Faraday Rotation Angle Research Articles

Landau levels and magneto-optical transport properties of a semi-Dirac system

We study magneto-optical (MO) properties of a semi-Dirac system in presence of a perpendicular magnetic field using kernel polynomial method (KPM) based on the Keldysh formalism in few hundreds of the terahertz (THz) frequency regime. For the semi-Dirac case, the band structure demonstrates a linear (Dirac-like) dispersion along the $y$ direction, while it has a quadratic (nonrelativistic) behavior along the $x$ direction in the Brillouin zone. For comparison, we have also included results for the Dirac systems as well, so that the interplay of the band structure deformation and MO conductivities can be studied. We have found that the MO conductivity shows features in the semi-Dirac system that are quite distinct from the Dirac case in the above mentioned frequency regime. The real parts of the longitudinal MO conductivities, namely $\mathrm{Re}({\ensuremath{\sigma}}_{xx})$ and $\mathrm{Re}({\ensuremath{\sigma}}_{yy})$ (which are different in the semi-Dirac case, as opposed to a Dirac one), present a series of resonance peaks as a function of the incident photon energy. We have also found that the absorption peaks corresponding to the $y$ direction are larger (roughly one order of magnitude) than those corresponding to the $x$ direction for the semi-Dirac case. In the case of the MO Hall conductivity, that is, $\mathrm{Re}({\ensuremath{\sigma}}_{xy})$, there are extra peaks in the spectra compared to the Dirac case, which originate from the distinct optical transitions of the carriers from one Landau level to another. These peaks are otherwise absent in a Dirac system, where some of these peaks result from transitions between pairs of Landau levels that differ by the same energy and hence those peaks can not be resolved. We have also explored how the carrier concentration influences the MO conductivities. In the semi-Dirac case, there is the emergence of additional peaks yet again in the absorption spectrum underscoring the presence of an asymmetric dispersion compared to the Dirac case. Further, we have explored the interplay between the polarization of the incident beam and the features of the absorption spectra, which can be probed in experiments. Finally, we evaluate the MO activity of the medium by computing the Faraday rotation angle ${\ensuremath{\theta}}_{F}$. The semi-Dirac case shows two maxima and two minima of ${\ensuremath{\theta}}_{F}$ at different photon energies, which can be captured in experiments.

Comparative study of Faraday rotation spectra of periodic and Fibonacci multilayer structures containing graphene sheets

In this paper, the transmission, Faraday rotation, and ellipticity spectra of the multilayered structures with the arrangement of the periodic and fifth-order Fibonacci sequence have been numerically studied in the THz frequency region. The building blocks of the structures are a graphene sheet on the SiC layer (G-SiC), and a SiO2 layer. An external magnetic field is perpendicularly applied to the structures to induce the gyrotropic characteristics of the graphene sheets. The graphene sheets are considered as the thickness-less surfaces, and the 4 by 4 transfer matrix method has been utilized to study the mentioned spectra for TM and TE polarizations. The effects of incident angles have been investigated on the responses of the structures. The results revealed that the Fibonacci structure indicates a high Faraday rotation angle at around 11 THz. This property originates from the particular arrangement of the constituting layers of the Fibonacci structure.

Giant enhancement of Faraday rotation in Weyl semimetal assisted by optical Tamm state

Faraday rotation effect possesses a broad range of applications in the design of non-reciprocal optical devices, such as optical isolators and circulators. By introducing conventional magneto-optical materials into resonant micro-structures, the Faraday rotation effect can be greatly enhanced. Nevertheless, the realization of giant Faraday rotation in micro-structure requires a strong external magnetic field. In this letter, we propose a heterojunction structure composed of a one-dimensional photonic crystal and a Weyl semimetal (WSM) layer to realize giant Faraday rotation without requiring an external magnetic field. Assisted by the optical Tamm state supported by the heterojunction structure, the Faraday rotation angle is greatly enhanced to −40.4 degrees and the transmittance still reaches 57.4%. This giant Faraday rotation effect in simple multilayer structure would possess potential applications in the design of compact non-reciprocal optical devices, such as optical isolators and circulators.

Polarimetric radar interferometry in the presence of differential Faraday rotation

Faraday rotation (FR) affects the low-frequency transionospheric radar by creating cross-talk between polarizations. The baseline part of FR can be compensated for by applying an appropriate linear transformation—rotation with a known FR angle. Yet the differential Faraday rotation (dFR), which is a frequency-dependent part of FR, persists and introduces distortions into the observations. We build a simplified model with two polarimetric scattering channels that allows us to evaluate the effect of dFR on the accuracy of PolInSAR reconstruction. We also assess the severity of distortions due to dFR for the future BIOMASS mission and several other spaceborne radar systems.

Large magneto-optical effect and magnetic anisotropy energy in two-dimensional metallic ferromagnet Fe3GeTe2

The recent discovery of long-range magnetic orders in atomically thin semiconductors ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ and $\mathrm{Cr}{\mathrm{I}}_{3}$ as well as metal ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ has opened up exciting opportunities for fundamental physics of two-dimensional (2D) magnetism and also for technological applications based on 2D magnetic materials. To exploit these 2D metallic magnets, the mechanisms that control their physical properties should be well understood. In this paper, based on systematic first-principles density functional theory calculations, we study the magnetic anisotropy energy (MAE) and magneto-optical (MO) effects of ferromagnetic multilayers [mono-, bi-, tri-, tetra-, and pentalayer] and bulk ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ as well as their connections with the underlying electronic structures of the materials. Firstly, all the considered ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ structures are found to prefer the out-of-plane magnetization and have gigantic MAEs of $\ensuremath{\sim}3.0$ meV/f.u. This gigantic perpendicular anisotropy results from the large magnetocrystalline anisotropy energy (MCE), which is ten times larger than the competing magnetic dipolar anisotropy energy. The giant MCEs are attributed to the large Te ${p}_{x,y}$ orbital density of states near the Fermi level and also to the topological nodal point just below the Fermi level at the K points in the Brillouin zone. Secondly, 2D and bulk ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ also exhibit strong MO effects with their Kerr and Faraday rotation angles being $\ensuremath{\sim}1.{0}^{\ensuremath{\circ}}$ and $\ensuremath{\sim}100 \mathrm{deg}/\ensuremath{\mu}\mathrm{m}$ in the visible-light frequency region, respectively. The strong MO Kerr and Faraday effects are found to result from the large MO conductivity (or strong magnetic circular dichroism) in these ferromagnetic materials. In particular, the calculated MO conductivity spectra are one order of magnitude larger than that of ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$. The calculated MO conductivity spectra are analysed in terms of the dipole-allowed optical transitions at high symmetry $\mathrm{\ensuremath{\Gamma}}$, K, and ${\mathrm{K}}^{\ensuremath{'}}$ points, which further indicate that atomically thin ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ films with odd layer-number might exhibit anomalous ferrovalley Hall effect. All these interesting findings thus suggest that 2D and bulk ferromagnetic ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ are promising materials for high-density MO and spintronic nanodevices.

Magneto-optical and fluorescence properties of Tb3+ doped glass-ceramics containing AlPO4

In this paper, Tb3+ doped AlPO4 magneto-optical glass-ceramics were prepared by traditional melt quenching process and heat treatment techniques. The crystal structural, morphology, magneto-optical and fluorescence properties were systematically characterized via X-ray diffraction (XRD), projection Electron Microscope (STEM), Faraday rotation Angle test, photoluminescence spectra and fluorescence decay time. The transmittance curve shows that the visible light transmittance can reach 78% at least. Magneto-optical properties of Tb3+ doped magneto-optical glass-ceramics were studied. When the incident wavelength is 633 nm, the 27B2O3-23GeO2-20Al2O3-28Tb2O3-2P2O5 glass is heat-treated for 15h, the Verdet constant reaches -118.31 rad/(T•m), the transmission rate is 81%. In addition, the luminous intensity of the prepared glass-ceramics decreases with the growth of AlPO4 crystallites. According to the CIE coordinate chart, all the coordinates are in the green range, and the chromaticity coordinates do not change significantly with the heat treatment time, indicating that the glass-ceramics prepared in this study have excellent luminescence stability.

Large Faraday effect in nanogranular films with a high refractive index matrix

Nanogranular films consisting of a complex of nanometer-sized magnetic granules and a dielectric insulator matrix exhibit a large Faraday rotation. In this study, the dielectric tensor of the nanogranular films with high refractive silicon nitride matrix are measured, and the effect of refractive index of the matrix and magnetic granules on the dielectric tensor is analyzed. Compared with the fluoride (low refractive index) matrix nanogranular films, the Faraday rotation angle is approximately two times higher in the nanogranular FeCo-SiN film, which exhibits a high refractive index effect on the Faraday rotation angle.

Correcting the FRA Systematic Error in VTEC Maps From SMOS Radiometric Data

The Faraday Rotation (FR) is a non-negligible effect at the L-band, which is the operation frequency of the Soil Moisture and Ocean Salinity (SMOS) mission. This effect introduces a rotation in the electromagnetic field polarization when propagating through the ionosphere that must be compensated. Recently, a methodology was developed in order to retrieve the Vertical Total Electron Content (VTEC) from SMOS radiometric data with the aim to better correct the Faraday rotation effect [1]. In that work, systematic patterns in the retrieved Faraday Rotation Angle (FRA) were detected. In this paper, these systematic patterns are characterized and corrected to improve the quality of the retrieved VTEC maps. These maps can be then re-used in the SMOS level 2 processor for the correction of the FRA in the mission. The impact of using the SMOS-derived VTEC maps instead of the VTEC data from GPS measurements on the ocean brightness temperature measurement has also been analyzed. Results of this analysis show that the usage of those maps allows a significant enhancement in the quality of the brightness temperatures, which will lead to an improvement on salinity retrievals.

Temperature Compensation of Optical Fiber Current Sensors With a Static Bias

Temperature cross-sensitivity is the main obstacle to the practical application of fiber current sensors based on the garnet crystal Faraday rotator. In this paper, a temperature compensation method is proposed and experimentally demonstrated. By introducing an appropriate static bias to the sensor, temperature compensation can be realized by simply measuring the Faraday rotation angles of the total field and the bias field. Experimental results show that the maximum relative error of the sensor is reduced from ±8.0% to ±2.0% in the temperature range of −20 °C to 60 °C after the application of the proposed method. After the correction of the nonlinearity of the Faraday crystal, the error is further reduced to be within ±1.0% in the whole temperature range. In common environmental temperature range, the maximum relative variation is within about ±0.5%. With the proposed method, AC signals can be continuously measured with temperature compensation in real-time. The fiber sensor with the proposed method can be used for metering or protection purpose in high-voltage power transmission systems.

Nonlinear Faraday effect and spin noise in rare-earth activated crystals

The spin-noise spectroscopy (SNS) method implies high efficiency of conversion of the spin-system magnetization to the Faraday rotation angle. Generally, this efficiency cannot be estimated using the characteristics of the regular magneto-optical activity of a paramagnet. However, it may be drastically enhanced in systems with strong inhomogeneous broadening of the optical transitions. This enhancement leads to the giant spin-noise gain effect and previously allowed one to apply the SNS to rare-earth-activated crystals. We show that the nonlinear resonant Faraday effect can be used to measure the homogeneous width of the inhomogeneously broadened transition and, thus, to estimate the applicability of the SNS to this type of paramagnet. We present the theoretical description of the effect and perform measurements on intraconfigurational ($4f$-$4f$) transitions of the trivalent rare-earth ions of neodymium and ytterbium in fluorite-based crystals. The proposed experimental approach establishes new links between the effects of nonlinear optics and spin-noise characteristics of crystals with paramagnetic impurities and offers new ways of research in the physics of impurity crystals.

Pulsed vapor cell atomic clock with a differential Faraday rotation angle detection.

Laser intensity noise is one of the main limiting factors in pulsed vapor cell clocks. To reduce the contribution of the laser intensity noise to detection signal in the pulsed optically pumped atomic clock, a scheme based on the differential Faraday rotation angle is proposed. Theoretically, the Ramsey fringes, the sensitivity of clock frequency to laser intensity fluctuation and the signal to noise ratio for absorption, differential, and Faraday rotation angle methods are calculated and compared. Using a Wollaston prism rotated 45°relative to the incident polarization, and two photodetectors, Ramsey fringes of three detection methods are obtained simultaneously. In the proposed scheme, the long-term Faraday rotation angle fluctuation is 0.66% at 30000s, which is much smaller than fluctuation of traditional absorption signal 3.9% at 30000s. And the contribution of laser intensity noise to clock instability is also reduced. Using optimized photodetector with high common mode rejection ratio, a better performance should be expected. This proposed scheme is attractive for the development of high performance vapor clock based on pulsed optically pumped.

Liquid phase epitaxy growth of (GdYbBi)3(FeGe)5O12 films for magneto-optical applications

As an important component in magneto-optical devices, bismuth-substituted rare-earth iron garnet films play a significant role in guarantying a unidirectional light propagation in optical communication system. In this study, (GdYbBi)3(FeGe)5O12 film with a thickness of 120 μm was successfully grown by liquid phase epitaxy (LPE) technology. Lattice mismatch and internal stress between the epitaxial film and substrates were discussed in detail. Tested results shown that (GdYbBi)3(FeGe)5O12 films exhibit high crystal quality and large specific faraday rotation angle, which indicate that the prepared (GdYbBi)3(FeGe)5O12 films have a great potential to be used in optical communication system.

Edge-defined film-fed growth of incongruent-melting Ce,Ga:GIG crystal with high magneto-optical performance

Ce-doped Gd3Fe5O12 (GIG) crystals, which are a kind of incongruent melting compound, were successfully grown into centimeter size and good quality by an improved edge-defined film-fed growth (EFG) method. Annealing has obviously affected crystal quality, optical transmittance and saturation magnetization. Doping Ce3+ ions greatly enhances the magnetic-optical properties of GIG crystals. For Ce:GIG crystal, a suitable concentration of Ga3+ ion replacing Fe3+ is helpful to improve its magneto-optical properties. The specific Faraday rotation angle of (Ce0.35Gd2.65)(Ga1.04Fe3.95V0.01)O12 crystal is great and reaches 896 Deg. cm−1 that meets commercial requirements.

Faraday rotator made of conjugated magneto active photonic crystal heterostructures

Two defective conjugated magneto active photonic crystals are proposed in this paper for fabrication of Faraday rotators. Optical features of the suggested structures are studied using 4 × 4 transfer matrix method and taking into consideration of the couplings of polarization states. Band structure of the crystals including generation of stop bands and resonant modes localizations are studied by exploring the dependence of the crystals' transmittance on the period number of the layers. It is shown that desirable responses are obtained by just very low number of periods. Furthermore, optical anisotropy of the crystals is considered to be purely magnetic field-induced. Then in addition to studying the dependencies on structural parameters, connection between wave incident angle and magneto-optical effects (Faraday rotations and changes of the ellipticity angle) are discussed in detail. Results clearly show the ease of tunability of the structures' responses in this way which is of prime importance from experimental point of view. Furthermore, the proposed structures offer remarkable Faraday rotation angles when transmittance amounts remain high enough simultaneously. Thus it seems that these crystals might be useful for fabrication of polarization dependent sensor/transducers based on Faraday rotators which are vital elements in development of integrated circuits as well as imaging systems.

Terahertz magneto-optical response of bismuth-gadolinium-substituted rare-earth garnet film.

We report the magneto-optical Faraday response of bismuth-gadolinium-substituted rare-earth iron garnet at terahertz frequencies ranging from 100 GHz to 1.2 THz. The maximum transmittance of ±45° component is about 60% near the frequency point of 0.63 THz. When the external magnetic field change from -100 mT to +100 mT, the Faraday rotation angle is between -6° and +7.5°. The overall change of ellipticity is relatively small. The maximum value of the Verdet constant is about 260 °/mm/T at 0.1 THz and then gradually decreases to 80 °/mm/T at 1.2 THz. Within the considered frequency range, the thick film exhibits magnetically tunable, non-reciprocal characters and a strong magneto-optical effect within a small external magnetic field at room temperature, which will be widely used for the terahertz isolators, circulators, nonreciprocal phase shifters, and magneto-optical modulators.

Preliminary analysis of experimental cross-polarization images from polarimetric aircraft synthetic aperture radar of P-band

An analysis of polarimetric synthetic aperture radar (SAR) space observations usage for measuring Faraday rotation angle of plane-polarized electromagnetic radiation on the satellite-Earth-satellite route and calibrating the radar is performed. It is shown that technical characteristics of SAR, the radar movement during the survey and features of electromagnetic waves reflection from the rough Earth’s surface, as well as small-scale ionospheric inhomogeneities affect the results of comparison the radar images at HV and VH cross-polarizations. As a result, there is a problem of SAR signal polarization plane Faraday rotation angle measuring accuracy, which is needed for proper calibration of linearly polarized polarimetric long-wave band SAR using methods proposed by soviet and foreign specialists. Currently, there are no studies of Earth’s surfaces reflection properties carried out by means of space-based long-wave band polarimetric synthesized aperture radars at HV and VH polarizations. At the same time, the authors are not aware of any works, in which the reciprocity principle of cross-polarized HV and VH radar images is analyzed. An attempt to use aircraft P-band radar images at HV and VH polarizations for studying the reciprocity principle is performed in this work.

Magneto-optical properties of borophosphate glasses co-doped with [formula omitted] and [formula omitted]ions

Glasses from lithium-aluminum-zinc-boron-phosphorous oxide system co-doped with terbium (Tb3+) and dysprosium (Dy3+) oxides were studied for magneto-optical applications in lasers. The Fourier Transform Infrared and Raman Spectroscopy complementary analysis suggested the depolymerization of the boro-phosphate glass network by adding and increasing the rare-earth (RE) oxide content. Main UV–vis absorption maxima of Tb and Dy ions were identified at 348 and 1266 nm. Spectroscopic ellipsometry indicated a maximum refractive index of 1.56, at 400 nm, for the highest RE content. The Verdet constant amplified by increasing the RE content, reaching for the 9 mol% RE co-doped sample a value of -0.075 min/Oe/cm at 630 nm. The Faraday rotation angle was additionally confirmed by using a Faraday Cell Device, being also related to the specific paramagnetic behavior evidenced by Superconducting Quantum Interference Device magnetometry. The magneto-optical properties recommend such vitreous co-doped materials for magneto-optical devices.

Terahertz optical Hall effect in p-type monolayer hexagonal boron nitride on fused silica substrate.

We demonstrate for the first time, to the best of our knowledge, that the optical Hall effect (OHE) can be observed in p-type monolayer (ML) hexagonal boron nitride (hBN) on a fused silica substrate by applying linearly polarized terahertz (THz) irradiation. When ML hBN is placed on fused silica, in which the incident pulsed THz field can create local and transient electromagnetic dipoles, proximity-induced interactions can be presented. The Rashba spin-orbit coupling can be enhanced, and the in-plane spin component can be induced, along with the lifting of valley degeneracy. Thus, in the presence of linearly polarized THz radiation, the nonzero transverse optical conductivity (or Hall conductivity) can be observed. We measure the THz transmission through ML hBN/fused silica in the temperature range from 80 to 280 K by using THz time-domain spectroscopy in combination with an optical polarization examination. The Faraday ellipticity and rotation angle, together with the complex longitudinal and transverse conductivities, are obtained. The temperature dependence of these quantities is examined. The results obtained from this work indicate that ML hBN is a valleytronic material, and proximity-induced interactions can lead to the observation of OHE in the absence of an external magnetic field.

Frequency dependence of magneto-optical phenomena in nonmagnetic dielectric nanostructures

The frequency dependences of the Faraday rotation angle and the ellipticity angle are studied taking into account light absorption in dielectric media. The extreme values of the above values are determined, as well as the field of their application in dielectric media.

Enhancing the Magnetic and Magneto-optical Properties of Praseodymium-substituted Bi-YIG Thin Film on Glass Substrate Prepared by Metal-organic Decomposition

Praseodymium (Pr)- and bismuth (Bi)-substituted yttrium (Y) iron (Fe) garnet (PrSUBx/SUBYSUB2-x/SUBBi₁FeSUB5/SUBOSUB12/SUB where x = 0.25, 0.5, 1, and 2) thin films were prepared on glass substrate using a metal-organic decomposition (MOD) method. Their magneto-optical properties were studied as a function of Pr concentration. Praseodymium has two functions in PrSUBx/SUBYSUB2-x/SUBBi₁FeSUB5/SUBOSUB12/SUB thin films, i.e., it (i) improves spin-orbit interaction strength and (ii) increases magnetic properties; both are expected to strongly enhance the Faraday rotation (FR) angle of the thin film. Our study demonstrated that the Pr₁Y₁Bi₁FeSUB5/SUBOSUB12/SUB thin-film displayed the highest FR angle, of –13 °/μm, which is 1.6-times higher than that of the PrSUBx/SUBYSUB2-x/SUBBi₁FeSUB5/SUBOSUB12/SUB thin film without Pr dopant. The Pr₁Bi₁Y₁FeSUB5/SUBOSUB12/SUB thin film fabricated on a glass substrate by the MOD method displayed excellent MO performance and is a potential candidate for application in optical devices.