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Abstract
Dielectric metasurface empowering efficient light polarization control at the nanoscale, has recently garnered tremendous research interests in the field of high-resolution image encryption and display, particularly at low-loss wavelengths in the visible band. Nevertheless, due to the single fixed polarization conversion function, the image (either positive or negative image) can always be decrypted in a host-uncontrollable manner as long as the user applies an analyzer to select the polarization component of the output light. Here, we resort to half-waveplate- and quarter-waveplate-like silicon nanopillars to form a metamolecule of a dielectric diatomic metasurface, which can yield versatile linearly polarized (LP) and circularly polarized (CP) light upon orthogonally linear-polarized incidences, providing new degrees of freedom for image display and encryption. We show both theoretically and numerically that versatile different paired LP and CP combinations could be achieved by simply adjusting the orientation angles of the two nanopillars. The bifunctional polarization conversion functions make possible that a meta-image can only be seen when incident light is linearly polarized at a specific polarization angle, whereas no image can be discerned for the orthogonal polarization incidence case, indicating the realization of incidence-polarization secured meta-image. This salient feature holds for all individual metamolecules, reaching a remarkable image resolution of 52,916 dots per inch. By fully exploiting all polarization conversions of four designed metamolecules, three-level incidence polarization-secured meta-image can also be expected.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Polarization is an important property of electromagnetic waves, and can be classified into linear polarization, circular polarization, and elliptical polarization for completely polarized light. The manipulation of light polarization can be achieved by polarization components such as polarizers and waveplates. In particular, crystal-based conventional waveplate realizes the polarization conversion through the birefringence effect where the input orthogonal linear polarization components experience different phase accumulations during the propagation within the medium. As such, these devices are usually bulky in size, requiring high manufacturing accuracy, and not suitable for miniaturized and highly integrated system construction. In recent years, metasurface has become one of the hot research topics in the field of nanophotonics. It is an ultra-thin nanostructured artificial electromagnetic material that can be designed to manipulate different properties of electromagnetic waves, among which the generation and conversion of polarization have garnered tremendous attention [1–12]. Meanwhile, on the basis of polarization manipulation, control of the polarized light phase makes the metasurface a promising candidate to integrate multiple light-wavefront shaping functionalities into a single platform [13]. So far, a variety of multifunctional polarization metasurfaces have been demonstrated in waveguide polarizers [14,15], metalens [16,17], beam splitter [18–20], polarization-regulated holography [21,22], vector beams [23–25], and polarization-sensitive sensing [26,27].
In addition to supplement or replace conventional polarization components, metasurface-based polarization control has also shown great potential in high-resolution grayscale image display. For example, metasurface composed of spatially distributed nanostructures or meta-atoms can be meticulously designed in terms of the orientation angles to conceal a grayscale image [28–34]. For metasurfaces incorporating meta-atoms functioning as the half-wave plate (HWP), different nanostructure orientation angles will convert the incident linear polarization into a spatially varying polarization profile with equal efficiency, and thus the visualization of the image can be made possible by viewing specific polarization components with the help of an analyzer [28–31]. On the other hand, nanopolarizer-based metasurfaces can directly display a grayscale image as the output light intensity has already been modified according to the general Malus’ law [32–34]. However, it should be noted that abovementioned polarization conversion functionality of the same type nanostructure remains unchanged regardless of the incidence polarization state, therefore resulting in two complementary grayscale images upon illuminations of orthogonally polarized light. Note that such metasurface with single fixed polarization converting function will always be plagued by the issue of uncontrollable image display (either positive or negative image) as long as a user utilizes an analyzer to select the polarization component of the output light. Recently, diatomic metasurfaces whose unit cell contains two meta-atoms featuring distinct polarization-dependent phase retardations have shown great potential for realizing new type of polarization manipulations [35–42], among which, various dielectric diatomic metasurfaces realizing bifunctional polarization and wavefront control in the far-field have been demonstrated in the terahertz band [39–42]. In addition, several dielectric diatomic metasurfaces have also realized the conversion of arbitrarily polarized light to a fixed polarization state [43–46]. These examples clearly show that diatomic metasurface is a promising platform for realizing intriguing light polarization manipulations, despite the fact that all of them only realize a single type bifunctional polarization conversion functionality.
In this work, we propose and numerically demonstrate an all-dielectric diatomic metasurface for realizing versatile bifunctional polarization conversion functionalities in the visible band. The diatomic metasurface is an array of metamolecules (MMs) that is composed of a quarter-wave plate (QWP)-like meta-atom and an HWP-like meta-atom. Through theoretical analysis and numerical simulations, we show that these two functionally distinct meta-atoms can be meticulously designed to transform orthogonal linearly polarized light to different combinations of linear and circular polarizations. This bifunctional polarization conversion feature opens a new opportunity in realizing asymmetric light amplitude engineering in the near-field, benefiting from which we further demonstrate its application in high-resolution incidence-polarization-secured meta-image display. Unlike previous works where complementary meta-images can be seen under either orthogonal polarization incidences or analyzing orthogonal polarization components of the output light, the meta-image hidden in our dielectric diatomic metasurface can only be accessible under incidence of the designated linear polarization state, whereas a uniform transmission intensity profile will always be seen if the incidence polarization is locked to the orthogonal polarization case. Furthermore, while previous diatomic metasurfaces only realize a single fixed bifunctional polarization conversion, we show that by engineering the rotation angles of both meta-atoms, versatile different combinations of linear and circular polarization pairs can be achieved. As such, the proposed diatomic metasurface can enrich the diversity of its applications in high-resolution image display with enhanced security.
2. Concept and theoretical derivations
Figure 1 presents the schematic concept of our proposed dielectric diatomic metasurface for versatile bifunctional polarization conversion and incidence-polarization-secured meta-image. In specific, the diatomic metasurface can convert incidence linear polarization of 45° (45LP) to linear polarization along x-axis (XLP) or y-axis (YLP) in the transmission space, while the incident linear polarization of 135° (135LP) will be converted to the right-handed circular polarization (RCP) or left-handed circular polarization (LCP). Toward that goal, we start with the theoretical analysis of the diatomic metasurface configuration by inspecting the jones matrix of its elemental metamolecule.
Fig. 1. Schematic diagram of dielectric diatomic metasurface for realizing bifunctional polarization conversion and incidence-polarization-secured meta-image.
It is known that the jones matrix of an unrotated rectangular-shaped meta-atom whose fast- or slow-axes are along the x-axis can be expressed as:
3. Numerical simulations and discussions
On the basis of the theoretical analysis, we conduct simulations to validate the proposed idea based on the finite-difference time-domain (FDTD) method-based tool (FDTD Solutions), and details of the simulation can be found in Supplement 1. We choose SiO2 as the substrate, on top of which hydrogenated amorphous silicon (a-Si:H) nanopillars are placed. The operation wavelength is set to be λ = 690 nm considering its high refractive index and low absorption (n ≈ 4.077 + 0.005i) as we verified previously [44]. As a-Si:H becomes more absorptive at shorter wavelengths in the visible band, other low loss materials including silicon nitride, gallium nitride or titanium dioxide will be more suitable as the constituent material of the meta-atom. As shown in Fig. 2(a), four nanopillars with two sets of geometric sizes and orientation angles are incorporated to form a metamolecule. The metamolecule period is P = 480 nm, and the height of all a-Si:H nanopillars is H = 320 nm. Based on our previous work, a nanopillar with width of 74 nm and length of 158 nm is directly selected as the HWP and its orientation angle is set to 0° with respect to the x-axis. As aforementioned, the second PMM nanopillar should be rotated by θ = 45° with respect to x-axis in order to fulfill the target goal. Under incidence polarization of 45LP (135LP), the light transmitting through the desired diatomic metasurface is expected to be XLP (RCP), featuring a degree of linear polarization (DOLP) of 1 (0) and major angle of 0°. Here, the DOLP is defined as DOLP = 1-2×γ/(1+γ2), where γ is the ratio of the length of the major axis to that of the minor axis. Note that the degree of linear polarization can also be evaluated by calculating the common Stokes parameters. More details can be found in Supplement 1 in Supplement 1. The DOLP and major angle under 45LP and 135LP incidences are examined in simulation as a function of the PMM’s width (W) and length (L). From the results in Figs. 2(b) through 2(e), we find the best structure that can fulfill the bifunction polarization conversion is L = 128 nm and W = 80 nm, as marked by black triangles. The selected meta-atoms can be potentially considered as truncated waveguides, which can impart different phase delays on the output light by varying their lateral dimension. Severa meta-atoms with different sizes locating withing the line trends in Fig. 2(b) are examined in terms of the electromagnetic field distributions in the xy- and xz-planes. It can be seen from the simulation results (Fig. S1 in Supplement 1) that the magnetic fields of the selected meta-atoms are all mainly concentrated inside of the meta-atoms, implying that each meta-atom can be considered as a truncated waveguide permitting certain modes to be propagated. As such, by varying the lateral size of the meta-atom, the effective index of modes can be tailored, which in turn causes the output light phase varied [47].
Fig. 2. (a) Front and top views of the metamolecule of the dielectric diatomic metasurface which is composed of four a-Si:H nanopillars (b) and (c) are the simulated DOLP and major angle as a function of the W and L under 45LP incidence. (d) and (e) are the simulated DOLP and major angle as a function of the W and L under 135LP incidence.
Interestingly, it can be further derived based on Eq. (4) that when the orientation angle of the HWP is changed to θ1 = 90°, the jones matrix of the metamolecule can be modified and the jones vector of transmitted light under 45LP and 135LP incidences can be expressed as:
Fig. 3. (a) A schematic diagram of the metamolecule MM1, and the simulated transmission polarization ellipse maps upon (b) 45LP and (c) 135LP incidences. (d) The schematic diagram of the metamolecule MM2, and the simulated transmission polarization ellipse maps upon (b) 45LP and (c) 135LP incidences.
While in traditional metasurface-based image display or optical encryption, complementary meta-images will be inherently seen upon illuminations of orthogonal linear polarizations due to the fixed polarization manipulation functionality. The abovementioned dielectric diatomic metasurface shows a new degree of freedom in this application as a designed meta-image can only be witnessed when an appropriate incidence polarization is applied. Subsequently, a metasurface array containing 40 × 40 pixels is constructed to validate this claim. Figure 4(a)(i) depicts an expected meta-image manifesting a QR code pattern. Each “bright” (“dark”) pixel in the QR code consists of 2 × 2 MM1 (MM2), and the metasurface array occupies a total footprint of 38.4 µm × 38.4 µm. First, under incidence of 45LP, it is known that light transmitted through MM1 will be XLP while that for MM2 is YLP. Therefore, by inserting an analyzer and adjusting its polarization angle, one can obtain high-fidelity complementary binary images at 0° and 90°, while uniform intensity profiles will be revealed under 45° and 135° analyzing angle, as can be verified from the theoretical and simulation results in Figs. 4(a)(i) through 4a(viii). Furthermore, with the light incidence of 135LP, MM1 and MM2 will convert the incident light polarization states to RCP and LCP, respectively. In this case, no QR code pattern can be revealed through simply applying an analyzer, as verified by the results in Figs. 4(b)(i) through 4b(viii). Therefore, unlike previous metasurfaces wherein complementary images are witnessed upon either illumination of orthogonally polarized light or analyzing orthogonal polarization components of the output light, the meta-image concealed in our dielectric diatomic metasurface is safely secured under 45LP incidence condition. Note that in Fig. 4(a)(vi), Fig. 4(a)(viii), and Figs. 4(b)(vi) through 4(b)(viii), some densely distributed white dots can be seen, a phenomenon which might be considered as a leakage of the encrypted information, to some extent. In order to quantify the encryption level, we introduce the correlation coefficient (CC) to quantitatively describe the similarity between the simulated and its corresponding theoretical images. Similarly, the CC between the simulated images and the QR code image is also derived to evaluate the degree of concealment of the QR code information. For the convenience of identification, we refer the CC in the two cases as CC1 and CC2. The corresponding results are summarized in Table S2 in Supplement 1. It can be seen that for these images, the derived CC1 are all higher than 0.6, meaning that there is a strong correlation between the simulated and theoretical images. On the other hand, CC2 are all below 0.1, implying that the simulated images are not like the QR code image at all. As a consequence, the encryption level can be thought of as higher enough and can be hardly speculated. Additionally, when it comes to the application of pure image encryptions, complexed illumination conditions such as circularly polarized light would be more advantageous than linear polarized light, since the former requires more optical components to decrypt the image [48]. Nevertheless, from the perspective of selective control of the meta-image, a simpler illumination condition such as linear polarization would be more appropriate.
Fig. 4. Theoretical and numerically simulated transmission light intensity profiles at various analyzing polarization angles upon incidence polarization of (a) 45LP and (b) 135LP.
In the case of MM1 and MM2, the versatile bifunctional polarization conversion functionalities are realized when the rotation angle of PMM is fixed to θ2 = 45° with respect to x-axis while the rotation angle of PCM is switched between θ1 = 0° and θ1 = 90°. Here, we will show that by simply adjusting the PMM rotation angle to θ2 = 135°, two categories of MMs with new polarization conversion functionalities can be achieved. On top of the previous design conditions, by setting the orientation angle of the PMM θ = θ2 = 135°, the jones matrix of the QWP meta-atom T4 can be re-written as:
Fig. 5. (a) A schematic diagram of the metamolecule MM3, and the simulated transmission polarization ellipse maps upon (b) 45LP and (c) 135LP incidences. (d) The schematic diagram of the metamolecule MM4, and the simulated transmission polarization ellipse maps upon (e)
For the previous two cases, XLP and RCP are the generated polarization pairs for MM1, whereas YLP and LCP are the paired polarizations for MM2. Interestingly, Eqs. (11) and (12) signify that the polarization conversion functionalities enabled by MM3 are not simply the reversal of MM1. It is seen that while incidence of 135LP will be transformed into XLP, incidence of 45LP will be converted to LCP instead of RCP. Furthermore, we can obtain the jones vector of light transmitting through MM4:
The entire polarization conversion functions for all MMs are summarized in Table 1. Note that the bifunction polarization conversions require relatively strict phase relationships between the two meta-atoms. As conventional meta-atoms usually exhibit dispersive phases, the designed meta-molecules are more likely to be effective in a relatively narrow band. As an example, the DOLPs of MM1 under 45LP and 135LP incidences are simulated in the wavelength range from 600 nm to 700 nm (see Supplement 1, Fig. S3), where the expected bifunctional polarization conversions only occur in the vicinity of the designed wavelength of 690 nm.
Table 1. Polarization conversion relationships for all MMs
The incidence-polarization secured image is an advance due to the versatile bifunctional polarization conversion functionality of the proposed dielectric diatomic metasurface, however, when it comes to the field of meta-image display, resolution is another critical characteristic to be examined. For the same meta-image as implemented in Fig. 4, we construct the metasurface again, yet this time each “bright” or “dark” pixel is only composed of one MM1 or MM2. Figures 6(a)(i) through 6(a)(iv) depict the theoretical and numerically simulated transmission intensity profiles from the metasurface. Obviously, these results show high consistency with the results in Fig. 4. As the size of the pixel is 0.48 µm × 0.48 µm, this can reach a remarkable resolution of 52,916 (dots per inch). Note that the MMs listed in Table 1 exhibit versatile polarization conversion for a given incident polarization and the high-resolution feature is expected to be preserved for all four MMs. In light of these possibilities, the aforementioned four MMs exhibiting four groups of linear and circular polarizations also provide a chance to realize sub-microscale three-level intensity modulation. Here, MM1, MM2, MM3, and MM4 are sequentially placed to form a supercell as shown in Fig. 6(b). The white, black, and gray areas in Fig. 6(b)(i) are extracted intensity values of transmitted XLP component under 45LP incidence along the supercell. Similarly, Fig. 6(b)(ii) displays the relevant results under 135LP incidence. Obviously, good agreements between simulation and theories successfully validate the claim.
Fig. 6. (a) Constructed new metasurface whose pixel contains only one MM. (i) through (iv) are the theoretical and simulated intensity profiles under 45LP and 135LP incidence and analyzing the XLP and YLP component. (b) Verification of the three-level intensity manipulation when MM1, MM2, MM3, and MM4 are sequentially placed. (i) and (ii) display the light intensity of XLP component under 45LP and 135LP incidences, respectively.
4. Conclusion
In conclusion, dielectric diatomic metasurface was proposed to realize versatile bifunctional polarization conversions functionalities in the visible band. Following the theoretical derivations, two a-Si:H nanopillars functioning as HWP and QWP were selected to constitute the unit cell or metamolecule of the metasurface. Upon incidence of 45LP and 135LP, four combinations of linear and circular polarization pairs were successfully achieved by constructing four MMs with different orientation angles of the nano-HWP and nano-QWP. Unlike previous metasurface-based optical display or encryption applications wherein the images can always be decrypted when an analyzer is used to select specifically polarized light, the bifunctional polarization conversion enabled by our dielectric diatomic metasurface allows a host-dominated meta-image that is safely secured under incidence of 45LP. It was also found that each individual MM containing four nanopillars can guarantee excellent intensity modulation at submicron scale, and versatile different paired linear- and circular-polarization combinations further offers the possibility of three-level intensity modulation, ensuring its promising application in high-security and high-resolution multi-level meta-image display.
Funding
Natural Science Foundation of Shandong Province (ZR2020QF105); National Natural Science Foundation of China (62005095, 61805101).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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