Perturbing Open Cavities: Anomalous Resonance Frequency Shifts in a Hybrid Cavity-Nanoantenna System

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Perturbing Open Cavities: Anomalous Resonance Frequency Shifts in a Hybrid Cavity-Nanoantenna System

Freek Ruesink, Hugo M. Doeleman, Ruud Hendrikx, A. Femius Koenderink, and Ewold Verhagen

Phys. Rev. Lett. 115, 203904 – Published 11 November 2015

Abstract

The influence of a small perturbation on a cavity mode plays an important role in fields like optical sensing, cavity quantum electrodynamics, and cavity optomechanics. Typically, the resulting cavity frequency shift directly relates to the polarizability of the perturbation. Here, we demonstrate that particles perturbing a radiating cavity can induce strong frequency shifts that are opposite to, and even exceed, the effects based on the particles’ polarizability. A full electrodynamic theory reveals that these anomalous results rely on a nontrivial phase relation between cavity and nanoparticle radiation, allowing backaction via the radiation continuum. In addition, an intuitive model based on coupled mode theory is presented that relates the phenomenon to retardation. Because of the ubiquity of dissipation, we expect these findings to benefit the understanding and engineering of a wide class of systems.

Received 10 August 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.203904

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Hybrid quantum systems Nanoantennas

Atomic, Molecular & Optical

Authors & Affiliations

Freek Ruesink¹, Hugo M. Doeleman^1,2, Ruud Hendrikx¹, A. Femius Koenderink^1,2, and Ewold Verhagen^1,*

¹FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
²Institute of Physics, University of Amsterdam, P.O. Box 94485, 1090 GL Amsterdam, The Netherlands

^*verhagen@amolf.nl

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Issue

Vol. 115, Iss. 20 — 13 November 2015

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Images

Figure 1
(a) Cavity frequency and linewidth change due to perturbation by a small resonator, considering only the resonator polarizability. Dashed lines indicate the real (top) and imaginary (bottom) part of the polarizability as a function of $Δ / γ$ . (b) An array of perturbing gold nanoantennas is placed in the near field of a toroidal microcavity. Light transmission through the tapered fiber is detected to determine the cavity eigenfrequency shift. (c) Scanning electron microscopy (SEM) image of a high- $Q$ silica microtoroid at the edge of a chip. (d) SEM image of gold nanoantennas on a glass substrate. (e) Transmittance through the tapered fiber around a cavity mode resonance. A Lorentzian fit (black solid line) is used to determine the optical linewidth ( $\approx 30 MHz$ ) and frequency of the cavity. The sidebands result from a 150-MHz phase modulation used to calibrate the frequency axis. (f) Normal-incidence transmission spectra of gold nanoantenna (design length $L$ ) arrays. Lorentzian fits (sold lines) give the antenna resonance frequency and linewidth. The dashed line indicates the cavity frequency.
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Figure 2
(a) Depending on $Δ$ , antenna arrays induce linewidth broadening (top) and narrowing (bottom), while simultaneously inducing the cavity resonance frequency to blueshift. The blue and red horizontal bars represent the linewidths of fitted Lorentzian line shapes (black lines). (b) Shift in resonance frequency and linewidth of the cavity mode, normalized to its linewidth in absence of the antennas [19], due to perturbation by antenna arrays with a constant pitch size and varying antenna length. Top: For all detunings, a blueshift of cavity resonance frequency is observed. Bottom: Approaching $Δ = 0$ induces linewidth narrowing. Both the blueshift and linewidth narrowing are contrary to the expectation based on the particles’ polarizability [Fig. 1]. Error bars depict standard deviation, vertical error bars fall within the plot markers. The solid lines represent a coupled mode theory fit.
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Figure 3
(a) Electric field profile in a simulated system containing cavity, antenna and substrate. Both antenna and cavity radiate into the glass under approximately the same angle, resulting in a radiation interaction. The contribution of this interaction is calculated on the dashed black line [integral of Eq. (1)]. The arrow points to the position of the antenna. (b) Top(bottom): the change in resonance frequency (linewidth) calculated using Eq. (1). Black crosses (“ $A$ ”) show the contribution of the polarizability to the eigenfrequency shift $δ ω$ , which resembles the line shape as we expect it from a resonant particle [Fig. 1]. The radiative contribution (green stars, “ $B$ ”) shows distinct blueshifts and linewidth narrowing near $Δ / γ = 0$ . Adding both terms (blue circles, “ $A + B$ ”) yields the complete cavity eigenfrequency shift, which matches the experimental trends.
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Figure 4
(a) The cavity and antenna are coupled with rate $g_{c}$ , which is the near-field interaction scaling with the polarizability of the antenna, and can radiate into the continuum with a certain delay ( $δ ϕ$ ) with respect to each other. The interference between both radiation profiles and the overlap with the cavity mode results in a backaction effect (single-headed dashed arrow) on the cavity mode. (b) Coupled-mode theory. The cavity and antenna are coupled with rate ${\tilde{g}}_{c}$ and couple to the continuum with complex rates ${\tilde{g}}_{κ} = g_{κ} e^{i ϕ_{κ}}$ and ${\tilde{g}}_{γ} = g_{γ} e^{i ϕ_{γ}}$ , respectively. The difference between $ϕ_{κ}$ and $ϕ_{γ}$ , summed with the phase response of the antenna, is now equal to the phase difference $δ ϕ$ . $κ_{0}$ and $γ_{0}$ are the losses of cavity and antenna into noncoupled channels. The environment is modeled as an oscillator with decay rate $ζ$ .
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