b) Imagine you are provided with a sample of a new solid-state laser material. T
ID: 3307800 • Letter: B
Question
b) Imagine you are provided with a sample of a new solid-state laser material. The material is prepared for use in a standard rod geometry. For this sample, you measure the time taken for the fluorescence to decay to 1/e of its initial level to be 16 ns. You then place the material in a laser resonator with a total round trip loss of 2%. You end pump this set-up with a diode laser operating at 450 nm. The pump radius (uniform along the length of the sample) is 50 m. You observe that threshold occurs at 0.14 of absorbed pump power Starting from the standard four-level rate equations, given below, estimate the stimulated emission cross-section of this new material. You can assume uniform pumping within the pump radius and along the length of the sample All working should be shown and all symbols should be defined. (Planck's constant, h, is 6.63x104 Js and the speed of light in vacuo, c, is 3x108 ms1) dN ?)21-F (Equation 2)Explanation / Answer
In this sloution the stimulated emission cross section of the material will be denoted as a:
Assuming that the pumping is within the pump radius and along the length of the sample. We have to find the stimulated emission cross section of the material which is sigma, a.
From the first equation,
dN/dt = Rp - N/u - aNF , so N is population in the particular initial level, taking total population in a levelas 1 since the decay will exponentially reduce the population by 1/e, Rp is the pump radius, u is the time in which the initial level is decayed to 1/e which is 16 ns, a is the stimulated emission cross section, F is the loss(%). Therefore, dN/dt represents the decay of the population in the initial level which is 1/e, then,
1/e = 50 x 10-6 - 1/16 x 10-9 s + a 2% ( taking loss as negative)
0.3679 = 5 x 10-5 - 0.0625 x 109 + a x 2 x 10-2
3679 x10-4 = 0.5 x 10-4 - 0.0625 x 109 + a2 x 10-2
(3679 - 0.5)x 10-4 = - 625 x 105 + a2 x 10-2
3678.5 x 10-4 = - 625 x 105 + a2 x 10-2
Multiplying left hand side by 109 , we get
3678.5 x 10-4 x 109 = -625 x 105 + a2 x 10-2
3678.5 x 105 + 625 x 105 = a2 x 10-2
4303.5 x 105 = a2 x 10-2
4303.5 x 107 = a2
a = 4303.5 x 107/2
a = 2151.75 x 107
a = 2.15175 x 103 units.
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