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Photonics Research
Vol. 5, Issue 3, 194 (2017)

Effects of the slot width and angular position on the mode splitting in slotted optical microdisk resonator

Lingling Dai^1、2, Yiheng Yin¹, Yanhui Hu^1、2, Biyao Yang¹, and Ming Ding^1、2、*

Author Affiliations

¹School of Instrument Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China

²International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China

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DOI: 10.1364/PRJ.5.000194 Cite this Article Set citation alerts

Lingling Dai, Yiheng Yin, Yanhui Hu, Biyao Yang, Ming Ding. Effects of the slot width and angular position on the mode splitting in slotted optical microdisk resonator[J]. Photonics Research, 2017, 5(3): 194 Copy Citation Text

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Abstract

A novel slotted optical microdisk resonator, which significantly enhances light–matter interaction and provides a promising approach for increasing the sensitivity of sensors, is theoretically and numerically investigated. In this slotted resonator, the mode splitting is generated due to reflection of the slot. Remarkably, effects of the slot width and angular position on the mode splitting are mainly studied. The results reveal that the mode splitting is a second function of the slot width, and the maximum mode splitting induced by the slot deformation is achieved with

2.7853 \times 10^{9} Hz / nm

. Therefore, the slotted resonator is an excellent candidate for pressure and force sensing. Besides, the influence of the slot angular position on the mode splitting is a cosine curve with the highest sensitivity of

1.23 \times 10^{11} Hz / \deg

; thus, the optical characteristic demonstrates that the slotted resonator can be used for inertial measurements.

Keywords

Fiber optics Fiber optics and optical communications Fiber optics components Optical devices Resonators

T = {| a_{CW}^{out} |}^{2} / {| a_{in} |}^{2} = {| 1 - \frac{κ_{ex} (- i Δ w + i γ_{c} + \frac{Γ + κ_{0} + κ_{ex}}{2})}{{(- i Δ w + i γ_{c} + \frac{Γ + κ_{0} + κ_{ex}}{2})}^{2} - {(i γ_{c} + \frac{Γ}{2})}^{2}} |}^{2},

(1)

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R = \frac{n - 1}{n + 1} [1 - \frac{4 n e^{2 i k a}}{{(n + 1)}^{2} - e^{2 i k a} {(n - 1)}^{2}}],

(2)

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γ_{c} = \frac{| R |}{τ_{0}} - γ,

(3)

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Γ = \frac{Γ_{s}}{τ_{0}} = \frac{\int_{δ S} n^{2} (r) {| E (r) |}^{2} d r}{τ_{0} \int n^{2} (r) {| E^{0} (r) |}^{2} d r},

(4)

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{\begin{matrix} E_{ρ} = \frac{j}{w^{2} μ_{0} ϵ_{i} - β^{2}} (β \frac{d E_{z}}{d φ} - \frac{j m w μ_{0}}{ρ} H_{z}) \\ E_{φ} = \frac{j}{w^{2} μ_{0} ϵ_{i} - β^{2}} (\frac{j m β}{ρ} E_{z} + w μ_{0} \frac{d H_{z}}{d ρ}) \\ H_{ρ} = \frac{j}{w^{2} μ_{0} ϵ_{i} - β^{2}} (β \frac{d H_{z}}{d φ} + \frac{j m w ϵ_{i}}{ρ} E_{z}) \\ H_{φ} = \frac{j}{w^{2} μ_{0} ϵ_{i} - β^{2}} (\frac{j m β}{ρ} H_{z} - w ϵ_{i} \frac{d E_{z}}{d ρ}) \end{matrix},

(5)

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Ψ (ρ) = {\begin{matrix} A_{m} J_{m} (k_{0} n_{eff} ρ), & ρ \leq R_{0} \\ B_{m} H_{m}^{(1)} (k_{0} ρ), & ρ > R_{0} \end{matrix},

(6)

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γ_{c} = | \frac{n - 1}{τ_{0} (n + 1)} [1 - \frac{4 n e^{2 i k a}}{{(n + 1)}^{2} - e^{2 i k a} {(n - 1)}^{2}}] | - [κ_{0} + κ_{ex} + \frac{\int_{δ S} n^{2} (r) {| E (r) |}^{2} d r}{\int n^{2} (r) {| E (r) |}^{2} d r}] / 2 .

(7)

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Δ f_{θ} = - \frac{f^{0}}{2} \frac{⟨ E_{CW} | Δ ϵ | E_{CCW} ⟩}{⟨ E^{0} | ϵ^{0} | E^{0} ⟩} + (Γ + κ_{ex} + κ_{0}) / 4 π,

(8)

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Δ f_{θ} = - \frac{f^{0} \int Δ ϵ (r) E_{CW} (r) E_{CCW}^{*} (r) d r}{2 \int ϵ^{0} (r) {| E^{0} (r) |}^{2} d r} + (Γ + κ_{ex} + κ_{0}) / 4 π .

(9)

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κ_{ex} = \frac{k}{4} \sqrt{\frac{ϵ_{0}}{μ_{0}}} \int δ n^{2} (r) E^{0} (r) E_{fiber} (r) d r,

(10)

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Lingling Dai, Yiheng Yin, Yanhui Hu, Biyao Yang, Ming Ding. Effects of the slot width and angular position on the mode splitting in slotted optical microdisk resonator[J]. Photonics Research, 2017, 5(3): 194

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