1. Introduction

Optical switches and modulators based on acousto-optic [1], electro-optic [2], all-optical [3], and MEMS [4] based technologies have been present for more than two decades. However, a new class of smart optical switches and modulators is envisaged in this paper such that they can be tuned to exhibit the switching and modulation behavior not only in the visible region of the spectrum, but also in the near-IR and IR regimes with an advantage of ultrafast switchability. An important class of materials — oxides of Vanadium like VO₂, V₂O₃, and V₂O₅ — are very suitable for use as switching materials at different wavelengths [5]. Vanadium Dioxide (VO₂) has been proposed in this paper to make an efficient switching device because of its ability to demonstrate a reversible phase transition from the semiconductor state to a metallic state. Moreover, VO₂ is attractive for switching needs because of its ultra high speed [6, 7], high spatial resolution [8], near-room temperature transition and viable processes available for VO₂ thin film deposition. In fact, transition time from semiconductor to metallic phase in VO₂ nanoparticles and thin films has been reported to be ~150 fs [9, 10], which is far lesser than the time taken by an acousto-optic switch (few microseconds [11]). VO₂ based switching elements have been used in thermo-chromic applications like flat panel displays, energy-efficient windows, and light modulators [5].

In this paper, we present for the first time — a numerical analysis of the optical characteristics of plasmonic narrow groove nano-gratings coated with a thin film of vanadium dioxide (VO₂) ― whose phase can be changed from semiconductor to metallic by the application of heat, IR radiation or voltage. These plasmonic narrow groove nano-gratings (Fig. 1) ― coated with a thin layer (2-10 nm) of VO₂ ― are proposed because of multi-fold reasons. These VO₂-coated plasmonic nano-gratings are plasmonic nanostructures that employ plasmonic waveguide modes unlike the ones proposed in the past that were based on either propagating surface plasmons or on localized plasmon resonances. Moreover, all the previously reported work was experimental and no numerical modeling work involving optical switching based on plasmonic nanostructures and vanadium dioxide exists in the literature. Furthermore, these nano-gratings allow coupling of incident light, even at normal incidence, into plasmonic waveguide modes. Hence, no coupling mechanism like the Kretschmann configuration is required to couple light into plasmons in these nano-gratings. Since angle-dependant coupling mechanisms such as prism coupling are not required in the proposed narrow groove nano-gratings, this can also help to miniaturize optical switches based on such gratings [12]. In the proposed narrow groove nano-gratings, plasmonic waveguide modes can be excited by either normal or by angled incidence of light. Additionally, these nano-gratings can allow optical switching at multiple wavelengths as there are multiple dips in the reflectance spectra of these nano-gratings. Moreover, the proposed structure is one of the simplest and easiest structures to fabricate, especially, when non-ideal nano-gratings, i.e. nano-gratings with slanted sides, are considered. The combination of this type of grating and the proposed switchable coating material (VO₂) is expected to produce efficient optical switches, potentially with very high switching speeds.

 

Fig. 1 (a) Schematic for the waveguide-mode gold nano-grating coated with a thin layer of VO₂. VO₂ changes phase from its monoclinic semiconductor form to a tetragonal metallic form when heated to ~68 °C, when IR radiation is applied, or under the effect of voltage and (b) Reflectance versus wavelength curve for VO₂ (S), i.e. R_S (λ), and VO₂ (M), i.e. R_M (λ) generated using RCWA simulations. The VO₂ coated narrow groove nano-grating can work as an optical switch in the visible, near-IR and IR range. (c) Schematic for the VO₂ coated narrow groove nano-grating showing the grating width (w₁), the groove width (w₂), the groove height (h), and the thickness (t) of the VO₂ layer.

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In plasmonic nano-gratings, several kinds of plasmonic modes can be coupled: (a) propagating surface plasmon polariton (SPP) modes, (b) hybrid modes in the groove, i.e., a combination of propagating SPP modes and standing waves localized in the groove depth [13–16], and (c) plasmonic cavity or waveguide modes. In the propagating SPP modes, strong EM fields are present primarily at the top surface of the nano-gratings and weak field exist inside the grooves, while in the case of hybrid modes they are present both at the top surface of the nano-gratings and inside the grooves. For deep gratings containing narrow grooves, with the groove-widths << λ as described in this paper, plasmonic waveguide modes are localized inside the grooves. These localized waveguide resonances are characterized by a sharp decrease in the reflectance spectra as well as a substantial enhancement of electric field inside the grooves. In these narrow groove plasmonic nano-gratings, the small groove-widths results in interaction of the surface plasmons on the two opposite walls of the grooves — to form coupled surface plasmon modes. These nano-gratings exhibit cavity resonances for certain plasmonic cavity depths, which are multiples of the wavelength of these coupled plasmon modes [14]. It has to be noted that in rectangular metallic nano-gratings similar to those described in this paper, geometrical cavity resonances can be excited by both TE-polarized and TM-polarized radiation [17–19] but the nature of the 'plasmonic waveguide or cavity modes' employed in this paper is different from those geometrical cavity resonances.

In the plasmonic waveguide mode nano-gratings, there are multiple dips in the reflectance spectra. These multiple dips result from multiple localized waveguide resonances, corresponding to the different standing wave orders of the coupled surface plasmons.As they allow coupling of multiple wavelengths into the plasmonic cavity modes, the VO₂-coated plasmonic waveguide mode nano-gratings allow a controllable and tunable optical switch to be developed such that the switchability could occur at multiple wavelengths.

There are dips in the reflectance spectra for certain wavelengths at which the incident light is coupled into the plasmonic waveguide modes of the VO₂-coated narrow groove nano-gratings. It is the shift of these plasmonic resonance-related dips in the reflectance spectra — due to the semiconductor-to-metal phase transition of VO₂ — which results in switchability of the proposed VO₂-coated plasmonic nano-gratings. The switchability can be quantified by differential reflectance curves ― i.e., difference between the reflectance spectra of VO₂ (S) and VO₂ (M) versus wavelength, i.e., R_S (λ) – R_M (λ). Variations in the groove width (w₂), groove height (h), grating width (w₁), and VO₂ layer thickness (t) change the reflectance spectra of VO₂ (S) and VO₂ (M) thus affecting the wavelengths at which maximum differential reflectance and hence maximum switchability appears, therefore making the structure suitable for use as a switch in a wide spectral range over the visible, near-IR and IR regimes. In a continuous thin film of VO₂ deposited over a continuous gold film (Fig. 2(b)), although the change in reflectance happens when the phase of VO₂ is changed from semiconductor to metal, there is no excitation of plasmonic modes because normally incident light can’t excite plasmonic modes in a continuous metallic film as no coupling mechanism is available. However, with the change in VO₂ layer thickness from 2 nm to 15 nm, the difference in the reflectance curves of VO₂ (M) and VO₂ (S) phase increases. When bulk VO₂ is considered (Fig. 2(a)), switchability is possible but no tunability of this switchability can be done as no structural parameters can be varied to achieve this tunability. This is opposed to the case of the plasmonic nano-grating structure proposed in this paper (Fig. 2(c)), when the plasmonic waveguide modes can be excited and tuned to different switching wavelengths and switching magnitudes. We would like to mention that tunability — both in terms of the magnitude of switchability and the wavelengths at which this switchability can be achieved — is possible in such optical switches by varying the various grating geometric parameters during the fabrication of these nano-gratings.

 

Fig. 2 RCWA simulations showing reflectance versus wavelength (λ) curves for (a) Bulk VO₂, (b) Thin film of VO₂ over gold, and (c) Gold narrow groove nano-gratings covered with a thin film of VO₂. The parameters such as the height of the grating above the substrate surface (h), the grating width (w₁), the narrow groove width (w₂), and the thickness of VO₂ (t) film were varied in the simulations.

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VO₂ is a transparent semiconductor [5, 20–22] with a band gap of ~0.6-0.7eV [8] at the room temperature but changes to a highly reflective metal at the semiconductor to metallic phase transition (SMPT) temperature of 68 °C. This results in a rapid decrease in optical transmittance in the near-IR range and an orders of magnitude change in electrical resistivity. The heating can also be induced by the application of an IR laser which could be either a continuous or a pulsed laser [23, 24]. Moreover, this change could also happen as a result of voltage application [25–27]. This reversible change happens due to the change of the crystal structure of VO₂ from its meta-stable monoclinic form to its stable tetragonal form above its transition temperature which is also accompanied by changes in the band structure [28–30].

The VO₂-based narrow groove nano-gratings proposed in this paper can be easily fabricated by improved technologies like TEB-Ablation Lithography [31], sub-10 nm imprint lithography [32], or Atomic Layer Deposition followed by etching [33]. VO₂ thin films of thicknesses ranging from 2 nm-10 nm can be fabricated by a highly conformal film deposition process such as Atomic Layer Deposition [34].

With the recent advances in nanofabrication and thin film deposition techniques, the VO₂-coated narrow groove plasmonic nano-gratings being proposed in this paper can be physically realized. Since the fabrication of the ideal nano-gratings with parallel side-walls can be complex, we also analyze 'non-ideal nano-gratings' ― the term 'non-ideal' being used to describe nano-gratings with slanted or non-parallel sidewalls. These 'non-ideal nano-gratings' are easy to fabricate as compared to the nano-gratings with parallel sidewalls and are hence promising from the point of view of physical realization of the proposed plasmonic switching devices. Moreover, the VO₂ coated 'non-ideal nano-gratings' show significant switching even for the minimum gap between the nano-gratings being greater than 20 nm, thereby making them easy to fabricate. These nano-gratings can therefore combine the switchability ― offered by the phase change of VO₂ ― and the tunability of this switching ability over different wavelengths ― offered by the varying the grating structure during its fabrication ― to yield an ultrafast tunable optical switch over different regimes of the wavelength spectrum.

2. Numerical modeling using RCWA

The gold narrow groove nano-grating structure with a thin layer of VO₂ was simulated for determining its reflectance as a function of wavelength (i.e. its reflectance spectra) using DiffractMOD 9 by RSoft. DiffractMOD is based on RCWA, i.e., Rigorous Wave Coupled Analysis which is a semi-analytical method in computational electrodynamics [35]. Since it’s a Fourier Modal method, the fields are represented as a sum of spatial harmonics. RCWA is based on Floquet’s theorem [36] which is used for expanding solutions of periodic differential equations. At each interface between the layers, the boundary conditions are matched and the computation is completed. However, higher order Floquet’s functions are ignored depending on the accuracy and convergence speed required [37]. This makes the infinitely large algebraic equations finite and solvable.

Using RCWA, gold nano-gratings on top of gold substrates — with a thin layer of VO₂ over-coating the nano-gratings — were studied. The grating width w₁ (Fig. 1(c)) and the groove width w₂ were changed to vary the periodicity of the grating and the width of the nanogroove, respectively. It is to be noted that w₂ is the groove width between the two adjacent VO₂ walls as shown in Fig. 1(c). In this paper, we study the effect of varying w₁ from 50 nm to 200 nm, and varying w₂, i.e., the groove width from 2 nm to 15 nm on the reflectance vs. wavelength curves. The height of the gold nano-gratings above the substrate surface, i.e., h is varied from 50 nm to 250 nm. Since the narrow groove nano-grating is covered with a thin layer of VO₂, the thickness of this layer (t) was varied from 2 nm to 9 nm to observe the effect of changing thickness on reflectance for both semiconductor and metallic phase of VO₂. Non-ideal nano-gratings with slanted side-walls were also simulated. Slanted gold and silver nano-gratings with flat and rounded tops were analyzed for their reflectance spectra as the thickness of the VO₂ layer is changed from 2 nm to 9 nm. After accounting for material dispersion, we analyzed the total reflected power for all the above cases with five Fourier harmonics using DiffractMOD in a wavelength range of 0.3 um to 2.5 um in steps of 1 nm between adjacent wavelengths. The differential reflectance — i.e., the difference between the reflectance spectra of VO₂ (S) and VO₂ (M) — was also calculated as a function of wavelength for all the cases. The dielectric constants of gold film [38] and VO₂ thin film [39] are based on Lorentz-Debye model. The polarization of the incident optical radiation is taken as TM polarization for all calculations described in this paper.

3. Results and discussions

The reflectance versus wavelength curves for the semiconductor phase of VO₂ and the metallic phase of VO₂ — as well as the differential reflectance versus wavelength curves between the semiconductor and the metal phase — were observed and analyzed. As mentioned previously, there is an existence of plasmonic waveguide modes, i.e. standing waves localized in the groove depth. The effect of changing the nano-grating height, the groove width, the grating width and the thickness of the VO₂ layer are analyzed in the following sections.

The authors would also like to add that the figure of merit of this optical switch is based on its ability to switch ─ which is given by the magnitude of the peak differential reflectance ─ as a function of the loss characteristics. The loss characteristic is given by the imaginary part of the permittivity for VO₂(S) and VO₂(M) at the wavelength of the peak differential reflectance. For the proposed VO₂ based plasmonic nano-grating, the switchability is proportional to the ratio of the imaginary part of VO₂(S) to the imaginary part of VO₂(M). If the complex permittivity of VO₂(S) at the peak differential reflectance wavelength is ε_S' + jε_S”, and that of VO₂(M) is ε_M' + jε_M” at the peak differential reflectance wavelength, then the figure of merit will be based on the ratio ε_M”/ ε_S” at the peak differential reflectance wavelength. Therefore, as the ratio of the imaginary part of the metal to the imaginary part of the semiconductor phase of VO₂ increases, there is a proportional increase in the switchability.

In the following sections, we present a numerical analysis of the effect of the grating parameters on the magnitude of switchability — provided by these VO₂ coated narrow groove nano-gratings — as well as on the wavelengths at which these optically switchable nano-gratings can be employed. We also analyze the effect of the angle of incidence of radiation on the magnitude of switchability. In the later sections, 2-D VO₂-coated plasmonic nano-gratings are also proposed for operation with un-polarized light.

3.1 Effect of changing the height (h) of the VO₂-coated narrow groove plasmonic nano-gratings on differential reflectance

The effect of changing the height of the VO₂-coated narrow groove plasmonic nano-gratings on differential reflectance is analyzed for two reasons — to observe the possibility of operating with different source or laser wavelengths when employing such nano-gratings as switches and to observe the magnitude of switchability at different nano-grating heights. On increasing the height of the nano-grating, i.e., the groove depth, multiple dips in reflectance spectra of these nano-gratings were observed. As the various dips in reflectance spectra of the narrow groove nano-gratings correspond to various plasmonic waveguide modes in these nano-gratings, there are more plasmonic waveguide modes present as the height of the nano-grating is increased. The differential reflectance maps as a function of wavelength and groove width, w₂, are shown for different heights, i.e., 50 nm, 150 nm, and 250 nm (Fig. 3(a), Fig. 3(c), Fig. 3(e)). The peaks in the differential reflectance spectra — i.e., the difference between the reflectance spectra of VO₂ (S) and VO₂ (M) — were obtained for the different plasmonic waveguide modes for the VO₂ (S) and the VO₂ (M) phases (i.e. mode 1, mode 2, etc.) and have been labeled as DR_Peak mode 1, DR_Peak mode 2, DR_Peak mode 3, etc. in this paper (Fig. 3(b), Fig. 3(d), and Fig. 3(f)). As the height increases, the number of wavelengths or the number of DR modes corresponding to the maxima/minima of differential reflectance increase, thereby allowing multiple wavelengths at which the switching can be carried out. With the height of the grating above the substrate surface being 50 nm (when t = 2 nm, w₂ = 2 nm and w₁ = 50 nm was used), the DR_Peak mode 1 corresponds to a wavelength of 1544 nm and DR_Peak mode 2 to a wavelength of 967 nm as shown in Fig. 3(b). In these simulations the complex permittivity of VO₂ (S) was taken as 8.6 + j2.8 [36] at the wavelength of the reflection dip, which is 1290 nm (See Fig. 3(a)). In the case of VO₂ (M), the complex permittivity was taken as −2.5 + j8.9 [36] at the wavelength of the reflection dip, which is 1424 nm.. It can thus be clearly seen that the loss in case of the VO₂ (M) coated nano-grating is more than that of the VO₂ (S) coated nano-grating as the imaginary part of the complex permittivity for VO₂ (S) is greater than that of VO₂ (M). However, as the height increases to a value of 100 nm, DR_Peak mode 1 and DR_Peak mode 2 are red shifted to wavelengths of 2406 nm and 1088 nm, whereas there also is an appearance of an additional DR_Peak mode 3 at 756 nm. When the height is increased to 150 nm, DR_Peak mode 2 and 3 appear at 1305 nm and 911 nm. DR_Peak mode 1 is not visible for h = 150 nm and w₂ = 2 nm as it has red shifted to a value beyond 2.5 μm (Fig. 3(d)). Moreover, a new mode appears at 729 nm which we designate as DR_Peak mode 4. As the height is increased further to 200 nm, wavelengths of peak differential reflectance for modes 2, 3 and 4 red shift to 1579 nm, 1075 nm, and 820 nm, respectively. These modes shift to values of wavelengths of 1850 nm, 1238 nm and 934 nm when the height is increased to 250 nm along with the appearance of DR_Peak mode 5 at 783 nm (see Fig. 3(f)). Therefore, with an increase in the groove depth or the height of the nano-gratings, we observe appearance of higher modes and disappearance of the lower modes along with a red-shift in the wavelengths of switchability for the individual modes.

 

Fig. 3 Effect of height, h, of the VO₂-coated narrow groove plasmonic nano-gratings on the differential reflectance map as a function of wavelength and groove width for (a) h = 50 nm, (c) h = 150 nm, and (e) h = 250 nm. These maps show several bands corresponding to different DR modes that are coupled into the nano-gratings. Effect of height on the differential reflectance versus wavelength curves for (b) h = 50 nm, (d) h = 150 nm, and (f) h = 250 nm. In all the cases above, t = 2 nm, w₂ = 2 nm, and w₁ = 50 nm were taken.

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This suggests the possibility of switching with different light sources having different wavelengths since multiple dips in the reflectance spectra are observable for larger heights of the nano-gratings. As the depth of these plasmonic waveguide mode nano-gratings is increased, the number of wavelengths at which there are dips in the reflectance spectra increases. This happens as when the depth of these nano-gratings is increased, multiple cavity resonances can be localized inside the narrow grooves between the opposite walls of the metallic nano-gratings [12–16]. This enables tunability of the optical switching wavelengths by varying the nano-grating height. In addition, Fig. 4 shows the electromagnetic field profiles for the plasmonic narrow groove nano-grating of 150 nm of height covered with a thin layer (2 nm) of VO₂ (S) when operated at the resonant wavelength of 1106 nm and at an off-resonant wavelength of 950 nm. The grating width is 50 nm in this case and the groove width is 2 nm which corresponds to a distance of 6 nm between adjacent gold walls. The enhancements in the narrow groove region can be seen in Fig. 4.

 

Fig. 4 Electric field intensity enhancement (|E|²/|E₀|)²) versus wavelength — calculated using finite difference time domain (FDTD) simulations for normally incident radiation — inside a VO₂-coated gold narrow groove nano-grating for the semiconductor state of the VO₂ thin film (i.e. VO₂(S)). The insets show the E-field spatial profiles inside the grooves (i.e. between the adjacent VO₂ walls of the VO₂-coated gold nano-gratings) at a resonant wavelength of 1106 nm and an off-resonant wavelength of 950 nm, as shown by arrows. In the FDTD simulations, the groove height was taken to be 150 nm. The groove width, w₂, was taken as 2 nm, while the thickness of the VO₂ layer was taken to be 2 nm. The grating width, w₁, for the above simulations was taken to be 50 nm.

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3.2 Differential reflectance maps

On observation of the relationship between changing wavelength and changing w₂ (which is connected to the narrow groove width and hence to the periodicity of the grating), we observed various bands with maxima and minima of differential reflectance at different wavelengths. It is this band which highlights the tunability of the maxima of differential reflectance with wavelength. Such bands are shown in Fig. 3(a), Fig. 3(c) and Fig. 3(e), where the scales on the right show the magnitude of differential reflectance.

In Fig. 5 and Fig. 6, the relationship between wavelength and w₂ — as a function of grating width, 'w₁' and the thickness of the VO₂ layer, ‘t’ — can be seen for a height of 50 nm and, 150 nm respectively. The scales on the right show the magnitude of differential reflectance.

 

Fig. 5 Maps showing differential reflectance plotted as a function of wavelength and the nano-grating groove width, w₂. The matrix of the differential reflectance maps is shown for different values of VO₂ layer thickness, t, and the grating width, w₁, at a constant nano-grating height, h = 50 nm.

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Fig. 6 Maps showing differential reflectance plotted as a function of wavelength and the groove width, w₂. The matrix of the differential reflectance maps is shown for different values of VO₂ layer thickness, t, and grating width, w₁, at a constant nano-grating height, h = 150 nm.

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In Fig. 5, a matrix is shown such that each differential reflectance map shows the bands for a particular value of the VO₂ layer thickness and w₁. When the height of the nano-grating is 50 nm, as the values of the VO₂ layer thickness are increased from 2 nm to 8 nm, there is a red shift in the band corresponding to DR_Peak mode 1. Also, as the values of w₁ are increased from 50 nm to 200 nm, there is a red shift in the wavelengths corresponding to both DR_Peak mode 1 and DR_Peak mode 2. It can be seen in the differential reflectance maps shown in Fig. 6 that, for a nano-grating height of 150 nm, a higher number of bands is present as compared to the case when the nano-grating height is 50 nm (Fig. 5). This is because for a height of 150 nm, there is an occurrence of additional plasmonic waveguide modes due to a deeper groovedepth. DR_Peak mode 1 can’t be seen since it occurs for values of wavelength beyond 2500 nm. Therefore, only DR_Peak modes 2, 3 and 4 can be observed (Fig. 6).

3.3 Effect of changing the nano-grating groove width (w₂)

RCWA simulations were carried out to study the effect of groove width on the differential reflectance spectra, in order to determine if larger groove widths could also provide significant switchability. On changing w₂, for a fixed w₁, t and h, it was observed that, for the semiconductor phase of VO₂, as w₂ was reduced from 15 nm to 2 nm, the dip of the reflectance spectra went deeper. This happens because as the value of groove width — which is the gap between the adjacent VO₂-coated sidewalls — is reduced, light is coupled more strongly into the plasmonic waveguide modes in the narrow grooves of these nano-gratings, which also leads to an increased field enhancement inside the grooves. In these narrow groove plasmonic nano-gratings, smaller groove-widths (w₂) results in more interaction of the surface plasmons on the two opposite walls of the grooves — to form strongly coupled surface plasmon modes. This leads a lower reflectance resulting in deepening of the dip in the reflectance spectra. However after the transition from VO₂ (S) to VO₂ (M), the metal part of the plasmonic waveguide formed increases. This causes an increase in the loss/absorption in the metal part, therefore causing damping and hence leading to more damping of the plasmonic waveguide modes. Since, reducing w₂ will imply a major part of the plasmonic waveguide mode encountering the metal, reduction of w₂ will lead to higher loss and lower coupling between the plasmonic waveguide modes in the adjacent grooves which in turn would imply a higher reflectance — i.e. the depth of reflectance dip reduces on reducing w₂. The differential reflectance curves revealed that the switchable characteristics of such narrow groove nano-gratings were tunable over different wavelengths. With the thickness of the VO₂ layer being 2 nm, the height of the grating above the gold substrate being 50 nm, and the value of w₁ (grating width) being 50 nm, the maximum differential reflectance occurred at wavelength values of 967 nm (17.54%) and 1544 nm (41.18%) for w₂ = 2 nm (Fig. 7).

 

Fig. 7 Graphs showing (a) Reflectance versus wavelength curves for VO₂ (S) coated nano-grating, (b) Reflectance versus wavelength curves for VO₂ (M) coated nano-grating, and (c) Differential reflectance versus wavelength curves for VO₂ coated nano-grating. (d) Differential reflectance versus wavelength showing the effect of normalized ‘w₂’, i.e., ‘w₂/P’ where the period of the nano-grating, P = w₂ + w₁ + 2*t on the maxima of the differential reflectance. For all the above cases, t = 2 nm, h = 50 nm, and w₁ = 50 nm were taken.

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The differential reflectance magnitude of 41.18% at 1544 nm shows that a large switchability can be achieved for smaller dimensions making the VO₂ based nano-grating an efficient switch for the near-IR and IR regimes also. However as the value of w₂ is changed to 4 nm, the wavelengths of maximum differential reflectance are altered to 871 nm (19.16%) and 1175 nm (28.39%) which shows that a change in w₂, i.e., the groove width can lead to tunability of the switching wavelength, i.e., the wavelength of maximum differential reflectance between semiconductor and metallic phases of VO₂. This tunability region extends from 629 nm for w₂ = 15 nm where the value of differential reflectance is 2.65% to 1544 nm for w₂ = 2 nm. Analysis in a wavelength range of 0.3 um to 2.5 um revealed that intermediate values of w₂ lead to a maximum differential reflectance at various wavelengths like 1403 nm and 944 nm (w₂ = 2.5 nm), 1300 nm and 918 nm (w₂ = 3 nm), 1175 nm and 871 nm (w₂ = 4 nm), 1047 nm and 791 nm (w₂ = 6 nm), 1009 nm and 722 nm (w₂ = 8 nm), 992 nm and 679 nm (w₂ = 10 nm), 947 nm and 657 nm (w₂ = 12 nm), and 930 nm and 638 nm (w₂ = 14 nm). In addition, Fig. 8 elaborates the effect of changing the groove width 'w₂' on the tunability of different DR modes for a nano-grating height of 250 nm. It was observed that — while the nano-grating height allows very large tuning of wavelengths of switchability, changing the groove width 'w₂' can provide an ability to fine-tune the different wavelengths of switchability as well as the magnitude of switchability at these wavelengths for a constant height.

 

Fig. 8 Differential reflectance maps as a function of wavelength and groove width, w₂, of the VO₂-coated narrow groove plasmonic nano-gratings for (a) w₂ = 4 nm, and (c) w₂ = 6 nm. These maps show the effect of groove width on the maxima in the differential reflectance (labeled as DR_Peak Modes) and the minima in the differential reflectance (labeled as DR_Dip Modes). Differential reflectance versus wavelength curves for (b) w₂ = 4 nm, and (d) w₂ = 6 nm showing the DR_Peak Modes and the DR_Dip Modes. In all the cases above, h = 250 nm, t = 2 nm, and w1 = 50 nm were taken.

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Hence switchability is possible in the near-IR and IR regions, and not just the visible region, with this VO₂ coated nano-grating. It was observed that the magnitude of the maxima of differential reflectance — at the peak resonance wavelength — decreases with an increase in the value of w₂ (see Figs. 9(a)-9(b)), which can also be seen in the variations in Figs. 7(a)-(b). In addition, the reflectance curves red shift on decreasing the groove thickness w₂ for both VO₂ (S) and VO₂ (M). As w₂, i.e., the groove width reduces; there is a reduction in the distance between the two opposite walls of an individual narrow groove. This reduces the restoring force (as the restoring force will be maximum when the walls are farthest apart, according to the Drude model), thereby reducing the plasmon resonance frequency and hence leading to a red shift in the wavelength of minimum reflection for both VO₂ (S) and VO₂ (M) on reducing w₂. Therefore, tuning the value of w₂ also tunes the wavelength at which maxima of differential reflectance occurs and thus offers an opportunity for the design of a switchable device over a wide wavelength spectrum.

 

Fig. 9 Effect of varying w₂ on: (a) Peak resonance wavelength for DR_Peak mode 2, (b) Peak differential reflectance for DR_Peak mode 2, (c) Peak resonance wavelength for DR_Peak mode 1, and (d) Peak differential reflectance for DR_Peak mode 1. For all the above cases, w₁ = 50 nm, h = 50 nm, and t = 2 nm were taken.

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The authors would also like to add that, although an exhaustive scan of the absolute parameter values has been carried out in this paper, normalized parameter values can also be used to aid in the quick design of such nano-gratings with a freedom to choose any opto-geometrical parameters while designing such switches. Figure 7(d) shows the effect of ‘normalized w₂’, i.e., w₂/P, on the differential reflectance curves, where w₂ has been normalized by dividing it by the total period (P) of the nano-grating which is w₁ + w₂ + 2*t.

3.4 Effect of changing thickness (t) of the VO₂ layer

In addition to the tunability offered by the changing grove width, there also is a possibility of varying the thickness of the VO₂ layer to achieve the fine tunability of the switching wavelength. Moreover, it is important to study the effect of thickness of the VO₂ layer to understand if small changes in the VO₂ layer thickness can lead to significant changes in switchability. On changing the thickness of the VO₂ layer, the wavelengths of maximumdifferential reflectance change, as does the magnitude of this reflectance (See Fig. 10 and Fig. 11). There is slight shift in the wavelengths of switchability as the thickness is increased from 2 nm to 9 nm. For w₂ = 2 nm, w₁ = 50 nm and height of the grating above the surface of the substrate being 50 nm, the wavelengths of maximum differential reflectance are 967 nm and 1544 nm at t = 2 nm for DR_Peak mode 2 and DR_Peak mode 1 respectively, whereas they shift to 894 and 1704 nm on changing t to 4 nm. Further tuning of the thickness to a value of 8 nm leads to the shift of these wavelengths to 831 nm and 1969 nm for DR_Peak mode 2 and 1 respectively. Therefore, it can be observed that although there is not a very big shift in the wavelengths corresponding to DR_Peak mode 2 (967 nm for t = 2 nm to 822 nm for t = 9 nm), a slight blue shift can be seen in Fig. 11(b).

 

Fig. 10 Graphs showing the effect of thickness, t, of the VO₂ layer on the (a) Reflectance versus wavelength curves for VO₂ (S) coated nano-grating, and (b) Reflectance versus wavelength curves for VO₂ (M) coated nano-grating, and (c) Differential reflectance versus wavelength curves showing the effect of thickness on the tunability of the peak differential reflectance wavelengths. For all the above cases, h = 50 nm, w₂ = 2 nm, and w₁ = 50 nm were taken.

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Fig. 11 Differential reflectance versus wavelength curves showing the effect of thickness, t, of the VO₂ layer on the tunability of the peak differential reflectance wavelengths for different groove widths: (a) w₂ = 6 nm (b) w₂ = 10 nm (c) w₂ = 15 nm. For all the above cases, h = 50 nm, and w₁ = 50 nm were taken.

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However, there is a visibly large red shift with the increase in thickness for wavelengths corresponding to DR_Peak mode 1 (1544 nm at t = 2 nm to 2016 nm at t = 9 nm), as shown in Fig. 12(b). Furthermore, Fig. 10(b) shows a broadening of the reflectance curve as the metal layer thickness is increased. This is due to an increase in damping with an increase in the metal layer thickness. We also observe in Fig. 10(a) that the amount of broadening of the plasmonic waveguide mode resonance-related dip is much less for VO₂ in the semiconductor state. Hence, the broadening of the peaks in the differential reflectance curves (shown in Fig. 10(c)) follows that of VO₂ in the metallic state (shown in Fig. 10(b)). Also, as the thickness of the VO₂ layer is increased,there is a reduction in the magnitude of the differential reflectance for DR_Peak mode 1, whereas the magnitude of differential reflectance for DR_Peak mode 2 remains same for almost all values of thickness. The reduction in differential reflectance for DR_Peak mode 1 happens when the thickness of the thin Vanadium dioxide film — when it exists in the metallic phase (i.e. VO₂ (M)) — is decreased, because the internal damping (Γ_i) or absorption in the metal reduces (the thinner the metal layer, the lesser is the loss). Moreover, with decreasing VO₂ (M) metal thickness, the out-coupling of the plasmonic waveguide modes into radiation increases [40]. Both these effects imply an increase in coupling and reduction in reflectance (Fig. 10(b)). As the thickness of the VO₂ (M) layer is increased, the electric field in the region (comprising of VO₂ (M) layer-air-VO₂ (M) layer) experiences a large increase in the effective refractive index. Hence, there is a very large red-shift in the plasmonic waveguide mode resonance-related peaks corresponding to this structure as the thickness of the VO₂ (M) layer is increased (see Fig. 10(b)).

 

Fig. 12 Effect of thickness, t, of the VO₂ layer on the (a) Peak resonance wavelength for DR_Peak mode 2 (b) Peak differential reflectance for DR_Peak mode 2 (c) Peak resonance wavelength for DR_Peak mode 1 (d) Peak differential reflectance for DR_Peak mode 1. For all the above cases, h = 50 nm, w₁ = 50 nm and w₂ = 2 nm were taken.

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Similarly, for the semiconductor phase of VO₂, the effective insulator medium of the VO₂-coated plasmonic waveguide structure is comprised of the VO₂ (S) layers on either side with air in between. Gold on either side of this effective insulator makes it a plasmonic waveguide structure. As the thickness of the VO₂ (S) layer is increased, the electric field in the insulator region (comprising of VO₂ (S) layer-air-VO₂ (S) layer) experiences a slight increase in the effective refractive index. Hence, there is a very small red-shift in the plasmonic waveguide mode resonance-related peaks corresponding to this structure as the thickness of the VO₂ (S) layer is increased (see Fig. 10(a)).

Since there is no major change in the semiconductor phase reflectance dip when the thickness of the semiconductor phase VO₂ changes (see Fig. 10(a)), the differential reflectance curve (see Fig. 10(c)) also shows that the magnitude of differential reflectance at the peak resonance wavelength reduces with increasing thickness. This is in agreement with the decrease in the plasmonic waveguide mode resonance-related dip with an increase in the thickness of the VO₂ layer in the case of VO₂ (M).

3.5 Effect of grating width (w₁) on wavelength tunability

We also explore the effect of varying grating width and hence periodicity of the nano-grating on the modes, on the magnitude of switchability, as well as on the wavelengths at which this switchability occurs. It can be seen in Fig. 13 that, as ‘w₁’_, the grating width — which is related directly to periodicity — is increased, there is a red shift in the wavelength corresponding to DR_Peak mode 1, when the height of the grating above the surface of gold is 50 nm, the groove width, w₂ is 2 nm and the thickness of the VO₂ film is 2 nm. It can be observed that along with a clear red shift from 967 nm to 1058 nm when w₁ changes from 50 nm to 250 nm, there is a reduction in the magnitude of maximum differential reflectance — from 17.54% for w₁ = 50 nm to 4.03% for w₁ = 250 nm — corresponding to DR_Peak mode 2. The same pattern is observed for DR_Peak mode 1 also. However, for DR_Peak mode 1, the red shift in the wavelengths is quite significant, i.e., from 1544 nm to 1766 nm. This is also accompanied by a reduction in the differential reflectance magnitude from 41.1% (w₁ = 50 nm) to 20.91% (w₁ = 250 nm) as shown in Fig. 14.

 

Fig. 13 Effect of the grating width, w₁, on the (a) Reflectance versus wavelength curve for VO₂ (S) coated nano-grating (b) Reflectance versus wavelength curve for VO₂ (M) coated nano-grating and (c) Differential reflectance versus wavelength curve. In all the above cases, w₂ = 2 nm, h = 50 nm and t = 2 nm were taken.

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Fig. 14 Effect of the grating width, w₁, on the (a) Peak resonance wavelength or DR_Peak mode 2 (b) Peak differential reflectance for DR_Peak mode 2 (c) Peak resonance wavelength for DR_Peak mode 1 (d) Peak differential reflectance for DR_Peak mode 1. For all the above cases, w₂ = 2 nm, h = 50 nm and t = 2 nm were taken.

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As the value of w₁ decreases — i.e. periodicity of the structure decreases — the interaction between the plasmonic waveguide modes in adjacent grooves increases, thereby reducing the reflection and leading to a deeper dip in the reflectance spectra. This behavior can be seen both in the semiconductor and metallic phase of VO_2. Hence, the grating width 'w₁' also allows fine-tuning of the wavelengths at which the switchability occurs.

3.6 Analysis of the VO₂-coated plasmonic nano-gratings for angled incidence of radiation

The authors would like to highlight that the proposed switch, in its operation in the reflection mode, can work well with both normally incident light as well as with angled incidence of light. However, in this paper, the analysis focuses primarily on normally incident light to highlight that incident light can be coupled into plasmonic waveguide modes in these nano-gratings without the need for any specific requirements for the angle of the incidence of light, as is the case in prism coupling mechanism. When normal incidence of radiation is employed, a polarization beam splitter would be needed to separate the incident and the reflected beams. In order to carry out optical switching using the VO₂-coated plasmonic nano-gratings without employing a beam splitter, an optical configuration can be employed in which light is incident on the nano-gratings at an angle and the reflected light is collected by a photodetector placed normal to the nano-grating surface.

In order to highlight the viability of this optical switch at angles of incidence other than zero degree with the normal, an analysis of the behavior of this optical switch with angled incidence was also carried out. Figure 15(a) shows the effect of the angle of the incident radiation (with the normal) on the reflectance spectra for a plasmonic nano-grating coated with a thin layer of VO₂(S) when the height of the nano-grating above the surface of the substrate is 150 nm. The narrow groove width (w₂) is 2 nm, the grating width (w₁) is 50 nm and the thickness (t) of the VO₂ layer is 2 nm. It can be observed that as the angle of incidence is increased from 0° to 75°, there is a decrease in the reflectance, i.e., the reflectance curve deepens more with the increase in the angle of incidence with the normal. This indicates that as the angle is increased, there is even more coupling of the incident radiation into the plasmonic waveguide modes of the nano-grating. However, as the angle increases further to 80°, the reflectance again begins to increase indicating a reduction in the coupling of light to the nano-grating. A similar effect can be seen for the plasmonic nano-grating with a thin layer of VO₂(M) in Fig. 15(b). Figure 15(c) shows the effect of the angle of incidence on the differential reflectance (reflectance of VO₂(S) – reflectance of VO₂(M)) of the VO₂-coated plasmonic nano-gratings. It is clearly visible that the maximum differential reflectance, and hence the maximum switchability, occurs when the angle of incidence is 75° with respect to the normal. The inset of the Fig. 15(c) shows the angular interrogation of the plasmonic nano-grating done at a wavelength of 1.28 µm for VO₂(M), VO₂(S) and the differential reflectance (1.28 µm is the wavelength of maximum differential reflectance for normal incidence). Therefore, the proposed optical switch is not limited to normally incident light, but can be employed for any angle of incidence.

 

Fig. 15 Effect of the angle of incident radiation on (a) the reflectance spectra of VO₂(S)-coated narrow groove plasmonic nano-gratings (b) the reflectance spectra of VO₂(M)-coated narrow groove plasmonic nano-gratings and (c) the differential reflectance spectra of the VO₂-coated narrow groove plasmonic nano-gratings. Inset shows the reflectance for VO₂(S) in blue color, reflectance for VO₂(M) in red color, and the differential reflectance in green color as a function of incident angle. In all the cases above, t = 2 nm, w₂ = 2 nm, w₁ = 50 nm and h = 150 nm were taken.

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3.7 Comparison of the ideal nano-gratings with non-ideal nano-gratings

A comparison between the ideal nano-gratings — i.e. nano-gratings with parallel side-walls — and the 'non-ideal nano-gratings' — i.e. nano-gratings with non-parallel or slanted side-walls — was also carried out using RCWA simulations. These 'non-ideal nano-gratings' are experimentally realizable using the currently available nanofabrication and deposition techniques [41, 42]. The RCWA analysis was carried out for two types of 'non-ideal nano-gratings'. The first set included slanted gold and silver nano-gratings with flat tops (see Figs. 16(a)-16(b)) covered with a thin film of VO₂. The second set included the slanted gold and silver nano-gratings with rounded tops (Figs. 16(e)-16(f)) and covered with a thin VO₂ film layer.

 

Fig. 16 (a) Schematic showing slanted gold (Au) nano-gratings with flat top, (b) Schematic showing slanted silver (Ag) nano-gratings with flat top. RCWA simulations showing the variation in the differential reflectance with wavelength as the thickness of the VO₂ layer is varied from 2 nm to 9 nm in the (c) Slanted gold nano-gratings with flat top and in the (d) Slanted silver nano-gratings with flat top. Height of the grating, h is 200 nm, period of the grating is 120 nm and the thickness of the VO₂ thin film is varied between 2 nm and 9 nm. (e) Schematic showing slanted gold (Au) nano-gratings with round-top and (f) Schematic showing slanted silver (Ag) nano-gratings with round-top. RCWA simulations showing the variation in the differential reflectance with wavelength as the thickness of the VO₂ layer is varied from 2 nm to 9 nm in the (g) Slanted gold nano-gratings with round top and in the (h) Slanted silver nano-gratings with round top. (i) SEM cross-section of the silicon mold used to prepare the flat-top silver nano-gratings. (j) SEM cross-section of the silver nano-gratings prepared by employing resistless nano-imprinting in metal (RNIM) [41]. (k) TEM cross-sections of the slanted gold nano-gratings with round-top [42]. The scale bar is 100 nm. These nano-gratings can be uniformly coated with a 2 nm-9 nm conformal layer of VO₂ by employing atomic layer deposition (ALD).

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RCWA Analysis was carried out for slanted gold and silver nano-gratings having flat tops, with the VO₂ thickness values ranging from 2 nm to 9 nm. The gap between two adjacent gold pillars (at the bottom of the pillars) was kept to be 20 nm and the height of the grating was kept as 200 nm. The groove width was modulated by the thickness of the VO₂ layer, reaching a minimum of 2 nm when the thickness of the VO₂ layer is 9 nm on either side of the narrow groove. It was observed that there was a red shift of the peak wavelength of the differential reflectance spectra as the value of thickness of the VO₂ layer was increased in both gold and silver based slanted nano-gratings (see Figs. 16(c)-16(d)). This arises from a red-shift of the plasmonic waveguide mode resonance-related dip in the reflectance spectra (for both the semiconductor and the metallic phases of VO₂) of the VO₂-coated plasmonic nano-gratings as the value of thickness of the VO₂ layer is increased. This red-shift in the plasmonic waveguide mode resonance-related dip in the reflectance spectra with an increase in the thickness of the VO₂ layer can be attributed to a greater change in the effective refractive index of the media (a combination of VO₂ film and the air gap, i.e. w₂) lying in between the sidewalls of the metal-coated nano-gratings. As the thickness is increased from 2 nm to 9 nm, the wavelengths of maximum differential reflectance, for the slanted gold nano-gratings with a flat-top, change from 1191 nm (~9%) to 1785 nm (32.6%). However, as the thickness is increased from 2 nm to 9 nm, the wavelengths of maximum differential reflectance, for the slanted silver nano- gratings with a flat-top, change from 1190 nm (~9%) to 1760 nm (~35.6%). It is observed that the magnitude of the maximum differential reflectance for the case of silver is slightly higher than that of the slanted gold nano-grating which can be attributed to the fact that silver is a less lossy material as compared to gold (i.e. it has a lower value of the magnitude of the imaginary part of its dielectric constant as compared to that of gold). The slanted silver nano-gratings with flat tops can be easily fabricated by employing resistless nanoimprinting (see Fig. 16(i)-16(j)) in silver metal (RNIM) [41]. Gold nano-gratings can also be made by employing resistless nanoimprinting in gold metal. Subsequently, these nano-gratings can be coated with a uniform thickness of VO₂ by employing Atomic Layer Deposition (ALD).

Another set of experimentally realizable non-ideal nano-gratings was also simulated. These included the slanted gold nano-gratings (see Fig. 16(e)) and the slanted silver nano-gratings (see Fig. 16(f)), both with rounded tops. For the slanted gold nano-gratings with rounded tops, we observe a change in the wavelength of maximum differential reflectance from 1212 nm (~10.8%) to 1657 nm (~34%) as the thickness of the VO₂ layer varies from 2 nm to 9 nm. The corresponding wavelength of maximum differential reflectance, in the case of slanted silver nano-grating with rounded top varies from 1095 nm (~12%) to 1599 nm (~38.1%). Thus, it can be concluded that the wavelengths of maximum differential reflectance are slightly blue shifted for the case of slanted silver nano-gratings as compared to the slanted gold nano-grating. This is because the regions of spectrum in which silver and gold display minimum loss — or minimum value of the imaginary part of the dielectric constant — are different. Moreover, the value of maximum differential reflectance, in the case of slanted silver nano-gratings is higher as compared to slanted gold nano-gratings as silver is a less lossy material as compared to gold. These 'non-ideal gratings' with rounded tops can be easily fabricated by employing a series of steps. The metal-coated nano-gratings with rounded tops can be developed by first fabricating one-dimensional triangular silicon gratings employing 193 nm deep-UV lithography (using an ASML 5500/950B scanner). Subsequently, in order to reduce the gap between the walls of adjacent nano-gratings — i.e., to bring it down to sub-10 nm gap size — a conformal layer of hafnium oxide or platinum is deposited on these nanowires using atomic layer deposition (ALD). Thereafter, E-beam evaporation is employed to cover these one-dimensional 'non-ideal nano-gratings' with gold or silver [41]. The TEM cross-section of these 'non-ideal nano-gratings' — which were previously fabricated by Dhawan et al. [42] — is shown in Fig. 16(k). These plasmonically active nano-gratings can then be covered with a conformal uniform coating of 2 nm-9 nm VO₂ using atomic layer deposition to fabricate the proposed optical switches.

It is also observed that the slanted nano-gratings (both the flat top and the rounded top nano-gratings) have broadened differential reflectance peaks as compared to those for ideal nano-gratings. This broadness of the differential reflectance curves (and of the reflectance curves for both the semiconductor and metallic states of the VO₂ coating on top of the nano-gratings) in 'non-ideal nano-gratings' can be attributed to superposition of a large number of plasmonic waveguide mode resonance-related dips corresponding to a large number of different gaps (between the sidewalls of adjacent nano-gratings) present in the slanted nano-grating structure; as this leads to several plasmonic waveguide modes being present in the slanted nano-gratings. However, we can observe that not only the ideal nano-gratings, but also the realistically realizable 'non-ideal nano-gratings' can be used as highly efficient optical switches. The VO₂ coated 'non-ideal nano-gratings' show significant switching even for the minimum gap between the nano-gratings being greater than 20 nm and do not have the requirement of the gaps to be less than ~15 nm as is the case of the ideal nano-gratings. As plasmonic nano-gratings with gaps less than 20 nm can be easily fabricated using the state-of-the art nanofabrication capabilities such as electron beam lithography or focused ion beam milling, these non-ideal nano-gratings are easy to fabricate. It has to be noted that although, the magnitude of optical switchability in the non-ideal nano-gratings may be lesser than in the case of ideal nano-gratings, it is high enough to be employed for optical switching applications.

3.8 Two-dimensional (2-D) VO₂-coated plasmonic nano-gratings

Although the 1-D 'VO₂ based plasmonic nano-gratings' proposed in this paper exhibit high switchability and tunability over a wide range of wavelengths, the resonances in the reflectance as well as the switchability can be obtained for all polarizations except when the polarization of the incident radiation is purely TE (although the resonances in the reflectance and the switchability are the highest for TM-polarized light, i.e. when the in-plane angle (θ) is zero). If the in-plane angle (θ) of the incident light (as shown in Fig. 17) falling on these nano-gratings is non-zero, light of any polarization can lead to switchability. It can be seen from Fig. 17 that the angle of incidence, φ, is the angle that the wave-vector makes in the plane of incidence and is measured with respect to the Z axis in the XZ plane. The in-plane angle, θ, is measured from the ZX plane. Figure 17 shows that for all cases where the polarization is not purely TE (Transverse Electric), i.e., the in-plane angle, θ, has a non-zero value, there is an existence of plasmonic waveguide modes. However, for lower values of θ, these modes are very weak and hence lead to very low switchability. This means that — if un-polarized light is incident on these nano-gratings, although the light rays with larger in-plane angles will lead to switchability (as some part of the incident TM radiation will be coupled in to the metallic nano-gratings as plasmonic waveguide modes), the light rays with smaller in-plane angles will lead to low or no contribution in the switchability of the 1-D nano-gratings. Therefore, in this section, we propose 2-D nano-gratings to give the reader an idea of how optical switching can be carried out using the '2-D VO₂ based plasmonic nano-gratings' by employing unpolarized light where all components (s-polarized, p-polarized or a combination of s- and p-polarized light) can lead to switchability even when the in-plane angle is zero. The switchability of these 2-D plasmonic nano-gratings will be significantly higher even at smaller in-plane angles, thus making them more suitable for operation with unpolarized light.

 

Fig. 17 (a) Schematic showing the angle of incidence (φ) and the in-plane angle (θ) for plasmonic nano-gratings. Graphs showing the reflectance spectra for VO₂(S) and VO₂(M) along with the differential reflectance spectra for the 1-D VO₂-coated nano-grating for TE-polarized light when light is incident normally on the nano-grating in the plane of incidence (φ = 0°) but the in-plane angle (θ) is varied as (a) 0° (b) 30° (c) 45° and (d) 90°. The magnitude of differential reflectance is low for lesser in-plane angles and increases as θ increases.

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When 2-D VO₂-coated plasmonic nano-gratings are employed, such that these nano-gratings are periodic along both X and Y directions (See Fig. 18), both TE and TM polarizations of the incident radiation (as well as other polarizations) can be employed for optical switching. The 2-D nano-gratings have the same grating width (w₁) in both X and Y directions, however their groove width is different in both directions, i.e., the groove width is w_2x in the X direction and w_2y in the Y direction. For our analysis, we have used three different ratios of w_2x:w_2y (1:1, 2:1, and 3:1) where the value of w_2y is fixed to 2 nm. The thickness of the VO₂ coating is 2 nm and the height of the grating above the surface of the substrate (h) is 150 nm for this analysis. As can be clearly seen from Fig. 18, the switchexhibits significant switchability with the polarization angle being 0° (s-polarization), 90° (p-polarization) or 45° (with both s- and p- polarizations present). It can be seen from Figs. 18(a)-18(c) that when the nano-grating is symmetric in the X and Y directions, the magnitude of switchability for all the three cases (the polarization angles being 0°, 45°, and 90°) remains the same. For the case of the 2-D nano-gratings being asymmetric (i.e. for w_2x:w_2y being 2:1 and 3:1, respectively) the magnitude of switchability is different for the three cases of polarization of the incident radiation (See Figs. 18(d)-18(i)). It is clearly visible from Figs. 18(d)-18(i) that the magnitude of switchability is significant even with TE-polarized light.

 

Fig. 18 Schematic showing a section of the 2-D 'VO₂ based plasmonic nano-gratings' with the groove widths w_2x and w_2y in the X and Y directions respectively. RCWA simulations, for normal incidence, showing the reflectance spectra and the differential reflectance versus wavelength for w_2x:w_2y = 1:1 when the polarization angle is (a) 0° (p-polarized light) (b) 45° (c) 90° (s-polarized light), w_2x:w_2y = 2:1 when the polarization angle is (d) 0° (p-polarized light) (e) 45° (f) 90° (s-polarized light) and w_2x:w_2y = 3:1 (g) 0° (p-polarized light) (h) 45° (i) 90° (s-polarized light). For all the above cases, w₁ = 50 nm, h = 150 nm and t = 2 nm were used. The in-plane angle, θ, is zero throughout these simulations.

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Tunable optical switches — tunable over different regimes of the wavelength spectrum — based on VO₂-coated narrow groove plasmonic nano-gratings are proposed in this paper. While the optical switching in these nano-gratings arises from the phase change of VO₂, the tunability of this switching ability over different wavelengths arises from varying the grating structure during its fabrication. These nano-gratings can be physically realized by employing the state-of-the-art nanofabrication and film deposition techniques.

4. Conclusions

In this paper, narrow groove gold nano-gratings covered with a thin film of VO₂ were proposed and it was found that there is a possibility of fabrication of an all-spectra tunable switch which can be tuned to different values of wavelengths, by changing the grating parameters like groove depth, groove width, grating line width, and thickness of the VO₂ layer. Since VO₂ changes from its semiconductor to its metallic phase on heating, exposure to infra-red light or on application of voltage, the optical properties of the underlying plasmonic nano-grating can be altered during this phase transition, thereby resulting in switchability. A change in the groove width can tune the switch to substantially high values of switchability in the near-IR and IR regimes and a change in thickness of the VO₂ layer or the width of the nanoline grating can help in fine tuning of the individual modes. Tuning the switch to multiple wavelength sources can be done by increasing the height of the nano-grating above the substrate. Moreover, it was observed that the proposed optical switch is not limited to normally incident light, but can be employed for any angle of incidence. We also showed that 2-D nano-gratings can be employed for optical switching of unpolarized light even when the in-plane angle is zero. Significant switchability was also observed in the case of slanted non-ideal nano-gratings, with flat and rounded tops, that are easy to fabricate. Hence, by varying the nano-grating parameters, the plasmonic waveguide modes in the proposed 1-D and 2-D nano-gratings can be shifted to wavelengths corresponding to particular source/laser wavelengths, and sufficiently large as well as ultra-fast switchability can be achieved at the wavelengths of choice.