PT-symmetric cross injection dual optoelectronic oscillator
An optoelectronic oscillator (OEO) is a time delay oscillator (TDO) that uses photonics technology to provide the long delay required to generate pristine microwave carriers. Parity-time (PT) symmetry concepts applied to an OEO offer the potential to achieve combined low phase noise and high sidemode suppression. A TDO composed of a pair of identical ring resonators coupled by a 2x2 coupler is modelled, and the coupler transmission matrix required for the oscillator to be PT- symmetric is derived. In a first configuration, the coupler is interpreted as the composition of a gain/loss block and a Mach-Zehnder interferometer (MZI) block. In practice, there are excess losses that must be compensated by a special dual amplifier with saturation characteristics compatible with PT- symmetry. The PT- symmetry phase transition determined by the gain/loss and the MZI differential phase parameters is found to be global and not local in its effect on modes. This is resolved by placing a short delay line within one arm of the MZI resulting in a frequency dependent and hence local mode-selective PT- symmetry phase transition. In addition, it is demonstrated that the first configuration may be transformed into a second but equivalent configuration as a cross-injection dual TDO with imbalanced delays. The local PT- symmetry phase transition may then be understood in terms of the Vernier effect. Advantageously, the second configuration enables the special dual amplifier to be replaced by a pair of matched but otherwise independent amplifiers. Thereby, the second configuration is amenable to practical implementation as a dual OEO using standard RF-photonic and RF-electronic components. The theory is validated by complex envelope model simulations using Simulink and phase model analytic results evaluated using MATLAB. There is excellent agreement between the theoretical and simulation results.