Answer to Question #125003 in Physics for kashaf

Question

consider an optical pump at 940nm for yb: YAG crystal placed in a cavity.The wavelength of ytterbium is 1030nm.if all the photons emitted by the pump are absorbed by the crystal and used for the lasing process.calculate the maximum power output .the pump power is 1 W.

Answer 1

At the output, we have smaller energy (and longer wavelength). The lasing wavelength of ytterbium is 1030 nm, which corresponds to the frequency and energy of

$$\nu_o=\frac{c}{\lambda_o},\\\space\\ E_o=h\nu_o=h\frac{c}{\lambda_o}.$$

The optical pumping (conditional input) occurs, of course, at higher energy (which is proportional to the frequency), or shorter wavelength of 940 nm:

$$\nu_i=\frac{c}{\lambda_i},\\\space\\ E_i=h\nu_i=h\frac{c}{\lambda_i}.$$

In laser, the time required to pump and the time required to give that energy out is equal:

$$t=\frac{E_i}{P_i}=\frac{E_o}{P_o},\\\space\\ h\frac{c}{P_i\lambda_i}=h\frac{c}{P_o\lambda_o},\\\space\\ P_i\lambda_i=P_o\lambda_o,\\\space\\ P_o=P_i\frac{\lambda_i}{\lambda}_o=1\frac{940}{1030}=0.9126\text{ W}.$$