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# ELEC425/6261 Assignment 2 1. A multimode fiber Consider a multimode fiber with a core diameter of 100 m, core refractive index of 1.475 and a...

. If intermode() is the rms dispersion in a graded index fiber with a profile index , and if o is the optimal profile index, then

and o is given by Eq. (2) in § 2.7. Consider the same  as in Q4, calculate the new dispersion and bit rate  distance product if  is 10% greater than the optimal value o.
ELEC425/6261 Assignment 2 1. A multimode fiber Consider a multimode fiber with a core diameter of 100 μ m, core refractive index of 1.475 and a cladding refractive index of 1.455 both at 850 nm. Consider operating this fiber at λ = 850 nm. (a) Calculate the V -number for the fiber and estimate the number of modes. (b) Calculate the wavelength beyond which the fiber becomes single mode. (c) Calculate the numerical aperture. (d) Calculate the maximum acceptance angle. (e) Calculate the modal dispersion τ and hence the bit rate × distance product given that rms dispersion σ 0.29 τ where τ is the full spread. 2. A single mode fiber Consider a fiber with a SiO 2 -13.5%GeO 2 core of diameter of 8 μ m and refractive index of 1.468 and a cladding refractive index of 1.464 both refractive indices at 1300 nm where the fiber is to be operated using a laser source with a half maximum width of 2 nm. (a) Calculate the V -number for the fiber. Is this a single mode fiber? (b) Calculate the wavelength below which the fiber becomes multimode. (c) Calculate the numerical aperture. (d) Calculate the maximum acceptance angle. (e) Obtain the material dispersion and waveguide dispersion and hence estimate the bit rate × distance product ( B × L ) of the fiber. 3. Consider an optimal graded index fiber with a core diameter of 30 μ m and a refractive index of 1.474 at the center of the core and a cladding refractive index of 1.453. Suppose that the fiber is coupled to a laser diode emitter at 1300 nm and a spectral linewidth (FWHM) of 3 nm. Suppose that the material dispersion coefficient at this wavelength is about - 5 ps km -1 nm -1 . Calculate, the total dispersion and estimate the bit rate × distance product of the fiber. How does this compare with the performance of a multimode fiber with the same core radius, and n 1 and n 2 ? What would be the total dispersion and maximum bit rate if an LED source of spectral width (FWHM) λ 1/2 80 nm is used? 4. If σ intermode ( γ ) is the rms dispersion in a graded index fiber with a profile index γ , and if γ o is the optimal profile index, then σ intermode ( γ ) σ intermode ( γ o ) = 2( γ - γ o ) ( γ + 2) and γ o is given by Eq. (2) in § 2.7. Consider the same as in Q4, calculate the new dispersion and bit rate × distance product if γ is 10% greater than the optimal value γ o . 5. Microbending loss It is found that for a single mode fiber with a cut-off wavelength λ c = 1180 nm, operating at 1300 nm, the microbending loss reaches 1 dB m -1 when the radius of curvature of the bend is roughly 6 mm for = 0.00825, 12 mm for = 0.00550 and 35 mm for = 0.00275. Explain these findings.

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