Page 288 - Fiber Optic Communications Fund

Optical Amplifiers 269

It is useful to calculate the ratio of the peak gain to the minimum gain. From Eq. (6.124), we find that the
2
gain is minimum when sin = 1, and it is given by
0
(1 − R )(1 − R )G (f)
2
s
1
G = , (6.134)
min 2
(1 + RG )
s
and G max = G peak . Using Eqs. (6.127) and (6.134), we find the gain ripple as
G max (1 + RG ) 2
s
ΔG = = . (6.135)
G min (1 − RG ) 2
s
Or in decibels,
ΔG(dB)= G (dB)− G (dB). (6.136)
max min
Fig. 6.12 shows the gain as a function of frequency of the input optical field and the gain ripple ΔG is the sepa-
ration between the points corresponding to the maximum and minimum gains. For example, when RG = 0.9,
s
ΔG is 25.5 dB. The fluctuations in gain as a function of frequency are undesirable for wide-band amplifiers.
To keep the gain ripple quite small, RG ≪ 1, which can be achieved by reducing the reflectivities of the end
s
facets. To have ΔG < 3dB, RG ≤ 0.17, which can be achieved by reducing the facet reflectivities.
s
From Eq. (6.135), we find that the gain ripple ΔG of an ideal TWA (R = 0) is 0 dB and it has a large
bandwidth determined solely from the characteristics of the gain medium. However, in practice, even with
the best antireflection (AR) coatings, there is some residual reflectivity. Therefore, some authors [5, 6] use
the term nearly traveling-wave amplifier (NTWA) to denote an amplifier with RG ≤ 0.17. For a NTWA, the
s
gain ripple ΔG ≤ 3 dB. A NTWA has been fabricated with R = 4 × 10 −4 [7] and it has a 3-dB bandwidth
25
RG s = 0.9

20

15

G (dB) 10 RG s = 0.17 ∆G = 25.5 dB

5
∆G = 3 dB

0

‒5
1.935 1.935 1.935 1.935 1.935 1.935 1.935 1.935 1.935
Frequency (THz) × 10 4

Figure 6.12 The gain ripple ΔG increases as RG approaches unity.
s