Imaginary couplings in non-Hermitian coupled-mode theory: Effects on exceptional points of optical resonators

TL;DR

This paper investigates how imaginary couplings in non-Hermitian coupled-mode theory affect exceptional points in optical resonators, revealing conditions under which EP degeneracies can be preserved or disrupted.

Contribution

It extends coupled-mode theory to include imaginary inter-cavity couplings, clarifies their effects on EP degeneracies, and proposes design strategies to restore or protect EPs.

Findings

Imaginary couplings can lift EP degeneracies in non-Hermitian resonator arrays.

Balanced gain and loss can cancel imaginary couplings, restoring EPs.

Radiation-induced imaginary couplings can be mitigated by cavity detuning.

Abstract

Exceptional point (EP) degeneracies in coupled cavities with gain and loss provide on-chip photonic devices with unconventional features and performance. However, such systems with realistic structures often miss the exact EPs even in simulation, and the mechanism of this EP disruption has yet to be thoroughly identified. Here, we extend the coupled-mode theory of one-dimensional non-Hermitian resonator arrays to study the effects of the imaginary part of the inter-cavity coupling, which is a second-order term and attributed to material amplification, absorption, and radiation. By taking an appropriate gauge for the model, we clarify that the imaginary coupling components have a symmetric form in the effective Hamiltonian and hence represent non-Hermiticity. These additional factors can lift the gain- and loss-based EP degeneracies. However, they are proportional to the sum of the imaginary permittivities for involved cavity pairs. Thus, when the amplification and absorption of adjacent cavities are balanced, their contribution to the imaginary coupling is canceled, and the EP singularity can be restored. Radiation-induced imaginary couplings measure the change in net radiation loss by the interference between cavity modes. Their impact on the EP can also be counteracted by small cavity resonance detuning even in loss-biased cases. We show and analyze eligible simulation examples based on photonic crystal nanocavities, and highlight design of an ideal EP degeneracy that is protected by generalized PT symmetry and induced by radiation.