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 exciting new phenomena that were not accessible in the past. In this talk, I will present several such experiments, all guided by numerical simulations and theory. A) Conventional textbook wisdom is that waves cannot be perfectly confined within the continuum spectrum of an open system. Exceptions called “bound states in the continuum”  were hypothesized by von Neumann and Wigner. I will describe the first realization of such unusual states  and their manifestation as polarization vortices protected by topologically conserved “charges” . B) I will show that by tailoring the radiation of optical modes, we can realize non-Hermitian photonic band structures with no counterpart in closed Hermitian systems, such as rings of exceptional points  and pairs of exceptional points connected by bulk Fermi arcs . 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 what was previously thought to be possible [6,7].
 C. W. Hsu*, B. Zhen* et al., Nature Reviews Materials 1, 16048 (2016).
 C. W. Hsu*, B. Zhen* et al., Nature 499, 188 (2013).
 B. Zhen*, C. W. Hsu* et al., Phys. Rev. Lett. 113, 257401 (2014).
 B. Zhen*, C. W. Hsu* et al., Nature 525, 354 (2015).
 H. Zhou et al., Science, eaap9859 (2018).
 C. W. Hsu et al., Phys. Rev. Lett. 115, 223901 (2015).
 C. W. Hsu et al., Nature Physics 13, 497 (2017).