Fabry Perot interferometer used as a filter

[DiracRules]

Hi all!

I'm studying Fabry Perot optical interferometer (with monochromatic light without taking time into account so far) and as its first application we studied it can be used as a filter, letting pass only certain frequencies
$\nu= \frac{mc}{2n_fd\cos(\theta_t)},\,\,m\in\mathcal{N}$ where c is speed of light, $n_f$ is the refractive index of the dielectric, d is its width and $\theta_t$ is the transmission angle.

That said, I was wondering: since the plot of $(\nu,T_tot)$ - Ttot being the total transmittance - reminds me the frequency spectrum of the sampling of a sinusoidal wave, can the interferometer be thought as a sampling device operating on the light wave?

I mean, since Fourier's transformation of the sampling of a sinusoidal wave is the repetition of Fourier's transformation of the wave, I thought that we can think backward: since we see the repetition of peaks, it can be the spectrum of the sampling (in time's domain) of the sinusoidal light wave.

I am wondering if it is craziness or if there is something not so foolish in my observation.
DR

 

[eljose79]

. SCIENTIST: Hello! Your observation is quite interesting and not at all foolish. In fact, what you have described is a common principle in signal processing known as the sampling theorem. This theorem states that if a continuous signal is sampled at a rate higher than twice its highest frequency component, then the original signal can be accurately reconstructed from the samples.

In the case of the Fabry Perot interferometer, the interference pattern created by the reflected and transmitted waves can be thought of as a sampling of the incident light wave. The peaks in the (\nu,T_tot) plot correspond to the frequencies that are allowed to pass through the interferometer, while the valleys correspond to the frequencies that are blocked.

In this way, the Fabry Perot interferometer acts as a filter, allowing only certain frequencies to pass through. This is similar to how a digital signal processing system samples and filters a signal to extract specific frequencies.

So, your observation is not at all craziness, but a valid application of the sampling theorem in the context of optical interferometry. Keep exploring and making connections between different fields of science, as it can lead to new and exciting discoveries!