( T) Blackbody Radiation. S hν. hν exp kt MODEL

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1 Let us use nsten's approach to relate gan and spontaneous emsson. ccordng to Plank:.The probablty o radaton takng place rom a black body decreased as the requency o the radaton ncreased.. The black body radaton low out n dscrete, lumpy quanttes hv lackbody Radaton MODL hν ( T) Planck postulated: Lecture 8b/ h J s hv ( hν) hν

2 Optcal gan spectrum measurements: rom T nsten's approach to gan and spontaneous emsson Lecture 8b/ Change o the photon numbers : hν M M ( ) ( ) ( ) Possble contrbuton o the varous electron transtons to emsson/absorpton o photons n energy nterval [hν,hνdhν] s accounted or n and constants. M M. qulbrum: 0 hv hν M The oscllators emttng lght n spectral range o nterest lackbody radaton: hv ( hν) hν k M M ( hν)

3 Lecture 8b/3 Comments hν ; 0 0: m qulbru M M M M M M M M M M M

4 Optcal gan spectrum measurements: rom T Gan and spontaneous emsson relaton Lecture 8b/4 No equlbrum:, 0. ( ) hν R R G hν x t x ( hν) υ υ ( - ) ( hν) G( hν) ( hv) ( g ) x ( ( - ) ) g x ( ) k I P ( hν) ( hν) G hν hν

5 Lecture 8b/5 Comments hν

6 Optcal gan spectrum measurements: rom T G ( hν) I P ( hν) ( hν) hν Lecture 8b/6 Laser pectrum nalyzer T Intensty (d) T5 o C 30 m m 6 m T Modal Optcal Gan (/cm) Modal gan I0 m T5 o C Wavelength (nm) Wavelength dvantage: measurable n wder spectral range comparng wth H-P. Complcaton: should be determned rom the ndependent erment. Needs calbraton to nd absolute value o the gan.

7 Lecture 8b/7 Determnaton o transparency energy: ndrekson technque Detecton propertes o laser dode I DC V DC bsorpton msson ( e ) ( e ) hν> hν< ( h ) ( h ), V, I, V, I NO VOLTG CHNG CRO DIOD WHN hν!

8 Lecture 8b/8 Determnaton o transparency energy: ndrekson technque Tunable modulated laser Dode laser under test I DC,V DC V C Induced C voltage (a.u.) VC Transparency wavelength at gven IDC, VDC Wavelength (nm) The transparency energy s equal to ( e ) -( h ). * Induced voltage s n phase wth or hν>( e ) -( h ) snce larger absorpton means larger voltage. or hν<( e ) -( h ) modes supported by resonator are ampled stronger and maxmum o corresponds to the voltage mnmum. The energy o voltage oscllaton phase change corresponds to transparency energy.

9 Measurements o optcal loss by Varable cavty length method Lecture 8b/9 ext α RROR α ext ext L m α α ln α αm α m L RR ssumpton: and α are cavty length ndependent m ext ln α R R L dvantage: mplcty o measurements hortcomng: or short cavtes or small nternal loss threshold s L-dependent and errors arse. lso a lot o laser materal s requred.

10 Measurements o optcal loss rom modal gan spectrum T TM Lecture 8b/0 g Modal Optcal Gan (/cm) T/TM 0 αtot λt T TM H T/TM T/TM T/TM ( hν) Γ G ( hν) α αtot T5 0 C I7 m Wavelength (nm) tot. T and TM modal gans ntersecton T comes rom C-HH transton; TM comes rom C-LH transton. Thus, spectra or T and TM gans are derent and correspondng gans and can be equal only when materal gan G0 (transparency pont).. aturaton or hν< g or photon energes below bandgap, materal gan s equal to zero. Modal (g) gan s equal to total loss wthn ths spectra regon. Usually, long wavelength tal o the modal gan spectra gves total loss value. When loss are determned, transparency energy (condton G0) can be estmated rom the gan spectrum.