What is the mechanism by which light induce polarity in tiny particles?

Question

I understand that the electric field in light induces polarity in tiny microparticles for example. Can someone explain the mechanism of how the vibrating electric field in light induces a dipole moment? From my understanding, the field vibrates in all directions and hence the net induced dipole moment should be zero

Answer 1

the field vibrates in all directions and hence the net induced dipole moment should be zero

If the light is unpolarized, then it is indeed accurate to say that the field vibrates in all directions, but that isn't the end of the story. Unpolarized light is unpolarized because it is incoherent, i.e. it can be modelled very effectively as the superposition of a bunch of wavepackets of some finite duration $\tau$, coming in at random times, with random phases, and at random polarizations. That characteristic timescale $\tau$ is known as the coherence time of the light source, and here is the kicker: for timescales shorter than that coherence time, the wave looks like a coherent beam with some static linear polarization.

If you have a beam of unpolarized light travelling through a typical dielectric material, the dielectric then sees each of those wavepackets in turn, and it responds to each successive wavepacket by developing an oscillating polarization, which then acts macroscopically to delay the light exactly like it would for a stable coherent source. On a longer timescale, because of the linearity of the interaction, the overall response to a field that 'vibrates in all directions' is effectively a dielectric polarization which also 'vibrates in all directions', but it does so with a rigid relationship to the field's vibrations and in such a way that it acts in the same way that the dielectric acts on a coherent source.

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Edit:

OK, from your additional comments,

Does a linearly polarized light induce a time-averaged dipole moment that is not equal to zero? If yes then How does it do it? because from my understanding a polarized electric field vibrates in both directions along the polarized axis and hence it should induce a dipole moment in both directions along the polarized axis alternating with time so essentially dipole moment should be zero..isn't it?

I'm just trying to understand the fundamental mechanism of Optical Tweezer and stretcher that makes the particles drift to the center of the laser beam

it's a bit clearer what's confusing you.

If you've got a dielectric nanoparticle that's being manipulated by an optical tweezer, you can assume that the tweezer light field is fully coherent laser light and that it is linearly polarized, so that the electric field of the light is well modelled by $$ \mathbf E(t) = \mathbf E_0 \cos(\omega t). $$ In this situation, the dielectric material of the particles will respond by acquiring an oscillating polarization, with a total electric dipole moment of the form $$ \mathbf p(t) = \mathbf p_0 \cos(\omega t - \phi) $$ for each nanoparticle. In your words,

it should induce a dipole moment in both directions along the polarized axis alternating with time

that is indeed correct, but

so essentially dipole moment should be zero

this isn't. The time average of the induced dipole moment, $$ ⟨\mathbf p(t)⟩ = \frac 1T \int_0^T \mathbf p(t) \mathrm dt, $$ will indeed be zero, but that is irrelevant, because it does not mean that the dipole itself is identically zero. What really matters for the optical tweezer is the time average of the interaction energy, i.e. $$ U = -⟨\mathbf p \cdot \mathbf E⟩ = \frac 1T \int_0^T \mathbf p(t) \cdot \mathbf E(t) \mathrm dt, $$ and this can be nonzero even if both of the individual averages $⟨\mathbf p(t)⟩$ and $⟨\mathbf E(t)⟩$ are zero.