Mathematical and Physical Aspects of Topologically Protected States

Robust guiding and control of light and sound in photonic and acoustic metamaterials

Alexander Khanikaev

City College of NY
[SLIDES]

The past three decades have witnessed the discovery of Quantum Hall Effect, Quantum Spin Hall Effect and Topological Insulators (TIs), which transformed our views on the quantum states of matter and wave phenomena, and have been recognized by Nobel Prize in physics in 2016. These exotic states are characterized by insulating behavior in the bulk and the presence of robust surface states contributing to charge or spin currents which persist even when the edge is distorted or contains impurities. In the last few years, a number of studies have shown that similar robust conducting states can be implemented in classical systems. In this talk I will review development of this field with focus on photonic and acoustic topological structures with and without time-reversal symmetry that we have recently proposed. I will discuss recent experimental realizations of topological order for electromagnetic waves with the use of bianisotropic metamaterials at microwave frequencies. New practical designs of photonic and acoustic topological insulators and their possible applications will be presented. I will show that topological photonic and acoustic topological systems offer an unprecedented platform for controlling light and sound, e.g. by enabling routing and steering of waves along arbitrarily shaped pathways without loss or backscattering.