Verdet Constant Research Articles

Giant Faraday rotation in atomically thin semiconductors

Faraday rotation is a fundamental effect in the magneto-optical response of solids, liquids and gases. Materials with a large Verdet constant find applications in optical modulators, sensors and non-reciprocal devices, such as optical isolators. Here, we demonstrate that the plane of polarization of light exhibits a giant Faraday rotation of several degrees around the A exciton transition in hBN-encapsulated monolayers of WSe2 and MoSe2 under moderate magnetic fields. This results in the highest known Verdet constant of -1.9 × 107 deg T−1 cm−1 for any material in the visible regime. Additionally, interlayer excitons in hBN-encapsulated bilayer MoS2 exhibit a large Verdet constant (VIL ≈ +2 × 105 deg T−1 cm−2) of opposite sign compared to A excitons in monolayers. The giant Faraday rotation is due to the giant oscillator strength and high g-factor of the excitons in atomically thin semiconducting transition metal dichalcogenides. We deduce the complete in-plane complex dielectric tensor of hBN-encapsulated WSe2 and MoSe2 monolayers, which is vital for the prediction of Kerr, Faraday and magneto-circular dichroism spectra of 2D heterostructures. Our results pose a crucial advance in the potential usage of two-dimensional materials in ultrathin optical polarization devices.

Magneto-optical and luminescent properties of Tb doped Ge-B-X (X=Ga/La) glasses

Extensive efforts have been devoted to magneto-optical (MO) glass, owing to its remarkable potential in modern optics, encompassing diverse applications such as optical isolation, modulation, and sensing. Although the Tb ions doped glass has good MO properties, high concentrations of Tb ions tend to cluster, resulting in glass crystallization. To further improve the performance of MO glass, we must improve the solubility of Tb ions and inhibit the oxidation of paramagnetic Tb3+ to diamagnetic Tb4+ by adjusting the glass composition. In this work, we conducted a comparative study on GeO2-B2O3-X2O3 glasses doped with Tb2O3 (TGBX, where X represents Ga or La) to elucidate the effects of Ga2O3 and La2O3 on glass properties. Our findings reveal that TGBG glasses exhibit superior MO performance compared to TGBL glasses. Notably, the Verdet constant of TGBG glass with 45 mol.% Tb2O3 at 650 nm reaches 105 rad/(T·m). Although TGBL glass exhibits a lower Verdet constant, its higher glass network connectivity and higher concentration of Tb3+ ions suggest its potential for preparing larger-sized glasses with an increased Tb3+ molar ratio.

Tesla-class single-cycle terahertz magnetic field pulses generated with a spiral-shaped metal microstructure

Abstract We study the terahertz (THz) magnetic field pulse enhanced by a spiral-shaped antenna resonator (SAR). We deposit the SAR on the surface of a terbium-gallium-garnet crystal, which has a large Verdet constant, and measure the Faraday rotation angle for strong THz pulse excitation by magneto-optical sampling (MOS) with near-infrared light. The determined magnetic field strength and field-enhancement spectrum are consistent with the theoretical predictions. This first report of the detection of the magnetic field of a Tesla-class picosecond pulse by magneto-optical sampling is expected to be useful in research on the control of magnetization in spintronic devices.

Magneto-optical characterization of TCO films using standard and enhanced configurations

Thin film samples like transparent conducting oxides (TCO) are typically investigated using measurements like Hall Effect and 4-point probe measurements. We use a sensitive AC Faraday rotation (FR) setup to study thin film samples for which a magneto-optic response is challenging to characterize. The experimental setup employs a stabilized He-Ne laser (633 nm) along with an AC magnetic field that enables lock-in detection. We investigate a series of TCO samples that are deposited on a glass substrate. The TCO samples include the more widely used Indium Tin Oxide (ITO) and the relatively newer Fluorine doped Tin Oxide films, usually referred to as FTO. These films have a magneto-optic response due to the presence of free carrier concentration and therefore measurement of this response (Verdet constant) could allow one to determine the carrier concentration of these films. Given that magneto optic responses like FR depend on the length of the sample length traveled by light, these sub-micron films pose considerable challenges in trying to extract the FR response of the film from that of the much thicker glass substrate. Furthermore, we present details of the design and FR characterization of samples using a Michelson interferometer-based measurement setup which enhances the Faraday rotation and affords a new means of studying harmonic peaks of the recorded optical signal in response to a sinusoidally-varying applied magnetic field. We compare some early results from this setup to the typical “single-pass” setup to highlight the difference in the recorded signals from the two setups. To showcase the advantages of the proposed measurements, we also include some early results from a very different type of sample, namely superparamagnetic nanoparticles (SNPs).

Continuous-wave cavity ringdown for high-sensitivity polarimetry and magnetometry measurements.

We report the development of a novel variant of cavity ringdown polarimetry using a continuous-wave laser operating at 532nm for highly precise chiroptical activity and magnetometry measurements. The key methodology of the apparatus relies upon the external modulation of the laser frequency at the frequency splitting between non-degenerate left- and right-circularly polarized cavity modes. The method is demonstrated by the evaluation of the Verdet constants of crystalline CeF3 and fused silica, in addition to the observation of gas- and solution-phase optical rotations of selected chiral molecules. Specifically, optical rotations of (i) vapors of α-pinene and R-(+)-limonene, (ii) mutarotating D-glucose in water, and (iii) acidified L-histidine solutions are determined. The detection sensitivities for the gas- and solution-phase chiral activity measurements are ∼30 and ∼120μdeg over a 30s detection period per cavity round trip pass, respectively. Furthermore, the measured optical rotations for R-(+)-limonene are compared with computations performed using the TURBOMOLE quantum chemistry package. The experimentally observed optically rotatory dispersion of this cyclic monoterpene was thus rationalized via a consideration of its room temperature conformer distribution as determined by the aforementioned single-point energy calculations.

Highly transparent Tb3Al5O12 ceramics for kilowatt‐level Faraday isolator

AbstractTb3Al5O12 (TAG) ceramics with high optical quality were fabricated successfully by a solid‐state reaction method combined with hot isostatic pressing (HIP) post‐treatment. The microstructure, optical transmittance, Verdet constant, and thermo‐optical properties were investigated. The obtained TAG ceramics showed a dense microstructure, and the in‐line transmittance reached 82.8% at 1070 nm after laser‐grade polishing. The Verdet constant of TAG ceramics was measured to be 50.9 rad·T1·m−1 at 1070 nm, which is higher than that of commercial Tb3Ga5O12 crystals. The Faraday isolator based on TAG ceramics can provide an isolation ratio of 30 dB with a laser power of more than 1 kW. With excellent optical quality, high Verdet constant, and maximum working power, TAG transparent ceramics are promising for applications of kilowatt‐level Faraday isolators.

Nickel element doping impacts on structure features and Faraday effects of magneto‐optical transparent holmium oxide ceramics

AbstractThe nickel element doped holmium oxide (Ho2O3:Ni) transparent magneto‐optical ceramics were fabricated by vacuum sintering and the dopant impacts on structure features and Faraday effects were investigated. The starting oxide powders were synthesized by pyrolyzing the resulting layered holmium‐based hydroxide nanosheets prepared from a chemical precipitation route using the sodium hydroxide as precipitant at the freezing temperature. Upon high‐temperature sintering, the defect is introduced by Ni2+ substitution for Ho3+ to form the interstitial solid solution. The 1 at.% Ni2+ doped Ho2O3 ceramic sample exhibits an in‐line transmittance of ∼70.04% at 1 550 nm with a relative density of ∼99.88%, while more Ni2+ incorporation (e.g., 2‒5 at.%) even leads to a completely opaque state. The magneto‐optical transparent Ho2O3:1%Ni ceramic developed in this work has Verdet constants of ∼−195, −65, and −29 rad/(T·m) at 635, 1 064, and 1 550 nm, respectively, which are ∼1.8‐fold higher than the commercial terbium gallium garnet crystal or ∼1.4‐fold higher than the pure Ho2O3 ceramic. This material also possesses relatively large figure of merit of ∼14.6°/T at 1 064 nm and relatively high thermal conductivity of ∼7.5 W/(m·K) at room temperature.

Fabrication and properties of a Tm3+ doped TbVO4 magneto-optical crystal

The Verdet constants of the TTV crystal at 532, 633 and 1064 nm are 50–250% higher than those of the TGG crystal.

A Faraday isolator based on fused silica in a Herriott cell

We demonstrated a multipass Faraday isolator based on fused silica. The polarization rotation angle of 45° was accumulated in a Herriott cell. The concept enables the use of magneto-optic materials with low Verdet constants in Faraday isolators.

Dy2O3–MgO composite ceramics: Fabrication and properties

An IR-transparent magneto-optical Dy2O3–MgO compositeceramics was fabricated by vacuum hot pressing of glycine-nitrate self-propagating high-temperature synthesized nanopowders. Composites significantly outperform dysprosium sesquioxide ceramics in terms of thermal conductivity and mechanical properties.The HV1 microhardness of the Dy2O3–MgO composite is 9.9 GPa and the fracture toughnessKIC, calculated by the Palmquist method, is 1.7 MPa m½. The thermal conductivity of the composite was measured in the range of 50–300 K and is 10.6 W/(m K) at room temperature. The transmittance of 1.5 mm thick Dy2O3–MgO sample is about 70 % in the wavelength range ∼2.1–2.2 μm and more than 80 % in the range ∼3.6–6.5 μm, which is close to the theoretical value for dysprosium sesquioxide.The value of Verdet constant of Dy2O3–MgO composite ceramics is 7.0 ± 0.3 rad/(T∙m)at 1940 nm.

Czochralski growth, optical and magneto-optical properties of Ce9.33(SiO4)6O2 crystal

Ce9.33(SiO4)6O2 (CSO) crystals were grown by the Czochralski (Cz) method. Rietveld refinement of XRD patterns confirmed the oxyapatite structure of CSO, XPS analysis revealed the valence of Ce ions in CSO crystals. Magnetization curve and temperature dependencies of the magnetic susceptibility were measured, paramagnetic behavior and magnetic anisotropy have been observed. Photoluminescence and Faraday rotation characteristics of the CSO crystal were investigated at room temperature. Verdet constants of CSO were about 1.6 times as large as those of TGG. Baesd on Van Vleck–Hebb theory, the effective transition wavelength and probability of CSO crystal were calculated and compared with other Ce3+-containing crystals. The absorption and magnetic circular dichroism (MCD) spectra of 4f→5d transitions in Ce3+ ions in CSO crystal were studied.

Spectroscopic and magneto-optical properties of novel bifunctional Nd,Er:CeF3 crystal

In this study, we report a successful Bridgman growth of Nd3+ and Er3+ co-doped CeF3 (Nd,Er:CeF3) single crystal with a size of Ø25 mm × 30 mm. The absorption and fluorescence characteristics of the Nd,Er:CeF3 crystal were studied systematically. The results show that the fluorescence emission peaks were positioned at 547, 669, 1062.6, and 1542.6 nm, respectively. The fluorescence lifetimes centered at 1062.6 and 1542.6 nm for Nd3+ and Er3+ were 0.313 and 1.12 ms, respectively. Meanwhile, the spectroscopic properties of Nd,Er:CeF3 crystals were investigated based on the Judd–Ofelt theory. Notably, the magneto-optical performance of the Nd,Er:CeF3 crystal was investigated for the first time. The Verdet constants of the Nd,Er:CeF3 crystal at 532, 632.8, 1064, and 1310 nm are 220.3, 142.4, 40.7, and 23.1 rad T−1 m−1, respectively, which are significantly higher than those of undoped CeF3 and traditional Tb3Ga5O12. The results show that Nd,Er:CeF3 is a bifunctional crystal with potential applications in laser and magneto-optical fields.

Giant excitonic magneto-optical Faraday rotation in single semimagnetic CdTe/Cd1-xMnxTe quantum ring

Magnetic tuning of the bound exciton states and corresponding giant Zeeman splitting (GZS) between σ+ and σ− excitonic transitions in CdTe/Cd1-xMnxTe quantum ring has been investigated in the Faraday configuration for various concentrations of Mn2+ ions, using the variational technique in the effective mass approximation. The sp-d exchange interaction between the localized magnetic impurity ions and the delocalized charge carriers has been accounted via mean-field theory with the inclusion of a modified Brillouin function. The enhancement of the GZS, and in turn, the effective g-factor with the application of an external magnetic field, is strikingly manifested in type-I – type-II transition in the band structure, which has been well explained by computing the overlap integral between the electron and hole, and the in-plane exciton radius. This highlights the extraordinary magneto-optical properties, including the giant Faraday rotation and associated Verdet constant, which have been calculated using single oscillator model. The oscillator strength has been estimated, and is found to be larger than in the bulk diluted magnetic semiconductors (DMS) and quantum wells, reflecting stronger confinement inside the quantum ring. More extensive Zeeman splitting and a higher oscillator strength in the DMS-based QR lead to an ultra-high Verdet constant of 2.6×109rad/Teslam, which are a few orders of magnitude larger than in the existing quantum systems and magneto-optical materials.

Magnetic and magneto-optical properties of manganese-containing antimony phosphate glasses – An alternative to Faraday rotators

Glasses in system 100-x(70SbPO4–10ZnO–20PbO) xMnO, with x = 0, 10, 20 and 30 mol %, where prepared by the conventional melting-quenching method. The glasses were cut, polished and characterized by XRD, DSC, Raman, FTIR, UV–Vis and luminescence and magnetic and magneto-optical aiming application ultimate as in magneto-optical devices. These samples containing manganese exhibit magnetic response to neodymium magnets at room temperature. In addition, they feature thermal stability above 100 °C, wide transparency in the visible and near infrared region. The optical absorption spectra of the glass revealed the presence of characteristic absorption bands of Mn2+ at 410 nm attributed to 6A1(S) → 4A1, 4E (4G) transition and possible oxidation at around 550 nm assigned to 5B1g → 5B2g transition of the Mn3+ ions. Refractive indices higher than 1.8 and characteristic emission bands around 680–720 nm, assigned to 4T1(G)→6A1(S) transition, were also observed. Magnetic susceptibility measurements revealed the paramagnetic character of the Mn-containing glasses, with antiparallel spin alignment. Finally, a linear growth trend was observed for the Verdet constant along with the Mn2+ concentration and the highest value measured, for sample containing 30 mol% of MnO, was −55.1 ± 3.2 rad T−1 m−1 at 632.8 nm. This value is close to those of some families of glasses containing rare earths, being an alternative of new low-cost magneto-optical vitreous materials.

Nonlinear refraction in high terbium content borogermanate glass bulk and fiber

High terbium content glasses have stood out in technological areas due to their simultaneous ability of magnetization and transparency in the visible spectrum. Such magneto-optical glasses are relevant for several optical devices, including optical modulators, sensors, and isolators. While terbium ions are responsible for magnetic response, glass formers, and modifiers provide a branch of desirable mechanical, chemical, and optical properties, which can further be tailored by compositional manipulation. Determination of Verdet constant is usual in magneto-optical glass, however, little attention has been devoted to the determination of the optical properties, moreover the nonlinear ones. Herein, we investigate the nonlinear index of refraction (n2) of a novel magneto-optical glass shaped in bulk and optical fibers. Although the fabrication of fibers with high terbium content is challenging, the usage of optical fibers is important to improve signal that arises from magneto-optical and Kerr effects, since both depend on light propagation path. Bulk and optical fiber of 96(60GeO2-25B2O3–4Al2O3–10Na2O–1PbO) – 4Tb4O7 (mol%) glass were characterized by Z-scan and D-scan techniques, respectively, using femtosecond laser pulses. It was obtained the n2 spectrum in the range of 550–1200 nm for the former, which was modeled based on BGO model, revealing the role of oxygen ions for the optical nonlinearity. The optical fiber fabrication process does not compromise the n2 value, remaining n2=(5±2)×10−20m2/W at 790 nm according to D-scan measurements, which is equivalent to values determined by Z-scan, i.e. (6±2)×10−20m2/W. Additionally, the chemical states of the various elemental components of GBANP-4Tb glasses were investigated by X-ray photoelectron spectroscopy (XPS). The analysis of the Ge 3d and Tb 4f photoelectron spectra of the GBANP-4Tb glasses revealed the presence of Ge4+, Tb3+ and Tb4+ oxidation states. These results are relevant to expand the knowledge on magneto-optical materials, moreover regarding their optical response in the femtosecond regime, broadening its application in ultrafast magneto-optical devices.

Pb2+/Co2+ modified growth and phase transitions of CsPbBr3 in heavy metal oxide glass with enhanced magnetic and magneto-optical properties

In this study, we investigated the impact of Pb/Co compositional ratios on the growth and phase transition of CsPbBr3 within PbO-Bi2O3-B2O3 glasses. We employed XRD Rietveld refinement and Raman spectra for a thorough analysis of structural modifications and crystal phases. To assess the morphology, size, and distribution of CsPbBr3 crystals, as well as the homogeneity of embedded glasses, we utilized SEM and TEM, along with SAED patterns. The results confirmed a phase transition from cubic CsPbBr3 to tetrahedral CsPb2Br5 at Pb content exceeding 60%, leading, however, to severe crystallization and the transformation of glassy phases into ceramics. Expanding on the optimal 45% PbO content, we also explored the influence of CoBr2. XRD refinement and Raman analysis revealed Co content-dependent growth and phase transition of CsPbBr3 within the glasses. XPS studies demonstrated the coexistence of Co2+ and Co3+ ions, and their spin states and coordination were verified through XANES and EPR analysis. Notably, the presence of high-spin octahedral Co2+ replacing Pb in the B-site of perovskite resulted in observed ferromagnetism in the Co-doped glasses. Magnetization increased within the 1–3% Co content range. Simultaneously, a high-value Verdet constant of 108 rad/T·m at 633 nm was obtained, presenting an attractive feature for diamagnetic glasses.

Optical, magneto-optical properties and fiber-drawing ability of tellurite glasses in the TeO2–ZnO–BaO ternary system

The presented work is focused on the optical and magneto-optical characterization of TeO2-ZnO-BaO (TZB) tellurite glasses. We investigated the refractive index and extinction coefficient dispersion by spectroscopic ellipsometry from ultraviolet, λ ≈ 0.193 μm, up to mid-infrared, λ ≈ 25 μm spectral region. Studied glasses exhibited large values of linear (n632 ≈ 1.91–2.09) and non-linear refractive index (n2 ≈ 1.20–2.67×10−11 esu), Verdet constant (V632 ≈ 22–33 radT−1m−1) and optical band gap energy (Eg ≈ 3.7–4.1 eV). The materials characterization revealed that BaO substitution by ZnO leads (at constant content of TeO2) to an increase in linear and nonlinear refractive index as well as Verdet constant while the optical band gap energy decreases. Fiber drawing ability of TeO2–ZnO–BaO glassy system has been demonstrated on 60TeO2–20ZnO–20BaO glass with presented mid-infrared attenuation coefficient. Specific parameters such as dispersion and single oscillator energy, Abbe number, and first-/third-order optical susceptibility are enclosed together with the values of magneto-optic anomaly derived from the calculation of measured dispersion of the refractive index.

Active correction of window Faraday effects for ITER laser diagnostics

Measurement of the change in polarization of a laser beam traversing a magnetized plasma is a standard diagnostic technique for extracting key plasma parameters, including density and current profile. Depending on the polarization orientation of the incident laser beam relative to theplasma magnetic field, the polarization change is denoted as either Faraday rotation or Cotton-Mouton effect. On ITER three laser diagnostics will make use of this effect to make their measurements. Unfortunately, this effect is also evident when the laser beam passes through the vacuum window. The large magnetic field and finite verdet constant of the window material mean that on ITER this effect — in particular faraday rotation — is non-negligible, and needs to be disentangled from the desired measurement parameter. The Toroidal Interferometer-Polarimeter (TIP) and Density Interferometer-Polarimeter (DIP), in particular, are affected. Both diagnostics use lasers in the 5–10 μm range, and will use zinc-selenide (ZnSe) as the vacuum window material. In order to compensate for the unwanted window distortion a sensor is being developed to monitor the magnetic field perpendicular to the window and activelycorrectfor the faraday rotation in real time. The sensor consists of an inductive coil closely fitted just in front of the window disc. It comprises several turns of fine wire in center-tap configuration. Both the raw voltage signal, as well as the integrated signal, will be monitored to estimate the magnetic field through the window disk. The system is designed to measure fields up to B <1 T with an accuracy of 0.01 T, at frequencies of D.C. to 1 kHz. The backend electronics will leverage off similar technology developed for other ITER magnetics systems. Using the real-time magnetic field information, in conjunction with published and/or measured data on the verdet constant of the ZnSe window material, in-house developed software will estimate the faraday rotation induced by passing through the window.An initial prototype of the sensor has been fabricated and results from preliminary characterization trials of the system are presented. Detailed testing is planned for the future using the DIP system prototype currently under development.

Effective Faraday rotator based on the TbYO3 crystal with a high Verdet constant and a high thermal conductivity.

Facing the demand of high-power laser development, a high-quality magneto-optical crystal with a high Verdet constant and a high thermal conductivity is needed. Herein, an effective Faraday rotation based on a TbYO3 single crystal with a strong magneto-optical effect, grown by the laser floating zone method, is demonstrated for the first time, to the best of our knowledge. The TbYO3 crystal has the Verdet constant which is 2.16 times (106 rad·m-1 T-1) higher than that of the TGG crystal (49 rad·m-1 T-1) at 880 nm. Additionally, the TbYO3 crystal also has a thermal conductivity of 11.8 W·m-1·K-1 and a laser-induced damage threshold of 1.59 GW·cm-2. These advantages can allow the TbYO3 crystal to be an attractive magneto-optical material.

Enhanced terahertz magneto-optical performance in substrate-free ultra-thick TbErBi:RIG crystal films

A wafer-scale single crystal thick film of rare-earth iron garnet (RIG) has been successfully produced on a 3-in. gadolinium gallium garnet (GGG) substrate using the liquid phase epitaxy method. The RIG crystal's thickness measures ∼550 μm. By removing the GGG substrate through polishing, we improved the terahertz (THz) transmittance of the RIG crystal. In the frequency range of 0.1–1.0 THz, the RIG material exhibits a large refractive index of around 4.50, with a transmittance of ∼60% and an absorption rate of only 10–50 cm−1. Furthermore, we investigated the THz magneto-optical effect in the RIG material through THz time-domain spectroscopy. The observed results demonstrate the presence and significance of the magneto-optical effect in the RIG crystal. To provide further insights, we measured the THz Faraday rotation angle of the 550 μm-thick RIG crystal using the THz-TDS system under an external magnetic field of 0.17 T. The measured Faraday rotation angle reached 22°, and the calculated Verdet constant for the RIG sample was ∼120°/mm/T. Considering these findings, our study highlights the unique properties of this wafer-scale single crystal thick film of RIG, including its low loss, high transmission, and strong magneto-optical effect in the THz range. These characteristics make it a promising candidate for various applications, such as THz magnetic polarization conversion, non-reciprocal phase shifters, and isolators.