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E - Bibliothèque et Archives Canada

E - Bibliothèque et Archives Canada

As for the plots

As for the plots included hem they al1 repmsent the surface ainent density on a strip of difbmnt width illuminateci by a TMz plane wave at difbrent angles of incidenœ: Figure 4.7 shows the case of a strip width of O.SA and an angle of incidence of 90'. The results of both rnefhods are identical and exhibit the same singularity at the dg=. Figure 4.8 is for a sûip of width of 0.2A mai angle of incidenœ of 90'. The resuits of both methods are identical. Figure 4.9 is for a strip of width of 0.21 with angle of 0.5' (almost grazing). The results of both mahods are veiy similar. They look alike at edge B and stay almt identical unti10.03 A from edge A wbre the moment methoci values seems to go singular before the UTD ones. A large number of points were used on the strip (using UTD) and this s h d that the curve also goes singular but much closer to the edge at A Figure 4.10 is for a strip of width of O. 11 with angle of incidenœ of 90'. The plots of both methods are almost identical in shape exœpt that the UTD one gives slightly higher amplitudes (around 8%). Figure 4.1 1 is for a stnp of width of 0.1 A mai angle of incidenoh of 1 0'. Both plots look alike et edge B and stay very similar up until0.03A from edge A where the moment M od plot s88m to go singular before the UTD plot. At A, the UTD plot goes singular also but much closer to the edge itself. In general the UTD plots and Moment methoâ plots am similar at lm frequency with the singular behavior dinbrenœ at the dge king incidenœ angle sensitive. It se3ems that the rate at which the singubrity is mcheâ drops tmmendously with decreasing angle of incidence (near grazing) for the edge which is farther away from the source of the illumination. This could be explaineâ

y the fact mat the wrrent density depends on a modified dope diffraction &cient. A qui& analysis of this modifieâ coefficient (&r to sec 4.1.2) shows that it is equivalent to the normal diffraction coefficient with + and +' swapped. This msans that with an illumination coming from the right side (alrnost at grazing incidence). the left edge difiradon contribution depends on the derivative of a coefficient with Iess variations unlike tha opposite side which is at higher rate of change next to the boumlaries. This again muld be the cause of the leading terni of the asymptotic solution not being the most prominent of all. It is however uride~stcxxi that this differenœ between UT0 and moment method is on how to represent a singularity by itseîf and as long as these singulanties are understood the final result could be acceptable.

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