Strong superradiance of coherently coupled magnetic dipole emitters mediated by whispering gallery modes of a subwavelength all-dielectric cavity

Ma-Long Hu, Xiao-Jing Du, Lin Ma, Jun He, and Zhong-Jian Yang

Phys. Rev. B 106, 205420 – Published 28 November 2022

Abstract

The interaction of magnetic dipole (MD) emitters and common photonic cavities is usually weak, which is partially due to the low magnetic near-field enhancements of the cavities. Here, we show that whispering gallery modes (WGMs) of a subwavelength dielectric cavity can not only greatly boost the emission rate of a MD emitter but also bring efficient couplings between coherent MD emitters. In a WGM cavity, the maximal emission rate ( $γ_{\max}$ ) of a single emitter occurs at an antinode of the field pattern. The emission of the MD emitter can also be greatly affected by another coherent one depending on the magnetic-field response of the WGM. The maximal contribution can also reach $γ_{\max}$ . Notably, the cooperative emission rate of the coherent MD emitters does not decay with distance in the considered range due to the high-quality feature of a WGM. In contrast to the emission, the absorption of an emitter is hardly affected by the coherent couplings between emitters mediated by a WGM. The difference between the performances of emission and absorption is highly related to the excitation behaviors of WGMs. Our results are important for enhanced magnetic light-matter interactions.

Received 13 September 2022
Revised 12 November 2022
Accepted 15 November 2022

DOI:https://doi.org/10.1103/PhysRevB.106.205420

Physics Subject Headings (PhySH)

Atoms, ions, & molecules in cavities Nanophotonics Optical coherence Optical microcavities Spontaneous emission

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Ma-Long Hu, Xiao-Jing Du, Lin Ma, Jun He, and Zhong-Jian Yang ^*

Hunan Key Laboratory of Nanophotonics and Devices, School of Physics and Electronics, Central South University, Changsha 410083, China

^*zjyang@csu.edu.cn

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Issue

Vol. 106, Iss. 20 — 15 November 2022

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Images

Figure 1
(a) Schematic of a hybrid structure composed of a Si disk cavity and two identical MD emitters. The height and diameter of the disk are $h = 630 nm$ and $D = 1260 nm$ , respectively. The polarization directions of the MD emitters are both along the $z$ -axis. The center of the Si disk is located at (0,0,0). A magnetic field distribution ( $| B / B_{0} |$ ) pattern on the x-y plane of a TE WGM ( $m = 6$ ) is also shown. (b) The total decay rate enhancement $γ_{tot}^{(m)} / 2 γ_{0}^{(m)}$ of the coherent and incoherent MD emitters in the disk cavity. The red dotted line and green solid lines are the results obtained from the FDTD and the analytic method, respectively.
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Figure 2
(a) Magnetic field enhancement distribution ( $| B / B_{0} |$ ) of a TE WGM ( $m = 6$ ) in the Si disk. The MD emitters move on a circle with a radius of 480 nm, and the distance between the two emitters is denoted by the angle $θ$ . (b) The ratio $γ_{tot}^{(m)} / 2 γ_{0}^{(m)}$ of the coherent and incoherent MD emitters as a function of $θ$ . (c) The schematic of the location of the two coherent MD emitters with different radial locations. The location of the MD1 is fixed. MD2 can move on the radial lines of θ = 30 ° or 60 °. The distance between MD2 and the disk center is $L$ . (d) The ratio $γ_{tot}^{(m)} / 2 γ_{0}^{(m)}$ of coherent MD emitters as a function of $L$ . (e) The distribution of the ratio $γ_{tot}^{(m)} / 2 γ_{0}^{(m)}$ for two coherent MD emitters, where the MD1 is fixed and MD2 moves on the whole plane.
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Figure 3
(a) The ratio $γ_{tot}^{(m)} / 3 γ_{0}^{(m)}$ of three MDs. The locations of the three MDs with the corresponding field distribution are shown in the inset. The WGM cavity is the same as that in Fig. 1. (b) The ratio $γ_{tot}^{(m)} / 3 γ_{0}^{(m)}$ distribution of three coherent MD emitters. The locations of MD1 and MD2 are fixed while MD3 moves on the plane. Parts (c) and (d) show the same content as (a) and (b), respectively, while the MD2 is fixed at a different location.
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Figure 4
(a) Schematic of a hybrid system consisting of a TM WGM ( $m = 6$ ) cavity and two coherent MD emitters. (b) The ratio $γ_{tot}^{(m)} / 2 γ_{0}^{(m)}$ of the coherent and incoherent MD emitters as a function of $θ$ .
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Figure 5
(a) The magnetic field distribution of the TE $m = 6$ WGM on the x-y plane in the Si disk. A hole with a radius of 20 nm is introduced at the location of a field antinode. (b) The ratios of $γ^{(m)} / γ_{0}^{(m)}$ in a solid disk and a disk with a small hole. The inset shows the ratio $γ^{(m)} / γ_{1}^{(m)}$ of the MD in a solid disk that was calculated directly by the FDTD. Parts (c) and (d) show the same contexts of (a) and (b), respectively, while the emitter is replaced by an ED one. The corresponding expressions for decay rate ratios of an ED are $γ^{(p)} / γ_{0}^{(p)}$ and $γ^{(p)} / γ_{1}^{(p)}$ . Parts (e) and (f) show the same contexts of (c) and (d), respectively, while the working mode is replaced by a TM WGM of $m = 6$ .
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Figure 6
(a),(b) Schematic of a hybrid system of (a) case 1 and (b) case 2. The cavity is the same as that in Fig. 1. (c) The extinction spectra of the hybrid system. (d) The absorption spectra of the coherent MDs in the cavity. The individual MD and a single MD in the cavity are also shown for comparison.
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