Abstract
The reciprocity of dissipative systems is usually justified by the microscopic reversibility of physical processes, i.e., relying on the time-reversal symmetry of physical laws at the microscopic level. Here, it is shown that it is unnecessary to invoke microscopic arguments to establish a direct link between the reciprocity of macroscopic systems and time-reversal invariance. It is demonstrated that lossy dielectrics have a hidden time-reversal symmetry, as the relevant dissipation channels can be mimicked by a distributed network of time-reversal invariant lossless transmission lines. It is proven that the reciprocity of lossy systems is fundamentally rooted on the hidden time-reversal invariance and linearity of the materials. Furthermore, it is demonstrated that the upper-half frequency plane response of dissipative materials can be approximated as much as desired by the response of some lossless material. The developed theory sheds new light on the link between dissipation, "open systems," and interactions with a "bath" of oscillators.
Highlights
The laws that rule the propagation of light in free space are invariant under the “time reversal” operation [1, 2, 3]
I prove that dissipative dielectrics have a hidden time-reversal symmetry, as the relevant dissipation channels can be mimicked by a distributed network of infinitely-extended time-reversal invariant lossless transmission lines
For an excitation of the system with a time variation e i t e e t i t with i in the upper-half frequency plane (UHP) ( 0 ), the line terminated with a short circuit may reproduce well the resistor response for any time instant
Summary
The laws that rule the propagation of light in free space are invariant under the “time reversal” operation [1, 2, 3]. If a wave can go through some channel with no back-reflections, the time-reversed wave can go through the same channel but propagating in the opposite direction This rather profound and intriguing bi-directional character of photonic systems is usually regarded a consequence of the Lorentz reciprocity law [4,5], which is more general than the time-reversal invariance. I show that it is unnecessary to invoke microscopic arguments to establish a direct link between the reciprocity of macroscopic systems and time-reversal invariance To this end, I prove that dissipative dielectrics have a hidden time-reversal symmetry, as the relevant dissipation channels can be mimicked by a distributed network of infinitely-extended time-reversal invariant lossless transmission lines. This article exploits and extends these known paradigms to unveil the hidden-symmetry of reciprocal materials
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