1
Lecture 2
2.0 Optical Fibers
Step-index fiber .The basic structure
tr
"l
-
l"'
I
F
tI
;l
I
I
L-
_@
\
cladding
re#ractive index
An opticalfiber is a thin, transparent, flexible
consists of a core surrounded by cladding'
strand and
Thecoreandcladdingaremadeofthesamematerial;a
of glass known as silica' The only differ in their
type
refractive indexes.
a step in terms of
ln step indexes, the structure looks like
their refractive index.
can be achieved
The differences in the refractive indexes
resulting into
by doping the silica with different dopants'
cladding'
strict optical boundary between the core and
a
I
over the cladding to
The third layer is a coating applied
of different
protect the entire structure (can be made
materials, e.g. PolYmers)
total internal reflection
The most important concept is the
atthecore-claddinginterface/boundary.Thecore,s
refractiveindexnrbegreaterthancladding,sindexnz:
n1 >n2
t!
1
(core)
critical ProPagation ansle'
-L
a
Criticalincidentangle,0l.
a
Critical ProPagation angle,
a
Thecriticalincidentangle,0l.istheanglethebeam
cr' )
rrormportantparameters
to the optical boundary
makes with the line perpendicular
between the core and cladding'
a'is the angle the beam
The critical propagation angle'
fiber (critical angle)'
makes the centerline of the optical
.
.I
i
Figure 2.2
triangle A-B-C:
From the figure, the right angle
o.=
90o
- 0r.
to have total internal
E&. nr=1.48 , (12= L.46
reflection (light traPPed)
nlSih
6r =
n2sih Sz , critical angle
'
0z =90o
sin 01. = fiz I nt
Therefore 0t' =
sin-'
#J = sin-1(s'9s65) =80'57o
t
This implies that 0 must be more
than 80.57o for the light to
be
trapped in the core through total internal reflection'
Whv is crrimPortant?
Let us say a beam has an angle
cr
= l'0o
) ct. (a>4.)
reflection has
then 01< e1. )The condition for total internal
the angle a less than
been violated ; it is important to maintain
a, (q<ar)
the
Note : The critical propagation angle clc represents
3 necessary
requirement to achieve total internal reflectioh '
condition to propagate light into fiber'
Find the critical
E-& core, nr =1.48 and cladding, nz=!.46.
propagation angle.
a)
From sin 01. = nzl h1 ' since cl'c = 90o - 0" '
:.
Hence,
cos
gin Sr.
q.c
cOS
= nz/ nt
Or sin ct. = 1Hence q.
=
= sin-l
" -,1
= Sln
= 9.43o
cssZ
oc*
,-Fl
1-[e,J
CI'c
((core)' nz=!.402 (cladding)
nr=1'495
fiber,
plastic
b) For
([c
=
.-1
sln
,-Fl
(2.2\
AccePtance Anele
oHowtolaunchthelightsothatsatisfiestheangle0'6
oLED
I
LD
rt
r
cladding
the beam at an angle
o At the gap fiber interface'
0'
is the
incidentbeamthatwillberefractedintothecorec...
0.= nrsin o(.
From snell,s Law, n.sin
...... (2.3)
to be air)
N. : air (gaP is assumed
sin 0.= nlsin
o(.
(2'3a)
oTohavelightinsidethefiber,Wehavetodirectitfromthe
of 0' or less'
outside of the fiber at an angle
2 0'
oShould be confined to within the core
Where 2O^= accePtance angle
B
for the fiber when
a) Find the acceptance angle
nr=1.48 and nz= L'46
From Snell's
For air ,
ha
Law'
ntsin 0'= nrsin oc'
= 1'00
i. oc = 9'43o
Hencesin0.=!'48,sin9'43o=o'2425
oTheacceptanceangleisnormallymeasuredasNA.Allthe
terms of NA'
sbove can be written in
oThenumericalaperature'NAisgivenas:
NA = sin
0.
....(2.4)
o'=
But sin 0. = hr sins. and sin
;, NA = fl1sin o.=
h1
r-
F [#
[ru]
L?t1J
refrsctive index of the core
cladding
h2: r€froctive index of the
h1 :
r t
I,
t
E.e. a) NA of fiber with hr=1'48, nz =L'46
NA
0.2425
b)For Plastic fiber,NA =
@
= 0.5192
Note:Wedependononlytwoparameters'fl1ahdh2'
Flow diagram
Or.
) ct.) e. )
NA
technology makes of the numerical
Fiber optic communication
ability of an optical fiber
the
as
described
is
which
aperture, NA,
ability to preserved'
the
then
and
source
a
from
to gather light
Note:NAcanalsoberelatedwiththedifferencesofthe
Ilr- hz (core-cladding)'
refractive indexes, An, where An =
&n =
hr-
hz
..... (2'6)
&ru is alwaYs Positive
II1-ILa
L=-
?t
A is the reflective
index
.,....(2.71
',
n
Note
'
is the average refractive index =
?tr+TtZ
T
: ln reality nl is very close to n2
i.NA=
=
ff{e**}
To change NA we need to vary n and &n
to make
to 0.3
o
SteP
How to measure NA?
t
:
=B
lightsource
Step 2 :
Iight source
p.
HA= ' L'TL
P-
=H,,
NA from 0'1