Q: Find the width of the anomalous dispersion region for the case of
Find the width of the anomalous dispersion region for the case of a single resonance at frequency ω0. Assume γ
See AnswerQ: Starting with Eq. 9.170, calculate the group velocity
Starting with Eq. 9.170, calculate the group velocity, assuming there is only one resonance, at ω0. Use a computer to graph y ≡ vg/c as a function of x ≡ (ω/ω0)2, from x = 0 to 2, (a) for γ = 0, and (...
See AnswerQ: (a) Derive Eqs. 9.179, and from
(a) Derive Eqs. 9.179, and from these obtain Eqs. 9.180. (b) Put Eq. 9.180 into Maxwell’s equations (i) and (ii) to obtain Eq. 9.181. Check that you get the same results using (i) and (iv) of Eq. 9.17...
See AnswerQ: Show that the mode TE00 cannot occur in a rectangular wave guide
Show that the mode TE00 cannot occur in a rectangular wave guide. [Hint: In this case ω/c=k, so Eqs. 9.180 are indeterminate, and you must go back to Eq. 9.179. Show that Bz is a constant, and hence—a...
See AnswerQ: Consider a rectangular wave guide with dimensions 2.28 cm*
Consider a rectangular wave guide with dimensions 2.28 cm*1.01 cm. What TE modes will propagate in this wave guide, if the driving frequency is 1.70* 1010 Hz? Suppose you wanted to excite only one TE...
See AnswerQ: Use Eq. 9.19 to determine A3 and δ3 in
Use Eq. 9.19 to determine A3 and δ3 in terms of A1, A2, δ1, and δ2.
See AnswerQ: Confirm that the energy in the TEmn mode travels at the group
Confirm that the energy in the TEmn mode travels at the group velocity. [Hint: Find the time averaged Poynting vector S and the energy density u (use Prob. 9.12 if you wish). Integrate over the cross s...
See AnswerQ: (a) Find the divergence of the function v =
(a) Find the divergence of the function v = s(2 + sin2 φ) sˆ + s sin φ cos φ φˆ+ 3z zˆ. (b) Test the divergence theorem fo...
See AnswerQ: Work out the theory of TM modes for a rectangular wave guide
Work out the theory of TM modes for a rectangular wave guide. In particular, find the longitudinal electric field, the cutoff frequencies, and the wave and group velocities. Find the ratio of the lowest...
See AnswerQ: (a) Show directly that Eqs. 9.197 satisfy
(a) Show directly that Eqs. 9.197 satisfy Maxwell’s equations (Eq. 9.177) and the boundary conditions (Eq. 9.175). (b) Find the charge density, λ(z, t), and the current, I (z, t), on the inner conduct...
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