H-mode, Bragg diffraction from a surface relief, square wave grating whose groove width occupies…

H-mode, Bragg diffraction from a surface relief, square wave
grating whose groove width occupies two-thirds of the grating period is to be
analyzed. Figure 5.10 illustrates a surface relief, square wave grating whose
groove width occupies half of the grating period. This problem concerns
studying the effect of changing groove width on diffraction efficiency when the
square wave grating is illuminated at the Bragg angle. The Bragg angle for this
problem is _i = _iB = 30°.

(a) Using the RCWA full-field formulation of Section 5.2.1,
calculate numerically for the geometry and numerical values
»

H-mode, Bragg diffraction from a surface relief, square wave
grating whose groove width occupies two-thirds of the grating period is to be
analyzed. Figure 5.10 illustrates a surface relief, square wave grating whose
groove width occupies half of the grating period. This problem concerns
studying the effect of changing groove width on diffraction efficiency when the
square wave grating is illuminated at the Bragg angle. The Bragg angle for this
problem is _i = _iB = 30°.

(a) Using the RCWA full-field formulation of Section 5.2.1,
calculate numerically for the geometry and numerical values of Figure 5.10 (1)
the i = _1, 0, 1 order, transmitted diffraction efficiencies of
this figure and (2) the i = 0 reflected diffraction efficiency. This
calculation is to be carried out to ensure that your diffraction efficiency
algorithm is working correctly. The i = 0 reflected diffraction
efficiency is presented in Ref. [19, Fig. 5].

(b) Calculate using the RCWA full-field formulation of
Section 5.3.1, the order i = 0,1 transmitted diffraction efficiencies
for an incidence of angle _i = 30° when the groove width
occupies 60% of the grating period.

(c) Make comparison plots of the transmitted diffraction
efficiencies as calculated in (a) and (b).

(d) Comment on the effect that groove width has on
diffraction from the gratings described in (a) and (b).

(e) In your solution of (a) and (b), be sure to check
numerically that the conservation of power holds to a high degree of accuracy.

»

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