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The interaction of an incoming slow neutron with a straight semi-infinite material waveguide (physically, a very lengthy one) located in vacuum (clad) in the infinite three-dimensional (3D) space is studied. The waveguide creates an attractive potential on the neutron. The physical quantum-mechanical wave phenomena are: (i) reflection and scattering of the neutron by the waveguide and (ii) its confined propagation along the latter, in specific propagation modes. The direct application of standard scattering integral equations meets several difficulties, arising mainly from the infinite length of the waveguide and (ii). New and more convenient 3D scattering integral equations are proposed and discussed, using suitable Green functions, adequate for the semi-infinite waveguide and accounting for (i) and the above difficulties. Approximate formulae for the probability amplitudes and fluxes for (i) and (ii) are given: in particular, the formulas for slow neutron confined propagation extend the ones given previously for optical waveguides. Some detailed applications and numerical computations for two-dimensional media and waveguides are presented.

A programmable digital circuit typically consists of a microprocessor, a memory device, an input data device and an output data device, with its corresponding communication busses. These devices work following a program which is stored in the memory device, as codified instructions. An opto-electronic system that emulates a programmable digital circuit is proposed and described in this work. This circuit is commanded by a sequential program stored as a spatial distribution of Fourier Holograms into a photorefractive crystal. The sequential program is conformed by instructions, which have been codified as binary pixels maps. To read and decode each instruction, the spatial position of the photorefractive crystal must change; and then a CCD camera captures the output image of the Fourier Hologram. Our LabVIEW software decodes the instruction from the captured output image and it commands the circuit to realize the decoded instruction. This software controls the CCD camera and an electromechanical system which moves the spatial position of the photorefractive crystal. The electromechanical system is continuously in communication with a PC through our software. This is because the electronic circuit of the electromechanical system, moves three stepper motors; depending on the position in which the crystal needs to be to read the next instruction. The experimental results and the complete description of the practical advantages and disadvantages of the complete engineering system and the emulation of the opto-electronic programmable digital circuit will be described in this work.

We introduce the gyrator transform which produces a rotation of two‐dimensional signal in phase space. Main properties of this transform are considered. The flexible optical set up for gyrator transform experimental implementation is discussed. The applications of the gyrator transform to image processing such as filtering, noise reduction, encryption are demonstrated.

The interaction and diffraction of a classical electromagnetic wave by a thin slab characterised by a periodic dielectric permeability is studied rigorously, thereby completing previously existing studies. New integral equations for the induction vector in terms of a suitable Green function, are presented, and a condition which ensures the convergence of their iterations is obtained. A bound for the error of the usual Debye-Born-Rayleigh-Gans approximation to the diffraction amplitudes is given.

We present here numerical estimates of the density and flux of energy based on physical parameters associated with the absorption properties of certain types of absorbing optical waveguides. These results are based on a theoretical formalism established previously for the initial field incident upon the entrance pupil of an absorbing optical waveguide. Based on these results, the mechanisms of confined energy transmission and possible cross talk between neighboring waveguides are discussed. Some comments on the behavior of Bessel functions with complex arguments are also included in the discussion.

A three-dimensional analysis of bending losses in dielectric optical waveguides is presented. It constitutes a nontrivial generalization of previous two- and three-dimensional studies by other authors. Our analysis is based on homogeneous integral equations for the total radiation field and suitable asymptotic approximations for Green’s functions. A key role is played by a new three-dimensional approximation for a relevant Bessel function with large order and argument (the former being larger than the latter). A nontrivial check of the consistency of all those approximations is given. General formulas are presented for the radiated field and the energy flow and for a bending-loss coefficient in three dimensions. Numerical results are also given, in order to assess the difference between the results of other authors and ours. Such a difference is rather small for monomode behavior near cutoff, increases as the behavior of the waveguide changes from monomode to multimode, and decreases as the parameter V increases for a given core radius and propagation mode.

The authors present a mathematically exact formulation of the initial field striking the aperture of an absorbing optical waveguide, via an integral equation description. An analysis of the residual scattering by the waveguide is presented. Because of the presence of the non-negligible absorption coefficient, the solution for the fraction of the confined power is obtained by performing non-trivial integrations of Bessel and Hankel functions with complex arguments. In order to carry out a numerical analysis a specific computational method is applied by using an approximated polynomial expansion whose validity is also discussed.

For pt.I see ibid., vol.17, p.475 (1984). The possible confined propagation of slow (thermal) neutrons along cladded waveguides of small cross section (fibres) is studied, in order to improve a previously published analysis. Quite suitable possibilities for the core of the waveguide could be either Al or Si (or vacuum), so as to allow for confined propagation of neutrons along reasonable lengths, without large scattering and absorption losses. Tentative possibilities for the cladding could be either Ni or Fe. The bending losses are analysed for a curved neutron fibre in two spatial dimensions. Such bending losses turn out to be completely negligible, except in the case of a small radius of curvature Rc. To quote some typical values, for any fibre diameter between 0.1 and 1 mu m and reasonable lengths for it (between 5 and 10 cm), bending losses can be neglected other than for Rc

An exact formulation of the electromagnetic field striking an optical waveguide is presented and compared with the decomposition relationship used in the literature. The expression for the critical angle is derived as a natural consequence of this formulation. Equations for the total fraction of power confined within a waveguide are derived and analyzed for the special case of absorbing waveguides. An explicit expression is derived for the fraction of energy confined within a waveguide supporting two sets of modes.