<s>
Double-clad	B-Device
fiber	I-Device
(	O
DCF	O
)	O
is	O
a	O
class	O
of	O
optical	B-Architecture
fiber	I-Architecture
with	O
a	O
structure	O
consisting	O
of	O
three	O
layers	O
of	O
optical	O
material	O
instead	O
of	O
the	O
usual	O
two	O
.	O
</s>
<s>
It	O
is	O
surrounded	O
by	O
the	O
inner	O
cladding	B-Device
,	O
which	O
is	O
surrounded	O
by	O
the	O
outer	O
cladding	B-Device
.	O
</s>
<s>
There	O
are	O
two	O
different	O
kinds	O
of	O
double-clad	B-Device
fibers	I-Device
.	O
</s>
<s>
The	O
first	O
was	O
developed	O
early	O
in	O
optical	B-Architecture
fiber	I-Architecture
history	O
with	O
the	O
purpose	O
of	O
engineering	O
the	O
dispersion	O
of	O
optical	B-Architecture
fibers	I-Architecture
.	O
</s>
<s>
In	O
these	O
fibers	O
,	O
the	O
core	O
carries	O
the	O
majority	O
of	O
the	O
light	O
,	O
and	O
the	O
inner	O
and	O
outer	O
cladding	B-Device
alter	O
the	O
waveguide	O
dispersion	O
of	O
the	O
core-guided	O
signal	O
.	O
</s>
<s>
The	O
second	O
kind	O
of	O
fiber	O
was	O
developed	O
in	O
the	O
late	O
1980s	O
for	O
use	O
with	O
high	O
power	O
fiber	O
amplifiers	O
and	O
fiber	B-Device
lasers	I-Device
.	O
</s>
<s>
The	O
inner	O
cladding	B-Device
and	O
core	O
together	O
guide	O
the	O
pump	O
light	O
,	O
which	O
provides	O
the	O
energy	O
needed	O
to	O
allow	O
amplification	O
in	O
the	O
core	O
.	O
</s>
<s>
In	O
these	O
fibers	O
,	O
the	O
core	O
has	O
the	O
highest	O
refractive	O
index	O
and	O
the	O
outer	O
cladding	B-Device
has	O
the	O
lowest	O
.	O
</s>
<s>
In	O
most	O
cases	O
the	O
outer	O
cladding	B-Device
is	O
made	O
of	O
a	O
polymer	B-Language
material	O
rather	O
than	O
glass	O
.	O
</s>
<s>
In	O
double-clad	B-Device
fiber	I-Device
for	O
dispersion	O
compensation	O
,	O
the	O
inner	O
cladding	B-Device
layer	O
has	O
lower	O
refractive	O
index	O
than	O
the	O
outer	O
layer	O
.	O
</s>
<s>
This	O
type	O
of	O
fiber	O
is	O
also	O
called	O
depressed-inner-cladding	B-Device
fiber	I-Device
and	O
W-profile	B-Device
fiber	I-Device
(	O
from	O
the	O
fact	O
that	O
a	O
symmetrical	O
plot	O
of	O
its	O
refractive	O
index	O
profile	O
superficially	O
resembles	O
the	O
letter	O
W	O
)	O
.	O
</s>
<s>
This	O
type	O
of	O
double-clad	B-Device
fiber	I-Device
has	O
the	O
advantage	O
of	O
very	O
low	O
microbending	O
losses	O
.	O
</s>
<s>
Since	O
the	O
dispersion	O
of	O
such	O
double-clad	B-Device
fibers	I-Device
can	O
be	O
engineered	O
to	O
a	O
great	O
extent	O
,	O
these	O
fibers	O
can	O
be	O
used	O
for	O
the	O
compensation	O
of	O
chromatic	O
dispersion	O
in	O
optical	O
communications	O
and	O
other	O
applications	O
.	O
</s>
<s>
In	O
modern	O
double-clad	B-Device
fibers	I-Device
for	O
high	O
power	O
fiber	O
amplifiers	O
and	O
lasers	O
,	O
the	O
inner	O
cladding	B-Device
has	O
a	O
higher	O
refractive	O
index	O
than	O
the	O
outer	O
cladding	B-Device
.	O
</s>
<s>
This	O
enables	O
the	O
inner	O
cladding	B-Device
to	O
guide	O
light	O
by	O
total	O
internal	O
reflection	O
in	O
the	O
same	O
way	O
the	O
core	O
does	O
,	O
but	O
for	O
a	O
different	O
range	O
of	O
wavelengths	O
.	O
</s>
<s>
This	O
allows	O
diode	O
lasers	O
,	O
which	O
have	O
high	O
power	O
but	O
low	O
radiance	B-Application
,	O
to	O
be	O
used	O
as	O
the	O
optical	O
pump	O
source	O
.	O
</s>
<s>
The	O
pump	O
light	O
can	O
be	O
easily	O
coupled	O
into	O
the	O
large	O
inner	O
cladding	B-Device
,	O
and	O
propagates	O
through	O
the	O
inner	O
cladding	B-Device
while	O
the	O
signal	O
propagates	O
in	O
the	O
smaller	O
core	O
.	O
</s>
<s>
The	O
doped	O
core	O
gradually	O
absorbs	O
the	O
cladding	B-Device
light	O
as	O
it	O
propagates	O
,	O
driving	O
the	O
amplification	O
process	O
.	O
</s>
<s>
This	O
pumping	O
scheme	O
is	O
often	O
called	O
cladding	B-Device
pumping	O
,	O
which	O
is	O
an	O
alternative	O
to	O
the	O
conventional	O
core	O
pumping	O
,	O
in	O
which	O
the	O
pump	O
light	O
is	O
coupled	O
into	O
the	O
small	O
core	O
.	O
</s>
<s>
The	O
invention	O
of	O
cladding	B-Device
pumping	O
by	O
a	O
Polaroid	O
fiber	O
research	O
team	O
(	O
H	O
.	O
Po	O
,	O
et	O
al	O
.	O
)	O
</s>
<s>
Using	O
this	O
method	O
,	O
modern	O
fiber	B-Device
lasers	I-Device
can	O
produce	O
continuous	O
power	O
up	O
to	O
several	O
kilowatts	O
,	O
while	O
the	O
signal	O
light	O
in	O
the	O
core	O
maintains	O
near	O
diffraction-limited	O
beam	O
quality	O
.	O
</s>
<s>
The	O
shape	O
of	O
the	O
cladding	B-Device
is	O
very	O
important	O
,	O
especially	O
when	O
the	O
core	O
diameter	O
is	O
small	O
compared	O
to	O
the	O
size	O
of	O
the	O
inner	O
cladding	B-Device
.	O
</s>
<s>
Circular	O
symmetry	O
in	O
a	O
double-clad	B-Device
fiber	I-Device
seems	O
to	O
be	O
the	O
worst	O
solution	O
for	O
a	O
fiber	B-Device
laser	I-Device
;	O
in	O
this	O
case	O
,	O
many	O
modes	O
of	O
the	O
light	O
in	O
the	O
cladding	B-Device
miss	O
the	O
core	O
and	O
hence	O
cannot	O
be	O
used	O
to	O
pump	O
it	O
.	O
</s>
<s>
In	O
the	O
language	O
of	O
geometrical	O
optics	O
,	O
most	O
of	O
the	O
rays	B-Device
of	O
the	O
pump	O
light	O
do	O
not	O
pass	O
through	O
the	O
core	O
,	O
and	O
hence	O
cannot	O
pump	O
it	O
.	O
</s>
<s>
Ray	B-Algorithm
tracing	I-Algorithm
,	O
simulations	O
of	O
the	O
paraxial	O
propagation	O
and	O
mode	O
analysis	O
give	O
similar	O
results	O
.	O
</s>
<s>
the	O
mode	O
is	O
not	O
coupled	O
,	O
and	O
it	O
is	O
vain	O
to	O
excite	O
such	O
a	O
mode	O
in	O
the	O
double-clad	B-Device
fiber	I-Device
amplifier	O
.	O
</s>
<s>
so-called	O
chaotic	O
fibers	O
have	O
more	O
complicated	O
cross-sectional	O
shape	O
and	O
provide	O
more	O
uniform	O
distribution	O
of	O
intensity	O
in	O
the	O
inner	O
cladding	B-Device
,	O
allowing	O
efficient	O
use	O
of	O
the	O
pump	O
light	O
.	O
</s>
<s>
The	O
core	O
,	O
placed	O
in	O
vicinity	O
of	O
this	O
chunk	O
,	O
is	O
intercepted	O
more	O
regularly	O
by	O
all	O
the	O
rays	B-Device
compared	O
to	O
other	O
chaotic	O
fibers	O
.	O
</s>
<s>
This	O
behavior	O
of	O
rays	B-Device
has	O
an	O
analogy	O
in	O
wave	O
optics	O
.	O
</s>
<s>
The	O
property	O
of	O
DCFs	O
with	O
spiral-shaped	O
cladding	B-Device
can	O
be	O
interpreted	O
as	O
conservation	O
of	O
angular	O
momentum	O
.	O
</s>
<s>
Modes	O
(	O
as	O
well	O
as	O
rays	B-Device
)	O
touching	O
the	O
spiral-shaped	O
boundary	O
transfer	O
some	O
angular	O
momentum	O
to	O
it	O
.	O
</s>
<s>
Modes	O
can	O
show	O
strong	O
scarring	O
along	O
the	O
classical	O
trajectories	O
(	O
rays	B-Device
)	O
and	O
wide	O
voids	O
,	O
but	O
at	O
least	O
one	O
of	O
scars	O
should	O
approach	O
the	O
chunk	O
to	O
compensate	O
for	O
the	O
angular	O
momentum	O
transferred	O
by	O
the	O
spiral	O
part	O
.	O
</s>
<s>
Stochastic	O
optimization	O
of	O
the	O
cladding	B-Device
shape	O
confirms	O
that	O
an	O
almost-circular	O
spiral	O
realizes	O
the	O
best	O
coupling	O
of	O
pump	O
into	O
the	O
core	O
.	O
</s>
<s>
Tapered	B-Device
double-clad	I-Device
fiber	I-Device
(	O
T-DCF	O
)	O
is	O
a	O
fiber	O
whose	O
outer	O
and	O
inner	O
claddings	B-Device
and	O
core	O
diameters	O
vary	O
smoothly	O
with	O
length	O
.	O
</s>
<s>
The	O
efficiency	O
of	O
absorption	O
of	O
pumping	O
energy	O
in	O
the	O
fiber	O
is	O
an	O
important	O
parameter	O
of	O
a	O
double-clad	B-Device
fiber	I-Device
laser	O
.	O
</s>
<s>
The	O
filling	O
factor	O
may	O
depend	O
on	O
the	O
initial	O
distribution	O
of	O
the	O
pump	O
light	O
,	O
the	O
shape	O
of	O
the	O
cladding	B-Device
,	O
and	O
the	O
position	O
of	O
the	O
core	O
within	O
it	O
.	O
</s>
<s>
One	O
could	O
expect	O
that	O
some	O
modes	O
of	O
the	O
cladding	B-Device
(	O
or	O
some	O
rays	B-Device
)	O
are	O
better	O
coupled	O
to	O
the	O
core	O
than	O
others	O
;	O
therefore	O
,	O
the	O
"	O
true	O
"	O
dependence	O
could	O
be	O
a	O
combination	O
of	O
several	O
exponentials	O
.	O
</s>
<s>
The	O
value	O
of	O
can	O
be	O
estimated	O
by	O
numerical	B-General_Concept
analysis	I-General_Concept
with	O
propagation	O
of	O
waves	O
,	O
expansion	O
by	O
modes	O
or	O
by	O
geometrical	O
optics	O
ray	B-Algorithm
tracing	I-Algorithm
,	O
and	O
values	O
0.8	O
and	O
0.9	O
are	O
only	O
empirical	O
adjusting	O
parameters	O
,	O
which	O
provide	O
good	O
agreement	O
of	O
the	O
simple	O
estimate	O
with	O
numerical	O
simulations	O
for	O
two	O
specific	O
classes	O
of	O
double-clad	B-Device
fibers	I-Device
:	O
circular	O
offset	O
and	O
rectangular	O
.	O
</s>
<s>
Obviously	O
,	O
the	O
simple	O
estimate	O
above	O
fails	O
when	O
the	O
offset	O
parameter	O
becomes	O
small	O
compared	O
to	O
the	O
size	O
of	O
cladding	B-Device
.	O
</s>
<s>
The	O
filling	O
factor	O
approaches	O
unity	O
especially	O
quickly	O
in	O
the	O
spiral-shaped	O
cladding	B-Device
,	O
due	O
to	O
the	O
special	O
boundary	O
behavior	O
of	O
the	O
modes	O
of	O
the	O
Dirichlet	O
Laplacian	O
.	O
</s>
<s>
Designers	O
of	O
double-clad	B-Device
fiber	I-Device
look	O
for	O
a	O
reasonable	O
compromise	O
between	O
the	O
optimized	O
shape	O
(	O
for	O
the	O
efficient	O
coupling	O
of	O
pump	O
into	O
the	O
core	O
)	O
and	O
the	O
simplicity	O
of	O
the	O
manufacturing	O
of	O
the	O
preform	O
used	O
to	O
draw	O
the	O
fibers	O
.	O
</s>
<s>
The	O
power	O
scaling	O
of	O
a	O
fiber	B-Device
laser	I-Device
is	O
limited	O
by	O
unwanted	O
nonlinear	O
effects	O
such	O
as	O
stimulated	B-Algorithm
Brillouin	I-Algorithm
scattering	I-Algorithm
and	O
stimulated	B-Architecture
Raman	I-Architecture
scattering	I-Architecture
.	O
</s>
<s>
These	O
effects	O
are	O
minimized	O
when	O
the	O
fiber	B-Device
laser	I-Device
is	O
short	O
.	O
</s>
<s>
In	O
particular	O
,	O
the	O
higher	O
the	O
step	O
in	O
refractive	O
index	O
from	O
inner	O
to	O
outer	O
cladding	B-Device
,	O
the	O
better-confined	O
the	O
pump	O
is	O
.	O
</s>
<s>
The	O
estimate	O
with	O
filling	O
factor	O
gives	O
an	O
estimate	O
of	O
how	O
short	O
an	O
efficient	O
double-clad	B-Device
fiber	I-Device
laser	O
can	O
be	O
,	O
due	O
to	O
reduction	O
in	O
size	O
of	O
the	O
inner	O
cladding	B-Device
.	O
</s>
<s>
For	O
good	O
cladding	B-Device
shapes	O
the	O
filling	O
factor	O
,	O
defined	O
above	O
,	O
approaches	O
unity	O
;	O
the	O
following	O
enhancement	O
is	O
possible	O
at	O
various	O
kinds	O
of	O
tapering	O
of	O
the	O
cladding	B-Device
;	O
non-conventional	O
shapes	O
of	O
such	O
cladding	B-Device
are	O
suggested	O
.	O
</s>
<s>
Planar	O
waveguides	O
with	O
an	O
active	O
gain	O
medium	O
take	O
an	O
intermediate	O
position	O
between	O
conventional	O
solid-state	O
lasers	O
and	O
double-clad	B-Device
fiber	I-Device
lasers	O
.	O
</s>
