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If I have the equation of a light pulse in the form

$$L(ω)=\frac{1}{π}\frac{\frac{1}{2}Γ}{((ω−ω_0)^2+(\frac{1}{2}Γ)^2)}$$

where $\Gamma$ is the linewidth of the pulse and $\omega_0$ is its resonant frequency, how do I find the amplitude of the pulse?

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L is the amplitude in the Fourier domain. The actual pulse will have an oscillating term such as $\cos(\omega t)$. In other words, the Lorentzian L is the envelope of the actual oscillatory field. Typically the Lorentzian (or a sum of Lorentzians) is used to model spectra. A more common model of a pulse would be a Gaussian modulated by $e^{i \omega t)$. Then the amplitude would just be the Gaussian. Or did I misunderstand the question? If your detector is not sensitive to phase, then you just see the envelope.

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