The Optical Communications Reference

to 1=r

3

co

, whereas fo r TM

01

modes, the loss is pro-

portional to 1/r

co

, where r

co

is the core radius of the fiber

[22]. Besides the refractive index contrast, modal radi-

ation loss of the Bragg fiber also depends on the number

of cladding layers, N, and scales as D

N

, where D is

a constant whose value depends on the mode being

considered [22].

3.4.2.3.2 Dispersion

Because of the multitude of index profile parameters

involved, Bragg fibers offer fiber designers wide latitude

in the choice of parameters to tailor their dispersion

characteristics for diverse functionality. Judicious choice

of the core radius, cladding layer thickness, and refractive

index contrast in the cladding layers can yie ld dispersion

characteristics that are virtually unique to Bragg fibers

and almost unachievable in conventional single-mode

fibers. For example, single-mode light propagation at

1.06 mm with zero dispersion at a wavelength z 1 mm

through a silica core Bragg fiber was experimentally

demonstrated in 2000 [9]. Subsequently, various designs

have been proposed to achieve multiple zero dispersion

[24] and high negative dispersion for dispersion com-

pensation purposes [24, 25] and single polarization

single-mode propagation [26].

3.4.3 Dispersion compensating

Bragg fiber

Dispersion compensators are an integral part of any long-

haul fiber optic telecommunications link. Conventional

high-silica single-mode fibers exhibit positive temporal

dispersion beyond a wavelength of 1310 nm. Conse-

quently, a signal carrying the LP

01

mode acquires positive

dispersion as it propagates through a conventional single-

mode transmission fiber, which unless canceled through

insertion of a component to combat it would limit signal

transmission capacity of the fiber. Thi s is achieved by

inserting a dispersion compensating module, which in

most cases is a dispersion compensating fiber (DCF; see

Chapter 1). A DCF is normally designed to exhibit a large

negative dispersion coefficient (D) across the signal

wavelength band such that a relatively short length (l

C

)of

the DCF could cancel the dispersion that the signal ac-

quires while propagating through much longer lengths of

the transmission fiber (l

Tx

). Equation (3.4.17) determines

the length of the DCF required for compensating the

dispersion accumulated in a transmission fiber.

D

C

l

C

þ D

Tx

l

Tx

¼ 0; (3.4.17)

where D

C

and D

Tx

are the dispersion coefficients of the

DCF and the transmission fiber, respectively. Besides

high negative dispersion, an efficient DCF must also

exhibit low loss in the operating wavelength range. The

overall efficiency of a DCF is measured in terms of an

integral parameter known as figure of merit (FOM),

which is defined as the ratio of dispersion to loss of the

DCF:

FOM ¼ D=

a

; (3.4.18)

where the loss is measured in dB/km, so that FOM is

expressed in units of ps/nm$dB. The larger the value of

FOM, the more efficient is the DCF. One can achieve

large negative dispersion in conventional silica fibers

through suitable tailoring of its refractive index profile.

The largest dispersion coefficient of 1800 ps/nm km

demonstrated to date was based on a dual-core DCF

design [27, 28]. However, the material loss of silica limits

the FOM that can be achieved, and typically FOM ranges

from w300 to 400 ps/nm$dB in commercially available

high FOM DCFs. Moreover, typical refractive index

profiles required to generate a large waveguide (negative)

dispersion to substantially offset the positive material

dispersion (within the gain spectrum of an erbium-doped

fiber amplifier) are necessarily characterized with a rela-

tively small mode effective area (A

eff

) z15–20 mm

2

,

which makes these DCFs sensitive to detrimental non-

linear effects unless the launched signal power into the

DCF is restricted.

Bragg fibers have evolved as an attractive alternative to

conventional DCFs, and various designs have been pro-

posed for realizing high negative dispersion fibers with

a relatively large A

eff

. One of the earliest designs reported

an estimated D up to approximately 25,000 ps/nm$km

through the hybrid HE

11

mode of a Bragg fiber [25].

However, the hybrid nature and higher loss of HE

11

mode (as compared with TE

01

mode) and small core

radius were major issues that limited the practical use of

this otherwise attractive design. Subsequently, it was

reported that high negative D could be achieved for the

TE

01

mode as well by intentionally incorporating a defect

layer within the periodic cladding layers [24]. The fiber is

so designed that the fundamental (TE

01

) mode of the

defect-free Bragg fiber and the defect mode supported

by the defect layer are in weak resonance, analogous to

phase matching of the sup ermodes in a fiber directional

coupler at a particular wavelength. Near the resonance

wavelength, the fiber exhibits very large negati ve dis-

persion. The thickness and localization of the defect layer

were crucial in determining precise dispersion charac-

teristics of such Bragg fibers. These parameters can be

altered suitably to match the dispersion and dispersion-

slope for achieving broadband dispersion compensation

characteristics. A fundamental design rule for such Bragg

fiber–based DCFs with an intentional defect layer(s) is

that its modal field must penetrate sufficiently into the

160

SECTION THREE Optical Fibers