# Is the Fabry-Perot Interference Dependent on Pulse Duration?

• IcedCoffee
In summary: No, you can't say that. The Wikipedia article says that "temporal coherence" is a property of "pulses", but it's not clear what that means for CW analysis.
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
vanhees71 said:
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)

So can I say that CW analysis of a structure is only valid when the structure's dimension is smaller than the temporal coherence length of the pulse?

## 1. What is wave interference of a pulse?

Wave interference of a pulse is a phenomenon that occurs when two or more waves of the same frequency overlap and combine, resulting in a new wave with a different amplitude and shape.

## 2. How does wave interference of a pulse affect the resulting wave?

The resulting wave from wave interference of a pulse can have a higher or lower amplitude, depending on whether the waves are in phase or out of phase. It can also result in a new wave with a different frequency or wavelength.

## 3. What are the types of wave interference of a pulse?

The two main types of wave interference of a pulse are constructive interference, where the waves are in phase and the resulting wave has a higher amplitude, and destructive interference, where the waves are out of phase and the resulting wave has a lower amplitude.

## 4. What is the principle of superposition in wave interference of a pulse?

The principle of superposition states that when two or more waves overlap, the resulting displacement at any point is equal to the sum of the individual displacements of the waves at that point.

## 5. How is wave interference of a pulse used in real-life applications?

Wave interference of a pulse is used in many real-life applications, such as noise-cancelling headphones, where two sound waves with opposite phases cancel each other out to reduce noise. It is also used in medical imaging techniques, such as ultrasound, to create images of internal structures by measuring the interference pattern of sound waves.

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