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Abstract
Chiroptical effects are instrumental for various intriguing applications like chiro-optical spectroscopy and chiral imaging. Their on-chip realization can open novel avenues for the demonstration of these applications at a miniaturized scale. One can leverage the unprecedented flexibility of metasurfaces to tailor the spinning light meticulously for realizing these chiroptical effects at a compact scale. Here, we present a unique methodology to effectively achieve such chiroptical effects by a single-layered metasurface consisting of a two-dimensional array of C2-symmetric meta-atoms. These meta-atoms are carefully engineered to break the mirror and n-fold (n=2) rotational symmetries. The optimized meta-atoms reflect 84% (cross-polarized light) under right circularly polarized illumination and transmit 80% (cross-polarized light) when left circularly polarized light is impinged. Such optical responses result in a giant asymmetric transmission (AT) of 80% in the reflection and 74% in the transmission mode along with full phase control (of 0-2π). To verify this asymmetric behavior in transmission and reflection, we implemented holograms both in the forward and backward directions. The proposed design methodology enables the realization of chiroptical effects via compact on-chip which can find promising applications in chiral sensing and imaging.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Chiral imaging and Chiro-optical spectroscopy are vital for numerous applications in biological and chemical sciences such as detecting molecule’s electronic transition, extracting information about protein structure, and small molecules presence [1–3]. These techniques usually involve combination of lenses with different numerical apertures along with an on-chip camera to provide features of different ranges and spectral resolutions that help in resolving helicity features of the light. In a conventional optical system to realize chiral imaging and spectroscopy, additional bulky optical devices are needed to control the light energy and phase due to the weak chiroptical signals [1,2,4,5]. Strength of chiroptical signals can be enhanced by maintaining a localized phase of circular polarization and augmenting the confinement of energy. To overcome these issues, the ability of metasurfaces to control light phase and amplitude is employed to achieve polarization-dependent optical response [6–8]. Moreover, optical metasurfaces provide a versatile platform to fulfill the growing requirements of integration and miniaturization benefitting from state-of-the-art fabrication techniques. Owing to these attractive features and promising potential, chiral structures and metasurfaces have sparked great interest amongst researchers.
Chiral structures are the ones that have broken mirror symmetry [5,9]. Essentially, when a beam impinges on this chiral structure, the incident wave is transformed into an elliptically polarized wave, that interacts differently with various molecules. These interactions can achieve exotic phenomena like handedness dependent non-linear response [10], and negative refraction [11–13] that helps in manipulating electromagnetic energy and localized phase. The variation of refractive index and extinction coefficient for right circularly polarized (RCP) and left circularly polarized (LCP) waves, when interacting with chiral structures results in chiroptical effects such as circular dichroism (CD) optical activity (OA) and asymmetric transmission (AT) [14,15].
The AT accompanied by metamaterials was first realized by Fedotov in 2006 [16] which attained great attention due to its high scalability, conversion efficiency, and flat profile [17]. It provides a prodigious path for realizing bifunctional devices that have the capability to achieve more than one phenomenon through a single metasurface. Recently, various metasurfaces and metamaterials are reported to behave as a polarizer that has a distinct optical response under certain polarization [18,19]. But very limited studies about chiral metasurfaces have presented a spin-dependent tailored asymmetric response in transmission and reflection simultaneously.
Recently, chiroptical interactions are enhanced with plasmonics that enabled the light confinement at the nanoscale [20–22]. This has been achieved by exciting surface plasmon resonances that happen due to the excitation of the chunk of electrons at the metal-dielectric interfaces [23–25]. The metal-based chiral structures are not only prone to high absorption loss [26–29] but also require sophisticated fabrication process [30]. High energy dissipation of metals can be avoided by using dielectric unit elements. In dielectrics, the excitation of magnetic dipole and electric dipoles happens upon hitting the light with frequency nearly equal to the bandgap frequency of the material [31]. These ohmic losses are eliminated by using dielectric meta-atoms.
For multi-layer metasurfaces, fabrication procedures such as electron beam-induced deposition and lithography [32,33] are not only time consuming and complex but also lacking flexibility and reproducibility. However, fabrication complexities of multi-layered structures can be overcome by using a single layer planar chiral structure. Also for dielectric metasurfaces, very limited studies have been presented that exhibit functioning in transmission and reflection simultaneously with full phase coverage [34]. Hence, a clear gap existed to present a single-layered on-chip metasurface for realizing chiroptical effects.
Here, we demonstrate a dielectric metasurface that exhibits functioning in transmission and reflection simultaneously with full phase coverage, which provides a superficial platform for on-chip devices. A unique way of achieving chiroptical effect that gives AT in transmission mode for left circularly polarized (LCP) and reflection AT for right circularly polarized (RCP) is demonstrated. A z-shaped meta-atom is designed in such a way that it transmits the right circularly polarized (RCP) wave for left circularly polarized (LCP) illumination at 1550 nm wavelength. While for RCP incident wave polarization, metasurface reflects LCP wave polarization and acts as a mirror that also converts CP wave. This distinct behavior of the meta-atom for different CP waves can be attributed to the simultaneous excitation of electric and magnetic resonances. Due to this functionality, the design provides the platform to control wave-fronts by modulating them with the handedness of CP light for designing multifunctional photonic metasurfaces. To the best of our knowledge, no such work exists that gives AT in both directions with single unit-element.
2. Design and methodology
The proposed metasurface to demonstrate the desired chiroptical effect i.e., bi-directional asymmetric transmission is presented in Fig. 1(a). A forward moving left circularly polarized (LCP) wave can be transformed into right circularly polarized (RCP) after transmission whereas LCP wave reflects off and converted into RCP wave. The metasuface structure is schematically illustrated in Fig. 1(a), which is composed of z-shaped meta-atom array extended periodically in x and y direction. The structural parameters of the meta-atom are denoted in the inset figure with dimensions l = 216 nm, d = 430 nm, w = 100 nm and thickness is set as h = 500 nm as shown in Figs. 1(b) and 1(c). The period p is set as 950 nm within sub-wavelength scale to avoid higher order diffractions. The geometrical parameters are optimized by Particle Swarm optimization. The SiO2 substrate, considered as lossless material with refractive index of 1.45, is used to support single layer structure for practical realization. The height of the substrate (Sh) is taken as 200 nm. Silicon is used as a material for meta-atoms because of its low absorption loss and high refractive index in near-infrared regime. Moreover, the exceptional features of Silicon-based device provide integration with the developed complementary metal oxide semiconductor (CMOS) technology and photonics circuits that make it superior to other materials. Moreover, since Silicon is lossless (due to its bandgap of 1.12 eV) after 1107 nm, which makes it an ideal candidate for realizing transmission-based devices that require minimal absorption. The performance of the meta-atom is analysed using finite difference time domain (FDTD) algorithm of computer simulation technology (CST) studio, where periodic boundary conditions are applied in x and y-direction. The perfect matched layer (PML) boundary condition is applied in the z-direction.
Fig. 1. Designed meta-atom with geometrical parameters (p = 950 nm); length (l = 215 nm); dimension (d = 430 nm); width (w = 100 nm); height (h = 500 nm) and substrate height (Sh = 200 nm). (a) Working principle of proposed meta-surface in transmission and reflection. (b) Top view of the meta-atom and (c) perspective view of meta-atom.
For better understanding of the cross-polarized conversion based on chirality, we invoke Jones matrix expression. The different elements in Jones matrix represents co and cross-polarized components for linear/circular polarization. Asymmetric behavior of the device is realized by breaking mirror and n-fold symmetry of the meta-atom. For the meta-atom that possess mirror symmetry, the off-diagonal transmission or reflection coefficient of Jones Matrix in Cartesian base are equal ${t_{xy}} = {t_{yx}}$ (Supplementary Information Note 1).
For reflection case, if we start considering the rotation effect on these matrices in x-y plane, the rotation effect can be introduced in Jones matrix by $R(\theta ) = \left( {\begin{array}{cc} {\cos (\theta )}&{ - \sin (\theta )}\\ {\sin (\theta )}&{\cos (\theta )} \end{array}} \right)$ that results in a new matrix ${R_{rot}} = \left( {\begin{array}{cc} {t_{11}^{\prime}}&{t_{21}^{\prime}}\\ {t_{21}^{\prime}}&{t_{22}^{\prime}} \end{array}} \right)\; $as follows:
Fig. 2. (a) Transmission coefficients of z-shaped meta-atom under linear incident light. (b) Reflection coefficients of z-shaped meta-atom under linear incident light. (c) Magnitude of transmission and phase with varying unit elements rotation. (d) Magnitude of reflection and phase with varying unit elements rotation. (e) AT in transmission with varying rotational angles of two neighboring unit elements. (f) AT in reflection with varying rotational angles of two neighboring unit elements.
In the above equation, cross-polarized component gets an additional term with phase whose magnitude is double the rotation angle of meta-atom denoted by θ. For the co-polarized terms referred as $\; r_{11}^{\prime}$ and $r_{22}^{\prime}$ do not have any phase terms, therefore, are not contributing towards efficiency. These terms add noise to system which can be minimized by the condition $r_{xx}^{\prime} ={-} {r_{yy}}$. Another way to satisfy Eq. (2) is to take both $r_{xx}^{\prime} = {r_{yy}} = 0$ which eventually transforms the transmission matrix (details in Supplementary Information Note 1) as
For linear base, ${r_{xx}} = {r_{yy}}$ as shown in Fig. 2(b) represents the design principle, which maintains AT in reflection mode as well. For the reflection case, the transmission efficiency is varying by rotating the meta-atom. Figures 2(c) and 2(d) represent phase and transmission/reflection with rotation of meta-atoms. Moreover, an array of 2 × 2 elements with varying rotation angles is simulated for coupling effect of neighbouring meta-atoms. For simplicity we can call these elements from 1-4. In order to retain symmetry, elements 1 and 3, and elements 2 and 4 would have same rotation angles. It was observed that when the neighboring unit elements have a relative rotation angle (rotation angle difference between two z-shaped unit elements) within 45˚ of each other, high AT is achieved, both in transmission and reflection [Figs. 2(e)–2(f)]. On the other hand, when the relative rotation angle exceeds 45, the AT starts to decrease. When the relative rotation goes closer to 180˚, high AT again starts to appear. This happens because at this point the structure again starts to have a relative phase less than 45˚, as the structure repeats itself at 180˚.
The meta-atom is also evaluated based on electric and magnetic field distribution on the surface. A dielectric meta-atom with high refractive index exhibits electric and magnetic Mie-resonances, hence results in achieving better efficiencies than their plasmonic counterparts. This magnetic resonance primarily originated from the induced currents due to electric field within the structure [35]. This causes enhanced efficiency of the dielectric meta-atom due to the constructive interference of the scattered wave caused by the electric and magnetic dipole excitation. A circular displacement current possessed by magnetic Mie-resonance increases the magnetic field at optical wavelengths at the centre of meta-atoms, whose direction can be varied to control the transmission in forward direction and reflection in backward direction [36]. Mie-resonances primarily originate by the displacement current in the high refractive index dielectric under applied electric field. This is due to polarizability in the material, which is caused by the applied electric field, couple with incoming light giving rise to the magnetic dipole resonances. The induced magnetic and electric resonances must be tailored so that they do not overlap and provide transmission and reflection, simultaneously [37].
To understand the optical response of electric and magnetic resonances in the z-shaped meta-atom, the electric and magnetic field distributions at the top and bottom of the meta-atom are analysed as shown in Fig. 3. Under LCP illumination, simulated electric (Ez) and magnetic field (Hy) distributions at the top (z = 0.5) of the meta-atom are shown if Figs. 3(a), 3(b), 3(e) and 3(f). The results for LCP illumination demonstrate that both electric and magnetic resonances appears on the top and bottom of chiral meta-atom to radiate in transmission direction. In case of RCP, no significant electric and magnetic resonances appear at the top surface as given in Figs. 3(c), and 3(g), which limits the transmission for RCP illumination. However, at the bottom of the z-shaped structure (z = 0), electric and magnetic resonances exist for RCP. These electric and magnetic resonances for RCP at z = 0 appears to be very strong as shown in Figs. 3(d) and 3(h), which cause the wave to reflect backward.
Fig. 3. Electric and magnetic field distribution shown under two circular polarization at z = 0 (between the substrate and meta-atom) and z = 0.5 (on the meta-atom). Electric field distribution under LCP at (a) z = 0, (b) z = 0.5 and under RCP at (c) z = 0. (d) z = 0.5. Magnetic field distribution under LCP at (e) z = 0, (f) z = 0.5 and under RCP at (g) z = 0, (h) z = 0.5. The Ⓧ represents magnetic field into the paper and Ⓞ represents field out of the paper.
3. Results and discussion
To enhance chiroptical effects in the meta-atom, a unit element is proposed that behaves differently under different circular polarization illumination. The C2 symmetric meta-atom reflects LCP under RCP illumination due to lack of mirror symmetry transverse to z-axis in contrast for the LCP that does not reflect due to the impedance matching. This criterion can be met only for ${R_{rot}} = \left( {\begin{array}{cc} 0&0\\ 1&0 \end{array}} \right)$ and ${T_{rot}} = \left( {\begin{array}{cc} 0&1\\ 0&0 \end{array}} \right)$ in case of RCP and LCP, respectively. Also, as long as ${t_{xy}} \ne 0,$ cross polarized component for circular base t12 and t21 remains different in transmission mode, returns total transmission for RCP distinct to LCP. Destructive interference results from the linear polarized components of scattered light under RCP illumination whereas constructive interference occurs for LCP incident light that results in high transmittance as shown in Fig. 4(a). For reflection mode, constructive interference results from the x and y polarized light if the incident beam is RCP resulted in high reflectance while for LCP incidence it destructively interferes which results in filtration of LCP as shown in Fig. 4(b). A z-shaped meta-atom returns txy not equal to zero, which results in different cross-polarized components for the transmission and reflection mode as shown in Fig. 4(a). The difference in the power transmission is a nonreciprocal phenomenon in a single layer meta-atom which does not violate time reversal symmetry and Lorentz Reciprocity. This difference in the two opposite direction is attributed to the substrate thickness and the meta-atom height that provide extra degree of freedom in the propagation direction breaking mirror symmetry. Figure 4(c) shows AT parameter for transmission which is around 0.74 whereas for reflection the magnitude touches 0.8. Figure 4(d) shows the extinction ratio, which is characterized by the ratio of two cross polarized components in transmission and reflection, respectively. Extinction ratio for our case is 10 in transmission side and 20 in the reflection side. Moreover, the designed structure provides tolerance angle (angle of incidence) of 15˚ in transmission, whereas, the tolerance of the incidence angle reached to 20˚ in reflection mode. It is evident that from Figs. 4(e) and 4(f) that the transmission of the structure over this range of angles is reasonably high with a little to no shift. For the bandwidth of the designed structure, chiral bandwidth [38] of the designed structure is calculated where the design gives half of its maximum AT. Chiral bandwidth of the meta-atom for transmission is 65 nm and for reflection case bandwidth is 75 nm as shown in Figs. 4(g) and 4(h).
Fig. 4. (a) Transmission spectra under LCP and RCP incident light. (b) Reflection coefficients of z-shaped meta-atom under RCP and LCP incident light. (c) AT parameter of 0.74 for transmission and 0.8 for reflection. (d) Extinction ratio for transmission and reflection cases are 10 and 20 for transmission and reflection, respectively. Tolerance angle for incident angle over the range from 0° to 80° (e) for transmission and (f) reflection. Simulated chiral bandwidth for the (h) transmission and (i) reflection.
So far, the designed unit element achieves AT in transmission and reflection. The subsequent step is to control the wave front by manipulating electromagnetic waves with varying structural parameters. Different reviews of metasurface phase manipulation has been presented in detail [39]. Broadly, the metasurfaces can be classified into linear and non-linear. For demonstrating hologram, we are interested in linear metasurfaces that can be further classified based on their working principle as resonant type, Huygens principle type, circuit phase type, transmission phase type and geometric phase.
For the control of photon spin, significant birefringence should be introduced which is utilized by z-shaped unit element. These unit elements impart orientation dependent phase shift of 2θ, where θ is the rotation of meta-atom with respect to z-axis, realizing geometric phase also known as Pancharatnam–Berry (PB) phase [40,41]. It is originated by the spin rotation effect when interacting with circularly polarized light and appears with the cross-polarized component. From Eqs. (2(b)) and (2(c)), cross-polarized component yields a phase shift while co-polarized components are near to zero that eventually reduce the noise [42]. From Fig. 2(c), it is evident that both phases of reflection and transmission are varying linearly with rotation which can be a suitable candidate for realizing bi-functional optical phenomena.
For the proof of concept, we designed the resonators to achieve 2D hologram which creates an image by the different point sources at the metasurface. For the 2D meta-holograms realization, a phase map is needed to correspond with the beam to cast hologram on observation plane in transmission and reflection. It can be obtained by Gerchberg-Saxton (GS) algorithm in the far field which generate interference pattern, of different point sources at the metasurface, to create image of non-existent objects (Supplementary Information Note 2). For non-existent object, we have chosen “C” alphabet word in transmission and “2D” in the reflection whose phase is calculated by GS phase-retrieval algorithm. The computer-generated hologram (CGH) of “2D” and “C”, showing the intensity plot images in reflection and transmission are presented in Figs. 5(a) and 5(b), respectively. The size of each metasurface is taken as 100 × 100 μm2 which creates the phase matrices of 105 × 105 with displacement of 0.95 μm that is implemented using finite difference time domain (FDTD) algorithm of CST studio. Perfect matched layer (PML) boundary conditions has been applied and monitor is placed at the distance equal to half the metasurface to record the electric fields. The unique unit element which does not only transmit LCP but also reflects RCP in reflection is demonstrated by implementing metasurfaces. Under LCP illumination, the metasurface allows the light for transmission and cast a C-shaped hologram on the surface monitor as shown in Fig. 5(c). The 2D-shaped hologram appears in reflection on RCP illumination which justified the metasurface operation in reflection [Fig. 5(d)]. The achieved results are not displaying holographic images as good as the other meta-holographic images as the size of the metasurface is only taken as 100 × 100 μm2 due to limited computational resources. If the metasurface size is further increased, our structure will show holographic images with high fidelity. Furthermore, the diffraction efficiency has been calculated, which is defined as the ratio of power cross-polarized component and the total power transmitted [43]. The diffraction efficiency of the designed lens is 42.38%.
Fig. 5. (a) CGH image for the “C” hologram in the transmission mode. (b) CGH image for the “2D” hologram in the reflection mode. (c) Hologram generated in reflection mode under RCP illumination. (d) Hologram generated under in transmission mode under LCP illumination.
4. Conclusion
In this paper, we demonstrated AT by judiciously breaking in-plane mirror and rotational symmetry theoretically and established its results consistency numerically. An anisotropic z-shaped unit element is realized uniquely that transmits one polarization while reflecting other polarization with full 0-2π control over phase of incident light. A C2 symmetric unit element realizing AT of 0.74 in transmission under LCP illumination, while for RCP illumination, it provides AT of 0.8 in reflection at 1550 nm. This behavior of AT is explained in detail using electric and magnetic field resonances of the unit element design. Since the design attains full phase control, various phase-dependent phenomena can be implemented such as lens, Bessel-beam generation, hologram, etc. Therefore, for a further proof of concept, metasurfaces, based on the proposed z-shaped unit elements are demonstrated, which realize independent holograms in forward and backward direction under LCP and RCP illumination, respectively. In light of these results, the proposed z-shaped design can enable compact on-chip chiroptical devices, which can be employed in chiral sensing and imaging.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
See Supplement 1 for supporting content.
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