# This problem concerns studying H-mode, Bragg diffraction from a sinusoidal surface relief grating…

This problem concerns studying H-mode, Bragg diffraction
from a sinusoidal surface relief grating whose grating period is equal to the
free-space wavelength. The grating is assumed to be nonmagnetic (_G
= 1), have a relative dielectric permittivity of _G =
2.5, and have a vacuum on the incident side. The Bragg angle for this problem
is _i   = _iB = 30°. The
geometry of the problem may be found in the Figure 5.20 inset and in Ref. [19,
Fig. 4].

(a) Using a multilayer RCWA full-field formulation,
including i = _2, _1,0,1,2 Fourier harmonics, calculate
numerically the i = _1,0,1 order,
»

This problem concerns studying H-mode, Bragg diffraction
from a sinusoidal surface relief grating whose grating period is equal to the
free-space wavelength. The grating is assumed to be nonmagnetic (_G
= 1), have a relative dielectric permittivity of _G =
2.5, and have a vacuum on the incident side. The Bragg angle for this problem
is _i   = _iB = 30°. The
geometry of the problem may be found in the Figure 5.20 inset and in Ref. [19,
Fig. 4].

(a) Using a multilayer RCWA full-field formulation,
including i = _2, _1,0,1,2 Fourier harmonics, calculate
numerically the i = _1,0,1 order, transmitted diffraction
efficiencies for this problem. Make i = _1,0,1 order,
transmitted diffraction efficiency plots versus grating thickness (peak-to-peak
distance of the sinusoid making up the surface relief grating). Plot also the
i = 0 reflected diffraction efficiency.

(b) Compare your solution plots to those found in Ref. [19,
Fig. 4].

(c) Comment on the effect that the grating thickness has on
diffraction from the gratings described in (a) and (b).

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

»

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