Controlling light polarization by swirling surface plasmons
Mengjia Wang, Roland Salut, Huihui Lu, Miguel-Angel Suarez, Nicolas Martin, T. Grosjean
aa r X i v : . [ phy s i c s . op ti c s ] D ec Controlling light polarization by swirling surfaceplasmons
Mengjia Wang, Roland Salut, Huihui Lu, ∗∗ Miguel-Angel Suarez, Nicolas Martin, and Thierry Grosjean, ∗ FEMTO-ST Institute UMR 6174, University of Bourgogne Franche-Comte - CNRS -Besancon, France Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications,Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, ChinaEmail: *[email protected] and **[email protected]
Light polarization is a key aspect of modern optics. Current meth-ods for polarization control utilize birefringence and dichroism ofanisotropic materials or of arrays of anisotropically shaped nanos-tructures. Based on collective optical effects, the resulting compo-nents remain much larger than the wavelength of light, which limitsdesign strategies. Here, we present a travelling-wave plasmonic an-tenna that overcomes this limit using a gold-coated helical nanowirenon-radiatively fed with a dipolar aperture nanoantenna. Our non-resonant hybrid nanoantenna enables tightly confined circularly po-larized light by swirling surface plasmons on the subwavelength scaleand taking advantage of optical spin-orbit interaction. Four closelypacked circularly polarized light sources of opposite handedness andtunable intensities are demonstrated. By reaching near-field interac-tion between neighboring nanoantennas, we obtain a highly minia-turized wave plate whose polarization properties have never previ-ously been demonstrated.
T M mode [28] (Fig. 1(b)). It is locally fed with the dipolarmode of a rectangular aperture nanoantenna that perforates a 100 nm thick gold layer rightat the helix’s pedestal. An incident wave on the back of the aperture is transmitted as asubdiffraction guided SP, which is non-radiatively converted into the wire mode of the helix.The contact between the aperture and the helix’s pedestal ensures efficient near-field couplingbetween the two plasmonic structures. To identify the travelling-wave nature of the antenna,we showed the intensity of the current along the metallic wire of a four-turn PHA (Fig. 1(d)).The thus-depicted mode closely resembles a travelling wave, as no clearly marked currentnodes are evidenced.In the course of propagation, the plasmon wire mode acquires EOAM oriented along thehelix axis (0z). At the same time, the SPs are released as free-space propagating wavescarrying an SAM of ± per photon (in ~ units). Part of the emitted waves interacts with thehelix and re-excites the plasmon wire mode, thereby participating in the swirling plasmoniceffect. This travelling wave property arises from the fact that our PHA is a chiral plasmonicwaveguide operating near cutoff. The degree of circular polarization (DOCP) of the emittedwaves refers to the distribution of photons prepared in the spin states +1 and − . The DOCPis defined as | I RCP − I LCP | / ( I RCP + I LCP ) where I RCP and I LCP stand for the intensities ofthe right and left circularly polarized components of the antenna emission, respectively [4]. APHA designed for operation at λ =1.5 µ m has been predicted to emit light with polarizationellipticity and a DOCP peaking at 0.97 and 0.999, respectively (Fig. 1(c)).Our fabrication of the corresponding structures started with the growth of carbon helicesby focused ion beam-induced deposition (FIBID) [1] on a 100 nm thick gold film coveringa glass substrate. The carbon helices were then coated with a thin layer of gold. The PHAwas terminated by focused ion beam (FIB) milling of a single rectangular aperture nanoan-tenna in contact with the helix pedestal and outside the winding area of the plasmonic wire(see Supplementary Fig. 5). Fig. 2(a) and the inset of Fig. 2(b) display scanning electronmicroscopy (SEM) images of a resulting structure. The PHAs were back-illuminated with3 .00.350.00.61.21.6 z ( m ) μ -0.35 0.0 0.35-0.35 y ( m ) μ x ( m ) μ l (nm) DOCPEllipticity (a) (b)(c) (d) a i r li gh t li ne l =1.5 mμ ħ c ’’ (eV)β ħ ( e V ) ω m=0m=1 m=0m=1 ħ c ’ (eV)β Fig. 1.
Helical plasmonic antenna as a circularly polarized subwavelength source.a , Schematics of the PHA and its operation principle. End-fire excitation is representedwith a white spike. Under a curved trajectory along the helix, SPs acquire EOAM and aresimultaneously released as freely propagating waves (white arrow). Part of the mode leakagere-excites the plasmon wire mode, thus participating in the swirling plasmonic effect. b ,Dispersion relations of the m = 0 and m = 1 modes of a gold-coated carbon wire (105-nmdiameter carbon wire, 25-nm thick gold coating). Energy is plotted versus ~ cβ ′ and ~ cβ ” .At λ =1.5 µ m, only the m = 0 mode is guided. Figure inset: intensity plot of the m = 0 mode for λ =1.5 µ m. c , Spectra of the ellipticity factor and DOCP of the PHA emission. d ,Amplitude of the electric current distribution along the gold-coated carbon wire, at λ =1.5 µ m.polarized light from a tunable laser at telecommunication wavelengths, the antenna emis-sions were measured and their polarization state was analyzed (see Methods). The observedpolarization properties (Fig. 2(b) and 2(c)) agree well with the theoretical model. As antici-pated in Fig. 2(b), a gold coating thinner than predicted may explain the noticeable redshift4n the experimental spectra with respect to the numerical simulation. l (nm) DOCPEllipticity1.00.80.70.9 l =1.64 µm l =1.55 µm 30210 6090120150 330180 0300240
500 nm 2 µm
L-helixR-helix270 30210 6090120150 330180 0300240 l =1.64 µm R RLL (a) (b) (c)(d) (e)(f) (g) (h)
LCPRCP
Fig. 2.
Circularly polarized optical emission from fabricated single plasmonic he-lical antennas. a , Scanning electron micrograph of a PHA. b , Experimental spectra ofthe ellipticity factor and DOCP of the PHA emission. Inset: top view of a . Image size: 1 µ m. Solid curves: theoretical spectra (ellipticity factor and DOCP) with a 10 nm thick goldlayer covering the carbon helix. c , State-of-polarization analysis at λ =1.55 µ m and λ =1.64 µ m. d , Scanning electron micrograph of two couples of PHAs of opposite handedness andorthogonal aperture nanoantennas. The right- and left handed PHAs are identified with theletters R and L, respectively. e-g , Far-field optical images of the four-PHA device in d , with f , a right-handed and g , a left-handed circular analyser in front of the camera. h , Helicityanalysis of two PHAs of opposite handedness. The measurement is conducted by placing arotating quarter-wave plate followed by a fixed polarizer in front of a detector and measuringthe transmitted power.When such HPAs of opposite handedness are arranged with a spacing of a few microns,the overall structure transmits light in the form of a small array of background-free right-and left-handed circularly polarized sources (Figs. 2(d)-2(h)). Moreover, by using PHAswith various orientations of the feed apertures, the relative intensities of these point-like5missions become controllable by the polarization of the incident light. We can thereforecreate ultracompact optical architectures made of tiny circularly polarized directional lightsources (Supplementary Fig. 6) with arbitrary handedness and tunable intensities, therebyobtaining unprecedented integrated devices for manipulating light polarization on a smallscale. The enhancement in the ellipticity factor with the number of turns of the helix revealsthe swirling plasmonic effect as the source of circular polarization (Supplementary Section1). The chiral nature of the PHA generates circular dichroism (Fig. 3). However, circulardichroism occurs only when the antenna is illuminated from the top (i.e., in collection mode;see Fig. 3(a)). The measured indicates a transmission process mainly governed by near-field coupling between the helix and the rectangular aperture nanoantenna. Such near-fieldcoupling is confirmed in Supplementary Section 2. The PHAs are thus also appealing tools todiscriminate right and left circular polarizations, for instance, to locally measure the DOCPof light and perform polarimetry on the subwavelength scale [30].A more complex polarization response can be achieved with a spacing between the PHAsthat is smaller than the wavelength, resulting in the coupling of the light emission processescreated by individual plasmonic antennas. We consider two couples of right and left PHAswith antennas of opposite handedness that are spaced at a distance of 560 nm apart, andare made up of orthogonal apertures (Figs. 4(a) and 4(b)). With this geometry, far-fieldemission shows a single spot regardless of the incident polarization (inset of Fig. 4(b)). Figs.4(c) and 4(e) compare the measured and calculated tilt angles ψ and ellipticity angles χ ofthe outcoming polarization (Poincare sphere approach) as a function of the direction angle θ of the incident linear polarization, at two different wavelengths (1.61 µ m and 1.47 µ m),respectively. The measured curves in Figs. 4(c) and 4(e) reveal the theoretically anticipatedtuning of the angular spacing ∆ θ between the two right- and left-handed outcoming circularpolarizations. Whereas ∆ θ is fixed at 90 ◦ with conventional phase retardation plates, it ishere equal to 69 ◦ at λ = 1.61 µ m and decreases down to 51 ◦ at λ =1.47 µ m. Such tunabilityin polarization manipulation is not standard at all. It arises from the ability of our structure6
480 1520 1560 1600 16400.00.20.40.60.81.0
Collection modeEmission mode l (nm) C i r c u l a r d i c h r o i s m E m i ss i on m ode C o ll e c t i on m ode (a) (b) RCPLCP
Fig. 3.
Plasmonic helical antenna and circular dichroism. a , Schematics of thetwo operation modes of the PHA, involving light wave propagation in two opposite di-rections along the antenna axis. b , Circular dichroism spectra measured with a left-handed PHA operating in emission and collection modes. Circular dichroism is defined as ( I RCP − I LCP ) / ( I RCP + I LCP ) , where I RCP and I LCP stand for the emission intensities of thePHA, with illumination by right and left circularly polarized light, respectively. Emissionintensity is measured from the helix, in air (in emission mode), or from the rectangular aper-ture nanoantenna through the substrate (in collection mode). Figure inset: helicity analysisin emission mode at λ =1.55 µ m.to generate circular polarizations from the combination of two elliptically polarized waves ofparallel ellipticities, as shown experimentally in Figs. 4(d) and 4(f), and tunable intensities(see Supplementary Section 3). By spectrally detuning the PHAs, the outcoming polarizationellipticities are modified, thereby resulting in a controlled angular spacing ∆ θ .Based on the SOI of light, our method is versatile and leads to ultracompact plasmonictravelling-wave antennas. Swirling surface plasmons thus provide functionalities that havenever previously been demonstrated. Taken as individual or coupled structures, the PHAsmay pave the way towards highly integrated polarization-encoded optics, particularly forthe generation and control of spin-encoded photon qubits in quantum information andoptical spintronics. They may also enable new polarization-based optical functionalities forsensing or communications, which could include the unique electromagnetic and mechanical7 CP RCPRCP O r i en t a t i ono ft heou t pu t po l a r i z a t i one lli p s e ( deg . ) (c)(a)
500 nm q (°) (d)
500 nm (b) (e) (f) q (°) | | ( ° ) c ( ° ) y | | ( ° ) c ( ° ) y LCP
30 300120 330060 24090 270210150 180L-HelixR-Helix30 300120 330060 24090 270210150 180L-HelixR-Helix18090
Fig. 4.
Subwavelength scale manipulation of light polarization by four coupledPHAs. a,b , Scanning electron micrographs of the device. a , Angled view, b , top view. c , e ,Polarization angles χ and ψ of the emitted field versus the polarization direction of incidentlinearly polarized light (Poincare sphere approach of polarization). The optical waves areimpinging from the substrate at normal incidence with c , λ =1.61 µ m and e , λ =1.47 µ m.Owing to the oscillatory nature of light fields, the full set of incident linear polarizationsis covered with a polarization angle θ ranging from 0 to 180 ◦ . Theoretical predictions areshown as solid lines (see Supplementary Section 3). d , f , Polarization diagram of the antennaemission for incident polarization corresponding to θ equal to 45 ◦ and 135 ◦ , leading to theselective excitation of the two couples of PHAs of opposite handedness: d , λ =1.61 µ m, f , λ =1.47 µ m. Near-field coupling between the PHAs of opposite handedness ensures paralleloutcoming polarization ellipses for orthogonal incident linear polarizations.properties of 3D metal-coated helical wires. Simulations
All the numerical simulations of the antenna emission process are realized using the 3DFDTD method. The plasmonic helix geometry considered in this study consists of a 105nm diameter carbon wire wound up in the form of a four-turn corkscrew-type structure and8overed with a 25 nm thick gold layer. The resulting helix has a 505 nm outer diameter andis 1.66 µ m high. It is positioned on a pedestal considered a 105 nm diameter and 100 nmhigh carbon rod whose cylindrical lateral side is covered with a 25 nm thick gold layer. Thehelix pitch angle is approximately 20.7 ◦ . The helix pedestal lies on a 100 nm thick gold layerdeposited onto a glass substrate. The rectangular aperture nanoantenna, with a width andlength equal to 40 nm and 370 nm, respectively, is engraved in the metal layer. Its centre islocated at x = y = 0. z = 0 corresponds to the upper surface of the gold layer that covers theglass substrate. To excite the PHA, a Gaussian beam (beam waist equal to 1.5 µ m) impingesonto the rectangular aperture nanoantenna at normal incidence from the backside.The spectral response of the PHA is obtained with a Gaussian excitation described bya single temporal pulse. The time-varying electric field is calculated at a single cell locatedon the helix axis, 4 µ m away from the end of the helix, along (0z). The spectra of thevector components E x and E y are calculated by Fourier transforming this result. From theseresults, the ellipticity factor is deduced as a function of the wavelength. The model used forthe spectrum calculations consists of a volume spanning 4.55 µ m in the x and y directionsperpendicular to the longitudinal helix axis. It extends 2 µ m below the gold layer in theglass substrate and terminates 4.3 µ m beyond the top of the helix in air. All six boundariesof the computation volume are terminated with perfectly matched layers to avoid spuriousunphysical reflections around the structure. The non-uniform grid resolution varies from 30nm for portions at the periphery of the simulation to 5 nm within and near the helix andthe aperture nanoantenna.In all the calculations conducted in the continuous wave regime, the wavelength is 1.5 µ m. The distribution of the current amplitude within the helix is plotted by integrating thesimulated optical current density across the gold coating of the helix-shaped carbon wire foreach curvilinear coordinate along the wire. The PHA geometry and mesh grid parametersremain unchanged. The computation volume spans 2.1 µ m in the x and y directions. Itextends 0.75 µ m below the gold layer in the glass substrate and terminates 2.61 µ m beyond9he top of the helix in air. Fabrication
PHAs have been fabricated in three steps using FIBID technology and FIB milling (DualBeam SEM/FIB FEI Helios 600i). A helical carbon skeleton was fabricated by FIBIDonto a commercial 100 nm thick gold film. For operation at 1.63 µ m (experimentally),the geometrical parameters are a pitch angle of approximately 19.8 ◦ , a radius of 155 nmand a pitch length of 350 nm. The structure was covered with a thin smooth layer ofgold sputter-deposited by glancing angle deposition. Then, a 370 nm long and 40 nmlarge rectangular aperture nanoantenna was milled in contact with the helix pedestal (seeSupplementary Fig. 5). Characterization
A schematic diagram of the experimental setup is represented in Supplementary Fig. 7. Itis mounted onto a Nikon TE2000 inverted microscope. Light of tunable wavelength, rangingfrom 1.47 µ m to 1.65 µ m, emerges from a tunable laser source (Yanista Tunics-T100S) andis coupled to a single-mode polarization-maintaining fibre (P3-1500PM-FC-2, Thorlabs). Itis collimated by an achromatic reflective fibre collimator (RC08APC-P01, Thorlabs) andfocused onto the plasmonic structures with either a (25X, 0.4) microscope objective for thestudy of the single PHAs or a (4X, 0.1) objective for the four-coupled PHA structures.Two operation modes of the PHA are here investigated. They involve optical propagationin two opposite directions within the PHAs (Supplementary Fig. 7). In the emission mode, we consider the illumination of the rectangular aperture nanoantenna from the backsideand the emission of circularly polarized light by the helix, whereas the collection modecorresponds to illumination of the helix from the front and emission of linearly polarized lightfrom the rectangular aperture nanoantenna on the backside. Measurement in the collectionmode are performed by inverting the illumination and collections benches in the optical10haracterization set-up.Two parameters of the antennas are here investigated: their polarization diagram inemission mode and their circular dichroism in both emission mode and collection mode(Supplementary Fig. 7). In the former case, the polarization of the incident collimatedwave is manipulated using a fixed polarizer (LPNIR100-MP2) and a half-wave plate(AHWP05M-1600, Thorlabs) positioned in between the collimator and the objective. Thehalf-wave plate is mounted onto a motorized stage (PRM1Z8, Thorlabs) to be accuratelyrotated with respect to the polarizer. The plasmonic structures are imaged with an (50X,0.65) infrared objective from Olympus (LCPlanN) coupled to an infrared camera (GoldEyemodel G-033, Allied Vision Technologies GmbH) and a proper field lens. To analyse thepolarization state of the light emitted by our plasmonic antennas, either a rotating linearpolarizer or a fixed polarizer coupled to a rotating quarter-wave plate (see inset) are insertedin front of the camera (Linear polarizer: LPNIR100-MP from Thorlabs, quarter-wave plate:AQWP05 M-1600 from Thorlabs, motorized stage: UE16CC from Newport). In Fig. 2,the spectra are obtained by analysing the state-of-polarization at each wavelength. Theincident polarization is oriented perpendicularly to the long axis of the rectangular aperturenanoantenna, to excite its fundamental plasmon mode. Right- and left-handed circularanalysers are obtained by orienting the fast-axis of the quarter wave plate at +45 ◦ and -45 ◦ relative to the polarizer axis, respectively. For circular dichroism measurements (Fig. 3),the combination of a linear polarizer and half-wave plate used in the illumination bench isreplaced by a polarizer coupled to a quarter-wave plate (see insets of Supplementary Fig.7). The detection bench consists of an objective, a field lens and a camera.The authors are indebted to Sarah Benchabane for the acquisition of the FIBID module.This work is supported by the Labex ACTION program (contract ANR-11-LABX-01-01),the EIPHI Graduate School (contract ANR-17-EURE-0002), and by the French RENATECHnetwork and its FEMTO-ST technological facility.11 eferences
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1. Helicity and swirling surface plasmons
Supplementary Fig. 8 represents the spectrum of the emission ellipticity factor of four dif-ferent helices showing increasing number of turns. From one to four turns, the measuredmaximum ellipticity factor varies from 0.64 to 0.96, while undergoing spectral redshift. Theenhancement of the ellipticity factor with the number of helix turns evidences the swirlingplasmonic effect in the definition of optical helicity.
2. End-fire excitation of the plasmonic helix
Supplementary Fig. 9 shows that polarization properties of the PHA rely on the end-fireexcitation of its plasmonic helical wire. We studied the emission ellipticity factor of three an-tenna configurations involving three different excitation schemes from a rectangular aperturenano-antenna. The ellipticity factor peaking at a value larger than 0.92 when the aperturenano-antenna is in contact to the helix pedestal drops down to 0.73 when it is removed 185nm away from the helix. When the rectangular nano-aperture antenna is rotated by 90 ◦ ,i.e., when the orientation of its dipolar plasmon mode becomes orthogonal to the radially-polarized wire mode of the plasmonic helix, the ellipticity factor of the PHA emission isreduced to 0.32. The 3D vectorial near-fields produced by the rectangular aperture nanoan-tenna may explain, in the latter case, the non-null coupling between the orthogonal nano-aperture and the helix. These results also show that the subdiffraction plasmonic wire modeof the helix is responsible for the polarization properties of the PHA.
3. Analytical model of the four-coupled PHA structure
The unconventional polarization manipulation of the four-PHA structure (Fig. 4) relies onthe combination of two elliptically polarized waves of opposite handedness, and the control of14heir respective intensities. Such a configuration can be simply modeled by the interferenceof two co-propagating plane waves described by parallel polarization ellipses.Owing to the field projection rules defined by the two pairs of orthogonal aperture nano-antennas, the electric fields E and E of these two waves can take the following form: E = sin( θ − π , ib ,
0) exp [ − i ( ωt − wz )] , (1) E = cos( θ − π , − ib ,
0) exp [ − i ( ωt − wz )] . (2)The two light waves show the same wave vector (0 , , w ) . ( x, y, z ) are the space coordinates, ω is the angular frequency, and t refers to time. b and b are two positive constants smallerthan 1, called ellipticity factors.Circular polarization arises when: E + E = K ( ± , i,
0) exp [ − i ( ωt − wz )] , (3)where K is a constant, thus imposing: tan( θ ) = (cid:12)(cid:12)(cid:12)(cid:12) ± b ∓ b (cid:12)(cid:12)(cid:12)(cid:12) + π , (4)Right and left circular polarizations are then obtained for two specific values of θ that aredependent on the ellipticity factors b and b of the two initial waves.More generally the electric field resulting from the wave combination can be written ( E x , E y ,
0) = sin( θ − π , ib ,
0) + cos( θ − π , − ib , . (5)We can consider this total field as an elliptically polarized wave whose major and minor radiitake respectively the form : a = √ (cid:20) | E x | + | E y | + q | E x | + | E y | + 2 | E x | | E y | cos (2∆ ξ ) (cid:21) , (6) b = √ (cid:20) | E x | + | E y | − q | E x | + | E y | + 2 | E x | | E y | cos (2∆ ξ ) (cid:21) , (7)where ∆ ξ refers to the phase difference between E x and E y [3]. From Eqs. 6 and 7, weanticipated the polarization state of the four-PHA emission, as a function of the projection15ngle θ (Supplementary Fig. 10). We considered the particular case where b = b , i.e., twowaves of identical ellipticities and opposite handedness. When these two waves are circularlypolarized, the angular spacing ∆ θ between right and left polarizations is 90 ◦ . The resultingpolarization manipulation is similar to that of a rotating polarizer in front of quarter-waveplate. In that case, θ refers to the projection angle of an incident linearly polarized waveonto the crystalline axes of the retardation plate.Polarization control deviates from this well-known conventional configuration when weconsider two elliptically polarized waves ( b and b become smaller than 1). Depending onthe ellipticity factor of the two initial waves, the angular spacing ∆ θ between right and leftcircular polarizations decreases down to 53 ◦ when b = b = 0 . and 11.5 ◦ when b = b = 0 . .The four-PHA structure would thus lead to a near-switching effect of circular polarizationhandedness while rotating linear polarization of an incoming light. By implementing thepolarization states shown in Figs. 4(d) and (f) in our model, we found the polarizationmanipulations described by the solid lines of Figs. 4(c) and (e), respectively. References
1. M. Esposito, et al. , Nano Lett. , 5823 (2016).2. J. D. Kraus, R. J. Marhefka, A. S. Khan, Antennas and wave propagation (Tata McGraw-Hill Education, 2006).3. C. Balanis,
Antenna theory: analysis and design (John Wiley & Sons, New-York, 1997).16 a) (b) (c)
500 nm
Fig. 5.
Fabrication of the plasmonic helical antenna (PHA): three steps.
Scanningelectron micrographs of the subwavelength structure after ( A ) fabrication of the carbon helixskeleton by FIBID [1], ( B ) gold deposition onto the helix skeleton, and ( C ) fabrication ofrectangular nano-aperture antenna by FIB milling.17 x0z), =0 f (y0z), =90° f Fig. 6.
PHA emission diagram.
The PHA shows a directional emission perpendicularlyto the (x0y) ground plane of the antenna, thus confirming its axial operation mode [2, 3].18 a) (b)
Fig. 7.
Experimental setup for optical characterization . Measurement of ( A ) the po-larization properties of the PHA in emission mode, and ( B ) the circular dichroism of thestructure in collection mode. The beam splitter does not affect the polarization state ofthe reflected light. BS: Beam Splitter, LP: Linear Polarizer, HWP: Half-Wave Plate, OBJ:Objective, QWP: Quarter-wave plate 19 .5 l (nm) N=4N=3 N=2N=1 E lli p t i c i t y f a c t o r Fig. 8.
Optical helicity while varying number of turns in the helix . Spectrum of theellipticity factor of the PHA emission for single structures with one turn (orange triangles),two turns (green diamonds), three turns (red circles), and four turns (blue squares)20
470 1510 1550 1590 16300.30.50.70.9 l (nm) E lli p t i c i t y f a c t o r Fig. 9.
Circularly polarized emission originates from the excitation of a subd-iffraction surface plasmon within the helix . Spectrum of the polarization ellipticityfactor of the PHA emission for a rectangular nano-aperture antenna in contact to the helixpedestal (blue squares), 185 nm away from the helix pedestal (red circles), and turned by90 ◦ regarding the two first cases (green diamonds).21 | | ( ° ) c ( ° ) y LCP RCP
Projection angle (°) q [1 1i][1 0.5i][1 0.1i] LCP RCP
Fig. 10.
Theoretical anticipation of the unconventional control of light polariza-tion . Prediction of the polarization state of the four-PHA emission (i.e., the polarizationangle | χ | and ψ on the Poincare sphere), as a function of the projection angle θ definingthe PHA emission intensities. Three ellipticity factors are considered: b = b = 1 (bluecurves), b = b = 0 . (red curves) and b = b = 0 .1