Phase-preserving nonreciprocal dynamics in coupled nonlinear oscillatorsa)

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.