title: Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion.
abstract: We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate-irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omnipolarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate.
authors.affiliation: CREOL/College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA.
authors.forename: Absar U
authors.initials: AU
authors.lastname: Hassan
authors.affiliation: Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.|Physics Department and Solid State Institute, Technion, Haifa 32000, Israel.
authors.forename: Bo
authors.initials: B
authors.lastname: Zhen
authors.affiliation: Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Marin
authors.initials: M
authors.lastname: Soljačić
authors.affiliation: CREOL/College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA.
authors.forename: Mercedeh
authors.initials: M
authors.lastname: Khajavikhan
authors.affiliation: CREOL/College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA.
authors.forename: Demetrios N
authors.initials: DN
authors.lastname: Christodoulides