H-mode, Bragg diffraction from a surface relief, square wave

(50% duty cycle) grating was studied in Figure 5.10 (first presented in [19,

Fig. 5]).This problem concerns studying the diffraction efficiency that results

when the incident angle deviates from the Bragg angle. The Bragg angle

corresponding to this figure was _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

»

H-mode, Bragg diffraction from a surface relief, square wave

(50% duty cycle) grating was studied in Figure 5.10 (first presented in [19,

Fig. 5]).This problem concerns studying the diffraction efficiency that results

when the incident angle deviates from the Bragg angle. The Bragg angle

corresponding to this figure was _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. These

calculations are 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 5.2.1, the order i = 0,1 transmitted diffraction efficiencies

for an incidence of angle _i = 20° (non-Bragg

angle). Make comparison plots of the i = 0,1 transmitted diffraction

efficiencies for _i = 20° and _i

= _iB = 30°.

(c) Comment on the effect that deviation from the Bragg

angle has on reflected and transmitted diffraction from the grating.

(d) In your solution of (a), (b), and (c), be sure to check

numerically that the conservation of power holds to a high degree of accuracy.

»

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