1. Introduction

Optical energy focusing structures have attracted intense research interest in the past years due to their unique ability to enhance electric or magnetic field intensity and confine it down to the nanoscale. These structures have been well developed based on surface plasmons (SPs)–the collective electromagnetic excitations that propagate at the interface between dielectric and metallic layers, decaying exponentially normal to the metal surface [1]. SPs have been deeply studied with respect to the fundamental properties for both localized surface plasmons (LSPs) and propagating surface plasmon polaritons (SPPs) [1]. Nano-optical antennas [2–9], e.g., Bowtie Nano-antennas, rod antennas and fan antennas [10], are able to confine energy into small volumes and dramatically enhance the local electric field due to the LSPs. The circular metal gratings, known as plasmonic lenses [11,12], support the propagating SPPs waves, which interfere with each other and concentrate the electromagnetic field at the focal points. On the other hand, pure dielectric structures, such as one-dimensional periodic gratings [13], two-dimensional photonic crystal slabs [14], and circular Bragg reflectors (CBRs) [15], can also be used to create substantial field enhancement due to the resonant photonic modes. Compared with plasmonic structures, these photonic structures normally exhibit much less absorption losses in the optical region [15]. Therefore, dielectric structures can be designed to have ultrahigh Q factors, which describe the spectral energy density of the cavity mode [16]. In contrast, metallic structures exhibit stronger field confinement and have smaller mode volume V_m, which represents the spatial energy density of the cavity mode [16].

By placing dielectric structures on top of metallic structures, a hybrid dielectric-metallic cavity [16–19] can be formed, combining the advantages of the stronger field confinement characteristic of metallic structures and the lower losses of dielectric structures. This new type of high $Q/V_m$ hybrid dielectric-metallic cavity is of great importance in enhancing light-matter interactions [20–23], such as in nanolasers, SERS, non-linear optics, and biological sensors.

In this article, we design a new optical energy focusing structure comprising a circular dielectric Bragg nanocavity atop a circular metallic plasmonic lens. Via the hybridization of dielectric photonic modes and metallic plasmonic modes, optical energy is highly focused in the central region of the Bragg nanocavity under linearly polarized light, and the electric and magnetic field are dramatically enhanced compared with a isolated Bragg nanocavity or a isolated plasmonic lens. In the process of optical energy convergence, the Bragg nanocavity utilizes the azimuthal component E_a [24,25] and radial component H_r of the linearly polarized light, while the plasmonic lens utilizes the radial component E_r [11,26] and azimuthal component H_a of the linearly polarized light; thus, the incident light is fully utilized. More importantly, when we put either a Bowtie Nano-antenna (BNA) or a Magnetic Resonator (MR, metal-dielectric-metal sandwich structure) [27–29] directly onto this optical energy focusing structure, the energy can be high-efficiently coupled and focused into the BNA or MR. Finite-difference time-domain (FDTD) simulations show that |E|/|E₀| in the BNA and |H|/|H₀| in the MR can be enhanced by more than 3000 times and 200 times, respectively. In the whole hybrid structure, the energy focusing structure plays the role of an energy reservoir for the BNA or MR, while the BNA or MR act as a nanoscale outlet for the energy focusing structure [30,31]. Our designed structure successfully realizes optical energy focusing; more importantly, the focusing energy can be high-efficiently coupled out with the aid of the BNA or MR.

2. Results and discussion

Figures 1(a) and 1(b) show the 3D schematic and cross-sectional view of the proposed optical energy focusing structure, which consists of a circular Bragg nanocavity above a circular plasmonic lens separated by a SiO₂ spacer layer. The circular Bragg nanocavity consists of a core SiO₂ disk (diameter D₁ = 160 nm and height H₁ = 150 nm) surrounded by ten pairs of concentric SiO₂ rings, with width W₁ = 450 nm, which are embedded in TiO₂ cladding. The low-index SiO₂ (refractive index n = 1.45) and high-index TiO₂ (refractive index n = 2.4) are periodically alternated along the radial direction, forming radial Bragg reflectors (RBRs). The circular plasmonic lens comprises a central Ag disk, with a diameter D₂ = 340 nm and a height H₂ = 50 nm, surrounded by concentric Ag rings on top of a Ag substrate. The center of the plasmonic lens is in alignment with that of the Bragg nanocavity along the z-axis. The width of the Ag rings is optimized as W₂ = 200 nm, and the distance between the central Ag disk and the innermost Ag ring is V = 160 nm. The variations of the period of the SiO₂ rings and Ag rings and the thickness L of the SiO₂ spacer layer will be discussed later. Numerical simulations are performed using the FDTD method to calculate the electromagnetic properties of this energy focusing structure. The structure is normally illuminated by a plane wave, polarized along the x-axis, as shown in Fig. 1(b).

 

Fig. 1 (a) Schematic and (b) cross-sectional view of the hybrid energy focusing structure.

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In our hybrid dielectric-metallic cavity, two different mechanisms contribute to the focusing by making full use of different polarization components of the incident light. The electric and magnetic fields of the linearly polarized incident light can be decomposed into two groups of orthogonal parts: the azimuthal component E_a and the radial component E_r and the azimuthal component H_a and the radial component H_r, respectively, where E_a, H_a are tangential to the SiO₂/TiO₂ rings and E_r, H_r are perpendicular to the SiO₂/TiO₂ rings [32], as depicted in Fig. 2(a). When normally illuminated with linearly polarized light, polarized along the x-axis, the circular dielectric Bragg nanocavity first diffracts and converts the normal light incident to in-plane guided waves; the guided waves then interfere with each other and are eventually focused in the center of the Bragg nanocavity [15]. Fig. 2(c) describes the |E|/|E₀| of Detector A₁ as a function of the period of the SiO₂ rings, calculated from 300 nm to 1000 nm, taking 25 nm as a step length; |E|/|E₀| reaches the maximum value when the period is 700 nm at the wavelength of 922 nm. Thus, the period of the SiO₂ rings in Fig. 1(b) is chosen to be P₁ = 700 nm; the widths of TiO₂ and SiO₂ rings are 250 nm and 450 nm. For an ideal distributed (conventional) Bragg reflector [33,34], the constituent layers are often one-quarter-wavelength thick; i.e., $d_i\approx m\lambda /4n_i$, where m is an integer, n_i is the refractive index of the i-th layer, d_i is the width of the i-th layer, and $\lambda$ is the wavelength of the incident light. Such a structure ensures that the partial reflections from the interfaces separating successive layers accumulate identical phase (an integer multiple of $2\pi$) and interfere constructively [33]. But for the circular or radial Bragg reflectors, the forward or backword propagating waves are replaced by outgoing and incoming cylindrical waves, represented by the Hankel functions of the first and second kinds [25,33,35]. In the radial geometry, the solutions (Hankel or Bessel functions) are not periodic, and the widths of the Bragg layers vary according to the oscillations of a Bessel/Hankel function [24,33]; in order to obtain maximal confinement, the interfaces of the Bragg layers should be positioned at the zeros and extrema of the field [35]. However, since the periodic structures are more reliable in terms of fabrication feasibility and the optimization process can be greatly simplified, periodic structures are still adopted for the circular or radial Bragg reflectors [15,36].

 

Fig. 2 (a) The E-field and H-field of linearly polarized light incident on a Bragg nanocavity can be decomposed into azimuthal component E_a, H_a and radial component E_r, H_r. (b) Schematic views of the isolated Bragg nanocavity (upper) and the isolated plasmonic lens (lower), respectively. Detector A₁ is at the center of the upper surface of the isolated Bragg nanocavity, and Detector A₂ is 10 nm above the right edge of the central Ag disk of the plasmonic lens. (c) The |E|/|E₀| of Detector A₁ of the isolated Bragg nanocavity for different periods of SiO₂ rings and wavelengths. (d) The |E|/|E₀| and |H|/|H₀| of Detector A₁ of the isolated Bragg nanocavity and the |E|/|E₀| and |H|/|H₀| (magnified 2 times) of Detector A₂ of the isolated plasmonic lens as a function of wavelength. The periods of the SiO₂ rings and Ag rings are P₁ = 700 nm and P₂ = 500 nm, respectively. (e), (f) The simulated |E|/|E₀| and |H|/|H₀| distributions of the xy-plane under linear polarization for the isolated Bragg nanocavity at a wavelength of 922 nm; the xy-plane is the upper surface of the Bragg nanocavity. (g), (h) The simulated |E|/|E₀| and |H|/|H₀| distributions of the xy-plane under linear polarization for the isolated plasmonic lens at a wavelength of 560 nm; the xy-plane is 10 nm above the plasmonic lens. The number of Ag rings of the plasmonic lens is N = 18. The white double-headed arrow represents the polarization direction of the linearly polarized incident light, polarized along the x-axis.

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For the linearly polarized incident light (polarized along the x-axis), it has larger E_a component and H_r component around the y-axis, and the Bragg nanocavity utilizes the azimuthal polarized light (E_a component and H_r component) in the process of optical energy focusing; thus, the in-plane guided waves are mainly generated and focused along the y-axis, as shown in Figs. 2(e) and 2(f). Note that the focused magnetic field does not form a sharp focus in the center but generates a two-lobe pattern along the y-axis due to the destructive interference of the main component H_z of the magnetic field in the center. In Fig. 2(d), the red and green lines show the wavelength dependence of |E|/|E₀| and |H|/|H₀| of the isolated Bragg nanocavity at Detector A₁, with the maximum values appearing at 922 nm, at which |E|/|E₀| and |H|/|H₀| can be up to 43 and 23, respectively. At this resonant wavelength, the quality factor of the isolated Bragg nanocavity is Q ≈102, and the mode volume is $V_m\approx 0.64{(\lambda /n)}^3$; $Q/V_m$reaches $159.38{(\lambda /n)}^{\text{-}3}$ and the Purcell factor [37] is $F_p=\frac{3}{4{\pi }^2}{(\frac{\lambda }{n})}^3(\frac{Q}{V_m})\approx 12$, where n is the refractive index at the field intensity maximum; here, n is 1.45, the refractive index of SiO₂.

However, for the isolated plasmonic lens, SPPs are preferentially generated along the polarized direction of the incident light because only the polarized component perpendicular to the Ag rings can excite SPPs [26]. To ensure that the generated SPPs are constructive interference in the center of the plasmonic lens, the period P₂ of the Ag rings is chosen to be the SPP wavelength [36,38] ${\lambda }_{spp}=2\pi /\mathrm{Re}(k_{spp})\approx 500nm$, where $k_{spp}$ is the wave vector, $k_{spp}=(2\pi /\lambda ){[{\epsilon }_m{\epsilon }_d/({\epsilon }_m+{\epsilon }_d)]}^{1/2}$; $\lambda$ is the resonant wavelength of the central Ag disk on top of the Ag substrate; ${\epsilon }_m$ and ${\epsilon }_d$ are the permittivities of the metal and dielectric (air), respectively. For the linearly polarized incident light (polarized along the x-axis), it has larger E_r component and H_a component around the x-axis, and the plasmonic lens utilizes the radial polarized light (E_r component and H_a component) in the process of optical energy focusing; thus, the SPPs are mainly generated and focused along the x-axis, as shown in Figs. 2(g) and 2(h), which are in sharp contrast to Figs. 2(e) and 2(f). Moreover, similar to the magnetic field in Fig. 2(f), the focused electric field does not form a sharp focus in the center of the plasmonic lens but generates a two-lobe pattern along the x-axis, due to the destructive interference of the main component E_z of the electric field in the center [26,39,40], as shown in Fig. 2(g).

Combining the Bragg nanocavity with the plasmonic lens, a hybrid photonic-plasmonic cavity is formed [17,18], as depicted in Fig. 3(a). Take the electric field as an example, the |E|/|E₀| at Detector B1 and the resonant wavelengths of the energy focusing structure can be further tuned by altering the thickness L of the SiO₂ spacer layer. When L is smaller than 200 nm, there is a strong coupling between the Bragg nanocavity and plasmonic lens, and |E|/|E₀| largely depends on the distance L and reaches the maximal value (|E|/|E₀| = 70) when L is 15 nm, at a wavelength of 850 nm. The thickness of SiO₂ spacer layer L also has an apparent influence on the resonant wavelengths of the energy focusing structure. When L is smaller than 200 nm, the resonant wavelengths increase rapidly as L increases, as shown in Fig. 3(b). The coupling among the Bragg nanocavity, plasmonic lens and the SiO₂ spacer leads to blue-shift of the resonant wavelengths for the isolated Bragg nanocavity, and red-shift for the isolated plasmonic lens. When L is larger than 200 nm, the resonant wavelengths of the energy focusing structure tend to stabilize with small fluctuation. Moreover, with the increase of the number N of Ag rings (L = 15 nm), the maximums of |E|/|E₀| and |H|/|H₀| gradually increase, reaching 70 and 100, respectively, when N = 18; the resonant wavelengths first blue-shift gradually and then tend to stabilize at the wavelength of 850 nm, as shown in Figs. 3(c) and 3(d). At the resonant wavelength, the quality factor of the energy focusing structure is Q ≈70, which is smaller than that of the isolated Bragg nanocavity (Q ≈102) due to the metal absorption losses. However, the mode volume is $V_m\approx 0.35{(\lambda /n)}^3$; $Q/V_m$ reaches $200{(\lambda /n)}^{\text{-}3}$, and the Purcell factor [37] is F_p ≈15, where n is 1.45, the refractive index of SiO₂, which increases by 1.25 times compared with that for the isolated Bragg nanocavity (F_p ≈12). The energy focusing structure combines the advantages of lower losses of the Bragg nanocavity and stronger field confinement characteristic of the plasmonic lens, and this large $Q/V_m$ ratio significantly increases the Purcell factor [37] and enhances the spontaneous emission rate for emitters in the cavity center [23,41].

 

Fig. 3 (a) Schematic view of the simplified energy focusing structure. (b) |E|/|E₀| (black line) and corresponding resonant wavelength (blue line) of Detector B₁ of the energy focusing structure as a function of the thickness of SiO₂ spacer layer L, using a logarithmic scale (Log10). Detector B₁ is at the center of the upper surface of the Bragg nanocavity. (c) |E|/|E₀| of Detector B₁ for different numbers of Ag rings and wavelengths when L is equal to 15nm. (d) |H|/|H₀| of Detector B₂ for different numbers of Ag rings and wavelengths when L is equal to 15nm. Detector B₂ is 10 nm above the center of the upper surface of the plasmonic lens. The periods of the SiO₂ rings and Ag rings are P₁ = 700 nm and P₂ = 500 nm.

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The corresponding electric and magnetic field distributions are calculated and shown in Fig. 4; the field is dramatically enhanced compared with a isolated Bragg nanocavity or a isolated plasmonic lens. In addition, when illuminated by oblique incident plane wave, the electric and magnetic field distributions are also calculated with the incident angle $1°$, $5°$ and $10°$. With the increase of the incident angle, the focusing field becomes gradually dispersed and the field enhancements are reduced accordingly.

 

Fig. 4 (a), (c), (e) |E|/|E₀| distributions and (b), (d), (f) |H|/|H₀| distributions of the xy-plane, xz-plane and yz-plane of the optimized energy focusing structure at a wavelength of 850 nm. The xy-plane is the upper surface of the Bragg nanocavity, and the xz-plane and yz-plane cross the center of the Bragg nanocavity. The borders are highlighted by white dotted lines. The thickness L of the SiO₂ spacer layer is L = 15 nm; the number of Ag rings of the plasmonic lens is N = 18; the total diameter of this energy focusing structure is about 20 μm.

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In Fig. 4, the energy is mainly focused in the central region of the energy focusing structure, which is unfavorable for energy utilization. To couple out the energy and make it available, we first put a gold BNA on top of the energy focusing structure, as shown in Fig. 5(a). To ensure that the hybrid structure has the same resonant wavelength as the energy focusing structure (850 nm), the following geometric parameters are chosen for the gold BNA: thickness, t = 10 nm; gap, g = 4 nm; length of the equilateral triangle, s = 80 nm; and radius of curvature of each corner, r = 5 nm. The gold BNA is placed along the x-axis, parallel to the polarization direction of the incident light. As shown in Fig. 5(b), |E|/|E₀| for a isolated gold BNA (black curve) and a gold BNA integrated with our energy focusing structure (red curve) are 195 and 3092, respectively, at the resonant wavelengths of 750 nm and 850 nm. This means that due to the coupling between the BNA and our energy focusing structure, |E|/|E₀| increases by more than 15 times compared with that for the isolated BNA. In Figs. 5(c) and 5(d), the energy is highly localized within the gap of the BNA, which strongly proves that the original focused energy in the Bragg nanocavity is high-efficiently transferred to the BNA. The energy focusing structure has higher quality factor (Q ≈70), which plays the role of photon and electron reservoir for the BNA (lower quality factor, Q ≈12) that operates like a nanometer scale loss channel for the energy focusing structure. The resulting huge energy transfer toward BNA is based on their coupling of strongly unbalanced quality factors [30].

 

Fig. 5 (a) Schematic view of the BNA sitting directly at the center of the upper surface of the energy focusing structure. (b) |E|/|E₀| detected at the center of the gap of the BNA for a isolated BNA and a BNA integrated with the optical energy focused structure. (c), (d) |E|/|E₀| distributions of the xz-plane and xy-plane at a wavelength of 850 nm (left) and their corresponding enlarged electric field distributions of the BNA gap (right). The xz-plane and xy-plane both cross the center of the gap. The white dotted lines show the borders of different structures.

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Second, we put a MR, a circular metal-dielectric-metal sandwiched structure, on top of the energy focusing structure, as shown in Fig. 6(a). Similarly, to have the same resonant wavelength as the energy focusing structure, the dielectric and metal are chosen to be TiO₂ (refractive index n = 2.4) and Au, respectively. The diameter of the MR is d = 125 nm, the height of the Au disk is h₁ = 80 nm, and the height of the TiO₂ disk is h₂ = 40 nm. As shown in Fig. 6(b), |H|/|H₀| is 22 (black curve) and 200 (red curve) at a wavelength of 850 nm for a isolated MR (Q ≈20) and an MR integrated with our energy focusing structure. This means that due to the coupling between the MR and our energy focusing structure, |H|/|H₀| increases by 9.1 times compared with the isolated MR. In Figs. 6(c) and 6(d), the magnetic field is highly localized at the dielectric layer of the MR, which strongly confirms that our designed energy focusing structure can also high-efficiently deliver the original focused energy in the Bragg nanocavity to the MR due to their unbalanced quality factors.

 

Fig. 6 (a) Schematic view of the MR, which sits directly at the center of the upper surface of the energy focusing structure. (b) |H|/|H₀|, detected at the center of the MR, for a isolated MR and an MR integrated with our optical energy focused structure. (c), (d) The |H|/|H₀| distributions of the xz-plane and yz-plane at a wavelength of 850 nm. The xz-plane and yz-plane cross the center of the MR. The white dotted lines show the borders of different structures.

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3. Conclusion

In conclusion, we have shown that optical energy can be effectively focused by combining a circular dielectric Bragg nanocavity with a circular metallic plasmonic lens. In the process of optical energy convergence, the dielectric Bragg nanocavity mainly utilizes the azimuthal component E_a and radial component H_r of the linearly polarized incident light, while the metallic plasmonic lens mainly utilizes the radial component E_r and azimuthal component H_a; thus, the incident light can be utilized efficiently. It is shown that the distance between the Bragg nanocavity and plasmonic lens plays a crucial role in achieving energy focusing and that, at the optimal distance, the electric and magnetic field enhancements of the energy focusing structure are significantly higher than those of the isolated Bragg nanocavity and isolated plasmonic lens due to their strong coupling. When we put a BNA or MR directly on the designed energy focusing structure, the energy is high-efficiently coupled and focused into the BNA or MR; the electric field enhancement (|E|/|E₀|) in the BNA or magnetic field enhancement (|H|/|H₀|) in the MR can be more than 3000 or 200, respectively. This designed structure opens a new avenue in optical energy focusing and transferring, while the giant electric and magnetic field enhancement can be advantageously exploited in modern optical nanotechnologies, e.g., single-molecule SERS, photolithography, optical trapping, local heating, imaging, magnetic sensors, and magnetic nonlinearity.