HW#12.. Assignment'11

HW#12.. Assignment'11 - you have already determined all the...

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EE540 (S’11) HW#12 Assignment. p.1 of 1. When the diode current i(t) to the junction in OII is always less than the threshold current i th , nearly all of the photons emitted from anywhere in the junction are emitted by spontaneous emission from a total of η (t) decaying excitons, including excitons that exist outside of the oscillator mode volume. After careful electrode construction, nearly all of these spontaneous photons will escape into all directions outside of the diode structure at a total rate of Φ (t) per second. In this form the diode is called a “light-emitting diode” or “LED”, and these emerging spontaneous photons have commercial applications. This homework is about a laser of this form, in the geometry of OII, operating as a broadband LED. You may assume that
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Unformatted text preview: you have already determined all the parameters for this laser that you did for Paoli’s laser ‘A’ in homeworks #8, #9 and #10. (1) Write the equation for d η /dt that is analogous to the Model A equation for dn/dt . (2) Write the fraction ε of incoming electrons that results in the emission of a spontaneous photon in CW LED operation. (3) Integrate the equation in (2) to find an integral that gives η (t) in terms of i(t) . Assume the diode current i(t) was until t=0 (when η had a known value η 0 ) and then varied arbitrarily ( but always well below i th ) with t after that. (4) When i(t)=i +i 1 cos( ω t) < i th , do the integral in (3) to find the resulting expression for η (t). (5) The exciton lifetime τ 2 can be made to vary in time, for example, by an impressed magnetic field. Find the simple change you can make in your answer to (3) that keeps it exact even when τ 2 is time-varying....
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