# Optical Engineering - Lasers

1. Nov 21, 2013

### GreenPrint

1. The problem statement, all variables and given/known data

Consider an amplifying medium, composed of homogeneous broadening four-level atoms as show in figure 26.5, page 557 of textbook.

http://img689.imageshack.us/img689/6108/lt2f.png [Broken]

Amplification is to occur on the 2-to-1 transition. The medium is pumped by a laser of intensity $I_{p}$, which is resonant with the 3-to-0 transition. The spontaneous decay processes are indicated on the diagram. The total number of gain atoms is $N_{T} = N_{0} + N_{1} + N_{2} + N_{3}$. The various parameters are:

$k_{32} = \frac{10^{8}}{s}; k_{21} = \frac{10^{3}}{s}; k_{10} = \frac{10^{8}}{s}; k_{30} = k_{31} = k_{20} = 0$
$σ_{p} = 4x10^{-19} cm^{2}; σ = 2.5x10^{-18} cm^{2}; λ_{30} = 300 nm; λ_{21} = 600 nm; N_{τ} = 2.0x10^{26} m^{-3}$

Assuming an ideal four-level laser system determine:

a) The pump irradiance required to sustain a small signal gain coefficient of $\frac{0.01}{cm}$
2. Relevant equations

3. The attempt at a solution
I know that $γ_{0} = σR_{p2}τ_{2}$

I know that $τ_{2} = \frac{1}{k_{2}}$. I'm just not exactly sure what $R_{p2}$ is and how to find it.

Thanks for any help.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 6, 2017