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Summary

This summary is machine-generated.

Transient growth occurs in non-Hermitian photonics despite decay, due to modal nonorthogonality. Nonmodal stability theory reveals power dynamics missed by eigenvalue analysis in coupled waveguide systems.

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Area of Science:

Non-Hermitian photonics
Waveguide systems
Complex systems

Background:

Coupled waveguide systems can exhibit higher-order exceptional points.
Modal nonorthogonality in non-Hermitian systems can lead to complex dynamics.
Traditional eigenvalue analysis may not fully describe power dynamics in such systems.

Purpose of the Study:

Investigate transient growth in coupled waveguide systems with higher-order exceptional points.
Demonstrate the counterintuitive transient amplification in dissipative environments.
Explore the relationship between exceptional point order and transient growth.

Main Methods:

Utilized nonmodal stability theory, including singular value decomposition and pseudospectra.
Analyzed eigenvalue behavior and its limitations in capturing power dynamics.
Examined coupled waveguide systems with complex elements exhibiting loss exceeding gain.

Main Results:

Demonstrated transient growth occurring counterintuitively despite a decaying spectrum.
Showcased the critical role of modal nonorthogonality in transient amplification.
Established that eigenvalue analysis is insufficient for understanding these power dynamics.

Conclusions:

Nonmodal stability theory is essential for analyzing transient phenomena in non-Hermitian systems.
The order of the exceptional point influences the extent of transient growth.
Developed a general methodology for studying transient amplification in dissipative non-Hermitian systems.