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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