Interference of two ultra short laser pulses

[Mubeen]

TL;DR

ultra short pulse

what will happen if two one femtosecond(1 fs) laser pulse interferes?

 

[Ibix]

Interference, I would expect. What do you expect?

 

[Mubeen]

i would expect too. i just want to know how will be the fringe looks like also how possible complication to attain this

 

[Ibix]

If you want to calculate the pattern just add up the electric fields. There's nothing special about femtosecond pulses in that sense that I'm aware of - the pulses are just very short so the pattern is likely to appear and disappear so rapidly that there's never a time-independent pattern.

Doing it practically means getting a femtosecond optical source. It's been twenty years since I had anything to do with practical optics, but I suspect that kind of thing still won't be cheap and will probably require expert supervision. So it's probably impossible unless you're rich or are a professional in the field.

 

[Mubeen]

iam not going to setup anyway. iam curious to know whether the fringes will have good contrast?. considering the pulse is transform limited and have broad spectrum, different spectrum will interefere.

 

[Ibix]

What do you mean by "interfere" in this case? I was assuming you were just going to make two beams cross, but I think you're thinking of something else.

 

[Andy Resnick]

TL;DR Summary: ultra short pulse

what will happen if two one femtosecond(1 fs) laser pulse interferes?

This is a very complicated question, actually. There's a lot going on with the "internal" coherence of the pulse itself, and unless you know the mutual coherence between the pulses, it's impossible to analyze.

The technique "frequency-resolved optical gating" was invented to measure pulse duration (and shape), it basically uses interference between a pulse and itself to perform the measurement.

A second relevant application, propagation through a scattering medium, is also difficult to analyze:

https://ieeexplore.ieee.org/document/1026724

I'm not that familiar with time-dependent Mie scattering codes, but they appear to be in active development.

 

[sophiecentaur]

iam curious to know whether the fringes will have good contrast?.

A simple case of 'not too short' pulses will only produce a pattern when the arrivals are near coincident and the depth of the fringes will depend on the relative amplitudes of the pulses over time. On boresight and coincident timing, the fringes should be deep but for other angles, the relative amplitudes will be different over time (because of the pulse delay in addition to the simple carrier phase effect). This is the same sort of effect that you get with Young's slits where the sources are finite widths and not omnidirectional and the fringes get weaker off axis.

You can take it from there to the case where @Andy Resnick is discussing extremely short pulses but my simple approach, based on familiar things like RF waves is easier to grasp (for me). The details of the pulse amplitudes with time and 'self coherence' will become more relevant.

 

[berkeman]

[Thread prefix changed A-->I]

 

[DaveE]

It's nearly impossible to say anything in general, I think. As you said, the pulses are wideband. Interference is only simple for monochromatic coherent light. It's in there, I'm sure, but will depend on lots of particular details of the setup and will be extremely hard to actually measure.

I think you'll have to research this yourself (google is a good place to start):
https://www.edmundoptics.com/knowle...-the-basic-principles-of-ultrafast-coherence/
https://pubmed.ncbi.nlm.nih.gov/12804290/

 

[tech99]

TL;DR Summary: ultra short pulse

what will happen if two one femtosecond(1 fs) laser pulse interferes?

This seems to be approximately one cycle of light. So, for Young's Slits for example, I would expect to see the bright central band but no other fringes. This is because if a diffracted path has a delay of one wavelength there is nothing there - it is after the pulse. In addition, the screen will be dimly illuminated by the diffracted light from the two slits, but interference will not occur due to the time difference being too great.

 

[tech99]

Further to my reply, it also seems that the interference pattern is multiplied by the modulation envelope. For instance, in the present case the modulation envelope is a brief rectangular pulse and so we see just one fringe. Had there been two brief pulses then two spaced fringes would have been seen each side of centre. This is provided that there are sufficient fringes to encompass the modulating waveform.

 

[sophiecentaur]

multiplied by the modulation envelope

IS the process just simple multiplication? The modulation envelope varies with time so it's not just loke multiplying the element pattern by the array pattern. It's a transitory phenomenon.

 

[tech99]

One ray is progressively delayed as we move from the centre line, so it is sweeping in time across the modulation envelope. The other ray is progressively advanced, so sweeps the other way in time. We then have interference between these two. So if there is just one pulse having a length of one cycle, that is all we see.

 

[sophiecentaur]

One ray is progressively delayed as we move from the centre line, so it is sweeping in time across the modulation envelope. The other ray is progressively advanced, so sweeps the other way in time. We then have interference between these two. So if there is just one pulse having a length of one cycle, that is all we see.

Can you back up that verbal description with some maths that contains x,y and t? It's true that only in one place and one time are the E fields equal in amplitude and phase but what happens at other times and in other directions. I think the problem with non-continuous waves is that the concept of simple interference could be actually misleading.

 

[sophiecentaur]

that the concept of simple interference could be actually misleading.

In fact, the 'pattern' would not be stationary, which is what happens with a conventional Young's slits pattern at switch on and switch off.