2.3. DISPERSION IN SINGLE-MODE FIBERS 37
Figure 2.7: (a) Normalized spot sizew/aas a function of theVparameter obtained by fitting the
fundamental fiber mode to a Gaussian distribution; (b) quality of fit forV= 2 .4. (After Ref. [35];
©c1978 OSA; reprinted with permission.)
of the actual field distribution with the fitted Gaussian is also shown forV= 2 .4. The
quality of fit is generally quite good for values ofVin the neighborhood of 2. The spot
sizewcan be determined from Fig. 2.7. It can also be determined from an analytic
approximation accurate to within 1% for 1. 2 <V< 2 .4 and given by [35]
w/a≈ 0. 65 + 1. 619 V−^3 /^2 + 2. 879 V−^6. (2.2.45)The effective core area, defined asAeff=πw^2 , is an important parameter for optical
fibers as it determines how tightly light is confined to the core. It will be seen later that
the nonlinear effects are stronger in fibers with smaller values ofAeff.
The fraction of the power contained in the core can be obtained by using Eq.
(2.2.44) and is given by theconfinement factor
Γ=
Pcore
Ptotal=
∫a
0 |Ex|(^2) ρdρ
∫∞
0 |Ex|
(^2) ρdρ=^1 −exp
(
−
2 a^2
w^2)
. (2.2.46)
Equations (2.2.45) and (2.2.46) determine the fraction of the mode power contained
inside the core for a given value ofV. Although nearly 75% of the mode power resides
in the core forV=2, this percentage drops down to 20% forV=1. For this reason most
telecommunication single-mode fibers are designed to operate in the range 2<V< 2 .4.
2.3 Dispersion in Single-Mode Fibers
It was seen in Section 2.1 that intermodal dispersion in multimode fibers leads to con-
siderable broadening of short optical pulses (∼10 ns/km). In the geometrical-optics