Reciprocity relations in the near field

Area of Science:

• Quantum mechanics
• Wave physics
• Classical electromagnetism

Background:

• Classical wave fields are typically described using unitary propagators.
• Evanescent waves, a component of classical wave fields, present unique mathematical challenges.
• Understanding wave field behavior is crucial for various physics and engineering applications.

Purpose of the Study:

• To express the propagator of a classical wave field, including evanescent waves, using quantum formalism.
• To derive uncertainty relations for such wave fields.
• To investigate the impact of evanescent waves on propagator unitarity and state normalization.

Main Methods:

• Application of quantum formalism to classical wave field propagators.
• Derivation of uncertainty relations within this quantum framework.
• Analysis of the mathematical properties of the propagator in the presence of evanescent waves.

Main Results:

• The propagator for scalar, monochromatic, classical wave fields with evanescent waves was successfully expressed using quantum formalism.
• The presence of evanescent waves was shown to result in a non-unitary propagator.
• Sub-normalized states and a modified uncertainty relation were derived as consequences of the non-unitary propagator.

Conclusions:

• Evanescent waves fundamentally alter the nature of classical wave field propagators, rendering them non-unitary.
• The quantum formalism approach provides a novel framework for understanding wave fields containing evanescent components.
• The derived modified uncertainty relation offers new insights into the behavior of these wave fields.