- #1

unscientific

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[tex] I (\omega,z) = I (\omega,0) e^{\alpha z} [/tex]

The small-signal gain coefficient is given by

[tex]\alpha_{21}(\omega-\omega_0) = N^* \sigma_{21}(\omega-\omega_0) = N^* \frac{\hbar \omega_0}{c}B_{21} g_B(\omega-\omega_0) = N^* \frac{\hbar \omega_0}{c}B_{21} \frac{1}{\pi} \frac{(\frac{\Delta \omega_L}{2})}{(\omega-\omega_0)^2+(\frac{\Delta \omega_L}{2})^2}[/tex]

So obviously, the gain will be the strongest when ##\omega=\omega_0##. But I don't understand the concept of 'Gain narrowing' as described: