Ray-wave duality of electromagnetic fields: a Feynman path integral approach to classical vectorial imaging

Area of Science:

• Quantum optics
• Mathematical physics

Background:

• Standard optical path length integrals treat light as scalar.
• Vectorial aspects like polarization are often neglected in scalar treatments.
• Feynman path integral methods offer a powerful framework for quantum phenomena.

Purpose of the Study:

• To develop a Feynman path integral approach for vectorial light propagation, incorporating polarization.
• To generalize scalar optical path integrals to matrix quantities.
• To demonstrate the scheme using a general gradient index background.

Main Methods:

• Generalizing the standard optical path length integral to a matrix quantity.
• Utilizing reparametrization invariance for a covariant formulation of light propagation along general curves.
• Applying the scheme to a general gradient index background.

Main Results:

• A covariant formulation for light propagation incorporating polarization effects.
• Successful demonstration of the scheme in a gradient index medium.
• The method provides a description of classical imaging optics with rapidly varying polarization.

Conclusions:

• The Feynman path integral approach successfully incorporates vectorial light propagation and polarization.
• The matrix generalization of optical path integrals is crucial for handling polarization.
• This framework is applicable to classical imaging optics where polarization is significant.