Faraday Rotation Spectra Research Articles

Faraday rotation and ellipticity spectroscopy between excited states of Rb vapor: Theory and experiment

The Faraday rotation and ellipticity spectra of rubidium $5{P}_{3/2}\ensuremath{\rightarrow}4{D}_{5/2}$ transition in a magnetic field have been calculated and experimentally measured. By using the rotating quarter-wave plate method, the Stokes parameters of the $5{P}_{3/2}\ensuremath{\rightarrow}4{D}_{5/2}$ near-resonant probe light are measured to obtain the Faraday rotation and the ellipticity. The variation of the rotation and the ellipticity spectra is analyzed in different magnetic fields, temperatures, and pump powers. The polarization rotation over 50 deg in 1529 nm with negligible elliptical distortion is obtained. Our study of the Faraday effect between excited states of atoms broadens the available wavelength of the Faraday effect in applications.

Polar magneto-optic Kerr and Faraday effects in finite periodic PT -symmetric systems

We discuss the anomalous behavior of the Faraday (transmission) and polar Kerr (reflection) rotation angles of the propagating light, in finite periodic parity-time ($\mathcal{P}\mathcal{T}$) symmetric structures, consisting of $N$ cells. The unit cell potential is two complex $\delta$-potentials placed on both boundaries of the ordinary dielectric slab. It is shown that, for a given set of parameters describing the system, a phase transition-like anomalous behavior of Faraday and Kerr rotation angles in a parity-time symmetric systems can take place. In the anomalous phase the value of one of the Faraday and Kerr rotation angles can become negative, and both angles suffer from spectral singularities and give a strong enhancement near the singularities. We also shown that the real part of the complex angle of KR, $\theta^{R}_1$, is always equal to the $\theta^{T}_1$ of FR, no matter what phase the system is in due to the symmetry constraints. The imaginary part of KR angles $\theta^{R^{r/l}}_2$ are related to the $\theta^{T}_2$ of FR by parity-time symmetry. Calculations based on the approach of the generalized nonperturbative characteristic determinant, which is valid for a layered system with randomly distributed delta potentials, show that the Faraday and Kerr rotation spectrum in such structures has several resonant peaks. Some of them coincide with transmission peaks, providing simultaneous large Faraday and Kerr rotations enhanced by an order one or two of magnitude. We provide a recipe for funding a one-to-one relation in between KR and FR.

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.

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.

A femtosecond magnetic circular dichroism spectrometer.

We describe the development of a broadband magneto-optical spectrometer with femtosecond temporal resolution. The absorption spectrometer is based on a white-light supercontinuum (∼320 to 750 nm) using shot-to-shot temporal and spectral referencing at 1 kHz. Static and transient absorption spectra using circularly polarized light are collected in a magnetic field. The difference spectra with respect to the external field direction give the static and transient magneto-optical Faraday rotation (magnetic optical rotary dispersion) and ellipticity (magnetic circular dichroism) spectra. An achromatic quarter-wave plate is used, and the impact of the deviation from ideal retardance on the spectra is discussed. Results from solution-based and thin-film samples are used to demonstrate the performance and wide applicability of the instrument. The sensitivities for the static and time-resolved data were found to be 5 and 0.4 mdeg, respectively. The method presents a simple way to measure magneto-optical spectra using a transient absorption spectrometer and an electromagnet.

A general method for calculation of Faraday rotation and transmittance in two-dimensional magneto-optic photonic crystals by solving vector-Helmholtz equation in anisotropic media

We propose a general method based on the plane wave expansion method for the calculation of the Faraday rotation and transmittance spectrum of the two-dimensional magneto-optic photonic crystal. The method is an extension of the conventional plane wave expansion method by and taking into account all the three components of the electromagnetic fields and considering the permittivity tensor with off-diagonal imaginary components representing the Faraday effect and then solving the vector Helmholtz equation. The formulation is explained in detail from the implementation points of view and the computation cost of the method. In the end, numerical results are presented to verify the accuracy and convergence of the method.

Magneto-optical properties of plasmonic hyperbolic metamaterials

The results of the experimental studies and numerical simulation of optical and magneto-optical properties of composite structures containing gold nanorods in porous anodic alumina templates and coated by a continuous nickel film are presented. We reveal two features in the Faraday rotation spectra of the structures in the vicinity of the wavelengths of 540 nm and 810 nm, which correspond to the epsilon-near-pole and epsilon-near-zero regions, respectively. Experimentally observed distinct enhancement of magneto-optical effects in the structures in the spectral vicinity of these points are consistent with the simulation results and open up novel opportunities for magnetic-field-assisted light manipulation.

Magneto-optical spectroscopy by the polarization modulation method using a multi-channel spectrometer

In the conventional magneto-optical (MO) spectrometer, MO spectra are measured for each wavelength using monochromatic light, resulting in a long measurement time of more than 1 h. To shorten the measurement time, we propose an MO spectrometer using a multi-channel spectrometer combined with the polarization modulation method, by which both Faraday rotation and Faraday ellipticity spectra can be simultaneously obtained in several minutes from three optical spectra measured with linearly, left- and right-circularly polarized lights. In this study, a measurement of Faraday rotation and Faraday ellipticity spectra of a bismuth-substituted neodymium iron garnet thin film was demonstrated.

Terahertz Faraday and Kerr rotation spectroscopy of Bi1−xSbx films in high magnetic fields up to 30 tesla

We report results of terahertz Faraday and Kerr rotation spectroscopy measurements on thin films of $\text{Bi}_{1-x}\text{Sb}_{x}$, an alloy system that exhibits a semimetal-to-topological-insulator transition as the Sb composition $x$ increases. By using a single-shot time-domain terahertz spectroscopy setup combined with a table-top pulsed mini-coil magnet, we conducted measurements in magnetic fields up to 30~T, observing distinctly different behaviors between semimetallic ($x < 0.07$) and topological insulator ($x > 0.07$) samples. Faraday and Kerr rotation spectra for the semimetallic films showed a pronounced dip that blue-shifted with the magnetic field, whereas spectra for the topological insulator films were positive and featureless, increasing in amplitude with increasing magnetic field and eventually saturating at high fields ($>$20~T). Ellipticity spectra for the semimetallic films showed resonances, whereas the topological insulator films showed no detectable ellipticity. To explain these observations, we developed a theoretical model based on realistic band parameters and the Kubo formula for calculating the optical conductivity of Landau-quantized charge carriers. Our calculations quantitatively reproduced all experimental features, establishing that the Faraday and Kerr signals in the semimetallic films predominantly arise from bulk hole cyclotron resonances while the signals in the topological insulator films represent combined effects of surface carriers originating from multiple electron and hole pockets. These results demonstrate that the use of high magnetic fields in terahertz magnetopolarimetry, combined with detailed electronic structure and conductivity calculations, allows us to unambiguously identify and quantitatively determine unique contributions from different species of carriers of topological and nontopological nature in Bi$_{1-x}$Sb$_x$.

Excitonic magneto-optics in monolayer transition metal dichalcogenides: From nanoribbons to two-dimensional response

The magneto-optical response of monolayer transition metal dichalcogenides (TMDs), including excitonic effects, is studied using a nanoribbon geometry. We compute the diagonal optical conductivity and the Hall conductivity. Comparing the excitonic optical Hall conductivity to results obtained in the independent particle approximation, we find an increase in the amplitude corresponding to one order of magnitude when excitonic effects are included. The Hall conductivities are used to calculate Faraday rotation spectra for MoS2 and WSe2. Finally, we have also calculated the diamagnetic shift of the exciton states of WSe2 in different dielectric environments. Comparing the calculated diamagnetic shift to recent experimental measurements, we find a very good agreement between the two.

Spectrometer based real-time magnetic Faraday rotation spectroscopy of Bi-YIG thin films

Abstract In this work, we have investigated the bismuth-substituted yttrium iron garnet (Bi-YIG) thin films prepared on glass substrate by modified metal-organic decomposition method. Real-time Faraday rotation spectrometer was used to characterize the magneto-optical properties of Bi-YIG films. The reliability of the measurement system and optimized analyzer setup was confirmed by comparing the Jones matrix calculations and measured results. The effect of annealing condition on the structural, magnetic and magneto-optical properties was investigated. A clear garnet-phase without secondary phase was observed for the Bi-YIG films annealed above 800 °C. Faraday rotation spectra of these films reveal the correlation between their crystallinity and magneto-optical properties. The highest Faraday rotation angle of −3.1 °/μm was achieved for 800 °C annealed sample. Simultaneous evaluation of real-time Faraday rotation spectra and the corresponding hysteresis loops can establish a path for the application of time-resolved magneto-optical spectroscopic analysis of magnetic thin films.

RGB Magnetophotonic Crystals for High-contrast Magnetooptical Spatial Light Modulators

Magnetooptical spatial light modulators (MOSLMs) are photonic devices that encode information in photonic waveforms by changing their amplitude and phase using magnetooptical Faraday or Kerr rotation. Despite the progress on both MO materials and switching methods, significant improvements on materials engineering and SLM design are needed for demonstrating low-power, multicolor, analog and high-contrast MOSLM devices. In this study, we present design rules and example designs for a high-contrast and large figure-of-merit MOSLM using three-color magnetophotonic crystals (MPC). We demonstrate for the first time, a three-defect MPC capable of simultaneously enhancing Faraday rotation, and high-contrast modulation at three fundamental wavelengths of red, green and blue (RGB) within the same pixel. We show using 2D finite-difference time-domain simulations that bismuth-substituted yttrium iron garnet films are promising for low-loss and high Faraday rotation MOSLM device in the visible band. Faraday rotation and loss spectra as well as figure-of-merit values are calculated for different magnetophotonic crystals of the form (H/L)p/(D/L)q/(H/L)p. After an optimization of layer thicknesses and MPC configuration, Faraday rotation values were found to be between 20–55° for losses below 20 dB in an overall thickness less than 1.5 µm including three submicron garnet defect layers. The experimental demonstration of our proposed 3-color MOSLM devices can enable bistable photonic projectors, holographic displays, indoor visible light communication devices, photonic beamforming for 5 G telecommunications and beyond.

Waveguiding in All-Garnet Heteroepitaxial Magneto-Optical Photonic Crystals

We report the properties of 1D all-garnet heteroepitaxial 21 layered magneto-optical photonic crystal designed and fabricated for the resonance wavelength 750 ± 3 nm. It is composed of alternating magnetooptical-active Bi3Fe5O12 and transparent Sm3Ga5O12 quarter-wavelength layers radio frequency magnetron sputtered onto single crystalline Ca, Mg, Zr:Gd3Ga5O12(111) substrate. Edges of the band gap and resonant central peaks in transmission and Faraday rotation spectra experience significant (about 60 nm) “blueshift” when the angle of light incidence increases up to 70°. Lower reflectance and strong enhancement of Faraday rotation of TE mode compared to the TM-polarized light testify a waveguiding of TE-mode within a resonant λ/2 Bi3Fe5O12 cavity.

Faraday rotation in cesium nano-layers in strong magnetic fields

ABSTRACTWe show that the Faraday rotation (FR) in strong longitudinal magnetic fields is a convenient tool to study atomic transitions by using the line in a Cs vapour confined in a nanocell of thickness nm. We use strong magnetic fields ranging from 0.1 to 6 kG, in which Cs atomic transitions are split into a large number of components, and FR signals of spectral width of ∼ 50 MHz are frequency-resolved allowing the investigation of individual transitions. For magnetic fields of several kG, the hyperfine Paschen–Back regime is reached that is manifested by the presence in the spectrum of the eight FR components having the amplitudes of the same height and located with almost equidistant frequencies. A remarkable feature of FR spectrum is the proportionality of its amplitude to the probability of an atomic transition in a strong magnetic field. A theoretical model which agrees well with the experiment is developed.

Faraday rotation maps of disc galaxies

Faraday rotation is one of the most widely used observables to infer the strength and configuration of the magnetic field in the ionised gas of the Milky Way and nearby spiral galaxies. Here we compute synthetic Faraday rotation maps at $z=0$ for a set of disk galaxies from the Auriga high-resolution cosmological simulations, for different observer positions within and outside the galaxy. We find that the strength of the Faraday rotation of our simulated galaxies for a hypothetic observer at the solar circle is broadly consistent with the Faraday rotation seen for the Milky Way. The same holds for an observer outside the galaxy and the observed signal of the nearby spiral galaxy M51. However, we also find that the structure and angular power spectra of the synthetic all-sky Faraday rotation maps vary strongly with azimuthal position along the solar circle. We argue that this variation is a result of the structure of the magnetic field of the galaxy that is dominated by an azimuthal magnetic field ordered scales of several kpc, but has radial and vertical magnetic field components that are only ordered on scales of 1-2 kpc. Because the magnetic field strength decreases exponentially with height above the disk, the Faraday rotation for an observer at the solar circle is dominated by the local environment. This represents a severe obstacle for attempts to reconstruct the global magnetic field of the Milky Way from Faraday rotation maps alone without including additional observables.

Electrically-controlled Faraday rotation and wavelength mismatch phenomena in a magnetophotonic structure containing nematic layers

In this study, we investigate the effects of the director reorientation on the spectral properties of a one-dimensional magnetophotonic crystal constituted by a sequence of magnetic and nematic layers, which exhibits a magneto-optical defect as the central layer. Using the Eidner-Oldano treatment to solve the Berreman equation, we numerically determine how the Faraday rotation and transmission spectrum of the photonic systems are affected by a field-induced reorientation in the nematic layers. Our results reveal that the transmittance spectrum of the magnetophotonic system is strongly sensitive to the director profile when the applied voltage is raised above the Freedericksz threshold. The director reorientation leads to the suppression of the typical wavelength mismatch between the Faraday rotation and light localization phenomena in one-dimensional photonic structures based on materials with different types of birefringence. Considering the polarization configurations of the propagation eigenmodes for a birefringent medium, the main mechanism behind mismatch suppression is analyzed, emphasizing the effects associated with the field-induced nematic reorientation. Our results show that the electric control of wavelength mismatch in magnetophotonic systems may be used as an efficient mechanism to develop a new class of optical switches and logic gate devices.

Polarization-Sensitive Fourier-Transform Spectroscopy of HgTe/CdHgTe Quantum Wells in the Far Infrared Range in a Magnetic Field

Spectra of magnetoabsorption and Faraday rotation in HgTe/CdHgTe heterostructures with single and double quantum wells in high magnetic fields up to 11 T have been studied by the Fourier-transform spectroscopy method. The study of Faraday rotation spectra makes it possible to determine the sign of resonance circular polarization of transitions between Landau levels of carriers, which allows identifying observed intraband and interband transitions in the far and middle infrared ranges.

Weak enhanced resonant Faraday rotation in pure cobalt plasmonic lattices: Thickness dependent Faraday rotation studies

The thickness dependent magneto-optical Faraday rotation in Co ferromagnetic thin films and perforated periodic Co nano-hole arrays were investigated. It was observed that the optical response and Faraday rotation of Co nano-hole arrays were strongly dependent on the thickness of the film, and the Faraday rotation reached the maximum amplitude at an optimal thickness value of 30–50 nm, which contrasted with the Co thin films where the Faraday rotation increased with the film thickness. In addition, the Faraday rotation spectra of Co nano-hole arrays showed a weak resonantly enhanced peak at the anti-resonance modes (or Wood’s anomalies) on the transmission spectra, which correspond to the enhanced local electric field at the film and surrounding medium interfaces. All experimental results were confirmed by the finite-difference time domain calculations.

Surface plasmon resonance enhanced light absorption and wavelength tuneable in gold-coated iron oxide spherical nanoparticle

Surface plasmon in nano-sized particles, such as gold, silver, copper and their composites, has recently attracted a great deal of attention due to its possible uses in many applications, especially in life sciences. It is desirable for application devices with a tenability of surface plasmon wavelength and optical properties enhancement. This article presents enhanced optical light absorption and tunable wavelength in gold-coated magnetite (Fe3O4@Au core-shell) nanoparticles embedded in water using the theoretical method of discrete dipole approximation (DDA). The absorption spectra in the wavelengths from 350 to 900 nm were found to be the spectra obtained from Fe3O4@Au core-shell nanoparticles, and when compared with pure Fe3O4 nanoparticles, the surface plasmon resonance can be enhanced and tuned over the entire visible spectrum (viz. 350–800 nm) of the electromagnetic spectrum by varying the Au shell thickness (2–5 nm). Similarly, the Faraday rotation spectra can also be obtained.

Theoretical calculation of optical and magneto optical properties of magnetite nanorods

The optical and magneto-optical called Faraday rotation of composites containing isolated Fe3O4 (magnetite) nanorods particles are presented in the wavelength range from 300-700 nm. The results were obtained by using the discrete dipole approximation (DDA) method. The composite materials are constructed by combining Fe3O4 nanorods particles and the material with fixed dielectric constant of 2.25. The Fe3O4 nanorods of different aspect ratio (AR), varied from 3 to 7, were used to embed in the host material. The influence of the orientation of Fe3O4 nanorods comparing with the incident light and number particles on the Faraday rotation spectrum were also presented. The absorption cross-section spectra of Fe3O4 nanorods were able to be observed only when the main axis was aligned parallel to the polarization direction and perpendicular with the direction propagation of excited light.