Photons and wavelength in ultrafast optics

[crashcat]

TL;DR Summary

How to interpret an ultrashort pulse and its interaction with matter in terms of photons and wavelength?

I am not understanding how to think of photons and wavelength in ultrafast optics. An ultrashort pulse is the summation of many wavelengths. So, if you refract an ultrafast pulse it will actually spread out spatially? Can you define a wavelength as sort of an average wavelength? And most of the applications are to do bio and materials measurements, so when it interacts with matter and you have to start thinking of it as photons, how does that make sense? Is it just nonlinear effects as it has to interact with many many photons at once? Or is it more useful to think of it as just an extremely high local electric field?

 

[Andy Resnick]

Summary:: How to interpret an ultrashort pulse and its interaction with matter in terms of photons and wavelength?

I am not understanding how to think of photons and wavelength in ultrafast optics. An ultrashort pulse is the summation of many wavelengths. So, if you refract an ultrafast pulse it will actually spread out spatially? Can you define a wavelength as sort of an average wavelength? And most of the applications are to do bio and materials measurements, so when it interacts with matter and you have to start thinking of it as photons, how does that make sense? Is it just nonlinear effects as it has to interact with many many photons at once? Or is it more useful to think of it as just an extremely high local electric field?

Pulses of light have not just a band of frequencies present, but those frequencies are all 'phase coherent' with each other- this is essential to create a pulse rather than 'white light'.

Pulses do indeed spread spatially (and temporally) due to dispersion; pulse compression technologies such as prism or grating pairs use 'anomalous dispersion' to compress the pulse (in time).

The interaction of an ultrafast pulse with matter can be quite complicated and really depends on the specifics- a picosecond pulse, for example, is used to probe very different processes as compared to femto- or attosecond pulses. Do you have anything specific in mind?

Does that help?

 

[crashcat]

Thanks Andy, that does help. I'm thinking the gap in my understanding is related to the interaction with matter. If you want to model it, is it most useful to think of the high local electric fields, and model the pulse that way? Or is it most useful to look at multi-photon absorption and nonlinear effects which become more relevant? I don't know enough to know if I want to know more about pico, femto, or attosecond pulses.

Basically, if you cannot clearly define the wavelength and it is not useful to model the interaction of 1 or multiple photons with atoms in the material, then how do you understand it?

 

[DrDu]

A photon does not have to have to be a momentum eigenstate. You can also have quite localized photon states:
https://arxiv.org/pdf/0903.3712.pdf

 

[Andy Resnick]

Basically, if you cannot clearly define the wavelength and it is not useful to model the interaction of 1 or multiple photons with atoms in the material, then how do you understand it?

It depends on what you are studying- for some applications, it's sufficient to simply account for the absorbed energy density, while for others, detailed information about the spectral refractive index is required.

https://www.routledge.com/Femtoseco...-and-Applications/Gamaly/p/book/9789814241816

 

[Redbelly98]

... if you cannot clearly define the wavelength ...

I would argue that you can clearly define the wavelength in terms of a well-defined spectrum or distribution of wavelengths.

 

[tech99]

Pulses of light have not just a band of frequencies present, but those frequencies are all 'phase coherent' with each other- this is essential to create a pulse rather than 'white light'.

Pulses do indeed spread spatially (and temporally) due to dispersion; pulse compression technologies such as prism or grating pairs use 'anomalous dispersion' to compress the pulse (in time).

The interaction of an ultrafast pulse with matter can be quite complicated and really depends on the specifics- a picosecond pulse, for example, is used to probe very different processes as compared to femto- or attosecond pulses. Do you have anything specific in mind?

Does that help?

I presume that each frequency present in the pulse must have a separate photon. In a Fourier Analysis of the pulse, it seems that each frequency exists long before and long after the pulse, so presumably the photons exist over the same period of time.

 

[DrDu]

I presume that each frequency present in the pulse must have a separate photon. In a Fourier Analysis of the pulse, it seems that each frequency exists long before and long after the pulse, so presumably the photons exist over the same period of time.

That's absurd! Would you also say that e.g. an electron in a wavepacket has by necessity to be described as a superposition of electrons of definite energy?

 

[Andy Resnick]

I presume that each frequency present in the pulse must have a separate photon. In a Fourier Analysis of the pulse, it seems that each frequency exists long before and long after the pulse, so presumably the photons exist over the same period of time.

I'm not sure that's a useful assumption. Try this: given a 5 fs pulse with energy 2 mJ and center wavelength 800 nm, how many photons are there per pulse?

 

[crashcat]

This had made me realize there are other fundamental things I am not understanding. Maybe the understanding of a fs pulse is related to the understanding of a photon.

Let's say a photon is a wave packet. So the single "photon" is made up of plane waves of a wide band of wavelengths. But when we usually talk about photons, we assign them a definite wavelength (momentum by p = h/l) and energy (frequency by E = hf). So it could be the same for a fs pulse, that it is just a different type of wave packet than a photon and not built of photons? This is not precluding that it could decay to several photons through dispersion or matter interaction.

It comes down to what is the most fundamental thing. We say there are standing waves in the laser resonator cavity. But actually it's photons which are related in phase whose electric fields interfere destructively at the nodes. But since, fundamentally, we are counting photons, you should see noise at the nodes related to the finite counting of photons. This noise is real, as I was brought to understand when I was reading about noise in LIGO. Every emag exchange of energy or momentum, even in something like a capacitor, is quantized and mediated by something like a photon. (Using a loose definition of photon as an emag wave packet, and not necessarily at visible frequencies or whatever).

Something else to unpack is if the momentum is precisely defined in a photon, the position must be imprecise. Although if you consider some real photons emitted from an electronic transition, there is a fair bit of uncertainty in the momentum. Photons from a laser going through a pinhole at 2 meters distance have much more position uncertainty than photons selected from a particular distant star, does this affect the uncertainty in wavelength? Probably not because h/4pi is such a tiny number.

Ok, I've run out of time right now.

 

[DrDu]

Did you have a look at the article I cited in #5? It answers most questions on how photons with non-constant momentum can be defined.

 

[crashcat]

No I missed it. I will read it this weekend. Thanks.