LASER PHYSICS I PH 481/581-VT (MIROV) Exam II (10/26/15) STUDENT NAME: _____Key________________ STUDENT id #: ___________________________ -------------------------------------------------------------------------------------------------------------------------------------------- Opened textbook, opened notes 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 out solutions and answers (circle the answers) by section for each part (a., b., c., etc.) 1. A Fabry-Perot interferometer consisting of two identical mirrors, air-spaced by a distance L, is illuminated by a monochromatic em wave of tunable frequency. From a measurement of the transmitted intensity versus the frequency of the input wave we find that the free spectral range of the interferometer is 3x109 Hz and its resolution is 30 MHz. Calculate the spacing L of the interferometer, its finesse, and the mirror reflectivity. 1) For a Fabry-Perot interferometer made of air-spaced mirrors, the free spectral range is: c v . Hence, the mirror spacing in our case is given by: FSR 2L cmms31011 1 Lmm91 50 22310vsFSR 2) The finesse of the interferometer, i.e. the ratio of free spectral range to width of the v 310 9 Hz transmission peak, is : F FSR 100 vHz30 106 3) The finesse is a function of mirror reflectivity, in the case of equal mirrors R we have F , which gives the equation 1 R 2 2 RR210, F the solution of which is R 0.968 3. A laser (=2.09 m, =1.15x10-20 cm2, =8 ms) measured to have an intensity of 100 W/cm2 emerging from one end of the laser, which has two identical mirrors each with transmission of 15%. The gain of the laser is also measured to be 0.5. a) What is the loss parameter “A” in the cavity? b) What is the optimum output mirror transmission? II(1 AR ) aLR) out s ln 22(1) R o hkW 6.62 10 34 1.435 10 14 I 1.03 s 1.15 1020 8 10 3cm 2 c 310 8 1.435 1014 Hz 2.09 10 6 2 RIWcmL0.85; out100 / ; o 0.5 Everything is given. Let us find A 100 1030 10.8A 5 0.5 ln 0.85 22(1 0 .8 5 ) (0.15 A ) 50 515 0.337; A 0.107 0.15 T L bA) U se opt o 1 to find AA L 0.5 TAo A0.107 0.107 0.124 12.4% opt A 0.107 4. A helium-neon laser transition (0.6328 m) is Doppler broadened with a FWHM of 1.5 GHz. Assume the pumping and the saturated signal gain coefficient are four times the threshold value, and the cavity is 100 cm long. (a) Find the number of longitudinal modes that can oscillate simultaneously. (Hint: 2 ( v v o ) ln 2 2 ( v ) ( v ) e v D ). (b) Supposeth all othe modes are locked together: (1) What is the pulse spacing? (2) Estimate the pulse width. 6.7 ns 5. (a) What would be the minimum pulse duration of a mode-locked chromium doped ZnS laser (gain bandwidth is 600 nm, central wavelength o is 2350 nm)? (b) What would be the coherence time and coherence length of the output beam? (c) If the separation between mirrors is 1.8 m, the ZnS gain element is 1 cm long, and the index of refraction of ZnS crystal is approximately 2.3. What would be the separation between mode-locked pulses? a) the mode-locked pulse width (bandwidth limited) 1 , where is the width of the gain profile c 3 1089 (600 10 ) 3.26 1013 Hz 292(2350 10 ) ~30fs 1 b) ~ 30fs ; L c9 m ccc c) Pulse spacing 2 1 (1.8 0.01) (2.3 0.01) t 12.1ns 310 8 6. Consider the active medium Cr:ZnSe (refractive index n=2.49, gain bandwidth (FWHM) =860 nm, central wavelength =2400 nm. (a) Consider first a resonator witho length L=20 cm, employing a rod of length l=1 cm. Find the number of longitudinal modes falling within the FWHM gain bandwidth. (b) Consider then a resonator made upon coating the end mirrors directly onto the active material surfaces (microchip laser). What is the maximum thickness l that allows oscillation of only one longitudinal mode? c 3 1089 (860 10 ) 3.26 1013 Hz 292(2350 10 ) 3.26x10^13 4.7 2.49x3.26x10^13 3.7 m.