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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Phase-preserving nonreciprocal dynamics in coupled nonlinear oscillatorsa).

Ali Kogani¹, Behrooz Yousefzadeh¹

¹Department of Mechanical, Industrial & Aerospace Engineering, Concordia University, Montreal, Québec H3G1M8, Canada.

The Journal of the Acoustical Society of America

|November 7, 2025

Summary

Nonreciprocity in coupled nonlinear systems arises from differences in transmitted energy and phase. This study reveals phase bias is crucial for breaking reciprocity, even enabling phase-preserving nonreciprocity.

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Area of Science:

Nonlinear dynamics
Vibrational mechanics
Acoustic and mechanical metamaterials

Background:

Nonreciprocity is typically characterized by unequal energy transmission when source and receiver positions are swapped.
This energy asymmetry often correlates with a phase difference in transmitted signals.
Understanding the interplay of energy and phase is key to controlling wave propagation.

Purpose of the Study:

To investigate the role of phase bias in breaking reciprocity in coupled nonlinear systems.
To explore conditions under which energy bias alone causes nonreciprocity.
To develop methods for achieving phase-preserving nonreciprocity.

Main Methods:

Analysis of steady-state vibration transmission in coupled nonlinear systems under harmonic excitation.
Mathematical modeling to identify contributions of energy and phase biases.
Introduction of symmetry-breaking parameters to control system response.

Main Results:

Nonreciprocity in these systems is commonly driven by simultaneous biases in transmitted energy and phase.
Energy bias alone can induce nonreciprocity, but requires highly specific system parameters.
A method was demonstrated to achieve nonreciprocity while preserving phase.

Conclusions:

Phase bias plays a significant role in nonlinear nonreciprocity.
Controlling both energy and phase dynamics is essential for designing nonreciprocal systems.
The proposed methodology offers a pathway to engineer novel nonreciprocal devices.