Formula sheet: Optical Fibres | Electromagnetics - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


Electromagnetic W a v es: Optical Fibres F orm ula
Sheet for GA TE
Optical Fibres Basics
• Principle : T otal in ternal reflection allo ws ligh t to propagate through the fibre core.
• Refractiv e Index : Ratio of sp eed of ligh t in v acuum to that in the medium.
n =
c
v
where c is the sp eed of ligh t in v acuum (3e8m/s ), v is the sp eed in the medium.
• Critical Angle : Angle of incidence for whic h the angle of refraction is 90
?
.
?
c
= sin
-1
(
n
2
n
1
)
where n
1
is the refractiv e index of the core, n
2
is the refractiv e index of the cladding
(n
1
>n
2
).
Numerical Ap erture and A cceptance Angle
• Numerical Ap erture (NA) : Measures the ligh t-gathering abilit y of the fibre.
NA =
v
n
2
1
-n
2
2
=n
0
sin?
a
where n
0
is the refractiv e index of the surrounding medium (usually air, n
0
˜ 1 ), ?
a
is the acceptance angle.
• A cceptance Angle : Maxim um angle at whic h ligh t can en ter the fibre and still b e
guided.
?
a
= sin
-1
(
v
n
2
1
-n
2
2
n
0
)
• A cceptance Cone : The cone of ligh t ra ys within the acceptance angle that can
propagate.
Propagation Characteristics
• Normalized F requency (V-n um b er) : Determines the n um b er of mo des in the
fibre.
V =
2pa
?
v
n
2
1
-n
2
2
where a is the core radius, ? is the w a v elength of ligh t in v acuum.
• Single-Mo de Condition : Fibre supp orts only one mo de if:
V = 2.405
1
Page 2


Electromagnetic W a v es: Optical Fibres F orm ula
Sheet for GA TE
Optical Fibres Basics
• Principle : T otal in ternal reflection allo ws ligh t to propagate through the fibre core.
• Refractiv e Index : Ratio of sp eed of ligh t in v acuum to that in the medium.
n =
c
v
where c is the sp eed of ligh t in v acuum (3e8m/s ), v is the sp eed in the medium.
• Critical Angle : Angle of incidence for whic h the angle of refraction is 90
?
.
?
c
= sin
-1
(
n
2
n
1
)
where n
1
is the refractiv e index of the core, n
2
is the refractiv e index of the cladding
(n
1
>n
2
).
Numerical Ap erture and A cceptance Angle
• Numerical Ap erture (NA) : Measures the ligh t-gathering abilit y of the fibre.
NA =
v
n
2
1
-n
2
2
=n
0
sin?
a
where n
0
is the refractiv e index of the surrounding medium (usually air, n
0
˜ 1 ), ?
a
is the acceptance angle.
• A cceptance Angle : Maxim um angle at whic h ligh t can en ter the fibre and still b e
guided.
?
a
= sin
-1
(
v
n
2
1
-n
2
2
n
0
)
• A cceptance Cone : The cone of ligh t ra ys within the acceptance angle that can
propagate.
Propagation Characteristics
• Normalized F requency (V-n um b er) : Determines the n um b er of mo des in the
fibre.
V =
2pa
?
v
n
2
1
-n
2
2
where a is the core radius, ? is the w a v elength of ligh t in v acuum.
• Single-Mo de Condition : Fibre supp orts only one mo de if:
V = 2.405
1
• Propagation Constan t : F or a mo de in the fibre.
ß =n
1
kcos?
where k =
2p
?
is the w a v e n um b er, ? is the angle of propagation.
A tten uation and Disp ersion
• A tten uation : P o w er loss p er unit length (in dBkm
-1
).
a =-
10
L
log
10
(
P
out
P
in
)
where L is the fibre length, P
in
and P
out
are input and output p o w ers.
• Material Disp ersion : Caused b y w a v elength-dep enden t refractiv e index.
D
m
=-
?
c
d
2
n
d?
2
• T otal Disp ersion : Sum of material and w a v eguide disp ersion.
Key Notes
• T ypical refractiv e indices: n
1
˜ 1.5 (core), n
2
˜ 1.45 (cladding), n
0
˜ 1 (air).
• Single-mo de fibres are used for long-distance comm unication, m ulti-mo de for short
distances.
• F or GA TE, fo cus on n umerical ap erture, V-n um b er, and atten uation calculations.
• Use consisten t units: ? in µm , a in µm , c = 3×10
8
ms
-1
.
2