Plots done using mathematica, figure 1 using equation 8.25 excluding the \(\phi\) dependence and using the appropriate l values for each mode.
Here I plotted Spot Size versus wavelength from \(.850 \mu m\) to \(1.55 \mu m \). What bothers me is that this does not agree with what I calculated out analytically for the first part of Part D, for spot size of \(1.55 \mu m\). Its not terribly off by \(w_p \approx 2 \mu m\). I took values of 850 nm to 1550 nm in 70 steps for 11 values total. Then had to find the b values for the corresponding v values for each. Then found the spot size for each corresponding u value for each wavelength.