Table Of ContentFree Space Optical Polarization De-multiplexing and Multiplexing
by means of Conical Refraction
Alex Turpin,1 Yurii Loiko,1 Todor K. Kalkandjiev,1,2 and Jordi Mompart1
1Departament de F´ısica, Universitat Auto`noma de Barcelona, E-08193 Bellaterra, Spain
2Conerefringent Optics SL, Avda Cubelles 28, Vilanova i la Geltru´, E-08800, Spain
(Dated: January 9, 2013)
Polarization de-multiplexing and multiplexing by means of conical refraction is proposed to in-
crease the channel capacity for free space optical communication applications. The proposed tech-
niqueis based on the forward-backward optical transform occurring when a light beam propagates
consecutivelyalongtheopticaxesoftwoidenticalbiaxialcrystalswithoppositeorientationsoftheir
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conical refraction characteristic vectors. Wepresent experimental proof of usefulness of theconical
1
refraction de-multiplexing and multiplexing technique by increasing in one order of magnitude the
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channelcapacity at optical frequencies in a propagation distance of 4m.
2
n PACSnumbers: ocis: 060.2605, 060.4230, 160.1190.
a
J
8 In optical communications, different properties of a
lightfield, suchasits intensity,wavelength,polarization,
] and orbital angular momentum (OAM), can be used to
s
c provide optical channels to efficiently transmit the in-
i formation. Thus, for example, the capacity of a com-
t
p munication channel can be substantially increased if one
o multiplexesdifferentwavelengthsofvariousinputoptical
.
s carrier signals into a single channel by using the Wave-
c lengthDivisionMultiplexing(WDM)technique[1]. Fora
i
s monochromaticlaserbeam, Laguerre–Gausslightbeams FIG. 1. (color online) (a) Transverse intensity pattern regis-
y carrying orbital angular momentum (OAM) in the he- teredatthefocalplaneforacircularly polarizedinputGaus-
h licity of their phase fronts have been proposed [2] as a sian beam after passing through a 28mm long KGd(WO4)2
p biaxial crystal. Yellow double arrows illustrate the polariza-
basis of carrier signals allowing, in principle, for an ar-
[ tion distribution along the ring for vertical orientation of Λ~.
bitrary increase of the channel capacity [3–6]. However,
Dashed circle represent linearly polarized beams. (b) Degen-
1 there are practical drawbacks that restrict the range of
erated 2-cascade conical refraction configuration yielding a
v
applicability of the OAM encoding technique [7, 8] such forward-backward transform of a circularly polarized input
4
asthe largedivergenceofhighorderOAMmodes,which Gaussianbeam. Theringplanecoincideswiththefocalplane
6
5 prevent their use for free space optical communications ofthefirstlens. FL:focusinglens. CL:collimatinglens. BC1:
1 (FSOC) at long distances. Alternatively, one could also first biaxial crystal. BC2: second biaxial crystal.
. use the polarizationdegreeoffreedomofa lightbeamas
1
a carrier basis of signals for FSOC links. In this case,
30 nevertheless, the use of a polarization beam splitter al- on the orientation of Λ~.
1 lows, at most, to double the FSOC channel capacity. In When two identical biaxial crystals are placed with
: this paper, we report a novel method to de-multiplex aligned optic axes and opposite orientations of their Λ~
v
and multiplex a monochromatic input light beam into, vectors, see Fig. 1(b), an input Gaussian beam is trans-
i
X in principle, an arbitrary large number of polarization formed,afterpropagatingthroughthefirstcrystal,intoa
r states by means of the conical refraction phenomenon light ring that, after passing through the second crystal,
a
[9–16]. gives back the input Gaussian beam [16]. This particu-
lar arrangement, which allows optical forward-backward
In conical refraction,when a circularly polarized colli- transform, will be called in what follows as the degener-
matedlightbeam passesalongthe optic axisofa biaxial ate 2-cascade conical refraction configuration.
crystalitrefractsconicallyinsidethecrystalandemerges We make use of this forward-backward transform of
as a collimated hollow cylinder whose transverse profile conical refraction to propose a novel method to de-
is a light ring. This light ring is laterally shifted be- multiplex and multiplex a monochromatic light beam
ing both the direction of the displacement as well as the into a large number of linearly polarized states as it
ring radius givenby the so-calledcharacteristicΛ~ vector is schematically shown in Fig. 2. The first crystal de-
of the biaxial crystal [12]. Each point of the light ring multiplexes the input beam into an infinite number of
is linearly polarized with the polarization plane rotating linearlypolarizedbeamsplacedalongaring(seeFig.1(a)
continuouslyalongthe ring insuchawaythateverytwo where each dashed circle represents a linearly polarized
oppositepointsoftheringhaveorthogonalpolarizations, beam). Each of these beams constitutes an information
seeFig.1(a). Thispolarizationdistributiondependsonly channel (note that the channels are polarization chan-
2
nels) that can be individually selected and modulated in are indeed selecting the communication channels. En-
amplitude. Later on, the second biaxial crystal multi- coding the information into the different channels could
plexes all the channels into one beam that propagatesin beperformedbytimevaryingthetransmissioncoefficient
free space. Finally, a third biaxial crystal can be used for each sector of the mask using, for instance, a spatial
to decode the transmitted signal at the receiver stage. light modulator.
In what follows we describe the conical refraction de- Inourexperiments,thefreespacepropagationdistance
multiplexing and multiplexing protocol in terms of the is4m. Wehavemeasuredthatthemultiplexedbeamhas
standardelementsthatformafreespaceopticaltelecom- a divergence similar to the initial Gaussian beam and,
municationssystem: thetransmitter,thefreespaceprop- therefore, we expect that our protocol could operate for
agation, and the receiver. The mutual alignment of the the same distances as other FSOC systems do it with
optic axes of the biaxial crystals should be maintained Gaussian beams. Results on the extension of our pro-
with precision within 50 µrad to make it work properly tocol to larger propagation distances will be presented
by means of the CR effect. elsewhere.
FIG.2. Sketchofthepolarizationde-multiplexingandmulti-
plexingexperimentalset-upbasedonconicalrefractionbeing
usedtoincreasethechannelcapacityofaFSOCsystem. The
FSOCsystemisformedbythetransmitterwithitstwoidenti-
calbiaxialcrystalspresentingoppositeΛ~ vectors,afreespace
propagation distance of 4m, and the receiver with the third
biaxialcrystal. LP:linearpolarizer. λ/4: quarterwaveplate.
AAM:angular amplitude mask.
The transmitter consists of an input monochromatic
lightbeam,twobiaxialcrystalsinadegenerate2-cascade
FIG. 3. Experimental transverse intensity patterns (third
configuration,anangularamplitudemask,andthelenses row) and the corresponding integrated azimuthal intensities
to focus and collimate the beam. As input beam, we (fourth row) obtained by the receiver for multiplexer masks
take a collimated linearly polarized Gaussian beam with (firstrow) with2(a),4(b),8(c),and12(d)opened sectors.
w = 1mm beam waist obtained from a 640nm diode Thesecondrowshowsthemultiplexedbeamsattheentrance
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laser coupled to a monomode fiber. A linear polarizer of the receiver.
and a quarter wave plate are placed to ensure a perfect
circularlypolarizedGaussianbeamattheentranceofthe The receiver itself consists of an objective of 50mm
firstcrystal. Notethattheexperimentcouldalsobeper- focal length, a 12mm long KGd(WO ) biaxial crystal,
4 2
formedwithalinearlypolarizedinputbeambutwiththe and a CCD camera. This biaxial crystal de-multiplexes
inconvenience of producing a crescent intensity pattern (final patterns shown in the third row of Fig. 3) the free
instead of a complete ring and, therefore, the polariza- space propagated beam (transversal patterns shown in
tion channels would possess different amplitudes. The the second row of Fig. 3), performing conical refraction
degenerated2-cascadeschemeispreparedwithtwoiden- and recovering the sectors that were modulated by the
tical KGd(WO ) biaxial crystals (< 100nm of differ- angularamplitudemasks(firstrowofFig.3)atthetrans-
4 2
ence)yieldingalightringafterthefirstcrystalof872µm mitter. As it can be observed in the third row of Fig. 3,
ringradius. Thepolishedentrancesurfacesofthetwobi- we are able to independently modulate up to 12 sectors,
axial crystals (cross-section 6×4mm2) have parallelism which constitutes an increase in one order of magnitude
withlessthan10arcsecondsandtheyareperpendicular of the channel capacity of the FSOC link. Last row in
to one of the two optic crystalaxes within 1.5mradmis- Fig. 3 shows the intensity variation along the azimuthal
alignmentangle. Tofocusandcollimatethebeamweuse direction of the corresponding de-multiplexed patterns
lenses with 200mm focal length. To select the polariza- from the third row of Fig. 3. The intensity peaks of
tion channels at the light ring we use angular amplitude the received channels are perfectly distinguishable with
masks forming a star burst-like pattern with n (up to respect to the background. Additionally, one can also
12) opened circular sectors. The amplitude masks actu- note that there is no crosstalk between neighbor chan-
ally allow passing only some parts of the ring, thus we nels,sincethereappearasnumberofpeaksasnumberof
3
channels selected at the transmitter. In summary, we have proposed a novel technique to
Crosstalk (XT) between the channels is one of the main de-multiplex andmultiplex a monochromaticlight beam
limitingfactorsforrealapplications. Themaincontribu- into a finite and, in the ideal case, an arbitrary number
tionintotheXTbetweenadjacentchannelsinoursystem of linearly polarized states. The technique is based on
comes from lightdiffraction onthe mask domainbound- theforward-backwardtransformproducedbytwobiaxial
aries. To characterize the XT, we have investigated the crystals under conditions of conical refraction. We have
influence of the closure angle of the masks, i.e. the az- demonstrated an increase of one order of magnitude in
imuthal angle separating neighbor open sectors (see θ in thechannelcapacityforFSOCofamonochromaticinput
the inset of Fig. 4), and the number of channels over it Gaussianbeamat640nmfora4mpropagationdistance
by measuring the residual intensity at the center of the with cross-talk being below 3%. In addition, we have
closedsector. Forthelattercase,theopenandclosedsec- investigated the XT with respect to the azimuthal angle
tors in the mask have the same azimuthalangular width of the closed sectors and the number of sectors of the
andwemeasuretheXTattheclosedsectors. Theresults masks used. The obtained results suggest that by sim-
for XT, i.e. residual intensity related to the intensity ply optimizing the channel selecting mechanism, i.e. the
maximum,arepresentedinFig. 4. The data revealthat, thickness of the open and closed sectors of the masks,
as it can be expected, the smaller the number of chan- one could increase the channel capacity or decrease the
nels the smaller the XT. Moreover,the thinner the open XT for a fixed number of channels. Details on such op-
sectors, which corresponds to larger closure angle θ, the timization will be reported elsewhere.
smaller the XT too. Red solid curve gives exponential
fitting to the experimentaldata that showthe XT decay
as θ increasesandN decreases. For the 12channels case
showninFig.3,the averageXTis lessthan3%. Finally,
we would like also to note that misalignment in crystals’
rotationaroundthe beam propagationdirection leads to As an encouragement for future investigations on the
lightpolarizationXTbetweenanyoppositepointsatthe technique proposed in this paper, we would like to note
CR ring. However, in our system it is well controlled thatby selectingappropriatebiaxialcrystalsitwouldbe
below 10−6. interesting to extend this novel method to other wave-
lengths in the optical and telecommunication bands at
whichthecrystalsaretransparentandtocombineitwith
the WDM technique. Finally, it would be very promis-
ing to look for new quantum cryptography protocols by
extending the technique to the single-photon case.
The authors gratefully acknowledge financial support
FIG. 4. Crosstalk (XT) between adjacent channels vs. the through Spanish MICINN contracts CSD2006-00019,
closureangleθ (bottomaxis)andvs. thenumberofchannels FIS2008-02425, FIS2010-10004-E, and FIS2011-23719,
N (top axis) of the masks used. Red solid curve represents and the Catalan Government contract SGR2009-00347.
exponential fitting to the experimental data. Uncertainty of A. T. acknowledges financial support through grant
o
theθ angle measurement was below 1 . AP2010-2310from the MICINN.
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