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Abstract
Integrating multiple independent functionalities into one single photonic device has been an important part in optoelectronic system. In this paper, we here propose a kind of asymmetric multifunctional metadevice operating at 1550 nm (in optical communication band), which can manipulate the light with four different functions, depending on the polarization and illumination direction of incident light. As a proof of our concept, we design this metadevice composed of the upper metasurface layer, middle grating layer and lower metasurface layer. For x-polarized incident light, the metadevice under forward illumination works as transmissive focusing lens and vortex beam generator of y-polarized light, while under backward illumination it acts as a reflective vortex beam generator. In contrast, for y-polarized incident light, the metadevice under forward illumination behaves as a reflective Bessel beam generator, while a combination of transmissive vortex beam generator and focusing lens of x-polarized light under backward illumination. Our findings may motivate the realization of high-performance multifunctional metadevices and extend the application in complex integrated optical system.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurface can control the light propagation by changing its amplitude, phase, polarization to completely manipulate the electromagnetic waves [1]. Various applications have been achieved by metasurfaces such as wave-plates [2], hologram generator [3], polarizers [4] and so on. It is worth mentioning that integrating multiple independent functionalities into one single photonic devices is highly desired in optoelectronic integration. Recently, some efforts have been devoted to mobilize the interest in multifunctional devices based on metasurfaces [5–17].
As we know, multifunctional metadevices usually include several layers to enrich the functionalities. Some of them perform the functions based on different polarization states of the same incoming optical wave [18–22]. For example, Ding et al. reported a bi-functional gap-plasmon metadevice acting as surface plasmon generator or beam deflector depending on the polarized state of incident wave [18]. In addition, one can also employ different kinds of unit cells in a metasurface to control optical phase and amplitude at different working wavelengths [23–27]. For instance, Hossein et al. designed a composite multilayer nanostructure, which can realize different hologram images at two separated operation wavelengths [23].
Another important research area is asymmetric transmission, which has been widely studied owing to its potential applications in integrated photonic systems for communications and information processing [28–32]. Many different methods can be employed to realize asymmetric transmission such as magnetic material, nonlinear material, photonic crystals, non-symmetric grating, chiral metamaterials, and so on. Asymmetric transmission for both circularly polarized waves and linearly polarized waves have been explored in either multilayer structures or single layer structures [28,29].
In fact, the above mentioned two investigation branches for metasurfaces are often considered as independent parts. Few researches concentrate on integrating the multi-functionalities and asymmetric transmission into one single metadevice. And, fully controlling the reflection and transmission light with different scattering characteristics by single polarized light (x or y direction) at certain wavelength in optical communication band has not been reported until now. To solve this problem, we here propose a general strategy to design a tri-layered asymmetric multifunctional metadevice, which can work in both transmitted mode and reflected mode at certain wavelength with four different functionalities at 1550 nm. The key idea is to combine polarization-controlled wave-front functionality and direction-selected asymmetric transmission performance freely to expand the functionality in the full space. As a proof of the concept, under x-polarized light illumination, the metadevice behaves as a composite of transmissive focusing lens and vortex OAM beam generator of y-polarized light, or a reflective vortex OAM beam generator depending on forward or backward illumination. While, under y-polarized light, the metadevice acts as a reflective Bessel beam generator, or a composite of transmissive vortex OAM beam generator and focusing lens of x-polarized light, depending on the light is incoming from the front or back side. It is worth mentioned that different polarized focusing OAM beams can be generated based on the metadevice, so we here classify these two functions as separate parts. To the best of our knowledge, it is the first time to design ultra-thin metadevice possessing four different functionalities with compactness and simplicity, simultaneously controlling not only the transmitted wave-fronts but also reflected wave-fronts on both sides of the interface at certain wavelength light. We believe this design may have significant guidance in designing passive metasurfaces and great application in data communication and encryption.
The organization of this paper is as follows, section 2 presents the structure for asymmetric multifunctional metadevice, and section 3 shows the results and discussion. Brief conclusion is given in the final section.
2. Metadevice structure and operation principle for asymmetric multifunctionalities
To illustrate the working mechanism, Fig. 1(a) schematically shows the configuration of the metadevice, which consists of an upper metasurface layer, middle grating layer and lower metasurface layer. Figures 1(b) and 1(c) represent stereogram and front view of the structural unit with period p = 600 nm, respectively. The upper metasurface layer is composed of a pair of orthogonal “I” shaped Si antennas with thickness t1 on a SiO2 layer (thickness t2). The lower metasurface layer includes an inclined “I” shaped Si antenna with thickness t5 below the SiO2 layer (thickness t4). The pre-mentioned grating layer is gold with thickness t3 and inserted into the middle of the metadevice. The whole metadevice structure includes 40 × 40 structural units in 24 µm × 24 µm area. Figures 1(d)–1(f) depict a part of layouts (xy-view) of the three layers respectively, which clearly indicate the arrangements of unit cells.
Fig. 1. (a) Schematic of the metadevice, (b) stereogram and (c) front view of the structural unit. A part of layouts (xy-view) of (d) the upper metasurface layer, (e) the middle grating layer, (f) the lower metasurface layer.
Quite different from the previous multifunctional metadevices with incident light coming from one direction, our designed metadevice can independently manipulate x-polarized light and y-polarized light from forward direction and backward direction respectively. As shown in Fig. 2(a), for x-polarized light from forward direction (i.e. along the negative z axis), the metadevice behaves as a focusing lens and vortex beam generator, which can change the transmitted light into vortex beam and focus it into a spot with polarization conversion. While under the backward illumination shown in Fig. 2(b), it acts as a reflected vortex beam generator, creating a reflected cross-polarized vortex beam. For y-polarized light, the metadevice functions as a reflected Bessel beam generator when excited by forward incident light shown in Fig. 2(c) and a composite of transmitted vortex beam generator and focusing lens when exited by backward incident light, obtaining a cross-polarized transmitted focusing vortex beam shown in Fig. 2(d).
Fig. 2. Metadevice performs different functions under (a) forward and (b) backward x-polarized incident light; (c) forward and (d) backward y-polarized incident light.
From the above instructions, we can see that in order to achieve the asymmetric multifunctional metadevice, the upper metasurface layer is designed to generate Bessel beam for y-polarized light while focus x-polarized light, and the middle grating layer behaves as a selective transmitter, which holds high reflection for y-polarized light and high transmission for x-polarized light. In addition, the bottom metasurface layer is a cross-polarized vortex beam generator for different polarized incident light. More details will be discussed in the following sections.
2.1 Upper metasurface layer
For upper metasurface layer, two different phase profiles of focusing lens and Bessel beam generator should be introduced at the position of (x, y) for respective orthogonal linear polarizations of incident light in the same interface, resulting in two different functionalities in the x–z plane, respectively. To generate focus beam for x-polarized light, the upper metasurface layer should provide a transmission phase distribution Φx (x, y) as follows [33,34]:
Figures 3(c) and 3(d) schematically indicates the structure unit of the upper metasurface layer with period p = 600 nm, which consists of orthogonal I-shaped Si antennas with thickness t1=700 nm and width w1 = 220 nm on a SiO2 layer with thickness t2=30 nm. The arm lengths of the orthogonal I-shaped Si antennas are L1 and L2 respectively. To obtain the polarization-dependent transmission phase expressed in Eqs. (1) and (2) at λ = 1550 nm, the two arm lengths should be optimized for the required phase profile for x polarized and y polarized light respectively. Then, we carried out full three-dimensional finite difference time-domain (FDTD) simulations, in which periodic boundary conditions were applied to the x- and y-direction, and perfectly matched layer condition was used along the z-directions. According to the principle of indexed waveguide theory, the phase shift decided by different arm length L1 (L2) can be expressed as $\Phi { = }{{2\pi {{n}_{{eff}}}{{t}_1}} \mathord{\left/ {\vphantom {{2\pi {{n}_{{eff}}}{{t}_1}} \lambda }} \right.} \lambda }$, where neff represents the effective refractive index. Figure 3(e) indicates that the effective refractive index (neff) can change enough to achieve the required phase control by adjusting the arm lengths L1 under y-polarized beam, which can serve as lookup data to choose suitable L1 for the required phase manipulation. Due to the symmetry in structure and polarization, it is also suitable to guide the design of the arm length L2 for x-polarized beam.
Fig. 3. The phase distribution of (a) focusing lens and (b) Bessel beam generator. (c) Structure unit of the upper metasurface layer (d) top view of the unit. (e) The effective refractive index as a function of L1 at wavelength λ = 1550 nm under y -polarized beam.
Firstly, to verify the focusing effect for x-polarized incident light, Fig. 4(a1) shows the transmission Ex component at the wavelength 1550 nm in the x-z plane. It can be seen that a clear focusing effect is obtained with the focus length f = 13.2 µm close to the re-designed value 14 µm. For a quantitative analysis of focusing characteristics, we depict the corresponding Ex component in the x-y plane and corresponding normalized intensity at the cross plane of transmissive focal point in Figs. 4(a2) and 4(a3) respectively. It can be seen that the full width at half maximum (FWHM) of electric intensity is around 0.78λ=1250 nm, smaller than the operation wavelength, showing good sub-wavelength focusing property for x-polarized light. We here define the transmitted focusing efficiency as the ratio of transmitted electric field intensity at the focus point to the incident intensity, which is calculated to be 52%.
Fig. 4. Under x-polarized illumination: (a1) transmission Ex component at 1550 nm in the x-z plane, (a2) Ex component in the x-y plane and (a3) corresponding normalized intensity at the cross plane of focal point. Under y-polarized illumination: (b1) transmission Ey component at 1550 nm in the x-z plane and (b2) in the x-y plane at 10 µm under the upper metasurface layer, (b3) corresponding phase distribution in the x-y plane. The white dashed rectangles represent the locations of the structures.
Next, we study the Bessel beam performance under y-polarized light. Figure 4(b1) illustrates the electric field intensity distribution in the x-z plane, where non-diffracting propagation behaviors are clearly observed in a range longer than 14λ (21.7 µm). Figures 4(b2) and 4(b3) show the corresponding electric field intensity distribution and phase distribution in the x-y plane at 10 µm under the upper metasurface layer, respectively. The bright spot and phase distribution exhibit clear features of a 0-order Bessel beam. The beam generation efficiency can be defined as the corresponding transmitted intensity at the beam center point to the incident intensity, which is equal to 55%.
Therefore, for the standalone upper metasurface layer, it can perform different functions dependent on the polarization direction of incident light.
2.2 Middle grating layer
As we all know, the effective refractive indices of 1D subwavelength grating are polarization dependent, so the grating can be designed to offer high transmission for x-polarized light and high reflection for y-polarized light. To further demonstrate this feature, we make detailed analysis in the following two paragraphs.
According to effective medium theory, the subwavelength grating can be modeled as homogenous material, whose refractive indices are decided by Rytov’s formulas [37,38]:
After numerous simulation and optimization, the appropriate grating structure can be achieved as shown in Figs. 5(a) and 5(b) with the grating constant Λ=600 nm, filling fraction η=0.38, width w2=230 nm and thickness t3=90 nm. Figures 5(c) and 5(d) show the transmissivity and reflectivity for x-polarized and y-polarized incident light respectively. We can find that x-polarized light can achieve >0.8 transmissivity, while y-polarized light with >0.7 reflectivity at 1550 nm, which indicates good performance of selective transmission and reflection for different polarized light.
Fig. 5. (a) Structure unit of the middle grating layer and (b) top view of the unit. Reflectivity and transmissivity of the middle grating layer under (c) x-polarized and (d) y-polarized incident light.
2.3 Lower metasurface layer
To generate vortex beam for x-polarized light and y-polarized light simultaneously, the dielectric interface should be created by arranging the eight parts antennas as shown in Fig. 6(a) [39]. The interface introduces a spiral-like phase shift for the planar wave-front of the incident light, making a vortex beam with l = 1 (l is the topological charge of vortex beam).
Fig. 6. (a) Phase distribution for creating vortex beam, (b) structure unit of the lower metasurface layer and (c) top view of the unit.
Figure 6(b) shows the structure unit of the lower metasurface layer, which consists of I-shaped Si antennas with thickness t5=700 nm under a SiO2 layer with thickness t4=100 nm. The top view of the unit is shown in Fig. 6(c). The width w3 and period p are 220 nm and 600 nm, and the arm length of the orthogonal I-shaped Si antennas is Lr, which needs to be optimized to obtain the transmissive phase for the cross-polarized component of incident light. After numerical simulations, we choose the appropriate Lr of first four unit cell as 544 nm, 441 nm, 338 nm, 235 nm with orientation angle θ = 45° to the x-axis to provide the former π phase. Just like other V- or C- shape structure in the previous literature [40,41], the later four unit cells with additional π phase can be obtained by flipping the first four units over the y-axis.
For further understanding, concrete simulation analysis has been carried out. As can be seen in Figs. 7(a2) and 7(a3), under x-polarized incident light along the –z axis, the spiral phase distribution and electric field of cross-polarized light are well produced respectively, by designing the calculated amplitude and phase responses of the “I” shaped antennas. In comparison, due to the property of polarization conversion, transmissive field of x-component exhibits annular phase distribution in Fig. 7(a1). Similarly, under y-polarized-light, the metasurface can also create well-performed vortex beam of cross-polarized light with clear spiral phase distribution and electric field shown in Figs. 7(b1) and 7(b3), while no such phenomenon for co-polarized light in Fig. 7(b2).
Fig. 7. Under x-polarized light illumination: phase distribution of (a1) x component and (a2) y component, (a3) electric field of y component in the x-y plane. Under y-polarization light illumination: phase distribution of (b1) x component, (b2) y component and (b3) electric field of x component in the x-y plane.
To further demonstrate the property, we here define the vortex beam generation efficiency as the far field transmitted intensity to incident intensity. The efficiencies are 44% under x-polarized light illumination and 43% under y-polarized light illumination.
3. Results and discussion
Based on the above operation principle, we need to combine the upper metasurface layer, middle grating layer and lower metasurface layer to make the asymmetric multifunctional metadevice and discuss its scattering properties, which can achieve multiple different functions including focusing, vortex beam and Bessel beam generation, depending on the light polarization direction and incident direction.
3.1 Under x-polarized light illumination
3.1.1 Forward illumination
In this case, the forward light passes through the upper and middle grating layer with beam-focusing ability, and then is converted to vortex beam by the lower metasurface layer with polarization conversion property. Figure 8(a) indicates the cross-polarized electric field intensity (|Ey|2) of metadevice in x-z plane under x-polarized incident light. It clearly shows that the output electric field focuses into a compact zone around z-axis. The white dashed line marks the position of the focal plane (f = 13.2 µm), close to the designed value 14 µm. Meanwhile, |Ey|2 of the metadevice at the cross plane of transmissive focal point in x-y plane is depicted in Fig. 8(b). Obviously, a spot with dark center is obtained for the energy intensity, which directly confirms the consequence of vortex beam. Figure 8(c) illustrates the intensity along a horizontal cut across the centers of Fig. 8(b). The simulated FWHM of the focusing vortex beam is about 0.62λ ≈ 969 nm at reasonable range. Like the method in section 2.1, the focusing vortex beam efficiency can be calculated as 25%. Compared with the focusing efficiency of standalone upper metasurface layer (52%), the loss attributes to the limit of polarization conversion of lower metasurface layer.
Fig. 8. (a) |Ey|2 of the metadevice in x-z plane under x-polarized incident light, (b) |Ey|2 and (c) normalized intensity spectra at the cross plane of focal point. The white dashed rectangle represents the location of the structure.
3.1.2 Backward illumination
For this case, when the backward x-polarized incident light hits the lower metasurface layer, the vortex beam can be generated with polarization conversion from x-polarized light to y-polarized light. Due to the highly reflection of the middle grating layer for y-polarized light, a reflected vortex beam can be achieved. Figures 9(a) and 9(b) indicate the phase distribution and electric field of y-component reflected vortex beam respectively, which clearly shows good performance of cross-polarized vortex beam with topological charge l = 1. Due to the high reflection of middle grating layer, the corresponding calculated transmitted efficiency is 70%. However, the phase distribution of x-component depicted in Fig. 9(c) exhibits no spiral pattern, with transmitted field amplitude approaching zero in Fig. 9(d), demonstrating good performance of asymmetric transmission.
Fig. 9. Under x-polarization light illumination: (a) reflective phase distribution and (b) electric field distribution of y component, (c) reflective x- component phase distribution, (d) transmissive y- component electric field distribution.
3.2 Under y-polarized light illumination
3.2.1 Forward illumination
As discussed above, when y-polarized light impinges the metadevice in the forward direction, the upper metasurface layer acts as a Bessel beam generator and the middle grating layer works as a high efficiency reflector, achieving a reflected y-polarized Bessel beam. Figure 10(a) illustrates the simulated y-polarized electric field intensity at λ = 1550 nm in the x-z plane, where non-diffracting propagation behaviors can be observed with length longer than 14 λ. Furthermore, the corresponding electric field intensity and phase distribution in the x-y plane at 11 µm above the metadevice are indicated in Figs. 10(b) and 10(c) respectively, which all represent good 0-th order Bessel beam. Due to the high reflection performance of the middle grating layer, the calculated efficiency is approaching 60%, bigger than the value of standalone upper metasurface layer mentioned in Section 2.1. On the other hand, as shown in Fig. 10(d), almost no scattering electric field appears in the transmitted part, verifying robust asymmetric transmission property.
Fig. 10. (a) Reflected y-polarized electric field intensity in the x-z plane at λ = 1550 nm, the corresponding (b) electric field intensity and (c) phase distribution in the x-y plane at 11 µm above the metadevice, (d) transmitted y-polarized electric field intensity. The white dashed rectangle represents the location of the structure.
3.2.2 Backward illumination
In this case, when the y-polarized light at 1550 nm “hits” the metadevice from backward direction (along z axis), the device works as a focusing lens and vortex beam generator, which changes the incident light to vortex state and focuses it into a spot with the polarization conversion from co-polarization to cross-polarization.
To verify the working principle, we carried out a series of simulations by the finite-difference-time-domain (FDTD) method. Figure 11(a) shows the x-polarized electric field intensity in the x-z plane under the backward y-polarized light (λ = 1550 nm) illumination, which unambiguously demonstrates the ideal focusing effect of the metadevice. The white dashed line marks the focusing length f = 13 µm, close to the designed value 14 µm. Subsequently, the x-polarized electric field intensity distribution at the cross plane of focus point is depicted in Fig. 11(b), which demonstrates squeezed spot with dark center around the focus and clearly indicates the formation of vortex beam. The normalized intensity spectra demonstrates that the FWHM of the focusing vortex beam is about 0.62λ ≈ 970nm, as shown in Fig. 11(c). The focus efficiency is calculated as 28% close to the value mentioned in section 3.1(a).
Fig. 11. Under backward illumination: |Ex|2 in the (a) x-z plane and (b) x-y plane, (c) normalized |Ex|2 at the cross plane of focus point. The white dashed rectangle represents the location of the structure.
Finally, in order to clearly and intuitively understand the functions realized by this polarization and direction-controlled asymmetric multifunctional metadevice, we here present the details in Table 1.
Table 1. Different functions realized by the asymmetric multifunctional metadevice.
4. Conclusion
In summary, a novel asymmetric multifunctional metadevice has been presented, which can achieve four different functionalities. Based on the selective transmission and reflection for different polarization light of the middle grating layer, the function of the proposed metadevice not only relates to the polarization direction of the incident light, but also strongly depends on whether the incoming light comes from the forward or backward side at λ = 1550 nm. In fact, by scaling down the unit size, the proposed design can be readily extended to other frequencies. Compared with previous reports, the proposed metadevice provides another degree of freedom in designing multifunctional metadevices, expands the application scope of passive metasurfaces. We believe the concept with great performance simplifies the design of multi-wavelength, multi-polarization optical systems and is promising for applications in photonic integration and device miniaturization.
Funding
National Natural Science Foundation of China (61635004, 61775069); NSFC-STINT Joint China-Sweden Mobility Programme (51911530159, CH2018-7700).
Disclosures
The authors declare no conflicts of interest.
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