Investigating non-reciprocity in time-periodic media using a perturbative approach

Area of Science:

• Electromagnetism
• Wave Propagation
• Materials Science

Background:

• Lorentz reciprocity theorem provides clear conditions for time-invariant media.
• Reciprocity conditions for linear time-varying media remain less explored.
• Understanding reciprocity in dynamic structures is essential for advanced applications.

Purpose of the Study:

• To investigate and define reciprocity conditions for structures with time-periodic media.
• To develop a method for identifying reciprocal or non-reciprocal behavior in dynamic electromagnetic structures.
• To analyze the non-reciprocity condition in terms of constitutive parameters and electromagnetic fields.

Main Methods:

• Derivation of a necessary and sufficient condition for reciprocity in time-varying media.
• Development of a perturbative approach using electromagnetic fields and Green's functions for weak time modulation.
• Application of the approach to canonical time-varying structures.
• Validation using analytical and Finite-Difference Time-Domain (FDTD) methods.

Main Results:

• A condition for reciprocity in time-periodic media is derived, considering both constitutive parameters and electromagnetic fields.
• The perturbative approach effectively analyzes non-reciprocity for structures with weak time modulation.
• The theory explains the observed maximization of non-reciprocity at a 90-degree modulation phase difference in a specific 1D case.
• Significant agreement was found between the perturbative approach, analytical solutions, and FDTD simulations.

Conclusions:

• The study provides a robust framework for assessing reciprocity in time-varying electromagnetic media.
• The proposed perturbative method offers a practical tool for analyzing complex dynamic structures.
• The findings clarify specific phenomena in time-varying media, advancing the understanding of electromagnetic wave manipulation.