Cross-spectrally pure light, cross-spectrally pure fields and statistical similarity in electromagnetic fields

Abstract

This paper describes the concept of cross-spectrally pure light, implications of statistical similarity of an optical field on its cross-spectral purity and cross-spectrally pure fields. First, the concept of cross-spectral purity of light is analysed in the space-frequency domain by taking into account the vectorial nature of the radiation, and the conditions and reduction formula are obtained. Then, by utilizing statistical similarity, the relationship between cross-spectral purity and spatial coherence is explored in the electromagnetic field. Last, the conditions for cross-spectrally pure fields are discussed, the polychromatic plane wave and the far field produced by a planar, secondary, stochastic electromagnetic source are studied as examples, and moreover, the relationship between cross-spectral purity and spatial coherence, which we have drawn, is verified during the study.

Keywords:

• cross-spectrally pure
• coherence
• statistical similarity
• electromagnetic field

Acknowledgements

Authors are indebted to the reviewers for their invaluable comments and suggestions.

Funding

This work was supported by the [National Natural Science Foundations of China] under [grant number 61107011], [grant number 61205121]; [Provincial Natural Science Foundation of Anhui] under [grant number 1208085QF111]; and [Fundamental Research Funds for the Central Universities] under [grant number J2014HGBZ0170].