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Journals >Photonics Research >Volume 5 >Issue 4 >Page 367 > Article

Photonics Research
Vol. 5, Issue 4, 367 (2017)

Optomechanically induced transparency in a spinning resonator

Hao Lü^1、2, Yajing Jiang³, Yu-Zhu Wang¹, and Hui Jing^4、*

Author Affiliations

¹Key Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²University of Chinese Academy of Sciences, Beijing 100049, China

³Department of Physics, Henan Normal University, Xinxiang 453007, China

⁴Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China

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DOI: 10.1364/PRJ.5.000367 Cite this Article Set citation alerts

Hao Lü, Yajing Jiang, Yu-Zhu Wang, Hui Jing. Optomechanically induced transparency in a spinning resonator[J]. Photonics Research, 2017, 5(4): 367 Copy Citation Text

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Abstract

We study optomechanically induced transparency in a spinning microresonator. We find that in the presence of rotation-induced Sagnac frequency shift, both the transmission rate and the group delay of the signal are strongly affected, leading to a Fano-like spectrum of transparency. In particular, tuning the rotary speed leads to the emergence of nonreciprocal optical sidebands. This indicates a promising new way to control hybrid light–sound devices with spinning resonators.

Keywords

Coherent optical effects Optomechanics

ω_{a} \to ω_{a} + Δ_{sag},

(1)

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Δ_{sag} = \frac{n r Ω ω_{a}}{c} (1 - \frac{1}{n^{2}} - \frac{λ}{n} \frac{d n}{d λ}),

(2)

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H = Δ_{+} a^{†} a - ξ x a^{†} a + \frac{p^{2}}{2 m} + \frac{1}{2} m ω_{m}^{2} x^{2} + \frac{p_{θ}^{2}}{2 m r^{2}} + i \sqrt{γ_{ex}} ϵ_{l} (a^{†} e^{- i ω_{l} t} - a e^{i ω_{l} t}) + i \sqrt{γ_{ex}} ϵ_{p} (a^{†} e^{- i ω_{p} t} - a e^{i ω_{p} t}),

(3)

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\dot{a} = - (i Δ_{+} - i ξ x + β) a + \sqrt{γ_{ex}} ϵ_{l} + \sqrt{γ_{ex}} ϵ_{p} e^{- i η t}, \ddot{x} + γ_{m} \dot{x} + ω_{m}^{2} x = \frac{ξ}{m} a^{†} a + \frac{p_{θ}^{2}}{m^{2} r^{3}}, \dot{θ} = \frac{p_{θ}}{m r^{2}}, {\dot{p}}_{θ} = 0,

(4)

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\bar{a} = \frac{\sqrt{γ_{ex}} ϵ_{l}}{β + i Δ_{+} - i ξ \bar{x}}, \bar{x} = \frac{γ_{ex} ξ {| ϵ_{l} |}^{2}}{m ω_{m}^{2} {[β^{2} + {(Δ_{+} - ξ \bar{x})}^{2}]}^{2}} + r {(\frac{Ω}{ω_{m}})}^{2},

(5)

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a = \bar{a} + δ a_{-} e^{- i η t} + δ a_{+} e^{i η t}, x = \bar{x} + δ x e^{- i η t} + δ x^{*} e^{i η t} .

(6)

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(β + i Δ_{+} - i ξ \bar{x} - i η) δ a_{-} - i ξ \bar{a} δ x = \sqrt{γ_{ex}} ϵ_{p}, (β - i Δ_{+} + i ξ \bar{x} - i η) δ a_{+}^{*} + i ξ {\bar{a}}^{*} δ x = 0, (ω_{m}^{2} - η^{2} - i η γ_{m}) δ x = \frac{ξ}{m} ({\bar{a}}^{*} δ a_{-} + \bar{a} δ a_{+}^{*}) .

(7)

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δ a_{-} = \frac{\sqrt{γ_{ex}} ϵ_{p}}{h_{1} (η)} [1 + \frac{i {| \bar{a} |}^{2} ξ^{2} χ (η)}{h_{1} (η) - 2 {| \bar{a} |}^{2} ξ^{2} χ (η) h_{2} (η)}],

(8)

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h_{1} (η) = β + i Δ_{+} - i ξ \bar{x} - i η, h_{2} (η) = \frac{Δ_{+} - ξ \bar{x}}{β - i Δ_{+} + i ξ \bar{x} - i η}, χ (η) = \frac{1}{m (ω_{m}^{2} - η^{2} - i γ_{m} η)} .

(9)

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a_{out} = a_{in} - \sqrt{γ_{ex}} δ a_{-},

(10)

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T = {| t_{p} |}^{2} = {| \frac{a_{out}}{a_{in}} |}^{2} = {| 1 - \frac{\sqrt{γ_{ex}}}{ϵ_{p}} δ a_{-} |}^{2} .

(11)

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f = {\frac{T (Ω \neq 0)}{T (Ω = 0)} |}_{Δ_{p} = 0} - 1 .

(12)

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τ_{g} = \frac{d \arg (t_{p})}{d Δ_{p}} .

(13)

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D = \frac{τ_{g} (Ω \neq 0)}{τ_{g} (Ω = 0)} - 1 .

(14)

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Hao Lü, Yajing Jiang, Yu-Zhu Wang, Hui Jing. Optomechanically induced transparency in a spinning resonator[J]. Photonics Research, 2017, 5(4): 367

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