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Abstract
Self-assembled photonic structures have greatly expanded the paradigm of optical materials due to their ease of access, the richness of results offered and the strong interaction with light. Among them, photonic heterostructure shows unprecedent advances in exploring novel optical responses that only can be realized by interfaces or multiple components. In this work, we realize visible and infrared dual-band anti-counterfeiting using metamaterial (MM) - photonic crystal (PhC) heterostructures for the first time. Sedimentation of TiO2 nanoparticles in horizontal mode and polystyrene (PS) microspheres in vertical mode self-assembles a van der Waals interface, connecting TiO2 MM to PS PhC. Difference of characteristic length scales between two components support photonic bandgap engineering in the visible band, and creates a concrete interface at mid-infrared to prevent interference. Consequently, the encoded TiO2 MM is hidden by structurally colored PS PhC and visualized either by adding refractive index matching liquid or by thermal imaging. The well-defined compatibility of optical modes and facility in interface treatments further paves the way for multifunctional photonic heterostructures.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photonic structure with characteristic length at operational wavelength scale, e.g. photonic crystals (PhC), or subwavelength scale, e.g. metamaterials (MMs), can interact strongly with light. Various remarkable optical responses ranging from photonic bandgap [1–3], slow light [4–7], to negative refraction [8–12] and other phenomena [13,14], are thus intrigued to beneficial many practical applications including lasing [15–18], fiber [19,20], sensing [21–23] and optical circuits [24–26]. These responses can be finely designed and tuned by the types and parameters of their structures. Being more specific, PhCs and MMs are two fundamental types of photonic structures developed from distinct light-matter interactions. As first proposed by Yablonovitch [27] and John [28] at 1987, PhCs are periodic dielectric structures that possess photonic band structure. They are functionalized by Bragg’s diffraction law, to confine, manipulate, and guide light. For MMs, quasi-static approximation allows the structures to be regarded as effective media with averaged parameters that can be engineered to modify the propagation of electromagnetic waves.
As a matter of fact, photonic heterostructures combining the merits from each component are well-known. Among them, self-assembled photonic heterostructures show great potential in application, due to their ease of fabrication, low cost, and arbitrary shape designer [29,30]. The most reported self-assembled photonic heterostructures are PhC heterostructures composed of various PhC components that are developed as a photonic analog to the semiconductor heterostructures [31]. The compatibility of optical modes and facility in interface treatments are well-guaranteed as working and fabricating in the same paradigm. Therefore, self-assembled PhC heterostructures with enlarged photonic bandgap and minimized propagation losses, have been explored for wideband optical mirror [32,33], low-loss photonic crystal waveguides [34], and etc [35–38]. Further expanding the interface and components, the combination of PhCs with other distinct photonic structures gives rise to more interesting optical responses. For example, self-assembled PhC-diffraction grating heterostructure has been proposed to propagate more light through breaking the sharp angular selectivity of the ordinary diffraction grating [39]. On the other hand, self-assembled MMs have been widely studied to achieve exotic optical parameters determined by elements and structures. Beyond the scope of PhCs [40–42], these MMs could enable a plethora of exciting application in the light trapping [43–45], subwavelength imaging [46,47], and wideband absorber [48,49]. Considering the rich physics and the extensive studies in self-assembled MMs that shows fabrication compatibility to self-assembled PhC, self-assembled MM-PhC or PhC-MM heterostructures are fundamentally and applicably promising.
PhCs matched in visible band would produce structural colors due to Bragg’s law of diffraction. Structural color derived from PhCs has attracted increasing interest in the field of anti-counterfeiting label in visible band [50–52]. Yao Meng et al. [53] achieved the anti-counterfeiting application of banknotes by using a 3D inverse opal structure. Lin Chu, et al. [54] realized the anti-counterfeiting of banknotes through hollow silica opals/cellulose acetate nanocomposite films with structural colors. Self-assembly of mono-dispersed colloidal microspheres is favorable approach to form periodic 3D PCs, based on a variety of assembly technologies [55–57]. The vertical deposition self-assembly method has been widely used in the fabrication of 3D colloidal microsphere photonic crystals due to the advantages of controllable crystal layer thickness, simple equipment, economic, short preparation period [58–61]. In addition to using 3D photonic crystals to realize the application of anti-counterfeiting labels in visible band, thermal radiation labels with customized infrared emissivity realized by MMs have received important research attention as a promising anti-counterfeiting candidate [62–65]. These thermal radiation labels are imperceptible to the human eyes and can only be revealed using thermographic equipment. Daniel Franklin, et al. [66] discussed a cavity-coupled plasmonic system with resonances that are tunable across the 3–5 or 8–14 µm infrared bands while retaining near-invariant spectral properties in the visible domain. Through experiments, they realized the covert infrared image encoding. Joong Hoon Lee, et al. [67] proposed a colored, covert infrared display with visible and thermally concurrently encoded data using perfect spectral division based on a hybrid planar-plasmonic cavities. Although there are many researches on visible light anti-counterfeiting label and infrared thermal radiation label, the previous researches have focused on a single function in a single band. So far, there is no research on visible and infrared dual-band anti-counterfeiting labels.
In this work, we realize photonic MM-PhC heterostructures for the first time by optical modes segmentation in design and two-step self-assembly in fabrication to demonstrate dual-band anti-counterfeiting labels. The proposed TiO2 MMs and polystyrene (PS) PhCs have characteristic length, i.e. self-assembled particle sizes, in nanometer (∼ 25 nm) scale and sub-micrometer (∼ 120 nm) scale respectively. Close packing of particles in three dimensions combines them together to form MM-PhC heterostructures. The difference in compositional length scale supports photonic bandgap engineering in the visible bands, and creates a concrete interface at mid-infrared to prevent interference. To demonstrate the dual band function of our heterostructures, a new type of anti-counterfeiting labels is introduced, where coding patterns are hidden by structural coloring and visualized by either adding refractive index matching liquid or thermal imaging. Our design and fabrication thus pave the way for multi-functional photonic heterostructures composed of distinct components.
2. Theory
To analyze the working mechanism of the proposed heterostructures, characteristics of the PhCs, MM, and MM-PhC heterostructures are compared through theoretical calculations and numerical simulations in this section. Multiphysics simulation software (COMSOL) is used to obtain photonic band structure of the PS PhCs via eigenfrequency solver, and spectral characteristics of all the proposed structures via frequency domain solver.
2.1 PS PhC
Self-assembled PhC is formed by PS microspheres of radius r = 110 nm in 3D face-centered cubic (FCC) lattice in air (see Fig. 1(a) for a unit cell) with lattice constant a = r / 0.3535. Complex permittivity of the PS microsphere is shown in Fig. S1 (a). The corresponding photonic band structure (see Fig. 1(b)) opens no complete band gap due to high symmetry of FCC structure. [68] However, a directional band gap (493 nm ∼ 525 nm) appears from LG (crystal plane (111) direction) as reported in [69], which leads to a square shaped high reflection spectrum in Fig. 1(c). This reflection band of reflection coefficient over 0.95 from 498.7 nm to 531.3 nm gives a structural color of green to the PS PhC (see the chromaticity diagram in Fig. S2). The center wavelength (λgap) of the bandgap can be verified by Bragg’s diffraction law for the (111) plane of FCC structure:
where ${{\rm d}_{{111}}}$. is (111) plane spacing (${{d}_{{111}}} { = D} \sqrt{2} / \sqrt{3} $., with D = 2r the diameter of PS microspheres) and neff is the effective refractive index of the PS PhC. The effective parameter is related to filling ratio fps of the PS microseres by: nps and nm the refractive index of PS microspheres and the medium they filled, respectively. Here, fps = 0.74, nps = 1.59 and nm = 1 for air, so the value of neff is 1.4366. Following Eq. (1), λgap is 516.11 nm, close to the simulated value, i.e. 515 nm. Note that the structural color disappears once the air gaps in PS PhC are filled by a refractive index matching media, e.g. alcohol. The weak refractive index contrast between the two components prevents the formation of photonic band structure [70]. Consequently, the PS PhC becomes transparent in alcohol. At infrared wavelength, the proposed PS PhC is highly transparent in addition to the weak absorption caused by the intrinsic loss of PS at 13.2 µm (see Fig. 1(d)).
Fig. 1. Numerical study of self-assembled PS PhC. (a) Schematic of the 3D FCC PhC unit cell (r/a = 0.3535, r = 110 nm). (b) Photonic band structure of the PS PhC. Inset: diagram of the First Brillouin zone. (c) The visible spectrum of the PS PhC in air and alcohol medium. Here, R / T means reflection / transmission. The dark green line indicates the center wavelength of reflection band. Inset: schematic of the simulated PhC structure with a thickness of 41 × (61/2/3) × (2r) + (2r), i.e. total 42 layers of PS microspheres. The colored arrow indicates the normal incidence of light. (d) The infrared spectrum of the PS PhC in air. The same configuration of (c). Here, A means absorption.
Next, we study the PS PhC with r = 130 nm (other structural and material parameters remain unchanged), which is shown in Fig. S3. Compared with the previous case, the band gap red-shifts about 93 nm for the center wavelength, and the reflection spectrum red-shifts about 89 nm. This phenomenon conforms to Bragg’s diffraction law as the increase in r causes the increase in λgap. The calculated λgap = 609.9 nm agrees with the simulated one (604 nm), promising a structural color of red. The radius of PS microspheres has negligible influence on other properties of the PS PhC, i.e. the invalidation of structural coloring in alcohol and the IR spectral characteristics.
2.2 TiO2 MM
Optical response in visible band for self-assembled TiO2 MM is mainly determined by the Mie scattering of nanoparticles [71]. According to Mie theory, the efficiency factor for scattering Qsca is calculated by [72]:
The infrared spectrum of TiO2 MM shows a high absorption at 9 µm - 14 µm due to the intrinsic loss of the material (in Fig. 2(d)). According to Kirchhoff's law [73], the absorptivity for a material body in thermodynamic equilibrium is equal to its emissivity. The TiO2 MM thus has high emissivity at 9 µm - 14 µm. Like [74,75], self-assembled TiO2 MM here is treated as a thin film structure to obtain the simulated spectra. The effective permittivity of the thin film is calculated using effective medium theory, i.e. using Eq. (2) but with TiO2 replacing PS. Here, the filling ratio (f) remains at 0.74 due to the close packing of TiO2 nanospheres in fcc lattice.
Fig. 2. Numerical study of the self-assembled TiO2 MM. (a) A diagram of light scattering by a single dielectric spherical nanoparticle due to Mie resonance. The color indicates visible band. (b) The scattering efficiency of spherical TiO2 nanoparticle with radius of 25 nm. Inset: electric field distribution at the center cross section of nanoparticles at 500 nm wavelength. (c) The visible spectrum of TiO2 MM. Inset: schematic of the simulated TiO2 MM structure as an equivalent thin film with thickness 10 µm. (d) The infrared simulation spectrum of TiO2 MM. The same structure of (c). Here, R / T / A means reflection / transmission / absorption.
2.3 TiO2 MM - PS PhC heterostructure
In the visible spectra, the self-assembled TiO2 MM-PS PhC heterostructures on a Si substrate host the reflection bands of the upper PS PhCs (see Fig. 3 (a, c)), as their photonic band-gap prohibits light transmission. Beyond the bandgap region, light transmits through the whole structure. Only weak diffraction peaks are observed, while the main energy attenuates in the highly loss Si (see Fig. S4). It is the MM-PS interface that smooths the highly reflectivity of TiO2 MMs and allows the shielding of their white color by structural coloring. The center wavelength of reflection band red-shifts about 90 nm when the radius of PS microspheres changes from 110 nm to 130 nm.
Fig. 3. Numerical study of the self-assembled TiO2 MM-PS PhC heterostructure on Si substrate. (a) The visible spectrum of TiO2 MM- PS (r = 110 nm) PhC heterostructure. Inset: schematic of the simulated TiO2 MM-PS PhC heterostructure. Here, the thickness of PhC, MM and Si components are 20 × (61/2/3) × (2r) + (2r), i.e. total 21 layers of PS microspheres, 2 µm and 2 µm, respectively. The colored arrow indicates the normal incidence of light. (b) The infrared simulation spectrum of TiO2 MM- PS (r = 110 nm) PhC heterostructure. (c) The visible spectrum of TiO2 MM- PS (r = 130 nm) PhC heterostructure. (d) The infrared simulation spectrum of TiO2 MM- PS (r = 130 nm) PhC heterostructure. (b-d) has same structure of (a). Here, R / T / A means reflection / transmission / absorption.
The infrared spectra of the heterostructures mainly show high absorptivity in the range of 9 µm - 14 µm (see Fig. 3(b, d)). Except for a slight increase in absorption at 13.2 µm due to the intrinsic loss of PS material, they are very similar to the infrared spectrum of TiO2 MM. Therefore, PS PhCs have little influence on the infrared response of TiO2 MM, corresponding to the high transmission of PS PhCs (see Fig. 1 (d) and Fig. S3 (d)). The heterostructures thus achieve independent control of optical modes in visible and infrared bands.
3. Results and discussion
In experiments, the PhCs, MMs, and MM-PhC heterostructures are fabricated and analyzed. To optimize the dual band performance, thickness of each structure, as well as PhC and MM components in heterostructures, are much larger than that proposed in simulation studies. Note that, neither photonic bandgap engineering nor infrared imaging are thickness-dependent. Therefore, the proposed mechanism, i.e. the simulated optical modes, are highly consistent with the experimental observations as discussed below.
3.1 Properties of PS PhCs
To fabricate PS PhCs, the hydrophilic silicon substrate is vertically inserted into a beaker containing PS microspheres dispersion solution. Then, the beaker is placed in an oven at 50 °C for vertical deposition self-assembly. The schematic diagram is shown in Fig. S5 (also see fabrication and measurement details there). It is clear that PS microspheres are closely packed in a 3D fcc lattice at thicknesses about 23 µm (for r = 110 nm, in Fig. 4(a-b)) or 17 µm (for r = 130 nm, in Fig. 4(e-f)). The center wavelength of photonic bandgap is measured by the spectrometer, i.e. at 519 nm / 606 nm for PS PhCs with r = 110 nm / 130 nm respectively (in Fig. 4(c) and (g)). Meanwhile, the shape of spectral peak is so much narrower and sharper in experiment than in simulation. It is because that he photonic crystal prepared in experiment is not perfect and has defects. In fact, there is substrate material in the samples [78]. At infrared, the PS PhCs are highly transparent except for weak absorption caused by the intrinsic loss of the PS at 13.2 µm (see Fig. 4(d) and (h)), comparing to the bare Si substrate.
Fig. 4. Experimental study of self-assembled PS PhCs. (a) SEM image of PS PhC (r = 110 nm) surface. Inset: zoom-in picture. (b) SEM image of PS PhC (r = 110 nm) cross-section. The thicknesses of PS PhCs are show in Fig. S6. (c-d) The visible and infrared spectrum of Si substrate with and without PS PhC (r = 110 nm) in air. (e) SEM image of PS PhC (r = 130 nm) surface. Inset: zoom-in picture. (f) SEM image of PS PhC (r = 130 nm) cross-section. (g-h) The visible and infrared spectrum of Si substrate with and without PS PhC (r = 130 nm) in air.
3.2 Properties of TiO2 MM
Unlike PS PhCs, TiO2 MM are self-assembled via horizontal sedimentation on a Si substrate. The TiO2 nanoparticles have uneven size distribution in range of ∼ 15 nm to 35 nm, that usually cause large crack spacing in vertical drying nanoparticle film [76]. Horizontal sedimentation helps to ease the effect. Moreover, the dense film formed by this method shows relatively rough surface (see Fig. 5(a-b)), that means good hydrophilicity [77]. It is beneficial to the subsequent vertical deposition of PS PhCs in the next session. Comparing to the bare Si substrate, the visible spectrum of self-assembled TiO2 MM shows a moderately increased reflection (see Fig. 5(c)). At infrared, the TiO2 MM has high absorption (emissivity) at 9 µm -14 µm.
Fig. 5. Experimental study of the self-assembled TiO2 MM. (a) SEM image of TiO2 MM surface. (b) SEM image of TiO2 MM cross-section. Inset: zoom-out of the film sample to mark the thickness. (c-d) The visible and infrared spectrum of Si substrate with and without TiO2 MM.
3.3 Properties of TiO2 MM- PS PhC heterostructures
The TiO2 MM - PS PhC (r = 110 nm and 130 nm) heterostructures are self-assembled via the combination of horizontal and vertical sedimentation methods in our experiment. The thickness of each component in our heterostructures (see Fig. S7) is basically consistent with that of the individual structures in sections 3.1 and 3.2. A van der Waals interface pastes TiO2 MM and PS PhCs together concretely (see Fig. 6(b) and (f)). Fabrication compatibility of two photonic structures are well-established at this interface, by virtue of the prominent size-tolerance in particle packing and hydrophilicity of TiO2 MM surface as discussed above. Compared with the visible spectra of PS PhCs (see Fig. 4(c) and (g)), the visible spectra of the heterostructures (see Fig. 6(c) and (g)) are basically the same. At infrared, the heterostructures have high absorption at 9 µm - 14 µm (in Fig. 6(d) and (h)), basically consistent with that of TiO2 MM.
Fig. 6. Experimental studies of the self-assembled TiO2 MM-PS PhC heterostructures. (a) SEM image of TiO2 MM-PS (r = 110 nm) PhC heterostructure surface. (b) SEM image of TiO2 MM-PS (r = 110 nm) PhC heterostructure cross-section. (c-d) The visible and infrared spectrum of Si substrate with and without TiO2 MM-PS (r = 110 nm) PhC heterostructure. (e) SEM image of TiO2 MM-PS (r = 130 nm) PhC heterostructure surface. (f) SEM image of TiO2 MM-PS (r = 130 nm) PhC heterostructure cross-section. (g-h) The visible and infrared spectrum of Si substrate with and without TiO2 MM-PS (r = 130 nm) PhC heterostructure. The thickness of PS PhC is about 22.4 µm (for r = 110 nm) or 18.6 µm (r = 130 nm) and the thickness of TiO2 MM is about 14 µm (see Fig. S7).
3.4 Properties of anti-counterfeiting label
In order to demonstrate the visible and infrared dual-band anti-counterfeiting effect, the self-assembled TiO2 MM-PS PhC heterostructures are prepared on pattern-engraved Si substrates. The thicknesses of PS PhC components in the obtained samples are the same as that in section 3.1. While the thicknesses of TiO2 MM components in the obtained samples are dependent on the engraving depth (see Fig. S8, large than that in section 3.2).
For the first sample, PS PhC with radius of 110 nm can hide the smiley face coding pattern containing TiO2 MM by green color (Fig. 7(a-b)). When the sample is immersed in alcohol medium, the underlying pattern can be clearly observed (Fig. 7(c)). This is because that PS PhC is highly transparent to visible light in alcohol medium (See Fig. 1(c)). After the alcohol volatilizes, the coding pattern can be hidden again (see Fig. 7(d)). Therefore, our heterostructure can realize the visible band anti-counterfeiting. Meanwhile, the underlying coding pattern emerges under FLIR thermal imaging camera (see Fig. 7(e-h)).
Fig. 7. Visible imaging results. (a) The smiley face coding pattern containing TiO2 MM in air. (b) TiO2 MM-PS PhC heterostructure in air. (c) TiO2 MM-PS PhC heterostructure in alcohol. (d) TiO2 MM-PS PhC heterostructure after alcohol volatilizes. Infrared imaging results. (e) The smiley face coding pattern containing TiO2 MM. (f) TiO2 MM-PS PhC heterostructure in air. (g) TiO2 MM-PS PhC heterostructure in alcohol. (h) TiO2 MM-PS PhC heterostructure after alcohol volatilizes.
Next, we study another coding pattern (UESTC) based on TiO2 MM-PS PhC (r = 130 nm) heterostructure (see Fig. 8(a-h)). The change of coding pattern and PS microsphere’s radius does not affect the function of the designed heterostructure. However, the displayed patterns are black in Fig. 7(c) and white in Fig. 8 (c), while the unpattern regions are gold and pink respectively. This is due to the thickness difference of TiO2 MM and PS PhC in two samples.
Fig. 8. Visible imaging results. (a) The “UESTC” coding pattern containing TiO2 MM in air. (b) TiO2 MM-PS PhC heterostructure in air. (c) TiO2 MM-PS PhC heterostructure in alcohol. (d) TiO2 MM-PS PhC heterostructure after alcohol volatilizes. Infrared imaging results. (e) The “UESTC” coding pattern containing TiO2 MM. (f) TiO2 MM-PS PhC heterostructure in air. (g) TiO2 MM-PS PhC heterostructure in alcohol. (h) TiO2 MM-PS PhC heterostructure after alcohol volatilizes.
4. Conclusion
In this study, we realize photonic MM-PhC heterostructures and demonstrate the function integration in a dual-band manner. Our design and fabrication methods make full use of large difference in characteristic lengths between MM and PhC components: theoretically, effective media approximation and photonic bandgap engineer allows different optical modes, and a refractive-index-matched interface moderates unwanted interferences; experimentally, uneven surfaces formed by dense packing of small particles facilitate large particle packing on them, making mechanically stable interfaces.
Explicitly, the self-assembled TiO2 MM-polystyrene (PS) PhC heterostructures are prepared by vertical and subsequent horizontal sedimentations. A van der Waals interface pastes the two distinct photonic structures. High emission TiO2 MMs filled in the substrate slit creates light paths in the visible and thermal imaging patterns at mid-infrared due to deep subwavelength-size of TiO2. Bandgap engineering of PS PhCs allows structural coloring in the visible due to wavelength-size of PSs. At mid-infrared, PS PhCs recede to a high transparent effective media to pass imaging lights.
Due to this kind of optical modes segmentation and interface matching, a new type of dual-band anti-counterfeiting labels is implemented by our heterostructures. We have also paved the way for design and fabrication of multi-functional photonic heterostructures and their application in photonics.
Funding
Regional Joint Key Fund of National Natural Science Foundation of China (U19A2096); National Natural Science Foundation of China (52021001, 52022018).
Acknowledgments
Peiheng Zhou ang Jianliang Xie thank the National Natural Science Foundation of China for help identifying collaborators for this work.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
Supplemental document
See Supplement 1 for supporting content.
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