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1 LASER PHYSICS I PH 481/581-VT (MIROV) Exam II (10/26/15) STUDENT NAME: Key STUDENT id #: Opened textbk, pened ntes ALL QUESTIONS ARE WORTH 37.5 POINTS FOR GRADUATES (WORK OUT ANY 4 PROBLEMS) AND 50 POINTS FOR UNDERGRADUATES (WORK OUT ANY 3 PROBLEMS) NOTE: Clearly write ut slutins and answers (circle the answers) by sectin fr each part (a., b., c., etc.) 1. A Fabry-Pert interfermeter cnsisting f tw identical mirrrs, air-spaced by a distance L, is illuminated by a mnchrmatic em wave f tunable frequency. Frm a measurement f the transmitted intensity versus the frequency f the input wave we find that the free spectral range f the interfermeter is 3x10 9 and its reslutin is 30 M. Calculate the spacing L f the interfermeter, its finesse, and the mirrr reflectivity. 1) Fr a Fabry-Pert interfermeter made f air-spaced mirrrs, the free spectral range is: c vfsr. Hence, the mirrr spacing in ur case is given by: 2L 11 1 c 310 mms L 50mm 9 1 2vFSR 2310 s 2) The finesse f the interfermeter, i.e. the rati f free spectral range t width f the 9 vfsr 310 transmissin peak, is : F v ) The finesse is a functin f mirrr reflectivity, in the case f equal mirrrs R we have F, which gives the equatin 1 R 2 2 R 2 R10, F the slutin f which is R 0.968
2
3 3. A laser (=2.09 m, =1.15x10-20 cm 2, =8 ms) measured t have an intensity f 100 W/cm 2 emerging frm ne end f the laser, which has tw identical mirrrs each with transmissin f 15%. The gain f the laser is als measured t be 0.5. a) What is the lss parameter A in the cavity? b) What is the ptimum utput mirrr transmissin? I ut I s (1 A R ) a ) L ln R 2 2 (1 R ) h k W I s cm 8 c R 0.85; I ut 100 W / c m ; L 0.5 Everything is given. Let us find A A ln ( ) (0.15 A ) ; A T pt L b ) U se 1 t find A A A L 0.5 T pt A A % A 0.107
4 4. A helium-nen laser transitin ( m) is Dppler bradened with a FWHM f 1.5 G. Assume the pumping and the saturated signal gain cefficient are fur times the threshld value, and the cavity is 100 cm lng. (a) Find the number f lngitudinal mdes that can scillate simultaneusly. (Hint: 2 ( v v ) ln 2 2 v D th ( v ) ( v ) e ). (b) Suppse all the mdes are lcked tgether: (1) What is the pulse spacing? (2) Estimate the pulse width. 6.7 ns
5 5. (a) What wuld be the minimum pulse duratin f a mde-lcked chrmium dped ZnS laser (gain bandwidth is 600 nm, central wavelength is 2350 nm)? (b) What wuld be the cherence time and cherence length f the utput beam? (c) If the separatin between mirrrs is 1.8 m, the ZnS gain element is 1 cm lng, and the index f refractin f ZnS crystal is apprximately 2.3. What wuld be the separatin between mde-lcked pulses? a) the mde-lcked pulse width (bandwidth limited) 1, where is the width f the gain prfile 8 9 c 310 (60010 ) ( ) ~30fs 1 b) c ~ 30 fs; Lc cc 9m c) Pulse spacing t 2 1 ( ) ( ) ns
6 6. Cnsider the active medium Cr:ZnSe (refractive index n=2.49, gain bandwidth (FWHM) =860 nm, central wavelength =2400 nm. (a) Cnsider first a resnatr with length L=20 cm, emplying a rd f length l=1 cm. Find the number f lngitudinal mdes falling within the FWHM gain bandwidth. (b) Cnsider then a resnatr made upn cating the end mirrrs directly nt the active material surfaces (micrchip laser). What is the maximum thickness l that allws scillatin f nly ne lngitudinal mde? 8 9 c 310 (86010 ) ( ) x10^ m 2.49x3.26x10^13
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