Page 327 - Electrical Engineering Dictionary

The simplest way to introduce perturbations usually refers to variations transverse to the
to the dynamics represented by affine con- direction of propagation, and quadratic trans-
trol actions is to add a bilinear term into the verse variations are especially important.
Gompertz equation

x max graded index fiber an optical fiber where
˙ x = gln − kux
x the core refractive index varies from a maxi-
where u is a control variable and k represents mum at its center to a minimum value at the
a perturbed population loss (or growth) pa- core-cladding interface. The profile is typ-
rameter. By applying the dimensionless scal- ically designed so that all modes of a mul-
ing, the equation could be once more trans- timode fiber propagate at approximately the
formed into the linear one with respect to same velocity. See also step index fiber.
variable y. The unperturbed Gompertz dy-
namics could also be represented by two first- graded index lens cylindrical optical el-
order differential linear equations ements with a refractive-index profile across
the cross section of the element to provide the
˙ x = q(t)x;˙q =−gq; x(0) = x 0 ; q(0) = q 0
transfer; lens in which the transmitted waves
q 0
−
with x 0 e g = x max . are focused or defocused by transverse vari-
ations of the index of refraction rather than
Gordon–Haus limit expresses the max- by transverse variations of the thickness.
imum performance of a soliton-based com-
munication system as a bitrate-length prod- graded index optical fiber an optical
uct. fiber with a refractive index in the core
that decreases monotonically from the fiber
GOS See grade of service. axis to the interface between the core and
cladding. The index usually goes from
governor a device connected to a rotat- a higher value in the center of the core
ing machine by which the speed-regulating to a lower value of refractive index at the
system is automatically adjusted to maintain core/cladding interface. See also graded
constant speed under various load conditions. index profile.

governor power flow the inherent re-
graded index optics optical elements that
sponse of prime movers or governors to a
usearefractive-indexprofileacrossthecross-
change in the operating condition of the
section of the element, typically a cylinder,
power system in an attempt to balance the
to provide particular transfer functions as for
power equation. All generators participate at
lenses; the profile is generally produced by
some level in the change, with larger gener-
ion implantation. Also called GRIN optics.
ators picking up relatively larger amounts.
graded index profile an index of refrac-
GPS See global positioning system.
tion in an optical fiber core that decreases
grade of service (GOS) a probabilistic with distance from the core axis out to the
measure of service or equipment availability core/cladding boundary. The variation of the
in a telecommunications network, expressed index of refraction with the radial distance
as the probability of a particular service (e.g., from the fiber axis can be given approxi-
a completed telephone connection) being de- mately as a power law.
nied at request time.
gradient a vector function denoted by ∇f
graded index medium in which the index or grad f , where f is a continuous, differ-
of refraction varies as a function of position; entiable scalar function. For a 2-D function

c
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