Improvement of the chirality near avoided resonance crossing in optical microcavity

QingHai SONG; ZhiYuan GU; Nan ZHANG; KaiYang WANG; NingBo YI; ShuMin XIAO

doi:10.1007/s11433-015-5729-9

SCIENCE CHINA Physics, Mechanics & Astronomy

SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 58, Issue 11: 114210(2015) https://doi.org/10.1007/s11433-015-5729-9

Improvement of the chirality near avoided resonance crossing in optical microcavity

QingHai SONG, ZhiYuan GU, Nan ZHANG, KaiYang WANG, NingBo YI, ShuMin XIAO

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ReceivedJul 1, 2015
AcceptedAug 12, 2015
PublishedSep 25, 2015

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Abstract

Chirality is one of the important phenomena at the vicinity of exceptional point (EP). The conventional understanding is that the chirality is determined by asymmetrical scattering efficiency (h), which reaches to zero only when the resonance approaches EP. Here we study the possibility to enhance the chirality in open systems with a more robust mechanism. By combining chirality with avoided resonance crossing, we show that the chirality and h can be dramatically modified. Taking a spiral shaped annular cavity as an example, we show that the chirality of optical resonances can be significantly improved when two sets of chiral states approach each other. The imbalance between counterclockwise (CCW) components and clockwise (CW) components has been enhanced by more than an order of magnitude. Our research provides a new route to tailor and control the chirality in open systems.

Funded by

Shenzhen Fundamental Researches . The author would like to thank Prof. WIERSIG Jan and Prof. CAO Hui for helpful questions and comments(JCYJ20130329155148184)

Shenzhen Peacock Plan(KQCX2012080709143322)

Program for New Century Excellent Talents in University(NCET-11-0809)

National Natural Science Foundation of China(11204055)

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Figure 1
(Color online) Real (a) and imaginary (b) parts of eigenenergies E_i as a function of D. Here E₁=D-0.05i, E₂=-0.005i, h₁=0.1, h₂=0.2, and $W_{1} ? W_{2} = 0.000275 ? 0.00005 i$ . (c) The dependence of asymmetrical scattering parameter hon D.
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Figure 2
(Color online) (a) A schematic picture of the spiral-shaped annular cavity. The outer boundary is a circle with r = R and the inner boundary is defined as $ρ = r_{0} + ε R \times (\frac{?}{2 π} ? 1) .$ (b) The resonances in an annular cavity with r₀ = 0.56R, and e = 0.15. (c) The field patterns of (|Hz|) of modes 1–3 marked in Figure 2(b).
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Figure 3
(Color online) The field distribution (|Hz|) along the outer cavity boundary of the inner-spiral cavity (a) and a circular cavity (b). Here the resonance has normalized frequency around kR=4.3456 and the Azimuthal number m=10.
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Figure 4
(Color online) (a) Normalized angular momentum distribution |a_m| of modes at kR = 4.3455-i0.00056. (b) The chirality a(squares) and K (dots) as a function of kR. The dashed line corresponds to K=1. For clear view, only the longer wavelength mode of every nearly degenerate pair is selected. The other mode of the degenerate pairs shows similar trends in botha and K. Here $K = \sum_{1}^{\infty} | α_{m}^{2} | / \sum_{? \infty}^{? 1} | α_{m}^{2} |$ corresponds to the imbalance between CCW and CW components.
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Figure 5
(Color online) The frequencies (a), Q factors (b), and K factors (c) of HQM with m=10, l=1 and LQM with m=6, l=2 as a function of e. The other parameters are the same as Figure 2. (d) The field patterns of modes i–vi in Figure 5(b).
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Figure 6
(Color online) (a) The dependence of K factor on the shape deformation at n=3.3 (dots) and n=3.25 (open squares). Here r₀ = 0.7R, w = 0.08R, and d = 0.055R. Unlike Figure 5(c), an additional sharp peak caused by EP can also be found. De and De₂ are defined as the width of K enhancement. (b) The position and peak value of the sharp peak as a function of d. Here we set r₀ = 0.7R and w=0.08R. (c) The far field pattern of the waveguide coupled spiral shaped annular disk at kR~12.5. Here r₀ = 0.7R, e=0.1166, w = 0.08R, and d = 0.045R. The schematic picture with field distribution is shown as the inset. (d) The dependence of unidirectional emission U (squares) and K (dots) on the shape deformation.
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Figure 7
(Color online) (a) The schematic picture of the annular ring with a spiral shaped inner boundary. (b), (c) The normalized resonant frequencies and Q factors as a function of later shift d. (d) The chirality of the high Q modes.
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Figure 8
(Color online) The field patterns of modes marked as 1–6 in Figure 7(b). Clear mixing in field patterns can be found in modes 3 and 4, where the mode crossing happens.

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42.50.Pq	Cavity quantum electrodynamics; micromasers
42.55.Sa	Microcavity and microdisk lasers
42.60.Da	Resonators, cavities, amplifiers, arrays, and rings
52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.

Improvement of the chirality near avoided resonance crossing in optical microcavity

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