# Does radiation pressure depend on the wave phase?

Uchida
Hello to all,

Does radiation pressure depends on the wave phase of the electromagnetic wave hitting a surface?

Or, can the radiation pressure be modeled as a sin/cos wave function, where force due to radiation pressure F = P/c would be the average over one cycle?

(P = power, c = light speed, F = force due to radiation pressure)

Mentor
It depends on the polarization of the radiation. You can calculate the Poynting vector.

• Uchida
Uchida
It depends on the polarization of the radiation. You can calculate the Poynting vector.

Hi mfb,

I understood what you said.

For a linearly polarized light, the poynting vector magnitude (or, light intensity) can be described as a sine wave function S*sin(wt+p). Thus, ~force due to radiation pressure should be F = P*sin(wt+p)/c

For a circularly polarized light, the poynting vector magnitude does not change over time, thus, radiation pressure should be constant.

Thank you!

HomogenousCow
That doesn't sound right, there's no reason for the momentum flux of the electromagnetic field to be constant in time in general. Do you understand the general treatment of the electromagnetic field and how to calculate the momentum flux?

• Uchida
Uchida
That doesn't sound right, there's no reason for the momentum flux of the electromagnetic field to be constant in time in general. Do you understand the general treatment of the electromagnetic field and how to calculate the momentum flux?

My knowledge about electromagnetic fields treatment is limited.

But I understand that a circular polarized electromagnetic beam have rotating E and B fields with constant magnitude, therefore, give constant magnitude (and direction) for energy flux S.

But for other cases (elliptical and linear polarization), E and B magnitude changes over time, thus giving a non constant energy flux S over a cycle.

I came to this conclusion after mfb reply and this video:

However, you have stated momentum flux. Can one say that momentum flux is directly proportional to energy flux?

Gold Member
Radiation pressure depends only on the power flowing, and not on the instantaneous field strength (or phase). So it is a steady value, not fluctuating at the frequency of the radiation. Neither is it polarization dependent.
If, for example, radiation pressure followed the electric field, we could have momentum arising from standing waves. As these waves do not represent power flow, this would make no sense.

• Uchida
Mentor
That doesn't sound right, there's no reason for the momentum flux of the electromagnetic field to be constant in time in general.
No one suggested it would be.
Radiation pressure depends only on the power flowing, and not on the instantaneous field strength (or phase).
How would you have pressure at a time of zero electric and magnetic field?
If, for example, radiation pressure followed the electric field, we could have momentum arising from standing waves.
How and where exactly?

• Uchida
Gold Member
2022 Award
However, you have stated momentum flux. Can one say that momentum flux is directly proportional to energy flux?
This is a subtle question. The one place in physics where the distribution of energy, momentum, and stress, has a clear physical meaning is in general relativity, where the energy-momentum tensor of matter and radiation fields enters in the Einstein equations as the sources of the gravitational field (analogous to charge-current distributions being the sources of the electromagnetic field).

Given that you can conclude that also within special relativity (i.e., neglecting gravitational interactions) the physical energy-momentum-stress tensor is the symmetric, gauge invariant Belinfante tensor, which can be derived from Noether's theorem taking carefully into account the fact that electromagnetic four-potentials that differ only by a gauge transformation represent the same physical state, and using the corresponding gauge-symmetry of the energy-momentum-stress tensor to make it gauge invariant. Then it also turns out to be symmetric, and the angular-momentum tensor of the em. field does not contain an explicit "spin-like piece".

Taking the symmetric energy-momentum tensor, the energy-flow density and the momentum-density differ only by a conversion factor of ##c##.

• Uchida
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