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

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

• "the field vibrates in all directions" - what if the light is polarized? Sep 6, 2018 at 14:03
• I Understand that if it is polarized then it will vibrate along one axis but doesn't it still meant that the net dipole moment averaged over time is still zero? because the polarized electric field is vibrating in both directions along the polarized axis and hence it induces a dipole moment in both directions alternating with time along the polarized axis so essentially it should still be zero..isn't it? Sep 6, 2018 at 14:25
• Interesting question. What are the specifics of the experiment? Do you have a link describing the experimental method and conditions where this effect was seen? Does it depend on the dielectric media, particle size, photon wavelength, polarization...? Is an induced net dipole moment/polarization stable and measurable in the bulk media? It makes sense that a dipole moment is induced by a field in a half cycle and then reversed in the next for individual molecules. A stable net polarization of a dielectric media is indeed an unexpected effect. Sep 6, 2018 at 15:43

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.

Edit:

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.

• That is a great answer! But I just want to clear up a subtle thing from my head. 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? Sep 6, 2018 at 14:48
• 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 Sep 6, 2018 at 15:22
• @bitbitbitter See edited answer. Sep 6, 2018 at 15:36
• The thing is I'm trying to understand what sort of force pattern is causing the particles on the periphery of the laser beam to move towards the center of the beam. Do you think you can explain in terms of forces rather than energy?? Sep 7, 2018 at 8:49
• It's really a straight forward question. Why do particles on the periphery of the laser beam in optical tweezers apparatus drift to the center of the beam? What force pattern causes this pull to the center? Sep 7, 2018 at 8:52