Radiation pressure and unpolarized light

[housemartin]

Hello,

I found myself a little bit lost in those concepts. Assume there are many linearly polarized plane waves, all with equal amplitudes, all traveling along z direction, and their polarizations are uniformly distributed in xy plane. Then by superposition principle amplitude of total electric and magnetic fields is zero - there are as many waves polarized in one direction as there are polarized in the opposite direction. But the net intensity and energy is not zero, right? Since intensity and energy are proportional to the square of the amplitude. And so linear momentum carried by the waves is also not zero. If all those waves strikes some surface lying in the xy plane and are absorbed in it or are reflected by it, by the conservation of linear momentum it seems that the surface must gain some momentum.
If I took this picture of radiation pressure:
when struck by plane wave, an electron in the surface moves in the direction opposite to that of electric field of the wave, then there is a magnetic force (v cross B) along the z direction.
I end up confused, because when the surface is hit by an unpolarized light, electric field is zero, so the electron does not move and there is no force on the surface, and no radiation pressure.
I hope I've made my problem clear and thanks in advance for any comment.

 

[Darwin123]

Hello,

I found myself a little bit lost in those concepts. Assume there are many linearly polarized plane waves, all with equal amplitudes, all traveling along z direction, and their polarizations are uniformly distributed in xy plane. Then by superposition principle amplitude of total electric and magnetic fields is zero - there are as many waves polarized in one direction as there are polarized in the opposite direction. But the net intensity and energy is not zero, right? Since intensity and energy are proportional to the square of the amplitude. And so linear momentum carried by the waves is also not zero. If all those waves strikes some surface lying in the xy plane and are absorbed in it or are reflected by it, by the conservation of linear momentum it seems that the surface must gain some momentum.
If I took this picture of radiation pressure:
when struck by plane wave, an electron in the surface moves in the direction opposite to that of electric field of the wave, then there is a magnetic force (v cross B) along the z direction.
I end up confused, because when the surface is hit by an unpolarized light, electric field is zero, so the electron does not move and there is no force on the surface, and no radiation pressure.
I hope I've made my problem clear and thanks in advance for any comment.

The instantaneous electric field is not zero. The instantaneous magnetic field is not zero. The directions of electric field and magnetic field are changing randomly in time. However, the directions of the electric and magnetic fields are always correlated. Therefore, the direction of the radiation field doesn't change as much.

The fields in unpolarized light are rapidly changing direction all the time. They change on a very short time scale is difficult to measure. However, the fields have a nonzero magnitude most of the time. The fields point in one direction on the time scale much less than the coherence time.

The radiation pressure is also always changing all the time. The radiation pressure is also effectively constant only over a time scale much less than the coherence time. However, the radiation pressure is weighted in one direction. The radiation pressure may be positive in a certain direction for most of the time and negative very seldom.

The average of each field component over a long length of time is zero. However, the radiation pressure is determined by the product of electric and magnetic fields. If both fields reverse sign simultaneously, the sign of the radiation pressure would remain unchanged.

That is the situation. The electric field and magnetic fields are changing in a way that is effectively random over long periods of time. However, there is a correlation. The direction of the electric field and the magnetic field change simultaneously most of the time. In other words, the signs of the field switch simultaneously.The direction of the radiation stays the same because the changes in electric and magnetic field cancel out. When the signs switch simultaneously, the sign of the radiation pressure remains the same.