In this paper we describe a superposition model for Bessel-Gauss beams, in which higher orders are included. An analogous model leads to a different class of beams, namely the modified Bessel-Gauss beams. Then a generalized set of beams, containing the previous beams as particular cases, is introduced. The behaviour of these beams upon propagation is investigated, both analytically and numerically
Flattened Gaussian beams are characterized by a waist profile that passes in a continuous way from a nearly flat illuminated region to darkness. The steepness of the transition region is controlled by an integer parameter N representing the order of the beam. Being expressible as a sum of N Laguerre-Gauss modes, a flattened Gaussian beam turns out to be very simple to study as far as propagation is concerned. We investigate the main features of the field distribution pertaining to a flattened Gaussian beam throughout the space and present experimental results relating to the laboratory production of this type of beam. (C) 1996 Optical Society of Americ
The scheme of a device that should have a simple and reliable implementation and that, under simply verifiable conditions, should generate a true random binary sequence is defined. Some tricks are used to suppress bias and correlation so that the desired statistical properties are obtained without using any pseudorandom transformation. The proposed scheme is well represented by an analytic model that describes the system behaviour both under normal conditions and when different failures occur. Within the model, it is shown that the system is robust to changes in the circuit parameters. Furthermore, a test procedure can be defined to verify the correct operation of the generator without performing any statistical analysis of its output.
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