We study the propagation of slow neutrons and their waveguiding properties in certain suitable thin films and in polycapillary glass fibres, having in mind their possible use in Boron Neutron Capture Therapy (BNCT) of small tumours. In PBSI2017 (and subsequently, in Phosphorus, Sulfur and Silicon and the Related Elements Volume 193, Issue 2, pages 64-73 (2018), we presented a general overview and some specific proposals for improved focalization of slow neutrons (at and a bit below one micron, with propagation up to about 1 m. with relatively small attenuation), by omitting a good number of quantitative aspects. The present work, based upon our presentation in PBSI2018, extends our previous proposals in PBSI2017 and provides more quantitative descriptions of them. Neutron wavelengths versus characteristic dimensions of the waveguides in our proposals typically require quantummechanical analysis: specifically, the description of the confined neutrons by means of propagation modes. The confined propagation of incoming waves along waveguides, the evolution of the resulting propagation modes and related issues are investigated.Those features give rise to computational challenges, depending on the smallness of (neutron wavelengths/ characteristic dimensions). Approximate analytical formulae are provided for the corresponding quantum-mechanical probabilities. Numerical estimates and the results of some simulations are presented. Consequences of the latter for BNCT will be discussed briefly.

The importance of the amplitude and phase in the fractional Fourier transform (FT) domain is analyzed on the basis of the rectangular signal and the real-world image. The quality of signal restoration from only the amplitude or from only the phase of its fractional FT by applying the inverse fractional FT is considered. It is shown that the signal reconstructed from the amplitude of the fractional FT usually reveals the main features of the original signal only for relatively low fractional orders. On the basis of phase information in the fractional FT domains, significant details of the signal can be obtained for nearly all fractional orders.

The theoretical model for an off-Bragg on-axis conversion between a Gaussian beam with cylindrical phase function and a plane wave by a volume aperiodic nonplanar inhomogeneous holographic grating is presented. A two-wave first-order coupled-wave theoretical framework is adopted. Analytical solutions for the amplitudes of two space harmonics of the field inside the grating zone are derived. Both the chromatic and the geometric deviations from the exact Bragg condition are studied. Numerical evaluations show that some anomalous phenomena (Pendellösung fringes, angle amplification effect, achromatism) can arise. High diffraction efficiency ͑ഠ1͒ is predicted even for relatively large off-Bragg deviations. The deterioration of the reconstruction fidelity due to the Pendellösung effect is discussed.

We develop a computational method for calculating the spatial profile of the electromagnetic field after scattering by an array of waveguides. Our formalism is very general and includes chromatic dependence, the influence of the array arrangement, and other effects such as the effect of stress. Our calculations of the amplitude and phase of scattered light provide valuable information about the features of the waveguides. These results can be applied to different areas of study, such as biological waveguides and fiber sensing.

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