Beam propagation model

It is proposed to do this by injecting a second rotating electron beam from the other end of the tube at a radius between the plasma formed by the first beam and the wall. The parameters of this second beam have been predicted using a beam propagation model that has been developed to explain the results obtained with the single beam [25]. ... 

FIGURE 16 Beam propagation model of passive zero-gap directional coupler using NLO and passive polymers with matching indices. 

Sun, H. Dalton, L. Chen, A., Systematic design and simulation of polymer microring resonators with the combination of beam propagation method and matrix model, In Digest of the IEEE LEOS Summer Topical Meetings, 2007, 217 218... 

R. Pregla, MoL-BPM Method of Lines Based Beam Propagation Method, in W. P. Huang (Ed.), Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices, Progress in Electromagnetic Research 11 (Elsevier, New York, 1995). 

H. Hoekstra, On beam propagation methods for modelling in integrated optics, Optical and Quantum Electronics 29, 157-171 (1997). 

Extensive treatment of optical waveguide and directional coupler theory has been addressed by many researchers for both continuous two-dimensional film waveguides and dielectric strip waveguides. Various methods, such as dielectric waveguide, coupled-mode theory, effective index, the beam propagation method, and finite-element analysis, have been used [15,24,25,75,77,78,83,89-114]. Analysis of these methods shows good agreement between all of the different models. 

We first supposed that the field radiated into the piece by the transducer is known, thanks to the Champ-Sons model. Then, the main approximation used consists in making far field assumptions in the beam defect interaction area. In the case of a focused transducer we assume that the incident wavefronts on the defect are plane. This is equivalent to say that the defect is located in or near the transducer focal area and that a defect located outside this zone does not cause a significant echo. In the case of planar contact transducer, the incident wavefronts on the defect are assumed to be spherical The incident field on the defect is therefore approximated by the product of a spatial function gfp,0,z)describing the amplitude distribution in the beam and a time-delayed waveform < ) ft) representing the plane or spherical propagation in the beam. The incident field on the defect can therefore be approximated for ... 

Similarly, the focusing capability of an array is the strongest focused beam which can be steered. The simplest way to evaluate it is to test a theoretical focusing time delay law, in the near-field and in the natural direction of propagation of the array. The beam pattern characteristics depth, lateral size and length of the focal spot must be found consistent with modelling and no lobe must appear above a predetermined level. 

By deriving or computing the Maxwell equation in the frame of a cylindrical geometry, it is possible to determine the modal structure for any refractive index shape. In this paragraph we are going to give a more intuitive model to determine the number of modes to be propagated. The refractive index profile allows to determine w and the numerical aperture NA = sin (3), as dehned in equation 2. The near held (hber output) and far field (diffracted beam) are related by a Fourier transform relationship Far field = TF(Near field). 

A simulation was carried out to model the fast electron beam density after propagation in a 30 J,m thick Fe layer and the result is displayed by plot of Fig. 7.11. 

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