# How to estimate the power of laser beam

1. Jul 23, 2015

### KFC

I posted a question about Rabi frequency here https://www.physicsforums.com/threads/what-is-rabi-frequency.331082/ some times ago. The replies there answer some of my questions but I am still looking for detail explanation on the relation between Rabi frequency and the power of the beam. I read some more materials online. There I understand that if I have a 2 level system where the Rabi frequency is a constant if the input laser is of constant power. I am thinking if we shine that laser beam (as pulse with duration $\Delta t$) to the system. How can we figure out the power of the laser if we know Rabi frequency ?

I am thinking $\hbar \Omega$ is of the unit of energy so is the power of laser should be $\hbar\Omega/\Delta t$ if $\Delta t$ is the duration of the pulse? Someone said this is not correct because if depends on how much the frequency of laser off from the resonance frequency also. But how do we add that and get the correct expression for power?

2. Jul 24, 2015

### blue_leaf77

I will give an estimate way for your problem. Assuming monochromatic or quasi-monochromatic laser beam (valid for CW laser) of frequency $\omega$, the Rabi frequency reads $\Omega = \sqrt{(\mu E_0)^2 + (\omega-\omega_0)^2}$, where $\omega_0$ the frequency between the two levels in question and $\mu$ the electric dipole moment between those two levels. If you know everything you can calculate $E_0$, then the average intensity (for plane wave) $I = \frac{1}{2}\epsilon_0 c E_0^2$, and finally the average power. To estimate the last one you need to multiply the average intensity with some area, let's say area bounded by the FWHM of the laser beam profile. Again I would like to stress that this is an estimate. In reality people would probably use pulsed instead of CW laser, and the non-uniform beam profile might contribute to further discrepancy.