Engineering of Active and Passive Loss in High-Quality-Factor Vanadium Dioxide-Based BIC Metasurfaces

Active functionalities of metasurfaces are of growing interest in nanophotonics. The main strategy employed to date is spectral resonance tuning affecting predominantly the far-field response. However, this barely influences other essential resonance properties like near-field enhancement, signal modulation, quality factor, and absorbance, which are all vital for numerous applications. Here we introduce an active metasurface approach that combines temperature-tunable losses in vanadium dioxide with far-field coupling tunable symmetry-protected bound states in the continuum. This method enables exceptional precision in independently controlling both radiative and nonradiative losses. Consequently, it allows for the adjustment of both the far-field response and, notably, the near-field characteristics like local field enhancement and absorbance. We experimentally demonstrate continuous tuning from under- through critical- to overcoupling, achieving quality factors of 200 and a relative switching contrast of 78%. Our research marks a significant step toward highly tunable metasurfaces, controlling both near- and far-field properties.


METHODS
Simulations for our study were performed using the commercial finite element solver CST Studio Suite (Simulia).The software was configured with adaptive mesh refinement, periodic boundary conditions, and operated in the frequency domain.
For sample fabrication, first, 600 nm of Si were deposited onto a fused silica substrate by an ion beam sputtering system with Kaufmann ion sources (Kaufman & Robinson, Inc.) at room temperature by using argon ions at 600 eV.Then, 30 nm of VO2 were deposited by 250 cycles atomic layer deposition (Cambridge NanoTech Fiji 200) running at 150°C.Tetrakis(dimethylamino)vanadium (TDMAV) pre-heated to 87°C and water were used as precursors, that were let into the chamber within 0.6 s pulses with the consecutive waiting times of 8 s and 3 s, respectively.Immediately after the deposition, the sample was annealed in a vacuum tube furnace at 500°C for 5 minutes under 15 sccm flow of oxygen.Finally, 120 nm of SiO2 for the etch mask were deposited onto the sample from a stoichiometric powder in an electron beam evaporator (Bestec, 8 kV, 1 Å/s) at room temperature.Note that the resulting VO2 films exhibited slightly lowered phase transition temperature (60°C instead of conventional 68°C).We ascribe this effect to weak unintentional doping by hafnium atoms 17 , most probably from the walls of our ALD chamber given it is often used for depositions of HfO2.This notion is supported by TEM EDX analysis of our films.
Nanostructuring of the Si -VO2 -SiO2 multilayer film starts with a deposition of a 400 nm layer of positive electron beam resist, ZEP520A (Zeon Corporation), followed by a coating of a conductive polymer, using ESPACER (Showa Denko K.K).Electron beam lithography was carried out at 20 kV using an eLINE Plus system (Raith).Development was achieved with a subsequent bath in amyl acetate and MIBK:IPA in a 1:9 ratio.The polymer mask was used to dryetch the SiO2 layer and then removed by the Microposit Remover 1165 (Microresist).A second, selective dry-etching process based on SF6 and Argon was applied to etch the VO2 and Si layers.The ellipse's long axis  measures 2460 nm, the short axis  is 980 nm, the x-direction pitch  ! is 4400 nm, and in the y-direction pitch  " is 2860 nm.
Optical measurements were conducted using a spectral imaging MIR microscope, Spero (Daylight Solutions).The microscope featured a 4× magnification objective ( = 0.15) and provided a 2 mm 2 field of view.This system features three tunable quantum cascade lasers that consistently cover the 5.6-10.5 μm wavelength range, offering a spectral resolution of 2 cm -1 .The lasers emit linearly polarized light.Since the SiO2 substrate restricts transmission, all measurements were carried out in reflection mode.To regulate the sample's temperature during experiments, a homemade sample holder was used.This holder consists of a thermally insulated copper contact surface, a temperature sensor, and four heating resistors.Temperature adjustments were controlled by a feedback loop to ensure stability.

SUPPORTING NOTES Supporting Note 1: Effective Medium Approximation
To model the inhomogeneous nature of the intermediate state of VO2 in our metasurfaces, we utilize the effective medium approximation which is widely adopted in literature 1,2,3 .It calculates the average permittivity of the composite material consisting of domains of VO2 in its hot and cold phases and treats it as a homogeneous medium.This approximation is justified due to the highly subwavelength size of the domains in different phases within the polycrystalline film.The effective permittivity  #$$ of the VO2 layer can be expressed as a weighted sum of the permittivities of its individual constituents, given by As the VO2 undergoes the phase transition, the volume fraction , defined as  = where  represents the scattering matrix given by By using equation ( 1) under steady state conditions, we are now able to calculate the reflectance  and the transmittance  via their relation to  /#$,#+*#-and  */02561**#-: denotes the coupling coefficient between the resonant mode and the external ports.We used this theoretical framework to fit our experimental reflectance spectra to extract parameters like  /0- and  12* .For fitting purposes we normalized  12 to 1. Table S1: Literature comparison on VO2 metasurfaces.Comparative overview of VO2 metasurfaces based on resonance type, operational spectral range, experimental Q-factor, and absolute switching contrast.The experimental Q-factor and absolute switching contrast were extracted from published plots, therefore, small deviations between the stated and actual values may be present.

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in the effective permittivity  #$$ , see FigureS4.By integrating this effective medium approximation-based permittivity into our models, we could simulate the metasurfaces behaviour in intermediate states more accurately.Supporting Note 2: TCMT ModelTCMT provides a straightforward method of modelling resonant structures.Fan  et al. presents a general description 4 , which we adapt for our single resonance system, coupled to two ports corresponding to reflectance and transmittance.The temporal dynamics of the resonance amplitude  can be written as d d = 6−  /0-+  12* 2 +  3 ;  + < /0- 12 (1) with  3 as the resonance frequency of the BIC. 12 represents the time dependent input field.Next, we define the relationship between the scattered field  )4* with the resonance mode and the incoming field by  )4* = >  /#$,#+*#-  */02561**#- ?=  >   12 ?
Figure S1: VO2 ellipsometry.Ellipsometry data between 4 and 8 μm for the used 30 nm VO2 film measured at 25°C for the cold phase and at 80°C for the hot phase.Blue solid (red dashed) lines represent thereal (imaginary) part  8 ( 7 ) of the VO2 dielectric function.

Figure S3 :
Figure S3: Numerical reflectance spectra for continuous VO2 films.The same structural parameters were used as in Figure 2 with α=20°, but with a continuous VO2 layer just below the resonators and above the substrate, without a VO2 layer on top of the resonators and no SiO2 capping layer.In (a), the VO2 layer thickness is 5 nm, in (b) 10 nm, and in (c) 30 nm.The switching performance, visible from the shown reflectance spectra in the cold and hot phases, is high for all

Figure S5 :
Figure S5: Numerical reflectance spectra in the near-IR.The geometry depicted in Figure 2 was uniformly scaled down by multiplying all geometrical parameters by a factor of 0.23, while maintaining a VO2 layer thickness of 20 nm and an ellipse tilt angle of 20°.The permittivities used were  8 = 9.24 and  7 = 2.47 in the cold phase, and  8 = −2.60 and  7 = 10.45 in the hot phase.These permittivity values were determined via ellipsometry.

Figure S6 :
Figure S6: Effective Permittivity.Effective permittivity of VO2 for different volume fractions , using  and  values at a wavelength of 6.5 µm.