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Curr. Opt. Photon. 2023; 7(3): 254-262

Published online June 25, 2023 https://doi.org/10.3807/COPP.2023.7.3.254

Copyright © Optical Society of Korea.

Design of Dynamically Focus-switchable Fresnel Zone Plates Based on Plasmonic Phase-change VO2 Metafilm Absorbers

Kyuho Kim1, Changhyun Kim1, Sun-Je Kim2 , Byoungho Lee1

1Inter-University Semiconductor Research Center, School of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
2Department of Physics, Myongji University, Yongin 17058, Korea

Corresponding author: *sunjekim@mju.ac.kr, ORCID 0000-0002-9627-4465
**byoungho@snu.ac.kr, ORCID 0000-0002-0477-9539
IIDeceased on November 7, 2020.

Received: March 6, 2023; Revised: May 4, 2023; Accepted: May 29, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Novel thermo-optically focus-switchable Fresnel zone plates based on phase-change metafilms are designed and analyzed at a visible wavelength (660 nm). By virtue of the large thermo-optic response of vanadium dioxide (VO2) thin film, a phase-change material, four different plasmonic phase-change absorbers are numerically designed as actively tunable Gires-Tournois Al-VO2 metafilms in two and three dimensions. The designed phase-change metafilm unit cells are used as the building blocks of actively focus-switchable Fresnel zone plates with strong focus switching contrast (40%, 83%) and high numerical apertures (1.52, 1.70). The Fresnel zone plates designed in two and three dimensions work as cylindrical and spherical lenses in reflection type, respectively. The coupling between the thermo-optic effect of VO2 and localized plasmonic resonances in the Al nanostructures offer a large degree of freedom in design and high-contrast focus-switching performance based on largely tunable absorption resonances. The proposed method may have great potential in photothermal and electrothermal active optical devices for nonlinear optics, microscopy, 3D scanning, optical trapping, and holographic displays over a wide spectral range including the visible and infrared regimes.

Keywords: Fresnel zone plate, Metasurface, Phase-change material, Surface plasmon, Thermo-optics

OCIS codes: (050.1965) Diffractive lenses; (050.6624) Subwavelength structures; (240.6680) Surface plasmons; (350.4238) Nanophotonics and photonic crystals

In the field of nanophotonics, optical metasurfaces made of dielectrics and metals have risen as promising next-generation diffractive optical element technologies by virtue of the extensive capabilities of engineering an on-demand arbitrary wavefront [1, 2], absorption and scattering spectra [3], polarization selectivity and multi-functionality [4], and even the dynamic tunability of designated optical functions [5]. In particular, beam steering and imaging functions with optical metasurfaces, metagrating deflectors [611] and metalenses [1220] with sub-micron thicknesses have been the most popular and significant applications in free space. Since the seminal papers on phase-gradient metasurfaces by the Capasso group in Harvard University [1] and Brongersma group in Stanford University [2], countless studies have been conducted to demonstrate advanced metagratings and metalenses with improved performance [620].

On the other hand, relatively less progress has been achieved with dynamically tunable optical metasurfaces where designated wavefront shaping functions can be switched or gradually tuned by active optical materials and corresponding external stimuli [5]. The main obstacle has been the lack of excellent optical material with large tunability, high refractive index (RI), and low intrinsic absorption in the visible and near-infrared regimes. Vanadium dioxide (VO2), a representative phase-change material, has been widely studied for the relatively good thermo-optic tunability of the optical dielectric function despite considerable absorption loss [11, 2130]. Since VO2 exhibits large thermo-optic tunability over the visible to infrared range, various VO2 based metasurfaces have been developed and tuned in thermo-optic and electro-thermo-optic manners. However, due to the intrinsically large absorption of VO2, dynamic phase modulation in the phase-change metasurface has rarely been achieved with high optical efficiency [25]. On the other hand, it has been proved that amplitude modulators based on the phase change of VO2 metasurfaces would be more useful and realizable for the multi-objective design of optical functions [11, 2729].

In this paper, we propose a novel design of thermo-optically focus-switchable Fresnel zone plates (FZPs) based on phase-change Gires-Tournois type metafilm (MF) absorbers [29, 3135]. To simultaneously increase numerical aperture (NA), focus switching contrast (SC), and focusing efficiency, we adopt four different types of reflection-type Al-VO2 MF structures as the building blocks of the reflection-type FZPs. These building blocks based on an Gires-Tournois interferometer with deep subwavelength thickness [29, 3135] are judiciously engineered to provide four distinct reflectance modulation functions.

The paper is organized as follows: First, the concepts and goals of the actively tunable FZPs are described in detail. Then, design principles based on electromagnetic simulations and scalar wave diffraction theory are suggested. Lastly, the focus-switching performances of the designed FZPs are analyzed. The electromagnetic full field and scalar wave diffraction simulations are performed by the finite element method (COMSOL Multiphysics RF solver; COMSOL, MA, USA) and customized angular spectrum method code written in MATLAB, respectively.

2.1. Concepts and Goals

Figure 1(a) describes the results of our previous measurement of the complex RI spectra of 50-nm-thick VO2 thin film grown by the pulsed-laser deposition method in the optical regime [29]. Owing to the large thermo-optic SC of the complex RI of our data, it is possible to design visible-range focus-switching FZPs with high NA and SC. The idea to design highly tunable MF unit cells is to use reflection-type tunable plasmonic absorption resonance similar to our previous work [29]. As the first step ahead of the simulations, Al is chosen as the plasmonic material that will be embedded as nanostructures inside the 50-nm-thick VO2 thin film and used as a back reflector.

Figure 1.Optical property of VO2. (a) Spectra of refractive indices and extinction coefficients of insulating and metallic VO2 thin films. (b) Complex refractive index map of Al, and insulating and metallic VO2 phases. B, G, and R represent the blue (473 nm), green (532 nm), and red (660 nm) wavelengths, respectively.

The RI data of Al [36] and Al2O3 [37] are cited from the literature. According to the complex RI map described in Fig. 1(b), it is clearly seen that the complex RI coordinates of Al are very far from VO2 in both phases in the visible range. Therefore, when Al-VO2 MF is engineered with composites of the two materials, it would be possible to design largely different thermally tunable effective RI and reflection amplitudes from MFs by tuning the filling factor and shape of Al nanostructures [29, 3840].

To build a focus-switchable FZP, a switchable hybrid profile of reflection amplitude is required. The FZP1 and FZP2 depicted in Fig. 2(a) correspond to amplitude profiles in the insulating and metallic phases for different focal lengths, respectively. In Fig. 2(a), the gray regions in FZP1 and FZP2 denote temperature-independent highly reflective regions, while the sky blue and red regions in FZP1 and FZP2 refer to nearly reflectionless regions. FZP1 and FZP2 with different focal lengths have different sets of radii of Fresnel zones according to the following Eq. (1).

Figure 2.Concepts of the focus-switchable Fresnel zone plates (FZPs). (a) Diagram of the design of amplitude profiles of active focus-switchable FZPs. Schemes describing the thermally focus-switchable (b) cylindrical and (c) spherical lenses. The red and blue foci in (c) and (d) imply the foci in the metallic (heated) and insulating (room temperature) phases, respectively. The type metafilm (MF) unit cell structures for (d) cylindrical and (e) spherical lenses. The unit cell configurations of (d) and (e) are based on 50-nm-thick VO2 film grown on an Al2O3 substrate and covered by a thick Al reflector.

rn=nλf+14n2λ2

Equation (1) dictates the design principle of the nth order Fresnel zone radius (rn) depending on the wavelength. Here, n, λ, and f refer to the order of Fresnel zone, wavelength in a medium (Al2O3 substrate), and focal length, respectively.

Since the two FZP profiles are to be merged into a single FZP [the third profile in Fig. 2(a)], it is necessary to deploy four different unit cell building blocks that provide different thermo-optic tunability of reflectance. The building blocks would play four different roles as tunable or not tunable reflectors depending on the phase change of VO2. The required unit cells are temperature-dependent switchable near-unity absorbers (bare VO2 with Al mirror, MF1), temperature-independent near-unity absorbers (MF2 for passive near-zero reflection), and temperature-independent weak absorbers (MF3 for passive high reflection). In particular, the most important unit cells are bare VO2 with Al reflector and MF1. The former acts as a near-unity absorber only in the insulating phase, while the latter acts as a near-unity absorber only in the metallic phase of VO2. This implies that the region of bare VO2 with an Al mirror reflects considerable light only in the metallic phase, while MF1 acts as a reflector only in the insulating phase, in the opposite manner.

With the abovementioned hybridization of the two FZPs with different focal lengths, high-NA focus switching in both 2D [Fig. 2(b)] and 3D [Fig. 2(c)] FZPs can be designed. For a demonstration of the unit cells of a 2D cylindrical lens and 3D spherical FZP lens, schemes of VO2 MFs containing embedded Al nanobeams [Fig. 2(d)] and nanodisks [Fig. 2(e)] are used, respectively.

2.2. Design Principles

The detailed electromagnetic design procedure is as follows. First, the target wavelength is set to be 660 nm (red) considering the large thermo-optic tunability at this wavelength. Second, for several unit cell periods, the filling factor of Al embeddings (fAl) in 50-nm-thick VO2 film capped by an Al reflector and a sapphire substrate is engineered to find the four unit cells.

Through the parameter sweeps of fAl by varying the Al nanobeam width and nanodisk radius (for several values of periods), the optimal geometric parameters for MF1, MF2, and MF3 are determined for 2D and 3D cases as shown in Figs. 3 and 4, respectively. Figures 3(a)3(c) represent the modulation depth spectra according to the fAl of the 2D unit cell, while Figs. 4(a)4(c) represent those of 3D cases obtained from electromagnetic full-field simulations. Here, modulation depth (η) is defined as the normalized value between 0 and 1, η = │RiRm│/ max(Ri, Rm). Ri and Rm refer to reflectance in the insulating and metallic phases, respectively.

Figure 3.Simulated modulation depth spectra according to the filling factor of aluminum nanobeams when the period is (a) 300 nm and (b) 400 nm. (c) Effect of Al nanobeam filling factor on reflectance at the wavelength of 660 nm.
Figure 4.Simulated modulation depth spectra according to the filling factor of aluminum nanodisks when the period is (a) 200 nm and (b) 425 nm. (c) Effect of Al nanodisk filling factor on reflectance at the wavelength of 660 nm.

At the target wavelength, design parameters (unit cell period and fAl) are chosen by considering modulation depth and reflectance. When MF1 is engineered, geometric parameters are chosen to make the modulation depth reach a near-unity value. On the contrary, MF2 (temperature-independent perfect absorber) and MF3 (temperature-independent strong reflector) are designed to exhibit a near-zero modulation depth. The pink marks in the modulation depth spectra in Figs. 3(a), 3(b), 4(a), and 4(b) refer to the MF1, MF2, and MF3 parameter conditions of 2D and 3D FZPs, respectively. The effects of chosen sets of the unit cells are seen in the plots in Figs. 3(c) and 4(c) and the figures show that our design goal is achieved. In particular, when fAl reaches 0.4 and 0.35 for the 2D nanobeam and 3D nanodisk schemes, respectively, the MF1 unit cells for 2D cylindrical and 3D spherical FZPs are well designed as near-perfect absorbers only in the metallic phase of VO2. On the other hand, zero-valued fAl (bare VO2 without Al embedding) acts oppositely, as a near-perfect absorber only in the insulating phase of VO2. The detailed design parameters of the unit cells are summarized in Table 1.

Table 1 Geometric parameters of unit cells

FZP Unit CellsfAlp (nm)wAl (nm)
Bare VO2 with Reflector000
2D MF1 (MF1-1)0.4300120
2D MF2 (MF1-2)0.2430072
2D MF3 (MF1-3)0.45400180
3D MF1 (MF2-1)0.35200133
3D MF2 (MF2-2)0.25200112
3D MF3 (MF2-3)0.45425322


The main reasons for switchable and non-switchable reflection amplitudes from FZP unit cells originate from nanoscale absorption resonances [29]. Figure 5(a) shows that reflectance from an ultrathin Gires-Tournois VO2 film absorber can be largely tuned by virtue of near-unity absorption in the insulating phase and the thermal RI change of VO2 film [29, 34].

Figure 5.Magnetic field intensity profiles of Fresnel zone plate (FZP) unit cells, (a) bare VO2 on Al, (b) MF 1-1, and (c) MF 2-1 in both phases of VO2. (a) and (b) depict field profiles on the xz-plane while (c) shows xy-plane profiles on a cross section in the middle of the VO2 film thickness.

Embedded Al nanostructures in MFs are designed to move positions of absorption resonances in both phases of VO2 in desired ways due to the tuning of localized surface plasmon resonances. In Figs. 3(c) and 4(c), the effects of Al filling factor for reflectance shift are suggested for the target wavelength. The cooling and heating of the device shift the resonance position toward shorter and longer wavelengths according to the red and blue shift of the VO2 RI, respectively. The field profiles of Figs. 5(b) and 5(c) graphically show that absorption in VO2 of MF1-1 and MF2-1 are enhanced by the Al nanostructures in the metallic phase so that they act as near-unity absorbers only in the metallic phase.

2.3. Results: Design of Cylindrical and Spherical FZPs

In this section, the switchable focusing performance of designed cylindrical (2D) and spherical (3D) FZPs is investigated with scalar wave optics simulation. As mentioned in the first section, the simulation results presented in Figs. 6 and 7 are produced by simulation codes based on the angular spectrum method of scalar wave optics using fast Fourier transform in MATLAB. Since our devices exhibit high NA focusing properties, Fresnel or Fraunhofer diffraction for paraxial approximation is not adequate for this case.

Figure 6.Simulation results of temperature-dependent focusing and switching of a 2D cylindrical lens. Diffraction intensity maps in the (a) insulating (room temp.) and (b) metallic (hot) phases of VO2 on the yz plane. (c) Focus-switching contrast along the optic axis. The blue and red lines denote the insulating and metallic phases of VO2, respectively.
Figure 7.Simulation results of temperature-dependent focusing and switching of a 3D spherical lens. Diffraction intensity maps in the (a) insulating (room temp.) and (b) metallic (hot) phases of VO2 on the yz plane. (c) Focus-switching contrast along the optic axis. The blue and red lines denote the insulating and metallic phases of VO2, respectively.

As illustrated in Figs. 6 and 7, high-contrast focus switching between two microscale FZPs (diameter: 20 μm) with largely different focal lengths (3 and 6 μm) is successfully achieved.

The quantitative performances of focusing and switching are summarized in Tables 2 and 3. The SC is defined as SC = (ImaxImin) / (Imax + Imin) in percentage. Imax and Imin are the maximum and minimum intensity along the optic axis, which can be found in Figs. 6(c) and 7(c). When it comes to full width at half maximum (FWHM) at the cross-section of the focal point, the sizes of the main lobes of the 2D (Fig. 8) and 3D foci (Fig. 9) resemble diffraction-limited Airy disks in both phases of VO2. However, in Figs. 8 and 9, it is seen that the 3D spherical lens has better focusing quality compared to that of the 2D cylindrical one. The difference in focusing quality seems to come from the difference in the switching quality of the sets of the 2D and 3D unit cells suggested in Figs. 3 and 4, respectively.

Table 2 Focusing performance: 2D cylindrical Fresnel zone plate (FZP)

LensesFocal Length (μm)NAFocusing Efficiency (%)FWHM (nm)Switching Contrast (%)
FZP1 (Insulating)5.901.522.67363.8523
FZP2 (Metallic)2.901.701.84210.7025

Table 3 Focusing performance: 3D spherical Fresnel zone plate (FZP)

LensesFocal Length (μm)NAFocusing Efficiency (%)FWHM (nm)Switching Contrast (%)
FZP1 (Insulating)5.901.529.3134140
FZP2 (Metallic)2.801.7013.4725083

Figure 8.Cross-sectional focusing properties (magnetic field intensity) of a switchable 2D cylindrical Fresnel zone plate (FZP) at the designated focal points at (a) z = 3 μm and (b) z = 6 μm, respectively.
Figure 9.Cross-sectional focusing properties (electric field intensity) of the switchable 3D spherical Fresnel zone plate (FZP) at the designated focal points at (a) z = 3 μm and (b) z = 6 μm. The inset figures are 2D focusing profiles in the (a) metallic and (b) insulator phases of VO2.

The most noteworthy point to discuss implied from Tables 2 and 3 is focusing efficiency. The theoretical maximum efficiency limit of FZP1 and FZP2 are 6.31 and 4.39% at 2D and 72.79 and 27.35% at 3D configurations, respectively. Since our device is based on the amplitude modulation method of FZP and largely tunable absorption resonances for the unit cell designs, a drop in focusing efficiency is inevitable.

Based on the proposed principles, focusing efficiency and quality could be further improved if an additional lossless dielectric thin film resonator is vertically stacked on the Al-VO2 MFs to increase the reflectance of the unit cells [29]. By inserting an additional thin film resonator, it could be possible to enhance the reflectance of MFs for higher focusing efficiency and quality with a negligible decrease in the modulation depth of the unit cells. The 2D unit cell configuration depicted in Figs. 10(a) and 10(b) illustrates an example of the abovementioned idea. Insertion of a lossless Si3N4 film [41] can provide an additional design degree of freedom so that the reflectance of the bare reflector (in the metallic phase), MF1-1 (in the insulating phase), and MF1-3 (in both phases of VO2) could be further increased. Some improvement of reflectance of the 2D FZP unit cells is found in our parameter sweep simulations [Fig. 10(c)] compared to the original design without the Si3N4 film. In addition, we expect that multi-variable geometry optimization based on numerical algorithms [42], considering fAl, the thickness values of VO2, Al2O3 spacer, and Si3N4, and the unit cell period, could push the efficiency and quality of focusing to the ideal limit to some degree.

Figure 10.(a) Schematic diagram of a switchable 2D MF unit cell with a 90-nm-thick film Si3N4 resonator with a 230-nm-thick Al2O3 spacer. (b) Magnetic field intensity profiles of the new MF 1-1 unit cell (fAl = 0.4) in the insulator (left) and metallic (right) phases. (c) Effect of the Al nanobeam filling factor on reflectance at the wavelength of 660 nm. The bold and dotted lines in (c) refer to reflectance with and without the Si3N4 film, respectively. The four colored legends in (c) account for the different unit cell periods and phases of VO2.

A novel design method and design examples of actively focus-switchable FZPs are proposed based on phase-change Al-VO2 nano-absorbers. The authors expect that the proposed method will be fruitful for the potential experimental demonstration of electro-thermal or photo-thermal switching of FZP focus. It means that this platform has great potential for applications of active diffractive optics elements and thermally induced nonlinear optics technologies.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2021R1F1A1062368). This work was also supported by the 2022 Research Fund of Myongji University.

National Research Foundation of Korea (NRF) (No. 2021R1F1A1062368); 2022 Research Fund of Myongji University.

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Article

Research Paper

Curr. Opt. Photon. 2023; 7(3): 254-262

Published online June 25, 2023 https://doi.org/10.3807/COPP.2023.7.3.254

Copyright © Optical Society of Korea.

Design of Dynamically Focus-switchable Fresnel Zone Plates Based on Plasmonic Phase-change VO2 Metafilm Absorbers

Kyuho Kim1, Changhyun Kim1, Sun-Je Kim2 , Byoungho Lee1

1Inter-University Semiconductor Research Center, School of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
2Department of Physics, Myongji University, Yongin 17058, Korea

Correspondence to:*sunjekim@mju.ac.kr, ORCID 0000-0002-9627-4465
**byoungho@snu.ac.kr, ORCID 0000-0002-0477-9539
IIDeceased on November 7, 2020.

Received: March 6, 2023; Revised: May 4, 2023; Accepted: May 29, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Novel thermo-optically focus-switchable Fresnel zone plates based on phase-change metafilms are designed and analyzed at a visible wavelength (660 nm). By virtue of the large thermo-optic response of vanadium dioxide (VO2) thin film, a phase-change material, four different plasmonic phase-change absorbers are numerically designed as actively tunable Gires-Tournois Al-VO2 metafilms in two and three dimensions. The designed phase-change metafilm unit cells are used as the building blocks of actively focus-switchable Fresnel zone plates with strong focus switching contrast (40%, 83%) and high numerical apertures (1.52, 1.70). The Fresnel zone plates designed in two and three dimensions work as cylindrical and spherical lenses in reflection type, respectively. The coupling between the thermo-optic effect of VO2 and localized plasmonic resonances in the Al nanostructures offer a large degree of freedom in design and high-contrast focus-switching performance based on largely tunable absorption resonances. The proposed method may have great potential in photothermal and electrothermal active optical devices for nonlinear optics, microscopy, 3D scanning, optical trapping, and holographic displays over a wide spectral range including the visible and infrared regimes.

Keywords: Fresnel zone plate, Metasurface, Phase-change material, Surface plasmon, Thermo-optics

I. INTRODUCTION

In the field of nanophotonics, optical metasurfaces made of dielectrics and metals have risen as promising next-generation diffractive optical element technologies by virtue of the extensive capabilities of engineering an on-demand arbitrary wavefront [1, 2], absorption and scattering spectra [3], polarization selectivity and multi-functionality [4], and even the dynamic tunability of designated optical functions [5]. In particular, beam steering and imaging functions with optical metasurfaces, metagrating deflectors [611] and metalenses [1220] with sub-micron thicknesses have been the most popular and significant applications in free space. Since the seminal papers on phase-gradient metasurfaces by the Capasso group in Harvard University [1] and Brongersma group in Stanford University [2], countless studies have been conducted to demonstrate advanced metagratings and metalenses with improved performance [620].

On the other hand, relatively less progress has been achieved with dynamically tunable optical metasurfaces where designated wavefront shaping functions can be switched or gradually tuned by active optical materials and corresponding external stimuli [5]. The main obstacle has been the lack of excellent optical material with large tunability, high refractive index (RI), and low intrinsic absorption in the visible and near-infrared regimes. Vanadium dioxide (VO2), a representative phase-change material, has been widely studied for the relatively good thermo-optic tunability of the optical dielectric function despite considerable absorption loss [11, 2130]. Since VO2 exhibits large thermo-optic tunability over the visible to infrared range, various VO2 based metasurfaces have been developed and tuned in thermo-optic and electro-thermo-optic manners. However, due to the intrinsically large absorption of VO2, dynamic phase modulation in the phase-change metasurface has rarely been achieved with high optical efficiency [25]. On the other hand, it has been proved that amplitude modulators based on the phase change of VO2 metasurfaces would be more useful and realizable for the multi-objective design of optical functions [11, 2729].

In this paper, we propose a novel design of thermo-optically focus-switchable Fresnel zone plates (FZPs) based on phase-change Gires-Tournois type metafilm (MF) absorbers [29, 3135]. To simultaneously increase numerical aperture (NA), focus switching contrast (SC), and focusing efficiency, we adopt four different types of reflection-type Al-VO2 MF structures as the building blocks of the reflection-type FZPs. These building blocks based on an Gires-Tournois interferometer with deep subwavelength thickness [29, 3135] are judiciously engineered to provide four distinct reflectance modulation functions.

The paper is organized as follows: First, the concepts and goals of the actively tunable FZPs are described in detail. Then, design principles based on electromagnetic simulations and scalar wave diffraction theory are suggested. Lastly, the focus-switching performances of the designed FZPs are analyzed. The electromagnetic full field and scalar wave diffraction simulations are performed by the finite element method (COMSOL Multiphysics RF solver; COMSOL, MA, USA) and customized angular spectrum method code written in MATLAB, respectively.

II. METHOD AND RESULTS

2.1. Concepts and Goals

Figure 1(a) describes the results of our previous measurement of the complex RI spectra of 50-nm-thick VO2 thin film grown by the pulsed-laser deposition method in the optical regime [29]. Owing to the large thermo-optic SC of the complex RI of our data, it is possible to design visible-range focus-switching FZPs with high NA and SC. The idea to design highly tunable MF unit cells is to use reflection-type tunable plasmonic absorption resonance similar to our previous work [29]. As the first step ahead of the simulations, Al is chosen as the plasmonic material that will be embedded as nanostructures inside the 50-nm-thick VO2 thin film and used as a back reflector.

Figure 1. Optical property of VO2. (a) Spectra of refractive indices and extinction coefficients of insulating and metallic VO2 thin films. (b) Complex refractive index map of Al, and insulating and metallic VO2 phases. B, G, and R represent the blue (473 nm), green (532 nm), and red (660 nm) wavelengths, respectively.

The RI data of Al [36] and Al2O3 [37] are cited from the literature. According to the complex RI map described in Fig. 1(b), it is clearly seen that the complex RI coordinates of Al are very far from VO2 in both phases in the visible range. Therefore, when Al-VO2 MF is engineered with composites of the two materials, it would be possible to design largely different thermally tunable effective RI and reflection amplitudes from MFs by tuning the filling factor and shape of Al nanostructures [29, 3840].

To build a focus-switchable FZP, a switchable hybrid profile of reflection amplitude is required. The FZP1 and FZP2 depicted in Fig. 2(a) correspond to amplitude profiles in the insulating and metallic phases for different focal lengths, respectively. In Fig. 2(a), the gray regions in FZP1 and FZP2 denote temperature-independent highly reflective regions, while the sky blue and red regions in FZP1 and FZP2 refer to nearly reflectionless regions. FZP1 and FZP2 with different focal lengths have different sets of radii of Fresnel zones according to the following Eq. (1).

Figure 2. Concepts of the focus-switchable Fresnel zone plates (FZPs). (a) Diagram of the design of amplitude profiles of active focus-switchable FZPs. Schemes describing the thermally focus-switchable (b) cylindrical and (c) spherical lenses. The red and blue foci in (c) and (d) imply the foci in the metallic (heated) and insulating (room temperature) phases, respectively. The type metafilm (MF) unit cell structures for (d) cylindrical and (e) spherical lenses. The unit cell configurations of (d) and (e) are based on 50-nm-thick VO2 film grown on an Al2O3 substrate and covered by a thick Al reflector.

rn=nλf+14n2λ2

Equation (1) dictates the design principle of the nth order Fresnel zone radius (rn) depending on the wavelength. Here, n, λ, and f refer to the order of Fresnel zone, wavelength in a medium (Al2O3 substrate), and focal length, respectively.

Since the two FZP profiles are to be merged into a single FZP [the third profile in Fig. 2(a)], it is necessary to deploy four different unit cell building blocks that provide different thermo-optic tunability of reflectance. The building blocks would play four different roles as tunable or not tunable reflectors depending on the phase change of VO2. The required unit cells are temperature-dependent switchable near-unity absorbers (bare VO2 with Al mirror, MF1), temperature-independent near-unity absorbers (MF2 for passive near-zero reflection), and temperature-independent weak absorbers (MF3 for passive high reflection). In particular, the most important unit cells are bare VO2 with Al reflector and MF1. The former acts as a near-unity absorber only in the insulating phase, while the latter acts as a near-unity absorber only in the metallic phase of VO2. This implies that the region of bare VO2 with an Al mirror reflects considerable light only in the metallic phase, while MF1 acts as a reflector only in the insulating phase, in the opposite manner.

With the abovementioned hybridization of the two FZPs with different focal lengths, high-NA focus switching in both 2D [Fig. 2(b)] and 3D [Fig. 2(c)] FZPs can be designed. For a demonstration of the unit cells of a 2D cylindrical lens and 3D spherical FZP lens, schemes of VO2 MFs containing embedded Al nanobeams [Fig. 2(d)] and nanodisks [Fig. 2(e)] are used, respectively.

2.2. Design Principles

The detailed electromagnetic design procedure is as follows. First, the target wavelength is set to be 660 nm (red) considering the large thermo-optic tunability at this wavelength. Second, for several unit cell periods, the filling factor of Al embeddings (fAl) in 50-nm-thick VO2 film capped by an Al reflector and a sapphire substrate is engineered to find the four unit cells.

Through the parameter sweeps of fAl by varying the Al nanobeam width and nanodisk radius (for several values of periods), the optimal geometric parameters for MF1, MF2, and MF3 are determined for 2D and 3D cases as shown in Figs. 3 and 4, respectively. Figures 3(a)3(c) represent the modulation depth spectra according to the fAl of the 2D unit cell, while Figs. 4(a)4(c) represent those of 3D cases obtained from electromagnetic full-field simulations. Here, modulation depth (η) is defined as the normalized value between 0 and 1, η = │RiRm│/ max(Ri, Rm). Ri and Rm refer to reflectance in the insulating and metallic phases, respectively.

Figure 3. Simulated modulation depth spectra according to the filling factor of aluminum nanobeams when the period is (a) 300 nm and (b) 400 nm. (c) Effect of Al nanobeam filling factor on reflectance at the wavelength of 660 nm.
Figure 4. Simulated modulation depth spectra according to the filling factor of aluminum nanodisks when the period is (a) 200 nm and (b) 425 nm. (c) Effect of Al nanodisk filling factor on reflectance at the wavelength of 660 nm.

At the target wavelength, design parameters (unit cell period and fAl) are chosen by considering modulation depth and reflectance. When MF1 is engineered, geometric parameters are chosen to make the modulation depth reach a near-unity value. On the contrary, MF2 (temperature-independent perfect absorber) and MF3 (temperature-independent strong reflector) are designed to exhibit a near-zero modulation depth. The pink marks in the modulation depth spectra in Figs. 3(a), 3(b), 4(a), and 4(b) refer to the MF1, MF2, and MF3 parameter conditions of 2D and 3D FZPs, respectively. The effects of chosen sets of the unit cells are seen in the plots in Figs. 3(c) and 4(c) and the figures show that our design goal is achieved. In particular, when fAl reaches 0.4 and 0.35 for the 2D nanobeam and 3D nanodisk schemes, respectively, the MF1 unit cells for 2D cylindrical and 3D spherical FZPs are well designed as near-perfect absorbers only in the metallic phase of VO2. On the other hand, zero-valued fAl (bare VO2 without Al embedding) acts oppositely, as a near-perfect absorber only in the insulating phase of VO2. The detailed design parameters of the unit cells are summarized in Table 1.

Table 1 . Geometric parameters of unit cells.

FZP Unit CellsfAlp (nm)wAl (nm)
Bare VO2 with Reflector000
2D MF1 (MF1-1)0.4300120
2D MF2 (MF1-2)0.2430072
2D MF3 (MF1-3)0.45400180
3D MF1 (MF2-1)0.35200133
3D MF2 (MF2-2)0.25200112
3D MF3 (MF2-3)0.45425322


The main reasons for switchable and non-switchable reflection amplitudes from FZP unit cells originate from nanoscale absorption resonances [29]. Figure 5(a) shows that reflectance from an ultrathin Gires-Tournois VO2 film absorber can be largely tuned by virtue of near-unity absorption in the insulating phase and the thermal RI change of VO2 film [29, 34].

Figure 5. Magnetic field intensity profiles of Fresnel zone plate (FZP) unit cells, (a) bare VO2 on Al, (b) MF 1-1, and (c) MF 2-1 in both phases of VO2. (a) and (b) depict field profiles on the xz-plane while (c) shows xy-plane profiles on a cross section in the middle of the VO2 film thickness.

Embedded Al nanostructures in MFs are designed to move positions of absorption resonances in both phases of VO2 in desired ways due to the tuning of localized surface plasmon resonances. In Figs. 3(c) and 4(c), the effects of Al filling factor for reflectance shift are suggested for the target wavelength. The cooling and heating of the device shift the resonance position toward shorter and longer wavelengths according to the red and blue shift of the VO2 RI, respectively. The field profiles of Figs. 5(b) and 5(c) graphically show that absorption in VO2 of MF1-1 and MF2-1 are enhanced by the Al nanostructures in the metallic phase so that they act as near-unity absorbers only in the metallic phase.

2.3. Results: Design of Cylindrical and Spherical FZPs

In this section, the switchable focusing performance of designed cylindrical (2D) and spherical (3D) FZPs is investigated with scalar wave optics simulation. As mentioned in the first section, the simulation results presented in Figs. 6 and 7 are produced by simulation codes based on the angular spectrum method of scalar wave optics using fast Fourier transform in MATLAB. Since our devices exhibit high NA focusing properties, Fresnel or Fraunhofer diffraction for paraxial approximation is not adequate for this case.

Figure 6. Simulation results of temperature-dependent focusing and switching of a 2D cylindrical lens. Diffraction intensity maps in the (a) insulating (room temp.) and (b) metallic (hot) phases of VO2 on the yz plane. (c) Focus-switching contrast along the optic axis. The blue and red lines denote the insulating and metallic phases of VO2, respectively.
Figure 7. Simulation results of temperature-dependent focusing and switching of a 3D spherical lens. Diffraction intensity maps in the (a) insulating (room temp.) and (b) metallic (hot) phases of VO2 on the yz plane. (c) Focus-switching contrast along the optic axis. The blue and red lines denote the insulating and metallic phases of VO2, respectively.

As illustrated in Figs. 6 and 7, high-contrast focus switching between two microscale FZPs (diameter: 20 μm) with largely different focal lengths (3 and 6 μm) is successfully achieved.

The quantitative performances of focusing and switching are summarized in Tables 2 and 3. The SC is defined as SC = (ImaxImin) / (Imax + Imin) in percentage. Imax and Imin are the maximum and minimum intensity along the optic axis, which can be found in Figs. 6(c) and 7(c). When it comes to full width at half maximum (FWHM) at the cross-section of the focal point, the sizes of the main lobes of the 2D (Fig. 8) and 3D foci (Fig. 9) resemble diffraction-limited Airy disks in both phases of VO2. However, in Figs. 8 and 9, it is seen that the 3D spherical lens has better focusing quality compared to that of the 2D cylindrical one. The difference in focusing quality seems to come from the difference in the switching quality of the sets of the 2D and 3D unit cells suggested in Figs. 3 and 4, respectively.

Table 2 . Focusing performance: 2D cylindrical Fresnel zone plate (FZP).

LensesFocal Length (μm)NAFocusing Efficiency (%)FWHM (nm)Switching Contrast (%)
FZP1 (Insulating)5.901.522.67363.8523
FZP2 (Metallic)2.901.701.84210.7025

Table 3 . Focusing performance: 3D spherical Fresnel zone plate (FZP).

LensesFocal Length (μm)NAFocusing Efficiency (%)FWHM (nm)Switching Contrast (%)
FZP1 (Insulating)5.901.529.3134140
FZP2 (Metallic)2.801.7013.4725083

Figure 8. Cross-sectional focusing properties (magnetic field intensity) of a switchable 2D cylindrical Fresnel zone plate (FZP) at the designated focal points at (a) z = 3 μm and (b) z = 6 μm, respectively.
Figure 9. Cross-sectional focusing properties (electric field intensity) of the switchable 3D spherical Fresnel zone plate (FZP) at the designated focal points at (a) z = 3 μm and (b) z = 6 μm. The inset figures are 2D focusing profiles in the (a) metallic and (b) insulator phases of VO2.

The most noteworthy point to discuss implied from Tables 2 and 3 is focusing efficiency. The theoretical maximum efficiency limit of FZP1 and FZP2 are 6.31 and 4.39% at 2D and 72.79 and 27.35% at 3D configurations, respectively. Since our device is based on the amplitude modulation method of FZP and largely tunable absorption resonances for the unit cell designs, a drop in focusing efficiency is inevitable.

Based on the proposed principles, focusing efficiency and quality could be further improved if an additional lossless dielectric thin film resonator is vertically stacked on the Al-VO2 MFs to increase the reflectance of the unit cells [29]. By inserting an additional thin film resonator, it could be possible to enhance the reflectance of MFs for higher focusing efficiency and quality with a negligible decrease in the modulation depth of the unit cells. The 2D unit cell configuration depicted in Figs. 10(a) and 10(b) illustrates an example of the abovementioned idea. Insertion of a lossless Si3N4 film [41] can provide an additional design degree of freedom so that the reflectance of the bare reflector (in the metallic phase), MF1-1 (in the insulating phase), and MF1-3 (in both phases of VO2) could be further increased. Some improvement of reflectance of the 2D FZP unit cells is found in our parameter sweep simulations [Fig. 10(c)] compared to the original design without the Si3N4 film. In addition, we expect that multi-variable geometry optimization based on numerical algorithms [42], considering fAl, the thickness values of VO2, Al2O3 spacer, and Si3N4, and the unit cell period, could push the efficiency and quality of focusing to the ideal limit to some degree.

Figure 10. (a) Schematic diagram of a switchable 2D MF unit cell with a 90-nm-thick film Si3N4 resonator with a 230-nm-thick Al2O3 spacer. (b) Magnetic field intensity profiles of the new MF 1-1 unit cell (fAl = 0.4) in the insulator (left) and metallic (right) phases. (c) Effect of the Al nanobeam filling factor on reflectance at the wavelength of 660 nm. The bold and dotted lines in (c) refer to reflectance with and without the Si3N4 film, respectively. The four colored legends in (c) account for the different unit cell periods and phases of VO2.

III. CONCLUSION

A novel design method and design examples of actively focus-switchable FZPs are proposed based on phase-change Al-VO2 nano-absorbers. The authors expect that the proposed method will be fruitful for the potential experimental demonstration of electro-thermal or photo-thermal switching of FZP focus. It means that this platform has great potential for applications of active diffractive optics elements and thermally induced nonlinear optics technologies.

DISCLOSURES

The authors declare no conflicts of interest.

DATA AVAILABILITY

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

ACKNOWLEDGMENTS

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2021R1F1A1062368). This work was also supported by the 2022 Research Fund of Myongji University.

FUNDING

National Research Foundation of Korea (NRF) (No. 2021R1F1A1062368); 2022 Research Fund of Myongji University.

Fig 1.

Figure 1.Optical property of VO2. (a) Spectra of refractive indices and extinction coefficients of insulating and metallic VO2 thin films. (b) Complex refractive index map of Al, and insulating and metallic VO2 phases. B, G, and R represent the blue (473 nm), green (532 nm), and red (660 nm) wavelengths, respectively.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 2.

Figure 2.Concepts of the focus-switchable Fresnel zone plates (FZPs). (a) Diagram of the design of amplitude profiles of active focus-switchable FZPs. Schemes describing the thermally focus-switchable (b) cylindrical and (c) spherical lenses. The red and blue foci in (c) and (d) imply the foci in the metallic (heated) and insulating (room temperature) phases, respectively. The type metafilm (MF) unit cell structures for (d) cylindrical and (e) spherical lenses. The unit cell configurations of (d) and (e) are based on 50-nm-thick VO2 film grown on an Al2O3 substrate and covered by a thick Al reflector.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 3.

Figure 3.Simulated modulation depth spectra according to the filling factor of aluminum nanobeams when the period is (a) 300 nm and (b) 400 nm. (c) Effect of Al nanobeam filling factor on reflectance at the wavelength of 660 nm.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 4.

Figure 4.Simulated modulation depth spectra according to the filling factor of aluminum nanodisks when the period is (a) 200 nm and (b) 425 nm. (c) Effect of Al nanodisk filling factor on reflectance at the wavelength of 660 nm.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 5.

Figure 5.Magnetic field intensity profiles of Fresnel zone plate (FZP) unit cells, (a) bare VO2 on Al, (b) MF 1-1, and (c) MF 2-1 in both phases of VO2. (a) and (b) depict field profiles on the xz-plane while (c) shows xy-plane profiles on a cross section in the middle of the VO2 film thickness.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 6.

Figure 6.Simulation results of temperature-dependent focusing and switching of a 2D cylindrical lens. Diffraction intensity maps in the (a) insulating (room temp.) and (b) metallic (hot) phases of VO2 on the yz plane. (c) Focus-switching contrast along the optic axis. The blue and red lines denote the insulating and metallic phases of VO2, respectively.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 7.

Figure 7.Simulation results of temperature-dependent focusing and switching of a 3D spherical lens. Diffraction intensity maps in the (a) insulating (room temp.) and (b) metallic (hot) phases of VO2 on the yz plane. (c) Focus-switching contrast along the optic axis. The blue and red lines denote the insulating and metallic phases of VO2, respectively.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 8.

Figure 8.Cross-sectional focusing properties (magnetic field intensity) of a switchable 2D cylindrical Fresnel zone plate (FZP) at the designated focal points at (a) z = 3 μm and (b) z = 6 μm, respectively.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 9.

Figure 9.Cross-sectional focusing properties (electric field intensity) of the switchable 3D spherical Fresnel zone plate (FZP) at the designated focal points at (a) z = 3 μm and (b) z = 6 μm. The inset figures are 2D focusing profiles in the (a) metallic and (b) insulator phases of VO2.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Fig 10.

Figure 10.(a) Schematic diagram of a switchable 2D MF unit cell with a 90-nm-thick film Si3N4 resonator with a 230-nm-thick Al2O3 spacer. (b) Magnetic field intensity profiles of the new MF 1-1 unit cell (fAl = 0.4) in the insulator (left) and metallic (right) phases. (c) Effect of the Al nanobeam filling factor on reflectance at the wavelength of 660 nm. The bold and dotted lines in (c) refer to reflectance with and without the Si3N4 film, respectively. The four colored legends in (c) account for the different unit cell periods and phases of VO2.
Current Optics and Photonics 2023; 7: 254-262https://doi.org/10.3807/COPP.2023.7.3.254

Table 1 Geometric parameters of unit cells

FZP Unit CellsfAlp (nm)wAl (nm)
Bare VO2 with Reflector000
2D MF1 (MF1-1)0.4300120
2D MF2 (MF1-2)0.2430072
2D MF3 (MF1-3)0.45400180
3D MF1 (MF2-1)0.35200133
3D MF2 (MF2-2)0.25200112
3D MF3 (MF2-3)0.45425322

Table 2 Focusing performance: 2D cylindrical Fresnel zone plate (FZP)

LensesFocal Length (μm)NAFocusing Efficiency (%)FWHM (nm)Switching Contrast (%)
FZP1 (Insulating)5.901.522.67363.8523
FZP2 (Metallic)2.901.701.84210.7025

Table 3 Focusing performance: 3D spherical Fresnel zone plate (FZP)

LensesFocal Length (μm)NAFocusing Efficiency (%)FWHM (nm)Switching Contrast (%)
FZP1 (Insulating)5.901.529.3134140
FZP2 (Metallic)2.801.7013.4725083

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