Propagation Constants and Group Velocities. A step-index fiber with refractive indices n = 1.444 and ng = 1.443 operates at A, = 1.55 um. Determine the core radius at which the fiber V parameter is 10. Use Fig. 10.2-3 to estimate the propagation constants of all the guided modes with I = 0. If the core radius is now changed so that V = 4, use Fig. 10.2- 6(a) to determine the phase velocity, the propagation constant, and the group velocity of the LPa mode. Ienore the effect of material dispersion.
Propagation Constants and Group Velocities. A step-index fiber with refractive indices n = 1.444 and ng = 1.443 operates at A, = 1.55 um. Determine the core radius at which the fiber V parameter is 10. Use Fig. 10.2-3 to estimate the propagation constants of all the guided modes with I = 0. If the core radius is now changed so that V = 4, use Fig. 10.2- 6(a) to determine the phase velocity, the propagation constant, and the group velocity of the LPa mode. Ienore the effect of material dispersion.
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Transcribed Image Text:Propagation Constants and Group Velocities. A step-index fiber with refractive indices
n = 1.444 and ng = 1.443 operates at A, = 1.55 um. Determine the core radius at which
the fiber V parameter is 10. Use Fig. 10.2-3 to estimate the propagation constants of all the
guided modes with l = 0. If the core radius is now changed so that V = 4, use Fig. 10.2-
6(a) to determine the phase velocity, the propagation constant, and the group velocity of the
LPni mode. Ignore the effect of material dispersion.
Light line
(a)
(b)
Light line
V
10
Figure 10.2-6 Schematic illustrations of the propagation characteristics of the fundamental LP01
mode. (a) Effective refractive index n = B/k, as a function of the V parameter. (b) Dispersion
relation (w versus Bo1).
LHS =
JX)
YK, (Y)
RHS =
KoY)
Y=/v2-x2
6.
Figure 10.2-3 Graphical construction for solving the characteristic equation (10.2-14). The left-
and right-hand sides are plotted as functions of X. The intersection points are the solutions. The
left-hand side (LHS) has multiple branches intersecting the abscissa at the roots of Jit1(X). The
right-hand side (RHS) intersects each branch once and meets the abscissa at X = V. The number of
modes therefore equals the number of roots of Jtt1(X) that are smaller than V. In this plot l = 0,
V = 10, and either the - or + signs in (10.2-14) may be used.
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