# Wave interference of a pulse

• IcedCoffee

#### IcedCoffee

I get that a single (optical) pulse is a superposition of continuous frequency components of its spectrum, but I'm a bit confused how Fabry-Perot interference can be interpreted in time domain.

In a single-frequency explanation, the idea is that the incident wave goes through multiple reflections inside a simple FP interferometer consisting of two partially transparent mirror. At resonant frequencies those reflected waves will interfere constructively (or destructively) and get transmitted (or reflected) completely.

But in a broadband pulse, it seems like:
(1) Given a long enough FP cavity, each pulse won't interfere with each other as they are separated in time.
(2) If we consider the initial incident pulse, it will simply go though the FP cavity, losing some of its energy due to the two reflections. However, it will still retain frequency components that would have been completely reflected due to destructive interference in the single-frequency picture.
EDIT: Ok, I guess the multi-reflected pulses that follow this initial pulse will have time interval based on the FP cavity. This will remove the destructively-interfering frequency components when I take the Fourier transform of the total output signal... But if I'm doing an experiment in which I record only the initial pulse and disregard the multi-reflected pulses, the FP interferometer will not remove those frequencies, right? And certainly, energy in that frequency component gets transferred through the FP interferometer?

So the output of the system is not a superposition of the single-frequency outputs? Or is there something wrong with my conjectures (1) & (2)?

Thank you all in advance :)

Last edited:

You are right. Any real-world pulse is of finite time-duration, and the smaller this time is the broader the pulse is in the frequency domain. A pulse can only interfere in a Fabry Perot interferometer if the pulse and the reflected pulse overlap, i.e., if the pulse is broad enough in the time (i.e., narrow enough in the frequency) domain. That's also known as (temporal) coherence. See the nice Wikipedia article (particularly the section about temporal coherence):

https://en.wikipedia.org/wiki/Coherence_(physics)

IcedCoffee and Ibix
You are right. Any real-world pulse is of finite time-duration, and the smaller this time is the broader the pulse is in the frequency domain. A pulse can only interfere in a Fabry Perot interferometer if the pulse and the reflected pulse overlap, i.e., if the pulse is broad enough in the time (i.e., narrow enough in the frequency) domain. That's also known as (temporal) coherence. See the nice Wikipedia article (particularly the section about temporal coherence):

https://en.wikipedia.org/wiki/Coherence_(physics)