# Does radiation pressure depend on the wave phase?

• Uchida
In summary, the conversation discusses whether radiation pressure depends on the wave phase of an electromagnetic wave and if it can be modeled as a sine/cosine wave function. It is determined that the polarization of the radiation plays a role and the Poynting vector can be used to calculate the radiation pressure. The concept of momentum flux is also brought up and it is clarified that radiation pressure is not dependent on the instantaneous field strength or phase, but rather on the power flowing. The conversation also delves into the energy-momentum tensor and its relationship to the electromagnetic field. Ultimately, it is concluded that radiation pressure is a steady value and not fluctuating at the frequency of the radiation.
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)

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

Uchida
mfb said:
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!

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
HomogenousCow said:
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?

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
HomogenousCow said:
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.
tech99 said:
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?
tech99 said:
If, for example, radiation pressure followed the electric field, we could have momentum arising from standing waves.
How and where exactly?

Uchida
Uchida said:
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
mfb said:
No one suggested it would be.How would you have pressure at a time of zero electric and magnetic field?How and where exactly?
On reflection I think you are right here. I don't know what happens to the stream of photons, does it pulsate at twice the frequency?

tech99 said:
On reflection I think you are right here. I don't know what happens to the stream of photons, does it pulsate at twice the frequency?
There is no stream of photons, just classical electromagnetic waves. Photons only come into the picture when we’re considering quantum mechanical effects, and there are none in this situation.

tech99, vanhees71 and weirdoguy

## 1. How does radiation pressure vary with wave phase?

Radiation pressure is the force exerted by electromagnetic radiation on an object. The amount of radiation pressure depends on the amplitude of the wave, but not on the phase. This means that the force remains constant regardless of where the object is in the wave cycle.

## 2. Does the direction of radiation pressure change with wave phase?

No, the direction of radiation pressure does not change with wave phase. The force always acts in the direction of the wave propagation, regardless of the phase of the wave.

## 3. Is there a difference in radiation pressure between different types of waves?

Yes, the amount of radiation pressure can vary depending on the type of wave. For example, for a plane wave, the radiation pressure is proportional to the square of the wave's amplitude. However, for a spherical wave, the radiation pressure is inversely proportional to the square of the distance from the source.

## 4. How does the frequency of the wave affect radiation pressure?

The frequency of the wave does not directly affect radiation pressure. However, it can indirectly impact the amount of radiation pressure by influencing the amplitude of the wave. Higher frequency waves generally have higher amplitudes and therefore exert more radiation pressure.

## 5. Can radiation pressure be measured in everyday life?

Yes, radiation pressure can be observed and measured in everyday life. For example, the pressure exerted by sunlight on the sails of a sailboat is a result of radiation pressure. It is also used in technologies such as solar sails and laser propulsion systems.

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