Interferometric Optics |
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- Derivation of the direct mathematical link between the probability amplitudes of quantum entanglement with Pauli matrices and Hadamard-class matrices (2019-2021).

- Generalization of the
*N*-slit interferometric methodology to derive quantum entanglement probability amplitudes for n = N = 2, 4, 8, 16 ... and n = N = 3, 6, 9... (2017).

- First transparent physical description, without using Bell's theorem, neutralizing the EPR paradox (2013).

- Derivation of the probability amplitude for quantum entanglement from a transparent
*N*-slit interferometric perspective (2013).

- First to report on very large
*N*-slit laser interferometers, in the 30-530 m range, and to superimpose fine diffraction profiles on propagating interferograms. These very large*N*-slit interferometers were applied to measure clear-air turbulence (2010-2013).

- Extension of the generalized multiple-prism dispersion theory to high-order (4th, 5th,... 9th) dispersions applicable to laser-pulse compression and nonlinear optics (2009).

- Multiple-prism dispersion theory for positive and negative refraction (2006).

- First report on high-visibility coherent emission from an electrically-pumped organic semiconductor within an interferometric configuration (2005).

- First report of organic polymer-nanoparticle laser emission (2003).

- First report on the use of interferometric characters for secure space-to-space communications (2002).

- First lithium isotope separation using narrow-linewidth tunable diode lasers (2002).

- First single-longitudinal-mode tunable solid-state dye laser oscillator emitting at the limit allowed by Heisenberg's
uncertainty principle (1999).

- Unified interference, diffraction, refraction, and reflection, via Dirac's notation (1997).

- Demonstration of the first single-longitudinal-mode solid-state tunable dye laser oscillator (1994).

- First report on a ruggedized single-longitudinal-mode tunable laser oscillator in the visible (1991).

- Invention of the multiple-prism collinear polarization rotator (1989).

- First description of the
*N*-slit laser interferometer photon propagation via Dirac's quantum notation, applicable to single photons and ensembles of indistinguishable photons, leading to the generalized*N*-slit interferometric equation (1987-1991).

- Introduction of extremely-elongated laser Gaussian beams, width to height ratios of up to 2000:1, for imaging, microdensitometry, and microscopy applications. This class of illumination is now known as light-sheet illumination (1987-1991).

- Invention of the
*N*-slit laser interferometer (1987).

- Extension of the multiple-prism dispersion theory to higher derivatives for laser-pulse compression (1987).

- First report of single-longitudinal-mode oscillation in long-pulse high-energy tunable lasers (1986).

- First report of multiple-prism grating and multiple-prism near grazing-incidence grating oscilltors in high-power CO
_{2}laser cavities (1984).

- First demonstration of single-longitudinal-mode laser oscillation using multiple-prism near grazing-incidence grating oscillators under high-repetition copper-laser excitation (1982-1984).

- Generelized multiple-prism grating dispersion theory (1982).

- First multiple-prism near grazing-incidence grating narrow-linewidth tunable laser oscillator (1981).

- Derivation of the correct Fourier-theory heat-transfer equation for radial heat-flow in a sphere (1979).

Documented firsts: the original advances highlighted here have been published in the refereed-archival literature with Duarte as sole author, or lead author, in over 90% of these publications. Co-authors include: A. M. Black, R. W. Conrad, W. E. Davenport, A. E. Duarte, J. J. Ehrlich, R. O. James, L. S. Liao, I. E. Olivares, J. A. Piper, E. A. Saravia, J. C. Slaten, T. S. Taylor, J. Unsworth, K. M. Vaeth, and P. G. Varmette.

Published on the

*9th of January, 2015*; updated on the*9th of November, 2021.*