The Optical Communications Reference

Note that compared with silica glass, most non-silica

glasses have significantly steeper viscosity curves, which

leads to greater demands on the process control during

fiber drawing. Nevertheless, a high degree of re-

producibility for the HF geometry has already been

demonstrated for both lead silicate glass [47] and bis-

muth glass [48]. The core diameter can be adjusted

during fiber drawing by an appropriate choice of the

external fiber diameter. Small-core dimensions are

chosen to provide tight mode confinement and thus high

effective non-linearity. For fiber designs of the type

shown in Fig. 3.3.3, core diameters in the range of 1.7–

2.3 mm correspond to struts that are typically >5 mm long

and <250 nm thick. These long thin struts act to isolate

the core optically from the external environment and

thus ensure that confinement loss is negligible (see Sec-

tion 3.3.4.3). Excellent structural reproducibility has

been demo nstrated using this fabrication technique.

3.3.3.3 State-of-the-art

A diverse range of high-quality transverse fiber cross-

sections based on a hexagonal lattice configuration can

now be fabricated in silica glass via the capillary stacking

fabrication technique. Continued improvements in the

fabrication procedures ha ve reduced the losses of

microstructured fibers dramatically in recent years. At

the time of this writing, transmission losses of 0.28 dB/

km for silica index-guiding HFs [53] and 1.7 dB/km for

silica PBGFs [54] were reported at 1550 nm. It is worth

noting that losses are typically larger for small-core

(highly nonlinear) fibers of the type described in Section

3.3.2.2. This is principally caused by nanometer-scale

surface roughness at the air–glass boundaries near the

core [55]. However, this is not a significant limitation,

because most applications of highly nonlinear fibers re-

quire the use of short fiber lengths.

As the numbers quoted above attest, within a decade

the loss of microstructured fibers has been reduced to

values close to those achieved in conventional solid

transmission fibers. The prospect of microstructured

silica fibers with a lower transmission loss than conven-

tional fibers represents a tantal izing possibility with the

potential to revolutionize telecommunications. Index-

guiding fibers are one potential route to lower fiber

losses, given that the core can be ma de from pure silica,

which potentially offers lower loss than a doped core.

Gas core bandgap fibers are another attractiv e potential

route to lower fiber losses, given that they can have as

little as 1 % of the light propogating in the silica within

the cladding.

The fabrication of soft glass microstructured fibers is

currently less mature. The first good quality single-mode

fibers were reported in 2002 [42], and it is now possible

to produce fibers in a broad range of glasses with losses on

the order of 2 dB/m at 1550 nm. It is anticipated that

further fabrication work should reduce the losses of

these fibers to below 1 dB/m in a number of soft glass

materials. Although this loss value is high relative to silica

glass, it still allows the development of soft glass–based

nonlinear fiber devices with better figures of merit than is

possible using existing technologies (see Section 3.3.6.2).

3.3.4 Fiber design methodologies

The presence of wavelength-scale holes in micro-

structured fibers leads to challenges in the accurate

modeling of their optical characteristics. A wide variety of

fiber des ign techniques can be used, ranging from effective

step-index fiber models to approaches that incorporate

the full complexity of the transverse cross-section. Here

these methods are reviewed and assessed in terms of their

suitability for modeling optical properties of both index-

guiding HFs and PBGFs. Some of the issues associated

with designing and modeling practical fibers are high-

lighted. Note that when dispersion predictions are

required, many of the approaches described below allow

the dispersion of the material to be included ab initio

through the usual Sellmeier formula.

3.3.4.1 Effective index methods

The complex nature of the cladding structure of the

microstructured optical fiber does not generally allow

for the direct use of analytical methods from traditional

fiber theory. However, for index-guidi ng HFs, a scalar

model based on an effective index of the cladding has

proven to give a good qualitative description of their

operation [7].

The fundamental idea behind this approach is to first

evaluate the properties of the periodically repeated air

hole lattice that forms the cladding. By solving the scalar

wave equat ion in a hexagonal cell centered on a single air

hole, the propagation constant of the lowest order mode

that could propagate in the infinite cladding material is

determined. In this work , the hexago nal unit cell is ap-

proximated by a circular one to simplify the analysis. This

procedure allows the effective cladding index of the

fundamental cladding mode, sometimes called the fun-

damental sp ace-filling mode (FSM), to be determined as

a function of the wavelength (n

FSM

(l)).

The next step of the method is then to model the fiber

as a standard step-index fiber, using n

FSM

as the cladding

index. The core of this equivalent fiber is assumed to

have the refractive index of pure silica with a core radius

typically taken to be 0.62L. (This assumes that the core

is created by the omission of one cladding air hole.)

132

SECTION THREE Optical Fibers