Ratio of atoms in different laser levels

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SUMMARY

The discussion focuses on calculating the maximum ratio of atoms in laser levels N1 and N3 under high pump intensity conditions. The equation derived is N3 = (Ip/Is) / ((Ip/Is) + 1) N1, where Ip represents pump intensity and Is denotes saturation intensity. Participants clarify that for large intensities, the ratio Ip/Is can be simplified, leading to the conclusion that N3 approaches N1 as the intensity increases. However, the presence of the +1 in the denominator prevents N3 from equaling N1 exactly, indicating a nuanced relationship between the two levels.

PREREQUISITES
  • Understanding of laser physics and atomic energy levels
  • Familiarity with the concepts of pump intensity (Ip) and saturation intensity (Is)
  • Basic algebraic manipulation skills
  • Knowledge of ratios and limits in mathematical analysis
NEXT STEPS
  • Study the principles of laser operation and atomic population inversion
  • Learn about the mathematical modeling of laser dynamics
  • Explore the implications of saturation intensity on laser performance
  • Investigate the effects of varying pump intensity on laser output
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Students and professionals in physics, particularly those studying laser technology and atomic interactions, as well as educators looking for insights into teaching laser dynamics.

Jon.G
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Homework Statement


For large intensities, what is the maximum ratio of atoms in N1 compared with N3?
I suppose this is just a bit of maths I'm struggling with, seems simple I just can't get it for whatever reason D:

Working through previous question, I got to:
N3= (Ip/Is) / ((Ip/Is) +1 ) N1
(Ip is the 'pump' intensity, Is is the saturation intensity)

Homework Equations

The Attempt at a Solution


My first thought was with the large intensities, they would be >> 1, so I could just ignore that and get N3 = N1. But then because it's the same fraction in the numerator and the denominator, and the +1 comes after the Ip/Is, I thought this to be wrong.
My only other thought is that if the fraction reaches the point where it becomes 1, then N3 = 0.5 N1.
But I'm not sure where my reasoning of this would come from. I don't think it would be ∞/∞ as, if I am correct, that is not defined, not 1.Any hints?
Thank in advance :)
 
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Jon.G said:
with the large intensities, they would be >> 1, so I could just ignore that
You could ignore the 1 if the ratio Ip/Is is large, but you don't seem to be told that.
 

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