Optics and photonics today enjoy unprecedented freedom. The ability to synthesize arbitrary light fields (through wavefront shaping) and the ability to design structures at the subwavelength scale (through nanofabrication) enable us to realize phenomena that could only be imagined in the past. In this talk, I will present several experiments and related theory that demonstrate exciting new phenomena which were previously inaccessible. A) Conventional textbook wisdom is that waves cannot be perfectly confined within the continuum spectrum of an open systems. Exceptions called “bound states in the continuum” were hypothesized by von Neumann and Wigner  but not realized. I will describe the first realization of such unusual states  and their manifestation as polarization vortices protected by topologically conserved “charges” . B) Our ability to control radiation also enables the realization of non-Hermitian phenomena with no counterpart in closed systems. I will show how non-Hermiticity generates unique topologies in photonic band structures and lead to enhanced light–matter interactions [4,5]. C) Strong disorder in naturally occurring light-scattering media allows us to study mesoscopic physics in a new arena. I will describe the control of optical transport via wavefront shaping, and how the long-range correlations between multiply scattered photons enable us to simultaneously control orders of magnitudes more degrees of freedom than previously thought possible [6,7].
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