【Chapter 5】 5.1 Solution: According to the formula, Δ =
n1 - n2 , since n1 =1.4692, Δ =0.36%, we can (n1 + n2 ) / 2
1.4639 ,
easily derive that n2 =
Байду номын сангаас
2- Δ 2 - 0.0036 n1 = ? 1.4692 2+ Δ 2 + 0.0036
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
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
【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:
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 ]
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.
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 )
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,
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
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.
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 =
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: