General coupled mode theory in non-Hermitian waveguides

Area of Science:

• Photonics and Optics
• Quantum Mechanics
• Electromagnetism

Background:

• Coupled mode theory (CMT) is standard for analyzing coupled optical systems.
• Non-Hermitian systems with gain and loss violate standard CMT assumptions.
• Existing theories struggle to accurately model mode hybridization in these systems.

Purpose of the Study:

• To generalize coupled mode theory for non-Hermitian optical systems.
• To accurately describe mode hybridization in waveguides and resonators with gain and loss.
• To enable the design of novel non-Hermitian optical devices.

Main Methods:

• Developed a generalized CMT using a reaction-invariant inner product.
• Applied the theory to non-Hermitian parity-time symmetric waveguides.
• Validated results against finite element full-wave simulations.

Main Results:

• The generalized CMT accurately predicts mode hybridization in non-Hermitian systems.
• Excellent agreement was found between theoretical predictions and numerical simulations.
• The theory successfully models asymmetric and nonreciprocal light propagation.

Conclusions:

• The new theory provides a robust framework for non-Hermitian coupled mode analysis.
• This work facilitates the design of advanced non-Hermitian photonic devices.
• The theory can be applied in both spatial and temporal domains for waveguides and resonators.