Chapter 13, Problem 13.24P

To determine

To prove:

For a given mode in a parallel-plate or rectangular waveguide the group dispersion parameter $\frac{d^2\beta }{d{\omega }^2}$ is given by:

   $\frac{d^2\beta }{d{\omega }^2}=-\frac{n}{\omega c}{\left(\frac{{\omega }_c}{\omega }\right)}^2{\left[1-{\left(\frac{{\omega }_c}{\omega }\right)}^2\right]}^{-\frac{3}{2}}$ , where ${\omega }_c$ is the radian cutoff frequency for the mode