Nonlinear Fiber Optics - 4 ed. Agrawal

11.4. Microstructured Fibers 441
hexagonal pattern around a solid silica rod [66]. The preform is then drawn into a fiber
form using a standard fiber-drawing apparatus. A polymer coating is added on the outside
to protect the resulting fiber. When viewed under a scanning electron microscope,
such a fiber shows a two-dimensional pattern of air holes around the central region acting
as a core. PCFs with a non-silica core can be made with the same technique. The
air channel is created by removing the central silica rod surrounding the capillary tubes
before the preform is drawn into a fiber. This channel can later be filled with a gas or
liquid that acts as the nonlinear medium. In contrast with the tapered fibers of Section
11.3, microstructured fibers can be made relatively long (up to >1 km), while maintaining
uniform properties. They are as easy to handle as conventional fibers because
of a polymer coating added on top of the cladding. They can also be spliced to other
kinds of fibers although splice losses can be as much as a few decibels.
Another technique used for fabricating microstructured fibers is known as the extrusion
technique. In this approach, the preform is produced by extruding material
selectively from a solid glass rod of 1 to 2 cm diameter. More specifically, the molten
glass rod is forced through a die containing the required pattern of holes. This technique
allows one to draw fibers directly from any bulk material, whether crystalline or
amorphous, and it is often used in practice with polymers or compound glasses. The
structured preform with the desired pattern of holes is reduced in scale using a fiberdrawing
tower in two steps. First, the outside diameter is reduced by a factor of 10 or
so. The resulting “cane” is inserted into a glass tube whose size is then further reduced
by a factor of more than 100.
A shortcoming of all microstructured fibers is that they exhibit much higher losses
than those of conventional fibers [75]. Typically, losses exceed 1000 dB/km when the
core diameter is reduced to enhance the nonlinear parameter γ. The origin of such
losses is related to the nature of mode confinement in such fibers. More specifically,
both the core and the cladding are made of silica, and the mode confinement to the
core is produced by air holes that are present in the cladding. Both the number and the
size of air holes affect how the optical mode is guided inside such a waveguide. With
a proper design, losses can be reduced to below 1 dB/km, if core diameter is made
relatively large (>5 μm), but only at the expense of a reduced value of the nonlinear
parameter [76]. In essence, a trade-off must be made between confinement losses and
γ values. High values of γ require a narrow core and thus suffer from larger losses.
It is not easy to analyze the modal and dispersive properties of microstructured
fibers or PCFs because the refractive index of the cladding is far from being homogeneous
in such fibers. A numerical approach based on plane-wave expansion, multipole
method, expansion using localized functions, or finite-element method is often used to
solve Maxwell’s equations with a realistic device geometry [77]–[84]. The objective
in all cases is to find the propagation constant β(ω) and the effective mode area for
various modes supported by such a fiber.
In the case of a PCF with periodic arrays of holes, such as the structure shown in
Figure 11.11(b), it turns out that the effective mode area A eff is nearly independent of
the number of hole rings, even though confinement losses α c depend strongly on this
number [83]. These two parameters also depend on the ratios d/Λ and λ/Λ, where
d is the air-hole diameter, Λ is the hole-to-hole spacing, and λ is the wavelength of
light. Figure 11.12 shows A eff /Λ 2 as a function of these two ratios for a fiber with 10