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Two-dimensional Green's function theory for the electrodynamics of a rotating medium.
Ben Zion Steinberg1, Adi Shamir, Amir Boag
1School of Electrical Engineering, Tel Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel.
Summary
Researchers derived an exact spectral representation for Green's functions in rotating environments, simplifying calculations for Maxwell's equations. This work offers a new view of optical responses in rotating systems, including the Sagnac effect.
Area of Science:
- Electromagnetism
- Theoretical Physics
- Optics
Background:
- Maxwell's equations govern electromagnetic phenomena.
- Rotating environments introduce complexities in physical system analysis.
- Green's functions are crucial for solving wave equations.
Purpose of the Study:
- To derive an exact spectral representation for the Green's function of Maxwell equations in a 2D homogeneous and rotating environment.
- To develop a formulation in the medium's rest frame for point source response.
- To provide a closed-form expression for slowly rotating media.
Main Methods:
- Derivation of an exact spectral representation for the Green's function.
- Formulation in the noninertial rest frame of the rotating medium.
- Development of an approximate expression for efficient evaluation, avoiding spherical harmonics summation.
Main Results:
- An exact spectral representation for the Green's function in a 2D rotating medium was derived.
- A closed-form expression for slowly rotating media at finite distances was obtained.
- An efficient approximate expression was developed and validated against the exact solution.
Conclusions:
- The spectral theory provides a comprehensive understanding of optical responses in rotating systems.
- The classical Sagnac effect emerges as a specific case within this framework.
- The derived Green's function simplifies analysis of electromagnetic phenomena in rotating environments.
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