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Abstract
Augmented Reality technology enables users to interact with virtual imagines and the real world. The emergence of AR has propelled the development of the next generation of optical devices towards miniaturization, lightweight design, and enhanced light field manipulation capabilities. However, current AR glass still suffer from shortcomings of low efficiency. This work proposes a near-eye display device based on bilayer chiral quasi-BIC (Bound States in the continuum) nonlocal metasurfaces which can reflect narrow bandwidth RGB light with high efficiency while being able to see the natural environment clearly. At the same time, the geometric phase is introduced to realize oblique emission and reflective focusing. Due to its ability to manipulate narrowband light fields, it can reduce the interaction of metasurfaces and environment light, and has potential applications in the fields of imaging and near-eye display.
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1. Introduction
AR (Augmented reality) is a new technology that can superimpose virtual information generated by computers on the real-world scenes, and can create direct, automatic and actionable links between the virtual world and the real world. AR glass is the key equipment for the realization of the concept of “Metaverse” [1]. With the continuous development of integrated optical devices, microscopic technology, and micro-computing equipment, VR and AR display technologies have developed rapidly and are widely used in aviation [2], medical [3], communication [4] and so on. Among various AR displays, transparent AR glasses have received great attention because of their portability, and commercial products available for sale have already emerged [5]. In order to bridge the gap between virtual world and real world, AR glasses require excellent optical characteristics. Therefore, the wearer of the AR glasses can clearly see the natural environment and at the same time present the virtual image to the designated position in the natural environment. During the past, a variety of optical structures has been demonstrated in AR technology, such as aspherical lens [6], free-form optical mirrors [7], metasurfaces [8–12], optical waveguides [13–15], holographic optical element [8,16,17], etc. However, there are still limitations in all these AR glasses, such as low efficiency, volume and weight factors brought by traditional lens groups, and stray light, rainbows, as well as artifacts caused by the overlay of virtual image and real world [3,11].
Metasurfaces are artificial two-dimensional materials at subwavelength scales that allow the manipulation of desired optical functionalities by controlling the parameters of the metasurface units [18–21]. There are already numerous studies on AR glasses based on metasurfaces [10,22–24], which have solved some of the difficulties in the design of AR glasses, such as full-color display, achromatic elimination, compact shape, and so on. The designed metasurfaces can support BIC modes, that is, special bound-state modes inside the continuum that coexist with extended waves but do not emit any radiation [25,26]. In the absence of perturbation, the BIC mode with symmetric protection is a non-radiative state, the quality factor (Q factor) tends to be positive infinity, and no energy is radiated outward. The quasi-BIC can be obtained by breaking the symmetry of metasurfaces which support perfect BIC, and the quasi-BIC produced by symmetry broken still has the characteristic of high Q factor [27–30]. Different from the BIC mode, the quasi-BIC can radiate energy outward in a narrow band, which appears as a sharp reflection peak or transmission peak in the spectrum [31]. The designed metasurfaces supporting quasi-BIC can precisely control the optical wavefront at a specific resonance wavelength, but does not affect the normal propagation of the optical field at the non-resonance wavelength [32]. Prior to this, BIC has been explored in the field of Augmented Reality (AR). It has been used in eye-tracking systems due to its unique property to independently manipulate resonant wavelengths [33]. Furthermore, BIC can be used to fabricate AR metasurfaces utilizing the characteristics of narrowband and high reflection [34]. However, due to the linear momentum conservation and plane symmetry of the traditional single-layer BIC structure, the final outgoing light will be divided into four channels according to the spin, and the target channel is only one of them. The final system diffraction efficiency is up to 25% [35,36]. As a result, the virtual image cannot be seen distinctly when the outdoor ambient light is too strong. While eliminating non-resonant circularly polarized light with spin selectivity, it can be coupled to the target channel at the resonance position with a diffraction efficiency far exceeding 25%. Because the bilayer design is an easy way to increase new degrees of freedom [37] or break mirror symmetry [38,39], it has been studied extensively at this stage. In our work, we choose the bilayer quasi-BIC metasurface to break mirror symmetry to realize spin selectity.
In our work, a nonlocal metasurface structure supporting quasi-BIC mode is designed, which can control the light wavefront at the resonance wavelengths of red ($\lambda $= 642.5 nm), green ($\lambda $= 569.9 nm) and blue ($\lambda $= 476.6 nm) to generate sharp reflection peaks without affecting the light wavefronts of other wavelengths. This design enables the human eye to clearly observe the real world and the reflected virtual image generated by the laser source at the same time through the metasurface glasses, as shown in Fig. 1(a). To further improve the diffraction efficiency, we introduced a chiral structure and designed a bilayer nonlocal metasurfaces [36]. Chiral BIC metasurfaces can couple the circularly polarized light to the target channel with higher efficiency, and almost completely transmit the non-resonant circularly polarized light, as illustrated in Fig. 1(b). We also introduced a geometric phase design into the nonlocal metasurface to enable wavefront shaping and realize beam deflection and focusing. This nonlocal metasurface structure supporting quasi-BIC mode, which can control the wavefront directly at the target wavelength, is expected to be applied in the development of AR glasses in the future.
Fig. 1. Schematic diagram and principle of chiral quasi-BIC metasurface. (a) Schematic diagram of AR glass based on chiral quasi-BIC metasurface. The quasi-BIC metasurface can transmit natural light and at the same time reflect light of three target wavelengths of red, green and blue emitted by micro laser source, so that the virtual image can be clearly presented in the actual natural environment. (b) Chiral quasi-BIC metasurface principle. Resonant circularly polarized light (RCP light with target wavelength λ in the figure) is reflected with high efficiency when incident. Non-resonant circularly polarized light (LCP light and RCP light with wavelength other than λ) is transmitted through the metasurface.
2. Generation of symmetry-broken quasi-BIC
A four-fold rotational-symmetric metasurface structure supporting bound-state modes is adopted, as demonstrated in Fig. 2(a). The upper figure is a real-space schematic of an unperturbed metasurface. The red area in the figure is titanium dioxide, the white area and the upper and lower substrates are all silicon dioxide, the period a = 215 nm, and the pore radius is r = 62 nm. The lower figure is a schematic diagram of the corresponding momentum space. Figure 2(c) shows the simulated structure of the undisturbed metasurface band. The red dotted line represents the light cone, and the red pentagram represents the bound state mode at point X in the momentum space supported by this structure. The bound state mode is located under the light cone, and the right figure in Fig. 2(c) is a schematic diagram of the corresponding mode. This mode is a perfect bound state, and the energy is confined within the metasurface without radiating energy outward. The figure on the right is a schematic diagram of the mode at the resonance position. Figure 2(e) is a schematic diagram of the mode leakage based on the magnetic field component. The left picture shows the component of the Hz component in the yz plane, and the right picture shows the component of the right-handed component Hx + iHy of the magnetic field H in the yz plane. Our mode does not leak at this time, and there is no coupling with the outside world. When we break the circular hole into a pair of identical elliptical holes whose major axes are perpendicular to each other, the period in the x-axis direction is doubled in real space. The circular hole becomes an elliptical cylinder with a long axis r2 = 90 nm and a short axis r1 = 45 nm. The X point of the first Brillouin zone in the momentum space is folded to the Γ point, and the period of the Γ-X direction is halved, as shown in Fig. 2(b). The mode is folded from X point to Γ point, which is located above the light cone, as shown in Fig. 2(d), and the right figure is a schematic diagram of the mode at the resonance position. Therefore, the bound state supported by the perturbed metasurface has been broken into a quasi-BIC, and energy is radiated outward at the resonance wavelength. This metasurface has an achiral structure, so the output RCP light has two output channels of reflection and transmission, and the diffraction efficiency of the reflection and transmission output channels is the same and does not exceed 25%, as shown in Fig. 2(f).
Fig. 2. Schematic diagrams of the metasurface before and after period doubling. (a) and (b) are the real-space and k-space structures of the metasurface before and after period doubling, respectively. The red part is TiO2 and the white part is SiO2. (c) and (d) are schematic diagrams of energy bands before and after period doubling, respectively. The red dotted line is the position of the light cone, and the red pentalpha is the position of BIC and Quasi-BIC mode. The picture on the right is a schematic diagram of the mode at the current position. (e) and (f) are the magnetic field components before and after period doubling, respectively. The BIC before period doubling does not leak outward, and the quasi-BIC after period doubling leaks to the positive and negative directions of the z-axis. (g) Comparison of reflectivity of unperturbed metasurface, achiral metasurface and chiral metasurface. (h) Schematic diagram of the mode and magnetic field components of a chiral metasurface, where most of the RCP light leaks into a single direction. (i) Schematic of a metasurface supporting chiral BIC. The upper and lower interfaces of the chiral model can couple the incident light to two different linearly polarized modes, $\varphi $ and $\varphi ^{\prime}$. The upward and downward leaky states $|{{e_{up}}} \rangle $ and $|{{e_{down}}} \rangle $ of the chiral mode can be realized by adjusting the values of $\varphi $ and $\varphi ^{\prime}$.
3. Theoretical model of chiral quasi-BIC
To realize a single diffractive channel that can be coupled to RCP light reflection with superior diffraction efficiency, we introduce optical chirality in this system to break the mirror symmetry of the up and down surface, as shown in Fig. 2(i). We introduce an ideal homogeneous structural model in which the upper and lower interfaces support eigenmodes with different linear polarization states. $\varphi $ and $\varphi ^{\prime}$ are the polarization angles of the eigenmodes on the up and down surfaces, respectively. With the help of temporal coupled-mode theory (TCMT) [36,40,41], we can write the upper surface leakage mode $|{{e_{up}}} \rangle $ and the lower surface leakage mode $|{{e_{down}}} \rangle $ as:
The above formula indicates that the polarization angles of the leaked states supported by the up and down surfaces are the same, and the leaked states on the up and down surfaces are both linearly polarized states without chirality. This article takes the top sign because our metasurface is symmetric in the z direction. If $\varphi = \varphi ^{\prime} + \pi /2$, formula (1) can be written as:
At this time, the leaky states on the up and down surfaces exhibit opposite chiral polarizations, and the metasurface exhibits full circular dichroism: RCP resonant light is reflected, while LCP light is non-resonantly transmitted. As shown in the right figure of Fig. 2(h), in this case, the RCP magnetic field component of the resonant mode supported by the structure leaks in the positive direction of the z-axis and couples with the external environment, while the leakage field strength in the negative direction of the z-axis is much smaller than that in the positive direction, exhibiting a clear chirality. Figure 2(g) shows a comparison of the reflectivity of the undisturbed metasurface, the non-chiral metasurface, and the chiral metasurface. The undisturbed metasurface supports fully confined modes, resulting in a smooth reflection spectrum. The chiral structure exhibits significantly higher reflection peaks than the non-chiral structure at resonance positions.
Based on the theoretical foundations mentioned above, we have designed a non-local metasurface structure with reflective quasi-BIC, as shown in Fig. 3. Figures 3(a1) and (a2) illustrate the schematic diagram of an achiral BIC structure. The red region represents TiO2 material. The up and down substrates are made of SiO2 material. The etched holes are filled with SiO2. The thickness of the TiO2 layer (2 h) is 500 nm for all three structures. The mode detection position is located 50 nm above the bottom surface within the TiO2 layer. The structure corresponding to blue light has a period of a = 160 nm, with a short axis of r1 = 30 nm and a long axis of r2 = 64 nm. When RCP light is incident, the resonance reflection peak is located at ${\lambda _0} = 476.6\textrm{ nm}$, as shown in Fig. 3(b1). The resonant mode is depicted in Fig. 3(b2). The structure corresponding to green light has a period of a = 170 nm, with a short axis of r1 = 34 nm and a long axis of r2 = 68 nm. The resonance reflection peak is located at ${\lambda _0} = 569.9\textrm{ nm}$, as shown in Fig3. (b1). The resonant mode is depicted in Fig. 3(b2). The structure corresponding to red light has a period of a = 215 nm, with a short axis of r1 = 45 nm and a long axis of r2 = 90 nm. The resonance reflection peak is located at ${\lambda _0} = 642.5\textrm{ nm}$, as shown in Fig. 3(b1). The resonant mode is depicted in Fig. 3(b2). It can be observed that the reflectivity at the resonant wavelengths of the three colors does not exceed 50%. Based on this, we introduce a chiral structure as shown in Fig. 3(e1) and (e2). The upper layer structure introduces a rotation angle $\Delta \alpha $ relative to the lower layer structure to provide chirality. Theoretically, when $\Delta \alpha $ is 45°, the metasurface exhibits full circular dichroism. The derivation process can be found later. However, in practical specific structures, the value of $\Delta \alpha $ needs to be adjusted to achieve the highest resonance reflection. The structural parameters of the chiral structure remain unchanged, and there is a slight difference in $\Delta \alpha $ for the three wavelengths. Figure 3(f1) - (h1) represent the simulated reflectivity results for the structures corresponding to blue light, green light, and red light. The blue solid line represents RCP incidence, while the red dashed line represents LCP incidence. Compared to the non-chiral structures, the reflectivity at the resonant wavelengths significantly increases for RCP incidence, while it remains close to zero for LCP incidence. The resonant mode diagrams are shown as Fig. 3(f2) - (h2).
Fig. 3. Achiral and chiral structure diagrams and reflectivity mode diagrams for the red, green, and blue wavelength ranges. (a1) and (e1) respectively depict schematic diagrams of the periodic unit structures for the achiral and chiral metasurfaces. (a2) and (e2) are top-view structure diagrams. (b1) - (d1) represent the reflectivity spectrum for the achiral blue, green, and red structures when RCP light is incident. (b2) - (d2) depict the mode diagrams corresponding to the respective quasi-BICs. (f1) - (h1) show the reflectivity graphs for the chiral blue, green, and red structures when RCP light is incident (represented by the blue solid line) and when LCP light is incident (represented by the red dashed line). (f2) - (h2) depict the mode diagrams corresponding to the respective quasi-BICs.
4. RGB chiral quasi-BIC metasurfaces design
Due to potential difficulties in the fabrication process of the bilayer chiral structure, such as the need for separately etching of the upper and lower layers, there may be an unavoidable layer of SiO2 with a certain thickness between the two layers. To address this, we also conducted simulations of chiral structures with an intermediate layer of SiO2, with a thickness (hr) gradually increasing from 0 nm to 80 nm. The robustness test is illustrated in Fig. 4(b)-(d), where the x-axis represents the intermediate layer thickness, and the y-axis represents the wavelength range. The red regions in the figure indicate the portions where the reflectivity exceeds 50%. It can be observed that for intermediate layer thicknesses below 40 nm, the chiral resonance reflection peaks of the red, green, and blue structures can be maintained above 50%, and the presence of non-target peaks is generally lower and smaller. This demonstrates that this structure possesses a certain level of robustness. As the intermediate layer thickness (hr) gradually increases, there will be a certain amount of shift in the resonance peak position. However, the shifted resonance wavelengths still remain within a reasonable range. We also calculate the robustness of the lateral displacement of the upper and lower structure, referencing Supplement 1.
Fig. 4. Robustness test of the chiral metasurface. (a) Schematic diagram of the robustness test. An intermediate layer of SiO2 with a thickness of hr is inserted between the bilayer TiO2 structure. By varying the value of hr, the changes in the reflectivity spectrum are calculated to test the robustness of the structure. (b) - (d) depict the reflectivity variation graphs for the blue, green, and red resonance structures as hr changes from 0 nm to 80 nm. The x-axis represents the value of hr, the y-axis represents the wavelength range, and the color bar represents the reflectivity level. The red color indicates the portion where the reflectivity exceeds 50%.
We discovered that in the chiral quasi-BIC metasurface system we designed, the relationship between the transmitted phase and the structure rotation angle is approximately 4 times (Supplement 1). We calculated the relationship between the rotation angle and phase for the resonant positions of the red, green, and blue structures by rotating the structure. The results are shown in Fig. 5(a). The red, green, and blue lines represented by the circular markers in the graph depict the changes in resonant wavelengths for the respective structures under different rotation angles. The corresponding y-axis is shown on the right. The square markers represent the phases supported by the resonant position of red, green, and blue structures under different rotation angles, with the corresponding y-axis shown on the left. The black dashed line represents the relationship $\Phi = 4\alpha $. It can be observed that rotating the structure hardly changes the position of the resonant wavelength, and the resonant phase approximately follows the relationship $\Phi = 4\alpha $.
Fig. 5. Schematic of oblique emission. (a) shows the relationship between the rotation angle of unit structures in chiral configurations and the resonant wavelength along with the emission phase. The insert image illustrates the concept of oblique emission. (b1) - (d1) The reflectance spectra of the red, green, and blue structures when illuminated by RCP (blue solid line) and LCP (red dashed line) light. (b2) - (d2) The schematic representations of the emitted fields at the resonant wavelengths for the red, green, and blue structures under RCP, each exhibiting an angular deviation of approximately 20°. (b3) - (d3) The schematic representations of the emitted fields at the resonant wavelengths for the red, green, and blue structures under LCP, characterized by low light intensity and minimal modulation. (b4) - (d4) The schematic representations of the emitted fields for the red, green, and blue structures under RCP at non-resonant wavelengths, characterized by low light intensity and minimal modulation effects.
By utilizing the phase-controlling characteristics of metasurface units, we have designed a non-local chiral metasurface with an emission angle of 20° on a structure that supports resonances for the red, green, and blue colors, as illustrated in the insert image of Fig. 5(a). Due to the distinct operational wavelengths and periods within the metasurface unit structures for the red, green, and blue colors, these three types of non-local chiral metasurfaces exhibit varying unit cell numbers and rotational phase gradients.
According to the law of reflection, the angle of reflection, denoted as ${\theta _r}$, can be expressed as [42]:
Non-local metasurfaces for near-eye displays not only require selectively reflecting the light field but also need the ability to focus the target light at a specific location (in practical applications, this means focusing onto the human retina). Therefore, we have designed a chiral non-local metasurface with reflective focusing capabilities, as illustrated in Fig. 6(a).
Fig. 6. Focusing illustration. (a) Focusing concept, utilizing LCP-response metasurface with 100 units per period, the formula insert represents the focusing phase supported by the structure. (b) Top view of a portion of the structures. (c) Phase profile supported by the metasurface. (d1) - (f1) Simulated field patterns at the resonant wavelengths of the red, green, and blue metasurface structures when illuminated with LCP light, showing focal points around 16 µm. (d2) - (f2) Simulated field patterns at the resonant wavelengths of the red, green, and blue metasurface structures when illuminated with RCP light.
The standard focusing phase formula is given by:
We design the periodic structure in the y-direction and implement the construction of a cylindrical lens with 100 finite unit structures in the x-direction. Therefore, the above formula where y = 0 can be rewritten as:
As the geometric phase is approximately four times the angle of unit structure rotation in this case, the rotation angle of the unit structure can be expressed as:
We set the focal point at 16 µm and constructed a chiral cylindrical lens metasurface with 100 units structures in the x-direction and periodic structures in the y-direction. When resonating, this structure reflects and focuses LCP light while transmitting RCP light, as illustrated in Fig. 6(a), where the blue structures represent unit cells, and their rotation angles comply with Eq. (12), with ni set to 1, and an upper SiO2 substrate of 500 nm. Figure 6(b) depicts a schematic of the rotation angles of some unit cells, while Fig. 6(c) shows the distribution of rotation angles. Figures 6(d1) -(f1) display the reflected light fields of LCP light at the resonant wavelengths for the three colors (red, green, and blue), with resonance wavelengths at 642.9 nm, 576.0 nm, and 479.3 nm, respectively, all focused around 16 µm. Figures 6(d2) -(f2) depict the reflected light fields of RCP light at the resonant wavelengths, where the focusing images disappear.
5. Conclusion
In this study, we have designed a chiral non-local metasurface based on quasi-BIC. This metasurface is capable of achieving high reflectance at resonant wavelengths, as well as high transmittance for orthogonal circularly polarized light. Furthermore, the robustness of the proposed structure has been demonstrated. By adjusting the parameters of the unit structures and periods, three resonant structures were constructed to generate resonances at specific wavelengths corresponding to red, green, and blue colors. Additionally, leveraging the geometric phase supported by chiral quasi-BIC metasurface units, we designed chiral oblique emission and chiral focusing structures. With its characteristic of narrowband high reflectance, this quasi-BIC-based chiral non-local metasurface holds promising potential for application in the development of next-generation AR glasses, aiming to achieve enhanced display performance.
Funding
National Program on Key Basic Research Project of China (2022YFA1404300); Fundamental Research Funds for the Central Universities (020414380175); The Open Research Fund of the State Key Laboratory of Transient Optics and Photonics, Chinese Academy of Sciences (SKLST202218); National Natural Science Foundation of China (11774162, 12325411, 62288101).
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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