Deck 12: Optical Fiber Systems 1: Intensity Modulationdirect Detection

Question 1

A telecommunications service provider wants a single-wavelength soliton transmission system that is to operate at 40 Gb/s over a 2000-km distance. How would you design such a system You are free to choose whatever components and design parameters are needed.

Answer 1

Soliton system design.

Question 2

Create a cost model for the soliton system designed in Prob. 12.7, so that the service provider can determine the funding required for the project.

Answer 2

Soliton system cost model.

Question 3

Consider a WDM system that utilizes two soliton channels at wavelengths 1 and 2. Since different wavelengths travel at slightly
different velocities in a fiber, the solitons of the faster channel will gradually overtake and pass through the slower-channel solitons. If the collision length L coll is defined as the distance between the beginning and end of the pulse overlap at the half-power points, then
where = 1 - 2 , T s is the pulse FWHM, and D is the dispersion parameter.
( a ) What is the collision length for T s = 16 ps, D = 0.5 ps/(nm · km), and = 0.8 nm
( b ) Four-wave mixing effects arise between the soliton pulses during their collision, but then collapse to zero afterward. To avoid amplifying these effects, the condi­tion L coll 2 L amp should be satisfied, where L amp is the amplifier spacing. What is the upper bound for L amp for the above case

Answer 3

(a) From the given equation, L coll = 80 km.
(b) From the given condition,

Question 4

Based on the conditions described in Prob. 12.9, what is the maximum number of allowed wavelength channels spaced 0.4 nm apart in a WDM soliton system when L amp = 25 km, T s = 20 ps, and D = 0.4 ps/(nm · km)

Question 5

Consider three copropagating optical signals at frequencies V₁, v 2 , and v 3.
( a ) If these frequencies are evenly spaced so that V₁= v 2 - v and v 3 = v 2 + v , where v is an incremental frequency change, list the third-order waves that are generated due to FWM and plot them in relation to the original three waves. Note that several of these FWM-generated waves coincide with the original frequencies.
( b ) Now examine the case when V₁= v 2 - v
and Find the FWM- generated frequencies and plot them in relation to the original three waves.

Question 6

A single-mode fiber has an attenuation of 0.55 dB/km at 1310 nm and 0.28 dB/km at 550 nm. Compare the effective lengths of this fiber at 1310 and 1550 nm.

Question 7

Consider a 1550-nm optical source that has a 40-MHz linewidth. Suppose we have a single-mode fiber that has a 72- m 2 effective area and a 0.2-dB/km attenuation at 1550 nm. Assuming that the polarization factor b = 2 and that the Brillouin gain coefficient is g B = 4 × 10 -11 m/W, what is the threshold power for stimulated Brillouin scattering at 1550 nm for a 40-km link If the attenuation for this fiber is 0.4 dB/km at 1310 nm and all other parameters are the same, what is the threshold power for stimulated Brillouin scattering at 1310 nm

Question 8

An engineer needs to design a four-wave­length WDM system using a dispersion-shifted fiber that has a zero-dispersion point at 1550 nm. The four wavelengths need to be in the 193.1- to-194.1-THz band on a 100-GHz grid. Where should these wavelengths be placed so that none of the four-wave mixing components interfere with any transmission wavelength

Question 9

A detailed expression for the FWM efficiency is given by 4
where the factor is the difference of the propagation constants of the various waves due to dispersion, and is given by
Here the value of the dispersion D ( v 0 ) and its slope dD/d , are taken at the optical frequency v 0. Using these expressions in Eq. (12.13), plot the ratio of the generated power P 112 to the transmitted channel power P₁as a function of the channel spacing for two +7-dBm channels. Find this ratio for the following dispersion and wavelength values:
( a ) D = 0 ps/(nm ·km) and = 1556.6 nm.
( b ) D = 0.13 ps/(nm ·km) and = 1556.1 nm.
( c ) D = 1.64 ps/(nm ·km) and = 1537.2 nm. Let the frequency spacing of the two channels range from 0 to 250 GHz. In each case, take dD/d = 0.08 ps/(nm 2 · km), = 0.0461 km -1 , L = 11 km, and A eff = 55 m 2. For 1111 and use the values given in Example 12.3.

Question 10

A soliton transmission system operates at 1550 nm with fibers that have a dispersion of 1.5 ps/(nm · km) and an effective core area of 50 m 2. Find the peak power required for fundamental solitons that have a 16-ps FWHM width. Use the value n 2 = 2.6 × 10 -16 cm 2 /W. What are the dispersion length and the soliton period What is the required peak power for 30-ps pulses