problem 1: Describe what is meant by graded index optical fiber giving an expression for the possible refractive index profile. Point out the main benefit of this kind of fiber with regard to the multimode propagation.

problem 2: A typical relative refractive difference for an optical fiber designed for long distance transmission is 1%. Estimate the NA and solid acceptance angle in the air for fiber, when the core index is 1.46. Further compute the critical angle at the core cladding interface in the fiber.

problem 3: A multimode step index fiber consists of a relative refractive index difference of 1%, and a core refractive index of 1.5. The number of modes propagating at a wavelength of 1.3um is 1100. Find out the diameter of fiber core.

problem 4: A graded index fiber with parabolic refractive index profile has a core refractive index of around 1.5 and relative refractive index difference of 1%. Estimate the maximum core diameter that permits single mode operation at a wavelength of 1.3m.

problem 5: A silica optical fiber with core diameter large adequate to be considered by ray theory analysis consists of a core refractive index of 1.50 and a cladding refractive index of 1.47. Determine

a) The critical angle at core cladding interface;
b) The NA for the fiber;
c) The acceptance angle for fiber.

problem 6: An optical fiber in air consists of an NA of 0.4. Compare the acceptance angle for the meridional rays with that for skew rays that change the direction by 100 degree at each reflection.

problem 7: The velocity of light in the core of a step index fiber is 2.01 X 10⁸ m/s and the critical angle at core cladding interface is 180 degree. Find out the numerical aperture and the acceptance angle for the fiber in air, supposing it has a core diameter appropriate for consideration by ray analysis. The velocity of light in a vacuum is 2.998 X 10³ m/s.

problem 8: A step index fiber consists of a solid acceptance angle in air of 0.115 radians and a relative refractive index difference of 0.9%. Find out the speed of light in the fiber core.

problem 9: A step index fiber in air consists of a NA of 0.16, a core refractive index of 1.45 and a core diameter of 60 micrometer. Find out the normalized frequency for the fiber when light at a wavelength of o.9 micrometer is transmitted further; determine the number of guided modes propagating in fiber.

problem 10: A multimode graded index fiber consists of an acceptance angle in air of 8 degree. Estimate the relative refractive index difference between the core axis and cladding when the refractive index at the core axis is 1.52.