Showing papers on "Circular polarization published in 2002"

Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings.

Abstract: We present a novel method for forming radially and azimuthally polarized beams by using computer-generated subwavelength dielectric gratings. The elements were deposited upon GaAs substrates and produced beams with a polarization purity of 99.2% at a wavelength of 10.6 µm. We have verified the polarization properties with full space-variant polarization analysis and measurement, and we show that such beams have certain vortexlike properties and that they carry angular momentum.

A reconfigurable patch antenna using switchable slots for circular polarization diversity

Abstract: A novel design of a microstrip patch antenna with switchable slots (PASS) is proposed to achieve circular polarization diversity. Two orthogonal slots are incorporated into the patch and two pin diodes are utilized to switch the slots on and off. By turning the diodes on or off, this antenna can radiate with either right hand circular polarization (RHCP) or left hand circular polarization (LHCP) using the same feeding probe. Experimental results validate this concept. This design demonstrates useful features for wireless communication applications and future planetary missions.

Formation of helical beams by use of Pancharatnam-Berry phase optical elements.

Abstract: Spiral phase elements with topological charges based on space-variant Pancharatnam-Berry phase optical elements are presented Such elements can be achieved by use of continuous computer-generated space-variant subwavelength dielectric gratings We present a theoretical analysis and experimentally demonstrate spiral geometrical phases for infrared radiation at a wavelength of 106microm

Electrical spin injection in a ferromagnet/tunnel barrier/semiconductor heterostructure

Abstract: We demonstrate experimentally the electrical electron spin injection from a ferromagnetic metal/tunnel barrier contact into a III–V semiconductor light emitting diode (LED). The injected electrons have in-plane spin orientation. By applying a relatively small oblique external magnetic field this spin orientation within the semiconductor can be manipulated to have a nonzero out-of-plane component. By measuring the resulting circular polarization of the emitted light, we observe injected spin polarization in excess of 9% at 80 K in a CoFe/AlOx/(Al,Ga)As/GaAs surface-emitting spin-LED.

Degree of polarization for optical near fields.

Abstract: We investigate an extension to the concept of degree of polarization that applies to arbitrary electromagnetic fields, i.e., fields whose wave fronts are not necessarily planar. The approach makes use of generalized spectral Stokes parameters that appear as coefficients, when the full 3 x 3 spectral coherence matrix is expanded in terms of the Gell-Mann matrices. By defining the degree of polarization in terms of these parameters in a manner analogous to the conventional planar-field case, we are led to a formula that consists of scalar invariants of the spectral coherence matrix only. We show that attractive physical insight is gained by expressing the three-dimensional degree of polarization explicitly with the help of the correlations between the three orthogonal spectral components of the electric field. Furthermore, we discuss the fundamental differences in characterizing the polarization state of a field by employing either the two- or the three-dimensional coherence-matrix formalism. The extension of the concept of the degree of polarization to include electromagnetic fields having structures of arbitrary form is expected to be particularly useful, for example, in near-field optics.

Polarization switching of crystal structure in the nonphotochemical light-induced nucleation of supersaturated aqueous glycine solutions

Abstract: By switching between linear and circular polarization in the irradiation of supersaturated solutions of the amino acid glycine in water with intense nanosecond pulses of near-infrared laser light, we have obtained the gamma and alpha phases, respectively, through nonphotochemical light-induced nucleation (NPLIN). This is the first report of light polarization controlling crystal structure. The intensity dependence of NPLIN in aqueous urea is also reported.

Printed ring slot antenna for circular polarization

Abstract: A new design of a microstrip-line-fed circularly polarized printed ring slot antenna is proposed. Circular polarization (CP) radiation of the proposed design is achieved by introducing proper asymmetry in the ring slot structure and feeding the ring slot using a microstrip line at 45/spl deg/ from the introduced asymmetry. The asymmetry introduced in the proposed design is a meandered-slot section and the proposed CP design can be applied to printed square and annular ring slot antennas. Prototypes of the proposed design have been implemented. Experimental results show that good CP radiation performances are obtained and the 3 dB axial-ratio CP bandwidths obtained for the square and annular ring slot antennas are about 4.3% and 3.5%, respectively.

Comparative study of polarized light propagation in biologic tissues.

Abstract: We report the depolarization of light scattered by a variety of birefringent and nonbirefringent tissues. We used Stokes polarime- try to investigate how scatterer structures in each tissue contribute to the depolarization of linearly versus circularly polarized light propa- gating through that tissue. Experiments were performed on porcine blood, fat, tendon, artery, and myocardium. The results indicate that the two incident polarization states are depolarized differently de- pending on the structure of the sample. As seen in sphere suspensions, for tissues containing dilute Mie scatterers, circularly polarized light is maintained preferentially over linearly polarized light. For more dense tissues, however, the reverse is true. The results illustrate situations where polarized light will provide an improvement over unpolarized light imaging, information that is crucial to optimizing existing pola- rimetric imaging techniques. © 2002 Society of Photo-Optical Instrumentation En-

Measuring magnetic fields of early-type stars with FORS1 at the VLT

Abstract: This paper describes an experiment aimed at evaluating the capability of the FORS1 instrument at the VLT for measuring weak (0.1%) Zeeman circular polarization signatures in stellar H Balmer lines. We have obtained low-resolution polarized spectra at 3500–5800 A of two bright A-type stars, HD 94660, and HD 96441. The former is a well known magnetic star, the latter an apparently non-magnetic, unpolarized star that was observed for comparison purposes. In order to test the possibility of performing multi-object spectropolarimetric measurements (e.g., for cluster studies), observations were taken both on-axis (i.e., at the CCD field center) and off-axis (i.e., at the edges of the CCD). In HD 94660 (the magnetic star), we detected a clear signal of circular polarization in all observed hydrogen Balmer lines (i.e., from Hβ to the Balmer limit), with a typical peak-to-peak amplitude of about 0.8%. From the analysis of Stokes V under the weak-field approximation, we have estimated a mean longitudinal field of G, a value fully consistent with previous studies of this star. Notably, we found that at wavelengths shorter than about 4100 A, the polarization signal detected off-axis is about 20–30% smaller than that detected on-axis. No polarization due to the Zeeman effect was detected in the comparison star HD 96441, and we estimate that the contribution due to instrumental circular polarization is limited to the order of . This experiment demonstrates the effectiveness of FORS1 at the VLT as a tool for high-sensitivity diagnosis of the magnetic field in upper main sequence stars, providing the potential for measuring fields in fainter and more rapidly rotating stars than has previously been possible.

The Spectrum and Variability of Circular Polarization in Sagittarius A* from 1.4 to 15 GHz

Abstract: We report here multiepoch, multifrequency observations of the circular polarization in Sagittarius A*, the compact radio source in the Galactic center. Data taken from the Very Large Array (VLA) archive indicate that the fractional circular polarization at 4.8 GHz was -0.31%, with an rms scatter of 0.13%, from 1981 to 1998, in spite of a factor of 2 change in the total intensity. The sign remained negative over the entire time range, indicating a stable magnetic field polarity. In the summer of 1999, we obtained 13 epochs of VLA A-configuration observations at 1.4, 4.8, 8.4, and 15 GHz. These observations employ a new technique that produces an error of 0.05% at 1.4, 4.8, and 8.4 GHz and 0.1% at 14.9 GHz. In 1999 May, September, and October, we obtained 11 epochs of Australia Telescope Compact Array (ATCA) observations at 4.8 and 8.5 GHz. In all three data sets, we find no evidence of linear polarization greater than 0.1%, in spite of strong circular polarization detections. Both VLA and ATCA data sets support three conclusions regarding the fractional circular polarization: (1) the average spectrum is inverted, with a spectral index α ≈ 0.5 ± 0.2; (2) the degree of variability is roughly constant on timescales of days to years; and (3) the degree of variability increases with frequency. We also observed that the largest increase in fractional circular polarization was coincident with the brightest flare in total intensity. Significant variability in the total intensity and fractional circular polarization on a timescale of 1 hr was observed during this flare, indicating an upper limit to the intrinsic size during outburst of 70 AU at 15 GHz. The fractional circular polarization at 15 GHz reached -1.1%, and the spectral index was strongly inverted (α ~ 1.5) during this flare. We tentatively conclude that the spectrum has two components that match the high- and low-frequency total intensity components.

["Nematic liquid-crystal polarization gratings by modification of surface alignment"]

Abstract: The stylus of an atomic force microscope is used to scribe preferred directions for liquid-crystal alignment on a polyimide-coated substrate. The opposing substrate that comprises the liquid-crystal cell is rubbed unidirectionally, resulting in a twisted nematic structure associated with each micrometer-sized pixel. The polarization of light entering from the uniformly rubbed substrate rotates with the nematic director by a different amount in each pixel, and each of the two emerging polarization eigenmodes interferes separately. Two examples are discussed: a square grating that allows only odd-order diffraction peaks and a grating that combines rotation with optical retardation to simulate a blazed grating for circularly polarized light. The gratings can be electrically switched if used with semitransparent electrodes.

Circular polarization of radio emission from relativistic jets

Abstract: In inhomogeneous optically thick synchrotron sources a substantial part of the electron population at low energies can be hidden by self-absorption and overpowered by high energy electrons in optically thin emission. These invisible electrons produce Faraday rotation and conversion, leaving their footprints in the linear and circular polarized radiation of the source. An important factor is also the magnetic field structure, which can be characterized in most cases by a global magnetic field and a turbulent component. We present the basic radiative transfer coefficients for polarized synchrotron radiation and apply them to the standard jet model for relativistic radio jets. The model can successfully explain the unusual circular and linear polarization of the Galactic Centre radio source Sgr A* and its sibling M 81*. It also can account for the circular polarization found in jets of more luminous quasars and X-ray binaries. The high ratio of circular to linear polarization requires the presence of a significant fraction of hidden matter and low-energy electrons in these jets. The stable handedness of circular polarization requires stable global magnetic field components with non-vanishing magnetic flux along the jet, while the low degree of total polarization implies also a significant turbulent field. The most favoured magnetic field configuration is that of a helix, while a purely toroidal field is unable to produce significant circular polarization. If connected to the magnetosphere of the black hole, the circular polarization and the jet direction determine the magnetic poles of the system which is stable over long periods of time. This may also have implications for possible magnetic field configurations in accretion flows.

Doppler Imaging of stellar magnetic fields. II. Numerical experiments

Abstract: We present numerical experiments designed to evaluate the performance of the new Magnetic Doppler Imaging (MDI) code INVERS10. Numerous test runs demonstrate what can be achieved with the MDI method and allow assessment of the systematic errors that can cause distortions of the maps. Our numerical experiments showed that given high-resolution observations in four Stokes parameters the code is capable of reconstructing abundance and magnetic field vector distributions simultaneously and without any prior assumptions about the magnetic field geometry. At the same time we found that in order to achieve reliable reconstruction using only circular polarization data it is necessary to impose additional constraints on the possible structure of the magnetic field. Numerical tests also reveal surprisingly different properties of the MDI maps from conventional scalar maps which we attribute to the complex relation between the orientation of the field and the polarization signal. We conclude that the information about the field is primarily extracted from the changes in magnetic orientation due to rotation rather than from the Doppler shifts critical for scalar Doppler Imaging maps making it possible to apply the MDI to even very slow rotators.

Circular Polarization from Stochastic Synchrotron Sources

Abstract: The transfer of polarized radiation in stochastic synchrotron sources is explored by means of analytic treatment and Monte Carlo simulations. We argue that the main mechanism responsible for the circular polarization properties compact synchrotron sources is likely to be Faraday conversion and that, contrary to common expectation, a significant rate of Faraday rotation does not necessarily imply strong depolarization. The long-term persistence of the sign of circular polarization, observed in many sources, is most likely due to a small net magnetic flux generated in the central engine, carried along the jet axis and superimposed on a highly turbulent magnetic field. We show that the mean levels of circular and linear polarizations depend on the number of field reversals along the line of sight and that the gradient in Faraday rotation across turbulent regions can lead to correlation depolarization. Our model is potentially applicable to a wide range of synchrotron sources. In particular, we demonstrate how our model can naturally explain the excess of circular over linear polarization in the Galactic center and the nearby spiral galaxy M81 and discuss its application to the quasar 3C 279, the intraday variable blazar PKS 1519-273, and the X-ray binary SS 433.

Circular polarization of water masers in the circumstellar envelopes of late type stars

Abstract: We present circular polarization measurements of circumstellar H2O masers. The magnetic fields in circumstellar envelopes are generally examd. by polarization observations of SiO and OH masers. SiO masers C probe the high temp. and d. regime close to the central star. OH masers are found at much lower densities and temps., generally much further out in the circumstellar envelope. The circular polarization detected in the (616-523) rotational transition of the H2O maser can be attributed to Zeeman splitting in the intermediate temp. and d. regime. The magnetic fields are derived using a general, LTE Zeeman anal. as well as a full radiative transfer method (non-LTE), which includes a treatment of all hyperfine components simultaneously as well as the effects of satn. and unequal populations of the magnetic substates. The differences and relevances of these interpretations are discussed extensively. We also address a non-Zeeman interpretation as the cause for the circular polarization, but this is found to be unlikely. We favor the non-LTE anal. The H2O masers are shown to be unsatd., on the basis of their line widths and the lack of linear polarization. The field strengths are compared with previous detections of the magnetic field on the SiO and OH masers. Assuming a r-2 dependence of the magnetic field on the distance to the star, similar to a solar-type magnetic field, our results seem to indicate that we are probing the highest d. maser clumps at the inner edge of the H2O maser region. This allows us to est. the d. of the clumps, and the extent of the H2O maser region. We show that the magnetic pressure dominates the thermal pressure by a factor of 20 or more. We also give an order of magnitude est. of the magnetic field on the surface of the stars. In particular we discuss the differences between supergiants and Mira variable stars. [on SciFinder (R)]

Scattering and Absorption by Aligned Grains in Circumstellar Environments

Abstract: We present radiative transfer calculations showing the polarization effects of scattering and absorption by aligned grains. The grain model consists of a size distribution of oblate or spinning prolate particles with varying degrees of alignment. To develop an understanding of the radiative transfer effects, we begin with the simple case of a spherical envelope illuminated by a central source with constant grain alignment axis throughout the envelope. Nonaligned grains produce no net polarization in such envelopes, while aligned grains produce substantial linear and circular polarization. The linear polarization results from the competing effects of differential extinction and scattering. The polarization varies strongly with optical depth, with scattering dominating at low optical depth and differential extinction dominating at high optical depth. The net, or integrated, circular polarization from the envelopes is zero; however, the circular polarization across the resolved nebula is large, reaching ±50% in the "diagonal" regions of the nebula. Next we calculate axisymmetric models of protostellar envelopes, again with the simplifying case of constant grain alignment axis throughout the envelope. The polarization maps show differences from the case of nonaligned grains, especially in the disk midplane, where differential extinction of even the scattered light causes the polarization vectors to align perpendicular to the disk plane, in contrast to many observations. This suggests either that grains are not aligned in protostellar envelopes or that the magnetic field (the presumed alignment mechanism) is not aligned along the disk rotational axis throughout the envelope and disk. A definitive test of grain alignment could come from resolved circular polarization maps of protostars. Aligned grains produce large values of circular polarization across the cloud, up to ±25%-40% in the models presented here, whereas nonaligned grains produce maximum polarizations of less than 1%. In objects with aligned grains, analysis of linear and circular polarization maps can probe magnetic geometries.

OH masers and magnetic fields in the bipolar outflow source W75N

Abstract: MERLIN polarization measurements of 1665-,1667- and 1720-MHz OH masers in the bipolar outflow source W75N are presented. The OH masers are distributed over a region 5 arcsec across (10 000 au at 2 kpc), which is elongated in a north-west‐ south-east (NW ‐SE) direction. The distribution is interpreted in terms of a rotating disc orthogonal to the bipolar outflow that is seen in CO and H2. A compact cluster of OH masers with a large velocity spread appears to mark the source of the outflow. Most of the OH masers detected have strong circular polarization up to 100 per cent. Seven Zeeman groups are identified, including the first example of a complete Zeeman triplet (two s-components and one p-component). The field strength measured from Zeeman pairs of opposite circular polarization ranges from 2 8 toa 8 mG, with a field reversal on opposite sides of the disc. This is interpreted in terms of a toroidal component of the magnetic field in the disc. Linear polarization is also detected in many of the OH masers with some 1665-MHz masers showing up to 100 per cent linear polarization. The polarization position angles are preferentially along the direction of the bipolar outflow or perpendicular to it. The polarization data lend support to the twisted magnetic field model originally proposed by Uchida & Shibata.

Dual-band quadrifilar helix antenna

Abstract: Resonant quadrifilar helix antennas are widely used on hand-held receivers for GPS (Global Positioning System) and for some mobile communication systems. The paper investigates a quadrifilar helix antenna over a ground plane and with trap loading. A model of this antenna was built to operate at two frequency bands, 1227 MHz and 1575 MHz, with more than 2% bandwidth in each band. The four wires of the helix were created using narrow copper strips on a flexible mylar sheet that is then rolled into a cylinder to form the helix. The trap circuit is placed across the gap in each strip. To obtain anti-resonance at the higher frequency, the trap circuit values are 6.8 nH and 1.5 pF. The four arms of the helix are attached to a base plate whose diameter is chosen to reflect the energy from the helix while still maintaining coverage for angles just below the horizon, a cardioid pattern. Examples of the right-hand circular polarization elevation plane patterns measured at those two frequencies are shown. The input match for the antenna is illustrated by an overlay of the reflection coefficients at the input to each of the four arms of the helix.

Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media.

Abstract: The polarization properties of light scattered in a lateral direction from turbid media were studied. Polarization modulation and synchronous detection were used to measure, and Mueller calcu- lus to model and derive, the degrees of surviving linear and circular polarization and the optical rotation induced by turbid samples. Poly- styrene microspheres were used as scatterers in water solutions con- taining dissolved chiral, racemic, and achiral molecules. The preser- vation of circular polarization was found to exceed the linear polarization preservation for all samples examined. The optical rota- tion induced increased with the chiral molecule concentration only, whereas both linear and circular polarizations increased with an in- crease in the concentrations of chiral, racemic, and achiral molecules. This latter effect was shown to stem solely from the refractive index matching mechanism induced by the solute molecules, independent of their chiral nature. © 2002 Society of Photo-Optical Instrumentation Engineers.

Polarizer and microlithography projection system with a polarizer

Abstract: A polarizer suitable for transforming incident linearly polarized or circularly polarized light into exiting radially or tangentially polarized light with virtually no transmission losses has, in one of its embodiments, a plate fabricated from birefringent material on whose entrance and exit faces small zones ( 11, 12 ) with deflecting structures ( 8, 9 ) in the form of gratings or Fresnel surfaces have been created. The crystal axis ( 5 ) of said birefringent material is aligned parallel to the incident light beam. Said deflecting structures deflect light along a transmission direction ( 13 ) that is inclined with respect to said crystal axis ( 5 ), causing a phase shift between the field components of the transmitted light. Suitable choices of the angle of inclination (NW) of said transmission direction with respect to said crystal axis and the thickness (D) of said plate will allow transforming incident linearly polarized or circularly polarized light into an exiting light beam with an axisymmetric (tangential or radial) polarization distribution.

Symmetry-breaking instability of multimode vector solitons.

Abstract: We show experimentally that the two-component multimode spatial optical vector soliton, i.e., a two-hump self-guided laser beam, exhibits in Kerr media a sharp space-inversion symmetry-breaking instability. The experiment is performed in a CS2 planar waveguide using the orthogonal circular polarization states of light as the two components of the vector soliton.

Polarization-sensitive optical spectral interferometric coherence tomography apparatus and measuring method for polarization information inside sample by the same

Abstract: PROBLEM TO BE SOLVED: To verify fine structures including birefringence distribution which has not been acquired by a conventional OCT (optical coherence tomography) measurement in the measurement of cross-sectional structures of biosamples including the birefringence distribution such as fish bones and human skin. SOLUTION: The sate of reference light and the state of object light are each selectively regulated into any one of the four ways of horizontal linear polarized light, vertical linearly polarized light, 45° linearly polarized light, and right-handed circularly polarized light. Each state of polarized light is combined by a beam splitter 10 into sixteen-way combinations of four by four, and is passed through a spectroscope having a diffraction grating 20 and lenses. Its interference fringes are photographed by a CCD camera 22 to acquire sixteen coherence tomographic images. By determining each element of the Mueller matrix capable of displaying the polarization characteristics of the sample from the sixteen coherence tomographic images, the polarization information inside the sample is measured. COPYRIGHT: (C)2004,JPO

Zeeman tomography of magnetic white dwarfs - I. Reconstruction of the field geometry from synthetic spectra

Abstract: We have computed optical Zeeman spectra of magnetic white dwarfs for field strengths between 10 and 200 MG and eective temperatures between 8000 and 40 000 K. They form a database containing 20 628 sets of flux and circular polarization spectra. A least-squares optimization code based on an evolutionary strategy can recover relatively complex magnetic field topologies from phase-resolved synthetic Zeeman spectra of rotating magnetic white dwarfs. We consider dipole and quadrupole components which are non-aligned and shifted o-centre. The model geometries include stars with a single high-field spot and with two spots separated by90. The accuracy of the recovered field structure increases with the signal-to-noise ratio of the input spectra and is significantly improved if circular polarization spectra are included in addition to flux spectra. We discuss the strategies proposed so far to unravel the field geometries of magnetic white dwarfs.

Beamwidth enhancement of a circularly polarized microstrip antenna mounted on a three-dimensional ground structure

Abstract: By mounting a regular circularly polarized microstrip antenna on a three-dimensional (3-D) square ground structure, beamwidth enhancement of the circular polarization (CP) radiation can be obtained. Experimental results show that, owing to the 3-D square ground structure, the 3 dB beamwidth of the CP radiation can reach more than 110°, which is about 30° greater than that of a corresponding regular microstrip antenna. Details of the proposed 3-D square ground structure are described, and the effects of various dimensions of the proposed square ground structure on the beamwidth enhancement of CP radiation are experimentally studied. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 149–153, 2002.

Zeeman tomography of magnetic white dwarfs, I. Reconstruction of the field geometry from synthetic spectra

Abstract: We have computed optical Zeeman spectra of magnetic white dwarfs for field strengths between 10 and 200MG and effective temperatures between 8000 and 40000K. They form a database containing 20628 sets of flux and circular polarization spectra. A least-squares optimization code based on an evolutionary strategy can recover relatively complex magnetic field topologies from phase-resolved synthetic Zeeman spectra of rotating magnetic white dwarfs. We consider dipole and quadrupole components which are non-aligned and shifted off-centre. The model geometries include stars with a single high-field spot and with two spots separated by approx. 90 degrees. The accuracy of the recovered field structure increases with the signal-to-noise ratio of the input spectra and is significantly improved if circular polarization spectra are included in addition to flux spectra. We discuss the strategies proposed so far to unravel the field geometries of magnetic white dwarfs.

Coherent control of an optically injected ballistic spin-polarized current in bulk GaAs

Abstract: We demonstrate coherent all-optical injection and control of a ballistic spin-polarized current in bulk, low-temperature-grown GaAs at room temperature. The spin current is injected by interfering the two-photon absorption of the fundamental (1.55 μm) and the single photon absorption of the second harmonic (0.775 μm) of ∼180 fs pulses that propagate collinearly and have the same circular polarization. Adjusting the relative phase of the two pulses controls the direction of this current. The component of the electrical current transverse to the pulse propagation direction is investigated by monitoring charge collection across a pair of gold electrodes deposited on the GaAs surface. Results are in agreement with recent theoretical predictions.

Spectral signature of magnetic flux tubes in sunspot penumbrae

Abstract: We study the polarization of spectral lines in the penumbra by integrating the radiative transfer equation of polarized light for a three-dimensional model atmosphere of a sunspot. In this model, the Evershed flow is confined to magnetic flux tubes which are embedded in a static background atmosphere, in accordance with the moving tube model of Schlichenmaier et al. (1998a,b). The gradients and/or discontinuities in the fluid velocity and the magnetic field at the flux tube boundaries give rise to asymmetric Stokes profiles. We concentrate on the Stokes-V profiles and study the net circular polarization (NCP) of two photospheric spectral lines of neutral iron, Fe I 630.25 nm and Fe I 1564.8 nm. The dierent behavior of these two lines, which are exemplary for atomic spectral lines with a large Lande factor and significantly dierent wavelength, is based on the dierence in excitation potential of the corresponding atomic transitions and the fact that the wavelength dependence of the Doppler shift is linear, while that of the Zeeman splitting is quadratic. We find that the azimuthal variation of the NCP,N( ), is a predominantly antisymmetric function of with respect to the line connecting disk center and spot center (line-of-symmetry) for the infrared line of Fe I 1564.8 nm, while the variation is predominantly symmetric for Fe I 630.25 nm. We show that the antisymmetric variation is caused by anomalous dispersion (Faraday pulsation) and the discontinuity in the azimuthal angle of the magnetic field, which is due to the relative inclination between flux tube and background field. We then compute synthetic NCP maps of a sunspot and compare them with observational results. Finally, the center-to-limb variation of the NCP,N(), of these spectral lines is investigated. We show that the location of the zero-crossing point ofN() on the center side of the line-of-symmetry represents a diagnostic tool to determine the inclination angle of the Evershed flow: A vanishing NCP on the center-side of the line-of-symmetry is an indirect evidence of downflows in the penumbra.