Observed enhanced emission at higher-order exceptional points in RF circuits

Abstract

The Purcell effect -- stemming directly from the celebrated Fermi's Golden Rule -- links the enhanced emissivity of an emitter to the local density of states (LDoS) of a surrounding cavity. Under typical circumstances the LDoS is assumed to have a Lorentzian lineshape. Here, we go beyond the traditional Purcell framework by designing RF cavities with non-Lorentzian LDoS caused by higher-order non-Hermitian exceptional point degeneracies (EPDs) where $N\geq 2$ eigenfrequencies and their associated eigenmodes coalesce. We experimentally demonstrate a non-conventional emissivity enhancement (as compared to the isolated resonance regime) that increases with the EPD order $N$. The theoretical analysis traces its origin to an $N$-th power Lorentzian LDoS line shape that dominates under judicious spatially designed cavity losses. Our results reveal a new route to design cavities that do not rely on ultrahigh $Q$-factor resonators or small modal volumes.

Figures (3)

• Figure 1: Schematics of a cavity consisting of (a) two and (b) three resonators that are coupled together via variable coupling $\kappa$, forming two and three supermodes. These supermodes coalesce at a critical coupling strength, forming an EPD-$N$ with $N=2,3$, respectively. A monochromatic emitter (light blue circle) is coupled to the cavity via a "dark" mode at $n=1$. The emission is measured from the other "bright" modes with losses $\Gamma_{n\neq 1}$. Normalized LDoS with its peak-values far from the EPD-$N$ for the (c) two-mode and (d) three-mode cavity versus coupling variations $\kappa=\kappa_{\mathrm{EPD}}+\varepsilon$, displaying an enhancement factor of $4$ and $7$ for $N=2,3$ respectively.
• Figure 2: (a,b) Schematics of experimental RF cavities consisting of (a) two (dimer) and (b) three (trimer) RLC resonators with differential loss. To emulate an emitter, a monochromatic current source is placed in parallel with a load $Z_{n}=Z_{0}+1/(i\omega C_{e})$, which weakly couples it to the cavity via the dark resonator $n=1$. The emitted power is measured at the transmission lines (TLs) attached to the other resonators. (c–f) Real and imaginary parts of eigenfrequencies for the dimer (c, d) and trimer (e, f). Colored diamonds: experimental data from best-fit of transmission spectra. Solid lines: eigenfrequencies of the RF cavities in the absence of coupling to TLs, using Kirchhoff's equations. (g,h) Averaged experimental normalized emitted power versus frequency $f$ and capacitive coupling detuning $\delta\kappa\equiv \kappa-\kappa_{ED}$ indicating $\tilde{P} \approx 2$ for the ED-2 and $\tilde{P} \approx 4$ for the ED-3. Solid black lines on the bottom plane indicate the eigenfrequencies of the circuit extracted from Kirchhoff's equations, while black dots show the average emitted power at such frequencies. The red line marks the power emitted from the most emissive supermode.
• Figure 3: EPD-based enhancement factor for (a) $N=2$ and $(b)$$N=3$ configurations versus coupling perturbations $\delta\kappa$ away from the ED-$N$. The solid black (red) line corresponds to NGSpice simulations accounting for the total dissipated power (transmitted power at TLs), while green diamonds (blue crosses) represent the experimental power measurements rescaled with the experimental (simulated) $Q$-factor. In both configurations, the emitted power grows dramatically as $\delta \kappa \rightarrow 0$. The dashed horizontal lines indicate the EPD enhancement $\mathcal{F_{\text{CMT}}(\kappa_{\text{EPD}})}$ predicted by the CMT.