Universal form of arrays with spectral singularities

Area of Science:

• * Photonics and Optics
• * Quantum Mechanics
• * Condensed Matter Physics

Background:

• * Non-Hermitian optical waveguide arrays exhibit unique spectral properties.
• * Spectral singularities in discrete complex potentials are linked to lasing and coherent perfect absorption.
• * Understanding the gain-and-loss distribution is key to controlling these phenomena.

Purpose of the Study:

• * To identify universal characteristics of lattice potentials with spectral singularities.
• * To systematically construct novel optical potentials with multiple or higher-order spectral singularities.
• * To investigate the impact of higher-order spectral singularities on light-matter interactions in waveguide arrays.

Main Methods:

• * Theoretical analysis of non-Hermitian lattice potentials.
• * Derivation of the universal form for gain-and-loss distributions associated with spectral singularities.
• * Construction of new potentials with tailored spectral singularity properties.
• * Numerical or experimental validation of enhanced responses from higher-order singularities (implied).

Main Results:

• * All lattice potentials with spectral singularities share a universal gain-and-loss distribution.
• * Systematic construction of potentials with multiple spectral singularities at desired wavelengths.
• * Creation of potentials exhibiting second-order spectral singularities.
• * Demonstration that higher-order spectral singularities lead to significantly enhanced responses to incident beams.

Conclusions:

• * The universal gain-and-loss distribution provides a powerful tool for designing non-Hermitian optical systems.
• * Novel optical potentials with multiple and higher-order spectral singularities can be engineered.
• * Higher-order spectral singularities offer a pathway to achieving high-intensity lasing modes and enhanced light-matter interactions.