Calculating Gamma, L, R1,2 for Excited Ions

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SUMMARY

This discussion focuses on calculating Gamma, L, and R1,2 for excited ions in a Nd:YAG laser system, which operates as a four-level system. Gamma represents the cavity loss coefficient, L denotes the length of the rod, and R1,2 refers to the reflectivities. The challenge highlighted is determining the number of ions in the excited state without knowing the ground state population, where it is reasonable to assume that the lower level population (N1) is negligible.

PREREQUISITES
  • Understanding of cavity loss coefficients in laser systems
  • Familiarity with four-level laser systems, specifically Nd:YAG
  • Knowledge of reflectivity calculations in optics
  • Basic principles of ion population dynamics in laser physics
NEXT STEPS
  • Research methods for calculating ion populations in laser systems
  • Explore the principles of cavity loss in Nd:YAG lasers
  • Study reflectivity measurements and their impact on laser performance
  • Learn about population inversion in four-level laser systems
USEFUL FOR

Physicists, optical engineers, and anyone involved in laser technology and ion dynamics in excited states will benefit from this discussion.

Jozefina Gramatikova
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Homework Statement
A Nd:YAG laser with a crystal Nd:Y3Al5O15 rod. Determine the number of Nd ions in the excited state at threshold in this laser.
Relevant Equations
$\gamma+\frac{1}{2L} ln(\frac{1}{R_{1}R_{2})=(N_{1}-N_{2})\sigma} $
1612705673963.png

For part b)
1612705596435.png

Gamma is the cavity loss coefficient, L is the length of the rod, R1,2 are the reflectivities. I am not sure how to find the number of ions in the excited state since I don't know the number of ions in the ground state.
 
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The Nd:YAG laser is a four-level system. Thus, it is sensible to assume the lower level population ##N_1## is negligible.
 
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