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Unformatted text preview: Power Launched into Fiber A stepindex multimode optical ﬁber has a core radius of a and an index of re
fraction of m. It has a cladding radius of b and an index of refraction of 77.2. A light—
emitting diode (LED) operates at a freespace wavelength A and is located on the axis of
the ﬁber at a distance d from the end face of the ﬁber. The LED emits a total power of
Pt into a Lambertian distribution centered on the ﬁber axis. Air is between the source
and the ﬁber. Derive, showing all work, the power launched, PL, into the ﬁber as a function of
the distance d. Neglect reﬂections from the end face of the ﬁber. Your answer should
consist of two separate expressions for PL: one for 0 < d < dt near the ﬁber end face
and one for dt < d < 00 far from the ﬁber end face, where dt is the distance at which the
transistion between the two expressions occurs. Derive, showing all work, the expression
for dt. Express your answers as functions of a, b, n1, 712, A, Pt, d, and constants only. Put your answers in the spaces provided below. 13L: for 0<d<dt
PL: for dt<d<oo
(it: In a particular case, an LED emits a Lambertian distribution at a wavelength of
890nm and has a total power of 1.0 milliwatt. It is on the axis of a ﬁber as described
above. The multimode ﬁber has a core of radius of 30 um and refractive index 1.52. ‘ The
ﬁber has a cladding of radius 62.5 pm and refractive index 1.50. Calculate and plot the power launched into the ﬁber as a function of distance d for 0 < d < 300 pm. Power Launched into Fiber Differential area on surface of sphere dA = (r d0)(r sin 0 dqb) Differential solid angle d9 = ﬂ _ modem 7.2 Total power emitted by LED 7r/2 27r
Pt = / / Iocosﬁsin6d0d¢
9:0 ¢=0 7r/2 27r sin26 :102 <15 0 0 = 7rIo Acceptance cone ﬁlls core of ﬁber when 0 = 6t where 31'th = E
or
2 _ 2 1/2 _ a
("1 n2) ‘ (d? + a2)1/2
solving
d = a 21131313 “2
‘ ni—na Near to ﬁber case (d < dt), power launched, PL 0: 21f
PL 2/ / Iocosesin6d0d¢
9:0 43:0 9t 27f sin20 =102 45 0 0 7r Io $17129; 7r Io — = Pt(n%—n§) Far from ﬁber case (d > dt), power launched, PL 0' 27r
PL z/ / Ioc0593in6d0d¢
0:0 ¢=o
$71209, 2"
= I
o 2 0 <1,0
= «Iosin26’
where
. , _ a
31710 — ———(a2+d2)1/2
and so
2
a
PL : Ioﬂa2+d2
2
PL "‘ Pt a For m = 1.52, 72.2 = 1.50, a = 30pm, and Pt 2 1milliwatt
dt = 118.324 um
and near ﬁber PL = 0.060400 milliwatts 0.07 0.06 0.05 9
o
b. P
o
(a Power Launched. P (milliwatts) 0.02 0.01 0 50 100 150 200 250 300
Distance From Fiber, d (microns) ...
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This note was uploaded on 04/29/2008 for the course ECE 4500 taught by Professor Gaylord during the Spring '08 term at Georgia Tech.
 Spring '08
 Gaylord

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