Summary
In recent papers a class of second order correlation tensors was introduced and certain differential equations which govern their propagation were postulated. These correlation tensors, which may be regarded as natural generalizations of functions used in the analysis of partially coherent optical wavefields, characterize the correlations which exist between the electromagnetic field vectors at any two points in the field, at any two instants of time. In the present paper a derivation of the basic differential equations is presented; and it is shown that the two sets into which the equations naturally split are not independent, but in fact follow from each other as a consequence of certain symmetry properties which the correlation tensors exhibit.
Riassunto
In scritti recenti è stata introdotta una classe di tensori di correlazione di secondo ordine e sono state postulate alcune equazioni differenziali che regolano la loro propagazione. Questi tensori di correlazione, che possono essere considerati generalizzazioni naturali di funzioni usate nell’analisi dei campi d’onda ottici parzialmente coerenti, caratterizzano le correlazioni esistenti fra i vettori del campo elettromagnetico in qualsiasi coppia di punti del campo, e in qualsiasi due istanti. In questo scritto si presenta una deduzione delle equazioni differenziali fondamentali; e si mostra che i due gruppi nei quali le equazioni si suddividono naturalmente non sono indipendenti, ma in effetti derivano uno dall’altro come conseguenze di alcune proprietà di simmetria possedute dai tensori di correlazione.
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References
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This research was supported in part by the United States Air Force under Contract no. AF 49(638)-602, monitored by the AF Office of Scientific Research of the Air Research and Development Command.
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Roman, P., Wolf, E. Correlation theory of stationary electromagnetic fields. Nuovo Cim 17, 462–476 (1960). https://doi.org/10.1007/BF02860405
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DOI: https://doi.org/10.1007/BF02860405