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1. An optical fiber has a core refractive index n1=1.5 and a cladding refractive index n2=1.48.  If the core diameter of the fiber is 50 microns, please calculate

(a) The numerical aperture of the fiber.

(b) The maximum incident angle of the fiber.

2. If the length of the fiber, in Problem 1, is 1 km, please calculate the maximum allowed transmission rate for

(a) Step index fiber

(b) Gradient index fiber.

3. For the fiber in problem 1, if the fiber is not perfect and the reflectivity of each reflection is 0.999999, please calculate the maximum propagation length for the incident power of the light drops to the level of 1% of incident light.

4. (a) Write down the Helmholtz wave equations for a cylindrical fiber in the core and cladding regions in cylindrical coordinate.

(b) Write down the conditions to derive the Helmholtz equation.

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