1. Introduction

Surface plasmons are the collective oscillations of conduction band electrons at the interface of a metal and a dielectric. When the incident electromagnetic fields are coupled to surface plasmons at the interface of a metallic thin film and a dielectric, electromagnetic waves called surface plasmon polariton (SPPs) are generated. Different mechanisms such as prism coupling, grating coupling, waveguide coupling and near-field excitation are required for excitation of SPPs. On the other hand, non-propagating collective oscillations of conduction band electrons at the surface of metallic nanoparticles are called Localized surface plasmons (LSPs), which can be excited directly by the incident electromagnetic waves without the need of any coupling mechanism [1]. Interaction of light with certain metallic nano-scale structures such as plasmonic nanoantennas can result in the focusing of light at the nanometer scale. Nanoantennas, due to their ability to function in either the transmitting mode or in the receiving mode, have found applications in various fields such as solar cells, photodetectors, data storage, single-molecule detection, nonlinear optics and sensing [2]. Moreover, different plasmonic nanostructures have recently been proposed to realize the passive as well as active compact optical devices, including switches [3–6]. Among the wide variety of plasmonic switches reported, the majority of devices operate on a principle where an active control over the material properties alters the surface plasmon polariton (SPP) characteristics such as propagation length [7–9]. In addition, graphene-based plasmonic switches have been proposed recently for switching based on polarization [10,11] and Goos–Hänchen shift [12,13] by tuning the conductivity of the graphene. However, there are very few reports that demonstrate the active control over the near-field properties of a nanoantenna. The manipulation of the near-field of a nanoantenna can assist in applications involving SERS [14,15], nonlinear optics [16], quantum emitters [17], coherent control [18]. John Kohoutek et al. [19] exploited the near-field properties of a nanoantenna to modulate a quantum cascade laser. The output power of the quantum cascade laser was modulated by switching the near-field intensity of a nanoantenna, which was placed at the front facet of the quantum cascade laser. In addition, it has also been demonstrated that by controlling the interaction between the tip of the atomic force microscope and the hotspot of a nanoantenna integrated with quantum cascade laser, it is possible to alter the frequency and output power of the quantum cascade laser [20]. Therefore, the active control over the near-field properties of a nanoantenna can be of great importance for those applications which exploit the near-field properties of a nanoantenna. In addition, the excitation as well as the emission rate of a nanoemitter, when the nanoemitter is placed in the near-field intensity of a nanoantenna, can be enhanced [21–24]. Therefore, when a nanoemitter is placed in the near-field of a nanoantenna, the active manipulation of the near-field properties of the nanoantenna can allow the switching of light intensity of the nanoemitter. The different potential applications of near-field properties of nanoantennas necessitate the design of nanoantenna-based plasmonic switches that can provide active control over the near-field properties of the nanoantennas. In addition, it is desirable that the design should be able to operate in the all-optical domain, in order to be integrated with photonic integrated circuits.

In this paper, we present plasmonic switches based on ring-shaped plasmonic nanoantennas lying on top of VO₂ thin films. These plasmonic switches allow active control on the near-field properties of the plasmonic nanoantennas. Vanadium oxide (VO₂) is a phase change material which undergoes a change in its state — from the semiconductor state to the metallic state — as its temperature is increased above a specific temperature (68°C for undoped VO₂ films). In the semiconductor state, VO₂ has a monoclinic structure. As the temperature is raised above 68°C, the energy of the system becomes favorable to a structural change from monoclinic structure to tetragonal structure. As a result, a completely filled band and completely empty band merge, and VO₂ behaves as a metal [25–27]. As vanadium oxide (VO₂) changes its state from the semiconductor state to the metallic state, there is a change in its refractive index — for both the real part ‘n’ and the imaginary part ‘k’ of the refractive index of VO₂ (see Appendix A). The semiconductor to metal phase transition in VO₂ can occur at femtosecond time scale [28]. Furthermore, the phase transition in VO₂ from semiconductor state to the metallic state can be induced by electromagnetic fields [28] as well as by applying an external electric field [29]. The ability of VO₂ material to exhibit the phase transition — from semiconductor state to metallic state — as well as the flexibility in the modes ­to induce the phase transition have allowed the use of VO₂ material to realize many practical applications including optical switches [9,30,31] modulators [30], photodetectors [31] and other optoelectronic devices [32].

The schematics of VO₂ based plasmonic switches presented in this paper are shown in Figs. 1(a) and 1(b). The ring-bowtie nanoantenna (RBN) switch consists of a ring-bowtie nanoantenna on top of a VO₂ thin film grown over a silica substrate (see Fig. 1(a)). Similarly, the ring-rhombus nanoantenna (RRN) switch consists of a ring-rhombus nanoantenna on top of a VO₂ thin film grown over a silica substrate. Figures 1(c)-(f), schematically, illustrate the concept of near-field switching for the RBN switch and for the RRN switch. When these plasmonic switches are illuminated with light, a very bright spot is observed at the center of the nanoantenna for the metallic state of VO₂ film (named as the On-state) (see Figs. 1(c) and 1(e)). As the VO₂ film is switched from metallic state to semiconductor state (named as the Off-state), the near-field intensity at the center of the nanoantenna reduces significantly (see Figs. 1(d) and 1(f)). Since the VO₂ film can be switched — between the metallic state and the semiconductor state — at ultrafast time scale, the near-field intensity at the center of a nanoantenna can also be manipulated at ultrafast time scale. Therefore, by switching the plasmonic switch between its On-state and Off-state, it is possible to switch the light intensity of a nanoemitter ― placed in the near-field intensity of the nanoantenna ― at ultrafast time scale. In order to quantitatively determine the active control over the near-field intensity of a nanoantenna, we calculate a quantity, called as intensity switching ratio $({I_{On}}/{I_{Off}})$, which is defined as the ratio of near-field intensity at the center of the nanoantenna (i.e., at point ‘A’ in Figs. 1(a) and 1(b)), in the On-state and the Off-state of the plasmonic switch.

 

Fig. 1. Schematic showing different plasmonic switches based on plasmonic nanoantennas on VO₂ thin films: (a) A ring-bowtie nanoantenna switch and (b) A ring-rhombus nanoantenna switch. The parameters mentioned in the schematic are the thickness ‘b’ of the VO₂ film, the thickness ‘t’ of the ring nanoantenna, the length ‘L’ of the nanoantenna, the angle ‘α’ of the nanoantenna, and height ‘h’ of the nanoantenna. The point ‘A’ lies in between the two arms of the plasmonic nanoantennas. The schematic illustration of active switching of the near-field intensity around the plasmonic nanoantennas for the: 1(c-d) Ring-bowtie nanoantenna switch and 1(e-f) Ring-rhombus nanoantenna switch.

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In order to quantify the switching of intensity of light emitted by a nanoemitter placed in the near-field intensity of the nanoantenna (i.e., at point A in Figs. 1(a) and 1(b)), we calculate the fluorescence enhancement switching ratio (FESR). The FESR is defined as the ratio of fluorescence enhancement factors in the On-state (with the VO₂ film in the metallic state) and the Off-state (with the VO₂ film in the semiconductor state) of the plasmonic switch. The FESR can be expressed by the following equation (see appendix B):

The main design objective in this paper is to present a near-field plasmonic switch, based on plasmonic nanoantennas and a phase change material, that provides the best possible performance in terms of near-field intensity switching ratio and is easy-to-fabricate. Another design objective is to obtain the maximum near-field switching ratio at a desired wavelength. In our manuscript, various other nanoantenna geometries present on top of VO₂ thin films were also simulated in order to obtain an optimal design for a near-field switch, i.e. to obtain the highest value of the near-field intensity switching ratio. However, the results of only those nanoantenna geometries that provide the highest switching ratio are presented, analyzed, and discussed in detail in this paper. The results for other nanoantenna geometries are briefly provided in Fig. 11 in Appendix D.

In this paper, the performance of the proposed plasmonic switches — in terms of switching of the near-field properties (such as the near-field intensity, fluorescence enhancement switching ratio, efficiency of the nanoemitter, etc.) — is evaluated. A maximum intensity switching ratio of ∼ 59.5 was obtained for the RBN switch at a wavelength of 1100 nm. On the other hand, a maximum intensity switching ratio of ∼ 80.85 was obtained for the RRN switch at a wavelength of 1140 nm. These values of the maximum intensity switching ratios are significantly higher than those previously reported in literature. In previous literature, the maximum intensity switching ratio was reported to be ∼12 for photoconductive loaded plasmonic nanoantennas [33], ∼7 for bowtie and rod-disc and trapezoidal toothed log-periodic switchable plasmonic nanoantenna [34], and ∼ 7 for VO₂ dipole nanostructure [35]. We also present the results of simulations carried out to optimize the different geometrical parameters of the plasmonic switches in order to obtain the maximum possible intensity switching ratio.

In this paper, we also employ FDTD simulations to show that the intensity of emission from the nanoemitters — placed in the centre of the gap between the arms of the plasmonic nanoantennas constituting the plasmonic switches — can be significantly switched by changing the phase of the VO₂ film between its metallic state and the semiconductor state. Hence, the plasmonic switches consisting of plasmonic nanoantennas and VO₂ thin films, as are being proposed in this paper, exhibit extremely large values of FESR — which is ratio of the enhancement of fluorescence from the nanoemitters when the VO₂ film lies in its metallic state to that when it lies in its semiconductor state. This is the first report of active switching of emission from nanoemitters lying in the vicinity of a plasmonic switch. While a maximum fluorescence enhancement switching ratio (FESR) of ∼ 163 is obtained at a wavelength of 1140 nm for the RBN switch, a maximum FESR of ∼ 200 is obtained at a wavelength of 1140 nm for the RRN switch. We also found that the efficiency of the nanoemitter can be modified by a factor of ∼ 2.9 for the RBN switch and by ∼ 2.5 times for the RRN switch by switching the VO₂ film between its metallic and semiconductor.

The plasmonic switches being proposed by us can be easily fabricated by first growing VO₂ thin films on planar substrates (silicon-di-oxide or sapphire substrates) using pulsed laser deposition. This can be followed by spin coating a positive e-beam resist on top of the VO₂ films and patterning the resist by using e-beam lithography. Subsequently, the development of the resist can be carried out, followed by the deposition of a thin layer of gold using e-beam evaporation. Finally, lift-off can be carried out to obtain the desired VO₂-based plasmonic switch structures.

2. Material and method

We have employed the finite difference time domain (FDTD) modeling to calculate the electric field intensity. The FDTD method involves the discretization of the of Maxwell equations in both space and time using a central-difference approximation. A commercial software (Lumerical FDTD solutions) is employed to calculate the near-field intensity at the center of the plasmonic nanoantennas studied in this paper. The optical constants of gold and the VO₂ employed in FDTD calculations are provided in Appendix C. These optical constants are imported into the Lumerical’s FDTD software through the material database [36]. A broad band plane wave source is launched from the top (i.e., from the air side) and the electric field intensity is observed at the center of the plasmonic switch (i.e., at point ‘A’ in Fig. 1). Perfectly matched layer (PML) boundary conditions are employed along x, y, and z-direction. For the calculation of the intensity switching ratio, while a mesh size of 1 nm is used in the gap region, a mesh of 2 nm is used over the entire region of space (excluding the gap region).

We choose PbS quantum dots as nanoemitters in our simulations as their emission spectra can be tuned in the near-infrared region [37,38]. In addition, the significant overlap of the broad absorption spectra with the emission spectra of PbS quantum dots [39,40] allows us to calculate the intensity switching ratio and the efficiency ratio at the same wavelength to determine the FESR. The nanoemitter was modeled using a dipole source, which is polarized along the axis of the nanoantenna and radiates with a signal amplitude equal to unity. The wavelength of the dipole source is varied from 800 nm to 2000nm to calculate the decay rates at different wavelengths. The decay rate calculations are sensitive to the position of the dipole source with respect to nanoantenna. Also, the lightning rod effect is caused by staircasing of nanoantenna tip when thick mesh size is used. Therefore, we performed the mesh convergence test to avoid unwanted effects and to obtain reliable results. Finally, a mesh of 0.5 nm along x and y direction, and a mesh of 1 nm along z-direction is used in the gap region. Other than the gap region, a uniform mesh size of 2 nm is chosen over the entire region. The normalized radiative decay rate ${\gamma _r}/{\gamma _0}$ of a nanoemitter in the vicinity of the nanoantenna can be calculated by determining the ratio of power radiated by the nanoemitter in the vicinity of the nanoantenna (P_r) to that in free space (P₀) i.e. ${P_r}/{P_0}$ [41,42]. Plasmonic materials are lossy in nature. Some of the photon radiated by the nanoemitter is reabsorbed by the nanoantenna, thereby, introducing the nonradiative decay rate ${\gamma _{abs}}$. The normalized nonradiative decay rate ${\gamma _{abs}}/{\gamma _0}$ is determined by subtracting the radiative power from the total power emitted by the dipole source.

3. Result and discussion

In this section, we describe the results of FDTD simulations carried out on the plasmonic switches to calculate the intensity switching ratio and the FESR. Figures 2(a) and 2(b) show the intensity switching ratio — as a function of wavelength — for the RBN switch and the RRN switch, respectively. The maximum intensity switching ratio achieved for RBN switch is ∼ 60 at a wavelength of 1100 nm. Whereas the maximum intensity switching ratio achieved for RRN switch is ∼ 81 at a wavelength of 1140 nm.

 

Fig. 2. The intensity switching ratio in the presence of the nanoantenna (red curve) and in absence of the nanoantenna (black curve) for: (a) the RBN switch (ring-bowtie nanoantenna switch) (b) the RRN switch (ring rhombus nanoantenna switch). The electric field intensity enhancement measured at the point ‘A’ shown in Fig. 1 (the point at the center of the two arms of the nanoantenna) as a function of wavelength for: (c) the RBN switch and (d) the RRN switch. In Figs. 2(c) and 2(d), red and black curves correspond to the metallic state and the semiconductor state of VO₂ film, respectively. For the RBN and RRN switches, the length ‘L’, angle ‘α’, the height ‘h’ of the nanostructure, and the thickness ‘b’ of the VO₂ film are 250 nm, 30°, 80 nm, and 20 nm respectively. The thickness ‘t’ of the ring is 20 nm for the RBN switch and 15 nm for the RRN switch.

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Figures 2(c) and 2(d) show the electric field intensity at point ‘A’ — as a function of wavelength — for the RBN switch and the RRN switch, respectively. For the RBN switch, the lowest order plasmonic mode (a plasmon resonance related peak in the electric field intensity enhancement spectra) occurs at ∼1240 nm wavelength for the VO₂ film in the metallic state. For the VO₂ film in the semiconductor state, the lowest order plasmonic mode shifts to ∼ 2100 nm wavelength (the electric field intensity curve from 400 nm to 2400 nm is shown in Fig. 10 in Appendix D). The shift in the plasmonic mode — for VO₂ film in the semiconductor state — allows the lowest order plasmonic mode for the metallic state of VO₂ film to coincide with the Off-resonance wavelength region (wavelength region towards shorter wavelength to the plasmonic mode) for the semiconductor state of VO₂ film. Therefore, a large contrast between the electric field intensity for the metallic state and that for semiconductor states of VO₂ film occurs, and as a consequence, a large intensity switching ratio is obtained. Similarly, a very large intensity switching ratio is obtained for the RRN switch. The maximum intensity switching ratio obtained for RRN switch occurs at a higher wavelength as compared to the RBN switch because the geometrical parameters taken for the RRN switch are different from those chosen for the RBN switch.

Figures 2(a) and 2(b) also show the intensity switching ratio in the absence of plasmonic nanoantennas over the VO₂ films. In the absence of the nanoantennas, the large electromagnetic field enhancements between the arms of the nanoantennas — occurring due to the plasmon resonance excitation — are not present (see Fig. 10(a) in Appendix D). Hence, the intensity switching ratio is significantly smaller (∼ 2.2) in the absence of the plasmonic nanoantennas. This small change in the intensity occurs primarily due to the different reflectivities from the surface of the VO₂ film in its semiconductor state and in its metallic state.

Figure 3 shows the spatial distribution of electric field — in the XY plane — for the RBN switch (Figs. 3(a) and 3(b)) and for the RRN switch (Figs. 3(c) and 3(d)), for the metallic and semiconductor states of the VO₂ film at the peak wavelength ‘λ_peak’, i.e. at a wavelength at which the maximum intensity switching ratio is obtained. It is evident from the figures that the electric field is tightly concentrated at the center of the nanoantenna for the VO₂ film in the metallic state. For the semiconductor state of VO₂ film, a less intense electric field is observed at the center of the nanoantenna.

 

Fig. 3. Spatial distribution of electric field at peak wavelength (λ_peak) for the RBN switch in: (a) metallic state and (b) the semiconductor state and for the RRN switch in: (c) metallic state and (d) the semiconductor state of VO₂ film. The geometrical parameters are same as mentioned in Fig. (2).

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Figures 4(a) and 4(c) show the maximum intensity switching ratio and the peak wavelength (λ_peak) as a function of the thickness of the ring for the RBN switch and the RRN switch, respectively. It is found that for both types of plasmonic switches, the maximum intensity switching ratio occurs for an optimal thickness ‘t’ of the ring. The maximum intensity switching ratio obtained for a RBN switch is ∼ 60 at 1100 nm wavelength and that for a RRN switch is ∼ 81 at 1140 nm wavelength. To explain the reasoning behind the optimum value of the thickness of the ring, the electric field intensity spectra are shown in Figs. 4(b) and 4(d) for the RBN switch and the RRN switch, respectively. It can be observed from Figs. 4(b) and 4(d) that the plasmonic mode — for the metallic state as well as for the semiconductor state of the VO₂ film — undergoes a blue shift as the thickness of the ring increases. This blue-shift can be explained by the plasmon hybridization mode theory [43]. The increase in the thickness ‘t’ of the ring shifts not only the resonance wavelength of plasmonic mode but also the off-resonance wavelength region of the electric field intensity spectra (see the inset in Figs. 4(b) and 4(d)). As a result, the maximum intensity switching ratio is obtained for an optimum ring thickness of ∼20 nm for the RBN switch and ∼ 15 nm for the RRN switch. In addition, there is blue-shift in the peak wavelength (λ_peak) as the thickness ‘t’ of the ring is increased as shown in Figs. 4(a) and 4(c). It happens because the blue-shift in the plasmonic mode for the metallic state of the VO₂ film is larger as compared to the shift in the off-resonance wavelength region. Thus, the peak wavelength (λ_peak) shifts towards shorter wavelength.

 

Fig. 4. The intensity switching ratio and the peak wavelength as a function of thickness ‘t’ of the ring for: (a) the RBN switch and (c) the RRN switch. The electric field intensity enhancement measured at point ‘A’ shown in Fig. 1, as a function of wavelength, for different thicknesses ‘t’ of the ring for: (b) the RBN switch and (d) the RRN switch. In Figs. 4(b) and 4(d), the curves with the rectangular marker correspond to the metallic state (i.e., the switch is in the On-state) of the VO₂ film and curves without any marker correspond to the semiconductor state (i.e., the switch is in Off-state) of the VO₂ film. For the RBN switch and the RRN switch, the length ‘L’, angle ‘α’, height ‘h’ of the nanoantenna, and the thickness ‘b’ of the VO₂ film are kept constant at 250 nm, 30°, 80 nm, and 40 nm, respectively.

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Figures 5(a) and 5(c) display the intensity switching ratio and the peak wavelength λ_peak as a function of thickness ‘b’ of the underlying VO₂ film for the RBN switch and the RRN switch, respectively. It is seen that the intensity switching ratio obtains maximum value for an optimum thickness of the VO₂ film. The maximum intensity switching ratio obtained for the RBN switch is ∼ 60 and that for the RRN switch is ∼ 81 at 40 nm thickness of the VO₂ film.

 

Fig. 5. The intensity switching ratio and the peak wavelength as a function of thickness ‘b’ of the VO₂ film for: (a) the RBN switch and (c) the RRN switch. The electric field intensity enhancement measured at point ‘A’ shown in Fig. 1, as a function of wavelength, for different thicknesses ‘b’ of the VO₂ film for: (b) the RBN switch and (d) the RRN switch. The curves with the rectangular markers correspond to the metallic state of the VO₂ film and the curves without any markers correspond to the semiconductor state of the VO₂ film. For the RBN switch and the RRN switch, the length ‘L’, angle ‘α’, height ‘h’ of the nanoantenna are 250 nm, 30°, 80 nm. The thickness ‘t’ of the ring is 20 nm and 15 nm for RBN switch and RRN switch, respectively.

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To explain the optimum thickness of the VO₂ film, the electric field intensity — as a function of wavelength — ­is shown in Figs. 5(b) and 5(d), for a RBN switch and for a RRN switch, respectively. For the VO₂ film in metallic state, the lowest order plasmonic mode shifts towards shorter wavelengths as the thickness ‘b’ of the VO₂ film is increased. The blue-shift in the plasmonic mode can be explained by using the effective medium approximation for the underlying material (VO₂ film and the silica substrate) as the plasmonic mode of the nanoantenna interacts with the VO₂ film as well as with the silica substrate [44]. In the metallic state, VO₂ exhibits a negative permittivity above ∼ 1130 nm wavelength. The permittivity of the silica substrate is positive. Therefore, above 1130 nm wavelength, the effective permittivity of the medium (the metallic VO₂ film and the silica substrate) is smaller than the permittivity of the silica substrate. Furthermore, the effective permittivity of the medium decreases with an increase in the thickness of the metallic VO₂ film due to an increase in the effective volume of the VO₂ material. Consequently, a blue shift is observed in the plasmonic mode of the VO₂-based plasmonic switches as the thickness of the metallic VO₂ film is increased. For the semiconductor state of the VO₂ film, the off-resonance wavelength region of the electric field intensity spectra shifts toward longer wavelength (since the plasmonic mode for semiconductor state of VO₂ film undergoes a red-shift as the permittivity of the VO₂ film in semiconductor state is positive). Therefore, as the thickness of the VO₂ film initially increases, the plasmonic mode for the metallic state of the VO₂ film and the off-resonance wavelength region for the semiconductor state of VO₂ film initially approach each other. As a result, intensity switching ratio increases and attains a maximum value. On further increase of the thickness of VO₂ film, the plasmonic mode for the metallic state of VO₂ film and off-resonance wavelength region for semiconductor state of VO₂ film cross each other. As a result, the intensity switching ratio begins to decrease. In addition, the peak wavelength undergoes a red-shift as the thickness of the VO₂ film is increased as shown in Figs. 5(a) and 5(c). This red-shift in the peak wavelength results from the fact that, as the thickness of the VO₂ film is increased, the red-shift in the off-resonance wavelength region for VO₂ film in semiconductor state, is larger than the blue-shift in the plasmonic mode for the VO₂ film in metallic state.

Figure 6 schematically illustrate the concept of controlling the emissive properties of a nanoemitter which is placed in between the arms of the nanoantenna. By switching the VO₂ film between its metallic state and the semiconductor state, the emission from the nanoemitter can be significantly switched. We calculate the FESR in order to quantitatively determine the characteristics of the proposed plasmonic switches. Different geometrical parameters of the plasmonic switch were varied in order to obtain maximum FESR.

 

Fig. 6. The schematic showing enhancement of fluorescence from a nanoemitter placed in between the arms of a plasmonic nanoantenna for the metallic state and for the semiconductor state of the VO₂ film for: (a-b) the RBN switch (ring-bowtie nanoantenna switch) and (c-d) the RRN switch (ring-rhombus nanoantenna switch).

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Figures 7(a) and 7(b) show the FESR (blue curve) — for optimized geometrical parameters of the plasmonic switches — for the RBN switch and the RRN switch, respectively. For the RBN switch, maximum FESR obtained is ∼ 163 at 1140 nm, and that for the RRN switch is ∼ 200 at 1140 nm. Therefore, the proposed plasmonic switches are capable of modulating the fluorescence from a nanoemitter, which is placed in between the arms of the nanoantenna, by a great extent. The fluorescent enhancement factors, in the metallic state (red curve) and the semiconductor state (black curve) of the VO₂ film, have also been shown in Figs. 7(a) and 7(b), respectively. It is to be noted that the maximum FESR occurs at a wavelength where the fluorescent enhancement factor for the semiconductor state of the VO₂ film reaches the minimum value (i.e., ∼ 0.2 for the RBN switch and ∼ 0.14 for the RRN switch). The value of fluorescent enhancement factor less than unity — for the semiconductor state of VO₂ film (i.e., Off-state of the plasmonic switch) ­­­— indicates the suppression of fluorescence from the nanoemitter. As VO₂ film is switched from semiconductor state to metallic state, the value of fluorescent enhancement factor reaches ∼36 for the RBN switch and ∼ 29 for the RRN switch. Therefore, these plasmonic switches are capable of blocking as well as enhancing the emission from a nanoemitter by switching the plasmonic switch between its two states.

 

Fig. 7. The FESR and the fluorescent enhancement factor for the metallic state (red curve) and for the semiconductor state (black curve) of the VO₂ film for: (a) the RBN switch and (b) the RRN switch. The ratio of the efficiencies of the nanoemitter (blue curve) as well as the ratio of the radiative decay rates (red curve) when the VO₂ film is in the metallic state to those when the film is in the semiconductor state for: (c) the RBN switch and (d) the RRN switch. A dipole source polarized along the X-axis is placed in between the arms of the nanoantenna. The geometrical parameters of the RBN switch and the RRN switch are the same as in Fig. 2.

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The ratio of normalized radiative decay rate (red curve), as well as the efficiency (blue curve), is plotted in Figs. 7(c) and 7(d) for the RBN switch and for the RRN switch. The absolute value of the normalized radiative decay rate and normalized absorption rate is presented in Appendix E. The large FESR results not only from the large intensity switching ratio but also due to the change in the efficiency of the nanoemitter, as the VO₂ film is switched between its metallic state and semiconductor state. It is evident from Fig. 7(c) that, for the RBN switch, the radiative decay rate is modified by a factor ∼ 6.1 at 1140 nm wavelength. As a result, the efficiency of the nanoemitter is modified by a factor ∼ 2.9 at 1140 nm wavelength. Similarly, for the RRN switch, the normalized radiative decay rate is changed by a factor ∼5.46 at 1140 nm wavelength. For the RRN switch, the efficiency is modified by a factor ∼ 2.48 at 1140 nm wavelength by switching the VO₂ film from semiconductor state to the metallic state. Therefore, it is evident that the large FESR obtained for the proposed plasmonic switches is not only due to a large intensity switching ratio but also due to the modification in the efficiency of the nanoemitter.

4. Conclusions

In this paper, we have presented novel plasmonic switches (the RBN switch and the RRN switch) based on ring-shaped plasmonic nanoantennas lying on top of a VO₂ thin film. We employed finite difference time domain (FDTD) simulations to demonstrate that the proposed plasmonic switches show excellent switching of the near-field intensity around the plasmonic nanoantennas when the phase of the VO₂ thin film is changed from the semiconductor state to the metallic state. We demonstrated that the ring-bowtie nanoantenna (RBN) switch can switch the near-field intensity by ∼ 60 times and the ring-rhombus nanoantenna (RRN) switch can switch the near-field intensity by a factor of ∼ 81 — these values of the intensity switching ratios being significantly higher than those reported in the literature. We also determined the effect of geometrical parameters of the plasmonic switches such as the thickness of the ring and the thickness of the VO₂ film. It was found that the maximum intensity switching ratio occurs for an optimum value of ring thickness and the VO₂ film thickness. In this paper, we also demonstrated that the intensity of emission from the nanoemitters placed in the gap between the arms of the plasmonic nanoantennas can be significantly switched by changing the phase of the VO₂ film between its semiconductor state and the metallic state. In order to quantify the switching of emission from the nanoemitter placed in the near-field of the nanoantenna, we defined a parameter, called FESR, the ratio of fluorescent enhancement factors in the On-state and Off-state of the plasmonic switch. It was found that the fluorescent enhancement factor can be switched by ∼ 163 times by employing the RBN switch and by ∼ 200 times by employing the RRN switch, when the phase of the VO₂ film is changed from semiconductor (Off-state) to metallic (On-state) state. We also observed that the radiative decay rate as well as the efficiency of the nanoemitter, placed in the near-field of the plasmonic nanoantenna, can also be switched by switching the VO₂ film between its metallic and semiconductor state.

Appendix A: effect of temperature on refractive indices and electric field intensity spectra for the RBN and RRN switches

Effect of tempreture on refractive indices (n & k) as well as on electic field intensity is shown in Fig. 8. It can be seen that VO₂ exhibits two different refractive indices below and above 68 °C. Consequently, the LSPR at different wavelength is observed below and above 68 °C for RBN switch as shown in Figs. 8(e) and 8(f). The spatial field distbutions, at a wavelength where maximum intensity switching ratio occurs, is shown below and above 68 °C in Figs. 8(f) and 8(h). A low and uniform intensiy is observed below 68 °C, whereas a hotspot is observed at the center of the nanoantenna above 68 °C. A similar effect can also be observed for RBN switch below and above 68 °C as shown in Figs. 8(i)–8(l).

 

Fig. 8. The real (n) and imagarny (k) part of refractive index of VO₂: (a-b) below 68 °C and (c-d) above 68 °C. The electric field intensity as a function of wavelength below 68 °C (e) and above 68 °C (g) for RBN switch. The spatial field distribution at 1100 nm wavelength below 68 °C (f) and above 68 °C (h) RBN switch. The electric field intensity as a function of wavelength below 68 °C (i) and above 68 °C (k) for RRN switch. The spatial field distribution at 1140 nm wavelength below 68 °C (j) and above 68 °C (i) for RRN switch. The geometrical parameters of the switches are the same as those mentioned in Fig. 2.

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Appendix B: theory of fluorescent enhancement and FESR

The fluorescent enhancement of a nanoemitter, kept in the vicinity of a nanoantenna which is being excited by a source, is expressed as the multiplication of enhancement of the excitation rate and the efficiency of the nanoemitter [45] i.e.,

(2)$$F = \frac{{{\gamma _{exc}}}}{{\gamma _{exc}^0}}\frac{\eta }{{{\eta ^0}}}$$

where $\gamma _{exc}$ and $\eta $ represent the excitation rate and the quantum efficiency, respectively, of the nanoemitter which is present in the vicinity of a nanoantenna. Whereas, the subscript ‘0’ stands for free-space quantities. For nanoemitter under weak excitation, the excitation rate enhancement can be expressed as [23]:

(3)$$\frac{{{\gamma _{exc}}}}{{\gamma _{exc}^0}} = \frac{{{{|E |}^2}}}{{{{|{{E_0}} |}^2}}}$$

where ${|E |^2}$ and ${|{{E_0}} |^2}$ is the electric field intensity at the position of the nanoemitter placed in the vicinity of an nanoantenna and in free space respectively. In free space, the total decay rate ${\gamma ^0}$ of an nanoemitter is the sum of the radiative decay rate $\gamma _r^0$ and the nonradioactive decay rate $\gamma _{nr}^0$ of the nanoemitter. Therefore the intrinsic quantum efficiency of a nanoemitter in free space can be determined by the equation ${\eta ^0} = \gamma _r^0/(\gamma _r^0 + \gamma _{nr}^0)$. When a nanoemitter is placed in the vicinity of a nanoantenna, the intrinsic decay rate of the nanoemitter is modified by the plasmonic nanoantenna. However, some of the radiated photon are reabsorbed due to the finite losses in plasmonic nanoantenna. Therefore, an additional nonradiative decay rate ${\gamma _{abs}}$ is introduced and reduces the quantum efficiency of the nanoemitter to $\eta = {\gamma _r}/({{\gamma_r} + {\gamma_{nr}} + {\gamma_{abs}}} )$. Assuming that the presence of nanoantenna does not affect the intrinsic nonradiative decay i.e., $\gamma _{nr}^0 = {\gamma _{nr}}$, the quantum efficiency of a nanoemitter, which has a very high intrinsic quantum efficiency i.e., ${\eta _0} \approx 1$, can be expressed as $\eta = {\gamma _r}/({{\gamma_r} + {\gamma_{abs}}} )$ [45].

The plasmonic switches presented by us in this paper consist of nanoantenna on a VO₂ film. The VO₂ film can be switched between its metallic state (i.e., On-state of the plasmonic switch) and the semiconductor state (i.e., Off-state of the plasmonic switch) and therefore, allows the active control over the near-field properties of the nanoantenna. For an emitter, which is placed in between the arms of the nanoantenna, the fluorescence enhancement ― in the metallic state and the semiconductor state of the VO₂ film ― can be calculated by the following equation:

(4)$${F_{metal,semi}} = {\left[ {\frac{{{\gamma_{exc}}}}{{\gamma_{exc}^0}}} \right]_{metal,semi}}{\left[ {\frac{\eta }{{{\eta^0}}}} \right]_{metal,semi}}$$

Using Eqs. (3) and (4), the fluorescent enhancement switching ratio (FESR), which is the ratio of fluorescent enhancement factors in the metallic state (On-state) of the film to the fluorescent enhancement factors in the semiconductor state (Off-state) of the VO₂ film, can be given by:

(5)$$FESR = \frac{{{I_{ON}}}}{{{I_{OFF}}}}\frac{{{\eta _{metal}}}}{{{\eta _{semi}}}}$$

Appendix C: optical constant of VO₂ and the Au used in FDTD simulations

The Lorentz-Drude dispersion relation was employed to determine the optical constant (relative permittivity) for the metallic state of VO₂ [26].

(6)$$\varepsilon (\omega ) = {\varepsilon _\infty } + \frac{{\Delta {\varepsilon _1}}}{{ - {a_1}{\omega ^{_2}} - i{b_1}\omega }} + \sum\limits_{k = 2}^6 {\frac{{\Delta {\varepsilon _k}}}{{ - {a_k}{\omega ^2} - i{b_k}\omega + {c_k}}}}$$

where the values of constants used are as follows - ε_∞: 3.95, Δε₁: 284.7835992, Δε₂: 34.49365809, Δε₃: 195.7081155, Δε₄: 323.4583261, Δε₅ 570.5996093, Δε₆: 0; a₁: 1, a₂: 1, a₃: 1, a₄: 1, a₅: 1, a₆: 0; b₁: 3.344700147, b₂: 7.914574094, b₃: 13.79232715, b₄: 18.34111935, b₅: 24.4771238, b₆: 0; c₁: 0, c₂: 18.99430511, c₃: 201.3457979, c₄: 311.0176212, c₅: 543.4281993, c₆: 0.

The optical constant (relative permittivity) for the semiconductor state of VO₂ is determined by the Lorentz dispersion relation:

(7)$$\varepsilon (\omega ) = {\varepsilon _\infty } + \sum\limits_{k = 1}^6 {\frac{{\Delta {\varepsilon _k}}}{{ - {a_k}{\omega ^2} - i{b_k}\omega + {c_k}}}}$$

where the values of the constants are as follows - ε_∞ : 4.26, Δε₁: 21.10833326, Δε₂: 20.57271235, Δε₃: 27.9097635, Δε₄: 104.1014275, Δε₅: 411.6548635, Δε₆: 384.8646853; a₁: 1, a₂: 1, a₃: 1, a₄: 1, a₅: 1, a₆: 1; b₁: 4.083574816, b₂: 3.122733683, b₃: 3.671568571, b₄: 7.469830329, b₅: 23.27526155, b₆: 20.19793471; c₁: 26.7194092, c₂: 43.40234673, c₃: 57.78418944, c₄: 194.2190812, c₅: 312.807647, c₆: 363.0798918.

The optical constant (relative permittivity) of gold is determined by employing Lorentz-Drude dispersion relation [46]:

(8)$$\varepsilon (\omega ) = 1 + \sum\limits_{k = 1}^6 {\frac{{\Delta {\varepsilon _k}}}{{ - {a_k}{\omega ^2} - i{b_k}\omega + {c_k}}}}$$

where the value of constants are as follows - ε_∞ : 4.26, Δε₁: 21.10833326, Δε₂: 20.57271235, Δε₃: 27.9097635, Δε₄: 104.1014275, Δε₅: 411.6548635, Δε₆: 384.8646853; a₁: 1, a₂: 1, a₃: 1, a₄: 1, a₅: 1, a₆: 1; b₁: 4.083574816, b₂: 3.122733683, b₃: 3.671568571, b₄: 7.469830329, b₅: 23.27526155, b₆: 20.19793471; c₁: 26.7194092, c₂: 43.40234673, c₃: 57.78418944, c₄: 194.2190812, c₅: 312.807647, c₆: 363.0798918.

The variation of real and imaginary part of the optical constants (reletive permittivities) of vanadium oxide (for both the metallic state and the semiconductor state) and gold are shown in Fig. 9.

 

Fig. 9. The variation of optical constant for: (a) the metallic state of VO₂ (which exists for temperatures of the VO₂ film greater than 68°C), (b) the semiconductor state of VO₂ (which exists for temperatures of the VO₂ film less than 68°C), and (c) gold.

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Appendix D: electric field intensity for extended range, the intensity switching ratio for other nanoantenna geometries and effect of length of nanoantenna on intensity swithing ratio and FESR

From Figs. 10(b) and (c), it is observed that for the RBN switch, the plasmon resonance occurs at ∼ 1240 nm wavelength. For semiconductor state of the VO₂ film, the plasmonic mode shifts to ∼ 2100 nm. Similarly, for the RRN switch, the plasmon resonance occurs at ∼1260 nm wavelength for metallic state of the VO₂ film. For semiconductor state of the VO₂ film, plasmonic mode shifts beyond 3200 nm wavelength. This shift in the plasmon resonance can be explained using effective medium approximation. VO₂ in metallic state exhibits negative permittivity whereas the permittivity of VO₂ material in semiconductor state is positive. The effective permittivity of the surrounding medium around the nanoantenna is less when the VO₂ is in metallic sate as compared to the effective permittivity of the surrounding medium when VO₂ is in semiconductor state. As a result, a red shift is observed in plasmon resonance as the VO₂ film is switched from metallic state to the semiconductor state [44].

 

Fig. 10. The electric field intensity enhancement as a function of wavelength in the absence of the nanoantenna for the 40 nm thickness of the VO₂ film. The electric field intensity enhancement as a function of wavelength for: (b) the RBN switch and (c) the RRN switch. The geometrical parameters of the switches are the same as in Fig. 2.

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Figure 11 shows the intensity switching ratio and FESR for various nanoantenna geometries. The maximum intensity switching ratios achieved for the circular ring nanoanntena, the elliptical ring nanoantenna, and the rectangular ring nanoantenna are ∼13, 11, and 9, respectively. The maximum FESRs obtained for the circular ring nanoanntena, the elliptical ring nanoantenna, and the rectangular ring nanoantenna are ∼ 28, ∼11, and ∼11, respectively. The maximum intensity switching ratios achieved for the circular disc nanoanntena, the elliptical disc nanoantenna, and the rectangular plate nanoantennas are ∼6.5, ∼5, and ∼5.8, respectively. The maximum FESRs obtained for the circular disc nanoanntena, the elliptical disc nanoantenna, and the rectangular plate nanoantenna are ∼ 28, ∼11, and ∼11 respectively. It is evident that the intensity switching ratio as well as the FESR are significantly higher for RBN switch and RRN switch as compared to the other ring nanonatnena switches such as circular ring, elliptical ring, and rectangular ring nanoatnena.

 

Fig. 11. The intensity switching ratios (blue) and the FESRs (red) for the plasmonic switches based on the: (a) circular ring nanoantenna, (b) elliptical ring nanoantenna, (c) rectangular ring nanoantenna, (d) circular disc nanonatnenna, (e) elliptical disc nanoantenna, and (f) rectangular plate nanoantenna. The length of the nanoantenna was taken to be 250 nm for both the RBN and RRN switches. The thickness ‘b’ of the VO₂ film was taken to be 40 nm. The thickness ‘t’ of the ring for the circular ring nanoantenna, the elliptical ring nanoantenna and, the rectangular ring nanoantenna was taken to be 20 nm, 15 nm, and 20 nm, respectively. The ratio of length of the major axis to the length of minor axis is 2. The width of the rectangular ring nanoantenna as well as that of the rectangular plate nanoantenna was taken to be 100 nm.

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The effect of length of the nanoantnna intensity switching ratio and FESR is shown in Fig. 12. It is observed that the intensity switching ratio as well as the FESR increases as the length of the nanoantenna is increased. In addition, the peak wavelength shifts undergoes a red-shift as the length of the nanoantenna is increased. The LSPR mode for the metallic state as well as for the semiconductor state undergoes a red shift with an increase in the length of the nanoantenna. As the intensity switching ratio depends on the intensity in the metallic state as well as the semiconductor state, a red-shift is observed in the intensity switching ratio. Moreover, the FESR depends on the intensity swithing ratio, therefore, a redshift is also observed for FESR.

 

Fig. 12. The effect of length of the nanoantenna on: (a) intensity swithing ratio and (b) FESR for RBN switch. The effect of length of nanoantenna on: (c) intensity swithing ratio and (d) FESR for RRN switch. The geometrical parameters of the RBN switch and the RRN switch are the same as those mentioned in Fig. 2.

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Appendix E: radiative decay rate and absorption rate for RBN switch and RRN switch

The normalized radiative rate and the normalized absorption rate for the metallic and semiconductor states of the VO₂­ film are shown in Fig. 13, for the RBN switch (Figs. 12(a) and 12(b)) and for the RRN switch (Figs. 12(c) and 12(d)). It can be noticed that for metallic state of the VO₂ film, a significant radiative rate is observed near to the wavelength of maximum switching ratio whereas, a much lower radiative rate is observed for the semiconductor state of the VO₂ film for both RBN switch as well as RBN switch.

 

Fig. 13. The normalized radiative decay rate (blue) and normalized absorption rate (red) for the metallic state and the semiconductor state of the VO₂ film for RBN switch (a & b) and RRN switch (b & d), respectively. The geometrical parameters of the RBN switch and the RRN switch are the same as those mentioned in Fig. 2.

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Funding

Ministry of Human Resource Development (RP03246G: UAY program, RP03417G: IMPRINT program); Science and Engineering Research Board (RP03932G); Department of Biotechnology, Ministry of Science and Technology, India (RP02829G, RP03150G); Defense Research and Development Organization (RP03356G, RP03436G).

Acknowledgments

We would also like to thank the Digital India Corporation. This publication is an outcome of the R&D work undertaken in the project under the Visvesvaraya PhD Scheme of Ministry of Electronics & Information Technology, Government of India, being implemented by Digital India Corporation (formerly Media Lab Asia). “Portions of this work were presented at the SPIE Photonics West OPTO Conference, San Francisco, California, United States in 2019, Proceedings Volume 10927, Photonic and Phononic Properties of Engineered Nanostructures IX, 1092729.”

Disclosures

The authors declare no conflicts of interest.

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