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We define the function
r(z,d) = v(z,d)/u(z,d) [3-2] and the Riccati equation can be found
by differentiating r with respect to z and substituting equations (3-2)
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(3-6) |
Using the boundary condition r(L,d) = 0,
the equation can be numerically solved from the end of the grating backward to
z = 0 using a Runge-Kutta method. The reflection coefficient
amplitude is found to be r(d) = r(0,d). The calculation needs a larger number of steps in the Runge-Kutta
routine to converge than for the T-matrix method presented hereafter.
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