# Laser rate equation modeling

1. Mar 25, 2010

### test1234

hi, I'm working on Tm3+ fiber laser rate equation modeling using Mathematica.
The rate equations I'm using for the model are largely based on the work of Jackson and King ("Theoretical Modeling of Tm doped silica fiber lasers", 1999), albeit neglecting some factors so as to simply the model.

However, I've ran into some problems...hope that someone can help shed some light. Thanks!
1) Upon performing dimension analysis on the expression for the local pump absorption rate based on the journal by Jackson and King, the dimensions on the LHS and RHS do not agree.

Referring to Xu, J. et al ("Efficient Double-Clad Thulium-Doped Fiber Laser with a Ring Cavity"), they included an extra term c (speed of light) in the expression for the pump absorption rate. I considered the dimensions of c to be M/L and performed the analysis again but to no avail.

Then I chanced upon this expression, $$c_p_a=\frac{\lambda_p_A \Gamma_p_A \sigma_a_s_B}{h c A}{}$$
where $$c_p_a$$: speed of pump wavelength (I think?)
$$\lambda_p_A$$: pump wavelength
$$\Gamma_p_A$$: confinement factor
$$\sigma_a_s_B$$: absorption cross section at laser wavelength
h: planck's constant
c: speed of light
A: area of fiber core

This yields dimensions that are agreeable with the rate equation. But I don't know how this formula came about. could someone enlighten me? Thanks!

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Last edited: Mar 25, 2010