UC Irvine

This thesis examines two distinct three-mode degeneracy problems. First, a third-order exceptional point of degeneracy (EPD3) is synthesized in a linear three-resonator RLC circuit. Kirchhoff’s laws yield a six-state model and two physical coupling branches. An op- amp negative-impedance converter (NIC) is then substituted for the ideal negative resistance. Finite gain, bandwidth, output resistance, loading, and saturation cause the simulated circuit to depart from the designed linear EPD3 condition. In the transient simulation, the circuit develops a finite-amplitude oscillation with a dominant spectral peak near 1.178 MHz rather than at the designed frequency of 1.45 MHz. Second, an independent normalized nonlinear coupled-mode-theory model with saturable gain is analyzed. Eliminating the modal amplitudes and saturated gain gives a real- fifth order steady-state frequency equation. A numerical design produces a fivefold real root, defined here as an SS-EPD5. Active-mode frequency detuning exhibits fifth-root frequency scaling. The stability of the steady state oscillation frequency is analyzed using the Lyapunov coefficients and a linearization. This leads to one neutral common-phase eigenvalue (Lyapunov coefficient) and five other eigenvalues with negative real parts, indicating local transverse linear stability of the steady state solution.