Page 265 - Introduction to Information Optics

250 4. Switching with Optics

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EXERCISES

4.1 Write a computer program to solve Eqs. (4.3) and (4.5), and generate
curves similar to Fig. 4.4. Assume the nonlinear medium in the etalon is
6
2
GaAs with « 2 = 2 x l(T cm /W.
4.2 Study the effect of loss on the performance of a nonlinear etalon. Assume
l
the nonlinear medium has a loss coefficient of a (cm ~ ). Derive the results
similar to Eqs. (4.3), (4.4), and (4.5).
4.3 Derive Eq. (4.8) from Eq. (4.7) using the initial conditions A(Q) = I, and
B(0) =0.
4.4 Solve Eq. (4.7) using initial condition A(Q) = 1/2 and B(0) = 1/2.
4.5 Show that Eq. (4.10) reduces to Eq. (4.8) when P « P c. (Hint: Find the
property of the elliptic function cn(x m) for special m values.)
4.6 Study the effect of loss on the performance of an NLDC. Assume the
1
nonlinear medium has a loss coefficient of a = 1 cm"" , and coupling
length L c — 1 cm. Obtain the results similar to Fig. 4.9.
4.7 Derive Eq. (4.12) from Eq. (4.11) assuming E l — E- m and E 2 = 0.