ECE 355 HOMEWORK 6 1 A 4 level laser has the energy levels shown below The 3 excited states are pumped at rates P1 P2 and P3 All de excitation of the excited states is by radiative decay with rates Aij The laser is in the cavity shown below The laser is homogeneously broadened by natural and collisional processes The collision rate for homogeneous broadening is 109s 1 The line center of the laser transition is midway between two cavity modes q q 1 There is an iris in the cavity which restricts oscillation to the TEM mode 3 E3 9 eV A32 108 s 1 P3 1 cm3 s P2 1 cm3 s 2 E2 5 5 eV g2 1 8 1 A21 10 s Laser 1 E1 1 eV g1 5 P1 1 cm3 s A10 108 s 1 0 55 cm 40 cm lgain R1 100 Transmission 98 R2 80 g q o q 1 1 Cavity Modes q a What is the threshold gain b What is the frequency spacing of the cavity modes c What is the line width of the laser transition d Construct rate equations for the steady state densities of levels 3 2 and 1 in the absence of stimulated emission You may assume the density of level 0 is constant Derive an expression for the inversion density e What is the stimulated emission cross section at the frequency of the cavity modes f Assume that P3 3P P2 2P P1 2P where P is a pump rate to be determined What is the pump rate P required to reach threshold at the frequency of one of the cavity modes What is the consequence of having offset from a cavity mode g What are the densities of the upper and lower laser levels at threshold for the frequency of the cavity modes How can an inversion be obtained with these densities h What is the saturation intensity i What is the inversion density and gain for pumping at a rate 2 times and 20 times threshold if we block the cavity j What is the laser output W cm2 when pumping at a rate of 2 times and 20 times threshold with the cavity unblocked k What is the intrinsic laser efficiency for pumping at 2 times and 20 times threshold Why do the efficiencies scale in this fashion Note We define the intrinsic laser efficiency as Laser Output Power Total Pump Power where the Laser Output Power is W W cm2 area of laser spot and the Total Pump Power is W atom cm3 s laser modal volume energy excitation l How do the efficiencies from part k compare to the quantum efficiency Recall that the quantum efficiency is laser photon energy energy of upper laser level 2 2 We have an actively Q switched naturally broadened laser with the cavity and laser levels shown below R1 100 T 99 T 85 R2 33 gain Q Switch 90 cm 115 cm 2 E2 3 eV A21 106 s 1 P2 1 E1 1 5 eV 1 10 7 s P1 0 Plot the peak laser power obtained by Q switching as a function of the initial inversion density above threshold at the time of opening the switch N t 0 Compute the peak power for enough values of N t 0 in the range 0 N t 0 20 Nth to get a representative curve Comment on the results 3 3 In this problem you will design a mode locked laser The inventory of parts you have is 50 cm GAS CELL A ceramic cylindrical cell filled with a gas which is the gain medium The gas has molecular weight M 40 AMU and the laser transition is at 500 nm The softening temperature of the ceramic is 1200 K 400 cm 200 cm OPTICAL TABLE You have 2 mirrors to make the cavity The mode locked laser must fit on a table which is 2 m x 4 m Mirror 1 Mirror 2 Design a mode locked laser using these parts which has the minimum possible pulse length What is the minimum pulse length you can obtain Provide and discuss the specifications of the laser and the layout of the optics 4