solution 2.19 - mm from the surface (if we disregard for a...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Solution 2.19 a) At what distance is the amplitude down by a factor of exp(-1)? exp(-alpha*distance) = exp(-1) alpha * distance = 1 distance = 1/alpha, where alpha = (2*pi/lambda) * sqrt[sin(pi/4)^2 - n^2], lambda = 500 nm, n = n2/n1 = 1/1.5 alpha = 0.00296192 nm^-1 distance = 1/alpha = 337.6 nm b) By what factor is the intensity down at a distance of 1 mm? d = 1 mm = 10^6 nm I(d)/I(0) = [amplitude(d)/amplitude(0)]^2 = exp(-alpha*d)^2 = exp(-2*alpha*d) = exp(-5923.84) = 10^- 2572.69 = 2 * 10^-2573 Note that this is an awfully small number, actually zero for all practical purposes. Consider that the total power output of the sun is “only” about 4*10^26 Watts, and the combined power output of all the stars in all the galaxies in the observable universe is of the order of 10^49 Watts. If the entire power of the universe were incident on our prism, only 10^49 * 10-2573 = 10^-2524 Watts would be left at 1
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: mm from the surface (if we disregard for a moment that the prism would be instantly vaporized). This corresponds to one photon every 10^2506 seconds or one photon in 10^2499 years. Considering that the age of the universe is only about 10^10 years, we would still have to wait for 10^2489 universe-ages until we would see a single photon at 1 mm from the surface! Even our outrageous astronomical number crunching didnt help to get a grip on this number, since it didnt bring down the value of the exponent much at all: 10^2489 is still unimaginably large. This fast decay of the evanescent wave is the reason why a relatively thin cladding layer is enough to completely block the evanescent field from leaking energy out of optical fibers....
View Full Document

This document was uploaded on 02/06/2012.

Ask a homework question - tutors are online