Page 528 - Engineering Electromagnetics, 8th Edition

510 ENGINEERING ELECTROMAGNETICS

Figure 13.26 See Problem 13.29.

pulse broadens to twice its initial width. What simple step can be taken to
reduce the amount of pulse broadening in this guide, while maintaining the
same initial pulse width? Additional background for this problem is found
in Section 12.6.
13.26 A symmetric dielectric slab waveguide has a slab thickness d = 10 µm,
with n 1 = 1.48 and n 2 = 1.45. If the operating wavelength is λ = 1.3 µm,
what modes will propagate?
13.27 A symmetric slab waveguide is known to support only a single pair of TE
and TM modes at wavelength λ = 1.55 µm. If the slab thickness is 5 µm,
what is the maximum value of n 1 if n 2 = 3.30?
13.28 In a symmetric slab waveguide, n 1 = 1.50, n 2 = 1.45, and d = 10 µm.
(a) What is the phase velocity of the m = 1TEorTM mode at cutoff?
(b)How will your part (a) result change for higher-order modes (if at all)?
13.29 An asymmetric slab waveguide is shown in Figure 13.26. In this case, the
regions above and below the slab have unequal refractive indices, where
n 1 > n 3 > n 2 .(a) Write, in terms of the appropriate indices, an expression
for the minimum possible wave angle, θ 1 , that a guided mode may have.
(b) Write an expression for the maximum phase velocity a guided mode
may have in this structure, using given or known parameters.
13.30 A step index optical fiber is known to be single mode at wavelengths
λ> 1.2 µm. Another fiber is to be fabricated from the same materials, but it
is to be single mode at wavelengths λ> 0.63 µm. By what percentage must
the core radius of the new fiber differ from the old one, and should it be
larger or smaller?
13.31 Is the mode field radius greater than or less than the fiber core radius in
single-mode step index fiber?
13.32 The mode field radius of a step index fiber is measured as 4.5 µmat
free-space wavelength λ = 1.30 µm. If the cutoff wavelength is specified as
λ c = 1.20 µm, find the expected mode field radius at λ = 1.55 µm.