F. J. Duarte and D. J. Paine, Quantum mechanical description of
N-slit interference phenomena, in Proceedings of the International
Conference on Lasers '88, R. C. Sze and F. J. Duarte (Eds.)
(STS, McLean, Va, 1989) pp. 42-47.
F. J. Duarte, Dispersive dye lasers, in High Power Dye Lasers, F. J. Duarte (Ed.) (Springer-Verlag, Berlin, 1991) pp. 7-43.
F. J. Duarte, Cavity dispersion equation: a note on its origin,
Appl. Opt. 31, 6979-6982 (1992).
F. J. Duarte, On a generalized interference equation and
interferometric measurements, Opt. Commun. 103, 8-14 (1993).
F. J. Duarte, Interferometric imaging, in Tunable Laser
Applications, F. J. Duarte (Ed.) (Marcel-Dekker, New York, 1995)
pp. 153-178.
F. J. Duarte, Generalized interference and optical processing,
in Proceedings of the International
Conference on Lasers '95, V. J. Corcoran and T. A. Goldman (Eds.)
(STS, McLean, Va, 1996) pp. 615-617.
F. J. Duarte, Answer to question #60. Interference of two independent sources,
Am. J. Phys. 66, 662-663 (1998).*
F. J. Duarte, Secure interferometric communications in free space, Opt. Commun. 205,
313-319 (2002).**
F. J. Duarte, Comment on "Reflection, refraction, and multislit interference," Eur. J. Phys. 25, L57-L58 (2004).***
F. J. Duarte, Secure interferometric communications in free space: enhanced sensitivity for propagation in the metre range, J. Opt. A: Pure Appl. Opt. 7, 73-75 (2005).**
* This note explains the Dirac approach to interference, in the context of the laser, and is included in the editor's choice for papers published in the American Journal of Physics for the 1988-2001 period (R. H. Romer, Editor's choice, Am. J. Phys. 69, 635-647 (2001)).
**Introduced the concept of interferometric characters in secure optical communications.
***This note expands slightly on the 1997 paper and explains how Dirac's quantum notation is used to provide a unified description of interference, diffraction, refraction, and reflection. It also describes why the probabilistic single-photon generalized interference equation, derived using Dirac's notation, can be applied to the description of interference of large numbers of indistinguishable photons, or ensemble of indistinguishable photons, observed in the macroscopic domain.
DIRAC AND INTERFERENCE
The first description of interference directly applicable to the interference of narrow-linewidth high-power laser beams was prophetically given by Dirac in 1930. Dirac's description of interference was not always understood, or accepted, and is referred to by some as "Dirac's dictum." Dirac's description of interference was explained, using practical laser terminology, in notes that include:
“… interference can be analyzed via the interaction of probability amplitudes. These probability amplitudes are said to be represented by wave functions. Hence, interference can be described via the multiplication of an addition of complex wave functions, with its corresponding complex conjugate… Dirac writes about a [monochromatic] beam of light consisting of a large number of photons… In the case of a large number of indistinguishable photons his words are just fine” [1].
"The Dirac discussion... begins with reference to a beam of roughly monochromatic light; then prior to his dictum on interference, he writes about a beam of light having a large number of photons... In present terms this is no different than the description of interference due to the interaction of a high-power narrow-linewidth laser beam with a two-beam interferometer" [2]
In the previous description a key concept is that a beam of monochromatic light is a beam is indistinguishable photons which is equivalent to a beam of narrow-linewidth laser emission [2].
References
1. F. J. Duarte, Interference of two independent sources, Am. J. Phys. 66, 662-663 (1998).
2. F. J. Duarte, Tunable Laser Optics (Elsevier-Academic, New York, 2003) Chapter 2.
This book contains a detailed description on the application of Dirac's notation to quantify photon propagation in macroscopic optics. It reviews the unified description of interference, diffraction, refraction, and reflection via Dirac's notation.
PATENTS BASED ON DIRAC OPTICS
F. J. Duarte, Electro-optical interferometric microdensitometer
system, US Patent 5255069 (19th of October, 1993).
F. J. Duarte, Laser sensitometer using multiple-prism beam expansion and a polarizer, US Patent 6236461 (22nd of May, 2001).
