267. Concept of cross-spectral purity in coherence theory

Hem Chandra Kandpal, Kanchan Saxena, Dalip Singh Mehta +2 more

Mayukh Lahiri, E. Wolf

L. Mandeļ

An examination of the conditions under which the normalized coherence function γ(x1,x2,τ), at two points x1 and x2 in an optical field, is reducible to the product of a function of x1, x2 and a function of τ leads to the concept of cross spectral purity. Spectrally pure beams of light are characterized by the property that their coherence function is so reducible and, operationally, by the fact that superposition does not affect the spectral distribution. Light beams that do not have this property are called spectrally impure, and it is shown to be characteristic of such beams that the interference fringes exhibit a detailed periodic coloring. A measure of the departure from cross-spectral purity is introduced and evaluated in some special cases. It is shown by an example that spectrally pure and spectrally impure beams of light may be derived from the same source with similar optical components. Moreover, these beams may be identical as regards their intensity, their spectral distribution, and their degree of coherence, and differ only as regards their state of spectral purity.

Soma, Gaius

Rajneesh Joshi, Tero Setälä, Ari T. Friberg +1 more

Cross-spectral purity was conceived in the context of coherence research and has remained largely unknown to the wider optics community. Over the past few decades, coherence researchers have made progress in uncovering the intricate properties of this fundamental concept. Cross-spectral purity has been shown to be intimately connected to the concept of spatiotemporal separability, generalizing the concept of separability from fields to correlation functions. It has an observable effect on a multitude of experiments, and purity is in fact assumed in many well-known experiments. In this tutorial, we discuss the basic definitions related to cross-spectral purity and investigate some special cases. Additionally, we show how to generate and detect this property, and consider its experimental significance in areas such as ultrashort pulses, quantum optics, scattering, and ghost imaging.

George Sudarshan