Fig. 6: Mode splitting versus antenna spacing for dimer antennas hybridized with microdisk modes of various azimuthal and radial quantum number.
From: Cooperative interactions between nano-antennas in a high-Q cavity for unidirectional light sources
a, b The difference in resonance frequency (blue, weakly varying) and linewidth (red, strongly varying) between symmetric and antisymmetric modes as a function of the antenna separation for antennas hybridized with a the 1st radial mode at azimuthal mode number m = 86 (TE 86–1) and b a mode of larger mode volume and different azimuthal mode number (2nd-order radial mode m = 80, TE 80–2). c, d show a similar study with strongly blue-detuned antennas, where c shows the difference in resonance frequency (blue) and linewidth (red) and d reports the individual linewidths of symmetric (blue) and antisymmetric (red) modes. e Azimuthal mode number m′ extracted from fitting the oscillation in the perturbed frequency to Eq. (10) versus the simulated mode number m for all WGM modes in the laser bandwidth. f Polar representation of the measured complex-valued \(\frac{\alpha }{{\tilde V}}\) obtained by fitting the amplitude and phase of oscillation in frequency and linewidth to Eq. (10) [Δ: TE 80–2, □: TE 81–2, +: TE 85–1, ×: TE 86–1 for the on-resonant antenna and ◯ for the strongly blue-detuned antenna]. For reference, the circular curve shows the expected frequency dependence of \(\frac{\alpha }{{\tilde V}}\) for a Lorentzian polarizability [choosing \(\tilde V = 300\lambda ^3\) and an on-resonance extinction cross section of 0.12 μm2]. With frequency detuning Δac from antenna resonance (colour coding of the curve, in units of antenna linewidth), the factor \(\frac{\alpha }{{\tilde V}}\) goes from purely imaginary to partly real (dashed and dotted lines: Δac set to ½ resp. 1/8th the antenna linewidth).
