These are references on the optics derived from the application of Dirac's notation to N-slit interferometry. As explained in the references Dirac's quantum approach is applicable to the propagation of a *single photon* or to the propagation of *indistinguishable photons*. The following terminology, and concepts, are discussed in the given references:

Optical architecture for the multiple-prism beam expander microscope/nanoscope (MPBEM/N). The beam incident on the object can be, for example, 25-50 mm wide X 25 µm high. This is an extremely elongated beam (in the plane of propagation) with a width to height ratio in the range of 1000:1 to 2000:1. The figure in the upper right illustrates the geometry of the architecture when used as a pure *N*-slit laser interferometer (*N*SLI). Comparisons between theory and experiments, in the *N*SLI configuration, have been performed for even values (*N* = 2, 4, 6...) and odd values (*N* = 3, 5, 7...) of *N*. This includes the cases of two-slit interference, three-slit interference, four-slit interference, etc. (Duarte, 1991, 2002, 2005). For reviews see *Tunable Laser Optics* and *Tunable Laser Applications*).

The 1991 and 1993 papers also reported, for the first time, on the use of quantum mechanics techniques, via Dirac's notation, in the field of imaging. In addition, these papers illustrated the prediction of measured interferograms using interferometric equations derived using Dirac's quantum notation.

- F. J. Duarte, Beam shaping with telescopes and multiple-prism beam expanders,
*J. Opt. Soc. Am. A*4, P30 (1987). - 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 Δ
*λ*≈ Δ*θ*(*∂θ/∂λ*)^{– 1}: a note on its origin,*Appl. Opt.*31, 6979-6982 (1992).^{*} - F. J. Duarte, Electro-optical interferometric microdensitometer system,
*US Patent*5255069 (1993).^{**} - 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) Chapter 5. - 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, Interference, diffraction, and refraction, via
Dirac's notation,
*Am. J. Phys.*65, 637-640 (1997). - 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,
*Tunable Laser Optics*(Elsevier-Academic, New York, 2003) Chapter 2 (Dirac optics). - 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). - F. J. Duarte, Interferometric imaging, in
*Tunable Laser Applications*, 2nd Ed., F. J. Duarte (Ed.) (CRC, New York, 2009) Chapter 12. - F. J. Duarte, T. S. Taylor, A. B. Clark, and W. E. Davenport, The N-slit interferometer: an extended configuration,
*J. Opt.*12, 015705 (2010). - F. J. Duarte, Triple-slit experiment,
*Optics & Photonics News*22(12), 7 (2010). - F. J. Duarte, T. S. Taylor, A. M. Black, W. E. Davenport, and P. G. Varmette,
*N*-slit interferometer for secure free-space optical communications: 527 m intra interferometric path length ,*J. Opt.*13, 035710 (2011).

- F. J. Duarte, T.S. Taylor, A.M. Black, I.E. Olivares, Diffractive patterns superimposed over
propagating
*N*-slit interferograms,*J. Mod. Opt.*60, 136-140 (2013). - F. J. Duarte, Tunable laser optics: applications to optics and quantum optics,
*Progress in Quantum Electronics*37, 326-347 (2013).

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].

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.

- F. J. Duarte,
*Tunable Laser Optics*(Elsevier Academic, New York, 2003).

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.

- 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).

*Keywords*: double-slit interference, double-slit interferometer, double-slit interferometry, four-slit interference, four-slit interferometer, four-slit interferometry, *N*-slit interference, *N*-slit interferometer, *N*-slit interferometry, quantum, quantum imaging, two-slit interference, two-slit interferometer, two-slit interferometry, three-slit interference, three-slit interferometer, three-slit interferometry, triple-slit interference, triple-slit interferometer, triple-slit interferometry