Extending the Taylor approximation to higher-order terms in high-loss materials. Consider a lossy medium having a finite conductivity a but, for purposes of this problem, no laser susceptibility Xt. First-order expressions for the propagation coefficient ft and the attenuation coefficient a for this case are derived in the text by a Taylor-series approximation in sigma/Wе. Extend this approximation to get the next higher-order corrections to both B and a. How large will the power attenuation have to become (in the first-order approximation) before either of these higher-order corrections amounts to 10% of the first-order expressions? Express your answer in units of dB of power attenuation per wavelength of distance
Pg 276, google gives a huge preview of the book
The Attempt at a Solution
I'm not understanding the question. I don't see the derivation they claim to have made in the book. Is the question asking for a taylor expansion where the a = sigma/еW?
I only see them talking about a taylor expansion of r = jb (1-jsigma/We + Xat) about x =0. However this question said Xat = 0. Wouldn't this make all derivatives taken become 0? Therefore no way to expand?
Anyone familiar with Siegmans laser book and can help me out.