Active tuning of the Fano resonance from a Si nanosphere dimer by the substrate effect

Abstract

All-dielectric materials have aroused great interest for their unique light scattering and lower losses compared with plasmonics. Generally, optical properties made by all-dielectric materials can be passively controlled by varying the geometry, size and refractive index at the design stage. Therefore, the realization of active tuning in the field of nanophotonics is important to improve the practicality and achieve light-on-chip technology in the future. Herein, we combine the high refractive index of Si and the phase transition of VO₂ to form an active tuning hybrid nanostructure with higher quality factor by depositing Si nanospheres on the VO₂ layer with an Al₂O₃ substrate. As the temperature goes up, the refractive index of the VO₂ layer switches from high to low. The scattering intensity of the magnetic dipole resonance of Si nanospheres decreases differently depending on their size, while the intensity of the electric dipole resonance remains almost unchanged. Meanwhile, Fano resonances are observed in the Si nanosphere dimers with a continuous variable Fano lineshape when adjusting the temperature. Mie theory and substrate-induced resonant magneto-electric effects are used to analyze and explain these phenomena. Tuning of the Fano resonance is attributed to the substrate effect from the interaction between Si nanospheres and phase transition of the VO₂ layer with temperature. These light scattering properties of such a hybrid nanostructure make it promising for temperature sensing or as a light source at the nanometer scale.

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Conceptual insights

As we know, active tuning of the optical properties of nanoantennas and metasurfaces is desirable for a wide range of applications, including building optical circuits, and signal and information processing. Although all-dielectric materials exhibit lots of advantages, how to realize the active control of all-dielectric nanostructures still remains to be explored. We, for the first time, combine the high refractive index of Si nanospheres and the phase transition of a VO₂ layer to form a hybrid nanostructure with higher quality factor. We have demonstrated the active tuning of the Fano resonance from a Si nanosphere dimer by the substrate effect in the visible range. We have also established that the phase change in the visible range can be described more precisely as a switch between a mid-refractive index state and a low-refractive index state. Furthermore, two different near field features of VO₂ under two states can bring about different interaction situations between VO₂ and Si nanospheres and realize the active control of the Fano resonance. Therefore, these findings suggest that devices based on individual phase-change materials and single-element structures will simplify the design of active photonic devices in the future.

Introduction

In the last decade, high- or moderate-refractive index semiconductor materials, which are also called all-dielectric materials, have aroused great interest among researchers in the field of nanophotonics.^1–7 Compared with plasmonic analogues, the energy losses of all-dielectric optical resonators are much lower at the visible wavelength.^1–3,8 Based on their unique light scattering and other optical properties, they are very promising to be a sort of substitution or supplement material for plasmonics in different application areas, such as directional scattering,^9,10 Fano resonance,^11–15 nonlinearity optic,^15–17 enhanced absorption^18,19 or emission^19–21 and metasurfaces for realizing a wide variety of functions.^22–25 Usually, the optical properties of a nanostructure will be changeless upon the completion of production, but can be passively controlled by varying the geometry, size and refractive index at the design stage.^{1,2,11,15,25,26} To achieve the same function at different wavelengths or under other specific conditions, one may need to redesign and manufacture the structure and device, which will require major expenditure of time, effort and resources. Therefore, the active controlling of a nanostructure makes a lot of sense to improve the practicality and achieve light-on-chip technology in the future.^27–31

To date, there are many groups that have turned their focus to this research item and carried out lots of demonstrations about it. For instance, Yan et al. realized the spectral tailoring of a hybrid dielectric-metal nanoantenna through changing the applied voltage to alter the carrier concentration of the silicon nanoparticle.³⁰ Based on voltage-controlled assembly, Montelongo et al. first reported a reversible electrotunable liquid mirror that can be switched from a refractive mirror to a transmissive window.³¹ As another example, by modifying the excitons in two-dimensional materials which are sensitive to the temperature, Wen et al. demonstrated active control over the strong coupling between gold nanorods and tungsten sulfide.²⁸ However, the strategy most frequently adopted to realize active tuning is combining nanostructures with liquid crystals, which provide a dielectric environment tuned by their phase transition.^21,22,32 Apart from the above-mentioned methods, some researchers have focused on the exploration of optically tunable and mechanically tunable all-dielectric Huygens’ metasurfaces to meet various needs of applications.^9,33

Vanadium dioxide (VO₂) is one of the most interesting and important materials due to the huge difference in electric and optical properties between the monoclinic phase and rutile phase,³⁴ which makes it widely used in recent tunable nanophotonics devices. This insulator-metal phase transition in VO₂ usually occurs around 68 °C.^29,34 To be specific, these unique features open up the use of VO₂ in modulators, color generation,²⁴ smart windows²⁹ and so on. Unfortunately, the refractive index of VO₂ only undergoes a little change at the visible wavelength (Fig. S1a and b, ESI†), which makes it difficult to be directly used as a film in an active controlled nanostructure.²⁴ To address this problem, one of the possible ways is to transform a film into a metasurface to support some kinds of resonances.^35,36 Even so, the nanostructures made by VO₂ have a low quality factor of resonance since its refractive index is not high enough (just about 3). Hence, it seems that combining VO₂ with other materials with a higher permittivity will be a more realistic implementation.^24,29

Among various semiconductor materials, silicon (Si) is one of the most abundant elements on the earth and especially suited as a building block in the electro-optic field.^{4,9,11,18–20,37} Its high refractive index (up to 4) is beneficial for forming a strong resonance with a higher quality factor, despite the low absorption losses in the visible region (Fig. S1c and d, ESI†).^2,3,37 An individual Si nanoparticle in a free space is a nanoresonator supporting multiple resonances, which can be well described by Mie theory.⁴ As the most basic research model, Si nanospheres have been heavily used in many fields, such as nanoantenna,⁴ waveguides,³⁸ sensors,³⁹ and resonant cavities for enhancing the light–matter interaction.^19,20,40 Since dielectric nanoparticles are sensitive to the refractive index of the surrounding environment, it is positive that the induction of a considerable refractive index substrate will modify the light scattering from the silicon nanoparticles.^41,42

In this contribution, we propose an active tuning hybrid nanostructure by depositing Si nanospheres on a VO₂ thin layer to make use of each of their advantages. The VO₂ layer is fabricated by a pulsed-laser deposition (PLD) method and the Si nanospheres are acquired by femtosecond laser ablation in liquids (fs-LAL) technology as done in our previous studies.¹¹ Individual Si nanospheres with different diameters on the VO₂ layer emit rainbow colors indicating that they supports resonance at different wavelengths, just like on the SO₂ substrate. When the temperature increased from 25 °C to 80 °C, the scattering intensity of the magnetic dipole (MD) resonance of the Si nanospheres will decrease differently depending on their size, while the intensity of electric dipole (ED) resonance remains almost unchanged. We use Mie theory and substrate-induced resonant magnetoelectric effects to describe and analyze the change in backward scattering spectra. The simulations have a similar trend with experimental results. Based on the result of the individual nanospheres, we measure the backward scattering spectra of Si nanosphere dimers on the VO₂ layer under different temperatures, which show as a lineshape of Fano resonance with different Fano asymmetric parameters q. In addition, the famous Fano formula is used to fit the experimental results and obtain the Fano parameter q. We demonstrate that the Fano resonance of Si nanosphere dimers can be tunable through changing the refractive index of the VO₂ layer which is sensitive to temperature. These light scattering properties of such a hybrid nanostructure mean that it can be used as a temperature sensor. Since the phase transition of VO₂ can be triggered by different applied electric currents, the hybrid nanostructure could act as a nanoscale light source with tunable illumination intensity or a nanoantenna for information processing.

Experimental and calculation section

Fabrication and characterization

The polycrystalline VO₂ thin film was fabricated by a PLD method. During the fabrication, a vanadium metal (99.99% purity) target was ablated by a KrF excimer laser pulse with a pulse rate of 4 Hz and a pulse width about 25 ns. Before the deposition process, the Al₂O₃ (0006) substrate was kept at 550 °C in a vacuum chamber under pressure of 4.0 Pa with flowing O₂ (45 sccm) and Ar₂ (30 sccm). To form this VO₂ thin film, the HV and the number were set as 25 kV and 12 000. Si nanoparticles were prepared by fs-LAL technology with pulse energy of 4 mJ and a pulse width about 35 fs. After 10 min of focused laser ablation on a monocrystal Si substrate in deionized water, the solution containing Si nanoparticles was collected. After more than 10 min ultrasonic dispersion, several drops of solution were removed onto the surface of VO₂ film. In this work, the scanning electron microscope (SEM) images were taken by an FIB-SEM crossbeam workstation (Carl Zeiss, Auriga-4523) with an extremely high electrical voltage of 3–5 kV. The room-temperature X-ray diffraction (XRD) testing was performed by an LIFM-X ray powder diffractometer. The thickness of the VO₂ film was confirmed by atomic force microscopy (AFM, Bruker, dimension fastscan bio). To study the hybrid nanostructure under different temperatures, the whole structure was put on an electrical microheater which can be turned from room temperature to about 80 °C.

Dark-field scattering spectral measurement

The dark-field (DF) backward scattering spectra of the nanostructures in this work were obtained by utilizing a dark-field optical microscope (BX51, Olympus) integrated with a quartz-tungsten-halogen lamp (120 W) with a cooled CCD camera (PiXis 400B-eXcelon, Princeton Instruments) next to it. In addition, the incident white light which was non-polarized irradiated the whole structure from an objective lens (magnification: 100, numerical aperture: 0.80) with an incident angle of 53 degree. Then the scattered light was collected by the same objective and sent to the spectrograph with a slit in front of it. To obtain S- or P-polarized light, a linear polarizer was added into the light path. Without special emphasis, the incident light was non-polarized.

Numerical simulation

The simulations including far-field backward scattering spectra and electromagnetic field amplitudes were carried out using a Finite-difference time-domain (FDTD) method. In the calculation model, a sphere whose size is determined by the SEM images was centered. By adding a semi-infinite substrate below the sphere, we could calculate the spectra in this work. The simulation area was meshed in three-dimensions (360 × 360 × 360 nm) composed of 2 nm cubic cells. In this case, we used two plane wave light sources (two electric fields were parallel to the x-axis and y-axis respectively) with normally incidence to the structure. This substitution of light sources proved simpler and more efficient without large deviation from the experimental data. The complex refractive index of VO₂ and Si at different temperatures was extracted from ref. 34, 43 and 44. We changed the refractive index of VO₂ in the models to simulate the insulator-metal phase transition.

Results and discussion

The proposed hybrid nanostructure composed of Si nanospheres and a VO₂ thin layer is shown in Fig. 1a. The VO₂ layer used in this work was grown on Al₂O₃ substrates by PLD and Si nanospheres were deposited onto the VO₂ layer by self-assembly. To explore the optical properties of the hybrid nanostructure under different temperatures, the whole structure was put onto a microheater which can be tuned from 25 °C to 80 °C. Before combining the Si nanospheres and VO₂ layer, we first investigated the properties of the VO₂ layer. Fig. 1b shows the SEM image of the VO₂ layer, which is featured by many small nanoparticles on its surface indicating that the sample is polycrystalline. For later analyses, the thickness of the VO₂ layer was measured by AFM, which is shown in Fig. 1c. The right region represents the VO₂ layer which is about 40 nm thick with a small roughness. Then the VO₂ layer was characterized by room-temperature XRD with respect to the Al₂O₃ substrate. From Fig. 1d, it is evident that the VO₂ layer has an orientation of (020) while the orientation of the Al₂O₃ substrate is (0006). To assess the phase-transition behavior of the VO₂ we prepared, we measured the resistance between two points on the surface of the VO₂ layer when heating the sample from 25 °C to 80 °C. The measurement results in Fig. 1e exhibit a hysteresis centered around 50 °C with a small hysteresis width of about 5 °C, which is suggestive of increased structural homogeneity and compactness, with little variation in grain size, crystallographic domain orientations and strain.²⁴

Fig. 1 Schematic illustration of the hybrid nanostructure and the properties of the VO₂ layer. (a) Hybrid nanostructure including Si nanospheres and a thin VO₂ layer below it, and the whole structure is put onto a microheater. (b) SEM image, (c) AFM image, (d) XRD spectrum and (e) electrical properties of the VO₂ layer we fabricated in this work (the scale bars in SEM and AFM images are 300 nm and 2 μm, respectively).

To explore the Si nanosphere dimers on the VO₂ layer, we first study the optical properties of single nanospheres. Due to the high refractive index of such Mie resonators and according to the relationship λ ≈ nd,⁴ the diameter of the particles we chose to study is about 100 nm to 200 nm to make sure the resonant wavelength will be confined in the visible region. Diameter, SEM images, DF images, experimental backward scattering spectra and the corresponding simulated results are displayed in Fig. 2. With the increase of diameter, the silicon nanospheres generate different colors ranging from blue, to green, yellow, orange and red, which correspond to different wavelengths of their strong magnetic and electric dipole scattering. To understand this observation in dark-field images, we performed the backward scattering spectrum measurement based on these five representative Si nanospheres on the VO₂ layer with the Al₂O₃ substrate, whose diameters confirmed by SEM images are 107.2 nm, 126.4 nm, 155.2 nm, 170.2 nm and 187.6 nm respectively. As it can be seen from the blue lines in Fig. 2c, the backward scattering spectra are mostly dominated by the MD and ED resonances. When the nanoparticles get larger, the MD and ED resonances will shift to the long-wavelength spectral side. Typically, when the nanospheres are large enough, the higher order resonant modes such as magnetic quadrupole (MQ) and electric quadrupole (EQ) gradually appear in the short-wavelength region, just as the experimental phenomenon in previous work.⁴⁵ The wavelength of the strongest resonant peak of each Si nanosphere matches their color observed in the backward direction. Using the same structures and parameters, we theoretically calculated the backward scattering spectra, which are displayed as celesta lines in Fig. 2d and well correspond to experiments. After that, a voltage was applied on the microheater below the whole hybrid nanostructure to heat it up to 80 °C directly. When the temperature settled down, we repeated the spectra measurement for these five Si nanospheres. Their backward scattering intensity has decreased differently. For each particle, the decreasing degree of MD resonance is always larger than that of ED resonance which remains nearly unchanged. As for the large particles, the decreasing degree of their MD is larger than that of smaller nanoparticle and the wavelength of MD resonance exhibits a slight blue-shift. Similarly, we preformed the calculation again to simulate the insulator-metal phase transition through changing the refractive index of VO₂. The latest simulations presented as orange lines in Fig. 2d have a similar trend with experimental phenomena including an alike spectral lineshape and decreasing scattering intensity. To determine whether the properties of Si nanospheres were changed by the increased temperature, we performed a contrast experiment by replacing the VO₂ layer on the Al₂O₃ substrate with a SiO₂ substrate which is very stable. The experimental results (Fig. S2, ESI†) suggest that the Si nanospheres with a diameter ranging from 132.9 nm to 201.6 nm won’t be affected by the temperature change. Also, the complex refractive index of Si at 20 °C and 100 °C also confirms this point (Fig. S1, ESI†).

Fig. 2 Experimental and simulated backward scattering spectra of a single Si nanosphere on the VO₂ layer. (a) SEM images, (b) DF images, (c) experimental and (d) simulated normalized backward scattering spectra of a single Si nanosphere with a diameter of 107.2 nm, 126.4 nm, 155.2 nm, 170.2 nm and 187.6 nm (the scale bar in the SEM images is 200 nm and the magnification of the optical microscope is 1000).

As mentioned above, it seems that the decreasing degrees become larger with the increase of diameter. Therefore, we measured twenty other Si nanospheres with different diameters (see Fig. S3, ESI†) and plot their change in Fig. 3a, which approaches a linear relationship approximately. The different decrease originates from the different changing degrees of the refractive index of VO₂ at different wavelengths and the different values of scattering cross section for different particles. It is noteworthy that the phase transition of the VO₂ layer is reversible, and we measure particle 4 for three cycles to test the reversibility of our active controlled hybrid nanostructure. As shown in Fig. 3b, the hybrid nanostructure exhibits reversiblity to some extent after heating and cooling several times. Finally, based on the same particle 4, we observed a continued changing process by varying the applied voltage on the microheater to heat the structure to different target temperatures, which is presented in Fig. 3c. Compared with the scattering intensity of MD resonance at 25 °C, it falls from 1 to 0.6 at 80 °C. As for that of ED resonance, this value falls from 0.4 to 0.3 for the same process.

Fig. 3 More optical properties of the hybrid nanostructure based on a single Si nanosphere. (a) The decreasing percentage of light scattering intensity of MD resonance of 25 particles with different diameters during the phase transition of a VO₂ layer. (b) The reversibility and (c) continuous tunability from particle 4.

To theoretically investigate this influence, we first consider a single Si nanosphere on different kinds of supporting substrates. The calculated backward scattering spectra of an individual Si nanosphere with a diameter of 170 nm deposited on different substrates are shown in Fig. 4a. As described by Mie theory, the light scattering of sub wavelength dielectric particles can be analyzed by dipole approximation,⁴

p₁ = ε₀α_EE₀ (1)

m₁ = α_HH₀ (2)

α_E = 6iπa₁/k³ (3)

α_H = 6iπb₁/k³ (4)

where p₁ and m₁ are the effective electric and magnetic dipole moments, ε₀ is the vacuum permittivity, α_E and α_H are the effective polarizabilities, E₀ and H₀ are the electric and magnetic fields of the incident light, and a₁ and b₁ are the Mie's dipole scattering coefficients. The calculated scattering cross section of a Si nanosphere under vacuum is plotted as a black line in Fig. 4a. Two resonances located at about 550 nm and 700 nm represent the MD and ED resonances. For the MQ and EQ resonances located at about 450 nm and 520 nm, we will neglect them since they are far away from the MD and ED resonances and of weak strength, so they won’t make a big difference to the analysis and discussion.

Fig. 4 Theoretical analysis of the substrate effect on a single subwavelength dielectric particle. (a) Simulated backward scattering spectra and (b) normalized electromagnetic field amplitudes at MD resonance of a Si nanosphere with a diameter of 170 nm on different kinds of substrates. (c) Calculated scattering cross section as a function of wavelength of a Si nanosphere with a diameter of 170 nm on a fictitious substrate with 2.5 ≤ n ≤ 3.5 and k = 0, in index steps of 0.1. (d) Calculated scattering cross section for the same particle in (c) on another fictitious substrate with n = 3 and 0 ≤ n ≤ 1, in index steps of 0.1. (e) Influence of a VO₂ layer toward active control for a Si nanosphere with a diameter of 170 nm. (f) Calculated backward scattering spectra of a Si nanodisk with a bottom diameter and height of 170 nm and (g) a Si nanocube with a side length of 170 nm on the same VO₂ layer as (a).

Then the same nanoparticle is put onto a SiO₂ substrate, whose spectra are the purple lines in Fig. 4a. This is no big difference compared with the situation when the particle is under vacuum. When the particle is transferred to a 40 nm-thick insulator-phase VO₂ layer with the Al₂O₃ substrate, however, the spectrum has changed obviously with an increasing scattering cross section at both ED and MD resonances. On inspection, it is not only the change in the refractive index of the supporting substrate that leads to the spectral difference since the particle and the supporting film have an extremely small contact point. Hence, we assume that this substrate effect mainly originated from the image dipoles in the supporting film induced by the dipole moments of the nanoparticles. When the refractive index of a substrate is high enough, the substrate will couple to the particles near it and the substrate-induced resonant magnetoelectric effects should be considered. In this situation, the image dipoles will apply an additional electric and magnetic field as a feedback to the particles. As a result, eqn (1) and (2) will be modified a little by taking the additional fields into consideration,⁴²

p₁ = ε₀[small alpha, Greek, circumflex]_EEE₀ + ε₀[small alpha, Greek, circumflex]_EMH₀ (5)

m₁ = [small alpha, Greek, circumflex]_MMH₀ + [small alpha, Greek, circumflex]_MEE₀ (6)

where [small alpha, Greek, circumflex]_EE, [small alpha, Greek, circumflex]_EM, [small alpha, Greek, circumflex]_MM and [small alpha, Greek, circumflex]_ME are the modified effective polarizabilities. The calculated normalized electromagnetic field amplitudes of a single Si nanosphere with different substrates at MD resonance are given in Fig. 4b. Compared with the nanoparticle under vacuum, the electric and magnetic fields near a particle with the SiO₂ substrate are almost the same. The electric fields are mostly distributed on two sides of the nanoparticle while the magnetic field is inside it. It is different that the electric field concentrates at the contact point between the Si nanosphere and insulator-phase VO₂ layer while the magnetic field profile inside the particle starts to increase. Based on the above discussion, hence, we think that it is the coupling between the Si nanospheres and the supporting substrate that also contributes to the spectral difference. However, if the same nanoparticle is deposited on a metal-phase VO₂ layer, the scattering cross section of ED and MD resonances will decrease to different degrees. We attribute this to the different changes of refractive index of a VO₂ layer at different wavelengths during the phase transition and the sensibility of ED and MD resonances. To understand this process, Fig. 4c shows the scattering cross section for the same resonator on a fictitious substrate with an imaginary part of the refractive index k = 0 and a real part in the range from 2.5 to 3.5, varying in steps of 0.1. The scattering cross sections of ED and MD resonances have almost the same decrease when increasing the index of the substrate. A small shift to the short-wavelength spectral side is observed for both the ED and MD resonances. Compared with a cylinder resonator, the valve of blue-shift of resonant wavelength is smaller because of the smaller contact point and most light is limited inside the resonator which is not as sensitive to the index of the substrate as the plasmonics.⁴¹ In the same way, we discuss the influence of the imaginary part of the refractive index of the substrate by putting the same resonator on another fictitious substrate with a real part of the refractive index n = 3 and an imaginary part in the range from 0 to 1, varying in steps of 0.1. Interestingly, the profile of MD modes reduces significantly while the ED modes remain nearly unchanged. By the above analysis and discussion, taking the change rule of the real and imaginary part of the refractive index of VO₂ during the phase transition (the decreases of n and k get higher with increased wavelength, see Fig. S1, ESI†) into consideration, the scattering intensity of MD resonance reduces a lot while the phase transitions of VO₂ have a small impact on that of ED resonance at the visible wavelength. In addition, we calculated the same nanosphere on a VO₂ layer with different thickness to determine how the thickness influences the active control in this case, which is summarized in Fig. 4e (more details in Fig. S4, ESI†). In the beginning, the scattering cross section of MD resonance increases with the thickening of the VO₂ layer. It reaches the maximum when the thickness is 40 nm and declines for a thicker VO₂ layer. To a certain extent, a 40-thick-VO₂ layer is the optimum for a Si nanosphere with a diameter of 170 nm. The decreasing percentage of scattering cross section when the VO₂ layer changes from an insulator-phase to metal-phase has a maximum of 22.7%. In the same model, if the Si nanosphere is replaced by a Si nanodisk or a Si nanocube, their backward scattering spectra are similar to the former situation (Fig. 4f and g). As mentioned above, the more contact area between them, the more obvious the change of backward scattering spectra because of the change in the refractive index of the supporting substrate. Based on that, their wavelength of MD resonance changes a lot during the phase transition of VO₂. However, considering the coupling between particle and substrate, the decreasing percentage of scattering cross section of MD resonance is 23.5% and 20.6% for the disk and cube. But, the sphere has a higher scattering cross section, which makes it advantageous to be used rather than a disk or a cube.

Then, we dealt with the Si nanosphere dimers in the same manner. Diameter, SEM images, DF images, experimental backward scattering spectra and the corresponding simulations of our studied dimers are displayed in Fig. 5. Discussed by our previous work based on Si nanosphere dimers,¹¹ the size we chose to investigate is 128.6 nm & 128.6 nm, 125.1 nm & 138.1 nm and 137.5 nm & 150.8 nm to generate a Fano dip in the visible region. At room temperature, all three dimers produce a small Fano dip at different wavelengths depended on their size. However, the light scattering intensity goes down when the 40 nm-thick VO₂ layer on the Al₂O₃ substrate transfers into the metal phase. In addition, the spectral line shapes change and the Fano dips become smaller. Through simulations, we observed a similar result that well corresponds with the experiment. Moreover, we repeated the measurement by using both S- and P-polarized incident light (Fig. S5, ESI†). The spectra obtained by using different polarized incident light for each dimer reveal a uniform trend.

Fig. 5 Experimental and simulated backward scattering spectra of Si nanosphere dimers on the VO₂ layer. (a) SEM images, (b) DF images, (c) experimental and (d) simulated normalized backward scattering spectra of a Si nanosphere dimer with a size of 128.6 nm & 128.6 nm, 125.1 nm & 138.1 nm and 137.5 nm & 150.8 nm (the scale bar in SEM images is 200 nm and the magnification of the optical microscope is 1000).

According to Albella's work, when two Si nanospheres on the VO₂ layer start to get close to each other, another additional electric and magnetic dipole will be induced by the nearby particle, apart from that caused by the image dipole in the substrate.⁴⁶ A dipole–dipole coupling model can be used to analyze this situation. If the polarization of incident light is parallel to the long axis of the dimer, the induced dipoles can be expressed in the following form:⁴⁶

p₂ = ε₀ε_h[small alpha, Greek, tilde]_eyE₀ (7)

m₂ = −[small alpha, Greek, tilde]_mxE₀/Z (8)

[small alpha, Greek, tilde]_ey = α_e′/(1 − α_e′k²g_yy) (9)

[small alpha, Greek, tilde]_mx = α_m′/(1 + α_m′k²g_xx) (10)

Z = (μ₀μ_h/(ε₀ε_h))^1/2 (11)

where [small alpha, Greek, tilde]_ey and [small alpha, Greek, tilde]_mx are the dressed polarizabilities, k is the wavenumber, α_e′ and α_m′ are related to the modified effective polarizabilities [small alpha, Greek, circumflex]_EE, [small alpha, Greek, circumflex]_EM, [small alpha, Greek, circumflex]_MM and [small alpha, Greek, circumflex]_ME in eqn (5) and (6), g_xx and g_yy are scalar Green's functions related to the distances between two particles, and Z is the vacuum impedance. Therefore, their ED resonance in each sphere couples strongly to another one to form a much broader resonant mode. While the MD resonances will reduce their resonant peak and become a little narrower after forming a dimer. As a result, these new-formed hybrid continuous ED modes and discrete MD modes overlap and generate a Fano resonance as illuminated in Fig. 6a. Based on the above analysis, when the VO₂ layer was transferred from an insulator phase to a metal phase, the scattering intensity of the dimer reduced. And because of the different decreasing degrees of ED and MD resonances in a single nanoparticle, the lineshape of Fano resonance from a dimer changed with them.

Fig. 6 Backward scattering spectra of a Si nanosphere dimer on the VO₂ layer at different temperatures. (a) Illustration of the formation mechanism of Fano resonance in the Si nanosphere dimer. (b) Continuous tunability from dimer 3. (c–h) Normalized experimental scattering spectra of dimer 4 showing similar Fano lineshapes at different temperatures and the results of theoretical analysis with different fitting Fano parameter q.

Taking dimer 3 for example, a continued changing process can be observed by gradually increasing the applied voltage on the microheater, which is presented in Fig. 6b. To study carefully this process, we employed a simple approach including the most famous Fano formula⁴⁷ and the original Fano model⁴⁸ to fit the experimental results to obtain the key Fano asymmetry parameter q,

σ_scat = σ_conσ_dis (12)

σ_con = a²/(1 + (2(ω − ω_E)/Γ_E)²) (13)

σ_dis = (D²((q + Ω)² + b))/(1 + Ω²) (14)

Ω = 2(ω − ω_M)/Γ_M (15)

D² = 4 sin² δ (16)

q = cot δ (17)

where ω_E and ω_M are the resonant frequency of the ED and MD modes, Γ_E and Γ_M are the half-width of the resonance line at a half-maximum of the ED and MD modes, q is the Fano asymmetry parameter, a and b are the maximal amplitude of the resonance and the damping parameter, and δ is the phase shift of the continuum. The results of fitting are summarized in Fig. 6c–h. From 25 °C to 80 °C, the observed spectra maintain a Fano lineshape while the Fano parameter q increases from −0.78 to −0.68. It is evidence that the Fano resonance from Si nanosphere dimers on the VO₂ layer can be tuned by the phase transition of VO₂ which is related to temperature. Such tunable Fano resonance has a variety of applications, such as in biochemical sensing, light switch, information processing.

However, one can easily see that there are some differences between the experimental results and theoretical calculations. For the single Si nanosphere, the ED resonance in the experiment is weaker than that in the simulations because of the non-ideality of the particle shape, which has been discussed in previous work.²⁶ Apart from the above analysis, the discrepancy between the refractive index of VO₂ we prepared and that we extract from a ref. 34 is another primary cause. It is worth mentioning that the contact point is different from the ideal situation since the VO₂ layer in this work does not have a perfectly smooth surface. In addition, the light source in the experiment is also different from the simulations. The oxide layer of Si nanospheres is unavoidable,⁴ which weakens the coupling between the particles and substrate. All these factors lead to the difference between the experiment and the simulation. In the same manner, the oxide layer of Si nanospheres increased the actual distance between two particles and weakens the coupling. At the same time, thinking again that the intensity of the continuous ED mode is weaker than the discrete MD mode, the Fano dips on the spectra are not very recognizable, which is unlike those very sharp Fano resonances.^15,47 Last but not least, during the measurement, the actual temperature of VO₂ will be hardly controlled accurately and a little lower than the setting object temperature. And because of personal error, there may be some difference for the same research object under the same conditions. In short, our simulation is still in good agreement with the experimental data.

Generally speaking, we use all-dielectric nanoparticles to take the place of plasmonics in this work for two main reasons. One reason is that the Fano resonance can be easily observed in all-dielectric nanosphere dimers, which is attributed to the abundant resonant modes in each single nanosphere. It is unlikely that active control of the Fano resonance will be achieved by using a metallic nanosphere dimer. As another reason, the inherent Ohmic loss will lead to Joule heating and hinder their applications considering the temperature.^3,8 The use of the metallic nanosphere in our case would lower the temperature of phase-transition of VO₂ and narrow the tuning range. Anyway, the utilization of VO₂ destines that the active control can only work near the temperature of phase-transition of VO₂. However, VO₂ in this platform can be replaced by other active materials to sense different environment parameters.

Conclusions

In summary, based on PLD, LAL and self-assembly methods, we have fabricated Si nanospheres and dimers on a VO₂ layer with an Al₂O₃ substrate. When the VO₂ layer transfers from an insulator phase to a metal phase, the scattering intensity of MD resonance of an individual Si nanosphere reduces more than that of ED resonance. The prime reason is that Si nanospheres couple to the VO₂ layer and the MD resonance is more sensitive to the change in the refractive index of VO₂ during phase transition. According to this feature, we investigated Si nanosphere dimers in the same manner and observed a significant change in the Fano resonant lineshape. In addition, we used the famous Fano formula to fit the experimental results and got the Fano parameter q. We demonstrated that the Fano resonance generated in Si nanosphere dimers can be actively tuned by utilizing the phase transition of VO₂ which is sensitive to temperature. Therefore, the light scattering properties of this hybrid nanostructure mean it can be used as a temperature sensor for healthcare or information processing. Considering that the phase transition of VO₂ can be triggered by different applied electric currents directly, the hybrid nanostructure could act as a nanoscale light source with tunable illumination intensity or a nanoantenna with varying signals.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The National Basic Research Program of China (2014CB931700), Guangzhou city (201804020074) and State Key Laboratory of Optoelectronic Materials and Technologies supported this work.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8nh00198g

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