Review for Final
1
2
LASER PHYSICS I PH 481/581-VT (MIROV) Exam 3 (11/02/13)
STUDENT NAME: ________________________ STUDENT id #: ___________________________ ------------------------------------------------ -------------------------------
Graduate -ALL QUESTIONS ARE WORTH 50 POINTS. Undergraduate- 75 ------------------------------------------------------------------------------------------------------------------------------------------NOTE: Clearly write out solutions and answers (circle the answers) by section for each part (a., b., c., etc.)
1. A Nd YAG rod 5 mm in diameter, 6 cm long, with 100% and 90% reflectivity mirrors depositedon its facets is pumped by a pulsed flashlamp with a pulse duration much shorter than thelifetime of Nd ions. The average wavelength of excitation is 810 nm and all the pump radiationis completely absorbed by a rod. Nd YAG cross section of emission of is 9x10-23 m2 and branching ratio is equal to 1. Assume the distributed loss in the cavity is 0.01 cm-1.
a) Calculate threshold population inversion. b) Calculate the absorbed pumped energy corresponding to threshold. c) Calculate the electrical pump energy of a lamp at threshold, assuming that the rod is
uniformly pumped with an overall pump efficiency=efg=1%.
Opened textbook
Graduate fellows WORK ONLY 3 questions Undergraduate – 2 questions
1 11 2
22 3
3 3
1 11) ln 0.01 ln 1 0.9 0.019 1.96
2) 2.1 10
3) 5.2 10 /( )
4)
th
thth
th pth
Threshold gain R R cm ml
Population inversion N m
N hvThe absorbed pump energy density U J m
vThe absorbed pump energy
6.15) 6.1 / 0.01 0.61
thU V mJThe electrical pump energy mJ J
3
2. Consider the rigid rotation of biatomic molecule, made of two atoms with masses M1 and M2 at intermolecular distance Ro. The moment of inertia I about an axis passing through the center of mass and
perpendicular to the internuclear axis can be obtained as 2 21 2
1 2o r o
M MI R M RM M
. Recalling the
quantization rule of angular momentum, 2 2 ( 1)L J J and the facts that rotational kinetic energy of a rigid body rotating around a given axis can be written as E=L2/2I and rotational energies of the biatomic molecule can be expressed as EJ
rot=J(J+1)Bhc, express the rotational constant B of the molecule as a function of the reduced mass and intermolecular distance.
2
2
2 2
11
2
2 8 4 4 r o
J JE J J Bhc
IhB
I hc Ic Ic cM R
4
3. A continuous wave Nd:YAG (1064 nm) laser is longitudinally pumped at 808 nm. The laser mode has a spot size of 1 mm and the length of the cavity is 10 cm; the stimulated emission cross-section is e= 2.8x10-19 cm2 and the upper level lifetime is =230 s. Assume that an output coupler with a transmission T=10% is used, passive cavity losses are 3% per pass, branching ratio p=1, and a pump utilization efficiency a=75 %. Calculate the threshold pump power, slope efficiency, as well as the pump power required to obtain an output power Pout=20W from this laser.
11 2
16 3
v 1 3
1 0.03 11) ln ln 1 0.90 0.008310 10
2) 2.96 10
3) P 4.23 10 /( )
4)
th
thth
th pth
qe a
Threshold gain R R cml
Population inversion N cm
N hvThe absorbed threshold pump power per unit volume W cm
v
2
2 0.03
834
42.3 0.1 / 4 10 3.3
(1 0.9) 205) 1 0.75 0.759 3.3 ; 3.3 57 ; =37.3%; Alternatively:[1 ( 0.9)] 0.373
3 106.6 10 16)
vth th
out p a qe c p th p p slope
s
The absorbed pump power P P V W
P P P P P We
hvI
93 2 3 2
19 6
2 0.03
2 0.
064 10 2.9 10 / ; 2.9 10 0.1 / 4 22.82.8 10 230 10
1 22.87) ln (1 ) [1 ( 0.9)] 6.18081 0.751064
(1 0.9)8) 1 0.75 0.759[1 (
s s
s sth
p qe a p qe a
out p a qe c p th
W cm P I A W
P PP S e WS
P P Pe
03
206.1 ; 6.1 600.9)] 0.373p pP P W
5
4.
0
0
6
1.946 um
Laser Physics I PH 481/581-3A (Mirov)Exam II (10/24/11)
=12 m
Two important methodological problems related to diode pumped solid state lasers
Assume ring cavity & clockwise traveling wave
R=1
R=1R=1
Exper. 1: R1<1; Exper. 2: R2<1;
1. Internal lossestimation