Enhancing single photon emission through quasi-bound states in the continuum of monolithic hexagonal boron nitride metasurface

A patterned structure of monolithic hexagonal boron nitride (hBN) on a glass substrate, which can enhance the emission of the embedded single photon emitters (SPEs), is useful for onchip single-photon sources of high-quality. Here, we design and demonstrate a monolithic hBN metasurface with quasi-bound states in the continuum mode at emission wavelength with ultrahigh Q values to enhance fluorescence emission of SPEs in hBN. Because of ultrahigh electric field enhancement inside the proposed hBN metasurface, an ultrahigh Purcell factor (3.3*10^4) is achieved. In addition, the Purcell factor can also be strongly enhanced in most part of the hBN structure, which makes the hBN metasurface suitable for e.g. monolithic quantum photonics.


3
The unique optical properties of hBN make it a fascinating candidate to be fabricated directly in a monolithic system. In particular, hBN maintains transparent in the visible range for its wide optical bandgap [10]. Furthermore, hBN exhibits high chemical stability and excellent thermal conductivity, which are beneficial to micro/nano fabrications [11]. Recently, hBN has already been used as a parent material to fabricate PCCs, micro-ring resonators, etc [12,13]. Although PCCs of high Q can be realized from the monolithic hBN layers, the Purcell enhancement was not as high as expected and one should precisely position the SPEs to electric field intensity hotspots of cavity modes.
In recent years, bound states in the continuum (BICs), which represent localized resonance modes embedded in radiative continuous spectra, have received many interests [14,15]. Kolodny et al reported that the enhancement of the Purcell factor in pillar microcavities can be realized by employing quasi-BIC modes [16]. However, this method requires top and bottom Bragg mirrors and the other material, and thus is more complex to fabricate and the SPEs should be precisely put into the location of maximal electric field intensity. High-Q Fano resonances originated from quasi-BICs can boost the light confinement inside the metasurfaces, which greatly enhance nonlinear harmonic conversion efficiency [17]. However, there are few studies to enhance internal SPEs by applying BICs or quasi-BICs. As a consequence, a hBN metasurface with BIC or quasi-BIC modes should be designed carefully for the Purcell enhancement of SPEs.
In this work, we design and demonstrate a monolithic hBN metasurface with 4 quasi-BIC mode at emission wavelength to enhance fluorescence emission of SPEs in hBN. The Purcell factor of the SPEs in an hBN metasurface can be tuned by changing the asymmetry parameter. An ultrahigh Purcell factor (3.3 × 10 4 ) is achieved. In addition, the Purcell factor can also be strongly enhanced in most parts of the patterned hBN structure, which can ease experimentally the precise positioning of the SPEs in the patterned hBN structure.

2.Methods
A TE-polarized plane wave normally incidents onto the metasurface, as shown in Fig.   1(a). The numerical analysis of the reflectance and eigenmode spectra for the designed metasurface with different asymmetry parameter δ (from 0 to 0.1) are performed based on commercial finite element technique (COMSOL Multiphysics).
The hBN was modeled as a uni-anisotropic material in this study and the used birefringence refractive indices of hBN are nx = ny= 1.84 and nz = 1.72 [12]. is inside the hBN structure.

BIC and quasi-BIC modes in an hBN metasurface
As shown in Fig. 1(a), we design a metasurface made of an hBN film and an hBN grating with broken in-plane inversion symmetry. The top layer is a two-part periodic grating with period P and thickness h1. The unit cell of the hBN grating is composed of a pair of infinite bars, which have widths wh + ∆w and wh−∆w, respectively. The gap between any two neighboring bars has the same value wa. The asymmetry parameter δ of the unit cell is defined as δ = ∆w/wh, as illustrated in Fig. 1(b). The thickness of the lower hBN film is h2.
The hBN metasurface is placed on a silica (n = 1.46) substrate. Figure 1(c) is the sectional view of the proposed metasurface in the x-z plane. The quasi-BIC modes with large internal field enhancement (upto 350 times) can be supported with proper structural parameters (P = 400 nm, h1 = 140 nm, h2 = 46 nm, wa = 0.2 P, and wh = 0.3 P). Accordingly, due to the high Q/V ratio of the patterned structure we have desgined, the Purcell factor is considerably enlarged, which significantly enhances the spontaneous emission rate of the SPEs (marked as the red dot in Fig. 1(c)) inside the hBN structure. The SPEs in hBN can be generated by using thermal annealing or ion [12,18]. The effects of these methods in experiments on the structure fabrication and Q-values will be discussed later. The dependence of the calculated reflectance spectra on the wavelength around 633 nm and the asymmetry parameter δ are shown in Fig. 2(a). The white dashed line indicates the eigenmode dispersion of the metasurface. With δ decreases from 0.1 to near 0, it can be seen that the linewidth of the resonance decreases clearly and the resonance peak slightly shifts toward long wavelengths. When δ=0, the resonance linewidth vanishes completely. As shown by the eigenmode dashed lines, the symmetric hBN metasurface supports the symmetry-protected BIC mode at 633.41 nm, which have infinite Q value. When breaking the symmetry with δ > 0, unstable BIC modes transform into quasi-BIC modes with a finite Q factor. The quasi-BIC modes can be seen in the reflectance spectra with ultranarrow linewidth resonance.
Furthermore, the corresponding Q factor of the quasi-BIC mode for different asymmetry parameter δ can be calculated by fitting the transmission spectra to Fano lineshape (see the Supplementary Material). When δ is 0.1, the Q factor of the 7 quasi-BIC mode is 2089.1. Then the Q factor increases fast, when δ gradually approaches zero. For instance, when δ is 0.01, the Q factor reaches 208648.1, which is much larger than that of PCCs in refs. 9 and 12. As depicted in Fig. 2(b), the relationship between radiative Q factor and asymmetry parameter δ follows the inverse quadratic law, i.e., Q factor is proportional to 1/δ 2 [19]. For the experiments, one can vary δ from 0.01 to 0.1.

Giant Purcell factor of single-photon emitters in the hBN metasurface with quasi-BIC modes
The radiative decay rate of the quantum emitters can be engineered by the tailored local density of optical states (LDOS), which can also be optimized by a metasurface [20]. The electric field profiles of quasi-BIC modes around 633 nm in the xOz cut plane at the corresponding resonances under δ=0.03 is shown in Fig. 3(a), which also 8 extends infinitely in the y-direction. The Figure S2 shows In the following simulations, the spatial positions of these four points are kept with different asymmetry parameter δ.
The Purcell factor of an electric dipole inside of the hBN metasurface is defined as [18]: where Veff is an effective mode volume and λ is the resonant wavelength. The effective mode volume Veff can be calculated by [21][22][23]: where rd and e are the position and polarization vector of the electric dipole, respectively. From Eq.
(2), one can find that Veff is in inverse proportion to the local electric field intensity. Then Veff for different δ at three different positions (A, B and C) are calculated and the results are shown in Fig. 3(b). For different δ (from 0.1 to 0.01), the effective mode volume changes slightly, which together with the sharp increase in Q factor benefits to enhance the Purcell factor. Due to electric field enhancement at 9 Point A is the highest among these three positions, Veff at Point A is the smallest when compared these three curves in Fig. 3(b).
The expected Purcell enhancement of single emitters due to the coupling to quasi-BIC modes are investigated by using 3D simulations of COMSOL Multiphysics.  Fig. 3(c). It can be found that the largest Purcell factor at Point A reaches up to 3.2 × 10 4 (δ=0.01), however, the Purcell factor decreases as the asymmetry parameter δ increases. Similar trends for the Purcell factor at Points B and C can also be observed from Fig. 3(c). For a specific δ, the Purcell factor at Point A is the largest because of its maximum enhancement of the electric field intensity among these four points. As a contrast, the Purcell factor for  The dependence of the Purcell factor on the emission wavelength of an electric dipole positioned at different points (Points A, B and C) and the asymmetry parameter δ (from 0.01 to 0.04) are shown in Fig. 4. For δ (from 0.05 to 0.08), the corresponding simulated Purcell factors are shown in Figure S6 in the Supplementary Material. It can be found that the full width at half maximum (FWHM) of the Purcell factor curve becomes narrower when δ is reduced from 0.08 to 0.01. For δ = 0.01, the FWHM is 0.018 nm, which means that its Q factor reaches 35181.1. Due to the coarser meshes and finite arrays used in simulations, this Q factor of Purcell factor is less than the Q factor of quasi-BIC mode (208648.15) (fitted by Eq. (S1); see Table S1 in Supplementary Material) when δ is 0.01. The Q factors of the Purcell factor curves are 21107.9, 14390.8, 9593.0 for δ =0.02, 0.03 and 0.04, respectively. Therefore, the emission of SPEs also has the property of ultra-narrow spectra. The wavelength of the Purcell factor peak exhibits blueshift when δ changes from 0.01 to 0.08, which accords with the blueshift of the quasi-BIC mode. It is worth noting that the wavelength of the Purcell factor curve has a small difference from the resonance wavelength of the quasi-BIC mode. This is because the mesh sizes for calculating the 3D Purcell factor of finite hBN arrays are a bit coarser (to save the calculation time) than those for calculating the 2D transmission spectra of infinite hBN metasurface.
For future experiments, two different methods can be used to precisely put the SPEs at positions where the electric field intensity of the quasi-BIC mode is maximal.
One is to find pre-existing SPEs and post-fabricate top hBN gratings around them [24]. The other approach is to deterministically create emitters in desired locations [25]. The periodicity of the hBN structure will be broken to some degrees when ions are implanted for SPEs. Then the quality factor of the quasi-BIC modes and the electric field enhancement will become much weaker, and ultimately, the Purcell 12 Factor will also diminish. Hence, in order to create SPEs in hBN, an additional annealing step at 850 °C can be employed after the fabrication of the pattern structure [12], although the SPEs will be in random locations. As Purcell factor can be strongly enhanced in most parts of the hBN structure, thermal annealing is suitable to create In addition, the present work can also be extended into other relevant material platforms, such as quantum dots in III/V semiconductors and color centers in diamond.
In future work, enhancing both the coupling efficiency and the emission of SPEs can be studied to make a useful source for quantum information processing. In general, the dipole orientations of emitters in 2D materials are random (see Ref. 26) and there will be no enhancements if the dipole orientations of the emitters are along x-or z-direction. One possible way to alleviate this problem is to design a patterned 13 structure with polarization-independent quasi-BIC modes so that the emission of both x-and y-oriented emitters can be enhanced.

Conclusions
In conclusion, we have proposed and demonstrated a monolithic hBN metasurface by quasi-BIC mode with ultrahigh Q factor to enhance the signals emitted by SPEs in hBN. Quasi-BIC modes have been utilized to enhance the Purcell factor of the SPEs in hBN. Furthermore, the relationship between the radiative Q factor and Purcell factor of the SPEs has been carefully studied for various asymmetric parameters.