Enhanced Faraday Rotation Research Articles

Plasmonic enhancement of Faraday rotation with gold nanodisks with low height-to-diameter aspect ratios

We investigate the Faraday rotation induced in gold nanodisks with low height-to-diameter aspect ratios. Through a systematic study, we analyze the phenomenon using electrostatic theory with the modified long-wavelength approximation. We show that the Faraday rotation is enhanced at the localized surface plasmon resonance when the nanodisk’s effective mean free path is equal to the mean free path of the conduction electrons in the bulk metal, where light absorption dominates over light scattering. We also show that the Faraday rotation is largely enhanced at shorter rather than longer wavelengths.

Controlling Bi/Fe ratio in bismuth iron garnet thin films deposited by confocal magnetron sputtering for enhanced Faraday rotation

We have successfully deposited high-quality bismuth-iron-garnet (BIG; Bi3Fe5O12) epitaxial thin films on single crystal gadolinium-gallium-garnet (GGG; Gd3Ga5O12) (111) substrates through Radio frequency (RF) confocal sputtering, utilizing separate bismuth and iron oxide sputtering targets and optimized thermal treatments. The Bi/Fe ratio in the deposited BIG thin films can be varied by controlling the sputter process parameters. These deposited thin films exhibit homogeneity and surface root mean square (rms) roughness of less than 2 nm. The epitaxial film quality is confirmed by X-ray diffraction (XRD) and Transmission electron microscopy (TEM). Moreover, the films demonstrate low optical loss and a magneto-optical Faraday rotation as high as −34o±1o /μm at a wavelength of 535 nm for a BIG thin film with a Bi/Fe ratio 0.7 and annealing temperature of 510oC. Additionally, the coercivity of the deposited films is lower than that of those deposited via RF sputtering using a single composite target. This co-sputtering approach provides real-time flexibility for the deposition of high-quality BIG films.

Enhanced Faraday rotation via Kerr nonlinearity in graphene metasurface

Enhanced Faraday rotation via Kerr nonlinearity in graphene metasurface

Enhancing temperature stability of Ce: RIG films Faraday rotation through magnetic sublattice control

Cerium doped rare-earth iron garnet (Ce: RIG) film is a promising candidate for magneto-optical devices in laser systems with giant Faraday effect; nevertheless, devices fail nonreciprocally with increasing temperature due to a negative Faraday rotation angle temperature coefficient. To mitigate this effect, the relationship between the magnetic moments of three distinct magnetic sublattices and the temperature coefficients of the Faraday rotation angle was investigated. Cerium doped holmium iron garnet (Ce: HoIG) film, where magnetic Ho3+ occupied the dodecahedrons, exhibited an enhanced Faraday rotation angle retention at a temperature of 400 K. However, the nonmagnetic ion doping in tetrahedral and octahedral sites yielded a negligible effect. The mechanism behind this occurrence is attributed to the magnetic compensation effect, which results in a small magnetic moment temperature coefficient within the range of 300–400 K. The study not only offers strategies for designing Ce: RIG components with reduced temperature coefficient, but also presents the development of a Ce: HoIG film exhibiting promising stability in Faraday rotation angle as a function of temperature.

Giant reduced magnetic anisotropy in magneto-optical garnet

Magneto-optical garnet shows great potential in integrated optical isolators due to its highly efficient non-reciprocity. In this work, we prepared magneto-optical lithium-modified terbium bismuth iron garnet films using the liquid phase epitaxy method and systemically investigated the effect of lithium modification on magnetic properties. We found a trace amount of lithium modification induced in-plane magnetization and a minimum in-plane driving field around 2 Oe. Meanwhile, high remanence over 70% was obtained in tensile-strain samples. Most importantly, in comparison to unmodified samples, the calculation of anisotropy demonstrated the giant reduction of growth-induced anisotropy in the Li: TbBiIG up to 105erg/cm3. It reveals a new rule of ions’ preferred occupation in dodecahedral sublattices indirectly. Furthermore, enhanced Faraday rotation in the near-infrared band was confirmed in the samples about 1 micrometer, up to 48% higher than unmodified samples. Our work shows Li:TbBiIGs enable a prime candidate material with substantial potential for integrated optical isolation applications.

Faraday rotation enhancement for colloidal spherical Au and Ag nanoparticles and their mixtures

So far, magnetooptical (MO) properties of silver nanoparticles (AgNPs) have been studied only by magnetic circular dichroism (MCD) spectroscopy at the surface plasmon resonance (SPR) band. However, direct knowledge of the Faraday rotation effect (FR) is very important in fundamental research and applications. In the present work, we study an enhancement of FR of individual gold nanoparticles (AuNPs) and AgNPs and their mixture of colloidal aqueous suspension. The Au and Ag spherical NPs were synthesized independently as colloids in an aqueous suspension and then such mixtures were studied (AgNPs were also studied as a suspension in hexane). The noble metal NPs were characterized by TEM, UV–Vis, and refraction methods. The enhancement of FR of individual NPs was observed and it is consistent with available MCD results. For the mixtures, observed changes of magnitude of FR is small, and coupling of both SPR is rather weak. The obtained FR spectra associated with SPR band have been successfully converted to MCD spectra using the Kramers-Kronig transformation. Calculated MCD spectra are consisted with that obtained by direct measurements.

Faraday rotation enhancement due to proximity effect of surface plasmon resonance in magnetoplasmonic colloidal mixtures

The modification of Magneto-optic Faraday Rotation (MFR) based on Surface Plasmon Resonance (SPR) of noble metal nanoparticles (NP) has been an exciting field of research. The underlying physical mechanisms are intriguing and correspond to various observation patterns in composite magnetoplasmonic systems. Exploiting the immense potential of SPR phenomenon for excellent electromagnetic field confinement and energy transfer to a wide variety of dimensionally different nanostructures, we report MFR measurements in typical magnetoplasmonic colloidal mixtures of separately synthesized cobalt ferrite (CoFe2O4) and gold (Au) NP at wavelength of 532 nm where we have observed a spectacular possibility for “proximity effect” based plasmonic enhancement of MFR, for the very first time. The Langevin-type MFR patterns show a strong dependence on the concentrations of participating systems, where a typical optimum concentration produced a significant enhancement in MFR. For both the entities present in the liquid, a mutually dependent optimum concentration was necessary to obtain the Langevin pattern as well as MFR enhancement, confirming the influence from SPR due to the proximity effect. The observations open up exciting possibilities to apply SPR to discover novel magnetoplasmonic phenomena underlined by proximity effects, in addition to eluding constrained procedures to synthesize composite magnetoplasmonic systems.

Faraday rotation enhancement and characteristic of the Weyl node separation and tilt degree by resonant tunneling

The 8 × 8 magneto-optical matrix has been derived to discuss the Faraday rotation (FR) effect, which is induced by the linear polarization wave passing through a sandwich structure composed of a dielectric layer and two identical Weyl semimetals (WSMs). The giant enhanced FR angle about 45° can be realized at the resonant tunneling wavelength of right hand circularly polarization (RCP) waves by enlarging the difference of the resonant tunneling wavelength of RCP and left hand circularly polarization waves suitably. It is shown that the resonant wavelengths depend on the Weyl node separation and tilt degree of Weyl cones in both type-I and type-II WSMs. More importantly, there exists a tunable one-to-one relationship between the Weyl node separation and the wavelength of the resonant FR angle, as well as the tilt degree and the wavelength of the resonant FR angle, which enables the characteristic of the Weyl node separation and tilt degree. Our research reveals an available method to determine the Weyl node separation and tilt degree of Weyl cones in both type-I and type-II WSMs.

Large Faraday rotation angle with high transmittance in Weyl semimetal assisted by resonant tunneling

Over the past decades, a series of nanostructures have been proposed to intensively enhance the Faraday rotation angle. However, the mutual inhibition between the Faraday rotation angle and the transmittance poses a challenge to achieve large Faraday rotation angle with high transmittance. In this paper, a sandwich structure consisting of two Weyl semimetal (WSM) layers of the same thickness and a dielectric layer is designed. Empowered by the resonant tunneling, the enhanced Faraday rotation effect is accompanied by an increase in transmittance. In the presence of realistic level of optical loss, the transmittance can be up to reach 97.4% when the resonant tunneling conditions of left-handed and right-handed polarized light are satisfied simultaneously, and its corresponding Faraday rotation angle can also be as high as −51.1 degrees. By adjusting the axial vector of the WSM layer, we design an optical isolator with a transmittance of up to 97% and a Faraday rotation angle of 45 degrees. This simple triple-layer structure provides some theoretical basis and reference value for future research into non-reciprocal devices.

Enhanced Faraday rotation by a Fano resonance in substrate-free three-dimensional magnetoplasmonic structures.

Three-dimensional magnetoplasmonic nanostructures possess more novel and richer optical and magneto-optical (MO) behaviors compared with planar nanostructures, and exhibit attractive potential applications in micro-nano non-reciprocal photonic devices. However, fabrication of three-dimensional magnetoplasmonic nanostructures is difficult using the usual nanofabrication methods. This work constructs three-dimensional substrate-free Au/Co/Au structures prepared using focused ion beam (FIB) technology. In the three-dimensional split-ring structure, with y-polarized light normal incidence, a three-dimensional coupling current is formed between the vertical split-ring and the bottom square hole, which causes excitation of the Fano resonance. The Fano resonance causes a significant enhancement of the local magnetic field, resulting in a larger Faraday rotation (FR). The resonance also brings about a sign reversal of FR, which is related to the direction of the Lorentz force on electrons. Similar effects also exist in the three-dimensional nanopillar structure and the three-dimensional nanoring structure in the simulation results. Due to the high flexibility of FIB machining, the height and shape of the three-dimensional split-ring can be arbitrarily changed, which means the FR intensity and the position of the FR null point are tunable. The designed three-dimensional structures provide a new route to regulate the Faraday effect, and broaden the possibilities for the design and construction of MO devices.

Tunable and enhanced Faraday rotation induced by the epsilon-near-zero response of a Weyl semimetal

In this paper, we theoretically study the Faraday (FR) rotation effect excited by a transverse-magnetic (TM)-polarized wave passing through a bulk Weyl semimetal (WSM). Results show that the FR angle maintains a large value $(\ensuremath{\sim}\text{--}{21}^{\ensuremath{\circ}})$ with high transmission $(|{t}_{pp}|\ensuremath{\sim}87%)$, which is caused by the close transmission coefficient of $|{t}_{ps}|$ $|{t}_{ps}|$ and $|{t}_{pp}|$. What is more important, the FR angle can be further enhanced at the epsilon-near-zero (ENZ) frequency, where a maximum FR rotation angle (absolute value) of 45\ifmmode^\circ\else\textdegree\fi{} has been obtained due to the sharp decreases of $|{t}_{pp}|$. Remarkably, the ENZ frequency of the WSM can be regulated by varying the Fermi energy and tilt degree, resulting in the tunable and enhanced FR angle at the different ENZ frequencies. Particularly, it is demonstrated that the incident angle should be declined with the increase of WSM thickness for enhancing the FR angle at the ENZ frequency. We also examine the effect of Weyl node separation on the FR angle. Our studies provide a simple and effective method to enhance and control the FR effect with a WSM or other topological semimetals.

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.

Enhanced Faraday rotation and control of pure spin-valley optical conductivity by topological phase in silicene

We investigate the Faraday rotation and optical conductivity in silicene under applying staggered exchange and perpendicular electric field. In silicene, combination of buckled atomic structure and strong spin orbit interaction (SOI) gives rise to electrons in the system behaving like 2-dimensional Dirac fermion with controllable mass. The Faraday rotation occurs when polarized light is passing through the silicene plane is calculated. The Faraday rotation related to topological phases is mainly focused. As a result, it is found that the presence of both exchange and electric fields is required to generate the Faraday rotation effect. The spin-valley dependent Dirac mass plays the role of the parameters to suppress the Faraday rotation. The Hall conductivity and Faraday rotation are still observed under the topological phases only in the cases of quantum anomalous Hall (QAH) and semimetal phase (SM), because their total Chern numbers do not go to zero. The very large angle is predicted for some specific electric and exchange field strengths. The perfect spin-valley filtered that only one electron specie is allowed to transport is also predicted in topological phase transition. This paves the way to perfectly control the pure spin-valley longitudinal current and to be applicable for beneficial spin-valley optoelectronic devices . • Faraday rotation (FR) and optical conductivity under topological phases in silicene is studied. • The presence of both exchange and electric staggered potentials is required to create FR. • FR is found at low photon frequency due only to the presence of quantum anomalous Hall and semimetal phases. • Large FR is enhanced by the presence of spin-valley dependent mass of Dirac fermions. • The controllable pure spin-valley current by photon frequency is related to topological phase transition.

Tunable Faraday rotation of ferromagnet thin film in whole visible region coupled with aluminum plasmonic arrays

Abstract To date, the plasmonic nanostructure utilized for magneto-optical (MO) enhancement has been limited to noble metals with resulted enhancement in the green-red part of visible spectrum. In this study, we fabricated a diffractive hexagonal array composed of Al nanoparticles (NPs) with a thin 7.5 nm ferromagnetic film and pushed the enhanced Faraday rotation (FR) into the blue to green range of the visible light. The freedom and ability to control the working spectral region in the whole visible range from 400 to 800 nm were also demonstrated by changing the lattice constant and the dielectric environment of plasmonic nanostructures. Particularly, in the blue range we obtained the maximum FR 0.57° at 410 nm with a broad boosting region around 0.5° from 400 to 500 nm. Moreover, the largest FR 1.66° was shown at 638 nm by tuning the dielectric environment into a higher refractive index medium. The results of our investigation demonstrate the potential of Al-based magnetoplasmonic effect and offer opportunities to push the MO spectral response out of visible range into the ultraviolet-blue range.

On the fabrication of one-dimensional magnetophotonic crystals from various oxides and metal–organic decomposition-made Bi0.5Y2.5Fe5O12

We demonstrate an approach for the fabrication of one-dimensional magnetophotonic crystals (1D MPCs) that are composed of electron beam evaporation-deposited Bragg mirrors (BMs) and a bismuth-substituted yttrium iron garnet layer made by metal–organic decomposition. Since such a garnet layer is crystallized at high temperatures, changes in structural and optical properties of BMs caused by annealing are studied. By subjecting single layers of SiO2, HfO2, ZrO2, and Ta2O5 to annealing, we found changes in their optical constants and thicknesses and interpreted stop band shifts in spectra of BMs. The ZrO2/SiO2 pair was found to be resistant to annealing and was used for 1D MPC fabrication. The resulting 1D MPCs were shown to exhibit Faraday rotation enhancement by an order of magnitude at a wavelength of the Fabry–Perot resonance.

Tunable enhanced Faraday rotation in a defected plasma photonic crystal under external magnetic field with different declinations

Magneto-optical responses and the potential for tunability when changing the variables of a one-dimensional defected magnetized plasma photonic crystal have been studied using a transfer matrix method for operation in the mm-range wavelength region. The effect of the number and dielectric defect layer thickness as well as the intensity and declination angle of magnetic field on transmittance, Faraday rotation, and its ellipticity has been investigated. The results demonstrate the ability to alter the resonant modes frequency at multiple levels of precision. The structures with four, six, and eight defect layers have been investigated. The number of defect dielectric layers changes the number of resonance modes. A single defect mode appears within the photonic bandgap with four defect dielectric layers while two defect modes were observed with six layers, and three modes with eight layers. An increase in magnetic field declination decreased the Faraday rotation intensity and width of Faraday resonance mode.

Magneto-optical performances of novel neodymium-doped CeF3 crystal

The highly transparent neodymium-doped CeF3 (Nd:CeF3) single crystal with diameter of 20 mm × 35 mm was grown by the Bridgman Stockbarger (BS) method. The optical and magneto-optical (MO) performances of Nd:CeF3 were experimentally investigated in UV–Vis and near-IR spectral range. Notably, Nd:CeF3 exhibits high transparency and significantly enhanced Faraday rotation. Compared with commercial terbium gallium garnet (TGG), Nd:CeF3 has higher Verdet constants at different measured wavelengths. The bulk laser-induced damage of c-cut Nd:CeF3 crystal was also determined by R-on-1 method. All the results demonstrate that the properties of Nd:CeF3 are superior to those of CeF3 and TGG. The excellent MO properties of Nd:CeF3 with a used wavelength of 0.3–2.2 µm are especially important for high power isolators in order to cover UV–Vis and the entire near-IR range.

Role of avoided crossing and weak value amplification on enhanced Faraday effect in magnetoplasmonic systems

Enhancement of magneto-optical effects in hybrid magneto-plasmonic systems has attracted considerable recent attention because of their potential for building non-reciprocal nanophotonic devices. Quantitative understanding of the fundamental origin and contributing mechanisms for the enhancement is crucial for optimizing applications. Here, we unravel different physical origins of the giant enhancement of Faraday rotation and ellipticity in a hybrid magneto-plasmonic system, namely, waveguided magneto-plasmonic crystal for excitation with transverse electric (TE) and transverse magnetic (TM) polarized light. With TE polarization excitation, where the surface plasmons are not directly excited, the natural weak value amplification of Faraday effects appearing due to the spectral domain interference of Fano resonance is the dominant cause of the enhancement. For TM polarization excitation, on the other hand, waveguide-plasmon strong coupling and its universal manifestation of avoided crossing plays an important role, leading to maximum enhancement of the magneto-optical effects in the avoided crossing regime.

Enhanced infrared Faraday rotations and transmission in nonreciprocal magneto-optical structure

At present, most of all the micro/nano scale structure is reciprocal material, that is, behave as reciprocity. Corresponding to the reciprocal material, the nonreciprocal materials can break the time reversal and detailed balance due to the special nonreciprocal effect, which can lead to nonreciprocal optical devices when magnetism is applied. In this paper, the Faraday rotation effect of an open square hole magnetic plasma structure with periodic corner openings has been studied. The size of the magneto-optical plasmon film is only 600 nm, which is extremely small compared to a hundred-micron magneto-optical garnet film. It is found that the Faraday deflection angle can be adjusted by changing the size of the applied magnetic field without affecting the transmittance. Moreover, the influence of the width of the metal structure and the thickness of the magneto-optical material on the Faraday effect is studied. The maximum Faraday deflection angle can be achieved as 22° and the transmittance is up to 0.63, as the side length of corner openings is set to 100 nm. At the same time, the mechanism of the giant Faraday effect is further explained through the output electric field distribution. It is found that the optical isolation had a high non-reciprocal Faraday rotation and optical transmission enhancement, which will has application in infrared optical isolation.

Enhanced Faraday rotation by dielectric metasurfaces with Bayesian shape-optimized scatterers.

In this Letter, we demonstrate how to optimize the magneto-optic response of a Huygens metasurface composed of square arrays of all-dielectric nano-disk scatterers. We compare cylindrical and shape-modified disks. Both provide a strongly enhanced Faraday rotation that is accompanied by almost 100% transmittance. The shape modification obtained via a Bayesian optimization algorithm results in a 50% increase in the magneto-optic response compared to the best cylindrical disk, providing 15° of polarization rotation for a 260 nm thick metasurface.