Generalized optical interferometry for modal analysis in arbitrary degrees of freedom

Area of Science:

• Quantum optics
• Wave phenomena
• Optical physics

Background:

• Traditional temporal optical interferometry is limited to specific applications.
• Coherent optical fields possess multiple degrees of freedom beyond temporal evolution.
• Modal analysis is crucial for understanding complex optical fields.

Purpose of the Study:

• To generalize temporal optical interferometry to arbitrary degrees of freedom.
• To introduce a novel framework for optical interferometry in any modal basis.
• To establish a theoretical link between fractional transforms and optical interferometry.

Main Methods:

• Generalization of temporal optical interferometry.
• Identification of a unitary optical transformation: the generalized phase operator.
• Application of the generalized phase operator in various modal bases.

Main Results:

• Optical interferometry can now be performed in any modal basis.
• The generalized phase operator is structurally equivalent to a fractional optical transform.
• A unified framework connecting fractional transforms, interferometry, and modal analysis is established.

Conclusions:

• The generalized phase operator provides a powerful tool for optical analysis.
• This work broadens the applicability of optical interferometry significantly.
• The findings pave the way for new optical measurement techniques.