**Equation for Light Recapture by Optical Fiber**The scattering parameter \( S \) for light recapture by an optical fiber is given by:\[ S \approx \frac{\pi (\text{NA})^2}{4 \pi n^2} = \frac{1}{4} \left( \frac{\text{NA}}{n} \right)^2 \]where:- **NA**: Fiber numerical aperture- **n**: Core refractive index- **NA/n**: Represents the half-angle of the cone of captured rays**Problem:**Given:- \( \text{NA} = 0.20 \)- \( n = 1.50 \)**Question:**What fraction of the scattered light is recaptured by the fiber in the reverse direction? **Topic: Rayleigh Scattering and Multimode Fibers****Problem Statement:**14.10 Assuming that Rayleigh scattering is approximately isotropic (uniform in all directions), demonstrate that the fraction \( S \) of scattered light trapped in a multimode fiber in the backward direction is given by:*Explanation:*This problem examines the behavior of Rayleigh scattering in multimode fibers, which are types of optical fibers that can propagate multiple modes or light paths. The assumption here is that Rayleigh scattering is isotropic, meaning the scattered light is uniformly distributed in all directions. The task is to prove how much of this scattered light, represented as fraction \( S \), is captured by the fiber when moving in the backward direction.

Given, that Raylight scattering is generally isotropic and equal in all directions. Let the letter R represent the radius of a sphere and the letter A represent the radius of the core. We know, The sphere's surface area is given by,As=4πR2The core's cross sectional area is given by,Ac=πA2In backward direction,The power collected by the fiber is given by,S=AcAsS=πA24πR2Put A=Rθso, S=πRθ24πR2S=πR2θ24πR2S=πR2θ24πR2S=θ24 ---(A)The formula for acceptance angle is given as,sin θ=NAnθ≈NAn [sin θ≈θ]Now, substitute the value of θ in equation A,S=θ24S=NAn24S=NA2n24S=(NA)24n2ORS=14(NAn)2 --(B)Hence, the above equation is the required expreesion for fraction S.Given,NA=0.20n=1.50Substitute the values in equation B,S=14NAn2 S=140.21.52 S=140.13332 S=14×0.01776S=4.44×10-3S=4.44×10-3 ×100S=0.444%Therefore,In reverse direction, 0.444% is the fraction of the light is recapyutrd by the fiber.

Engineering

Electrical Engineering

14.10 Assuming that Rayleight scattering is approxi- mately isotropic (uniform in all directions), show that the fraction S of scattered light trapped in a multimode fiber in the backward direction is given by

14.10 Assuming that Rayleight scattering is approxi- mately isotropic (uniform in all directions), show that the fraction S of scattered light trapped in a multimode fiber in the backward direction is given by

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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