OPTICS | ENGINEERING
A wake of vortices is formed with the onset
of atmospheric turbulence as marine clouds
encounter a volcanic peak in Guadalupe
Island near Baja California, Mexico.
In Your Phase:
All About Optical Vortices
USGS/NASA Landsat
Carlos López-Mariscal and Julio C. Gutiérrez-Vega
This primer on optical vortices describes the physics behind
electromagnetic phase singularities and highlights their
importance in nature, science and society.
Electromagnetic wavefields exhibit a
number of exciting phenomena that
are inherent to their wave nature. A few
well-known examples are interference,
refraction and diffraction. These manifestations of light’s undulating character have been extensively studied, not
only in optics, but also in the realms of
acoustics, seismology and other subfields
of physics.
The spatial configuration of a wavefield can be described using a function
E(r), which assigns a complex number
E to each point in the spatial domain
r. The magnitude and phase of E are
then interpreted as the local amplitude
and phase of the field, respectively. The
function representing the field is a simple
mathematical description of a transverse
wave. However, a field takes on many
interesting shapes, depending on its
functional form. Many modern optical
engineering applications require a clear
understanding of the properties of complex fields. Understanding and exploiting specific properties of complex fields
has resulted in applications such as
optical coherence tomography, Raman
spectroscopy and laser beam shaping.
In fluids, vortices are
easily identified as the
eddies or whirlpool-like
patterns that result from
turbulent flow.
One peculiar feature of wavefields is
the incidence of vortices within them. A
vortex is a special point in the wavefield
around which there is continuous circulation of a physical quantity. In fluids,
for instance, vortices are easily identified
as the eddies or whirlpool-like patterns
that result from turbulent flow. In this
particular case, the direction of the local
velocity of the fluid circulates around the
location of the vortex.
Perhaps the best-known example of
a vortex in nature is a tropical cyclone.
These large-scale, rotating storm systems
are the outcome of the complex interplay
between convection, gravity and the
Earth’s rotation. They release enormous
amounts of energy as they move over
the surface of our planet. Their accurate
prediction is vital to those who live in
tropical regions.
Another example of whirling flows are
wake vortices; they originate in the airflow fields that form behind jet aircraft
as a result of turbulence generated by the
turbines in jet engines. These vortices
have been extensively studied and are
crucial to determining the minimum distance that aircraft can maintain between
one another and still land safely. Vortices
are a natural occurrence of wavefields
and thus have been observed in many
forms and at different lengths and timescales. Additional examples include the
electric currents around magnetic flux
lines in superconducting materials, spinning galaxies and cloud vortices.
In general, electromagnetic fields
exist in the three spatial dimensions and
exhibit temporal evolution. A wavefield
can also have radically varying frequency
properties, and a particular polarization
state that depends on the source of the
field. If one were to take an instantaneous two-dimensional slice of an arbitrary, propagating electromagnetic field
and then map the values of the field in
space, there would be a number of points
at which the field vanishes identically
