1. Derive the eigenvalue equation (2.2.33) by matching the boundary conditions at the core-cladding interface of a step-index fiber.
2. A single-mode fiber has an index step n1 -n2 = 0.005. Calculate the core radiusif the fiber has a cutoff wavelength of 1 µm. Estimate the spot size (FWHM) of the fiber mode and the fraction of the mode power inside the core when this fiber is used at 1.3 µm. Use n1 = 1.45.