Degree of coherence for electromagnetic fields

Jani Tervo,Tero Setala,Ari Friberg

doi:10.1364/oe.11.001137

Abstract

The relationship between the visibility of fringes and the degree of spatial coherence in electromagnetic two-pinhole interference is assessed. It is demonstrated that the customary definition of the degree of coherence of an electromagnetic field is flawed and a new quantity, free of the formal drawbacks, is introduced. The new definition, which is shown to be consistent with known results for Gaussian statistics, has some unusual properties characteristic only for electromagnetic fields. The degree of coherence is measurable by a sequence of interference experiments.

Highlights

Young’s double-slit interference experiment has played a pivotal role in the development of optics and quantum physics, the analyses so far have been performed almost exclusively in scalar description
The coherence studies of electromagnetic fields often deal with paraxial fields or wide-angle far fields, the emergence of nano photonics has given an impetus to comprehensive investigation of general three-dimensional, nonparaxial electromagnetic fields
Unlike in the scalar coherence theory, there does not exist a single scalar quantity that is capable of describing the coherence of electromagnetic fields at two separate space–time points

Summary

Introduction

Young’s double-slit interference experiment has played a pivotal role in the development of optics and quantum physics, the analyses so far have been performed almost exclusively in scalar description. The electromagnetic theory of optical coherence has become increasingly important not just for the evaluation of polarization properties but due to the recent advances in microstructured materials in general [1,2,3,4,5,6]. The correlation properties are far examined by using the concept of the degree of polarization, which is capable of describing the correlations at a one point only. We introduce a scalar quantity describing the second-order correlation properties of electromagnetic fields. We show that this quantity is closely connected to the existing definitions for the degree of polarization and that it has the properties required for the degree of coherence. We discuss possibilities for its measurement by using simple interference experiments

Young’s interference experiment and measures of visibility

Electromagnetic degree of coherence

Measurements of the degree of coherence

Conclusions