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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

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Published on: December 15, 2021

Defect solitons in parity-time periodic potentials.

Hang Wang¹, Jiandong Wang

¹School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu, China.

|March 4, 2011

Summary

Investigating solitons in parity-time lattices with defects reveals distinct stability behaviors. Positive defects ensure soliton stability in semi-infinite gaps, while negative defects lead to instability in the first gap.

Area of Science:

Nonlinear physics
Condensed matter physics
Optical lattices

Background:

Solitons are robust wave packets with particle-like properties.
Parity-time (PT) symmetric systems offer unique possibilities for controlling wave phenomena.
Lattices with defects can significantly alter soliton dynamics.

Purpose of the Study:

To investigate the stability of solitons in one-dimensional parity-time periodical lattices.
To analyze the influence of single-sited positive and negative defects on soliton stability.
To compare theoretical predictions with numerical simulations.

Main Methods:

Linear stability analysis was employed to determine soliton stability regions.
Numerical simulations were conducted to corroborate the analytical findings.

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The study considered both positive and negative defect potentials.

Main Results:

For positive defects, solitons are stable in the semi-infinite gap and mostly unstable in the first gap, except near the second band edge.
For negative defects, solitons are mostly stable in the semi-infinite gap (except near the first band edge) and entirely unstable in the first gap.
Stability predictions from linear analysis were confirmed by numerical simulations.

Conclusions:

The type and sign of the defect critically influence soliton stability in PT-symmetric lattices.
Specific defect configurations can lead to stable or unstable soliton propagation.
This research provides insights into the design of stable soliton-based systems in engineered lattices.