Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semimetal systems, it is not well suited to identifying topological phenomena in metallic or gapless systems. Here, we develop a theory of topological metals based on the system's spectral localizer and associated Clifford pseudospectrum, which can both determine whether a system exhibits boundary-localized states despite the presence of degenerate bulk bands and provide a measure of these states' topological protection even in the absence of a bulk band gap. We demonstrate the generality of this method across symmetry classes in two lattice systems, a Chern metal and a higher-order topological metal, and prove the topology of these systems is robust to relatively strong perturbations. The ability to define invariants for metallic and gapless systems allows for the possibility of finding topological phenomena in a broad range of natural, photonic, and other artificial materials that could not be previously explored.
Brillouin based distributed fiber sensors present a unique set of characteristics amongst fiber sensing architectures. They are able to measure absolute strain and temperature over long distances, with high spatial resolution, and very large dynamic range in off-the-shelf fiber. However, Brillouin sensors traditionally provide only modest sensitivity due to the weak dependence of the Brillouin frequency on strain and the high signal to noise ratio required to identify the resonance’s peak frequency to within a small fraction of its linewidth. Recently, we introduced a technique which substantially improves the precision of Brillouin fiber sensors by exciting a series of lasing modes in a fiber loop cavity that experience Brillouin amplification at discrete locations in the fiber. The narrow-linewidth and high intensity of the lasing modes enabled ultra-low noise Brillouin sensors with large dynamic range. However, our initial demonstration was only modestly distributed: measuring strain at 40, non-contiguous positions along a 400 m fiber. In this work, we greatly extend this methodology to enable fully distributed sensing at 1000 contiguous locations along 3.5 km of fiber—an order of magnitude increase in sensor count and range. This highly-multiplexed Brillouin fiber laser sensor provides a strain noise as low as 34 nε/√Hz and we analyze the limiting factors in this approach.
We introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by "multipole chiral numbers,"bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole chiral number indicates how many degenerate zero-energy states localize at each corner of a system. These higher-order topological phases of matter are generally boundary-obstructed and robust in the presence of chiral-symmetry-preserving disorder.
Cerjan, Alexander W.; Jorg, Christina; Vaidya, Sachin; Noh, Jiho; Augustine, Shyam; Von Freymann, Georg; Rechtsman, Mikael C.
Weyl points are point degeneracies that occur in momentum space of 3D periodic materials and are associated with a quantized topological charge. Here, the splitting of a quadratic (charge-2) Weyl point into two linear (charge-1) Weyl points in a 3D micro-printed photonic crystal is observed experimentally via Fourier-transform infrared spectroscopy. Using a theoretical analysis rooted in symmetry arguments, it is shown that this splitting occurs along high-symmetry directions in the Brillouin zone. This micro-scale observation and control of Weyl points is important for realizing robust topological devices in the near-infrared.
We present a distributed Brillouin fiber sensor that operates by exciting a series of discrete lasing modes. This approach provides inherently wide dynamic range (5m) while the narrow linewidth lasing modes enable low noise (8n/Hz)
Cerjan, Alexander W.; Jorg, Christina; Vaidya, Sachin; Augustine, Shyam; Benalcazar, Wladimir A.; Hsu, Chia W.; Von Freymann, Georg; Rechtsman, Mikael C.
In the past decade, symmetry-protected bound states in the continuum (BICs) have proven to be an important design principle for creating and enhancing devices reliant upon states with high-quality (Q) factors, such as sensors, lasers, and those for harmonic generation. However, as we show, current implementations of symmetry-protected BICs in photonic crystal slabs can only be found at the center of the Brillouin zone and below the Bragg diffraction limit, which fundamentally restricts their use to single-frequency applications. By microprinting a three-dimensional (3D) photonic crystal structure using two-photon polymerization, we demonstrate that this limitation can be overcome by altering the radiative environment surrounding the slab to be a 3D photonic crystal. This allows for the protection of a line of BICs by embedding it in a symmetry bandgap of the crystal. This concept substantially expands the design freedom available for developing next-generation devices with high-Q states.
Vaidya, Sachin; Benalcazar, Wladimir A.; Cerjan, Alexander W.; Rechtsman, Mikael C.
We show that point defects in two-dimensional photonic crystals can support bound states in the continuum (BICs). The mechanism of confinement is a symmetry mismatch between the defect mode and the Bloch modes of the photonic crystal. These BICs occur in the absence of band gaps and therefore provide an alternative mechanism to confine light. Furthermore, we show that such BICs can propagate in a fiber geometry and exhibit arbitrarily small group velocity which could serve as a platform for enhancing nonlinear effects and light-matter interactions in structured fibers.
