4500PP03 - Power Launched into Fiber A step-index multimode...

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Unformatted text preview: Power Launched into Fiber A step-index 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.

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4500PP03 - Power Launched into Fiber A step-index multimode...

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