March 22, 2011 EE 424 Mid-Term II Do All Problems Time: 2:30 PM – 3:30 PM [1 hour] 1. [total 10 points] A gaseous medium contains No atoms [per cm3] whose energy levels are as shown. Level 3 and 2 are both broadened by spontaneous emissions to level 1, with a Lorentzian profile: g( ) = /{ 2 [ (0)2 + ( /2)2] } where o is the transition frequency of the corresponding transition. Levels 3 and 2 are separated by a frequency difference of 50 MHz. The linewidths of both levels are the same and is given by 31=21= = 10 MHz. A monochromatic laser of weak intensity I= 1 microWatt/cm2 is incident on the system; its frequency is on resonance with the 3 to 1 transition, i.e., = 31= 5x1014 Hz. 1A [2 points] From the data given, calculate the spontaneous lifetime of levels 2 and 3? 1B [4 points] An experiment using the weak-intensity (I= 1 microWatt/cm2] laser shows that upon traversing the medium, it experiences a gain constant = 10 cm-1, but with a 10 microWatt/cm2 intensity, the gain constant observed decreases to = 5 cm-1. From these data, calculate the saturation intensity Is of the atomic system. [Note: Give the reason for using a particular saturation gain formula, i.e. attributed to homogeneous or inhomogeneous broadening]. 1C [4 points] An external pumping agent excite the atoms from level 1 to levels 2 and 3 at a equal rate of R. (i) Write down the rate equations for all the level population densities N1, N2 and N3 in terms of the various transition rates A‘s and W’s. (ii) In the absence of the laser, calculate the steady state values for the level population number densities N1, N2 and N3 in terms of R and A’s….etc.2. [6 point] A Fabry Perot interferometer consisting of two plane parallel mirrors of reflectivity R is used to analyze the emission from such atomic medium. What is the requirement on the cavity length [longer or shorter than a certain value] such that Free Spectral Range of the Fabry Perot is larger than the frequency difference between levels 3 and 2? What is the requirement on the reflectivity R of the Fabry Perot in order that it is capable of resolving the two emission lines? [Your answer should be in the form of R> ? or R <?