Laser rate equation modeling

[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!

 

[jvicens]

Hello,

I am also a scientist working in the field of fiber lasers and have experience with rate equation modeling using Mathematica. I would be happy to help you with your problems.

Firstly, it is important to check your equations and make sure you are using the correct units for all variables. Dimensional analysis is a good approach to ensure consistency in your equations.

Regarding the expression for local pump absorption rate, the extra term of c (speed of light) is most likely included to account for the units of the absorption cross section (cm^2). This is a common practice in rate equation modeling and helps to ensure that the dimensions on both sides of the equation are consistent.

The expression you found, c_p_a=\frac{\lambda_p_A \Gamma_p_A \sigma_a_s_B}{h c A}, is a simplified form of the full expression for pump absorption rate. This simplified form is often used in rate equation modeling as it takes into account the most important factors and is easier to work with.

I would suggest referring to other sources and literature on fiber lasers to gain a better understanding of the equations and their derivations. It is also helpful to consult with other scientists in the field and discuss your findings and equations with them.

I hope this helps to shed some light on your problems. Best of luck with your modeling.