Diffraction pattern of circular and rectangular apertures in the spinor formalism of electromagnetism

Spinor and Hertzian Differential Forms in Electromagnetism

“…The spinor formalism was precedently used in two different domains: analysis of diffraction patterns of electromagnetic fields by apertures [30] and comparison of the Witten-Penrose [31,32] and Infeld = Van Der Waerden spinor approaches to General Relativity [33]. But recently, the spinor formalism has appeared as an appropriate tool to explain the superstring theory [34,35].…”

Thermal Blooming of Laser Beams in the Framework of Spinor Formalism

“…The second point concerns diffraction effects on beam propagation . This question is not considered here for reasons of length but it is discussed in a separate work [14] for circular and rectangular apertures .…”

“…and that we use instead of (8) To obtain a numerical solution of the thermal blooming problem, we now have to make discreet (14), (15), (16) . For the last one, we used the Simpson method and when the integration range contains an even number of points, the trapezoidal rule can be used on the last interval .…”

“…The solution of equations (14) is then obtained by an implicit alternating-direction method incorporating a suggestion made by Voevodin [9] .…”

“…Starting with the values f jk and f 7 obtained at the mth step, equations (14) give at the first stage, of the …”