这个作业是研究分析多模光纤、渐变折射率分布类型

EE6428 OPTICAL COMMUNICATIONS

Assignment 2

1. Describe briefly why in multimode fibers, graded-index profile type will give a much

smaller pulse dispersion than step-index profile type. Hence give a typical

mathematical expression for the refractive index of such graded-index fibers as a

function of the radial distance, fiber core radius, fractional change of core-cladding

index, and other relevant parameters.

2. Compare the intermodal pulse dispersion and the bandwidth in a multimode fiber

whose core index, n1 = 1.50 and = 0.01 for the following three cases :

(a) the core index is a step-index function,

(b) the core index is graded-index governed by the power law index function with

=2,

(c) same as part (b) except = opt.

3. Design a multimode step-index fiber whose normalized V number is 100 and whose

numerical aperture NA is 0.30. The fiber will be used in a data link with a 0.85µm

LED source. Determine the fiber parameters a, n1 and n2 if fused quartz with

refractive index 1.457 is used (a) as the core material, and (b) as the cladding

material.

4. Assuming plane mirrors are used in the laser resonant cavity and that we have the

following two cases :

(a) a gas laser with cavity length 50cm, and

(b) a GaAs laser diode with a cavity length of 300µm.

(i) Calculate the number of possible axial modes that can exist in both cases and

determine the frequency spacing between adjacent axial modes. Assuming

the operating wavelength is 0.8µm, the refractive index of the gas cavity is 1.0

and that of GaAs is 3.5 at such operating wavelength.

What will be the corresponding wavelength spacing between adjacent axial modes?

(ii) Estimate the maximum length of the cavity in both cases if the laser has to be

single mode and if the gain curve of the laser material covers a bandwidth of

1500MHz.

5. (i) An LED has a circular emitting area of radius 400µm. The power emitted by

the diode is 1mW. Its radiation pattern is described by cosθ. This diode is buttjointed to a step index fiber of core diameter 50µm, numerical aperture 0.25, core

index 1.479 and attenuation 2dB/km. Calculate the optical power accepted by the

fiber, assuming 100% transmissivity between the source and the fiber.

(ii) If the optical source in (i) is now replaced by a laser diode with emitting area

of 0.2µm x 12µm and emitting power 10mW, radiation pattern cos200θ, calculate the

power accepted by the fiber.

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