1. Introduction

Reconfigurable modulation of optical transmission intensity is one of the fundamental key technologies in building optical information processing systems for various display, imaging, and communication applications [1,2]. Owing to large demand on miniaturization and integration of such transmission modulator, various physical principles and devices have been demonstrated for the decades in the field of nanophotonics using reconfigurable optical materials [3–26].

For instance, graphene [3–5] and indium tin oxide (ITO) [6], electrically tunable materials, have been thoroughly studied for modulation of free space transmission in the near-infrared (NIR) and infrared (IR) regime. However, transmission modulators with graphene or ITO have significant limitation in common, ultrathin thickness of active region. Graphene shows excellent tunability of dielectric function in the infrared. For large modulation depth with large interaction with light, however, field-concentrating resonances in metasurfaces should be exploited around atomically thin spaces [3–5]. Similarly, ITO shows few nanometer-sized ultrathin active regions with tunable dielectric function owing to electron depletion in field-effect based capacitive scheme. Thus, ITO-based field-effect modulators also need nanophotonic resonances in metasurfaces with large electromagnetic field enhancement [6]. It implies that achieving large modulation depth with broad operation bandwidth is limited inevitably when we use graphene or ITO for such transmission modulator. Due to this difficulty, less attention has been paid on it compared to reflective modulator schemes exploiting strong plasmonic resonances near the ultrathin active regions [7,8].

On the other hand, phase-transition materials (PTMs) such as VO₂ [11–19], Ge₂Sb₂Te₅ (GST) [20–25], and SmNiO₃ [26] are advantageous in terms of larger change of dielectric function via application of external thermal, electrical, or optical stimuli. In the NIR and IR regime, such PTMs prevail ITO and graphene in terms of tunability of dielectric functions via applied external stimuli. However, despite these advantages of PTMs, efficient, high-contrast, and broadband non-resonant modulation of optical transmissivity using nanophotonic modulator has not been achieved even with PTMs. Since PTMs are highly absorptive in the NIR and IR, subwavelength-spaced resonant metasurface strategies inevitably deteriorate efficiency of transmission unless the thickness of PTM gets extremely thin so that modulation depth of transmission is limited [14,16–19,21–25].

Here, we propose and experimentally verify a novel, reconfigurable ultracompact transmission modulator working over the broad NIR wavelength region with high efficiency and large modulation depth. Rather than conventional resonant metasurface approach, we use tunable optical diffraction with high diffraction angle depending on the temperature and the corresponding phase of VO₂ over a broad bandwidth. As a reconfigurable optical material, we introduce a volatile PTM, VO₂. Utilizing the continuous dielectric-to-plasmonic transition (DPT) effect of VO₂, at first, we design VO₂ ridge waveguide (VRW) structure for efficient and tunable waveguiding effect for transverse electric (TE) polarization. As the proposed VRW shows largely tunable radiation pattern over broad bandwidth, forward transmission is largely modulated. Our key idea is broadband and nearly destructive interference between waveguided light and detour light in the insulating phase. On the other hand, light-VO₂ interaction is suppressed in the metallic phase for TE-polarized normal illumination. As a result, incident light is highly deflected with large deflection angle in the insulating phase, while normally incident light mainly passes through the VRWs in the metallic phase. Then, we numerically investigate periodically arranged VRWs, phase-transition diffraction grating, for modulation of the 0th order forward transmission while other oblique diffraction waves with large diffraction angle are considered useless and excluded. After numerical investigation, experimental verification and conclusion would be suggested sequentially. Throughout the paper, we used the commercial finite element method tool (COMSOL Multiphysics 5.3, RF module) for numerical simulation and optical properties of Al₂O₃ [27] and Cr [28] from the literature.

2. Results and discussions

2.1 Characterization of a thick VO₂ film and design of the VRW grating modulator

For the fabrication of thick VO₂ film, we exploited the conventional pulsed laser deposition (PLD) system (LAMBDA PHYSIK, COMPEX 205) with a KrF excimer laser at 248 nm [29]. Figure 1(a) presents non-contact type atomic force micrograph showing rough surface of an approximately 340 nm-thick VO₂ film fabricated by PLD method. The root mean square surface roughness is about 9.8 nm. Then, we verified the insulator-to-metal transition (IMT) of VO₂ by measurement of electrical resistance depending on temperature using a source meter, a hot plate, and a thermocouple. As shown in Fig. 1(b), the conventional electrical characteristic of the IMT is clearly verified.

 

Fig. 1 (a) Three-dimensional atomic force micrograph of a VO₂ surface. The size of scanned area is 2 μm by 2 μm. (b) Measured temperature-dependent resistance of a VO₂ film with hysteric insulator-to-metal phase transition. (c) Dielectric function spectra both at the insulating and metallic phases in the near-infrared range.

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Then, the dielectric function spectra are investigated from an approximately 260 nm-thick VO₂ film at the insulating (at the room temperature) and metallic (at the 383 K) phases, respectively, using spectroscopic ellipsometer (J. A. Woollam, V-VASE) with thermocouple and heater. For raw data analysis, a VO₂ sample is modelled as a triple layer structure consisting of a half-infinite sapphire substrate, a 248 nm-thick homogeneous VO₂ layer, and a Bruggeman effective medium layer where volume fractions of air and VO₂ are set to be same as 0.5 and depolarization factor is set to be 1/3 [30]. The modeling is conducted via simultaneously fitting refractive index, extinction coefficient, and thickness of homogeneous VO₂ layer under the spectral constraint of the Kramers-Kronig relation. During fitting process, thickness of the top effective medium layer is set to be 14 nm considering film roughness. Figure 1(c) presents clearly different complex dielectric functions according to the phase of VO₂ in the NIR. Particularly, real part of VO₂ dielectric function shows the well-known change from positive to negative value in the wavelength region from 1000 nm to 1650 nm [31]. It implies that in the region, VO₂ shows optical DPT via the thermally-driven IMT. Thus, if TE-polarized light is incident, light can be guided and well-confined inside the insulating VRW structure. On the other hand, in the metallic phase, light cannot penetrate into the VRW structure, thus interaction between light and VO₂ is highly suppressed. In addition, one more noteworthy point is that the dielectric function in the insulating phase is nearly non-dispersive compared to that in the metallic phase.

High index contrast enables subwavelength light guiding in the insulating VRW. As shown in Fig. 2(a), the dispersion relations are numerically calculated for understanding TE-polarized light-VRW interaction. The dispersion graph and inset field profile of Fig. 2(a) imply that the fundamental TE eigenmode guided in the 300 nm-wide insulating VRW has much larger effective index and gradient of a dispersion curve, compared to those of the TE mode guided in the 100 nm-wide VRW.

 

Fig. 2 (a) Dispersion relations of plane wave in the homogeneous air, the homogeneous insulating VO₂, the homogeneous metallic VO₂, the fundamental TE mode in the 100 nm-wide insulating VRW, and the fundamental TE mode in the 300 nm-wide insulating VRW. The right inset image depicts normalized E_Z field profile of transverse electric mode guided in the 300 nm-wide insulating VRW at the wavelength of 1400 nm. (b) Schematic image illustrating a VRW and two different types of waves around it (guided light wave and detour light wave) that interfere with each other after transmission process. (c) VRW thickness (t) conditions of destructive interference between detour light and guided light in the insulating VRW over the broad NIR range. The legends denote corresponding width of the insulating VRW. The dashed line denotes t value of 340 nm.

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Here, we can consider the two types of light waves, a detour light wave and a guided light wave, when TE light is normally incident on the insulating VRW structure as depicted in Fig. 2(b). While guided light in the 300 nm-wide insulating VRW has the large effective mode index [Fig. 2(a)], detour light can be considered approximately as plane wave propagating in the air with effective mode index of 1. Thus, inspired by the papers written by M. Khorasaninejad et al. about the designed nanoscale interference around subwavelength dielectric ridge waveguides [32–34], we calculated approximate destructive interference condition for forward diffraction direction which originates from the effective mode index difference between light that is guided in the insulating VRW and radiated at the end of VRW and detour light. Equation (1) exhibits the approximate analytical phase matching condition of VRW thickness for forward destructive interference (FDI) [32].

In Eq. (1), λ and n_eff indicate the wavelength and effective mode index of the guided fundamental TE eigenmode, respectively. Figure 2(c) presents calculated wavelength-dependent thickness condition of FDI according to Eq. (1) for several widths of VRW. The interesting thing shown in Fig. 2(c) is that the abovementioned FDI condition does not vary much over the broad NIR wavelength range for the wide VRWs (width of 300-500 nm). As marked as the black dashed line in Fig. 2(c), if the t of insulating 300 nm-wide VRW is set to be 340 nm, FDI condition is approximately met for broad wavelength range around the wavelength of 1400 nm. It means that broadband suppression of forward diffraction with nearly destructive interference is achieved around the wavelength of 1400 nm if the amplitude of detour light and that of light radiated from the end of the insulating VRW are balanced. Moreover, it has been shown that large angle (above 30°) beam diffraction is achieved when the FDI condition is met in the previous studies involving DRWs by Khorasaninejad et al. [32–34]. Thus, we can expect such a large angle diffraction around the wavelength of 1400 nm with amplitude balancing optimization.

However, ahead of the isolated VRW unit cell design, we should design diffraction grating period (the total x-directional width of the unit cell) large enough to bend the first diffraction order with the angle around 30 °, the width of the VRW unit cell. Thus, grating period is set to be 2.2 μm so that the diffraction angle (sin⁻¹(λ/p)) in the wavelength region of interest (1000-1650 nm) ranges from 27 ° (at 1000 nm) to 49 ° (at 1650 nm).

Due to the large grating period, however, it is hard to balance the amounts of detour light and guided light using a single 300 nm-wide VRW since most amount of incident light becomes detour light [32]. Hence, we located two identical 300 nm-wide VRWs with separation distance (d) of 450 nm for the optimization of the balancing as described in Fig. 3(a). Figure 3(b) depicts the guided fundamental TE eigenmode in the dual VRW whose w and d values are 300 nm and 450 nm, respectively. It is graphically shown that negligible coupling occurs between the two distinct VRWs owing to subwavelength confinement. The 10 nm-thick Cr is located on the VRWs considering more accurate fabrication with ion beam milling process. In the simulation configuration, the two 10 nm-thick perfect electric conductor (PEC) plates are located to set the incident beam size to be 2.2 μm while plane wave with TE polarization is incident from the substrate side. The PEC plates filter the incident light far from VRW structures so that the diffraction mechanism of the isolated unit cell is accurately analyzed in terms of the detour and waveguiding channels.

 

Fig. 3 (a) Schematic illustration of the isolated dual VRW unitcell for TE-polarized normal illumination. w, t, d, and p are 300 nm, 340 nm, 450 nm, and 2200 nm, respectively. (b) Spatial E_z field distribution of the numerically solved fundamental TE eigenmode of the dual VRW described in part (a) whose w and d values are 300 nm and 450 nm, respectively. The guided eigenmode is calculated at the wavelength of 1400 nm. Transmissivity plot of the dual VRW unitcell described according to radiation angle and wavelength at (c) the insulating and (d) metallic phases, respectively. The white and white dashed lines in (c) and (d) denote theoretical constructive and destructive diffraction conditions of the grating with period of 2.2 μm, respectively. Normalized transmitted electric field intensity distributions at (e) the insulating and (f) metallic phases, respectively. The wavelength is set to be 1500 nm in common.

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Highly tunable performance of diffraction directivity with the dual VRW unit cell is investigated for TE illumination from the Al₂O₃ substrate side [Figs. 3(c-f)]. Figure 3(c) shows that the forward transmission is suppressed for broad bandwidth at the insulating phase. In particular, FDI occurs clearly at the wavelength region of 1400-1650 nm while moderate suppression of forward transmission occurs at the wavelength region of 1100-1400 nm. On the other hand, at the metallic phase, owing to the DPT phenomenon, interaction between TE-polarized light and the dual VRW decreases dramatically over broad bandwidth. Hence, most of light transmission is heading forward at the metallic phase [Fig. 3(d)]. Figures 3(e) and 3(f) exhibit graphical verification of such high contrast change of forward transmitted diffraction via the DPT.

The theoretical 1st order destructive (psinθ = λ/2) and constructive (psinθ = λ) conditions of diffraction grating whose period is p are marked as the white and white dashed lines in Figs. 3(c) and 3(d), respectively. The interesting point revealed here is that theoretical destructive and constructive diffraction conditions of the dual VRW unit cell nearly correspond to the diffraction theory of the grating with the period of p regardless of the VO₂ phase. In other words, if the unit cell is periodically arranged as a diffractive grating with the period of p, the −1st and 1st diffraction orders of the grating would be deflected with the angle nearly similar to the angles of the oblique diffraction by the dual VRW unit cell. Such interesting phenomenon occurs via combination of light guiding into VRWs and diffraction of detour light [See appendix 4.1.].

The dual VRW grating described in inset image of Fig. 4(a) is composed by periodic arrangement of the optimized dual VRW unit cells, each of which consists of 2.2 μm-wide aperture and the dual VRW. As mentioned above, the grating period is equal to the unit cell width defined by the PEC aperture size (2.2 μm). Since the unit cell is designed to suppress forward transmission not in the metallic phase but in the insulating phase, transmissivity of the grating in the metallic phase is shown to be much higher over the broad bandwidth (1100-1650 nm) in non-resonant manner [Figs. 4(a) and 4(b)]. In particular, the 0th order transmission is highly tuned by phase transition rather than other diffraction orders of transmission as expected from the unit cell design. In case of reflections suggested in Figs. 4(c) and 4(d), their intensities are weaker than transmissions in the both phases of VO₂ over the broad bandwidth since the device is designed as a transmission type with relatively large grating period and small VRW size. The absorption loss would be larger in the insulating phase compared to the metallic phase as light guiding into the VRW structure is activated in the insulating phase [See Appendix 4.2.].

 

Fig. 4 Numerically calculated transmissivity spectra of the diffraction grating modulator in the (a) insulating and (b) metallic phases. The inset picture in (a) describes the scheme of the dual VRW based diffraction grating (period = 2.2 μm). Numerically calculated reflectivity spectra of the diffraction grating modulator in the (c) insulating and (d) metallic phases, respectively. The legends in (a)-(d) describe the corresponding diffraction orders. (e) Simulation results of the 0th order transmissivity depending on the filling factor (f) of the metallic VO₂ during continuous phase transition. The legends denote corresponding f of the metallic VO₂. Here, f = 0 and f = 1 imply the insulating and metallic phases, respectively. The intermediate f values between them correspond to the intermediate temperatures of the mixed phases where the two distinct phases coexist. (f) Numerically calculated modulation depth spectrum.

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In short wavelength region of 1000-1100 nm, the three sharp transmission dips and reflection peaks are observed in the both phases of VO₂ and every diffraction orders [See Figs. 4(a)-4(d) and Appendix 4.2.]. As our purpose is non-resonant broadband modulation via FDI condition matching, the region of 1000-1100 nm is excluded from the operation bandwidth.

The reconfigurable VRW grating modulator can continuously modulate transmission signal according to continuous change of the sample temperature. For numerical estimation of the continuous modulation capability in the intermediate VO₂ phases where the insulating and metallic phases coexist [35,36], we also investigate the 0th order transmissivity at the intermediate phases according to filling factor (f) of the metallic phase by help of Maxwell-Garnett effective medium theory (EMT) [37]. When f varies from 0 to 0.4, host material is set to be the insulating VO₂ (${\epsilon }_{eff}(f)={\epsilon }_i[{\epsilon }_m(1+2f)+{\epsilon }_i(2-2f)]/[{\epsilon }_m(1-f)+{\epsilon }_i(2+f)]$). On the other hand, when f varies from 0.6 to 1, host material is set to be the metallic VO₂ (${\epsilon }_{eff}(f)={\epsilon }_m[{\epsilon }_m(2f)+{\epsilon }_i(3-2f)]/[{\epsilon }_m(3-f)+{\epsilon }_{i}f]$). By using such f-dependent dielectric functions of intermediate phases, the continuously modulated 0th order transmissivity is numerically verified and presented in Fig. 4(e). Furthermore, for quantitative analysis of the modulation performance, the modulation depth is also numerically investigated in Fig. 4(f). Here, modulation depth of transmissivity, η_m, is defined as ${\eta }_m=\left|T_i-T_m\right|/\max (T_i,T_m)$ where T_i and T_m denote the 0th order transmissivities in the insulating and metallic phases, respectively. η_m between about 0.35 and 1 is achieved over the broad bandwidth about 550 nm (from 1100 to1650 nm) [Fig. 4(f)].

2.2 Experimental demonstration of VRW grating for the 0th order forward transmission modulation

For experimental verification, the VRW grating transmission modulator sample is fabricated through the three processes. At first, a 340 nm-thick VO₂ film is deposited via conventional PLD method as described in the section 2.1. Then, 10 nm-thick Cr protection hard mask is deposited via e-beam evaporation (Korea Vacuum Tech, KVE-3004) on a VO₂ film. The thin Cr hard mask plays a role to reduce tapering effect of ion beam milling and reduce stoichiometric effect of Ga⁺ ion on VO₂ [38]. At last, 110 μm by 110 μm sample is defined by multiple processes of focused ion beam milling (FIB) with translational movements (FEI, Quanta 200 3D). Figure 5 shows the scanning electron micrographs of the fabricated VRW grating modulator. The inset image of Fig. 5(b) shows that the VRW structure is well defined with moderate tapering effect.

 

Fig. 5 Scanning electron micrographs of the fabricated VRW grating of (a) oblique and (b) top views. The inset image of (b) shows cross-sectional view of the FIB cut VRW grating with local Pt layer coated on it.

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The 0th order transmission spectrum is measured with a custom-built free space near-infrared spectroscopy setup described in Fig. 6(a). The super-continuum light source (NKT Photonics, Super EXTREME EXR 15) is tightly focused with objective lens on the sample as a broadband source. Then, only forward transmission signal is collected by objective lens whose numerical aperture (NA) is 0.45. As the minimum first-order diffraction angle is about 27° and the corresponding necessary NA is about 0.5 at the wavelength of 1000 nm, filtering of the oblique diffraction waves is achieved over the broad measurement bandwidth (1000-1650 nm). The signal is collected by an optical fiber and decomposed by optical spectrum analyzer (YOKOGAWA, AQ6370D). Figures 6(b) and 6(c) correspond to measured transmission spectra while heating and cooling processes. The gradual modulation of the 0th order forward transmission is obviously shown in Figs. 6(b) and 6(c).

 

Fig. 6 (a) Custom-built temperature-controlled micro-spectroscopy setup scheme for the 0th order transmission measurement. The measured 0th order transmissivity spectra in (b) heating and (c) cooling processes, respectively. (d) Linear curve fitting analysis of the measured 0th order transmissivity. The legends describe measured data and fitted linear line at the insulating and metallic phases. (e) Measured modulation depth and linearly fitted line.

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The large noise of measured transmission spectra is due to bandwidth restrictions of the optic components (1000-1600 nm) and optical spectrum analyzer (800-1700 nm) and significant power reduction by input beam filtering parts with an iris, a beam expander, and a ND filter [Fig. 6(a)]. Consequently, power spectrum of input source is significantly lowered specifically in the long wavelength region near 1400-1650 nm. Thus, linear curve fitting is conducted for analyzing linear trends of the measured spectra at the insulating and metallic phases and modulation depth [Figs. 6(d) and 6(e)]. By the fitting procedures, it is more clearly verified that the fabricated sample shows similar and excellent reconfigurable modulation trends compared to the numerical designs in Fig. 4(e). The effects of Cr mask thickness and VO₂ surface roughness on the proposed device performance were proved to be negligible by additional numerical studies [See Appendix 4.3]. However, deep sharp cracks and large surface roughness [Fig. 1(a)] produced inherently in PLD process hinder stable and accurately reproducible performances of the proposed grating modulator. Such cracks are formed via PLD process inhomogeneously in a wafer scale. Thus, it is necessary to select film region with relatively good surface quality formed at the center of a substrate wafer. Such unstable film quality is harmful for large throughput of the device. This problem can be improved by atomic layer deposition of VO₂ with high surface quality and similarly tunable dielectric functions [31]. Moreover, restricted throughput and area of the device can be largely improved by changing nano-patterning technology. Electron beam lithography with chemical etching can be used for high-quality, large-area, and high-throughput fabrication instead of sequential FIB millings [13]. Additionally, if one uses silicon dioxide with lower index rather than sapphire substrate [31], it would be more efficient to relieve high field confinement on the surface and absorptive loss at the metallic phase with increased transmission efficiency.

For thorough complex evaluation of the demonstrated device, the comparative and quantitative study is performed as shown in Table 1. The three different experimental studies of optical transmission modulation based on ITO, graphene, and SmNiO₃ are investigated in terms of design principle, reconfigurable material ingredient, off-state spectral broadness, maximum modulation depth, maximum on-state transmissivity, and operation wavelength regime based on measurement data of them [5,6,26]. It is noteworthy that our experimental work shows the broadest spectrum characteristic with the highest Δλ/λ around the off-state transmission dip, moderate transmissivity, and the second-high maximum modulation depth, simultaneously. Moreover, in case of Δλ/λ, it could be nearly doubled if the device performance is characterized additionally in the wavelength region over 1650 nm. Overall comparison of transmission modulation performance suggested in Table 1 implies that SmNiO₃ based work by Li et al. [26] seems to be the best competing scheme. However, when we consider potential possibility of electrically driven all-solid-state modulation speed, our work would be more advantageous than the work based on SmNiO₃ which requires ms-scale time consumption for nm-scale transport of Li⁺ ions [26,39], while nano-structured VO₂ can be electro-thermally tuned even in the few nanoseconds [40].

Table 1. Comparison of transmissivity modulation mechanism and performance with the recent representative studies

View Table

3. Conclusion

In this paper, a novel reconfigurable nanophotonic solution for ultracompact high performance modulation of optical transmission is designed and experimentally verified. The proposed phase-transition VRW grating acts as a transmission modulator based on waveguiding of TE-polarized light, optical DPT phenomenon of VO₂, and diffraction grating strategy. The operation bandwidth about 550 nm (wavelength region of 1100-1650 nm) is verified with nearly non-resonant on-state transmissivity around 0.3 and minimum modulation depth about 0.35. The fast electrical modulation and pixel-by-pixel phase transition would be also possible when the metallic thin film micro-heater is integrated to the device [12,40,41]. Furthermore, the proposed idea is also applicable to other PTMs such as GST which exhibits similar DPT effect in the UV spectral range [21] and SmNiO₃ which shows simultaneously large tunability of refractive index and extinction coefficient [26]. We expect that the proposed device and idea would be fruitful for switchable optical router, optical phase modulator, polarization modulator, and development of novel spatial light modulators with small pixel pitch in the NIR and IR regime.

4 Appendix

4.1 Theoretical analysis of diffraction pattern formation through the isolated dual VRW unit cell

The similarity between the diffraction directivity of the unit cell and that of the periodically arranged grating can be explained by investigation of the two different light-VO₂ interaction channels. When TE polarized light illuminates the dual VRW structure, light is transmitted by detour or waveguiding as described in the section 2.1. Thus, diffraction pattern is generated by the detoured aperture diffraction effect and re-radiation of horizontal magnetic dipolar radiation at the end facets of VRWs. The schematic image of Fig. 7(a) describes effect of the two in-phase magnetic dipoles excited at the end facets of two VRWs. The right polar plot of Fig. 7(a) shows that nearly forward diffraction occurs dominantly for broad bandwidth. It means that re-radiated light from the VRWs does not contribute to oblique sidelobes. On the other hand, transmitted light which detours the dual VRW and 2.2 um-wide aperture is diffracted mainly into the three directions in the wavelength range of 1000-1650 nm. Figure 7(b) shows the analytically derived Fraunhofer intensity patterns for the single (I = I₀(sinΨ/Ψ)²) and double (I = 4I₀{cos(0.875Ψ)sin(0.125Ψ)/Ψ}²) apertures (Ψ = kpsinθ/2). Here, k and θ stand for free space wavenumber and diffraction angle measured from y direction, respectively. The single aperture diffraction pattern deviates from the diffraction orders of grating largely since the 1st minimum of single aperture correspond to the 1st diffraction order of grating [The blue curve in Fig. 7(b)]. However, the double aperture scheme which considers VRW detour effect shows a more reasonable diffraction pattern accountable for the dual VRW radiation pattern. The double aperture scheme is constructed by adding a PEC plate at the center of the single aperture scheme by considering effective scattering cross-section of the dual VRW structure. The width of additional PEC plate at the center of the aperture is approximately set to be 1650 nm by investigating Poynting vector flow around the dual VRW unitcell. As a result, the position of 1st minimum and 1st maximum approach toward kpsinθ/2 is about π/2 and π, respectively. It implies that the proposed double aperture Fraunhofer diffraction modeling is clearly accountable for the VRW detour effect and aperture diffraction sidelobes simultaneously.

 

Fig. 7 (a) Scheme of the dual VRW unit cell excited by the two horizontal magnetic dipoles right above the end facets of two VRW structures (left Figure). The right Figure of angular power spectrum shows nearly forward scattering of the unit cell induced by the corresponding excitation. (b) Theoretical calculation results of the single and double aperture Fraunhofer diffraction intensities with the similarly located minima and maxima. The inset images denote the two Fraunhofer diffraction configurations. The double aperture is constructed by symmetrically blocking the central part of the single aperture by 3p/4 (1.65 μm) wide perfect electric conductor plates between them described in Fig. 3(a). The whole width of single and double apertures is same with the unit cell width, p (2.2 μm).

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4.2 Power flow and dissipation around the VRW diffraction grating

Change of power dissipation and flow is investigated for in-depth physical analysis of the transmission modulator. Absorptivity spectra in Fig. 8(a) shows that absorptivity is enlarged in the insulating phase compared to the metallic phase over the broad NIR bandwidth. It is owing to enhancement of waveguiding and decreased detour effect as shown in Fig. 8(b). At the wavelength of 1600 nm where FDI condition is accurately achieved, field confinement is enhanced and suppressed in the insulating and metallic phases, respectively. Fig. 8(b) describes such phenomena with the change of Poynting vector flow marked as white stream lines. In the insulating phase, considerable amount of stream line is inhaled by the VRWs. On the other hand, in the metallic phase, most of power stream detours them.

 

Fig. 8 (a) Broadband absorptivity spectra of the VRW grating modulator from simulations. (b) Spatial distributions of electric field intensity and stream line of Poynting vector near the grating structure at the insulating (right) and metallic (left) phases, respectively. The wavelength is 1600 nm in common.

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The three sharp resonances at the both phases in the short wavelength region of 1000-1100 nm are leaky mode resonances [Figs. 4 and 8(a)]. These resonances facilitate absorption by resonantly localizing leaky waves between the VRW structures rather than in them [Fig. 9]. Thus, leaky wave interaction with the VRW structure is enhanced at the both phases of VO₂. As electric field is mainly confined between the VRW structures, not the locations of resonance wavelengths but the resonance strengths are affected by phase transition of VO₂.

 

Fig. 9 Spatial distributions of electric field intensity near the grating structure at the three leaky mode resonances at the (a)-(c) insulating and (d)-(f) metallic phases. The resonance wavelength is (a) and (d) 1044 nm, (b) and (e) 1075 nm, (c) and (f) 1094 nm.

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4.3 Effect of thin Cr mask and variation of VRW thickness on transmitted diffraction

Figures 10(a) and 10(b) imply negligible effect of ultrathin thickness of Cr mask on transmission regardless of phase transition. Moreover, Figs. 10(c and d) imply that effects of surface roughness would not deteriorate transmission significantly as transmissivity is not much dependent on the thickness of VRWs.

 

Fig. 10 The 0th order forward transmissivity spectra of the VRW grating modulator for various Cr mask thicknesses at the (a) insulating and (b) metallic phases, respectively. The effect of VRW thickness on the 0th order forward transmissivity spectra of the VRW grating modulator at the (c) insulating and (d) metallic phases, respectively. The legends in (a) and (b) denote the thickness of Cr mask, while the legends in (c) and (d) denote the thickness of VRWs of the VRW grating modulator. The spectra in (a)-(d) are numerically calculated.

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Funding

Center for Advanced Meta-Materials (CAMM) funded by the Ministry of Science and ICT as Global Frontier Project (CAMM-2014M3A6B3063710). National Research Foundation (NRF-21A20131612805).

Acknowledgments

The authors thank Ms. Soyeun Kim and Prof. Taewon Noh for the the help of the VO₂ ellipsometry measurement with data analysis. We also thank Mr. Changhyun Kim and Mr. Junhyeok Jang for the help of experiment. Parts of this study have been performed using facilities at IBS Center for Correlated Electron Systems, Seoul National University and Electronics and Telecommunications Research Institute.

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