micrometers. However, the photoexcitation produces a gammadion-shaped photocarrier distribution complementary to the gammadion-shaped metal pattern in the silicon substrate, as shown by the yellow part in Fig. 2(a). Since the spatial dispersion effect is increased by the pseudo-double-layer structure formed by the combination of the metal structure and the photoexcited carriers, the optical activity is observed only during photoexcitation. They also confirmed that the amplitude of the optical activity depends on the pump power, and the experimental results are well reproduced by simulation. Subsequently, Zhou et al. achieved much larger optical rotation controlled by photoexciting a gammadion bilayer structure separated by a thin polyimide layer.⁴¹ In this method, the optical activity is controlled by extinguishing the chirality of the bilayered chiral structure that originally exhibits a polarization rotation of about 40° (maximum) by photoexcited carriers.

Active control using photoexcited carriers offers high-speed control, but it is difficult to implement it as a compact device. Thus, for actual device applications, electrical modulation is required. As a candidate for providing electrical control in the terahertz region, graphene, which can control plasmonic resonance from terahertz to mid-infrared frequencies by electrical control of Fermi level, has attracted attention.⁴² Kim et al. succeeded in active control of circularly polarized light in the terahertz range by electrically controlling the resonance frequency of a chiral structure by placing graphene adjacent to one of the double-layered metal chiral structures [Fig. 2(b)].⁴³ On the other hand, a method of tuning circular polarization by mechanical deformation of chiral metamaterials has been developed using “Kirigami.”⁴⁴ Kirigami is a paper-cutting technique that enables three-dimensional shape control by applying in-plane pressure to deform the substrate. By using this technique, Choi et al. showed that the polarization rotation of more than 30° can be actively controlled in the terahertz region [Fig. 2(c)].⁴⁵ They have also successfully measured, using this device, terahertz circular dichroism of biological samples, such as a leaf and an elytron of the green beetle.

However, these studies on tunable chiral metamaterials focused on controlling the magnitude of polarization rotation and did not allow changing the sign of polarization, which is required for the polarization modulator. Therefore, it is necessary to switch the handedness of the chirality of structures to switch the sign of the optical activity. Such chiral switching was observed when a chiral molecule is irradiated with ultraviolet light,⁴⁶ but the magnitude of polarization change is only of the order of mdeg. Thus, it is attempted to realize such chiral switching by a metamaterial having a giant optical activity.

Switching the sign of polarization of chiral metamaterials was first reported by Zhang et al.⁴⁷ The presented device switches the sign of polarization rotation via short-circuiting and photoexcitation of silicon, thereby switching the resonance conditions for left- and right-handed circularly polarized light. In the infrared region, Yin et al. showed that the sign of polarization rotation can be switched by combining a phase-change material (Ge₃Sb₂Te₆) with a chiral metamaterial to shorten the operating wavelength of this technique.⁴⁸ Controlling the sign of polarization by controlling the orientation direction of the DNA-based metal nanospirals using a chemical method has also been demonstrated by utilizing a chemical orientation control of DNA.⁴⁹ 

Then, it was realized to switch the mechanical shape of the metamaterial itself between enantiomers, as shown in Fig. 3(a). Kanda et al. achieved a pioneering result realizing such enantiomeric chiral switching with all-photo-induced optical activity.⁵⁰ In this scheme, the chiral-patterned photocarrier distributions are directly generated in a bare high-resistivity silicon substrate by a spatially intensity-modulated pump beam as shown in Fig. 3(b). The distribution of photoexcitation carriers has chirality so that the photo-induced gammadion-array structure functions as a chiral metamaterial. Since the intensity profiles of the optical pump beam are modulated using a spatial light modulator (SLM) and there is no metal structure, it is possible to easily reverse the handedness of the chirality of the photoexcited chiral metamaterials by switching the pattern input to the SLM. They demonstrated that the THz polarization rotation spectrum can be inverted by enantiomerically switching the excited chiral pattern and shifted by changing the size of the gammadion-array, although the magnitude of the polarization rotation is less than 1°.

To broaden the tunable range of the amplitude of optical activity, mechanical deformation of the metal structure itself is a promising method, but it is seemingly difficult to realize the enantiomeric mechanical deformation, as shown in Fig. 3(a). Kuzyk et al. realized the chiral switching in the optical region with a polarization rotation of several hundred mdeg by controlling the relative angle of two metal nanorods by DNA-regulated conformation change driven by adding specifically designed DNA fuel strands. [Fig. 3(c)].⁵¹ On the other hand, Kan et al. found a planar spiral structure for realizing an enantiomeric structural change. They found that this structure not only generates chirality when deformed vertically but also reverses the sign of handedness depending on the direction of deformation [Fig. 3(d)].⁵² They vertically deformed the structure using a pneumatic force that switched the chirality of the structure. Furthermore, by measuring the transmission polarization spectrum of the terahertz wave, the sign can be switched, while maintaining the polarization rotation spectrum shape depending on the direction of deformation. The magnitude of the observed polarization rotation has reached about 30°. Regarding the vertical deformation of a spiral structure, a method using electrostatic force⁵³ and liquid crystal deformation⁵⁴ has also been proposed. Very recently, Lin et al. succeeded in arranging multiple nanoparticles of different types and sizes using light and switching the handedness of the complex structures⁵⁵ [Fig. 3(e)]. The periodic arrangement of such a structure can make it suitable as an enantiomeric chiral metamaterial in the visible region.

Chirality plays an important role in circular polarization selectivity in the linear response, while rotational symmetry of the structure plays an important role in selecting rules for circular polarization in the nonlinear optical response. This has long been understood based on the conservation law of angular momentum in nonlinear optical processes.⁵⁶ The left- and right-handed circularly polarized photon each has an angular momentum of $±ℏ$⁠. In addition, elementary excitation in material and the crystal itself can also contribute to the conservation law of angular momentum. In the interaction between light and matter, angular momentum is exchanged between them. In this case, the conservation law of angular momentum must be satisfied. Therefore, in a second-harmonic generation (SHG), two left-handed circularly polarized photons are converted into one circularly polarized photon, and the angular momentum $J E M=2ℏ$ of the electromagnetic field loses when the two left-handed circularly polarized photons disappear. Therefore, it is required that the angular momentum of $2ℏ$ be given back to the electromagnetic field from the material to satisfy the conservation law of angular momentum. However, such an optical process does not occur because the angular momentum that one photon can possess is at most ħ. On the other hand, when a material has discrete N-fold rotational symmetry about an axis, such as a crystal, it is possible to define the pseudo-angular momentum $J c=±Nnℏ$ (n is an integer) around that axis. For example, when a crystal has threefold rotational symmetry, $Δ J c=±3nℏ$ holds, and the exchange of angular momentum with the crystal is allowed in integer multiples of $3ℏ$⁠. In this case, since the momentum of $−3ℏ$ can be received from the crystal during SHG, the angular momentum to be given from the material to the electromagnetic field is $−ℏ$ instead of $2ℏ$⁠, as described above. Therefore, in a crystal with threefold rotational symmetry, the SHG is allowed. In this process, two left-handed circularly polarized photons generate one photon with angular momentum $−ℏ$⁠, that is, a right-handed circularly polarized photon. The helicity of the circularly polarized light of the second harmonic is opposite to that of the fundamental wave. As described above, the relationship between the SHG process and the conservation law of angular momentum in a crystal with threefold rotational symmetry was described by Bloembergen about 50 years ago at the dawn of nonlinear optics.^56,57 In the case of a crystal having threefold rotational symmetry, the generation of the fourth harmonic is also allowed in the excitation of circularly polarized light, and at this time, the helicity of the circularly polarized light of the fundamental wave and the harmonic becomes the same. In general, if the structure has N-fold rotational symmetry, the generation of harmonics of the same (reverse) circular polarization of order N + 1 (N−1) is allowed.⁵⁸ Note that a similar polarization selection rule held for the down-conversion process, namely, the terahertz generation by femtosecond laser pulses via impulsive stimulated Raman scattering.⁵⁹ 

Furthermore, the relationship between the rotational symmetry and the nonlinear optical response of metamaterials was recently established, although the nonlinear optical response of plasmonic structures with no rotational symmetry has been extensively studied.^60–63 Konishi et al. reported that a threefold rotationally symmetric plasmonic nanostructure [Fig. 4(a)], in which triangular gold nanostructures were periodically arranged on a sapphire substrate, was irradiated at 780 nm with a circularly polarized femtosecond laser to generate a second-harmonic wave and measured the polarization state of the generated second-harmonic wave.⁶⁴ As a result, the circularly polarized second-harmonic wave was generated with the opposite helicity to the fundamental wave. When a similar experiment was performed with a onefold rotationally symmetric structure, both left- and right-circular polarized second harmonics were generated. In the case of a sixfold rotationally symmetric structure, SHG was not observed. Simultaneously, Chen et al. showed that plasmonic nanostructures with fourfold rotational symmetry [Fig. 4(b)] produce counter-rotating circularly polarized third harmonic generation (THG).⁶⁵ These experiments revealed that the relationship between the rotational symmetry and the selection rule for circular polarization in the nonlinear optical response holds even in the macroscopic structure of metamaterials.

That is, when the structure has (n + 1)-fold rotational symmetry and the structure rotates by ϕ in the plane, the resulting circularly polarized light demonstrates a phase change of (n + 1)ϕ. Since ϕ depends on the orientation of the structure in a plane perpendicular to the axis of rotational symmetry, it is possible to control the phase of harmonics by controlling the in-plane rotation angle of the structural units of the metamaterial [Fig. 4(c)].

By applying this principle, the phase of harmonics emitted from each unit of the metamaterial can be controlled by individually changing their in-plane directions. The possibility of such phase control was experimentally confirmed by demonstrating propagation control of the harmonic waves in the far field.⁶⁶ By using this technique, harmonic propagation control by means of diffraction,⁶⁶ holography,⁶⁸ condensing,⁶⁹ and polarization control⁷⁰ has been demonstrated. The operation of propagating the wavelength-converted light by in-plane rotation has been performed even with a onefold rotationally symmetric structure, such as a split ring resonator.^71–74 In this case, both the left- and right-circular polarized light whose wavelengths are converted are emitted. Note that Eq. (20) holds even in the case of a linear response. That is, when circularly polarized light enters the twofold rotationally symmetric metamaterial, it is converted into counterclockwise circularly polarized light, and its phase can be controlled in the in-plane direction of the metamaterial structure. This principle is used to realize a flat lens with a metamaterial: metalens.⁷⁵ 

In recent years, the possibility of conversion from linear to circular polarization in a nonlinear process has been demonstrated by using a chiral metamaterial for a rotational symmetry.^78,79 Equation (22) represents the polarization state of a harmonic wave generated from a chiral structure having no mirror symmetry. Here, in the case of $α≫β$ or $α≪β$⁠, the harmonic wave is circularly polarized even if the fundamental wave is linearly polarized: $E +(ω)= E −(ω)$⁠. Chen et al. experimentally demonstrated that a linearly polarized fundamental beam incident on a plasmonic chiral nanostructure with threefold rotational symmetry, as shown in Fig. 5(a), generates almost perfect circularly polarized second harmonics at a specific wavelength [Fig. 5(b)]. They also demonstrated conversion from linear to circular polarization in the third-harmonic generation process in a plasmonic chiral nanostructure with fourfold rotational symmetry.⁷⁹ 

In recent years, practical metamaterial devices that can replace conventional optical elements such as metalenses, which can be thin and aberration-free unlike conventional lenses, have been demonstrated.⁷⁵ The above-mentioned rotationally symmetric nonlinear metamaterial simultaneously performs wavelength conversion and propagation control.^66,68–74 Many of the findings obtained in the current research should be applied to wavelength conversion and propagation control in the wavelength region where light wave control is challenging, that is, in the extremely short-wavelength region such as the vacuum and extreme ultraviolet region. This section discusses the possibilities of such a deployment.

Coherent circularly polarized light has important applications in the vacuum and extreme ultraviolet regions, such as nanoscale imaging,⁸⁰ element-selective ultrafast dynamics measurement,⁸¹ spin-selective angle-resolved photoemission spectroscopy,^82,83 biological circular dichroism,⁸⁴ and magnetic circular dichroism (MCD).⁸⁵ In recent years, the evaluation of masks for EUV lithography⁸⁶ has also been becoming an important application of EUV light sources in the industry. When considering such applications, downsizing the light source is crucial. Generating ultrashort-wavelength coherent light on a tabletop by laser-based wavelength conversion technology has been studied as a high-harmonic generation (HHG)⁸⁷ in which high-order harmonics are emitted from a sample by a non-perturbative nonlinear optical process that occurs when a material is irradiated with a high-intensity ultrashort pulse laser. This phenomenon was first discovered by focusing an ultrashort pulse laser on a gas.⁸⁸ Since HHG generated from isotropic gas is usually linearly polarized light, it is necessary to use a polarization element to make it circularly polarized. However, in the extremely short-wavelength region, the polarization control element is insufficient; thus, the reflection elements must be used resulting in complex setup and optical loss.⁸⁹ Therefore, in recent years, methods for directly generating circularly polarized high harmonics by making full use of advanced ultrashort pulse laser control technology have been reported; Cohern et al. experimentally demonstrated circularly polarized HHG with high efficiency by irradiating superimposed circularly polarized fundamental and second-harmonic wave with opposite helicity.^90,91 They showed that the conservation law of angular momentum plays an important role also in considering the possibility of circularly polarized HHG. That is, the circularly polarized HHG is allowed when the absolute value of the sum of the spin angular momentums of the fundamental wave and the second-harmonic wave related to the HHG process is $±ℏ$⁠. Furthermore, they demonstrated that the polarization state of HHG can be controlled by controlling the polarization state of the fundamental and the second-harmonic waves.⁹¹ Subsequently, it was also reported that non-collinear superposition of counter-circular polarized light could generate spatially separated circularly polarized HHG pulses for each order.^92,93 These circularly polarized HHG light sources have already been demonstrated for use in EUV MCD measurements⁹¹ and photoelectron circular dichroism.⁹⁴ 

Is it possible to generate circularly polarized higher-order harmonics by utilizing the symmetry of a nonlinear medium instead of controlling the polarization state of the excitation wave? This corresponds to extending the selection rule for circular polarization based on the rotational symmetry of structures to a high-order harmonic region. Although the possibility of controlling the polarization state of harmonics by aligning gas molecules has been discussed,^95,96 aligning molecules requires advanced experimental techniques. However, if the nonlinear medium is a solid crystal, such difficulties do not occur because the constituent atoms are originally aligned. Therefore, Ghimire et al. succeeded in observing the generation of higher-order harmonics from solids.⁹⁷ When an ultrashort pulse laser with a center wavelength of 3.25 μm was incident on a ZnO crystal, high-order harmonics up to the 25th order (about 8 eV) were generated. Since the solid crystal itself has rotational symmetry, it is expected that polarization control of higher harmonics due to rotation symmetry is possible. Later, Saito et al. experimentally demonstrated that the circular polarization selection of higher harmonics can be controlled owing to the rotational symmetry of the crystal.⁹⁸ They observed high-order harmonics up to the eighth order from GaSe crystals with threefold rotational symmetry and that circularly polarized harmonics with different helicities were generated depending on the harmonic order. On the other hand, higher-order harmonic generation from graphene has been recently reported,^99,100 and the possibility of circularly polarized HHG utilizing the sixfold rotational symmetry of graphene has been theoretically shown by first-principles calculations.¹⁰¹ As described, the relationship between the rotational symmetry of the structure and the circular polarization selection rule provides an important guideline for determining the polarization state even in the generation of higher harmonics.

In recent years, it has also been reported that the enhancement and control of high-order harmonics can be realized using a metal or photonic nanostructure; Vampa et al. demonstrated that by forming a metal nanorod array structure on the silicon surface, the observed higher-order harmonics in the visible region were enhanced by one order of magnitude due to the electric-field-enhancing effect of plasmon resonance.¹⁰² Han et al. also reported that HHG from metal-coated sapphire nanocone array structures was enhanced in the EUV region.¹⁰³ Krasavin et al. theoretically showed the possibility of generating higher harmonics from the spiral-shaped metal nanostructure itself.¹⁰⁴ The increase and control of higher harmonics via an artificial structure have been reported recently in semiconductors¹⁰⁵ and graphene.¹⁰⁶ Although artificial structures with one- or twofold rotational symmetry have been mainly used for controlling higher harmonics so far, it may be possible to control the circular polarization of higher harmonics by artificial nanostructures owing to the higher rotational symmetry of the structures. In the case of a solid crystal, the types of rotational symmetry are limited; however, for an artificial structure, it can be designed freely. As a result, if high-order circularly polarized light can be generated in an extremely short-wavelength region by simply placing such an artificial structure onto the optical path of the fundamental wave, more users would easily use circularly polarized high-order harmonics.

When considering practical applications, the intensity of the generated wavelength-converted light is important. The laser damage threshold of the nonlinear medium determines the upper limit of that intensity. This is crucial when using a solid or an artificial structure as a nonlinear medium for HHG, unlike a gas. In particular, the low damage threshold of metal nanostructures¹⁰⁷ makes it difficult to increase the maximum intensity of HHG, even if it can contribute to enhancing HHG when compared at the same excitation intensity. As a solution to this problem, attention has been recently paid to a dielectric metamaterial that does not use a metallic nanostructure.¹⁰⁸ In general, dielectrics such as SiO₂ and Al₂O₃ have much higher laser damage threshold compared to metals.¹⁰⁹ Therefore, by using a dielectric material for the nonlinear medium, it becomes possible to increase the excitation light intensity. This not only contributes to increasing the intensity of HHG but also raises the cutoff frequency to generate higher-order harmonics with shorter wavelengths.^97,110 It is expected that the development of a method of generating a harmonic having a wavelength shorter than that of vacuum ultraviolet using an all-dielectric metamaterial structure will become more important in the future. Actually, the generation of 197-nm¹¹¹ and 185-nm¹¹² coherent light using the SHG and THG, although not a higher harmonic, from dielectric metamaterials has been reported.

Relatedly, we have been focusing on dielectric free-standing thin films (nanomembrane) with a thickness of less than the optical wavelength, i.e., several hundred nanometers. Lee et al. successfully demonstrated to generate high-order harmonics up to 50 eV by a 100-nm-thick SiO₂ nanomembrane as a nonlinear medium irradiated by nearly single-cycle 800-nm ultrashort pulsed light,¹¹³ which is the shortest wavelength of solid-state higher harmonics reported so far.¹¹⁰ In addition, dielectric nanomembranes have the advantage of avoiding the effects of phase disturbances due to self-phase modulation caused by high electric field strength, which is a problem with bulk samples.¹¹⁴ We also recently demonstrated THG in the vacuum ultraviolet (VUV) region from dielectric nanomembranes with sufficient intensity for spectroscopic applications,¹¹⁵ such as spin-selective laser photoelectron spectroscopy and VUV biomolecular circular dichroism. The submicron thickness of the nanomembranes is optimal for maximizing VUV generation efficiency and prevents self-phase modulation and spectral broadening of the fundamental beam. The observed VUV output generated from a commercially available 300-nm SiO₂ nanomembrane contains up to 107 photons per pulse at 157 nm at a 1-kHz repetition rate, corresponding to a conversion efficiency of 10−6. Moreover, the central VUV wavelength can be tuned in the 146–190-nm wavelength range simply by changing the fundamental wavelength [Fig. 6(a)] because the nonlinear medium does not satisfy the phase-matching condition in this method. We have also shown that an epitaxial γ-Al₂O₃ nanomembrane, which can be fabricated from a γ-Al₂O₃ thin film epitaxially grown on a silicon substrate,¹¹⁶ enables high generation efficiency. Nanomembrane metamaterials on which artificial nanostructures are formed are becoming important for controlling higher harmonics in extremely short-wavelength regions. As an example, we fabricated a γ-Al₂O₃ photonic crystal nanomembrane on which periodic nanoholes were fabricated. We demonstrated that circularly polarized coherent light in the VUV region is generated through third-harmonic generation [Fig. 6 (b)].¹¹⁷ This experiment demonstrates circularly polarized third-harmonic generation, but circularly polarized higher-order harmonic generation in a shorter wavelength region is expected to be also observed. Such photonic crystal nanomembrane structures will be an important platform for realizing circular polarization operation in the extremely short-wavelength region.

The development of tunable metamaterials has been closely linked to advances in microelectromechanical systems (MEMS) technology.¹¹⁸ The functionality required for tunable metamaterials often leads to the development of novel MEMS technologies (or vice versa). To achieve tunability by mechanical deformation of metamaterials, methods that utilize in-plane deformation have been mainly studied.^119–122 On the other hand, studies have also been performed to realize functionality by deformation in the vertical direction perpendicular to the surface, but most of the methods involved the control of the warpage using the effect of electrostatic force or thermal expansion.^123–127 However, in this method, it is difficult to realize large deformation in the vertical direction, and a larger deformation is required for enantiomer switching of a chiral metamaterial. Even with the pneumatic drive we demonstrated, only about one-third of the diameter of the spiral can be deformed,⁵² and a high-speed drive is also difficult.

Therefore, we have developed a method for mechanically pulling chiral metamaterials in the vertical direction to achieve large vertical deformation directly (Fig. 7).¹²⁸ In this method, the spiral structure is largely deformed in the vertical direction by fixing both ends of the spiral to different substrates and mechanically controlling the distance between them. Since the optical rotation depends on the amount of deformation in the vertical direction, it allows achieving perfect tunability for circular polarization of transmitted light.

If such a large deformation is possible, since the deformation will be large, a structural design that prevents stress concentration and does not break is required. For example, in the case of this spiral structure, when conducting long and flexible large deformation, it is important to clarify, both experimentally and theoretically, the optimal structure that prevents both the stress concentration at the joint surface and the strong resonance with light. The knowledge obtained from such a large vertical deformation can be applied to applications such as MEMS actuators with large strokes in addition to chiral metamaterials.

On the other hand, technologies to miniaturize MEMS and using it for nanostructure control are also being developed. Recently, Chen et al. succeeded in observing the giant optical activity in the optical region by creating a three-dimensional metal chiral nanostructure by applying Kirigami technology at the nanoscale.¹²⁹ Studies on the mechanism and control of complex three-dimensional deformation of the Kirigami structure have been studied from the viewpoint of structural mechanics.¹³⁰ If such knowledge can be applied to a Kirigami nanostructure, it would be possible to realize an extremely small-sized active circular polarization modulator in the optical and shorter wavelength region.

A chiral Kirigami nanostructure can also be considered as a rotationally symmetric metamaterial; hence, the generation of harmonics is expected. In particular, the generation of harmonics from metallic chiral nanostructures produces very large circular dichroism as described.^78,79 If changes in the Kirigami structure can provide tunability to the three-dimensional chirality, it may be possible to actively control the degree of circular polarization of wavelength-converted light, including higher-order harmonics. This can lead to the realization of a new device that realizes active polarization modulation in the extremely short-wavelength region, such as the VUV and EUV regions.

In this article, we have outlined current and future research trends on tunable chiral metamaterials and nonlinear metamaterials with rotational symmetry that enable circular polarization control. Here, we focused on the metamaterials with isotropic linear response.

In the early 2000s, when metamaterials research began, research was being conducted based on whether a unique optical phenomenon such as a negative refractive index would occur. We are now at the stage of developing metamaterials into practical light control technologies. In particular, metamaterials and metasurfaces are very promising and important for light wave control in wavelength regions where practical optical elements fail to perform, such as the terahertz, vacuum ultraviolet, and extreme ultraviolet regions.

In addition to their utilization for applications, many points remain to be elucidated in terms of basic physics. For example, what is the optimal structural resonance to increase the higher-order non-perturbative nonlinear optical response? If rotational symmetry and chirality coexist, how do they affect the HHG? What is the optimal structure to cause mechanical three-dimensional structural change? In particular, future studies are needed to clarify the effects of the symmetry of matter, the symmetry of the artificial structure, and the symmetry of the optical electric field on circular polarization control. To advance these studies, we envision that metamaterials should be integrated with other research fields, such as MEMS and strong electric field science.

We thank H. Sakurai for helpful discussion. This work was supported by JST PRESTO (No. JPMJPR17G2), JSPS KAKENHI (Nos. 18H01147 and 18H01843), MEXT Q-LEAP (No. JPMXS0118067246), MEXT Photon Frontier Network Program, and the Center of Innovation Program funded by the Japan Science and Technology Agency.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.