Summary
We study a light pulse for which the ratio between its time length and its coherence time can assume any possible value. This light pulse is obtained by an incoherent superposition of identical polychromatic photons. Its density matrix, evaluated by making use of the convolution law of theP representation, is analysed. A new definition of coherence time that is a generalization of previous definitions is proposed; this new definition does not require the field to be stationary and consequently may apply to some light pulses.
Riassunto
Si studia un impulso di luce per il quale il rapporto tra la durata e il tempo di coerenza può assumere qualunque valore. Tale impulso è ottenuto da una sovrapposizione incoerente di fotoni policromatici tutti uguali. Si analizza la sua matrice densità valutata usufruendo della legge di convoluzione della rappresentazioneP. Si propone inoltre una nuova definizione di tempo di coerenza che è una generalizzazione delle precedenti definizioni; questa nuova definizione non richiede che il campo sia stazionario e conseguentemente può applicarsi ad un più ampio numero di campi.
Реэюме
Мы исследуем световой импульс, для которого соотнощение между его временной длиной и его когерентным временем можно предположить любой воэможной величине. Этот световой импульс получается некогерентным наложением тождественных полихроматических фотонов. Аналиэируется его матрица плотности посредством испольэования эакона свертки дляP представления. Предлагается новое определение когерентности, которое является обобшением предыдуших определений. Это новое определение не требует, чтобы поле было стационарным и, следовательно, может быть применено к некоторым импульсам света.
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References
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If the effective bandwidth δv of the packet is defined by eq. (27b), as we shall see later, we have (δT)min · (δv)=1/4π and therefore the Pauli inequality (H. Weyl:The Theory of Groups and Quantum Mechanics (New York, 1950), p. 77, 393) (δT)·(δv)⩾1/4π assumes its minimum value.
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This research was supported by the Consiglio Nazionale delle Ricerche through the Gruppo Nazionale di Elettronica Quantistica e Plasmi.
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Carusotto, S. Incoherent light pulses. Nuovo Cimento B (1965-1970) 70, 73–89 (1970). https://doi.org/10.1007/BF02712494
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DOI: https://doi.org/10.1007/BF02712494