Nonreciprocal Effects Research Articles

Schrödinger plasmon–solitons in Kerr nonlinear heterostructures with magnetic manipulation

We investigate surface plasmon-soliton (SPS) propagation in transverse magnetic field in heterostructures with Kerr nonlinearity. The nonlinear Schrödinger equation in the framework of perturbation theory has been derived for three cases: a single-interface metal/nonlinear-dielectric structure and double-interface structures of nonlinear-dielectric/metal/dielectric with either ferromagnetic or nonmagnetic dielectric. The effect of the magneto-optical nonreciprocity in the Schrödinger equation is found. The estimations show that the effect is the strongest for the double-interface structure with a magnetic substrate in the vicinity of the resonant plasmonic frequency. We have also shown that the external magnetic field modifies SPS amplitude and width.

Surface magneto plasmons and their applications in the infrared frequencies

Abstract Due to their promising properties, surface magneto plasmons have attracted great interests in the field of plasmonics recently. Apart from flexible modulation of the plasmonic properties by an external magnetic field, surface magneto plasmons also promise nonreciprocal effect and multi-bands of propagation, which can be applied into the design of integrated plasmonic devices for biosensing and telecommunication applications. In the visible frequencies, because it demands extremely strong magnetic fields for the manipulation of metallic plasmonic materials, nano-devices consisting of metals and magnetic materials based on surface magneto plasmon are difficult to be realized due to the challenges in device fabrication and high losses. In the infrared frequencies, highly-doped semiconductors can replace metals, owning to the lower incident wave frequencies and lower plasma frequencies. The required magnetic field is also low, which makes the tunable devices based on surface magneto plasmons more practically to be realized. Furthermore, a promising 2D material-graphene shows great potential in infrared magnetic plasmonics. In this paper, we review the magneto plasmonics in the infrared frequencies with a focus on device designs and applications. We investigate surface magneto plasmons propagating in different structures, including plane surface structures and slot waveguides. Based on the fundamental investigation and theoretical studies, we illustrate various magneto plasmonic micro/nano devices in the infrared, such as tunable waveguides, filters, and beam-splitters. Novel plasmonic devices such as one-way waveguides and broad-band waveguides are also introduced.

Nonreciprocal TE–TM Mode Conversion Based on Photonic Crystal Fiber of Air Holes Filled With Magnetic Fluid Into a Terbium Gallium Garnet Fiber

The nonreciprocal optical effect of Faraday rotation (FR) is widely exploited in optical isolators to suppress back-reflections to protect optical sources and other devices from injection noise, or in optical circulators to route counter-propagating signals in a single physical channel to different ports [1]. The first concept of an integrated isolator was based on nonreciprocal TE-TM mode conversion. However, most proposals of the waveguide type isolators are based on nonreciprocal TE-TM mode conversion [2], the nonreciprocal coupling between these modes is caused by the FR if the magnetization is aligned along the z-axis, parallel to mode propagation. FR effect can be used for magnet sensors, because the Verdet constant of silica fibre is small (∼1.1 rad/(T.m) at 1064 nm) [3]. In this work, we propose to study the nonreciprocal TE-TM mode conversion phenomenon, by the simulation of magneto photonic crystal fibre (MPCF). It consists of a periodic triangular lattice of air-holes filled with magnetic fluids (Fe 3 O 4 ) into a Terbium Gallium Garnet (TGG) fibre which is a kind of synthetic garnet with chemical composition Tb 3 Ga 5 O 12 . This garnet was chosen as a Faraday rotator material which has excellent transparency properties and is very resistant to laser damage. TGG has also a high Verdet constant which results in the FR effect. We simulated the influence of gyrotropy and the wavelength, and calculated the FR and modal birefringence. In this MPCF fibre, the light is guided by internal total reflection, like classical fibres. However, it was shown that they could function on a mode conversion much stronger than conventional fibres.

Scalable Fabrication of Quasi-Three-Dimensional Chiral Plasmonic Oligomers Based on Stepwise Colloid Sphere Lithography Technology.

We report a simple and scalable method for the fabrication of spiral-type chiral plasmonic oligomers based on the stepwise colloid sphere lithography technology. Through carefully adjusting the azimuthal angle Φ of polystyrene (PS) sphere array monolayer and the deposition thickness kn, the chiral plasmonic oligomers composed of four achiral particles can be successfully fabricated on a desired substrate. And their chiral sign, i.e., left-hand or right-hand, is dependent on the anticlockwise or clockwise deposition sequence of the achiral particles. The measured results show a large chiroptical resonance in the visible region, and this resonance can be easily adjusted by using different sizes of PS spheres. Our in-depth theoretical and experimental researches further reveal that the obtained chiral plasmonic oligomers are indeed a kind of quasi-three-dimensional chiral nanostructures, which own a three-dimensional geometrical morphology, but with nonreciprocity chiroptical effect. The ease and scalability (>1 cm2) of the fabrication method make chiral plasmonic oligomers promising candidates for many applications, such as chiral biosensor and catalysis.

Non-reciprocity and refraction of elastic waves in a solid with aligned parallel gaps

Non-reciprocal and refractive devices for elastic waves are designed using a solid with aligned parallel gaps. The gaps are assumed to be thin so that they can be considered as parallel rectangular cracks separating effective thin plates. To formulate the transmission and reflection coefficients for SV- and P-wave, an analytical model is established using thin plate theory with displacement and force continuous at the junction between plate and exterior body. The analytical model compares well with full FEM simulations. The non-reciprocity effect for P-waves is achieved by sending an incident P-wave at a critical angle, at which total conversion to SV-wave happens, with respect to the normal of a free boundary. An array of parallel gaps perpendicular to the propagation direction of the reflected waves stop the SV-wave but let P-wave travel through. Thus, the energy transmission is high from one side to another and is low from the opposite direction. The refractive effect for SV-waves is achieved by choosing the slope of the edge of plate array, and plate members for |T| = 1 at the same frequency with the ratio between plate length and flexural wavelength fixed. Examples of elastic non-reciprocal and wave steering devices will be discussed.

High sensitivity magnetic field sensing method based on magneto-photonic crystal slow light Sagnac interferometers

The magnetic field sensing properties based on the slow light effect of magneto-photonic crystals are studied. The nonreciprocal slow light effect of the magneto-photonic crystal immersed into an applied magnetic field is deduced by the scattering matrix method. A Sagnac interferometer is designed to enhance the sensitivity coefficient to the magnetic field and suppress the influences of reciprocal disturbances. Numerical results show that the sensitivity coefficient of a MPC slow light sensor is about 50 times that of the sensor made of bulk magneto-optic material with the same thickness. The influences of structural parameters of the magneto-photonic crystal, such as the number of periods, the duty ratio and the chirp, on the sensitivity coefficient are discussed.

Simulation of thermal fields using different types of wide burnishing

The article features simulation of heat build-up in the tool while treatment using different types wide burnishing. The understanding of conditions of heat build-up and heat distribution and the quantitative estimation on the finishing stages of part's treatment is always challenging, because there is a possibility of negative and nonreciprocal effect onto the development of performance properties of treated parts. This issue gains particular importance during treatment, including burnishing using no means of lubrication.

A Search for Parent-of-Origin Effects on Honey Bee Gene Expression.

Parent-specific gene expression (PSGE) is little known outside of mammals and plants. PSGE occurs when the expression level of a gene depends on whether an allele was inherited from the mother or the father. Kin selection theory predicts that there should be extensive PSGE in social insects because social insect parents can gain inclusive fitness benefits by silencing parental alleles in female offspring. We searched for evidence of PSGE in honey bees using transcriptomes from reciprocal crosses between European and Africanized strains. We found 46 transcripts with significant parent-of-origin effects on gene expression, many of which overexpressed the maternal allele. Interestingly, we also found a large proportion of genes showing a bias toward maternal alleles in only one of the reciprocal crosses. These results indicate that PSGE may occur in social insects. The nonreciprocal effects could be largely driven by hybrid incompatibility between these strains. Future work will help to determine if these are indeed parent-of-origin effects that can modulate inclusive fitness benefits.

Nonreciprocal propagation of hybrid electromagnetic waves in a layered ferrite–ferroelectric structure with a finite width

Effects of the nonreciprocal propagation of electromagnetic waves in a transversally limited ferrite–ferroelectric structure with a finite width and tangential magnetization have been considered. Nonreciprocal effects are manifested in the range of frequencies corresponding to the hybridization of electromagnetic waves of the ferrite and ferroelectric waveguides. The electrodynamic characteristics of waves propagating in the layered structure with a finite width in different directions have been calculated by the finite element method. The nonreciprocity factors have been calculated for transverse waveguide modes. It has been shown that nonreciprocity owing to the gyrotropy of the ferrite waveguide leads to a change in the spatial distribution of the components of electromagnetic fields in the layered structure and to the redistribution of the power transferred by an electromagnetic wave between the layers of the structure. The results obtained can be used to create nonreciprocal microwave microdevices with double control.

Reciprocity failure in piezoelectric polymer composite

Reciprocity principles, which entail equivalent outcome on exchange of cause and effect, are widely used and accepted. We present a piezoelectric composite system designed so that reciprocity does not hold; sensitivity is substantially enhanced. Reciprocity failure is observed in which the piezoelectric direct effect (stress causes polarization) sensitivity is unequal to the converse effect (electric field causes deformation) sensitivity . The piezoelectric polymer PVDF under isothermal conditions on a polymer substrate obeys reciprocity. Reciprocity failure occurs when a bumpy contact condition causes stress gradients. Reciprocity failure with strong frequency dependence occurs in the presence of thermal flux that is modulated by force: a non-equilibrium condition. Non-reciprocal effects give rise to a maximum enhancement of a factor of five in sensitivity.

Current control of light by nonreciprocal magnetoplasmonics

The ability to actively control light has long been a major scientific and technological goal. We proposed a scheme that allows for active control of light by utilizing the nonreciprocal magnetoplasmonic effect. As a proof of concept, we applied current signal through an ultrathin metallic film in a magneto-plasmonic multilayer and found that dynamic photonic nonreciprocity appears in magnetic-optical material layer due to the magnetic field being induced from current signal and modulates surface plasmon polaritons trapped in the metal surface and the light reflected. The proposed concept provides a possible way for the active control of light and could find potential applications such as ultrafast optoelectronic signal processing for plasmonic nanocircuit technology and ultrafast/large-aperture free-space electro-optic modulation platform for wireless laser communication technology.

Enhanced nonreciprocal effects in magnetoplasmonic systems supporting simultaneously localized and propagating plasmons.

Perforated magnetoplasmonic Au/Co/Au multilayers support both localized and propagating surface plasmon resonances. The presence of holes produces an enhancement of the magnetic field modulation of the propagating surface plasmon wavevector with respect to the isostructural continuous film in the spectral region corresponding to the hole associated localized plasmon resonance. This is due to the increased electromagnetic field in the surrounding area of the resonant hole, and the subsequent additional contribution to the magnetic modulation of the continuous film. This novel concept that gives rise to enhanced magnetic field induced nonreciprocal effects can be of interest in the development of innovative platforms for sensing applications, optical isolators and modulators.

First and second order in magnetization effects in optical second-harmonic generation from a trilayer magnetic structure

Linear and nonlinear optical properties of a thin planar CoFe/Al2O3/CoFe structure for different angles of incidence of the fundamental radiation are studied by means of the magneto-optical Kerr effect and magnetization-induced second-harmonic generation (SHG). The composition of this multilayered structure supports the appearance of the antiferromagnetic state, which leads to nonreciprocal optical effects and is discussed in terms of the magnetic toroid moment. We show that in accordance with the phenomenological description, SHG magnetic hysteresis loops for a linearly polarized pump beam are determined by linear in magnetization M components of the SHG polarization, while for a circularly polarized pump such a description necessarily involves both linear and quadratic in M components of the nonlinear polarization. Symmetry analysis of the magnetization-induced SHG supports the differences between the cases of linear and circular polarization of the incident radiation observed in the experiment, as well as a partial suppression of first in magnetization SHG contributions. Relative values of the linear and quadratic in magnetization components of the SHG polarization are estimated for the trilayer structure and for a reference homogeneous ferromagnetic film.

Nonreciprocal transmission in a nonlinear photonic-crystal Fano structure with broken symmetry

Nanostructures that feature nonreciprocal light transmission are highly desirable building blocks for realizing photonic integrated circuits. Here, a simple and ultracompact photonic-crystal structure, where a waveguide is coupled to a single nanocavity, is proposed and experimentally demonstrated, showing very efficient optical diode functionality. The key novelty of the structure is the use of cavity-enhanced material nonlinearities in combination with spatial symmetry breaking and a Fano resonance to realize nonreciprocal propagation effects at ultralow power and with good wavelength tunability. The nonlinearity of the device relies on ultrafast carrier dynamics, rather than the thermal effects usually considered, allowing the demonstration of nonreciprocal operation at a bit-rate of 10 Gbit s−1 with a low energy consumption of 4.5 fJ bit−1.

Fabry-Perot interferometer with quantum mirrors: nonlinear light transport and rectification.

Optical transport represents a natural route towards fast communications, and it is currently used in large scale data transfer. The progressive miniaturization of devices for information processing calls for the microscopic tailoring of light transport and confinement at length scales appropriate for upcoming technologies. With this goal in mind, we present a theoretical analysis of a one-dimensional Fabry-Perot interferometer built with two highly saturable nonlinear mirrors: a pair of two-level systems. Our approach captures nonlinear and nonreciprocal effects of light transport that were not reported previously. Remarkably, we show that such an elementary device can operate as a microscopic integrated optical rectifier.

Optical nonreciprocity of a five-level M-type atomic optical lattice in move

We investigate the dual-channel optical nonreciprocity effects of a moving atomic multilayer structure driven into a five-level M-type configuration by two strong coupling fields and two weak probe fields. We find that both the two probe fields propagating along the moving lattice will experience forward–backward asymmetry in transmission. For each one of the two probe fields, two frequency regions with very large nonreciprocity effect may exist and fit within the two AT splitting transparent windows contributed by the two coupling fields, and the degree and position of the nonreciprocity parameter could be controlled by modulating the coupling intensities and frequencies.

Non-reciprocal geometric wave diode by engineering asymmetric shapes of nonlinear materials.

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports.

Magnetoelectric effects in local light-matter interactions.

We study the generic dipole interaction of a monochromatic free-space electromagnetic field with a bi-isotropic nanoparticle or a molecule. Contributions associated with the breaking of dual, P, and T symmetries are responsible for electric-magnetic asymmetry, chirality, and the nonreciprocal magnetoelectric effect, respectively. We calculate absorption rates, radiation forces, and radiation torques for the nanoparticle and introduce novel field characteristics quantifying the transfer of energy, momentum, and angular momentum due to the three symmetry-breaking effects. In particular, we put forward a concept of "magnetoelectric energy density," quantifying the local PT symmetry of the field. Akin to the "superchiral" light suggested recently for local probing of molecular chirality, here we suggest employing complex fields for a sensitive probing of the nonreciprocal magnetoelectric effect in nanoparticles or molecules.

Surface plasmons in nanowires with toroidal magnetic structure.

We consider the problem of the influence of a toroidal magnetization on a cylindrical surface plasmon polariton (SPP) propagating along a nanowire of a circular cross section. It follows from the dispersion equations that the SPP wavenumber linearly depends on the toroidal moment and the effect of magneto-optical nonreciprocity appears. The numerical solution of the dispersion equations demonstrates that the corresponding splitting of the SPP dispersion curves for two opposite directions of the toroidal moment is increased by an order of magnitude with respect to the planar case. The largest values of this splitting are observed for systems with relatively low optical losses, as is demonstrated by calculations for SPPs in a gold cylinder surrounded by rare-earth bismuth iron garnet.

Accurate vectorial finite element mode solver for magneto-optic and anisotropic waveguides.

In this work, a dielectric waveguide mode solver is presented considering a general nonreciprocal permittivity tensor. The proposed method allows us to investigate important cases of practical interest in the field of integrated optics, such as magneto-optical isolators and anisotropic waveguides. Unlike the earlier developed mode solver, our approach allows for the precise computation of both forward and backward propagating modes in the nonreciprocal case, ensuring high accuracy and computational efficiency. As a result, the nonreciprocal loss/phase shift can be directly computed, avoiding the use of the perturbation method. To compute the electromagnetic modes, the Rayleigh-Ritz functional is derived for the non-self adjoint case, it is discretized using the node-based finite element method and the penalty function is added to remove the spurious solutions. The resulting quadratic eigenvalue problem is linearized and solved in terms of the propagation constant for a given frequency (i.e., γ-formulation). The main benefits of this formulation are that it avoids the time-consuming iterations and preserves the matrix sparsity. Finally, the method is used to study two examples of integrated optical isolators based on nonreciprocal phase shift and nonreciprocal loss effect, respectively. The developed method is then compared with the perturbation approach and its simplified formulation based on semivectorial approximation.