# Optical tweezers

Can someone give an intuitive explanation for this effect? I didn't go through the derivation carefully, but I know that the upshot of the math is that the dipole feels a force in the direction of the intensity gradient, so it goes to the focus of the laser. But I feel like there must be some simple physical argument for why the energy is lower at high intensity, or something like that.

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Born2bwire
Gold Member
The electric field induces a dipole moment in the object. However, since the intensity of the electric field is higher at the center of the beam than at the peripheries, there is a larger force on the dipole charge that is closest to the center than on the opposite dipole charge. Thus, there is a net force on the object that pulls it to the center of the beam. Assuming that the beam is axially symmetric, then there is a potential well that exists centered on the beam since all the forces will point towards the focal point and there will be a minimum net force at the focal point.

Check out: http://en.wikipedia.org/wiki/Optical_tweezers
The section "The physics of optical tweezers" and the captions of the diagrams explain pretty well, if you're still confused about something, ask away.
Or just listen to Born2bwire ^

Andy Resnick
Can someone give an intuitive explanation for this effect? I didn't go through the derivation carefully, but I know that the upshot of the math is that the dipole feels a force in the direction of the intensity gradient, so it goes to the focus of the laser. But I feel like there must be some simple physical argument for why the energy is lower at high intensity, or something like that.
The intensity gradient is equivalent to a force (F = -grad(U)= -grad(I)). At the focus, the intensity gradient is small, so the force is small.

A trapped particle (which is smaller than the focal spot of the trap) located at the center of a trap feels no force and is free to diffuse. As the particle approaches the sides of the trap, the restoring force moves it back to the center.

Ok, I think I understand now that the field induces a dipole, and since the half of the dipole that's close to the center feels a stronger field, the object moves to the center of the beam. . Just to clarify, the optical field at a point in the beam is changing directions something like 10^15 times a second, so is it correct that the object's dipole is following this oscillation and also changing directions with negligible lag?

Born2bwire
Gold Member
Ok, I think I understand now that the field induces a dipole, and since the half of the dipole that's close to the center feels a stronger field, the object moves to the center of the beam. . Just to clarify, the optical field at a point in the beam is changing directions something like 10^15 times a second, so is it correct that the object's dipole is following this oscillation and also changing directions with negligible lag?
Actually, heh, I think this falls under a yes and technically no answer.

Technically, the model I described in my post, the inducement of a dipole moment in a gradient electric field, works in giving valid results but it is a classical approximation of what is really a quantum or quasi-classical phenomenon. The classical explanation is better used at low frequencies though and I have seen papers discussing using this to sort nanoparticles and stuff like that. In these cases, the dipole moment thought of as being physical charge does follow the oscillations of the electric field.

However, at higher frequencies, the inertia of actual physical charges is great enough that they can no longer directly follow the oscillation of the electric fields. If you look at electromagnetic waves travelling through a cold plasma you will see that above a certain frequency the waves can propagate since the free charges have too much inertia to create the currents to cancel out the incident waves. I don't know if this is the case at optical frequencies with these materials though and one also should mind the additional factors of the forces that keep the molecules together. Terahertz and optical frequencies are the beginning of the range where such basic "plasma" models would predict pronounced lagging of the charges. Note, for example though, that metals are still opaque but many dielectrics like water are transparent at optical frequencies. At the same time though metals can be thought of as a plasma but not a dielectric like water which does not allow free flow of charges.

Rather the more appropriate model is momentum transfer from the laser's photons. It works pretty much in a similar manner as the dipole model except that the mechanism of force is no longer the electric field acting on the dipole charges but the collision and transference of momentum from the photons. The aforementioned wikipedia article discusses this in their "ray optics" part and they also note that this is the mechanism in the dipole approximation. As for the wikipedia article's dipole approximation, they assume a point-source dipole where the charge separation is infinitesimal. Basically, we are ascribing behavior of the object to that of a macroscopic polarization (they rely on the relationship of a linear media with the polarization and this is a macroscopic property of a material) but the length scales of the objects themselves is approaching a quantum level (molecular sized objects).

When it comes to scattering with atoms, we can use quasi-classical methods and still get good results. In fact classical electrodynamics predicts momentum transfer by light and so using classical methods here will still predict the appropriate physics. So while we can treat the object as having a dipole moment, we are not saying that there is a physical separation of charges as now we are working with small number of objects (as opposed to a bulk) and on scales that are approaching quantum.

EDIT: Basically I guess what I am trying to say is that if you take the model literally, then yes, the dipole moment is following the oscillations of the wave. However, we are in a region where we should take note of the true(er) mechanism here which is the transfer of momentum by the photons. This is in the same vein of thought of as treating the atom roughly as an electron on a spring. If we treat the spring, or oscillator, as a quantum oscillator then we can actually get away with it with a lot of things (like the London-Van der Waal force) but we know that the current model is much more complicated (quantum wavefunction).

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