Summary
The optical propagator for the Helmholtz equation is given by the Fourier transform of a path integral; here we try to express it directly by a path integral. The usual limiting cases (short wavelength, asymptotic approximation, paraxial approximation) are recovered.
Riassunto
II propagatore ottico per l–equazione di Helmholtz è dato dalla trasformata di Fourier di un integrale funzionale; si cerca di esprimerlo direttamente come integrale funzionale. Si riottengono i noti casi limite (piccola lunghezza d–onda, approssimazione asintotica, approssimazione parassiale).
Резюме
Оптический пропагатор для уравнения Гельмгольца задается с помощью преобразования Фурье интеграла по траектории. В этой работе мы пытаемся выразить оптический пропагатор непосредственно через интеграл по траектории. Исследуются обычные предельные случаи (коротковолновой предел, асимптотическое приближение, параксиальное приближение).
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Liñares, J., Moretti, P. The optical propagator as a path integral: A formal derivation and limiting cases. Nuov Cim B 101, 577–584 (1988). https://doi.org/10.1007/BF02748961
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DOI: https://doi.org/10.1007/BF02748961