Problem 1

Part C
Plots done using mathematica, figure 1 using equation 8.25 excluding the $$\phi$$ dependence and using the appropriate l values for each mode.

Plots of R(r) for $$LP_{01}$$ and $$LP_{11}$$ modes versus r.

Part D
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.