How Does Pump Irradiance Affect Gain in a Four-Level Laser System?

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Homework Statement

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

Amplification is to occur on the 2-to-1 transition. The medium is pumped by a laser of intensity [itex]I_{p}[/itex], 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 [itex]N_{T} = N_{0} + N_{1} + N_{2} + N_{3}[/itex]. The various parameters are:

[itex]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[/itex]
[itex]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}[/itex]

Assuming an ideal four-level laser system determine:

a) The pump irradiance required to sustain a small signal gain coefficient of [itex]\frac{0.01}{cm}[/itex]
b) The saturation innradiance.

Homework Equations

The Attempt at a Solution

I know that [itex]γ_{0} = σR_{p2}τ_{2}[/itex]

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

Thanks for any help.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Valkarie]

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.