Nonlinear Fiber Optics - 4 ed. Agrawal

442 Chapter 11. Highly Nonlinear Fibers
Effective Mode Area (normalized)
d/Λ = 0.3
A eff /Λ2
πw2/Λ2
Wavelength, λ/Λ
Figure 11.12: Normalized A eff as a function of λ/Λ for several values of the ratio d/Λ. The
dashed curves show, for comparison, the ratio πw 2 /Λ 2 . (After Ref. [83]; c○2003 OSA.)
hole rings. The dashed curves show the ratio πw 2 /Λ 2 , where w is the RMS value of
the mode radius. Although A eff nearly equals πw 2 when d/Λ is close to 1, this relation
does not hold for d < Λ/2. The important point to note is that A eff ∼ Λ 2 over a wide
range of fiber parameters. It is thus possible to realize A eff ∼ 1 μm 2 with a proper
design. The nonlinear parameter for such fibers exceeds 40 W −1 /km.
The number of modes supported by a PCF also depends on the two ratios d/Λ and
λ/Λ [81]. The concept of an effective cladding index, n eci , is quite useful in this context
as it represents the extent to which the air holes reduce the refractive index of silica in
the cladding region. Figure 11.13(a) shows how n eci depends on the ratios d/Λ and
λ/Λ. As one would expect, larger and closely spaced air holes reduce n eci , resulting in
a tighter mode confinement. One can even introduce an effective V parameter using
V eff =(2π/λ)a e (n 2 1 − n 2 eci )1/2 , (11.4.1)
where the effective core radius of the PCF is defined as a e = Λ/ √ 3 [84]. With this
choice of a e , the single-mode condition V eff = 2.405 coincides with that of standard
fibers. The solid curve in Figure 11.13(a) shows this condition in the parameter space
of the ratios d/Λ and λ/Λ. As seen there, a PCF may support multiple modes for
relatively large-size air holes. However, the PCF supports only the fundamental mode
at all wavelengths if d/Λ < 0.45; such a fiber is referred to as the endlessly single-mode
fiber [66]. For larger values of d/Λ, the PCF supports higher-order modes if λ/Λ is
less than a critical value.
The dispersive properties of PCFs are also very sensitive to the same two parameters,
namely the air-hole diameter d and the hole-to-hole spacing Λ. Figure 11.14
shows the wavelength dependence of the dispersion parameter D as a function of the ratio
d/Λ for Λ = 1 and 2 μm [84]. Notice how much GVD changes even with relatively
small variations in d and Λ. This feature indicates that microstructured fibers allow
much more tailoring of dispersion compared with that possible with tapered fibers. The