0198506961.pdf

196 Laser cooling and trapping

Fig. 9.12Absorption has a Lorentzian
line shape with a peak at the resonance
frequencyω 0. The refractive index is
zero on resonance, where it changes
sign, and this characteristic dependence
on frequency leads to dispersion.

Absorption

Refractive

index

Fig. 9.13A tightly-focused beam of
light exerts a radiation force on a di-
electric sphere that pulls it towards the
region of high intensity (at the focus).
Not all of the light is transmitted at the
interfaces and the reflected rays are in-
dicated. After Ashkin (1997).

Incident light

Refracted light

B

A B

A

Focus

Lens

Dielectric

sphere

cal model in which bound electrons execute damped harmonic oscillation

with resonance frequencyω 0 , see Section 7.5.1 and Fox (2001), but the

relationship between the refractive index and absorption at the resonant

frequency is very general (independent of any particular model). Dis-

persion and absorption are different facets of the same interaction of

light with matter; strong absorption leads to large changes in refractive

index. The variation in the refractive index extends over a larger fre-

quency range than the absorption, e.g. although air and glass (of good

optical quality) are both transparent at visible wavelengths they have

refractive indices of 1.0003 and 1.5, respectively, associated with strong

absorption in the ultraviolet region;nglass− 1 nair−1 because a solid

(^34) Generally speaking, the effects of re- has a higher density of atoms than a gas. 34
fraction are most apparent when they
are not obscured by absorption, i.e.
away from a resonance. A similar situ-
ation arises for forces on the individual
atoms.
The force that attracts an object towards a region of high intensity
has been used to manipulate microscopic objects in a technique called
optical tweezers that was developed by Arthur Ashkin (Ashkinet al.
1986). The objective lens in an optical microscope is used to focus a
laser beam tightly so that there is a strong gradient force along the axis,
as shown in Fig. 9.13, in addition to trapping in the radial direction