Polarization conversion in a silica microsphere
Polarization conversion in a silica microsphere
Pablo Bianucci, Chris Fietz, John W. Robertson, Gennady Shvets, and Chih-Kang Shih∗
Physics Department, The University of Texas at Austin, Austin, Texas 78712
(Dated: May 22nd, 2007)
Abstract
We experimentally demonstrate controlled polarization-selective phenomena in a whispering
gallery mode resonator. We observed efficient (≈ 75%) polarization conversion of light in a silica
microsphere coupled to a tapered optical fiber with proper optimization of the polarization of the
propagating light. A simple model treating the microsphere as a ring resonator provides a good fit
to the observed behavior.
In the past few years, microresonators
have received a lot of attention1. Whis-
pering gallery mode (WGM) resonators2,
such as microspheres,3 microtoroids4 and
microrings5 have been the object of inten-
sive research, both in their fundamental prop-
erties (such as quality factors, non-linear
effects6,7 and coupling to quantum systems8
among many) and applications that include
lasers9,10, chemical11 and biological12 sens-
ing and photonic devices13. Microsphere res-
onators, particularly when coupled to a ta-
pered optical fiber14,15, are very useful to
characterize these properties and test new
ideas due to their high Q-factors and ease of
fabrication.
Recent reports have shown a further step,
taking into account the difference between
modes with different polarizations in micro-
spheres. In particular, changes in the output
polarization after coupling into the resonator
have been observed16 and transverse electric
(TE) and transverse magnetic (TM) modes
have been discriminated17.
Polarization conversion has been observed
in microrings5 and explained as a resonant
enhancement of polarization coupling caused
by waveguide bending. However, the mode
structure of microspheres makes it possible
to completely decouple the polarizations and
still obtain conversion. In this article, we re-
port on the observation of efficient, controlled
polarization conversion by using a silica mi-
crosphere resonator coupled to a tapered op-
tical fiber. We demonstrate that highly ef-
ficient polarization conversion (75% for our
particular case, higher for better optimized
conditions) is enabled by a specific orienta-
tion between the incoming light polarization
and fiber-resonator displacement. Specifi-
http://arxiv.org/abs/0704.0422v2
cally, for a horizontally stacked, strongly cou-
pled, fiber and resonator combination, a 45◦
incident polarization results in the largest
conversion. The conversion results in a
strong dip of the transmitted light with the
original polarization and a strong spike in the
orthogonally polarized transmission.
We fabricated the tapered fiber using the
“flame brush” technique18. This technique
involves mechanically stretching the optical
fiber while scanning a flame (oxy-hydrogen
in our case) over the region to be tapered.
Due to constraints in the maximum pulling
length, the fiber tapers are not completely
adiabatic, but typical losses are never larger
than 50%. SEM studies of the tapers reveal
a characteristic diameter close to 1 µm. The
microsphere was fabricated using a CO2 laser
to stretch and melt an optical fiber tip19. In
this way it is easy to obtain spheres with di-
ameters ranging from 10 µm to 200 µm. For
this particular experiment the sphere diame-
ter was measured using an optical microscope
to be 52 µm (corresponding to an estimated
free spectral range of 1.2 THz).
We mounted the microsphere on a piezo-
electric scanner which allowed us to finely
position the sphere over a range of a few
micrometers, and the stretched fiber taper
on a piezoelectric stick-slip walker permitting
both coarse and fine positioning of the fiber
taper next to the sphere. Both sphere and
PD PC2 PC1
Tapered
Fiber
Laser PR FC
Microsphere
10 um
FIG. 1: Experimental setup schematic. PR is
a polarization rotator, FC a fiber coupler, PC1
and 2 are fiber polarization controllers, P a po-
larizer and PD is an amplified photodiode. Inset:
Image of a sphere near a tapered fiber.
taper were then situated inside a compact,
closed chamber. We used an external cav-
ity tunable diode laser purchased from New
Focus as the excitation source, centered at
a wavelength near 927.85 nm. The polariza-
tion rotator set the polarization of the laser
which was then coupled into the optical fiber
using a free-space coupler. A polarizer and
an amplified photodiode at the fiber output
were used to analyze the transmitted light.
Space constraints in the chamber and lim-
itations on the arrangement of the optical
fiber caused bending of the fiber in differ-
ent locations and subsequent scrambling of
the input polarization. As a way to compen-
sate for these changes in the polarization, we
used two polarization controllers. The first
one preceded the fiber taper, compensating
for polarization changes up to the position of
the microsphere. The second controller was
placed after the fiber taper to ensure the lin-
earity of the output polarization. Figure 1
shows a schematic of this experimental setup.
We used the following procedure to mea-
sure the degree of polarization conversion.
First, the incoming polarization was selected
by using the polarization rotator. Then we
adjusted the first polarization controller to
ensure the polarization at the fiber taper was
linear and matched to one set of modes (“x-
polarized”). The next step was to uncouple
the taper from the sphere and make sure the
output polarization was linear (we achieved
this by turning the detection polarizer to its
position for minimum transmission and then
minimizing this transmission further with the
second polarization controller). This orienta-
tion of the detection polarizer is the one we
call “orthogonal”. Rotating the polarizer 90
degrees (the “parallel” orientation) resulted
in maximum transmission, with a contrast
of about 95%, confirming the linear polar-
ization of the output light. Finally, we posi-
tioned the sphere and the tapered fiber try-
ing to optimize the coupling, while measur-
ing transmission spectra for both orientations
of the detection polarizer. We repeated the
procedure for two other incoming polariza-
tions: one matched to the other set of sphere
modes (“y-polarized”) and another at 45◦ be-
tween the x- and y- polarization axis (“xy-
polarized”).
Figure 2 shows the resulting transmission
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Frequency shift (GHz)
Input Detection
polariz. polariz.
FIG. 2: Transmission spectra for different in-
put polarizations. The resonant frequencies cor-
respond to modes with l ≈ 496. The x- and
y-polarizations are orthogonal and correspond
to the polarization eigenmodes of the resonator.
The xy-polarization is oriented at 45 degrees
from both x and y. The dark traces correspond
to the detection polarizer parallel to the input
polarization and the light traces correspond to a
crossed detection polarization.
spectra for the different configurations. The
cases for both the x- and y- polarized light
show the same behavior: a set of transmission
dips whenever the laser frequency hit a whis-
pering gallery resonance when the detection
polarization is parallel and no signal when
it is perpendicular. The xy-polarized case is
more interesting: the parallel detection po-
larization shows dips for both sets of modes,
while the orthogonal one shows transmission
peaks at the whispering gallery resonances.
At the highest peak, more than 70% of the
incident light had its polarization converted.
Most of the observed polarization conver-
sion can be understood by using a simple ring
resonator model for the whispering gallery
modes. In this model, the transmission of
polarized light through the resonator is given
by14,20
τ(φ) =
r − aeiφ
1− raeiφ
, (1)
where r is the field coupling coefficient be-
tween the resonator and the waveguide, a is
the attenuation due to the resonator intrinsic
losses and φ = 2π(ν−ν0)tRT is the phase shift
imposed by the resonator (ν and ν0 are the in-
coming light frequency and the resonant fre-
quency respectively, while tRT is the round-
trip time in the resonator). The model is
scalar, but we can include the polarization by
simply assuming that modes with orthogonal
polarizations are independent and neglecting
cross-polarized couplings (using an analysis
similar to that by Little and Chu21). In this
way we obtain the same expression, with pos-
sibly different parameters, for the transmis-
sion of both polarizations. In our particu-
lar case of whispering gallery modes in mi-
crospheres, we can safely assume that modes
with different polarizations are not degener-
ate, so one of the polarizations will be unaf-
fected by the presence of a resonance. This
differs from the case of microrings5, where the
conversion depends on coupling between TE
and TM modes.
The essence of the effect lies in the differ-
ent resonator response for each polarization.
For a strongly coupled fiber and microsphere,
|τ | ≈ 1, but the phase shift ψ = arg(τ)
is changed by ∆ψ = π as the frequency is
sweeped across the resonance. Because the
orthogonal polarization is transmitted unal-
tered, the transmitted polarization rotates by
as much as 90◦ for the initial xy-polarization.
When the fiber and the resonator are horizon-
tally stacked, the effect is maximized when
the incident polarization is at 45◦ degrees
with respect to the horizontal plane.
Conversion efficiencies of up to 25% can
be achieved if one of the polarizations is crit-
ically coupled to the ring, i.e. is completely
absorbed in+the resonator. Achieving higher
efficiencies requires increasing the resonator-
waveguide coupling to obtain a significant po-
larization dependent phase shift which will
change the final polarization state into one
closer to the desired one.
We can look in more detail at the data
by concentrating into a pair of modes show-
ing good conversion, now accounting for laser
frequency drift between scans using a Fabry-
Perot interferometer as a reference. This de-
tailed spectrum can be seen in in Fig. 3. The
resonance on the right side of Fig. 3, near a
shift of 31 GHz, shows a polarization conver-
sion of about 60%. The left-side resonance
shows a conversion near 75%. The higher ef-
ficiency is due to the leftmost mode being
26 27 28 29 30 31
Frequency shift (GHz)
30.5 31
26 26.5 27 27.5 28
FIG. 3: Detailed view of two modes showing
polarization conversion. The dashed lines are
fits using equations of the form of equation 1.
The fit parameters for the leftmost features are
a = 0.99997, r = 0.99977. The corresponding
ones for the rightmost feature are a = 0.99999,
r = 0.99993.
more strongly coupled (displaying a broader
feature) to the tapered fiber than the right-
most one. Consistent with theoretical predic-
tions, in both cases one of the polarizations
is over-coupled to the ring. The lack of a
shift in the center frequency of the features
also indicates that each pair of peak and dip
corresponds to a single resonant mode.
This phenomenon could be useful for po-
larization control in photonic devices, such
as narrowband polarization-dependent filter-
ing or switching, as shown in Fig. 4 or even
arbitrary polarization manipulation.
We have observed efficient polarization
conversion on a microsphere resonator cou-
PBSPBS
a) b)
FIG. 4: Schematic of a resonator working as
wavelength-selective polarization switch. a)
Two signals with different wavelengths+ (green
and blue) and orthogonal polarizations pass un-
changed through the waveguide and the un-
coupled resonator. A polarization beamsplitter
then routes the signals to different paths. b)
The polarization of the resonant signal (blue) is
converted by the coupled resonator, and both
signals are sent through the same path. The
resonator-waveguide coupling can be changed in
different ways, including mechanical or optical22
means.
pled to a tapered optical fiber and used a
simple theoretical model to understand the
phenomenon. The model does not involve di-
rect coupling of the orthogonal polarizations,
but rather a polarization-selective phase shift
induced by the resonator. This effect should
be common to all whispering gallery mode
resonators and could be useful for polariza-
tion control in photonic devices.
Acknowledgments
This work was supported by NSF-NIRT
(DMR-0210383), the Texas Advanced Tech-
nology program, and the W.M. Keck Foun-
dation. G.S. and C.F. acknowledge support
from ARO MURI grant no. W911NF-04-01-
0203.
∗ Electronic address: shih@physics.utexas.edu
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