Fresnel–Arago fifth law of interference: the first description of a geometric phase in optics

ABSTRACT

The Fresnel–Arago laws of interference are five laws describing the interference of polarized light and published in 1819. The fifth law has been systematically forgotten in almost all available references published during the last century, leading to the common, but incorrect, belief that Arago and Fresnel gave only four laws of interference. The fifth law describes the existence of an additional phase of 180${}^{\circ }$, not due to path or speed differences, in linearly polarized beams that undergo certain polarization transformations in double refracting crystals. Two years later, Fresnel provided a complete explanation for this unexpected phase, showing that he had a good understanding of what can unequivocally be pointed out as the first description of a geometric phase in optics.

Keywords:

• Polarization
• interference
• geometric phase
• history of optics

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

Ministerio de Ciencia e Innovación y Universidades (RTI2018-098410-J-I00 and RYC2018-024997-I) (MCIU/AEI/FEDER, UE).