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Abstract
We propose to achieve switchable polarization manipulation at the telecom wavelength at nanoscale based on L-shaped plasmonic nanoholes in an Au-VO2 film. The L-shaped nanohole acts as a quarter-wave plate or a half-wave plate owing to the phase differences between different plasmon resonant modes, which is controlled by the insulator or metallic phases of VO2. In addition, by changing the structure and removing the bottom Au layer, a switchable full-/quarter-wave plate can be achieved when VO2 transits from the insulating state to the metallic state. Furthermore, we vary the geometrical parameters of the L-shaped hole to tune its resonant spectra and achieve a switchable full-wave plate/polarizer. The multifunctional switchable polarization manipulation abilities together with large bandwidths enable the proposed structures promising applications in nanophotonics and integrated optics.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarization state is an essential characteristic of a light field. Polarization manipulation is a key issue in many areas and applications, such as biosensing, spectroscopy, optical communication, and information processing. Traditional polarization manipulation is mainly based on the optical anisotropy of crystals [1]. The large geometrical size of the crystals prevents their applications in nanophotonics and integrated optics. In the past decades, metallic materials based on surface plasmon polaritons (SPPs) have been proposed to achieve polarization manipulation on nanoscale [2–9], which is crucial for the applications of SPP devices in nanophotonics and integrated optics [10,11]. However, most of these plasmonic structures composed of metal and dielectrics are designed for a fixed function because of their static optical properties and their polarization manipulation function cannot be dynamically tuned.
Recently, active materials such as germanium-antimony-tellurium (GST) [12–15], vanadium dioxide (VO2) [16–22], indium tin oxide (ITO) [23], graphene [24,25], and liquid crystals [26] have been employed to tune the optical properties of the metamaterials and metasurfaces dynamically. The phase change material VO2 has drawn much interest because it shows an insulator-to-metal transition around room temperature (∼67°), which benefits its practical applications. Compared with GST, VO2 has the advantages of a lower phase change temperature, an easier fabrication process and a lower cost. Earl et al. proposed a metasurface comprised of an array of silver nanorods and a layer of VO2 film to achieve polarization rotation for the reflection at visible wavelengths [16]. Jia et al. proposed a composite plasmonic structure containing VO2 to dynamically tune the polarization state of the reflected light [20]. Switchable perfect absorption and polarization conversion have been achieved using metasurfaces containing VO2 at telecom [27] and terahertz frequencies [28,29]. Hybrid metal-VO2 metamaterials were recently proposed to achieve switchable terahertz half-/quarter-wave plate at terahertz frequencies [30–32]. Li et al. proposed a rectangle antenna based metasurface composed of phase change material Ge2Sb2Te5 to achieve a switchable quarter-/half-wave plate in the mid-infrared frequencies [15]. Most of these structures are based on multilayer nanoparticles and films, and nanoholes in hybrid metal-VO2 film have not yet been investigated much in the active polarization manipulation area. The resonances of the nanoholes in the hybrid metal-VO2 film depend on the coupling between the electric field oscillations in the two surfaces of the nanohole [33,34] and can be tuned conveniently by changing the thickness of the metal films, enabling potential multifunctional switchable polarization manipulation. Besides, plasmonic nanoholes located in the metallic films can convert the incident light into propagating surface plasmon polaritons (SPPs) and be used in the SPP polarization manipulation. Devices based on nanoholes are compact and easy-integrated in the two-dimensional surface of the metal films, which benefits their applications in nano-optics and integrated optics.
In this work, switchable quarter-/half-wave plates at telecom wavelengths are proposed using an L-shaped nanohole in hybrid Au-VO2 films. Multiple plasmon resonances can be excited in the L-shaped hole and the phase differences between different resonant modes can be tuned with the phase transition of VO2, which enables switchable polarization manipulation. For VO2 in insulating phase, the nanohole acts as a quarter-wave plate with a phase difference of nearly 90° between the symmetric axis of the hole and its orthogonal direction while for VO2 in metallic phase, the nanohole acts as a half-wave plate and the polarization conversion ratio reaches 1.0. Besides, we change the structure and the geometrical parameters of the hybrid Au-VO2 nanoholes which are related to the plasmon resonances, and achieve full-/quarter- wave plate and full-wave plate/linear polarizer switchable functions. The proposed structure has strong abilities in active polarization manipulation and potential applications in many areas, such as near-field polarization manipulation, SPP excitation, focusing and hologram. The compact size and aperture structure are especially suitable for in-plane optical field manipulation.
2. Design and simulation method
To achieve a plasmonic waveplate, the proposed structure should provide electric field oscillations in two orthogonal directions with equal amplitudes and a phase difference (90° for quarter-wave plates and 180° for half-wave plates). L-shaped nanoholes in metallic films have been demonstrated to support plasmon resonant modes both in the directions parallel and perpendicular to the symmetric axis of the structures [33,35]. In this work we design L-shaped nanoholes in Au-VO2-Au films. The phase differences between the two orthogonal resonant modes is dynamically controlled using the phase transition of VO2 from insulating state to metallic state. Thus, a switchable waveplate can be achieved.
A schematic of the proposed hybrid Au-VO2 structure is shown in Fig. 1(a). The structure which is fabricated on a silica substrate is composed of two Au layers and a VO2 layer. The thicknesses of the three layers are labeled as t1, t2 and t3. An L-shaped nanohole is fabricated in the films, of which two arms are oriented in x and y axes and have the same lengths and widths, which are labeled as L and w, respectively. The original point O is at the outer corner point of the L-shaped hole at the Au-air interface. The near-field resonances and the far-field radiation properties of the nanohole are investigated using a finite difference time domain (FDTD) method. A linearly polarized plane wave with an electric field amplitude of 1 V/m is incident from the bottom of the silica substrate along + z axis. The angle between the polarization direction of the incident field and the + x axis is labeled as θ [see Fig. 1(b)]. The meshing cell size is 2 nm. The perfectly matched layer (PML) adsorbing boundary conditions are applied in the simulation. The dielectric constants of gold and VO2 are set according to the data in Refs. [36] and [37,38], respectively. More simulation details are provided in the Appendix. The geometrical parameters of the L-shaped nanohole in the calculation are L = 500 nm, w = 76 nm, t1 = 50 nm, t2 = 430 nm, and t3 = 100 nm.
Fig. 1. (a) Schematic of the L-shaped hybrid Au-VO2 nanohole for a switchable quarter-/half-wave plate. (b) top view of the structure.
3. Results and discussion
First, we investigate the resonance of the L-shaped nanohole at room temperature (T=27°C) when VO2 is in insulating state. A plane field monitor with a distance of 80 nm above the top surface of the hole is used to project the near-field electric fields to the far field and electric fields on a hemispherical surface with a radius of 1 m can be obtained. The transmitted electric field intensity |E|2 at the point F (0, 0, 1 m) in the far field is calculated with the change of incident wavelength and the results are shown in Fig. 2(a). When the incident polarization is along the symmetric axis of the structure, i.e., θ = 45°, there is a resonant peak at 1116 nm. When the incident polarization is perpendicular to the symmetric axis of the structure, i.e., θ = 135°, the resonant peak appears at 1086 nm. To investigate the optical performance of the nanohole at the telecom wavelength 1550 nm, we calculate the near-field electric field distributions both on the top surface of the nanohole, i.e., Au-air interface, and the bottom surface of the nanohole, i.e., Au-silica interface. The results are shown in the top panel in Fig. 2(b). For θ = 45°, there is only plasmon resonance at the Au-air interface whereas for θ = 135° both the Au-air interface and the Au-silica interface have plasmon resonance. Magnetic field distributions are also calculated and the results are shown in the bottom panel in Fig. 2(b), which agree well with the conclusions drawn from the electric field distributions.
Fig. 2. Simulation of the optical performance of the L-shaped hybrid Au-VO2 nanohole (L = 500 nm, w = 76 nm, t1 = 50 nm, t2 = 430 nm, and t3 = 100 nm) as a quarter-wave plate for VO2 in insulating state (T=27°C). (a) Far-field electric field intensity spectra. (b) Top panel: near-field electric field E distributions on the top surface of the nanohole (i.e., Au-air interface) and the bottom surface of the nanohole (i.e., Au-silica interface); bottom panel: related magnetic field |H| distributions corresponding to the top panel. The incident wavelength is 1550 nm. The arrows show the incident polarization directions, i.e. θ = 45° or 135°. (c) the amplitude ratio r and the phase difference Δφ. (d) the electric field amplitudes Exy, Eyy, and the DOCP of the transmitted far-field electric field for a linearly y-polarized incidence.
The different plasmon resonances excited in the two orthogonal directions in the L-shaped nanohole give rise to a phase difference between the transmitted electric fields in the far-field for θ = 45° and 135° excitations [33,35]. We calculate the far-field transmitted electric fields at the point F (0, 0, 1 m) for θ = 45° and 135° excitations and their amplitudes and phases are labeled as E45°, E135°, φ45°, and φ135°, respectively. The amplitude ratio r = E45°/E135° and the phase difference Δφ = φ45°−φ135° for VO2 in insulating state are calculated and shown in Fig. 2(c). Within the wavelength range of 1496∼1560 nm, the phase difference Δφ is in the range of 90°±5° and the amplitude ratio is in the range of 1.00 ± 0.01. At 1550 nm Δφ reaches 93° and the ratio r equals 1.0. Therefore, both the amplitude and phase conditions of a quarter-wave plate are satisfied. The symmetric axis of the L-shaped hole (θ = 45°) can be seen as the fast axis of the wave plate and its orthogonal direction (θ = 135°) can be seen as the slow axis.
To investigate the performance of the linear-to-circular polarization function of the proposed quarter-wave plate, we set the incident light as linearly y-polarized and calculate the far-field transmitted electric fields Exy and Eyy, which represent the transmitted linearly x- and y-polarized electric field components, respectively, and the results are shown in Fig. 2(d). At the telecom wavelength 1550 nm the amplitudes of Exy and Eyy are nearly equal and the phase difference of Exy and Eyy are nearly 90° (not shown here). We also calculate the degree of circular polarization (DOCP) for the transmitted field [1] and the result is also shown in Fig. 2(d). The DOCP reaches −1.0 at 1550 nm and ranges from −0.95 to −1.0 when the incident wavelength changes from 1400 to 1630 nm. Therefore, a broadband quarter-wave plate is achieved using the proposed L-shaped nanohole when VO2 is in insulating state.
We also calculate the resonance of the nanohole when VO2 is in metallic state (T=82°C) and the results are shown in Fig. 3(a). There is a resonant mode at 1953 nm for θ = 45° and a resonant mode at 1326 nm for θ = 135°. When VO2 transits from the insulating state to the metallic state, the resonant peaks redshift and the resonant intensities increase resulting larger transmitted electric field intensities. However, the far-field electric field intensities for θ = 45° and 135° keep equal at the telecom wavelength 1550 nm when VO2 is in metallic state. The near-field electric field and magnetic field distributions at 1550 nm are also calculated and the results are shown in Fig. 3(b). Similar results are achieved compared to the case for VO2 in insulating state.
Fig. 3. Simulation of the optical performance of the L-shaped hybrid Au-VO2 nanohole (L = 500 nm, w = 76 nm, t1 = 50 nm, t2 = 430 nm, and t3 = 100 nm) as a half-wave plate for VO2 in metallic state (T=82°C). (a) Far-field electric field intensity spectra. (b) Top panel: near-field electric field E distributions on the top surface of the nanohole (i.e., Au-air interface) and the bottom surface of the nanohole (i.e., Au-silica interface); bottom panel: related magnetic field |H| distributions corresponding to the top panel. The incident wavelength is 1550 nm. The arrows show the incident polarization directions, i.e. θ = 45° or 135°. (c) the amplitude ratio r and the phase difference Δφ. (d) the field amplitudes Exy, Eyy, the PCR and DOLP of the transmitted far-field electric field for a linearly y-polarized incidence.
For a given incident wavelength, the phase shift of the plasmon field (relative to the phase of the driving field) increases with the redshift of the resonant wavelength of the oscillator [4]. When VO2 transits from the insulating state to the metallic state, the redshift of the resonant peak for θ = 45° (from 1166 to 1953 nm, i.e., a redshift of 787 nm) is larger than that for θ = 135° (from 1086 to 1326 nm, i.e., a redshift of 240 nm), which means that the increase of φ45° is larger than that of φ135°. Therefore, the phase difference Δφ = φ45°−φ135° is expected to be larger for VO2 in metallic state than that for VO2 in insulating state. We calculate the phase difference Δφ and the amplitude ratio r for VO2 in metallic state, and the results are shown in Fig. 3(c). When the incident wavelength changes from 1535 to 1580 nm, the phase difference Δφ is in the range of 180°±5° and the amplitude ratio r is in the range of 0.85∼1.05. At 1550 nm Δφ reaches 178° and the ratio r equals 0.92. Thus, both the amplitude and phase conditions of a half-wave plate are nearly satisfied with the symmetric axis of the L-shaped hole (θ = 45°) as the fast axis and its orthogonal direction (θ = 135°) as the slow axis.
To verify the polarization conversion function of the proposed half-wave plate, we also set the incident light as linearly y-polarized and calculate the far-field transmitted electric fields Exy and Eyy, the amplitudes of which are shown in Fig. 3(d). The electric field amplitude Exy is much larger than Eyy at 1550 nm. We use the polarization conversion ratio (PCR) to describe the polarization conversion function of the structure, which is defined as
We calculate the PCR within the wavelength range of 1300∼1700 nm and the results are shown in Fig. 3(d). The PCR ranges from 0.95∼1.0 when the incident wavelength changes from 1480 to 1645 nm and reaches 1.0 at 1550 nm. Besides, the degree of linear polarization (DOLP) of the transmitted electric field is also calculated [1] and the result is shown in Fig. 3(d). The DOLP ranges from 0.95∼1.0 when the incident wavelength changes from 1474 to 1658 nm and reaches 1.0 at 1550 nm. Thus, a broadband half-wave plate is achieved using the L-shaped nanohole when VO2 is in metallic state.
Therefore, when the temperature T increases from 27 to 82°C, the proposed L-shaped hybrid Au-VO2 nanohole switches from a quarter-wave plate to a half-wave plate. Within the wavelength range of 1480∼1630 nm, the proposed structure has good polarization manipulation performances both in room temperature (T=27°C) and high temperature (T=82°C). The large bandwidth (∼150 nm) is attributed to the broad resonant peaks of the hybrid nanoholes and beneficial to the practical applications.
The proposed L-shaped hole structure can be fabricated by standard focused ion beam (FIB) etching process. First, a layer of 100 nm gold film, a layer of 430 nm VO2 film and a layer of 50 nm gold film are deposited in sequence on a silica substrate by magnetron sputtering method or pulsed laser deposition method [39]. To improve the crystallinity of VO2, a single-crystalline gold platelet with a thickness of 100 nm grown on a glass substrate by wet-chemical synthesis method [40] can be used instead of the bottom 100 nm gold film, and then the layer of 430 nm VO2 film and the top layer of 50 nm gold film are deposited in sequence on the gold platelet. Finally, the L-shaped hole can be fabricated in the hybrid films using the FIB process.
4. Switchable full-/quarter-wave plate
The resonances of the L-shaped hybrid Au-VO2 nanoholes depend on the structure and its geometrical parameters. Our simulation results indicate that the phases of the electric field oscillations in the nanohole can be tuned by changing the thickness of the gold film (not shown here for simplicity), which can be used for achieving different waveplates. In this section we remove the bottom Au layer and change the arm length and width of the L-shaped hybrid Au-VO2 nanoholes in Fig. 1(a) to achieve a switchable full-/quarter-wave plate. A schematic of the varied structure is shown in the inset of Fig. 4(a). A gold film and a VO2 film lie on the top of a silica substrate in sequence and an L-shaped hole is located in the films. The depth of the hole h equals to the sum of the thicknesses of the gold film and VO2 film (i.e., h = t1+t2). The geometrical parameters of the new L-shaped nanohole are L = 470 nm, w = 60 nm, t1 = 40 nm and t2 = 340 nm. To investigate the resonances of the structure, we calculate its far-field transmitted electric field intensities at the point F (0, 0, 1 m) with the change of the incident wavelength when VO2 is in insulating and metallic states and the results are shown in Figs. 4(a) and 4(b), respectively. For VO2 in insulating state, the symmetric resonant mode appears at 1209 nm (θ = 45°) and the anti-symmetric resonant mode is at 1516 nm (θ = 135°). For VO2 in metallic state, the symmetric resonant mode appears at 1711 nm and the anti-symmetric resonant mode is at 1215 nm.
Fig. 4. Switchable full-/quarter-wave plate with a new L-shaped nanohole (L = 470 nm, w = 60 nm, t1 = 40 nm and t2 = 340 nm). (a) the far-field electric field intensity spectra for VO2 in insulating state. Inset: schematic of the new L-shaped nanohole. (b) the far-field electric field intensity spectra for VO2 in metallic state. (c) the amplitude ratio r and the phase difference Δφ for VO2 in insulating state. (d) the field amplitudes Exy, Eyy, the PTR and DOLP of the transmitted far-field electric field for a linearly y-polarized incidence when VO2 is in insulating state. (e) the amplitude ratio r and the phase difference Δφ for VO2 in metallic state. (f) the field amplitudes Exy, Eyy, and the DOCP of the transmitted far-field electric field for a linearly y-polarized incidence when VO2 is in metallic state.
We calculate the amplitude ratio r and the phase difference Δφ when VO2 is in insulting state (T=27°C), and the results are shown in Fig. 4(c). Within the calculated wavelength range of 1300∼1700 nm, the amplitude ratio r and the phase difference Δφ are in the ranges of 0.88∼1.26 and −1.3°∼10.4°, respectively. At 1550 nm r equals 1.0 and Δφ reaches 2.3°. Therefore, the amplitude and the phase conditions of a full-wave plate are nearly satisfied. To confirm the function of the full-wave plate, we set the incident field linearly y-polarized and calculate the field amplitudes of Exy, Eyy and the DOLP of the far-field transmitted electric field. The results are shown in Fig. 4(d). The field amplitude Eyy is much larger than Exy around 1550 nm. The DOLP is in the range of 0.98∼1.0 within the calculated wavelength range of 1300∼1700 nm and reaches 1.0 at 1550 nm. Besides, we use the polarization transmission ratio (PTR) to describe the polarization transmission function of the structure, which is defined as
We calculate the PTR for the new structure and the result is also shown in Fig. 4(d). The PTR is in the range of 0.98∼1.0 within the wavelength range of 1300∼1700 nm and reaches 1.0 at 1550 nm. Therefore, a broadband full-wave plate is achieved via the new L-shaped nanohole for VO2 in insulating state.
We also calculate the amplitude ratio r and the phase difference Δφ for VO2 in metallic state (T=82°C) and the results are shown in Fig. 4(e). When the incident wavelength changes from 1462 to 1611 nm, r and Δφ are in the ranges of 0.89∼1.2 and 90°±5°, respectively. At 1550 nm, r equals 1.07 and Δφ reaches 92°, which satisfy the amplitude and the phase conditions for a quarter-wave plate. We also set the incident light linearly y-polarized and calculate the field amplitudes of Exy, Eyy and the DOCP of the far-field transmitted electric field. The results are shown in Fig. 4(f). The field amplitude Exy approaches Eyy around 1550 nm. The DOCP reaches −1.0 at 1550 nm and ranges from −0.95 to −1.0 when the incident wavelength changes from 1400 to 1650 nm. Therefore, a broadband quarter-wave plate is achieved via a new L-shaped nanohole for VO2 in metallic state. When the temperature T increases from 27°C to 82°C, the new L-shaped hole switches from the full-wave plate to quarter-wave plate with the symmetric axis of the structure and its orthogonal direction as its fast and slow axes, respectively. The structure has good polarization manipulation performances within the wavelength range of 1400∼1650 nm, which means a bandwidth of nearly 250 nm.
5. Switchable full-wave plate/polarizer
When VO2 transits from the insulating state to the metallic state, the resonant peaks shift and the transmission intensities vary, resulting in the change of amplitude ratios. For the new L-shaped nanohole in the inset of Fig. 4(a), when the incident wavelength is in the range of 1700∼2100 nm, the far-field intensity E245° approaches E2135° for VO2 in insulating state [see Fig. 4(a)], whereas it is much larger than E2135 for VO2 in metallic state [see Fig. 4(b)]. The nearly same electric field amplitudes benefit the function as a waveplate whereas the large asymmetric transmission is a typical character of a polarizer. We change the geometrical parameters of the new L-shaped nanohole (L = 300 nm, w = 70 nm, t1 = 50 nm and t2 = 450 nm) to achieve a full-wave plate for VO2 in insulating state and a polarizer for VO2 in metallic state at 1550 nm. We calculate its far-field transmitted electric field intensities at the point F (0, 0, 1 m) and the results are shown in Figs. 5(a) and 5(b). For VO2 in insulating state, the symmetric resonant mode appears at 1997 nm and the anti-symmetric resonant mode is at 1408 nm [see Fig. 5(a)]. For VO2 in metallic state, the symmetric resonant mode appears at 1400 nm and the anti-symmetric resonant mode is at 839 nm [see Fig. 5(b)].
Fig. 5. Switchable full-wave plate/polarizer with an L-shaped nanohole (L = 300 nm, w = 70 nm, t1 = 50 nm and t2 = 450 nm). (a) and (b) are the far-field electric field intensity spectra for VO2 in insulating and metallic state, respectively. (c) the amplitude ratio r and the phase difference Δφ for VO2 in insulating state. (d) the field amplitudes Exy, Eyy, the DOLP and PTR of the transmitted far-field electric field for a linearly y-polarized incidence when VO2 is in insulating state. (e) the amplitude ratio r for VO2 in metallic state. (f) the change of the normalized transmitted electric field E45° with the incident polarization angle θ when VO2 is in metallic state (black circular dots). The incident wavelength is 1550 nm. The red solid curve represents the cosine curve of the Malus law, i.e., E45°/Einc=cos(θ−45°).
We calculate the amplitude ratio r and the phase difference Δφ when VO2 is in insulting state (T=27°C), and the results are shown in Fig. 5(c). When the incident wavelength changes from 1430 to 1618 nm, the amplitude ratio r and the phase difference Δφ are in the ranges of 0.92∼1.14 and −10°∼10°, respectively. At 1550 nm r equals 1.04 and Δφ reaches 3.6°. Therefore, the amplitude and the phase conditions of a full-wave plate are approximately satisfied. To confirm the function of the full-wave plate, we calculate the field amplitudes of Exy, Eyy and the DOLP of the far-field transmitted electric field and the results are shown in Fig. 5(d). The field amplitude Eyy is much larger than Exy around 1550 nm. The DOLP is in the range of 0.98∼1.0 within the calculated wavelength range of 1421∼1638 nm and reaches 1.0 at 1550 nm. Besides, the PTR of the structure is calculated and the result is also shown in Fig. 5(d). The PTR is in the range of 0.98∼1.0 within the wavelength range of 1396∼1651 nm and reaches 1.0 at 1550 nm. Therefore, a broadband full-wave plate is achieved via this modified new L-shaped nanohole for VO2 in insulating state.
When VO2 is in metallic state, the far-field electric field amplitude E45° is much larger than E135° around 1550 nm [see Fig. 5(b)], which means that the far-field transmitted electric field is mainly linearly polarized along the symmetric axis of the structure (θ = 45°). We calculate the amplitude ratio r and the result is shown in Fig. 5(e). When the incident wavelength changes from 1537 to 1700 nm, the amplitude ratio r increases from 10 to 13.3 and reaches 10.3 at 1550 nm. We change the incident polarization direction θ at 1550 nm and calculate the normalized transmitted electric field amplitude along the symmetric axis of the structure (i.e., E45°). The result is shown in Fig. 5(f). The transmitted electric field has a maximum for θ = 45° and a minimum for θ = 135° and −45°. For a polarizer with the optical axis along the symmetric axis of the structure (θ = 45°), the change of the transmitted electric field amplitude with the incident polarization direction should satisfies the Malus law, i.e., E45°/Einc=cos(θ−45°), where Einc represents the amplitude of the incident electric field. We plot the cosine curve in Fig. 5(f) and confirm that our simulation result agrees well with the Malus law. Therefore, a polarizer can be achieved with this modified new L-shaped nanohole and its optical axis is along the symmetric axis of the structure. When the temperature T increases from 27°C to 82°C, the proposed structure switches from a full-wave plate to a polarizer within a wavelength range of 1537∼1638 nm, i.e. a bandwidth of about 100 nm.
6. Conclusions
In summary, we propose L-shaped Au-VO2 hybrid nanoholes to achieve switchable polarization manipulation. The phase transition of VO2 is used to tune the phase difference between different plasmon resonant modes of the nanoholes. We achieve a quarter-wave plate for VO2 in insulating state and a half-wave plate for VO2 in metallic state at the telecom wavelength 1550 nm with a bandwidth of 150 nm. Besides, by varying the structure of the L-shaped hole and removing the bottom Au layer to tune the phases of the electric field oscillations in the nanohole, we achieve a switchable full-/quarter-wave plate when VO2 transits from insulating state to metallic state and the bandwidth of the structure reaches nearly 250 nm. In addition, we change the geometrical parameters of the new structure to tune the shift and the intensities of the resonant spectra, a switchable full-wave plate/polarizer is achieved. Our simulation results suggest that the proposed L-shaped nanohole structures have strong abilities in active polarization manipulation in plasmonics and nanophotonics.
Appendix: simulation details
A. Dielectric constants of VO2
At room temperature (T=27°C), VO2 is in the insulating state and we use the following Lorentz model [37,38] to describe its dielectric constant:
The conductivities of VO2 at T=27 and 82°C can be obtained by the relation $\sigma (\omega )= i{\varepsilon _0}\omega [{1 - \varepsilon (\omega )} ]$, where ɛ0 is vacuum permittivity.
B. Convergence studies in the simulation
To check the convergence of the simulations, early shut-off conditions are used, i.e. the simulation will end when the total energy in the simulation volume drops to 10−5 fraction of the incident energy or rises to 105 times the incident energy. All the simulations in this work are convergent and satisfy the former shut-off condition, which means most of the energy has left the simulation volume at the end of the simulation.
For the mesh grid size, we tried different meshing sizes of ranging from 2 to 5 nm in the simulation and the simulations are all convergent. For the distance of nanostructures from the boundaries, we tried a distance ranging from 200 to 900 nm and the simulations are all convergent. For the corner radius of the structure, we use a small meshing cell size (2 nm) to make sure it does not influence the convergence of the simulations.
C. Boundary conditions
In this work we focus on the optical performance of a single hole and the PML adsorbing boundary conditions are applied in the simulation. For practical applications an array of holes can be used to enhance the amplitude of the transmitted field. To simulate the optical performance of an array of holes, periodic boundary conditions in the x and y directions and PML boundary conditions in the z direction can be used.
Funding
National Natural Science Foundation of China (91850104).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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