1. Introduction

Fano resonances in metamaterials and plasmonic structures have attracted a tremendous amount of attention in recent years [1, 2]. The origin of such resonance is generally related to the interaction of bright mode (in-phased dipole resonance) and dark mode (anti-phased dipole resonance) supported by coupled nanostructures [3–5], such as dimer [6, 7], asymmetric bars [8–10], nanoclusters [11], and oligomer [12, 13]. Due to its sharp profile and high sensitivity to local media, it has found various applications such as biosensor, modulator, surface-enhanced Raman scattering (SERS), and surface plasmon laser (Spaser) which are dominated by the resonant nature of their response [14–20]. The overall performance of such Fano-resonance-based devices is, to a great extent, determined by its Q factor and spectral contrast. However, nanostructures made of metal intrinsically suffer from strong Ohmic loss and saturation effects which limit the Q factor and spectral contrast under rather small values precluding further performance improvement [21–25].

Fortunately, recent theoretical and experimental studies show that the resonant dark modes can also be excited in nanostructures made of dielectric, which then interact with corresponding bright modes and generate pronounced Fano profiles [26–28]. More recently, we proposed a novel binary silicon particle array and numerically studied the multi-trapped modes and corresponding Fano resonances resulting from lattice coupling effects in the array [29]. Due to the low loss nature of dielectric, the Q factor and spectral contrast of such resonances can be strongly improved. In this research paper, we demonstrate the experimental realization of Fano resonance in such binary all-dielectric particle array. The anti-phased lattice collective resonance in the binary silicon nanodisk array serves as the dark mode while the phased one acts as the bright mode. The Fano profile is closely associated with the radii of the particles offering an effective way to tailor the resonance. Experimental results agree well with the calculations using finite-difference-time-domain (FDTD) method. Further calculations demonstrate that such scheme can be used as an optical filter and the linewidth of the filter can be efficiently tuned simply by changing the radius of the particles. As the radius $R_2$ increases from 60 nm to 115 nm, the linewidth changes from 12 nm to 0.7 nm and corresponding Q factor from 72 to 1290.

2. Fano resonance in binary silicon nanodisk array

Figure 1(a) and 1(b) show the scheme of proposed binary nanodisk array and corresponding scanning electron microscope (SEM) image. Two sets of silicon nanodisk arrays with different radii denoted by $R_1$ and $R_2$ interlace with each other in the X-Y plane and have a lateral displacement of half period in both directions. The periods of two arrays are $P$ (570 nm) in both X and Y directions and the thickness of nanodisks is denoted by Η. To fabricate the silicon nanodisk arrays, 80 nm thick amorphous silicon layer is deposited by plasma-enhanced chemical vapor deposition (PECVD) on a glass substrate pre-deposited an indium tin oxide (ITO) layer of 185 nm. Then, the silicon nanodisk arrays with areas of 100 μm × 100 μm are fabricated using standard electron beam lithography followed by ion beam etching process. In order to measure the reflection of the samples, white light from a halogen tungsten lamp is focused on a spot size of nearly 30 μm in diameter by a 5X objective with numerical aperture of 0.14, and then collected by an optical fiber spectrometer (USB2000 + , Ocean Optics). The microscope objective transforms the white light source into a Guassian beam. The nano-fabricated samples are placed on the beam waist plane of the Guassian beam where the incidence light can be treated as quasi-planewave with normal incidence angle. Reflection spectra are also carried out using commercial FDTD software package (FDTD solutions) from Lumerical Inc.. In the calculations, the incident plane wave is normal to the array plane with polarization along the X direction, and periodic condition is used in each boundary of the unit cell to reduce the amount of computation. The permittivity of glass, silicon, and ITO are extracted from the experimental data [30, 31].

 

Fig. 1 (a) 3-D scheme of binary silicon nanodisk array with particle radii of $R_1$ and $R_2$. (b) top view of corresponding SEM image. Reflection spectra from (c) FDTD calculation and (d) experiment. The geometric parameters are chosen as $R_1=120\text{nm}$, $R_2=90\text{nm}$, $P=570\text{nm}$, and $H=80\text{nm}$.

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Figure 1(c) illustrates the calculated reflection spectrum of the binary silicon nanodisk array with $R_1=120\text{nm}$ and $R_2=90\text{nm}$. The origin of the distinct Fano profile near 840 nm can be understood by employing the hybridization theory [4]. Each silicon particle array supports corresponding lattice collective resonance, accounting for the lattice collective excitation of the constituent nanoparticle members in the array [32]. The resonant frequency of such lattice collective resonance is determined by the shape, period, and surrounding environment of the particles. When two particle arrays with different radii as well as different resonant frequencies are combined to form a binary array, they will hybridize to form anti-phased lattice collective resonance (ALCR) mode and in-phased lattice collective resonance (ILCR) mode through lattice coupling effects. In the ALCR mode, one particle array oscillates in-phase while the other oscillates anti-phase with the incident light. Their re-radiated fields interfere destructively in the far-field and lead to the elimination of scattering loss, which can be seen as “dark mode”. This resonant mode has a long lifetime due to its weak coupling to free space radiation and appears to be “trapped” in the vicinity of the array surface, also be known as “trapped mode”. In the ILCR mode, both particle arrays oscillate in-phase or anti-phase with the incident light, thus, the re-radiated fields of two sets of particle arrays interfere constructively and can be seen as “bright mode”. The bright mode effectively couples to the incident light and the reflection is enhanced. The superposition of such “bright mode” and “dark mode” gives rise to the sharp asymmetric Fano lineshape in reflection. Figure 1(d) shows the experimental reflection spectrum of the binary silicon nanodisk array with $R_1=120\text{nm}$ and $R_2=90\text{nm}$. The experimental result agrees well with the calculation [Fig. 1(c)] except a broadening of resonance linewidth and a minor resonance wavelength shift.

In order to interpret the ILCR mode and ALCR mode more clearly, we plot the X component of electric field distribution (${\text{E}}_{\text{X}}$) of the binary array for a unit cell near Fano resonance at the plane across the centers of each particle (Z = 40 nm). Figures 2(a) and 2(b) show the ${\text{E}}_{\text{X}}$ distribution at 680 nm and 900 nm, respectively. The particles can be treated as electric dipoles and oscillate collectively with the incident light. The coupling between particles in the two arrays is relatively weak and the field mainly concentrates on the vicinity of each particle. ILCR mode dominates the radiation with particles in two arrays oscillating in the same direction and their re-radiated fields interfere constructively in the far-field. Figure 2(c) illustrates the ${\text{E}}_{\text{X}}$ distribution at 840 nm where ALCR mode is excited, particles in the two arrays oscillate with phase difference of $\pi$. The re-radiated fields of two arrays strongly cancel each other in the far-field and the reflection is significantly minimized. The magnetic response of such binary particle array is very weak resulting from the strong cancellation of magnetic field shown in Fig. 2(d), which is very different from nanostructures under strong near-field coupling where the magnetic response is dominating [8].

 

Fig. 2 ${\text{E}}_{\text{X}}$ distribution of binary silicon nanodisk array with particle radii of $R_1$ and $R_2$ at the plane across the centers of each particle ($\text{Z=40}\text{nm}$) at (a) $\lambda \text{=680}\text{nm}$, (b) $\lambda \text{=900}\text{nm}$, and (c) $\lambda \text{=840}\text{nm}$. (d) ${\text{H}}_Z$ distribution of binary silicon nanodisk array at the plane of $\text{Z=40}\text{nm}$ for $\lambda \text{=840}\text{nm}$. The radii are chosen as $R_1=120\text{nm}$ and $R_2=90\text{nm}$.

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The response of such binary silicon nanodisk array can be interpreted by a system of harmonic oscillators. The oscillating nanodisk arrays are represented by two large harmonic oscillators with different resonant frequencies of ${\omega }_1$ and ${\omega }_2$ as shown in Fig. 3(a). Two oscillators are connected to solid walls, while also couple to each other through a third small oscillator which accounts for the far-field interference of the two particle arrays. The incident electromagnetic wave can be seen as the external force, which is exerted on the large oscillators, while friction force subjected to small oscillator represents for the scattering loss in the binary particle array. Generally, the small oscillator will oscillate for all driving frequencies under the action of large oscillators leading to energy dissipation through the friction, in other words scattering loss, which can be seen as a bright mode. However, due to the difference in resonant frequencies, a dark mode can be established at a specific frequency. In such mode two heavy oscillators oscillate with same amplitudes and opposite phases resulting in zero net force on the small oscillator. Thus, the small oscillator remains still and the scattering loss in the system are strongly minimized; all the energy will be stored in the oscillations of the large oscillators.

 

Fig. 3 (a) Coupled classical oscillator model, two large oscillators are connected to a small oscillator by springs. The small oscillator is subjected to friction force representing for the scattering loss of the binary silicon nanodisk array, while the two large oscillators are exerted on external forces accounting for the incident electromagnetic wave. (b) Reflections from analytical model and FDTD simulation, respectively. The radii are chosen as $R_1=120\text{nm}$ and $R_2=90\text{nm}$ in simulation.

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The equations of motion of the three oscillators can be described as [33],

The reflection calculated from the model agrees well with the results from FDTD simulation [Fig. 3(b)] and verifies the feasibility to use this model to describe the optical response of the binary nanodisk array. The parameters are chosen as ${\omega }_1=2.47\text{eV}$, ${\omega }_2=1.40\text{eV}$, ${\omega }_3=1.71\text{eV}$, $k_{13}=2.00$, $k_{23}=0.02$, $\gamma =0.05$, $\text{F}=0.02$.

The Fano profiles of the binary silicon nanodisk array are closely associated with the radii of the particles. Especially, the spectral contrast gradually reduces as the radius difference of the particles in the two arrays getting small. Figure 4 shows the reflection spectra under different $R_2$ while $R_1$ is fixed at 120 nm. The Fano resonance has a strong dependence on the radii difference of the particles in the two arrays. For the case of $R_2=R_1$, the dark mode cannot be directly excited by normally incident light, thus, the Fano profile also disappears. As $R_2$ increases, the resonance wavelength of the ILCR (bright mode) has a slight red shift but the linewidth remains almost identical. Compared with the bright mode, the dark mode processes the merits of much narrow resonance linewidth and high sensitivity to local environment which are very helpful especially for applications such as refractive sensors and optical modulators.

 

Fig. 4 Reflections for different particle radii; the left columns are calculated from FDTD simulations, and the right columns are from experiment. The central columns are the corresponding SEMs. $R_2$ from the top to the bottom are 90 nm, 100 nm, and 120 nm.

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The linewidths of the resonances from experimental measurements are much wider than that from FDTD calculations and the resonance wavelengths have slight deviations. The inconsistencies between experiments and simulations are mainly attributed to the roughness and deviation of particles from ideal shape during fabrication process. The intrinsic losses also play an important role in determining the linewidth, as $R_2$ increases the Q factor gradually grows, indicating the growing energy density of the electric field stored in the resonances of the system. Thus, in the binary particle array with small radius difference (large $R_2$), the energy density of the electric field is much stronger, and a small loss introduced by silicon can result in a large dissipation of energy, which weakens the Fano profile and reduces the spectral contrast. In other words, the effects of intrinsic losses become more pronounced when $R_2$ gets larger (approaching $R_1$). It is well known that the intrinsic losses in the nano-fabricated sample are much larger than that in bulk structures. The additional losses introduced in nano-fabricated samples will speed up the broadening of linewidth and the reducing of the spectral contrast. The non-normal incidence and the incidence polarization in experimental reflection measurements can also play a role in determining the linewidths, but the effects can be, to a large extent, avoided by improving the adjustment accuracy. Also, the geometric parameters are chosen to make the structures insensitive to polarization for normal incidence (Period of 570nm in both X and Y directions). We also measured the reflections of the samples under polarized light (not shown here); the reflections of unpolarized light, X-polarized light, and Y-polarized light are almost identical.

3. Fano-resonance based optical filter

The sharpness of the resonance is strongly limited by the dissipation and asymmetric surrounding environment of the binary silicon nanodisk array. The dissipation mainly comes from the ITO layer which acts as the discharge layer pre-deposited on the glass during fabrication process. The absorption of ITO in visible frequency range can be safely neglected; however, as the frequency extends into the near-infrared range the absorption significantly increases and plays a vital role in the performance of the resonance. In order to get optimal results, in the following numerical study we remove the ITO layer from the binary silicon nanodisk array and assume the silicon arrays are embedded into uniform glass. As shown in Fig. 5(a), the reflection of binary silicon particle array under optimal conditions possesses much sharper Fano resonance with higher Q factor and spectral contrast. Such binary silicon nanodisk array possesses very high reflection up to 96.6% at the Fano peak and keeps relatively low reflection in a wide frequency range, which makes it very suitable for optical filter in near-infrared range.

 

Fig. 5 (a) Reflections of binary silicon nanodisk array with ITO layer and under optimal conditions. (b) Reflections of binary silicon nanodisk array under different $R_2$. (c) Evolution of linewidth of Fano resonance as $R_2$ approaches 120 nm. (d) Evolution of reflection of Fano peak and dip as $R_2$ approaches 120 nm. For all the cases, $R_1$ is fixed at 120 nm.

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For optical filter, it is necessary to design the central wavelengths and linewidths according to specific applications. However, conventional filters based on interference or absorption is bulky and lacking efficient tunability [34]. The distinct advantage of such binary silicon nanodisk array is its ability to tune the filtering performance simply by changing the geometric parameters. The central wavelength of the Fano resonance in the binary silicon nanodisk array can be designed at any frequency by adjusting the period of the array. Furthermore, as the radii of the particles in the two arrays approach gradually, the width of Fano resonance decreases opening an effective way to tune the linewidth of the filter. Figure 5(b) shows the reflection spectra of such binary silicon nanodisk array under different $R_2$ while $R_1$ is fixed at 120 nm. As the radius of one particle array, $R_2$, approaches $R_1$, 120 nm, the lineshape changes slightly accompanying with a gradual narrowing of the resonance linewidth. The extracted linewidth of the Fano resonance under different $R_2$ is illustrated in Fig. 5(c). The linewidth (the full width at half maximum) is defined as the difference between the wavelength corresponding to the half maximum at one side of the resonance and the wavelength at half maximum at another side of the resonance. The linewidth of the resonance linearly decreases as $R_2$ increases for $R_2<100\mathrm{nm}$. As $R_2$ exceeds 100 nm the evolution of linewidth strongly deviates from linear relation and reaches saturation. This originates from the growing absorption in the silicon particles due to the increasing energy density in the array under small radius difference. The reflection of Fano peak remains above 95% for a wide $R_2$ range [Fig. 5(d)], while the Fano dip are always zero for any $R_2$. When the radii of the particles in the two arrays are nearly identical, the reflection of Fano peak sharply decreases. This comes from the fact that the absorption of the silicon particles becomes more dominant under small radius difference. Such a binary silicon nanodisk array offers a powerful ability to tune the linewidth of the optical filter from 12 nm to 0.7 nm (corresponding Q factor from 72 to 1290) as $R_2$ increases from 60 nm to 115 nm.

One can also notice that even for the case of $R_1=120\mathrm{nm}$, $R_2=100\mathrm{nm}$, the Q factor and corresponding spectral contrast are 420 and 99.8%, respectively. Because of the strong elimination of scattering loss and low loss nature of silicon in near-infrared range, such binary silicon nanodisk array possessing high Q factor and spectral contrast is also very promising in a series of applications where sharp resonance is essential for the performance.

4. Conclusion

In conclusion, we perform the experimental study of the Fano resonance in an all-dielectric binary nanodisk array. Experimental results agree well with the FDTD calculations and show the strong dependence of Fano resonance linewidth on the radius difference of the particles. The electric filed distributions clearly illustrate the excitation of ILCR and ALCR modes and further calculations under optimal conditions demonstrate a more pronounced lineshape which has the potentials for optical filter. The distinct advantage of such filter is the ability to tune the linewidth easily by changing the particle radius, and the linewidth (Q factor) changes from 12 nm (72) to 0.7 nm (1290) as the radius $R_2$ increases from 60 nm to 115 nm while $R_1$ is fixed at 120 nm. Such scheme processes the merits of being easily fabricated, simulated, and tuned making it very promising for practical applications.