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Abstract
It is highly desirable to develop asymmetric transmission (AT) devices for both linearly and circularly polarized light. However, currently existing metamaterial-based AT devices require multi-step micro-nano fabrication processes and usually realize AT responses only for linearly or circularly polarized waves, not simultaneously for both. We here propose a dual-band AT device for both linearly and circularly polarized waves in the near-infrared region by using a bilayer coupled complementary chiral metasurface, which includes a half-gammadion-shape gold (Au) structural layer and its Babinet’s complimentary copy. Unlike other multilayer AT devices working at optical frequencies, it takes less micro-nano fabrication steps. Besides, with the help of chirality and the inherent near-field coupling effect between the two complementary Au layers, the maximal AT parameters for linearly and circularly polarized waves can reach up to 0.45 and 0.56, respectively. The underlying mechanisms of dual-band AT responses are also investigated in depth from the perspectives of chirality and coupling effect. Our work offers a new and simple approach to high-performance AT devices, helps to better understand near-filed coupling effect in coupled complementary metasurfaces, and also expands their application fields.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Chirality refers to the geometric property of a structure that cannot be superimposed with its mirror by simple rotation or translation. In recent years, owing to their unique properties characterized by a cross-coupling between the electric and magnetic fields to tailor the polarization state and amplitude of light [1–3], chiral metamaterials or metasurfaces have been drawing enormous interest in optical activity [4], circular dichroism [5], the generation, manipulation and detection of circularly polarized light [6,7], spiral field generation in Smith-Purcell radiation [8], spin-locked retro-reflection [9], and asymmetric transmission (AT) [10,11]. Particularly, AT devices play an indispensable role in noise control or cancelation [12,13], source protection [14], one-side detection/sensing [15,16] and signal processing [17], etc. However, traditional AT devices employing magneto-optical materials suffer from bulky volume and incompatibility with mature integrated photonic platforms. The realization of AT via metamaterial was first experimentally demonstrated by Fedotov et al. in 2006 [18], but it only worked for circularly polarized light in microwave band. Four years later, Menzel et al. [19] achieved AT of linearly polarized waves by using three-dimensional chiral metamaterials. Since then, an increasing number of chiral metamaterial structures have been used to realize AT response, and the operation wavelengths have covered from microwave to visible [20–23].
Because single-layer chiral metasurface cannot exhibit AT response for linearly polarized waves, double- or multi-layer cascaded structures are developed, such as two mutually twisted U-shaped structures [24], multilayered anisotropic chiral metamaterials [25], and two perpendicular split-cube resonators [26], etc. However, such multiple-layered structures are not suitable for the miniaturization of devices and photonic integration. Moreover, they usually face multi-step and challenging manufacturing processes, especially for those working in the visible and near-infrared bands, multiple complex and time-consuming micro-nano fabrication steps are required [26,27]. In addition, these chiral metasurfaces realize AT responses only for linearly or circularly polarized waves, not simultaneously for both of them [10,24,28]. Therefore, it is highly desirable to develop AT devices for both linearly and circularly polarized light with easier and relatively convenient fabrication processes.
Most recently, a new type of bilayer coupled complementary metasurface was developed to manipulate electromagnetic wave based on Babinet complementary principle [29–31]. Compared with other bilayer or multilayer metasurface or metamaterial structures [25,27], it can be readily fabricated over a large area at a relatively low cost [29,31]. What’s more, according to Babinet’s law, the coupled complementary bilayer structures can naturally possess electric and effective magnetic responses over a wide range of electromagnetic spectra [30–32]. When the two metallic layers are close enough, strong near-field coupling can induce antiparallel electrical currents and form a magnetic resonance inside the structure. The interaction between the electric and magnetic responses can provide more freedom to tailor the amplitude, phase and polarization of electromagnetic waves [33]. For instance, they have been utilized to realize broadband infrared absorber [30], enhance visible light transmission [31], and improve the coloration resolution of metasurface-based plastic consumer products [29], etc.
Here, we employ a bilayer coupled complementary chiral metasurface to realize dual-band asymmetric transmission (AT) for both linearly and circularly polarized light at near-infrared frequencies. It consists of a half-gammadion-shaped gold (Au) structural layer and its Babinet’s complimentary copy separated by a dielectric silica (SiO2) layer. Simulated results show that it can reach maximum AT values of 0.45 and 0.56 for linearly and circularly polarized waves, respectively. This strong AT response is found to originate not only from the chiral feature of the proposed device, but also from the inherent coupling effect between the two complementary metallic layers.
The paper is organized as follows. In section 2, we present device structure of the proposed coupled complementary chiral metasurface. Then the results and discussions are given in section 3, in which dual-band AT phenomenon and its underlying mechanism are investigated in detail by discussing the roles of chiral feature and coupling effect. Finally, a conclusion is made in section 4.
2. Device structure
Figure 1 schematically shows the structural unit array of the proposed AT device, along with the optical configuration and the coordinate system. It consists of two coupled complementary gold (Au) structural layers separated by conformal pillars made of silica (SiO2) dielectric layer. The upper Au structural layer is composed of half-gammadion-shaped Au structures, while the lower one is its Babinet-inverted version. The half-gammadion structure, often used as the building block of chiral metamaterials [28,34,35], can be viewed as the combination of a long bar along the y-axis and two side bars along the x-axis, and the lengths of horizontal and vertical arms are l1=150 nm and l2=250 nm, respectively. The thickness of the Au layers is h1=30 nm, and the spacing distance between the two Au layers is g = 30 nm, which is much smaller than the near-infrared working wavelength and implies strong near-field coupling effect between the upper and lower complementary metallic layers. The period of the structural unit is p = 500 nm. Unless otherwise specified, these parameter values will not change throughout this paper.
Fig. 1. Schematic diagram of the proposed device. (a) Perspective view of the structural unit array of the proposed device. (b) Top view of the structural unit in the x-y cut-plane (right-upper panel) and the side view of the structural unit in the y-z cut-plane (right-lower panel) with optimized geometrical parameters: p = 500 nm, l1=150 nm, l2=250 nm, w = 100 nm, h1=30 nm, g = 30 nm.
Compared with other bilayer or multilayer AT devices working at near-infrared or visible frequencies which require multiple micro-nano fabrication steps to obtain the bilayer or multilayer metallic structures [27,28], the double Au layers of the proposed AT device can be obtained by just one metallic deposition step on the patterned SiO2 substrate [31]. Besides, such bilayer complementary structures also have the advantage of convenient integration with various photonic platforms [30].
In order to study the asymmetric transmission (AT) property of the designed device, we adopt full three-dimensional finite-difference time-domain (FDTD) for numerical simulations. Periodic boundary conditions are applied in the x- and y-directions, and perfectly matched layer condition is applied in the z-direction. The dielectric substrate is chosen as silica with relative permittivity of 2.1 and the gold is modeled with a lossy Drude dispersion [36]. It is worth noting that the periodicity p = 500 nm is much smaller than the operation wavelengths (800 ∼ 1700 nm) in our study, therefore, the device only supports the 0th diffraction order.
3. Results and discussion
3.1. AT response of the coupled complementary chiral metasurface
In order to understand how the designed chiral metasurface exhibits AT responses for both linearly and circularly polarized waves, we employ Jones matrix method to describe its transmission characteristics. When an incoming plane wave normally impinges on the device along the forward direction (i.e., the positive z-direction), the electric field of the incident and transmitted light can be expressed as [19]
For a Lorentz reciprocity system, the Jones matrix for the backward propagation direction (along the negative z-axis) is [19,37]
When circularly polarized light is incident, the relationship between the transmission matrixes of circularly and linearly polarized waves is given as [19,37]
As illustrated in Fig. 2(a), the proposed metasurface under forward illumination exhibits quite different cross-polarization transmission coefficients Tyx and Tyx, suggesting it is able to realize AT response for linearly polarized waves. According to Eqs. (5) and (6), we calculate and plot the corresponding AT parameters against optical wavelengths in Fig. 2(c). It shows the AT parameters for x- and y-polarized light are almost contrary to each other, that is, Δlin(x) = -Δlin(y). Interestingly, dual-band AT phenomenon emerges. The first AT band is around λA=1214 nm with wider spectral range and bigger AT parameter, and the biggest one is 0.45 at λA=1214 nm. The other AT band is around λC=823 nm with narrower spectral range and smaller AT parameter. It is noted that the AT parameters in the two bands have opposite signs, one is positive, the other negative. In contrast, the AT parameter is nearly zero at the intermediate wavelength λB=900 nm.
Fig. 2. Simulated transmission coefficients (absolute value) for linearly polarized wave in (a) forward propagating and (b) backward directions. AT parameter of linearly (c) and circularly (d) polarized light. “F” and “B” in the legend represent “Forward” and “Backward”, respectively. The letters “A”, “B” and “C” in (c) mark the three typical wavelengths discussed later.
In addition, Fig. 2(a) also indicates co-polarization transmission coefficient Txx is different from Tyy in the whole operating band. As is already verified [19,37], the difference between Txx and Tyy could ensure asymmetric transmission for circular polarization waves. According to Eq. (8), we calculate the AT parameters for circularly polarized waves and show the result in Fig. 2(d). Similar to linearly polarized waves, circularly polarized waves also display two AT bands, the two corresponding peak wavelengths are near to those for the linearly polarized light, and the maximal AT parameter for circularly polarized wave is 0.56 at λ=1190 nm. It is worth mentioning that few work has reported such dual-band AT phenomenon for both linearly and circularly polarized waves.
To more concisely unearth the underlying mechanism behind the AT property of the proposed coupled complementary chiral metasurface, in the following we discuss the roles of chiral feature and near-field coupling effect in the AT behavior only for the case of linearly polarized waves.
3.2. The role of chirality in asymmetric transmission
In the proposed coupled complementary chiral metasurface, the upper Au structural layer is composed of half-gammadion-shaped Au structures, while the lower one is of its Babinet-inverted version, and both of them are also with chiral features [38]. In the next, we first analyze the effect of chirality on the AT behavior of the whole AT device, and then discuss the chirality of the individual upper/lower Au structural layer.
3.2.1. Transmission properties of the whole device
For the whole device (i.e., the proposed coupled complementary chiral metasurface shown in Fig. 1), the lengths of the two short arms and the long arm, i.e., l1 and l2, are related to the device chirality. Figures 3(a) and 3(b) plot the AT parameter Δlin(x) as a function of incidence wavelength for different values of l1 and l2, respectively. As shown in Fig. 3(a), when the length of the two short arms, l1, is decreased from 175 nm to 125 nm (with other geometrical parameters unchanged), the position of longer resonance wavelength gradually blue-shifts. These varying trend can be explained by the inductor–capacitor (LC) circuit model presented in [39]. Notably, when l1 is set to zero, asymmetric transmission (AT) parameter Δlin(x) becomes 0, and AT phenomenon disappears. This is because when l1 is zero, the half-gammadion–shape will be degenerated into a nanorod–shape, and then the whole structure becomes axisymmetric and loses chiral characteristic, hence no cross-polarization conversion effect can take place, and then Txy= Tyx=0 in such case. Therefore, according to Eqs. (5) and (6), it no longer supports AT function. Because of the same reason, similar result can also be observed in Fig. 3(b) when l2 is applied to zero. These results imply that chiral feature is an important factor that contributes to the AT response of the whole device.
Fig. 3. AT parameter Δlin(x) varies as a function of incidence wavelength for different values of l1 (a) and l2 (b).
3.2.2. Transmission properties of the individual upper/lower Au structural layer
Now, we analyze the transmittance properties of the individual upper Au structural layer and the individual lower Au layer. For the sake of convenience, we name the first structure as chiral structure I, and the second as chiral structure II.
For chiral structure I, it has only the upper half-gammadion-shape Au layer on the SiO2 substrate, while the corresponding parameter values are kept equal to those shown in Fig. 1. One can see from Fig. 4(a1), no matter x- or y-polarized light is incident, forward and backward transmittance spectra always coincide with each other. Namely, there is no AT response in this situation. The corresponding Jones matrix elements are presented in Fig. 4(a2), it indicates that the cross-polarization transmission elements Tyx and Txy are non-zero but equal to each other, reflecting that such a single half-gammadion layer has the function of cross-polarization conversion but it cannot support AT response.
Fig. 4. Total transmittance (a1) and the forward transmission coefficients (a2) of chiral stucture I. (b1) and (b2) are the transmittance and the forward transmission coefficients of chiral stucture II. The insets in (a1) and (b1) schematicaly show the two chiral structures, respectively. “F” and “B” in the legend represent “Forward” and “Backward”, respectively.
Judging from the above analyses, one can conclude that, a structure only with chirality cannot guarantee AT response for linearly polarized light. For the proposed complementary chiral metasurface, apart from chirality, the near-field coupling effect between the two complementary Au structural layers should also be taken into consideration.
3.3. The role of coupling effect in dual-band AT responses
Since the proposed AT device is composed of bilayer complementary Au layers and the thickness of dielectric spacer layer is far less than operation wavelength, strong near-field coupling effect exists between the two metallic layers. For simplification, here, we just consider the case of x-polarized light incidence, a similar method can be taken for the y-polarized light.
3.3.1. Formation mechanism of dual-band AT responses
As observed earlier in Fig. 2(c) for linearly-polarized light, dual-band AT phenomenon emerges, one broader band is around λA=1214 nm with bigger AT parameter, another narrower band is around λC=823 nm with smaller AT response strength, and the AT parameters in the two bands have opposite signs, one is positive, the other negative; while at the intermediate wavelength λB=900 nm, the AT parameter is nearly zero. In the following, the formation mechanism of dual-band AT responses are explored from the perspectives of the coupled electric field and current density distributions.
A). Coupled electric field distribution
The electric-field component Ez distribution in the y-z plane under x-polarized light forward illumination is mapped in Fig. 5. Strong Ez field can be clearly seen between the upper and lower Au structures for all the three wavelengths, suggesting the existence of near-field coupling effect. While the positive (marked as ‘+’) and negative (marked as ‘-’) charges concentrated near the upper/lower Au structures signify the existence of electric dipole or electric multipolar response. Especially at the shorter resonance wavelength λC=823 nm, notable electric multipolar response is observed near the lower Au structural layer, in sharp contrast to the electric dipole at the longer resonance wavelength λA=1214 nm. In comparison with lower-order dipole resonance peaks, higher-order multipolar resonance peaks usually exhibit larger quality factor (Q-factor) with narrower band characteristics because of lower radiative loss [40], this explains why the AT band around λC=823 nm is narrower than that around λA=1214 nm, as shown in Fig. 2(c).
Fig. 5. Ez distribution in the y-z plane at λA=1214 nm (a), λB=900 nm (b) and λC=823 nm (c). The black dashed lines display the outlines of the two metallic layers.
Moreover, Fig. 5 also shows that the Ez on the surface of the upper Au structures is out-of-phase with respect to that on the lower ones, antiparallel current consequently forms and thus magnetic dipole along the x-direction is induced. The coexistence of electric and effective magnetic responses is a typical feature of coupled complementary bilayer structures, and it enables multi-dimensional control on electromagnetic waves [41,42].
What’s more, by referring to the axis limits of the color bars in Fig. 5, one can find that the Ez amplitude at λC=823 nm is only half of that at λA=1214 nm, while that at λB=900 nm is much smaller and can be neglected, which means the coupling strength is accordingly weakened. Interestingly, their corresponding AT parameters shows a similar trend (see Fig. 2(c)), with the |Δlin(x)| value being 0.45 at λA=1214 nm, 0.26 at λC=823 nm, and near-zero at λB=900 nm. Such correlation between coupled electric-field Ez and the AT parameter can be attributed to the re-radiation of cross-polarized electric dipole induced by the coupling effect. And the cross-polarized transmission coefficient Tji relates to cross-polarized electric field distribution by [43]:
Equation (9) tells that the cross-polarized transmission coefficients can be identified by the amplitude of dipole excitation, and a larger cross-polarized electric dipole will in turn lead to a higher cross-polarized transmission. This may also explains why the abovementioned two bands exhibit different AT response strengths.
B). Current density distribution
It is well known that no cross-coupling effect can take place between the orthogonal incident electric field and the induced magnetic field, and they never contribute to polarization conversion [44,45]. Therefore, in the case of x-polarized light incidence, only when the induced magnetic field H has x-component Hx, can it makes contribution to polarization rotation for transmitted waves. Hence, we are more concerned about the current distribution in the long arm which is along the y-axis, because only the current on its surface can generate induced magnetic field along the x-direction, which can interact with the incoming x-polarized electric field Ein.
Figures 6(a)-6(c) map the current density distributions on the surfaces of the upper and lower metallic layers under forward incidence of x-polarized light at λA=1214 nm, λB=900 nm and λC=823 nm, respectively.
Fig. 6. Current density distribution on the surfaces of the lower (a1-c1) and upper (a2-c2) metallic layers under forward incidence of x-polarized light at λA=1214 nm, λB=900 nm and λC=823 nm. (a3) is the zoom map of (a2). The solid black arrows show the current direction, the dotted black lines mark current distribution nodes, and the dashed green lines in (a1)-(c1) mark the outlines of the lower metallic layer.
At λA=1214 nm, as displayed in Figs. 6(a1) and 6(a2), the currents directions (marked by solid black arrows) on the lower and upper Au layers are opposite to each other, one is along the negative y-axis, the other along the positive y-axis. These anti-parallel currents will induce magnetic dipoles M along the x-axis and the induced magnetic field Hx. Because Hx is parallel to the incident x-polarized electric field Ein, cross-coupling effect occurs, and this can explain the origins of the chirality and cross polarization of the proposed device. Moreover, the current distribution nodes (marked by the dotted black lines) in Fig. 6 is the result of opposite currents colliding with each other [46], and the oscillating currents between two adjacent nodes form standing waves. The number of nodes can be used to judge the plasmonic resonance order level [47], the more the nodes there are, the higher the resonance order is.
At λC=823 nm, Figs. 6(c1) and 6(c2) show that the node number is bigger than that at λA=1214 nm. This means that a higher order resonance mode is excited at λC=823 nm, which is consistent with Fig. 5(c). Besides, a higher order resonance requires higher energy from the incident wave, which may lead to lower cross-polarization transmission with x-to-y polarization conversion [46]. Moreover, the magnetic dipoles are with reverse directions for these nodes, as shown in Figs. 6(c1) and 6(c2), this will further weaken the transmission conversion at λC=823 nm.
At the non-resonant wavelength λB=900 nm, as shown in Figs. 6(b1) and 6(b2), the current density amplitude is much smaller, suggesting the coupling strength is much weaker than those at λA=1214 nm and λC=823 nm. Thereby, it is not difficult to understand why the transmittance and the AT parameter at λB=900 nm are both very low.
However, when the x-polarized wave is reversed from forward to backward incidence, the light will first hits the lower metallic layer. The light with longer wavelength (λA=1214 nm) cannot propagate through the metasurface readily due to the weaker coupling effect (not shown here) than the forward case, thus it gets a lower transmittance, and then Ttotal(F) - Ttotal(B) > 0, the AT parameters Δlin(x) has a positive value of 0.45. In contrast, the light with shorter wavelength λC=823 nm can easily penetrate the device through stronger coupling effect (not shown here), thus it can realize higher transmittance, and then Ttotal(F) - Ttotal(B) < 0, the AT parameters Δlin(x) has a negative value of -0.26. As a consequence, the proposed device exhibits dual-band AT property, one band is around λA=1214 nm at which more energy is allowed to pass through in the forward direction, and the other is around λC=823 nm at which more energy is allowed to transmit in the backward direction.
3.3.2. Influence of spacing thickness
As is well known, coupling strength is directly related to the vertical distance g between the two metallic layers [48,49]. Here, we plot the AT parameter Δlin(x) as a function of incidence wavelength for different spacing distance g. As shown in Fig. 7, when g increases from 30 nm to 90 nm, the magnitude of AT parameter Δlin(x) becomes smaller. Obviously, with the increase of g, coupling strength between the two metallic layers is decreased, and consequently the AT effect gets attenuated, too.
4. Conclusion
In summary, we propose and numerically demonstrate dual-band asymmetric transmission for both linearly and circularly polarized waves in the near-infrared region by using a bilayer coupled complementary chiral metasurface. Its structural unit, composed of a half-gammadion-shape Au structure and its Babinet-inverted copy separated by silica, is of chiral feature. With the help of chirality and inherent near-field coupling effect between the two coupled complementary Au layers, the maximal AT value can reach up to 0.45 and 0.56 for linearly and circularly polarized waves, respectively. By employing Jones matrix method and analyzing the electric field and current density distributions, the physical mechanism of dual-band AT phenomenon is investigated in detail. The results reveal that, apart from the device chirality, the coupling effect between the two complementary metallic layers plays a vital role in the AT behavior, especially in the formation of dual-band AT responses.
Unlike other chiral metasurfaces used for near-infrared or visible AT response, which are of multi-layer structure and thus need very complex and time-consuming multiple-step nano-fabrication processes, the coupled complementary chiral metasurface presented here is largely free from these limitations. The designed device can also work in other frequency bands by scaling up the dimensions, and we believe that it will find potential applications including, but not limited to, interference suppression, noise control, one-side detection/sensing, polarization rotating, and photonic integrated circuits.
Funding
National Natural Science Foundation of China (61675074, 61705127, 61805078).
Disclosures
The authors declare no conflicts of interest.
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