Observation of non-Hermitian point gap in photonic crystals

Abstract

Non-Hermitian point gap (NHPG) is a unique phenomenon in non-Hermitian systems and induces non-Hermitian skin effect (NHSE). In photonic crystals, NHPG and the NHSE have previously been explored mainly through material loss, where the typically low $Q$ factors make direct observation of complex frequencies challenging. Here, we demonstrate the direct experimental observation of an NHPG by using a radiation-loss-based non-Hermitian photonic crystal. Radiation loss can be engineered through structural design, enabling control of the imaginary part of the complex frequency and allowing relatively high $Q$ factors. This approach is compatible with widely used absorption-free silicon-slab photonic crystals. We developed a measurement system that can measure photonic bands along arbitrary lines in $k$-space. Our measurements demonstrated direct observation of the NHPG in photonic crystals, and the reversal of non-Hermitian topology through the flip of loop rotation in a complex plane. Our platform, which requires neither gain media nor synthetic dimensions, establishes radiation-loss engineering as a simple and versatile route for photonic functionality using an NHSE in nanophotonic systems.

Figures (3)

• Figure 1: (a) Structure of Si photonic crystal with an anisotropic unit cell. (b) Real and (c) imaginary parts of simulated complex frequency bands (only the second TE bands are plotted). The dashed lines in (b) indicate the light lines for $k_{y} = 0$ and $0.4$. (d) Complex frequency plot of complex eigenfrequencies. Black and red markers correspond to $k_{y}a/\pi = 0$ and $0.4$, respectively. Iso-frequency plots of (e) real and (f) imaginary parts of simulated eigenfrequencies. The structure is floating in the air and refractive index of Si slab is set to 3.48.
• Figure 2: (a) SEM image of the fabricated Si photonic crystal slab. (b) Schematic of the setup used to measure photonic bands along arbitrary lines in $k$-space. The optical system can be translated relative to the slit of the imaging spectrometer to access different momentum-space cuts.
• Figure 3: (a,b) Measured iso-frequency surface at 1500 nm under $y$- and $x$-polarized incidence, respectively. (c-f) Measured photonic bands for $k_y/k_0 =0$, $k_y/k_0 = +0.0382$, $k_y/k_0 = -0.0382$, and $k_y = k_x + 0.181k_0$. Incident polarization was set to $y$-polarization for (c) and (f), and $x$-polarization for (d) and (e). Since the NA is constant for all wavelengths, the horizontal axes are normalized by the wave number $k_0$ for each wavelength. The horizontal axis in (f) corresponds to the direction along the yellow–green line in (a). (g-j) Retrieved complex eigenfrequencies obtained from the measured bands (c-f). (k-n) Simulated complex eigenfrequencies corresponding to (g-j). In the simulations, $k_0$ is fixed to 1.5 $\mu$m. For visual quality, the markers for positive $k_x$ are drawn with reduced size in (k) and (n).