I'm not sure where to ask this question or if it even makes sense...

Say an electromagnetic wave passes through a point in space. The point experiences some fluctuation of electric and magnetic fields. But what happens after the wave has passed? Are there any lingering effects, like a "wake" of some kind, or does the wave leave absolutely no evidence of its having been there?

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sophiecentaur
Gold Member
The wave you are referring to can either be a 'continuous wave', which will be going on for ever or it will be a burst or single pulse, lasting for a finite time. The effect on the space it passes through will take the same time interval as the burst / pulse itself. (If you are talking of free, empty space) If your 'space' has anything in it ( even a very rarified gas or plasma) the EM will interact with the medium and some of the energy will be absorbed by the medium and released after a delay. (Probably very short) the original waveform will become dispersed (which is what you refer to, I think)
You could insert some fancy resonators into your space that would spread the wave out and delay it by a significant amount of time.

The wave you are referring to can either be a 'continuous wave', which will be going on for ever or it will be a burst or single pulse, lasting for a finite time. The effect on the space it passes through will take the same time interval as the burst / pulse itself. (If you are talking of free, empty space) If your 'space' has anything in it ( even a very rarified gas or plasma) the EM will interact with the medium and some of the energy will be absorbed by the medium and released after a delay. (Probably very short) the original waveform will become dispersed (which is what you refer to, I think)
You could insert some fancy resonators into your space that would spread the wave out and delay it by a significant amount of time.
Thanks for your answer. When you say it will be absorbed and then re-released by the medium, in what form would it be re-released? As kinetic energy in the medium, or do you mean that it would be re-released as radiation?

Drakkith
Staff Emeritus
Thanks for your answer. When you say it will be absorbed and then re-released by the medium, in what form would it be re-released? As kinetic energy in the medium, or do you mean that it would be re-released as radiation?
It depends upon the type of medium and the frequency and intensity of the EM wave. If the medium is my cell phone antenna, then the energy is transformed into the motion of the charges and the electric and magnetic effects from that motion.

DrDu
At least in vacuum, the wave is nothing but electric and magnetic fields. So you can't say there remains anything once a wave has passed.

Andy Resnick
I'm not sure where to ask this question or if it even makes sense...

Say an electromagnetic wave passes through a point in space. The point experiences some fluctuation of electric and magnetic fields. But what happens after the wave has passed? Are there any lingering effects, like a "wake" of some kind, or does the wave leave absolutely no evidence of its having been there?
This question can be phrased in terms of a constitutive relation- the response of a material (including 'vacuum') to an applied field. Most commonly-used constitutive relations do not have 'memory' (stochastic processes like this are called 'Markovian'), but it is possible to write down a constitutive equation that has 'fading memory'- stress relaxation and hypoelastic materials are mechanical analogs of this. The constitutive equations are typically of the 'Volterra type', see for example, http://repository.cmu.edu/cgi/viewcontent.cgi?article=1202&context=math

DrDu
This question can be phrased in terms of a constitutive relation- the response of a material (including 'vacuum') to an applied field. Most commonly-used constitutive relations do not have 'memory' (stochastic processes like this are called 'Markovian'), but it is possible to write down a constitutive equation that has 'fading memory'- stress relaxation and hypoelastic materials are mechanical analogs of this. The constitutive equations are typically of the 'Volterra type', see for example, http://repository.cmu.edu/cgi/viewcontent.cgi?article=1202&context=math
In most materials (ecluding vacuum) the dielectric function depends on frequency. It can be shown that this corresponds to a fading memory.

Andy Resnick
In most materials (ecluding vacuum) the dielectric function depends on frequency. It can be shown that this corresponds to a fading memory.
I'm not sure that's right- my understanding is that the frequency dependence is due to causality- the material cannot respond before the field arrives; alternatively, the Hilbert transform of the Heaviside step function.

sophiecentaur
Gold Member
The "fading memory" idea needs to be considered carefully. If there is no actual resonance in the medium, any after effects will only be a 'smearing' of the waveform (dispersion) and not 'ringing' due to the medium.

Andy Resnick
The "fading memory" idea needs to be considered carefully. If there is no actual resonance in the medium, any after effects will only be a 'smearing' of the waveform (dispersion) and not 'ringing' due to the medium.
Yes and no- for example, optical damage/darkening of a material can be modeled this way (maybe that's a trivial example). Optical bleaching of a fluorophore could be another (silly) example. My point is simply that the current optical response of a material could depend on the past history.

sophiecentaur
Gold Member
Yes. That's all non linear effects though ( as in photography) and there is no equivalent to a wave being left behind. No remaining 'oscillations' (?).
I guess that applies to mechanical waves too, when there are no resonances in the structure of the medium.

Andy Resnick
Yes. That's all non linear effects though ( as in photography) and there is no equivalent to a wave being left behind. No remaining 'oscillations' (?).
I guess that applies to mechanical waves too, when there are no resonances in the structure of the medium.
No, that's not what I mean- it's certainly true that it's a nonlinear effect, but the nonlinear susceptibility is usually written as a time-independent thing: harmonic generation 4-wave mixing, stark effect, etc...

Boyd has a brief blurb about photodamage that's fairly qualitative, Gamaly's book

https://www.amazon.com/dp/9814241814/?tag=pfamazon01-20&tag=pfamazon01-20

sophiecentaur
Gold Member
How about photochromic sunglasses? That's a temporary effect.
But all I am suggesting is that there are no (/very few) occasions when the wave leaves behind it some vibrational energy. An example would be interesting. Perhaps a decaying vibration would be enough, as long as it's not just a simple exponential (CR style) decay.