Channeling Chaotic Rays into Waveguides for Efficient Collection of Microcavity Emission

Qinghai Song, Li Ge, Brandon Redding, and Hui Cao

Phys. Rev. Lett. 108, 243902 – Published 15 June 2012; Erratum Phys. Rev. Lett. 109, 039903 (2012)

Abstract

We demonstrate a robust and generic mechanism, which we term “chaos-assisted channeling,” to achieve unidirectional output from wave-chaotic microcavities with long-lived resonances. It utilizes the coexistence of regular and chaotic ray dynamics in most deformed microcavities. Long-lived resonances are formed by total internal reflection on classical periodic orbits, and their leakage into the chaotic region of the phase space is efficiently channeled into an attached waveguide without additional loss. We explain this behavior using a ray dynamics analysis which is confirmed via numerical simulations and experimental demonstration.

Received 31 January 2012
Corrected 19 June 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.243902

Corrections

19 June 2012

Erratum

Publisher’s Note: Channeling Chaotic Rays into Waveguides for Efficient Collection of Microcavity Emission [Phys. Rev. Lett. 108, 243902 (2012)]

Qinghai Song, Li Ge, Brandon Redding, and Hui Cao

Phys. Rev. Lett. 109, 039903 (2012)

Authors & Affiliations

Qinghai Song^1,*, Li Ge², Brandon Redding³, and Hui Cao³

¹Department of Electronic and Information Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China
²Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
³Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8482, USA

^*qinghai.song@hitsz.edu.cn

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Vol. 108, Iss. 24 — 15 June 2012

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Images

Figure 1
(a) Poincaré SOS for a quadruple cavity at $ϵ = 0.08$ . The cavity is taken to be closed. Fine details of the SOS are removed for clarity. Light in a high- $Q$ mode undergoes chaotic motion once it tunnels from islands into the neighboring chaotic region. The first 800 bounces of a typical trajectory outside the period-4 “diamond” islands are indicated by the blue dots, which form a chaotic layer around the islands. Its real space representation is shown in (b). Vertical solid lines in (a) indicate the position of the exit window [joint position between waveguide and cavity in (b)] centered at $θ = 0.633$ with an angular width of $Δ θ = 0.125$ . Red square in (a) marks the incident angle $χ_{w}$ of the light that enters straight into the waveguide.Reuse & Permissions
Figure 2
Normalized survival probability for (a) transverse electric (TE) and (b) transverse magnetic (TM) polarization in cavity-waveguide system as Fig. 1b with $n = 3.3$ . We start 40 000 rays of equal intensity uniformly above the critical angle in the SOS and their intensity evolves by the modified Fresnel law [31]. For simplicity, we reduce the intensity of each ray to zero once it impinges on the exit window. Color represents the total intensity of rays in a tiny area around each point in the SOS. The vertical solid lines and horizontal dotted line indicate the exit window to the waveguide and the critical line, respectively.Reuse & Permissions
Figure 3
(a) Resonance spectrum of the cavity-waveguide system shown in Fig. 1b. Diamond modes are indicated by $\times$ and the others are marked by $+$ . They appear as quasidegenerate pairs due to the slightly different influences of the waveguide on modes of different quasireflection symmetry. Open squares show the unidirectionality ( $U$ ) of modes 1–5. (b) FFP of mode 4 measured at $r = 2.3 R$ as a function of the observation angle $ϕ_{FF}$ . Inset: Corresponding mode structure ( $| H_{z} |$ ). (c) Enhanced Husimi projection of mode 4. Vertical solid lines indicate the exit windows to the waveguide.Reuse & Permissions
Figure 4
$Q$ -factor (a) and unidirectionality $U$ (b) of mode 4 in Fig. 3a as a function of the refractive index.Reuse & Permissions
Figure 5
(a) Measured emission spectrum from a quadruple-shaped microdisk with a waveguide. Inset: top-view SEM image. (b) Measured FFPs of the three lasing modes shown in (a). Top two lines of mode 2 and mode 3 are shifted vertically 0.2 and 0.4 for clarity, and each line is normalized by its peak intensity. Inset: top-view microscope image of mode 1. Dark regions indicate strong intensity and the dashed ring shows the position of the measurement ring, the scattering from which is measured to give the emission pattern.Reuse & Permissions

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