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9.5 Introduction to the dipole force 195

Glass prism

Incident light

Refracted light

Fig. 9.10Radiation that is deflected

by a glass prism (or a mirror) exerts a

force on that object equal and opposite

to the rate of change of momentum of

the radiation.

Laser beam

Gaussian distribution

of light intensity

Atom

B

B

A

A

Fig. 9.11The refraction of light by a

dielectric sphere with a refractive in-

dex greater than that of the surround-

ing medium. In a laser beam with a

Gaussian profile the intensity along ray

A is greater than for ray B. This leads

to a resultant force on the sphere to-

wards the region of high intensity (cen-

tre of the laser beam), in addition to

an axial force pushing in the direction

of the beam. Analogous forces arise on

smaller particles such as atoms. After

Ashkin (1997).

These simple considerations show that the forces associated with ab-
sorption and refraction by an object have similar magnitude but they
have different characteristics; this can be seen by considering a small
dielectric sphere that acts as a converging lens with a short focal length,
as shown in Fig. 9.11. In a laser beam of non-uniform intensity, the
difference in the intensity of the light refracted on opposite sides of the
sphere leads to a resultant force that depends on the gradient of the
intensity: a sphere with a refractive index greater than the surrounding
medium,nsphere>nmedium, feels a force in the direction of increasing
intensity, whereas a sphere withnsphere<nmediumis pushed away from
the region of high intensity.^33 Thus the sign of thisgradient force(also^33 The calculation of this force using ge-
ometrical optics is straightforward in
principle, but integration over all the
different rays and inclusion of reflection
coefficients makes it complicated.

known as the dipole force) depends onnsphere. The refractive index
of materials varies with frequency in the characteristic way shown in
Fig. 9.12. This behaviour can be understood in terms of a simple classi-