Abstract. We study continuous-wave light propagation through a twisted birefringent single-mode fiber amplifier with saturable nonlinearity. The corresponding coupled-mode system is isomorphic to a non-Hermitian nonlinear dimer, and gives rise to analytic polarization-mode dynamics. It provides an optical simulation of the semiclassical non-Hermitian Bose-Hubbard model, and suggests its use for the design of polarization circulators and filters, as well as sources of polarized light.

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Exceptional points (EPs) are degeneracies of non-Hermitian systems, where both eigenvalues and eigenvectors coalesce. Classical and quantum systems exhibiting high-order EPs have recently been identified as fundamental building blocks for the development of novel, ultra-sensitive opto-electronic devices. However, arguably one of their major drawbacks is that they rely on non-linear amplification processes that could limit their potential applications, particularly in the quantum realm. In this work, we show that high-order EPs can be designed by means of linear, time-modulated, chain of inductively coupled RLC (where R stands for resistance, L for inductance, and C for capacitance) electronic circuits. With a general theory, we show that N coupled circuits with 2N dynamical variables and time-dependent parameters can be mapped onto an N -site, time-dependent, non-Hermitian Hamiltonian, and obtain constraints for PT -symmetry in such models. With numerical calculations, we obtain the Floquet exceptional contours of order N by studying the energy dynamics in the circuit. Our results pave the way toward realizing robust, arbitrary-order EPs by means of synthetic gauge fields, with important implications for sensing, energy transfer, and topology.

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