Biomedical Engineering Reference
In-Depth Information
10.1 Introduction
Optical vortices [1-5], for instance, the Laguerre-Gaussian mode
(an eigenmode of the electromagnetic equation in a cylindrical
coordinate system), have been widely investigated in many areas,
such as optical tweezers [6, 7], superresolution microscopes, [8-
10], and quantum information [11, 12], because they exhibit unique
features including annular intensity profiles and helical (twisted)
wavefronts due to a phase singularity shown by
l
ϕ
(where
l
is an
integer known as the topological charge and
is the azimuthal
angle) in the transverse plane and they carry orbital angular
momentum (
l
).
Lights with circular polarization also possess a helical electric
fieldandaspinangularmomentum(
s
)associatedwiththeircircular
polarization. Consequently, circularly polarized optical vortices,
known as “twisted light with spin,” carry a helicity referred to as
the total angular momentum (
j
=
l
+
s
) (see Fig. 10.1), defined by
the vector sum of the orbital (
l
) and spin (
s
) angular momenta [13,
14]. The total angular momentum has been evidenced by causing
acceleration (or deceleration) of orbital motion of submicron
particles in optical tweezers.
Recently, we discovered, for the first time, that the helicity
(wavefront, polarization helicities, or both helicities characterized
ϕ
Figure 10.1
Angular momentumof light.
