4500PE01

# 4500PE01 - Emission Spectrum In the emission of light by...

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Unformatted text preview: Emission Spectrum In the emission of light by atoms, homogeneous broadening is produced by atoms having a ﬁnite lifetime of emission 7‘. The emission from the excited state corresponds to a damped oscillator. Thus the complex electric ﬁeld may be represented by E(t) = E0 emp(—t/'r) emp(+jwot) for t > 0, E(t) =0 for t< 0. The instantaneous ﬁeld is given by the real part of the complex ﬁeld. The emission spec- tral density for this type of emitter has a Lorentzian lineshape for frequencies near the optical radian frequency we. a) Calculate, showing all work, the Fourier transform of Put your ﬁnal answer in rationalized form in the space provided. b) Calculate, showing all work, the emission spectral density (the square of the magni- tude of the Fourier transform). 1300) = [Em-ca)? = Emission Spectrum E(t) 2 E0 exp(—-t/7') exp(+jw0t) for t > O, E(t) =0 for t<0. Fourier transform +00 E(jw) = E(t) exp(—jwt) dt —00 +00 Emu) = E0 €50P{[j(wo — w) — 1m t} dt emwa — w) — 1/7] t} +°° EU”) 2 E0 mwo —w> — 1/7] 0 - __ _1__ E‘jw)‘ E0j(w0—w)—1/T , _ j(w0—w)+1/7‘ Bow—.EO (wo—w)2+1/T2 Spectral density (010 — 002 + 1/72 |E(jw)|2 = E3 W 1 E’ 2=E2————— I (JWM 0 (w_w0)2+1/T2 Lorentzian lineshape ...
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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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4500PE01 - Emission Spectrum In the emission of light by...

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