N-slit interferometer
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N-slit interferometer
The N-slit interferometer is an extension of the double-slit interferometer also known as Young's double-slit interferometer. One of the first known uses of N-slit arrays in optics was illustrated by Newton.[1] In the first part of last century, Michelson[2] described various cases of N-slit diffraction.
Feynman[3] described thought experiments, of two-slit quantum interference, of electrons using Dirac's notation.[4] This approach was extended to N-slit interferometers, by Duarte and colleagues in 1989,[5] using narrow-linewidth laser illumination, that is, illumination by indistinguishable photons. The first application of the N-slit interferometer was the generation and measurement of complex interference patterns.[5][6] These interferograms are accurately reproduced, or predicted, by the N-slit interferometric equation for either even (N = 2, 4, 6,…), or odd (N = 3, 5, 7,…), numbers of slits.[6]
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N-slit laser interferometer
The N-slit laser interferometer, introduced by Duarte[5][6][7], uses prismatic beam expansion to illuminate a transmission grating, or N-slit array, and a photoelectric detector array (such as a CCD or CMOS) at the interference plane to register the interferometric signal.[6][7][8] The expanded laser beam illumination in the N-slit interferometer can also take the shape, via the introduction of a convex lens prior to the prismatic expander, of a beam extremely elongated in the propagation plane and extremely thin in the orthogonal plane.[6][7] This use of one-dimensional (or line) illumination eliminates the need of point-by-point scanning in microscopy and microdensitometry.[6][7] Thus, these instruments can be used as straight forward N-slit interferometers or as interferometric microscopes (see section on microscopy).
Secure optical communications
These interferometers, originally introduced for applications in imaging,[6] are also useful in optical metrology and have been proposed for secure optical communications in free space.[9] Recent experimental developments include intra-interferometric path lengths of 35 meters[10] and 527 meters.[11]
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These large, and very large, N-slit interferometers[10][11] are also being used to study the effect of intra interferometric clear air turbulence[10] and the effect of microscopic disturbances[11] on propagating interferometric signals. This work has yielded the first observation of diffraction patterns superimposed over propagating interferograms.[11]
These diffraction patterns (as shown in the first photograph) are generated by inserting a spider web fiber (or spider silk thread) into the propagation path of the N-slit interferogram. The position of the spider web fiber is perpendicular to the plane of propagation.[11]
Note: N-slit interferometers include three-slit interferometers (or triple-slit interferometers), four-slit interferometers, etc.[9][10][11]
Expanded beam interferometric microscopy
As previously mentioned the original application of the N-slit laser interferometer was interferometric imaging.[6][7][12] In particular, the one dimensionally expanded laser beam (with a cross section 25-50 mm wide by ~25 μm high) was used to illuminate imaging surfaces (such as silver-halide films) to measure the microscopic density of the illuminated surface. Hence the use of the description interferometric microdensitometer.[7] Resolution down to the nano regime can be provided via the use of interinterferometric calculations.[6]
The multiple-prism expanded laser beam is also described as an extremely elongated laser beam. The elongated dimension of the beam (25-50 mm) is in the plane of propagation while the very thin dimension (~25 μm) of the beam is in the orthogonal plane. This was demonstrated, for imaging and microscopy applications, in 1993.[6][7] Alternative descriptions of this type of extremely elongated illumination might include the terms line illumination, linear illumination, thin light sheet illumination, and plane illumination.
N-slit interferometers are also of interest to researchers working in atom optics,[13] Fourier imaging,[14] and quantum computing.[15]
See also
- Beam expander
- Double-slit experiment
- Free-space optical communication
- Microscopy
- N-slit interferometric equation
- List of laser articles
References
- ^ I. Newton, Opticks (Royal Society, London, 1704).
- ^ A. A. Michelson, Studies in Optics (Chicago University, Chicago, 1927).
- ^ R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. III (Addison Wesley, Reading, 1965).
- ^ P. A. M. Dirac, The Principles of Quantum Mechanics, 4th Ed. (Oxford, London, 1978).
- ^ a b c 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.
- ^ a b c d e f g h i j F. J. Duarte, On a generalized interference equation and interferometric measurements, Opt. Commun. 103, 8-14 (1993).
- ^ a b c d e f g F. J. Duarte, Electro-optical interferometric microdensitometer system, US Patent 5255069 (1993).
- ^ F. J. Duarte, in High Power Dye Lasers (Springer-Verlag, Berlin, 1991) Chapter 2.
- ^ a b 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).
- ^ a b c d 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).
- ^ a b c d e f g h 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, Interferometric imaging, in Tunable Laser Applications (Marcel-Dekker, New York, 1995) Chapter 5.
- ^ L-B. Deng, Theory of atom optics: Feynman path integral approach, Frontiers Phys. China 1, 47-53 (2006).
- ^ H. Liu et al., Fourier-transform ghost imaging with pure far field correlated thermal light,Phys. Rev. A. 76, 053808 (2007).
- ^ J. F. Clauser and J. P. Dowling, Factoring integers with Young’s N-slit interferometer, Phys. Rev. A 53, 4587–4590 (1996).
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