光纤通信英文版答案

narrowing processes. 6.17 Solution: a. FWM is one of the major nonlinear phenomenon which can be described as follows: three waves copropagating over the same fiber generate the fourth wave, whose frequency is the combination of the three original wave frequencies. b. Because FWM has become the most sever limitation of a system’s transmission capacity. 6.18 Solution: As in formula 6.23:
6.19 Solution: a. SRS scattered light moves mostly forwards & backwards and the phonons associated with this process are optical ones; while SBS scattered light moves backwards & forwards and the phonons associated with it are acoustic.
【Chapter 6】 6.1 Solution: The formula for a step-index refractive-index profile is:
n(r ) = n1 n ( r ) = n 2
6.5 Solution: According to definition of attenunation: Pout − 10 log10 P in L= A
【Chapter 7】 7.1 Solution: Today’s fiber-fabrication process includes two major steps: the first step is to manufacture a preform, a cylinder of silica composition with a dimension of about 20cm in diameter by 100cm in length. The final optical characteristics of fiber most dependent on the preform such as RI profile, attenuation, dispersion and so on. The second stage is to draw an optical fiber of the size desired from the preform. 7.3 Solution:
b.
Pth ( SRS ) ≈
16 Aeff g R Leff
=
16 × 72 µm 2 = 576mw 1 × 10 −13 m / w × 20km
Pth ( SBS ) ≈
21Aeff g B Leff
=
21 × 72 µm 2 = 1.5mw 5 × 10 −11 m / w × 20km
3.14 × 8.3 × 10 −6 πd 2 2 n1 − n 2 = 1.4692 2 − 1.4639 2 = 2.1 therefore, V = − 9 λ 1550 × 10
5.2 Solution:
According to the formulas, NA =
2 n12 - n2 and Δ =
Pj (ω j ) = ε0 (3) * χ xxxx [( E1 ⋅ E1 ) E j + ( E1 ⋅ E j ) E1* + ( E1* ⋅ E j ) E1 2 * * * * * * + (E2 ⋅ E2 )E j + (E2 ⋅ E j )E2 + (E2 ⋅ E j )E2 + (Em ⋅ E1 ) E 2 + ( E m ⋅ E 2 ) E1 + ( E1 ⋅ E 2 ) E m ]
P(r, t) = ε 0 χ e E (r , t ) + ε 0 χ e E (r , t ) ，
( 3)
3
taking the scalar form for simplicity:
E = Re ∑i =1 E j cos(ω j t − β j z ) , and Pnl = Re ∑i =1 Pj cos(ω j t − β j z )
b. To make a dispersion-shifted or a dispersion-flattened fiber, manufactures have to devise specific profile of a RI. For example, the W-like profile is usually used to make a dispersion-flattened fiber.
6.7 Solution: a. Because the demands for the speed and quality of communications is insatiable, and any type fiber, including DSF, will never be an end for eliminating dispersion, so we need to cope with dispersion by better means. b. dispersion-shift, dispersion-flatten fibers, chirp grating and so on. 6.9 Solution: Chirped-grating can reflect a set of wavelengths. When the input light beam incidents into the grating, the reflected light will include not only one wavelength. According to the chirped grating design, it includes a various period grating aligned along the fiber axile. The shorter the period of grating, the longer the wavelength it reflects. This effect can be used to compensate the time delays for different wavelengths. 6.16 Solution: a. SPM which stems from the fact that different parts of a propagating pulse have different levels of power is a limitation in a single-channel system while XPM is in a multichannel system whose modulation is induced by the power of the adjacent channel. b. Soliton is a pulse which is able to keep its shape and width steady as a result of mutual compensation of dispersion-broadening and self-phase-modulated
Pj (ω j ) = ε0 (3) * * * * χ xxxx [( E j ⋅ Ej ) E * j + 2( E j ⋅ E j ) E j + 2( E m ⋅ E m ) E j + 2( E m ⋅ E j ) E m + 2( E m ⋅ E j ) E m ] 4
where j , m = 1 or 2 and j ≠ m . And using the same process to get the part of Pnl at frequency ω3 and ω4,
r≤a r>a
0.5 × 10 −6 − 10 log 10 40 × 10 −6 = 0.25(dB / km)
(dB) = 76.12(km)
6.6 Solution: a. Chromatic dispersion, the sum of material dispersion, waveguide dispersion and profile dispersion is caused by wavelength-dependent phenomena. For different wavelengths, the material RI is changeable and the mode fields are different which result in material dispersion and waveguide dispersion. As for profile dispersion, D p (λ ) = d Δ / d λ , it is definitely depend on wavelength.
5.5 Solution: The coupling loss is:
Losscoupling (dB) = - 10 log[4 /(2w01 / 2 w02 + 2w02 / 2w01 ) 2 ]
= - 10 log[4 /(10.5 / 9.3 + 9.3 /10.5) 2 ] = 0.064(dB )
a. For r = 0.5ω0 , the portion of the maximum intensity Gaussian is:
2 η = exp(- 2r 2 / w0 ) = exp(- 0.5) = 0.607
b. The same calculation made for r = 0.75w0 , we can derive that η = 0.325
4 4
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In polarizaiton vector: P(r, t) = ε 0 χ e E(r,t) + ε 0 χ e the nonlinear part of the polarization vector:
(3)
E 3(r,t)
(3)
Pnl = ε 0 χ e
E 3(r,t)
submit the E(r,t) into Pnl, we have part of Pnl at pumping frequency ω1 and ω2,
where j , m = 3 or 4 and j ≠ m . Since the influency of SPM and XPM resulted from wave with frequency ω3 and ω4 are tiny in the above equations, we take only the SPM and XPM of the two pumping wave into account.
n1 - n2 , just let (N.A.) (n1 + n2 ) / 2
be 0.125, ( Δ ) equal to 0.0036, by solving the equations we can derive that n1 =1.4767
5.3 Solution: I don’t think so. MFD is a parameter using only for SMF which represents characteristic of a field distribution, while in MMF we use core diameter instead. 5.4 Solution:
【Chapter 5】 5.1 Solution: According to the formula, Δ =
n1 - n2 , since n1 =1源自文库4692, Δ =0.36%, we can (n1 + n2 ) / 2
1.4639 ,
easily derive that n2 =
2- Δ 2 - 0.0036 n1 = ? 1.4692 2+ Δ 2 + 0.0036