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RESEARCH
NOTE
Winter
2003
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ORBITS
OF LIGHT: Kerry
Vahala and His Miniature Lasing Spheres
onsider
a tiny glass sphere or spherical droplet. What would happen if
light could be launched at near-grazing incidence along its interior
wall? This would yield the optical equivalent of the familiar
acoustical whispering gallery.
In
optical whispering galleries, solution of Maxwell's equations
shows that light can be guided along trajectories that are tightly
confined near the surface of the sphere. Because of spherical
symmetry, these whispering-gallery solutions (also known as modes)
correspond with solutions to the classic hydrogen system of atomic
physics. If the sphere is large—compared to the scale of
the wavelength of light—we can expect to be able to interpret
the whispering-gallery motion as an orbit in the sense of an approximate
ray-optics picture.
Light
trapped within a glass sphere as a ring orbit is shown on the
opposite page. Although the sphere shown here has a diameter less
than the thickness of this page, it is nonetheless large on the
scale of the wavelength of light, and the mode in this case clearly
meets our notion of an orbit. One comment is in order: the "light"
that has been trapped in this sphere is actually in the infrared,
but has been made visible by the addition of a tracer element
within the sphere that enables up-conversion to the visible green
band.
Optical
whispering galleries can be made in several geometries. In addition
to spheres or droplets, it is possible to fabricate disks, rings,
and racetrack geometries using combinations of lithography and
etching processes similar to those used in the semiconductor industry.
However,
what makes droplets (or spheres formed first as droplets) special
is the near atomic perfection of their surface finish. Unlike
lithographed or etched whispering galleries, which are considerably
rougher, a sphere's shape is determined in the molten state by
surface tension. It therefore exhibits a degree of surface perfection
very difficult to match by other means. Surface blemishes and
roughness tend to randomly scatter light from whispering-gallery
orbits and thereby degrade light storage time.
The
lifetime of the mode as given by its quality factor, or Q value,
is an easy way to measure the superior performance of spherical
micro-cavities in comparison to semiconductor-processed micro-cavities.
Q values for silica micro-spheres formed as molten droplets can
exceed 1 billion, while the record for a lithographically processed
structure is nearly 5 orders of magnitude lower. This difference
has made droplets and spheres an object of interest for some time
in a number of different fields.
In
a ray-optics picture, a Q value this high means that light inside
a sphere about 30 microns in diameter will trace out orbits up
to a million times before leaving the cavity. Returning to the
acoustic analogy, a true whispering gallery with an equivalent
Q value of 100 million could resonate or "ring" for over an hour.
Introducing
or "coupling" light into the high-Q modes of a spherical
whispering gallery is non-trivial. Efficient coupling requires
first that the orbiting wave's phase velocity be matched with
the input wave, something not possible from free space. Then,
through a process called directional coupling, it is possible
to excite whispering-gallery orbits using waveguides of similar
(but not necessarily identical) cross section and refractive index.
Remarkably,
these waveguides can be fashioned from optical fiber filaments
in the form of a narrow taper. This is of considerable practical
importance. Optical power, initially guided within the interior
of a fiber cable, can be converted by the tapers into waves guided
along micron-wide filaments, and then back again.
Some
time ago the Vahala group demonstrated that such tapers could
be prepared in such a way that coupling both to and from orbital
modes is exceedingly efficient. This process "links"
the spherical whispering-gallery system to the technologically
important world of fiber-optic communications.
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Micrograph
showing a 40-micron diameter silica microsphere that is
doped with the rare earth erbium. Upon incorporation into
silica, erbium ionizes to the 3+ state and exhibits dipole
transitions in the green and near infrared. In the micrograph
one of these transitions has been excited by optical pumping
through a fiber taper. The taper can be seen in the micrograph
as the slightly out-of-focus horizontal line. The green
ring emission from the sphere corresponds to a fundamental
whispering-gallery mode of the sphere. This particular sphere
is also lasing in the 1.5 micron band (the important telecom
band). The lasing emission is efficiently coupled onto the
same fiber taper used for optical pumping.
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number
of new devices have demonstrated the capabilities of these systems:
for example, a laser that uses only the glass itself as the lasing
medium. To understand how this device functions, note that ultra-high
Q in a tiny package can concentrate optical energy in a tiny volume.
Imagine a ring orbit excited by an optical fiber taper. Consider
the buildup of power within the ring volume. When the taper and
the sphere are coupled appropriately, energy will store with a
time constant given by the cavity Q such that the higher the Q,
the greater the energy stored. For spheres with diameters in the
range of 30-40 microns, optical power circulates within a ring
volume of about 10-15 meter3.
Putting
all of this together, a fiber taper providing incident power in
the range of 1 milli-watt, coupled to a sphere with Q of 100 million,
will induce an intensity buildup within the ring orbit in excess
of 1 giga-watt/cm2. At these intensity levels, normal
glass—one of the most linear of optical media—exhibits
properties out of the range of our normal experience. Optical
propagation can no longer be understood using linear optics, as
the molecular motion of the glass becomes highly distorted and
gives rise to new optical frequencies and behavior.
One
manifestation of this transition is Raman
emission, a process in which glass actually amplifies
certain wavelengths, rather than becoming weakly lossy. With this
optical amplification in a cavity, the glass whispering gallery
emits new laser frequencies back into the same taper used to couple
the "pump" wave. Other startling effects are observed
associated with low-frequency phonons of the glass bead, as well
as nonlinear mixing.
Vahala's
group continues to research properties of this and other whispering-gallery-based
devices. The Raman laser described above, in addition to providing
a window on nonlinear cavity physics, may be of practical importance
as a compact, ultra-efficient wavelength source. Vahala and Applied
Physics graduate students Sean Spillance and Tobias Kippenberg
reported on this device in Nature,
February 7, 2002. The device set a record for threshold power
(the power necessary to induce laser oscillation) of only 60 micro-watts.
With further improvements in Q underway, it should be possible
to lower this value to mere nano-watts. ENG
Professor
Kerry Vahala (BS '80, MS '81, PhD '85) is the first occupant of
the Ted and Ginger Jenkins Professorship in Information Science
and Technology. Ted Jenkins (MS '66) and his wife, Ginger, established
the professorship in early 2002.
More
on Professor Vahala's work at http://www.aph.caltech.edu/people/vahala_k.html
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