Visualization of branch points in PT-symmetric waveguides

Area of Science:

• Quantum mechanics
• Non-Hermitian physics
• Optical systems

Background:

• Parity-time (PT)-symmetric systems exhibit unique spectral properties.
• Exceptional points (EPs) are singularities in the parameter space of non-Hermitian systems.
• Directional couplers are fundamental components in integrated optics.

Purpose of the Study:

• To visualize and probe exceptional points in PT-symmetric directional couplers.
• To utilize PT-symmetric systems for measuring the radius of convergence in non-PT-symmetric structures.
• To provide a physical interpretation for the radius of convergence.

Main Methods:

• Demonstration of EP visualization in a PT-symmetric directional coupler.
• Application of Rayleigh-Schrödinger perturbation theory.
• Probing EPs by varying a single parameter.

Main Results:

• Successful visualization of an exceptional point in a PT-symmetric directional coupler.
• Proof that the spectrum of a PT-symmetric Hamiltonian remains real within the radius of convergence.
• Demonstration of using PT-symmetric directional couplers to measure the radius of convergence for non-PT-symmetric systems.

Conclusions:

• PT-symmetric directional couplers offer a practical method for probing exceptional points.
• The study elucidates the physical significance of the radius of convergence in non-PT-symmetric systems.
• This work bridges theoretical concepts in non-Hermitian physics with experimental applications in optics.