Faraday Rotation Angle Research Articles

Growth Considering Lattice Mismatch and Thermal Expansion and Magneto-Optical Properties of Bismuth-Doped Rare Earth Iron Garnet Crystals

Bi3+-doped iron garnet crystals (Bi:RIG) have received extensive attention for their excellent magneto-optical properties. The quality of garnet crystals has a great relationship with mismatch in the lattice and thermal expansion between crystals and seeds. Compared with TGG seeds, Sc,Ga:YIG is more suitable as the seed for growing Bi:(HoEu)IG crystals. The crystal quality and match in the lattice and thermal expansion have been discussed. The as-grown Bi:(HoEu)IG crystal has a specific Faraday rotation angle of −467° cm–1 and shows a strong magneto-optical effect.

Ionospheric Phase Scintillation Correction Based on Multi-Aperture Faraday Rotation Estimation in Spaceborne P-Band Full-Polarimetric SAR Data

The spaceborne P-band fully polarimetric synthetic aperture radar (SAR) working system is highly susceptible to the scintillation effects induced by ionospheric irregularities due to its low carrier frequency. The scintillation phase error (SPE) is a dominant factor that leads to azimuth decorrelation. The aperture-dependent and spatial-varying characteristics of the SPE promote the complexity of the SPE estimation and compensation. In this paper, a methodology is described that compensates the SPE by estimating the Faraday rotation (FR) angle from fully polarimetric SAR data. The multi-aperture scheme is adopted, including the sub-aperture FR estimation, multi-aperture splicing, and overall compensation, to take the complicated characteristics of the aperture-dependent and spatial-varying SPE into account. The methodology is finally validated on simulated data derived from the airborne P-band SAR real data, and compared with an existing method. The new method does not need prior knowledge of the ionospheric height. Furthermore, its performance is investigated in relation to several key factors in different simulation conditions.

Ionospheric Inhomogeneities and Their Influences on the Earth’s Remote Sensing from Space

An important problem that arises when planning experiments on remote sensing from space in the P-band is taking into account the influence of the Earth’s ionosphere. We investigated the influence of ionospheric inhomogeneities on the results of remote sensing of the Earth from space, taking into account the curvature of the propagation medium. One- and two-layer models of the ionosphere, both with and without large-scale inhomogeneities of the cold ionospheric plasma, were considered. To obtain numerical results, a bicharacteristic system was used, which makes it possible to adequately take into account the complex structures of ionospheric plasma layers. The dependence of the rate of phase change on the height and the dependence of the total electron concentration on the horizontal distance and group time were investigated. The case was compared when the vector of the strength of the Earth’s magnetic field is perpendicular to the plane of propagation, and the case when this vector lies in the plane of propagation. The dependence of the difference between the refractive indices on the height along the rays was studied. Estimates of the Faraday rotation angle and phase deviation were obtained for various models. The magnitude of the angle of Faraday rotation depends significantly on the orientation of the trajectory relative to the Earth’s magnetic field. Polarization coefficients are investigated. It is shown that the o- and x-waves are separately circularly polarized, and the contribution of the longitudinal component of the electric field in the electromagnetic wave is insignificant.

Quantum corrections to frame-dragging in scattering amplitudes

Frame-dragging effect manifests itself as polarization direction rotation when linearly polarized electromagnetic/gravitational wave scatters from a spinning point source through gravitational interactions, an effect also known as the gravitational Faraday rotation. Treating general relativity as an effective field theory, the Faraday rotation angle and its quantum corrections are computed using scattering amplitudes. While the classical rotation angle is universal as expected from the equivalence principle, the quantum corrections are found to be different between electromagnetic and gravitational waves, supporting earlier studies that some formulations of the equivalence principle may need reformulation in the quantum regime.

Thickness-dependent magnetooptical properties of ion beam sputtered polycrystalline Ce1Y2Fe5O12 films

Polycrystalline cerium-substituted yttrium iron garnet (Ce:YIG, Ce1Y2Fe5O12) films were deposited on synthetic fused silica substrates with various thicknesses using ion beam sputtering, and their roughness, transmissivity, optical constants, microstructure, and their magnetic and magnetooptical properties were measured. Thicker films exhibit cracking due to thermal mismatch stress. A ∼5 nm thick amorphous layer was observed at the interface between Ce:YIG and the substrates, resulting in a non-monotonic thickness dependence of the measured properties. A 338 nm thick Ce:YIG film showed the largest magnetooptical figure of merit defined as the ratio of Faraday rotation angle to absorption coefficient, 127°/dB at a wavelength of 1550 nm, more than three times larger than prior work.

Anomalous Faraday effect in a [formula omitted]-symmetric dielectric slab

In this letter we discuss a phase transition-like anomalous behavior of Faraday rotation angles in a simple parity-time (PT) symmetric model with two complex δ-potential placed at both boundaries of a regular dielectric slab. In anomalous phase, the value of one of Faraday rotation angles turns negative, and both angles suffer spectral singularities and yield strong enhancement near singularities.

Magneto-optical diffractive deep neural network.

We propose a magneto-optical diffractive deep neural network (MO-D2NN). We simulated several MO-D2NNs, each of which consists of five hidden layers made of a magnetic material that contains 100 × 100 magnetic domains with a domain width of 1 µm and an interlayer distance of 0.7 mm. The networks demonstrate a classification accuracy of > 90% for the MNIST dataset when light intensity is used as the classification measure. Moreover, an accuracy of > 80% is obtained even for a small Faraday rotation angle of π/100 rad when the angle of polarization is used as the classification measure. The MO-D2NN allows the hidden layers to be rewritten, which is not possible with previous implementations of D2NNs.

Faraday effect in CoPt-CaF2 nanogranular films with hard magnetic property for magnetic-field-free faraday devices

Magneto-optical Faraday devices, such as optical isolators, require a structure to apply a magnetic field to the incorporated magneto-optical material. The application of a magnetic field hinders the miniaturization and integration of these devices. Nanogranular films show Faraday rotation angles up to 40 times larger than Bi-YIG in the optical communication band (1,550 nm). Nanogranular films are submicron-to several-micrometer-thick and contribute to the miniaturization and integration of optical devices. Here, we introduce (Co-Pt)–(CaF2) nanogranular films exhibiting a magnetic-field-free magneto-optical Faraday effect, which are Co3Pt alloy that are hard magnets with residual magnetization. These nanogranular films exhibit the Faraday effect without requiring a magnetic field owing to their residual magnetization.

Sensitivity enhancement of magneto-optical Faraday effect immunoassay method based on biofunctionalized γ-Fe2O3@Au core-shell magneto-plasmonic nanoparticles for the blood detection of Alzheimer's disease

In this work, we conducted a proof-of-concept experiment based on biofunctionalized magneto-plasmonic nanoparticles (MPNs) and magneto-optical Faraday effect for in vitro Alzheimer's disease (AD) assay. The biofunctionalized γ-Fe2O3@Au MPNs of which the surfaces are modified with the antibody of Tau protein (anti-τ). As anti-τ reacts with Tau protein, biofunctionalized MPNs aggregate to form magnetic clusters which will hence induce the change of the reagent's Faraday rotation angle. The result showed that the γ-Fe2O3@Au core-shell MPNs can enhance the Faraday rotation with respect to the raw γ-Fe2O3 nanoparticles. Because of their magneto-optical enhancement effect, biofunctionalized γ-Fe2O3@Au MPNs effectively improve the detection sensitivity. The detection limit of Tau protein as low as 9 pg/mL (9 ppt) was achieved. Furthermore, the measurements of the clinical samples from AD patients agreed with the CDR evaluated by the neurologist. The results suggest that our method has the potential for disease assay applications.

Fabrication and characteristics of Ce‐doped Y3Fe5O12 ceramics by hot‐press sintering with oxygen/nitrogen atmosphere

AbstractInfrared transparent Ce‐doped Y3Fe5O12 (Ce: YIG, CexY3‐xFe5O12, x = 0, 0.12, 0.24, 0.36) ceramics were successfully produced by the solid‐state reaction using a hot‐press sintering process from the Y2O3, Fe2O3, and CeO2 powders. The phase structure, microstructure, infrared transmittance, and magnetic and magneto‐optical properties of the Ce‐doped Y3Fe5O12 ceramics were measured and analyzed. The in‐line transmittances of the Ce‐doped Y3Fe5O12 ceramics with the x = 0, 0.12, 0.24 (L = 0.5 mm) at 1550 nm were about 72%, 66.5%, and 57.6%, respectively. In the state of saturation magnetization, the Faraday rotation angle per centimeter (θF) of CexY3‐xFe5O12 (x = 0, 0.12, 0.24) ceramics measured by the light extinction method was 182.5, −410.4, and −958.3 deg./cm, respectively. The change of the θF was about −142.5 deg./cm when per 1at.% Ce was substituted in the dodecahedral site of YIG materials. The (Ce0.24Y2.76)Fe5O12 ceramics were determined as the optimized composition for its excellent infrared optical and magneto‐optical properties.

Comparison of Magneto-Optical Faraday Effect Method and Magnetic Camera for Imaging the 2-D Static Leakage Magnetic Flux Density

Magnetic flux leaks around the defect on the magnetized ferromagnetic specimen. The magnetic flux leakage testing (MFLT) use the magnetic sensor to measure the leaked magnetic flux density (LMFD). The high sensitivity of sensor need to increase the probability of detection (POD). Also the small size and high spatial resolution of sensor need to increase POD and to sizing defect. Uniform and small lift-off are another necessary to increase POD and sizing ability. Also, the real time imaging of magnetic flux density can increase the inspection time. So the period of planned preventive maintenance could reduce. Two dimensional semiconductor-based magnetic sensor array with high spatial resolution satisfies these requirements. Projection of magnetic flux density on a sensor itself would be another method. We compare the magnetic camera and the magneto-optical Faraday effect (MOE) for MFLT. Magnetic camera uses the two dimensional Hall sensor arrays to imaging the LMFD. And the MOE project LMFD. The plane of polarized light rotates inside of magneto-optical film (MOF). The Faraday rotation angle proportional to direction and intensity of magnetic flux density. Sensitivity, spatial resolution, magnetic hysteresis, repeatability, full-scaled operational range compared. Also shape of target specimen compares too.

Improvement on Faraday rotation measurement affected by the stray lights on the HL-2A tokamak

Formic-acid (HCOOH, λ = 432.5 μm) laser P olarimeter- I nterferomet er ( PIer ) has been developed on the HL-2A tokamak, which provides 4 channels of line-integrated electron densities and 4 channels of Faraday rotation angles, respectively. Affected by the stray lights arising from the reflection of the probe waves in the optical system, the measurement of Faraday rotation angles was drastically contaminated during the HL-2A experiments, showing an obvious oscillation modulation during the electron density ramp-up/down. This paper introduces an effective correction approach used to improve the accuracy of Faraday rotation measurement on the HL-2A tokamak. Based on the method, the deviation term originating from the stray lights can be effectively subtracted from the contaminated Faraday rotation measurement. The preliminary result indicates that the interference amplitude on Faraday rotation angle is reduced by about 80%, and the corrected data is consistent with the experimental measurement by using the optical isolator that consists of a λ/4 wave-plate and polarizer under the similar discharges.

Strong magneto-optical effect of incongruent-melting Ce,Sc,Ca:GIG crystal with heavy Ce3+ doping

To achieve high concentration of Ce3+ ions in Gd3Fe5O12 (GIG) crystal, the structure of co-doped Sc3+ and Ce3+ ions was designed and the doping energy was evaluated by the first-principles density functional theory. Based on this, Ce,Sc,Ca:GIG crystals with centimeter size and good quality were successfully grown by an improved edge-defined film-fed growth method. The transmission, magnetism, and magneto-optical effects were investigated in detailed. The Ce-doped concentration as high as 18 at% results in the (Ce0.54Gd2.41Ca0.05) (Sc0.45Fe4.55)O12 crystal having excellent magneto-optical properties. Its Faraday rotation angle increased to about −1534 deg. cm−1 at λ = 1550 nm. Therefore, the excellent magneto-optical performances reveal that Ce,Sc,Ca:Gd3Fe5O12 crystal has great potential to be utilized for miniaturized and high performance optical isolators in 1550 nm.

Study on laser-induced damage of TbBiIG crystal at 1064 nm.

With the development of miniaturization of high-energy laser systems, a new Faraday rotator material must be studied to realize the miniaturization and integration of optical isolators. In this paper, high-quality (TbBi)3Fe5O12 (TbBiIG) and Ca-doped (TbBi)3Fe5O12 (Ca: TbBiIG) single crystal films with hundreds of microns thickness were grown by liquid phase epitaxy method on (111) oriented garnet substrate. The crystal structure, magneto-optical (MO), optical and laser induced damage properties were investigated in detail. We found that the (TbBi)3Fe5O12 film has outstanding magneto-optical and laser-induced damage properties. Optical and MO properties indicate that TbBiIG films have a high specific faraday rotation angle of 1452 deg/cm at 1310 nm, and 2812 deg/cm at 1064 nm, absorption coefficient (α) is 5.63 cm-1 and 15.7 cm-1 at 1310 nm and 1064 nm, respectively. The laser-induced damage threshold (LIDT) of TbBiIG irradiated by a multi-frequency laser is 8.91 J/cm2. The light absorption has a significant impact on LIDT value. Rare-earth ion doped iron garnet (RIG) material is a very potential MO material, which can greatly reduce the size and weight of optical isolators in the 1064 nm band.

Tunable Faraday effect in Graphene/SiO2/Ta2O5 layered structure using a pump He-Ne laser light

Faraday rotation spectrum of a Graphene/SiO2/Ta2O5 layered structure under an external magnetic field and a pump light of a He-Ne laser with the wavelength of 632.8 nm is investigated in the THz frequency region. The results showed that, when the pump light is turned off and the magnetic field strength is increased, the maximum Faraday rotation angle frequency shifts toward the higher frequencies, as well as, the value of the maximum Faraday rotation angle increases. Furthermore, for a constant external magnetic field, by increasing the pump light power, the value of Faraday rotation increases, and the maximum Faraday rotation frequency shifts toward the lower frequencies. However, the noticeable changes in the transmission spectrum were not observed by changing the magnetic field strength and the pump light power. These results would have potential applications in designing the magneto-optical devices with tuning property of the Faraday rotation using a pump He-Ne laser.

Spinel ferrites NiFe2O4 NCs enhanced Mössbauer spectra, magnetization and Faraday rotation of diamagnetic tellurite glasses

Glass containing magnetic nanocrystals are attractive for obtaining high magnetic and magneto-optical properties. In this study, for the first time, 10 nm cubic NiFe2O4 (NFO) nanocrystals doped heavy metal oxide glasses were fabricated and the influence of NFO to glass structure, chemical bonds, Mössbauer spectra, magnetization and Faraday rotation was studied. X-ray diffraction, Raman and X-ray photoelectron spectra revealed the existence of multi-valence states of Fe/Ni ions, oxygen vacancies in cubic lattice and modifications on glass structure, which in turn adjusted the polarizability, oxygen packing density, Mössbauer spectra, magnetic property and magneto-optical behaviors. Through Mössbauer study, the increase of NFO amount enhanced the hyperfine field intensity of tetrahedral Fe3+ ions at the expense of octahedral ones. NFO doped glasses exhibited ferromagnetic behavior whose Ms and Hc increased with the NFO amount due to the NCs size effect. Verdet constant and Faraday rotation angle were studied as function of wavelength, magnetic field, polarizer angle and NFO amount. 3%NFO glass exhibited significant enhancement in magnetization and Verdet constant of 91 rad/T.m at 633 nm which is 5-fold of host glass and superior than literatures. In addition, due to the nanoscale NCs, the thermal stability of obtained NFO glasses remained higher than 100 °C which is promising for photonics devices fabrication.

Measurement of rubidium vapor number density based on Faraday modulator

The actual vapor density characterizing the alkali metal spin-exchange rate remains a compelling issue for spin-exchange optical pumping. Based on the deduced relationship between the Faraday rotation angle and the rubidium vapor number density using the electrodynamics theory, we report a measurement of the number density for rubidium vapor sealed inside a cell based on a Faraday modulator. The measurement relies on the optical rotation angle due to rubidium vapor under a bias magnetic field (∼0.08 T) produced by a samarium–cobalt magnet. A Faraday modulator with a lock-in amplifier is used to accurately measure the tiny optical rotation angle in a temperature range of 387–468 K. In addition, a synchronization verification is performed by the photoelastic modulator (PEM). The recurring data showed that the two methods are consistent with each other. Compared with the PEM method, the Faraday modulator detection system does not need to adjust the optical axis difference of 45° in the PEM detection system, thereby reducing the complexity of the experiment and the error caused by the alignment of the optical axis, which showed that the Faraday modulator detection method more advantageous in measuring the alkali metal density.

High-frequency measurement of the interferometric phase, the Faraday rotation, and the Cotton-Mouton effect with a single detector in a far-infrared interferometer-polarimeter

A novel polarization modulation method is proposed, for a possible application in the measurement of the electron density and magnetic field profiles by an interferometer-polarimeter diagnostic in the Divertor Test Tokamak (DTT) device. Starting from the output of a CO2 pumped CHCOH3 far-infrared (FIR) laser (λ = 118.8 μm), three waves with frequencies ω, ω − δω, and ω + δω are generated and coherently combined to produce a polarization modulated laser beam suitable to probe the DTT plasma in a multichord, double-pass scheme. A second, coherently pumped, FIR cavity operating at the slightly detuned ω′ frequency, acts as a local oscillator for the interferometric measurement. By this polarization modulation method, it is possible to simultaneously measure the interferometric phase, the Faraday rotation angle, and the Cotton-Mouton effect, all by a single detector, while keeping to an acceptable value the perturbation of the interferometric phase due to the time modulated polarization. In this paper, we describe the principles of the method and discuss its possible application in the poloidal interferometer-polarimeter diagnostic of the DTT device. A single chord mock-up experiment is in preparation to experimentally test the technique.

Effects of Ionospheric Inhomogeneities on Remote Sensing of the Earth by Space‐Borne P‐Band SAR

AbstractNumerical modeling of the effect of the polarization vector rotation in the ionospheric plasma on the radio waves of the high frequency range is performed. The relevance of the work is associated with the creation of space‐based P‐band synthetic aperture radars (SARs) for the Biomass mission and the MKS‐RSA (P) experiment on board ISS station. These instruments are intended for surface and subsurface sounding of the Earth and their readings are strongly influenced by the ionosphere. Another problem of EM propagation is the reconstruction of the profile e‐ionospheric plasma density by radio tomography methods. The source of radiation is located on the moving spacecraft at a distance of 400 km from the Earth's surface. The angle of rays inclination varies from 150 to 30° relative to the horizontal axis. The receiver is located on the surface of the Earth. Three spherical two‐layer models of the ionosphere are compared. To determine the ray paths, a bi‐characteristic system of equations is used. The dependence of the aiming angle deviation on group time is investigated. The phase variation due to the influence of the ionosphere and the angle of the Faraday rotation are studied. It is shown that the changes in the Faraday rotation angle for the selected parameters lie in the range from 6° to 54°, which will have a strong impact on the operation of the P‐band SAR and requires a sufficiently accurate quantitative account of the variability of the angle when probing vegetation and soil covers.

Recent progress on the J-TEXT three-wave polarimeter-interferometer

The J-TEXT three-wave polarimeter-interferometer system (POLARIS), which measures time-space distribution of electron density and current density, has been optimized with both the optical system and the equilibrium reconstruction method. The phase resolution of a Faraday rotation angle has been improved from 0.1 to 0.06 degree in chords from –0.18 to 0.18 m (plasma minor radius), and the sawtooth oscillation behavior has been detected by Faraday rotation angle measurement. By combining the POLARIS measured data and the equilibrium and fitting code (EFIT), an upgraded equilibrium reconstruction method has been developed, which provides a more accurate temporal and spatial distribution of current density and electron density. By means of the optimized POLARIS and improved equilibrium reconstruction, variations of profiles with increasing density have been carried out, under both Ohmic and electron cyclotron resonance heating discharges.