Polarization de-multiplexing and multiplexing by means of conical refraction
is proposed to increase the channel capacity for free space optical
communication applications. The proposed technique is based on the
forward-backward optical transform occurring when a light beam propagates
consecutively along the optic axes of two identical biaxial crystals with
opposite orientations of their conical refraction characteristic vectors. We
present experimental proof of usefulness of the conical refraction
de-multiplexing and multiplexing technique by increasing in one order of
magnitude the channel capacity at optical frequencies in a propagation distance
of 4m

Kalkandjiev, Todor K.

Loiko, Yurii

Mompart, Jordi

Turpin, Alex

English

arXiv

Polarization demultiplexing and multiplexing by means of conical refraction is proposed to increase the channel capacity for free-space optical communication applications. The proposed technique is based on the forward-backward optical transform occurring when a light beam propagates consecutively along the optic axes of two identical biaxial crystals with opposite orientations of their conical refraction characteristic vectors. We present an experimental proof of usefulness of the conical refraction demultiplexing and multiplexing technique by increasing in one order of magnitude the channel capacity at optical frequencies in a propagation distance of 4 m

Enlighten: Publications

Free-space optical polarization demultiplexing and multiplexing by means of conical refraction

Alex Turpin

Yurii Loiko

Todor K. Kalkandjiev

Jordi Mompart

Crossref

Optics Letters

Turpin Avilés, Alejandro

Kalkandjiev, Todor Kirilov

Mompart Penina, Jordi

Diposit Digital de Documents de la UAB

Free-space optical polarization demultiplexing andmultiplexing by means of conical refractionAlex Turpin,1,* Yurii Loiko,1 Todor K. Kalkandjiev,1,2 and Jordi Mompart11Departament de Física, Universitat Autònoma de Barcelona, Bellaterra E-08193, Spain2Conerefringent Optics SL, Avda Cubelles 28, Vilanova i la Geltrú E-08800, Spain*Corresponding author: alejandro.turpin@uab.catReceived June 20, 2012; revised August 24, 2012; accepted August 27, 2012;posted August 30, 2012 (Doc. ID 170964); published October 3, 2012Polarization demultiplexing and multiplexing by means of conical refraction is proposed to increase the channelcapacity for free-space optical communication applications. The proposed technique is based on the forward-backward optical transform occurring when a light beam propagates consecutively along the optic axes of two iden-tical biaxial crystals with opposite orientations of their conical refraction characteristic vectors. We present anexperimental proof of usefulness of the conical refraction demultiplexing and multiplexing technique by increasingin one order of magnitude the channel capacity at optical frequencies in a propagation distance of 4 m. © 2012Optical Society of AmericaOCIS codes: 060.2605, 060.4230, 160.1190.In optical communications, different properties of a lightfield, such as its intensity, wavelength, polarization, andorbital angular momentum (OAM), can be used to pro-vide optical channels to efficiently transmit the informa-tion. Thus, for example, the capacity of a communicationchannel can be substantially increased if one multiplexesdifferent wavelengths of various input optical carriersignals into a single channel by using the wavelengthdivision multiplexing (WDM) technique [1]. For a mono-chromatic laser beam, Laguerre–Gauss light beams car-rying OAM in the helicity of their phase fronts have beenproposed [2] as a basis of carrier signals allowing, in prin-ciple, for an arbitrary increase of the channel capacity[3–6]. However, there are practical drawbacks that re-strict the range of applicability of the OAM encodingtechnique [7,8] such as the large divergence of high-orderOAM modes, which prevent their use for free-spaceoptical communications (FSOC) at long distances. Alter-natively, one could also use the polarization degree offreedom of a light beam as a carrier basis of signals forFSOC links. In this case, nevertheless, the use of a polar-ization beam splitter allows, at most, to double the FSOCchannel capacity. In this Letter, we report a novel methodto demultiplex and multiplex a monochromatic inputlight beam into, in principle, an arbitrary large numberof polarization states by means of the conical refractionphenomenon [9–16].In conical refraction, when a circularly polarized col-limated light beam passes along the optic axis of a biaxialcrystal, it refracts conically inside the crystal andemerges as a collimated hollow cylinder whose trans-verse profile is a light ring. This light ring is laterallyshifted being both the direction of the displacement aswell as the ring radius given by the so-called character-istic ~Λ vector of the biaxial crystal [12]. Each point of thelight ring is linearly polarized with the polarization planerotating continuously along the ring in such a way thatevery two opposite points of the ring have orthogonal po-larizations; see Fig. 1(a). This polarization distributiondepends only on the orientation of ~Λ.When two identical biaxial crystals are placed withaligned optic axes and opposite orientations of their ~Λvectors [see Fig. 1(b)], an input Gaussian beam is trans-formed, after propagating through the first crystal, into alight ring that, after passing through the second crystal,gives back the input Gaussian beam [16]. This particulararrangement, which allows optical forward-backwardtransform, will be called in what follows as the degener-ate two-cascade conical refraction configuration.We make use of this forward-backward transform ofconical refraction to propose a novel method to demul-tiplex and multiplex a monochromatic light beam into alarge number of linearly polarized states as it is schema-tically shown in Fig. 2. The first crystal demultiplexes theinput beam into an infinite number of linearly polarizedbeams placed along a ring [see Fig. 1(a), where eachdashed circle represents a linearly polarized beam]. Eachof these beams constitutes an information channel (notethat the channels are polarization channels) that can beindividually selected and modulated in amplitude. Lateron, the second biaxial crystal multiplexes all the chan-nels into one beam that propagates in free space. Finally,Fig. 1. (Color online) (a) Transverse intensity pattern regis-tered at the focal plane for a circularly polarized input Gaussianbeam after passing through a 28 mm long KGdWO42 biaxialcrystal. Yellow double arrows illustrate the polarization distri-bution along the ring for vertical orientation of ~Λ. Dashedcircles represent linearly polarized beams. (b) Degeneratedtwo-cascade conical refraction configuration yielding aforward–backward transform of a circularly polarized inputGaussian beam. The ring plane coincides with the focal planeof the first lens. FL, focusing lens; CL, collimating lens; BC1, firstbiaxial crystal; BC2, second biaxial crystal.October 15, 2012 / Vol. 37, No. 20 / OPTICS LETTERS 41970146-9592/12/204197-03$15.00/0 © 2012 Optical Society of Americaa third biaxial crystal can be used to decode the trans-mitted signal at the receiver stage. In what followswe describe the conical refraction demultiplexing andmultiplexing protocol in terms of the standard elementsthat form a free-space optical telecommunications sys-tem: the transmitter, the free-space propagation, and thereceiver. The mutual alignment of the optic axes of thebiaxial crystals should be maintained with precisionwithin 50 μrad to make it work properly by means ofthe conical refraction (CR) effect.The transmitter consists of an input monochromaticlight beam, two biaxial crystals in a degenerate two-cascade configuration, an angular amplitude mask, andthe lenses to focus and collimate the beam. As inputbeam, we take a collimated linearly polarized Gaussianbeam with w0  1 mm beam waist obtained from a640 nm diode laser coupled to a monomode fiber. A lin-ear polarizer and a quarter-wave plate are placed to en-sure a perfect circularly polarized Gaussian beam at theentrance of the first crystal. Note that the experimentcould also be performed with a linearly polarized inputbeam but with the inconvenience of producing a crescentintensity pattern instead of a complete ring and, there-fore, the polarization channels would possess differentamplitudes. The degenerated two-cascade scheme is pre-pared with two identical KGdWO42 biaxial crystals(<100 nm of difference) yielding a light ring after thefirst crystal of 872 μm ring radius. The polished entrancesurfaces of the two biaxial crystals (cross-section6 × 4 mm2) have parallelism with less than 10 arc sec,and they are perpendicular to one of the two optic crystalaxes within 1.5 mrad misalignment angle. To focus andcollimate the beam, we use lenses with 200 mm focallength. To select the polarization channels at the lightring, we use angular amplitude masks forming a starburst like pattern with n (up to 12) opened circular sec-tors. The amplitude masks actually allow passing onlysome parts of the ring; thus we are indeed selectingthe communication channels. Encoding the informationinto the different channels could be performed by timevarying the transmission coefficient for each sector ofthe mask using, for instance, a spatial light modulator.In our experiments, the free-space propagation dis-tance is 4 m. We have measured that the multiplexedbeam has a divergence similar to the initial Gaussianbeam and, therefore, we expect that our protocol couldoperate for the same distances as other FSOC systems doit with Gaussian beams. Results on the extension of ourprotocol to larger propagation distances will be pre-sented elsewhere.The receiver itself consists of an objective of 50 mmfocal length, a 12 mm long KGdWO42 biaxial crystal,and a CCD camera. This biaxial crystal demultiplexes(final patterns shown in the third row of Fig. 3) thefree-space propagated beam (transversal patterns shownin the second row of Fig. 3), performing conical refrac-tion and recovering the sectors that were modulated bythe angular amplitude masks (first row of Fig. 3) at thetransmitter. As it can be observed in the third row ofFig. 3, we are able to independently modulate up to 12sectors, which constitutes an increase in one order ofmagnitude of the channel capacity of the FSOC link.The last row in Fig. 3 shows the intensity variation alongthe azimuthal direction of the corresponding demulti-plexed patterns from the third row of Fig. 3. The intensitypeaks of the received channels are perfectly distinguish-able with respect to the background. Additionally, thenumber of peaks observed at the receiver is exactly equalto the number of channels selected by the transmitter.XT between the channels is one of the main limitingfactors for real applications. The main contribution intothe XT between adjacent channels in our system comesfrom light diffraction on the mask domain boundaries. Tocharacterize the XT, we have investigated the influenceof the closure angle of the masks, i.e., the azimuthal angleseparating neighbor open sectors (see θ in the inset ofFig. 4), and the number of channels over it by measuringthe residual intensity at the center of the closed sector.For the latter case, the open and closed sectors in themask have the same azimuthal angular width and wemeasure the XT at the closed sectors. The results forXT, i.e., residual intensity related to the intensityFig. 2. (Color online) Sketch of the polarization demultiplex-ing and multiplexing experimental setup based on conical re-fraction being used to increase the channel capacity of aFSOC system. The FSOC system is formed by the transmitterwith its two identical biaxial crystals presenting opposite ~Λ vec-tors, a free-space propagation distance of 4 m, and the receiverwith the third biaxial crystal. LP, linear polarizer; λ ∕4, quarter-wave plate; AAM, angular amplitude mask.Fig. 3. Experimental transverse intensity patterns (third row)and the corresponding integrated azimuthal intensities (fourthrow) obtained by the receiver for multiplexer masks (firstrow) with 2 (a), 4 (b), 8 (c), and 12 (d) opened sectors. Thesecond row shows the multiplexed beams at the entrance ofthe receiver.4198 OPTICS LETTERS / Vol. 37, No. 20 / October 15, 2012maximum, are presented in Fig. 4. The data reveal that, ascan be expected, the smaller the number of channels, thesmaller the XT. Moreover, the thinner the open sectors,which corresponds to larger closure angle θ, the smallerthe XT too. The red solid curve gives the exponential fit-ting to the experimental data that show the XT decay as θincreases and N decreases. For the 12-channel caseshown in Fig. 3, the average XT is less than 3%. Finally,we would like also to note that misalignment in crystals’rotation around the beam propagation direction leads tolight polarization XT between any opposite points atthe CR ring. However, in our system it is well controlledbelow 10−6.In summary, we have proposed a novel technique todemultiplex and multiplex a monochromatic light beaminto a finite and, in the ideal case, an arbitrary number oflinearly polarized states. The technique is based on theforward-backward transform produced by two biaxialcrystals under conditions of conical refraction. We havedemonstrated an increase of one order of magnitude inthe channel capacity for FSOC of a monochromatic inputGaussian beam at 640 nm for a 4 m propagation distancewith XT being below 3%. In addition, we have investi-gated the XT with respect to the azimuthal angle of theclosed sectors and the number of sectors of the masksused. The obtained results suggest that by simply opti-mizing the channel selecting mechanism, i.e., the thick-ness of the open and closed sectors of the masks, onecould increase the channel capacity or decrease theXT for a fixed number of channels. Details on such opti-mization will be reported elsewhere.As an encouragement for future investigations on thetechnique proposed in this Letter, we would like to notethat by selecting appropriate biaxial crystals it would beinteresting to extend this novel method to other wave-lengths in the optical and telecommunication bands atwhich the crystals are transparent and to combine it withthe WDM technique. Finally, it would be very promisingto look for new quantum cryptography protocols byextending the technique to the single-photon case.The authors gratefully acknowledge financial supportthrough Spanish MICINN contracts CSD2006-00019,FIS2008-02425, FIS2010-10004-E, and FIS2011-23719,and the Catalan Government contract SGR2009-00347.A. T. acknowledges financial support through grantAP2010-2310 from the MICINN.References1. B. Mukherjee, IEEE J. Select. Areas Commun. 18, 1810(2000).2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P.Woerdman, Phys. Rev. A 45, 8185 (1992).3. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V.Pas’ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express12, 5448 (2004).4. S. Slussarenko, E. Karimi, B. Piccirillo, L. Marrucci, and E.Santamato, J. Opt. Soc. Am. A 28, 61 (2011).5. A. Gatto, M. Tacca, P. Martelli, P. Boffi, and M. Martinelli, J.Opt. 13, 064018 (2011).6. Z. Wang, N. Zhang, and X.-C. Yuan, Opt. Express 19, 482(2011).7. B. Jack, M. J. Padgett, and S. Franke-Arnold, New J. Phys.10, 103013 (2008).8. S. Franke-Arnold, S. M. Barnett, E. Yao, J. Leach, J. Courtial,and M. J. Padgett, New J. Phys. 6, 103 (2004).9. A. M. Belskii and A. P. Khapalyuk, Opt. Spectrosc. 44, 436(1978).10. A. M. Belsky and M. A. Stepanov, Opt. Commun. 167, 1(1999).11. M. V. Berry and M. R. Jeffrey, Prog. Opt. 50, 13 (2007).12. T. K. Kalkandjiev and M. Bursukova, Proc. SPIE 6994,69940B (2008).13. M. V. Berry, J. Opt. 12, 075704 (2010).14. A. Abdolvand, App. Phys. B 103, 281 (2011).15. A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U.Rafailov, Opt. Express 18, 2753 (2010).16. A. Turpin, “Cascaded conical refraction,” Master’s thesis(Universitat Politécnica de Catalunya (UPC), Barcelona,2011), http://upcommons.upc.edu/pfc/handle/2099.1/13007.Fig. 4. (Color online) Crosstalk (XT) between adjacent chan-nels versus the closure angle θ (bottom axis) and versus thenumber of channels N (top axis) of the masks used. The redsolid curve represents the exponential fitting to the experimen-tal data. Uncertainty of the θ angle measurement was below 1°.October 15, 2012 / Vol. 37, No. 20 / OPTICS LETTERS 4199

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A. Turpin

Y. L. Loiko

T. K. Kalkandjiev

J. Mompart

Free Space Optical Polarization De-multiplexing and Multiplexing by
  means of Conical Refraction

Free Space Optical Polarization De-multiplexing and Multiplexing by means of Conical Refraction

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