Researching | Strong light–matter interactions based on excitons and the abnormal all-dielectric anapole mode with both large field enhancement and low loss

Journals >Photonics Research >Volume 12 >Issue 4 >Page 854 > Article

Photonics Research
Vol. 12, Issue 4, 854 (2024)

Strong light–matter interactions based on excitons and the abnormal all-dielectric anapole mode with both large field enhancement and low loss

Yan-Hui Deng¹, Yu-Wei Lu^1、2, Hou-Jiao Zhang¹, Zhong-Hong Shi¹, Zhang-Kai Zhou^1、3、*, and Xue-Hua Wang^1、4、*

Author Affiliations

¹State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-sen University, Guangzhou 510275, China

²Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area (Guangdong), Shenzhen 518045, China

³e-mail: zhouzhk@mail.sysu.edu.cn

⁴e-mail: wangxueh@mail.sysu.edu.cn

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DOI: 10.1364/PRJ.514576 Cite this Article Set citation alerts

Yan-Hui Deng, Yu-Wei Lu, Hou-Jiao Zhang, Zhong-Hong Shi, Zhang-Kai Zhou, Xue-Hua Wang. Strong light–matter interactions based on excitons and the abnormal all-dielectric anapole mode with both large field enhancement and low loss[J]. Photonics Research, 2024, 12(4): 854 Copy Citation Text

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Abstract

The room temperature strong coupling between the photonic modes of micro/nanocavities and quantum emitters (QEs) can bring about promising advantages for fundamental and applied physics. Improving the electric fields (EFs) by using plasmonic modes and reducing their losses by applying dielectric nanocavities are widely employed approaches to achieve room temperature strong coupling. However, ideal photonic modes with both large EFs and low loss have been lacking. Herein, we propose the abnormal anapole mode (AAM), showing both a strong EF enhancement of

\sim 70

-fold (comparable to plasmonic modes) and a low loss of 34 meV, which is much smaller than previous records of isolated all-dielectric nanocavities. Besides realizing strong coupling, we further show that by replacing the normal anapole mode with the AAM, the lasing threshold of the AAM-coupled QEs can be reduced by one order of magnitude, implying a vital step toward on-chip integration of nanophotonic devices.

e (ω) = a_{r} + \sum_{j = 1, 2} \frac{b_{j} γ_{j} e^{i ϕ_{j}}}{ω - ω_{j} + i γ_{j}},

(1)

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ε_{ex} (ω) = ε_{\infty} + \frac{f ω_{ex}^{2}}{ω_{ex}^{2} - ω^{2} - i ω γ_{ex}},

(2)

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{\ddot{x}}_{ca 1} (t) + γ_{ca 1} {\dot{x}}_{ca 1} (t) + ω_{ca 1}^{2} x_{ca 1} + 2 g_{1} {\dot{x}}_{ex} (t) = F_{ca} (t),

(3a)

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{\ddot{x}}_{ca 2} (t) + γ_{ca 2} {\dot{x}}_{ca 2} (t) + ω_{ca 2}^{2} x_{ca 2} + 2 g_{2} {\dot{x}}_{ex} (t) = F_{ca} (t),

(3b)

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{\ddot{x}}_{ex} (t) + γ_{ex} {\dot{x}}_{ex} (t) + ω_{ex}^{2} x_{ex} - 2 g_{1} {\dot{x}}_{ca 1} (t) = 0,

(3c)

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x_{ca 1} (ω) = \frac{(ω_{ex}^{2} - ω^{2} - i γ_{ex} ω) F_{ca} (ω)}{(ω^{2} - ω_{ca 1}^{2} + i γ_{ca 1} ω) (ω^{2} - ω_{ex}^{2} + i γ_{ex} ω) - 4 ω^{2} g_{1}^{2}},

(4a)

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x_{ca 2} (ω) = \frac{(ω_{ex}^{2} - ω^{2} - i γ_{ex} ω) F_{ca} (ω)}{(ω^{2} - ω_{ca 2}^{2} + i γ_{ca 2} ω) (ω^{2} - ω_{ex}^{2} + i γ_{ex} ω) - 4 ω^{2} g_{2}^{2}},

(4b)

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x_{ex} (ω) = \frac{- i g_{1} ω F_{ca} (ω)}{(ω^{2} - ω_{ca 1}^{2} + i γ_{ca 1} ω) (ω^{2} - ω_{ex}^{2} + i γ_{ex} ω) - 4 ω^{2} g_{1}^{2}} .

(4c)

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C_{sca} (ω) = \frac{8 π}{3} k^{4} {| α |}^{2} \propto A ω^{4} {| x_{ca} |}^{2},

(4d)

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C_{sca} (ω) \propto A ω^{4} {{| \frac{ω_{ex}^{2} - ω^{2} - i γ_{ex} ω}{(ω^{2} - ω_{ca 1}^{2} + i γ_{ca 1} ω) (ω^{2} - ω_{ex}^{2} + i γ_{ex} ω) - 4 ω^{2} g_{1}^{2}} |}^{2} + {| \frac{ω_{ex}^{2} - ω^{2} - i γ_{ex} ω}{(ω^{2} - ω_{ca 2}^{2} + i γ_{ca 2} ω) (ω^{2} - ω_{ex}^{2} + i γ_{ex} ω) - 4 ω^{2} g_{2}^{2}} |}^{2} + 2 | \frac{(ω_{ex}^{2} - ω^{2} - i γ_{ex} ω)^{2}}{[(ω^{2} - ω_{ca 1}^{2} + i γ_{ca 1} ω) (ω^{2} - ω_{ex}^{2} + i γ_{ex} ω) - 4 ω^{2} g_{1}^{2}] [(ω^{2} - ω_{ca 2}^{2} + i γ_{ca 2} ω) (ω^{2} - ω_{ex}^{2} + i γ_{ex} ω) - 4 ω^{2} g_{2}^{2}]} |},

(5a)

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C_{sca} (ω) = \frac{8 π}{3} k^{4} {| α |}^{2} \propto A ω^{4} ({| x_{ca} |}^{2} + {| x_{ex} |}^{2} + 2 | x_{ca} x_{ex} |) = A ω^{4} [\sum_{i, j} ({| x_{i} |}^{2} + {| x_{j} |}^{2} + 2 | x_{i} x_{j} |)] .

(5b)

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(\begin{matrix} ℏ ω_{ca} - i ℏ \frac{γ_{ca}}{2} & g \\ g & ℏ ω_{ex} - i ℏ \frac{γ_{ex}}{2} \end{matrix}) (\begin{matrix} α \\ β \end{matrix}) = ℏ ω (\begin{matrix} α \\ β \end{matrix}) .

(A1)

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ℏ ω_{\pm} = \frac{ℏ ω_{ca} + ℏ ω_{ex}}{2} - \frac{i ℏ (γ_{ca} + γ_{ex})}{4} \pm \frac{\sqrt{4 g^{2} + {(ℏ ω_{ca} - ℏ ω_{ex} - i ℏ \frac{γ_{ca}}{2} + i ℏ \frac{γ_{ex}}{2})}^{2}}}{2} .

(A2a)

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g^{2} > \frac{{(γ_{ca} - γ_{ex})}^{2}}{16} .

(A2b)

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g > g_{c} = \sqrt{\frac{γ_{ca}^{2} + γ_{ex}^{2}}{8}},

(A3)

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ℏ Ω_{ca} = 2 \sqrt{g (1 + \frac{γ_{ex}}{γ_{ca}}) {(g^{2} + \frac{γ_{ex} γ_{ca}}{4})}^{\frac{1}{2}} - (g^{2} + \frac{γ_{ex} γ_{ca}}{4}) \frac{γ_{ex}}{γ_{ca}}}, if g^{2} > \frac{γ_{ex}^{2}}{8 (1 + γ_{ca} / 2 γ_{ex})},

(A4)

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{ℏ Ω}_{ex} = 2 \sqrt{g (1 + \frac{γ_{ca}}{γ_{ex}}) {(g^{2} + \frac{γ_{ex} γ_{ca}}{4})}^{\frac{1}{2}} - (g^{2} + \frac{γ_{ex} γ_{ca}}{4}) \frac{γ_{ca}}{γ_{ex}}}, if g^{2} > \frac{γ_{ca}^{2}}{8 (1 + γ_{ex} / 2 γ_{ca})} .

(A5)

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\nabla \times \nabla \times G (r, r^{'}, ω) - k_{0}^{2} ε (r, ω) G (r, r^{'}, ω) = k_{0}^{2} I δ (r - r^{'}),

(B1)

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PF = \frac{Im [n \cdot G (r_{A}, r_{A}, ω) \cdot n]}{G_{0}},

(B2)

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p_{α} = - \frac{1}{i ω} {\int d^{3} \hat{r} J_{α}^{ω} j_{0} (k r) + \frac{k^{2}}{2} \int d^{3} \hat{r} [3 (\hat{r} \cdot {\hat{J}}_{ω}) r_{α} - r^{2} J_{α}^{ω}] \frac{j_{2} (k r)}{{(k r)}^{2}}} .

(C1a)

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m_{α} = \frac{3}{2} \int d^{3} \hat{r} {(\hat{r} \times {\hat{J}}_{ω})}_{α} \frac{j_{1} (k r)}{k r} .

(C1b)

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Q_{α β}^{e} = - \frac{3}{i ω} {\int d^{3} \hat{r} [3 (r_{β} J_{α}^{ω} + r_{α} J_{β}^{ω} - 2 (\hat{r} \cdot {\hat{J}}_{ω}) δ_{α β}] \frac{j_{1} (k r)}{k r} + 2 k^{2} \int d^{3} \hat{r} [5 r_{α} r_{β} (\hat{r} \cdot {\hat{J}}_{ω}) - (r_{α} J_{β} + r_{β} J_{α}) r^{2} + r^{2} (\hat{r} \cdot {\hat{J}}_{ω}) δ_{α β}] \frac{j_{3} (k r)}{{(k r)}^{3}}},

(C1c)

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Q_{α β}^{m} = 15 \int d^{3} \hat{r} [r_{α} {(\hat{r} \times {\hat{J}}_{ω})}_{β} + r_{β} {(\hat{r} \times {\hat{J}}_{ω})}_{α}] \frac{j_{2} (k r)}{{(k r)}^{2}},

(C1d)

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C_{sca}^{total} = C_{sca}^{p} + C_{sca}^{m} + C_{sca}^{Q^{e}} + C_{sca}^{Q^{m}} + \dots = \frac{k^{4}}{6 π ε_{0}^{2} {| E_{inc} |}^{2}} [\sum_{α} ({| p_{α} |}^{2} + \frac{{| m_{α} |}^{2}}{c}) + \frac{1}{120} \sum_{α} ({| k Q_{α β}^{e} |}^{2} + {| \frac{k Q_{α β}^{e}}{c} |}^{2}) + \dots],

(C2)

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p_{α} = \frac{1}{i ω} \int d^{3} \hat{r} J_{α}^{ω},

(C3a)

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T_{α} = \frac{1}{10 c} \int d^{3} \hat{r} [(\hat{r} \cdot {\hat{J}}_{ω}) r_{α} - 2 r^{2} J_{α}^{ω}] .

(C3b)

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H = ω_{c} c^{†} c + ω_{0} \sum_{k}^{N} σ_{+}^{k} σ_{-}^{k} + \sum_{k}^{N} g_{0}^{k} (c^{†} σ_{-}^{k} + σ_{+}^{k} c),

(D1)

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L_{L_{i}} (ρ) = \frac{1}{2} (2 L_{i} ρ L_{i}^{†} - {L_{i}^{†} L_{i}, ρ}),

(D2)

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\dot{c} = - i (ω_{c} - i \frac{κ_{c}}{2}) c - i \sum_{k}^{N} g_{0}^{k} σ_{-}^{k},

(D3a)

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{\dot{σ}}_{-}^{k} = - i (ω_{0} - i \frac{γ_{⊥}}{2}) σ_{-}^{k} + i g_{0}^{k} σ_{z}^{k} c,

(D3b)

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{\dot{σ}}_{z}^{k} = 2 i g_{c}^{k} (c^{†} σ_{-}^{k} - σ_{+}^{k} c) - γ_{0} (σ_{z}^{k} + 1) + γ_{0} η P (1 - σ_{z}^{k}),

(D3c)

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P_{th} = \frac{γ_{0}}{η} \frac{\bar{n} + v_{p}}{\bar{n} - v_{p}},

(D4)

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Yan-Hui Deng, Yu-Wei Lu, Hou-Jiao Zhang, Zhong-Hong Shi, Zhang-Kai Zhou, Xue-Hua Wang. Strong light–matter interactions based on excitons and the abnormal all-dielectric anapole mode with both large field enhancement and low loss[J]. Photonics Research, 2024, 12(4): 854

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