If a neutral atom is placed in an electric field, the negative electron cloud surrounding the positive nucleus will be displaced, leading to a separation between the centres of mass of the positive and negative charge distributions, as shown in Fig. 3.1. The resulting induced dipole can experience electrostatic forces arising from its interaction with the inducing electric field. An oscillating electromagnetic field, such as that of the laser beam used to generate an optical tweezers, will induce an oscillating dipole, which will also experience forces arising from its interaction with the inducing electromagnetic field. Furthermore, an oscillating dipole radiates an electromagnetic field that can produce a mechanical effect on other induced dipoles leading to, in some cases, the formation of stable ordered structures, a phenomenon known as optical binding. In this Chapter, we will study how induced dipoles can experience optical forces in an electromagnetic field. This approach is valid not only for the study of optical forces on neutral atoms, but also on other small particles, such as molecules and nanoparticles. Here, “small” means “much smaller than the electromagnetic wavelength” and, in this sense, the dipole approximation is the an- tithesis of the geometrical optics thesis described in Chapter 2. Nevertheless, we will come to the synthesis in Chapters 5 and 6, where we describe the general exact approach based on electromagnetic theory.
3.1 The electric dipole in electrostatics
3.2 Polarisability and the Clausius–Mossotti relation
3.3 The electric dipole in an oscillating electric field
3.4 Radiative reaction correction to the polarisability
3.5 Cross-sections
3.6 The optical theorem
3.7 Optical forces
3.7.1 Gradient force
3.7.2 Scattering force
3.7.3 Spin–curl force
3.8 Atomic polarisability
3.9 Plasmonic particles
3.10 Optical binding
Problems
References
Figure 3.1 Electric dipole induced on an atom
Figure 3.2 — Electric dipole in an electrostatic field
Figure 3.3 — Dipole potential and electric field
Figure 3.4 — Separation of charges due to polarisation
Figure 3.5 — Oscillating dipole
Figure 3.7 — The optical theorem
Figure 3.11 — Complex polarisability