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Abstract
Nowadays, the manipulation of the chiral light field is highly desired to characterize chiral substances more effectively, since the chiral responses of most molecules are generally weak. Terahertz (THz) waves are related to the vibration-rotational energy levels of chiral molecules, so it is significant to actively control and enhance the chirality of THz field. Here, we propose a metal/magneto-optical (MO) hybrid Pancharatnam-Berry (PB) phase structure, which can serve as tunable broadband half-wave plate and control the conversion of THz chiral states with the highest efficiency of over 80%. Based on this active PB element, MO PB metasurfaces are proposed to manipulate THz chiral states as different behaviors: beam deflector and scanning, Bessel beam, and vortex beam. Due to the magnetic-tunablibity, these proposed MO PB metasurfaces can be turned from an “OFF” to “ON” state by changing the external magnetic field. We further investigate the near-field optical chirality and the chirality enhancement factors in far field of the chiral Bessel beam and vortex beam, achieving the superchiral field with the highest chiral enhancement factor of 40 for 0th Bessel beam. These active, high efficiency and broadband chiral PB metasurfaces have promising applications for manipulation the THz chiral light and chiroptical spectroscopic techniques.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Chirality is a concept that describes the special geometric properties whose mirror image can be superimposed on its original image. Chiral light field is also a chiral object, which owns importance due to help characterizing chiral matters, such as amino acids and glucose in biological metabolism. And the vibration-rotational energy levels of most chiral molecules are located in the terahertz (THz) band, which can be distinguished by the chiral response such as circular dichroism and optical activity [1,2]. However, these chiral responses are typically weak, making it hard to be detected. Thus, the manipulation and enhancement of chiral field are therefore highly desired due to both curiosities in fundamental physics, such as nonreciprocal transmission of light related to spatial-time symmetry and spin-orbit angular momentum coupling [3–6], as well technological applications in efficient chiral spectroscopic detection, polarization imaging, wide channel multiplexing optical communication, etc [7,8]. However, the conventional materials in THz regime are suffering with the issues such as low-efficiency and bulk size.
To conquer these difficulties, there are many researches focus on the two-dimensional (2D) metasurfaces, which have demonstrated the novel properties in controlling the amplitude, phase, polarization, wavefront of electromagnetic waves [9–16] and even manipulating the chiroptical response such as circular dichroism [17–21]. Among them, Pancharatnam-Berry (PB) metasurfaces exhibit the intriguing properties in manipulating the phase and spin chiral conversion of circularly polarized (CP) waves [22–31]. The geometric phase with respect to the rotating angle can be obtained by only rotating the axis of each PB unit, and this phenomenon is frequency irrelevant, making the PB devices could be broadband [24,25]. Due to the unique abilities in control the wavefronts of cross-polarized chiral light, many functional devices have been proposed based on PB metasurfaces such as the generation of special beams (e.g., Bessel beams) [26], the giant photonic spin Hall (PSH) effect [32–34]. Although PB metasurfaces have shown the strong capacities of manipulating the light, it is still challenging for active PB metasurfaces which can broaden the potential for various applications that require dynamical control over the THz frequency band [25,29,30]. For instance, by combing the graphene with metallic PB metasurface, T. Kim et al. [29] proposed a gate-controlled THz metasurface, realizing active amplitude modulation of anomalously refracted waves. However, the modulation depth (28%) and efficiency (30%) are limited. Cong et al. [25] developed a THz metadevice to modulate polarization of the THz wave. Though it realized the efficient dispersion-free manipulation of the phase of the polarized THz beams by integrating two grating-based metasurfaces. the tuning process need to rotate the structure with high response time. Moreover, the active THz devices typically suffer from issues like low efficiency or narrow effective frequency band. So far, although there are some researches focus on the active PB metasurfaces, it is still hard to solve the above difficulties.
The magneto-optic (MO) materials are traditionally used as isolators and phase shifter due to the Faraday MO effect in optical and microwave regime. Moreover, recent researches have demonstrated that the MO material as well as MO structural devices [35–41] also have strong potentials in optical field manipulation and topological photonics due to its magnetic tunability, charity and nonreciprocity. For instance, J. Qin et al. [35] proposed the MO material based metasurface that can manipulate the circular dichroism at far-infrared band, the circular dichroism modulation is up to 2.5° by applying magnetic field. Moreover, due to the MO microstructure can break the time-reversal symmetry, Z. Wang et al. [37] reported the experimental observation of chiral edge states in a MO photonic crystal, finding the intriguing phenomenon of one-way transmission and are very robust against scattering from disorder. All these researches proved that the MO effect can be obviously enhanced by combing MO materials with microstructure, therefore, many novel functions and phenomena are realized.
In particular, the gyroelectric MO material InSb, whose cyclotron resonance frequency is just located in the THz band when an external magnetic field is applied, has been demonstrated its novel properties of magnetic tunability, nonreciprocity and the special circular dichroism effect to CP light. For instance, D. Wang et al. [39] found the photonic Weyl points in transverse magnetized InSb combined with a plasmonic grating, which is the topologically photonic properties in the THz band. Lin et al. [40] also proposed a nonreciprocal one-way mirror using InSb under the Voigt configuration, achieving 35 dB isolation with −6.2 dB loss. Moreover, our previous work [41] experimentally reported THz nonreciprocal circular dichroism and giant Faraday effect of over 90° rotation angle in InSb at 80 K under a weak magnetic field of 0.17 T. Therefore, the novel properties of InSb are promising for manipulating both wave front and chiral states with strong magnetic tunability and nonreciprocity. However, there are rare researches using MO metasurface to control and enhance THz chiral light.
Here, by combing the MO material InSb with PB metasurfaces structure, we propose a MO meta-atom (MMA) which shows strong capability in controlling the chiral light. We demonstrate that this MMA can serves as an active broadband half wave plate by changing the external magnetic field (EMF), which can be turned from the “OFF” to the “ON” state with the highest efficiency of ∼80% and broad working frequency range in 1∼1.5 THz. Then, the MO PB metasurfaces are proposed for different functions: beam deflection and scanning, Bessel beam and Vortex beam generations with CP state. Moreover, we find the optical chirality of these chiral fields is enhanced, which also called as superchiral effect, and the highest chiral enhancement is nearly 40 for the Bessel beam.
2. Terahertz MO meta-atom
For the classical PB meta-atom, the spatial asymmetry of the structural elements leads to the anisotropy of polarized light. The spatial dependent optical axis distribution θ brings the phase difference φ to the two orthogonal polarized components. Here, for the right circularly polarized (RCP) and left circularly polarized (LCP) states, when the φ = 0, the chiral state of the output component is still as same as the incident one, which means this MMA is on “OFF” state. When the PB meta-atom is φ =π and the amplitudes r of the two orthogonal components are the same (i.e. typically a half wave-plate), the output beam for two CP components will be transformed as follows:
Fig. 1. (a) Sketch map of the MMA: hd = 5 µm, hSiO2 = 22 µm. (b) Top view, WInSb = 42 µm, Wsub = 71 µm, rinner = 18.5 µm and rout = 26 µm, the spatial axis is defined as the dashed line, and the rotational angle is θ. Real part of relative dielectric function map of the InSb as the functions of frequency and the EMF for the (c) LCP state (εL) and (d) RCP state (εR). And the real part of the electric conductivity map of the InSb for the (e) LCP state (σL) and (f) RCP state (σL) expressed in the logarithmic coordinate system.
The MO property of InSb can be expressed in a nonreciprocal tensor as follows [38,40,41]:
Then, we introduce Eq. (2) into Maxwell’s wave equation, so two eigensolutions can be obtained as a pair of orthogonal spin chiral states, LCP and RCP, as follows:
According to Eqs. (3) and (4), we calculated the real part of the dielectric functions εR and εL of these orthogonal chiral states in Figs. 1(c) and 1(d), respectively. Then we also calculated the conductivity σ = −ωε0Im(ε), which is proportional to the imaginary part of the dielectric function and reflects the ohmic loss of the material, as shown in Figs. 1(e) and 1(f). We find that when B = 0 T, both LCP and RCP are the same. The InSb have both large negative dielectric constant and conductivity, making the proposed structure like a metallic circular ring. But when the EMF is applied, there is a large difference between LCP and RCP wave for both the conductivity and dielectric function. The RCP state shows a cyclotron resonance band at the ωc = eB/m∗ with a Lorentz spectral line as shown in Figs. 1(d) and 1(f). At this frequency band, the dielectric function changes dramatically [the crossing line between blue and red color is just the ωc in the Fig. 1(d)], and the conductivity also has a peak value [red band in the Fig. 1(f)]. The RCP state within this frequency band cannot pass through the InSb. But the LCP state shows a Drude spectral line with the effective plasma frequency ${\omega _{PL}} = (\sqrt {\omega _\textrm{c}^2 + 4\omega _p^2} - {\omega _c})/2$ as shown in Figs. 1(c) and 1(e). The crossing line between blue and red color is just the ωLP in Fig. 1(c), as the magnetic field increases, the ωPL moves to a lower frequency. When ω>ωPL, the LCP state can propagate through the InSb. As a consequence, the InSb has the different chiral response to the LCP and RCP states, and the nonreciprocal chiral-selective effect (i.e. circular dichroism) can be obtained in the frequency band between ωPL and ωc, which allow transmitting LCP state but forbidding RCP state [41]. Therefore, InSb shows the strong magnetic tunability and nonreciprocity for the chiral light.
To characterize the reflection and cross-polarization efficiency of MMA for these two orthogonal spin states, we simulate this model in COMSOL Multiphysics. As shown in Fig. 2(a), when B = 0 T, below the 1.5 THz band, the unconverted components RLL and RRR are much higher than the converted components (RRL and RLR), which means there is no conversion between spin chiral states without any wave phase retardation. On the contrary, when the EMF B = 2 T, the LCP (or RCP) state will be transferred to RCP (or LCP) state with very high conversion rates as shown in Fig. 2(b), thus the reflective beam will obtain half wave phase retardation of 180°, which means it can be work as a good PB phase element.
Fig. 2. The reflectance of LCP or RCP chiral states from the MMA when (a) B = 0 T and (b) B = 2 T, the yellow region denotes the working frequency band. RRL means the reflectance of the converted RCP component, and RLL represents the reflectance of the unconverted LCP component when the LCP is incident.
Next, we discuss the PB geometric phase of the MMA. For any LCP or RCP chiral states, the above conclusion about broadband half-wave plate is still valid with any the spatial rotating angle θ of the MMA. As shown in Fig. 3(a), a PB supercell consists of 6 MMAs with spatial discrete rotation step θ = 30°. When B = 0 T, the EMF induces the MO phase shift to each MMA, which leads that there is no geometric phase among these different MMAs in Figs. 3(a) and 3(b). When B = 2 T, this MMA could serves as a broadband half wave-plate, for the converted components (LCP-RCP or RCP-LCP), the geometric phase 2θ(x, y) dependent on the rotating angle are obtained, as shown in Figs. 3(c) and 3(d). For the incident wave of LCP and RCP, these MMAs will introduce conjugated spatial phase shift: −60° and 60° with the rotation of the spatial axis. This result indicates that by adjusting the EMF, this PB supercell could generate a spatial gradient phase from 0 to 2π.
Fig. 3. When B = 0 T, the output phase of each MMA of the unconverted components: (a) LCP to LCP and (c) RCP to RCP. When B = 2 T, the output phase of the converted components: (b) RCP to LCP and (d) RCP to LCP. Inset: the proposed supercell consists of 6 MMAs with gradient rotation step θ = 30°.
3. Manipulation of terahertz chiral field by MPBM
3.1 Beam deflection
At first, we construct a magneto-optic PB metasurface (MPBM) based on the MMAs discussed above. The structure of this MPBM is periodically composed by several supercells with 6MMAs with spatial discrete rotation step θ = 30° arranged along x direction as shown in Fig. 4(a). To characterize the deflection characteristics of this MPBM, we simulate the diffraction efficiency by using rigorous coupled wave analysis (RCWA) as shown in Figs. 4(b) and 4(c). Here, the diffraction efficiency is defined as the intensity of the selected diffractive order in proportion to the total intensity of the incident wave expressed as: Dn = Rn/Itotal (n = 0, ±1 denotes the diffractive orders). When B = 0 T, the reflective beam is almost on the 0th diffractive order without chiral conversion, and has the broad working band around 1-1.5 THz with the highest diffraction efficiency over 60% at 1.3 THz, as shown in Fig. 4(b). However, when the EMF of B = 2 T is applied, the output beam is mainly on the +1st order for the incident LCP wave with the highest efficiency of over 80% (i.e. −0.96 dB reflectance) as shown in Figs. 2(b) and 4(c). Then, we simulated the far field patterns of THz beam deflection through the MPBM. When B = 0 T, the beam almost reflected normally as shown in Fig. 4(d). But as B = 2 T shown in Figs. 4(e) and 4(f), the LCP (RCP) beam normally incident onto this MPBM and reflect with a deflection angle α which is determined by the diffraction equation: Psinα = mλ, where m denotes the diffraction orders. Due to the period of the supercell λ<P<2λ, the diffraction orders only have 0th and ±1st orders. Moreover, due to this MPBM has a broad working band and the deflection angle is dependent on the λ, this device can realize frequency-dependent beam sweeping angle range from 28°∼44.8° with high efficiency.
Fig. 4. (a) Schematic diagram of THz beam deflection based on the MPBM structure. The diffraction efficiency for the MPBM when (b) B = 0 T and (c) B = 2 T. The simulated far field patterns of THz beam deflection though the MPBM: (d) B = 0 T for both LCP and RCP incidence. and 2 T with (e) LCP and (f) RCP incidence.
3.2 Bessel beam
Next, the active MPBMs for generating Bessel and vortex beam are demonstrated. Bessel beams have exhibited many interesting properties such as non-diffraction, self-reconstruction and even providing optical pulling forces. Thus, they can be applied in high-quality imaging, precision measurement, and optical alignment. Non-diffracting 0th-order Bessel beam J0 have transverse intensity profiles that can be described by the Bessel functions of the first kind, and the propagation of 0th-order Bessel beam along z axis can be described by $E(r,\theta ,z) = A \cdot {e^{i{k_z}z}}{J_0}({k_r}r)$ in cylindrical coordinates. Conventionally, a 0th-order Bessel beam is generated by using symmetrically refracting incident plane waves toward the optical axis of a conical prism, i.e. an axicon. The numerical aperture of the axion NA = sin[arcsin(n·sin(α)) – α], where α is the angle and n is the refractive index of the axion. However, the conventional method is bulky, low efficient and fixed. By applying PB metasurface, these drawbacks can be efficiently avoided. From the generalized Snell’s law, the generation of a zeroth-order Bessel beam, a metasurface requires a radial phase profile φ(r) with spatial phase distribution [26]:
where NA = 0.7, and this phase profile shown in Fig. 5(b) can be obtained by the rotation of each MMA at a position r with a rotating angle θPB = φ(r)/2.Fig. 5. (a) Schematic view of the MPBM for active generating the Bessel beam. (b) The theoretical phase profile for generating the 0th Bessel beam. (c) The amplitude distribution of the x-y cutting plane at z=300 µm when an incident LCP Gaussian beam of 1.3 THz is reflected by the MPBM. The MPBM can be turned from “OFF” state to the “ON” state when the EMF changes from 0 to 2 T.
Based on the above phase profile, the active 0th-order Bessel beam generator based on MPBM is proposed as shown in Fig. 5(a). The size of this MPBM is 21P×21P, and the waist radius of the incident Gaussian beam rG = 500 µm. We obtain the near field distribution of the x-y cutting plane at 1.3 THz when z is set to 300 µm. As shown in Fig. 5(c), when B = 0 T, this MPBM is on the “OFF” state and the reflective beam is still Gaussian beam. With the growing of the EMF, the MPBM can be tuned to the “ON” state, in this process, the output beam is gradually changed to a Bessel beam with a focusing spot. The light intensity of the center point at 2 T is more than 10 times stronger than that of the Gaussian beam without the EMF at 0 T.
3.3 Vortex beam
We also proposed two MPBMs for vortex beam. Vortex beams that carry orbital angular momentums have promising applications in high-dimensional communication systems and optical manipulation [42–44]. Conventional, vortex beams are generated by using spiral phase plates which is also suffering from several issues such as low efficiency, bulk size and untunablility. Therefore, several active MPBMs is designed for high-efficiency, tunable vortex beam generation.
For generating the vortex beams the profile of the transmission coefficients can be describe by exp(ilθ), where the orbital angular momentum l = Lћ, L is the topological charge and ћ is the Planck constant. Here, the first- and second-order THz active vortex beam generators (V1, V2, respectively) are designed. The MPBMs are then arranged into different sections by their azimuthal angles θ to form 2π and 4π spiral phase loops, respectively, in which each section consists of only one MMA as shown in Fig. 6(b). We also simulate the active vortex beam for both V1 and V2 beams, as shown in Fig. 6(a). The size of all this MPBMs is 21P×21P, and the waist radius of the incident Gaussian beam rG = 500 µm. We detect the near field distribution of the x-y cutting plane when z is set to z = 300 µm. As shown in Figs. 6(c) and 6(d), when B = 0 T, both these MPBMs are on the “OFF” state, thus the output beams are still Gaussian beams. Figures 6(c) and 6(d) shows the simulated phase distribution of the electric field in the x-y cutting plane when B = 0 T, the phase distribution is uniform. However, when we applied the EMF B = 2 T, the output beams tuned to the vortex beams and have good doughnut shapes. In this case, the phase distribution of these output vortex beams is spiral that are coincide with the above phase profile for V1 and V2 beams respectively. The hollow center is larger in vortex beams with a larger topological charge. This is also a direct consequence of the self-canceling effect induced by the spiral phase distribution. All in all, due to the MMA has high cross-polarization efficiency and broad working band, the proposed Bessel and vortex active beam generators could also high-efficiency and broadband, making it promising in the future THz application systems.
Fig. 6. (a) Schematic view of the MPBM for generating the vortex beams. (b) The theoretical phase profile for generating V1 and V2 vortex beams. (c) The phase and amplitude distributions of E-field on the x-y cutting plane at z=300 µm when a LCP Gaussian beam of 1.3 THz is reflected by the MPBM with topological charge L=1 and (d) L=2.
3.4 Active superchiral field generation
Finally, we analysis the chirality enhancement of the special beams, so-called superchiral effect. As we known, a chiral molecule has different absorption when illuminated with LCP or RCP, thus we can distinguish chemically identical molecules with different chiral response. This circular dichroism expressed by the dissymmetry factor g that is defined as g = 2(AL – AR)/(AL + AR), where AL(R) is the absorption rate in LCP or RCP light. However, for most small molecules, g < 10−3, thus some researches use the chiral metasurfaces to enhance the g of the molecules [16–21]. Moreover, the dissymmetry factor g for the detected object is not only related to the properties of itself, but also influenced by the optical chirality C of the detecting electromagnetic field by generating the special superchiral electromagnetic field [21,45]. It is demonstrated that by applying the superchiral field, the sensitivity of chiroptical measurement could be greatly enhanced (e.g. at the nodes of the standing a wave). The optical chirality C can be characterized by the following time-even pseudoscalar termed as [45]:
As shown in Fig. 7, we calculate the localized optical chirality of the MPBM supercell at the interface between metal split-ring and SiO2 substrate. When B = 0 T, the localized superchiral field is weak (|Sx|<2) around the split rings, and independent to the rotation of the split rings. Meanwhile, when B = 2 T, the localized hot spot of superchiral field forms to be distributed inside the ring with the max chiral enhancement |Sx| >5, and dependently rotated with the InSb split rotating in space. The superchiral field distribution is mirror symmetry and the sign of Sx is changed when the incident chiral state is changed as shown in Figs. 7(a) and 7(b).
Fig. 7. The localized optical chirality distribution of the MPBM surpercell on the interface between the metal and SiO2 substrate when B = 0 T and 2 T for (a) LCP incidence and (b) RCP incidence.
Furthermore, we obtain the surperchiral field distributions of MPBMs for vortex beam and Bessel beam in Fig. 8. When B = 2 T, these LCP Gaussian beams incident onto these metasurfaces and reflect as Bessel beam or vortex beams, we detect the field distribution in the xy-plane at z=300µm. In this situation, the chirality is enhanced in some specific regions. For vortex beams, the chirality enhanced region has the doughnut shaped as shown in Figs. 8(a) and 8(b). For V1 beam, the max chirality enhancement can be 2.3, where for the V2 beam it can achieve nearly 3. In Fig. 8(c), when the output beam is tuned to Bessel beam, the center spot of the Bessel beam obtains the chirality enhancement Sx more than 40. Thus. Based on the above discussion, it indicates that the optical chirality can be also enhanced and manipulated by the EMF by combing the MO materials with PB metasurfaces.
Fig. 8. The surperchiral field distribution of MPBM in the xy-plane at z=300 µm when B = 2 T: (a) V1 vortex beam; (b) V2 vortex beam; (c) Bessel beam.
4. Conclusions
On summary, we combine the MO material with the PB metasurface to actively manipulate the phase and polarization for the chiral THz waves. Based on these results, three MPBMs are designed for Bessel beam and Vortex beams in the THz regime. All of these MPBMs are high efficiency and can be turned from “OFF” state to “ON” state by applying the EMF. The MPBM can also separates the THz chiral states with different deflection angle from 28 to 44.8°, which realize active beam sweeping. The active Vortex and Bessel beams are also realized, and further, by analyzing the superchiral effect, we find that the optical chirality can be manipulated in the MMA units. As a result, these MPBMs can enhance the optical chirality of chiral electromagnetic field when applying the EMF. In particular, for the generated Bessel beam, the largest chirality enhancement factor could obtain almost 40. This low-loss, broadband active metasurface has several promising functions for THz chiral light, beam scanning and optical detection with great potentials in THz wireless communication, spectrum and sensing systems.
Funding
National Natural Science Foundation of China (61831012, 61971242); National Key Research and Development Program of China (2017YFA0701000); Natural Science Foundation of Tianjin City (19JCYBJC16600); Young Elite Scientists Sponsorship Program by Tianjin (TJSQNTJ-2017-12).
Disclosures
The authors declare no conflicts of interest.
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