1
$\begingroup$

I'm currently studying about lorentz oscillation and fano resonance (ref: https://doi.org/10.1088%2F0031-8949%2F74%2F2%2F020).

According to the lorentz model, also known as driven damped oscillated system, the amplitude of the oscillation is given by

$$ A(w)=\frac{a}{\sqrt{w_0^2-w^2+i\gamma w} }. $$ And the phase $\phi$ will be converted from 0 to $\pi$ as the frequency $w$ is moving from zero to infinity.

I totally understand that equation, how to derive it, and the behavior of amplitude and phase evolve as frequency is going throught the resonance frequency. My question is, how can I undestande that the phase shift will be $\pi/2$ at the resonance frequency. Furthermore I'm wonderting how to understand the fact that $\phi$ will be zero and $\pi$ at $w<<w_0$ and $w>>w_0$, respectively. What is the origin of phase delay? My intuitions tell me that we apply the force on the oscillating system, which should be oscilated in phase.

Moreover, the assymmetry will be arising in the case of fano resonance where coupling between two oscillation model is condered(plz refer to figure). Again, I can follow the mathematical expression of fanoresonance and understand below figure using just several equations. But I'm also wondering why the phase delay looks like this figures.

enter image description here

In summary,

  1. what is the intuitive interpretation of phase delay in lorentz model(driven damped oscillation) and fano model.
Improve this question
$\endgroup$
2
  • $\begingroup$ Fano resonance is not due to applying force to a system (which is usual resonance in a driven oscillator) - it is due to interference of oscillations/waves. E.g., in a Fano resonance in a quantum dot, it is a direct wave, and a wave scattered by a discrete level. $\endgroup$
    – Roger V.
    Commented Sep 4 at 8:41
  • $\begingroup$ @RogerV. In classical analogy you mean it is originated from the "coupling term" between two oscillation. right? $\endgroup$
    – Jhn
    Commented Sep 4 at 8:47

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.