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Alexander Hwang1 Gururaj Naik1

1, Rice University, Houston, Texas, United States

Non-Hermitian systems can possess real eigenvalues if their Hamiltonians have parity- and time-symmetries (PT-symmetry). Such systems have been actively studied because they demonstrate extensions of conventional Hermitian quantum mechanics into a more generalized framework. Recently, PT-symmetry has gained much attention, especially in optics because of ease of implementation. PT-symmetry in optics translates to a conjugate-symmetric refractive index distribution, i.e. a balanced loss-gain system. Implementing such systems is easier for larger-scale photonic systems than for nanophotonic systems. Thus, so far, experimental studies have primarily focused on larger-scale photonic systems, though there are proposals for nanoscale optical devices with PT-symmetry.

Nano-optical devices often have high losses, which require equally high gain to implement PT-symmetric potentials. Such high gains are impractical and alternative methods to circumvent this problem have been investigated. One such alternative is a passive PT-symmetric system, where the characteristics of PT-symmetry can be observed using lossless and lossy components. These passive systems are simpler to implement using various fabrication techniques and materials available to nanophotonics. Here, we demonstrate a PT-phase transition in a passive dimer system consisting of silicon and silver nanoparticle pairs fabricated using electron-beam lithography. We characterize the system’s PT-symmetric behavior by measuring the scattering spectrum and far-field radiation pattern as a function of coupling, or distance between the particles. From the scattering spectrum, we can deduce the real and imaginary eigenvalues by identifying resonant peaks and linewidths. At the same time, the far-field radiation pattern, observed from the back Fourier plane image, represents the eigenmodes of the system.

In the PT-symmetric phase, where coupling is strong, far-field radiation is dipolar symmetric and scattering spectrum shows two resonant peaks. As coupling is weakened by increasing separation distance, the resonances move closer together in frequency, with little change in linewidth. At the exceptional point, these resonances coincide, resulting in a degenerate mode. Decreasing coupling past the exceptional point leads to a PT-broken phase, where the system exhibits a single resonant peak, with smaller linewidths. In the PT-broken phase, the far-field radiation pattern becomes increasingly asymmetric as coupling lowers, with more scattering towards the lossless particle. This behavior in the transition from the symmetric to symmetry-broken phase demonstrates passive PT-symmetry breaking at the nanoscale. Our understanding of PT-symmetry in this nanoantenna dimer opens opportunities to explore the rich physics underlying PT-symmetric nanosystems.

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