One-dimensional Magnetophotonic Crystals Research Articles

THE NARROW-BAND FILTER BASED ON A MAGNETOPHOTONIC CRYSTAL INVOLVING LAYERS WITH HYPERBOLIC DISPERSION LAWS

Subject and Purpose. Narrow-band filters are among the basic components of modern communication systems, instruments for spectros- copy, high-sensitivity sensors, etc. Photonic crystal structures open up broad possibilities for creating compact-sized, narrow-band filters in the optical and terahertz ranges. Tuning of spectral characteristics of photonic crystal filters is usually carried out through introduction of certain elements into their structure that are sensitive to external electric and magnetic fields. This work has been aimed at investigating electrodynamic characteristics of one-dimensional magnetophotonic crystals with structural layers characterized by "hyperbolic" disper- sion, and suggesting a multichannel, narrow-band filter on their base. Methods and Methodology. The dispersion equation for excitations in an infinite magnetophotonic crystal has been obtained within the framework of the Floquet-Bloch theory, with the use of fundamental solutions of Hill’s equation. The transfer matrix approach has been used to obtain an analytical expression for the transmission coefficient. Results. The band diagram of the one-dimensional magnetophotonic crystal has been analyzed for the case where one of the layers on the structure’s spatial period is characterized by a hyperbolic dispersion law. The areas of existence of surface wave regimes have been found for such layers for the case of normal incidence of the wave upon the finite-seized magnetophotonic crystal. Frequency dependences of the transmission coefficient are characterized by a set of high-Q resonant peaks relating to Fabry-Perot resonances in a periodic struc- ture of finite length. Conclusions. Application of a finite-seized, one-dimensional magnetophotonic crystal is considered as of a means forachieving mul- tichannel optical filtering and formation of a frequency comb. Expressions for the dispersion equation and transmission coefficient have been obtained within the framework of the Floquet-Bloch theory and with the use of the transfer matrix. The feasibility of surface mode excitation has been shown for gyrotropic layers of the periodic structure characterized by a hyperbolic dispersion law, for the case of nor- mal incidence upon the magnetophotonic crystal. The spectral response of the filter contains narrow-band peaks with a high transmission efficiency. By increasing the number of the structure’s periods it is possible to form a frequency comb, which effect can be useful for appli- cations in metrology and modern optical communication systems.

Surface waves Fabry-Perot modes of the finite magnetophotonic crystal in Voigt configuration

We have solved the problem of plane wave scattering by a finite gyrotropic magnetophotonic crystal in the Voigt configuration. To find an analytical solution, the method of the Floquet-Bloch wave theory with Cauchy boundary conditions for a one-dimensional magnetophotonic crystal and the transfer matrix method were used. The reflection and transmission coefficients are obtained in analytical form for arbitrary material parameters of the gyrotropic layers of the crystal. The field distributions within the finite crystal are found in explicit form. The regime of excitation of modified Zenneck-Sommerfeld waves and a new regime of unusual gyrotropic surface waves with positive values of the effective permittivity of one of the crystal layers are revealed. The features of the distribution of surface wave fields for the considered regimes of all Fabry–Perot modes at full transmission are studied. The nonreciprocal properties of the considered crystals are established depending on the incidence angle sign.

Magnetooptical properties of one-dimensional aperiodic magneto-photonic crystals based on Kolakoski sequences

Magnetooptical properties of one-dimensional aperiodic structures formed by stacking together magnetic and nonmagnetic layers according to the Kolakoski self-generation scheme are studied theoretically using the 4times4 transfer matrix method. The effect of the generation stage of the sequence, and the helicity and direction of light propagation through the magneto-photonic crystals on the transmission/reflection spectra as well as Faraday and ellipticity rotations, have been investigated. Our results reveal that this kind of aperiodic magneto-photonic crystals can be used for the fabrication of multifrequency laser cavities, and optical filters/sensors.

Dual-band nonreciprocal thermal radiation by coupling optical Tamm states in magnetophotonic multilayers

Kirchhoff's law is one of the most fundamental law in thermal radiation. The violation of traditional Kirchhoff's law provides possibilities for achieving energy conversion with higher efficiency. Various micro-structures have been designed to realize single-band nonreciprocal thermal emitters. However, dual-band nonreciprocal thermal radiations are still rarely studied. Here, we introduce magneto-optical material into a cascading one-dimensional (1-D) magnetophotonic crystal (MPC) heterostructure composed of two 1-D MPCs and a metal layer. Assisted by the nonreciprocity of the magneto-optical material and the coupling effect of two optical Tamm states (OTSs), a dual-band nonreciprocal lithography-free thermal emitter is achieved. The emitter exhibits near-complete dual-channel nonreciprocal thermal radiation at the wavelengths of 15.337 μm and 15.731 μm for an external magnetic field of 3 T and an incident angle of 56°. Besides, the magnetic field distribution is also calculated to confirm that the dual-band nonreciprocal radiation originates from the coupling effect between two OTSs. Our work may pave the way for constructing dual-band and multi-band nonreciprocal thermal emitters.

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.

Near-field radiative heat transfer between one-dimensional magnetophotonic crystals

We present a theoretical study of the effect of an external dc magnetic field in the near-field radiative heat transfer between two one-dimensional magneto-photonic crystals with unit cells comprising a magneto-optical layer made of n-doped InSb and a dielectric layer. We find that in absence of an external field, and depending on the gap size, the radiative heat transfer between these multilayer structures can be larger or smaller than that of the case of two InSb infinite plates. On the other hand, when an external magnetic field is applied, the near-field radiative heat transfer is reduced as a consequence of the suppression of hybridized surface polariton waves that are supported for transverse magnetic polarized light. We show that such reduction is exclusively due to the appearance of magnetic-field induced hyperbolic modes, and not to the polarization conversion in this magneto-optical system.

Floquet-Bloch waves in magnetophotonic crystals with transverse magnetic field

We solved the problem of Floquet-Bloch waves propagation in the one-dimensional gyrotropic magnetophotonic crystal with transverse magnetic field. New fundamental solutions of the Hill’s equation in crystal layers based on the Floquet theory for a third boundary value problem are obtained in the analytical form. The dispersion equation is found through fundamental solutions. The analysis of the dispersion properties of the structures depending on the material parameters was carried out and extraordinary surface waves inherent only in gyrotropic magnetophotonic crystals have been discovered.

Nematic reorientation effects on resonant modes, wavelength mismatch, and slow-light phenomena in one-dimensional magnetophotonic crystals with a dual anisotropic defect.

The present study is devoted to the investigation of spectral properties of an alternated sequence of magnetic and dielectric layers containing a dual defect based on magnetic and nematic layers. Combining the Hydrodynamic Continuum Theory for nematic liquid crystals and Berreman's formalism, we determine how the nematic ordering affects the light localization, polarization rotation, and slow-light phenomena observed in the magnetophotonic system. In particular, we analyze the effects associated with a field-induced reorientation of the director in a nematic defect with strong planar boundary conditions. Our results reveal that field-induced reorientation of the nematic ordering can be used as an efficient mechanism to tune and control the spectral properties of magnetophotonic structure, anomalies in group velocity, and the wavelength mismatch between resonant mode and maximum polarization. The effects of nematic layer thickness are also analyzed.

Design of multipeak one-way light absorber based on one-dimensional magnetophotonic crystal

The study of magnetophotonic crystals is usually based on its reflection and transmission of light waves, but its absorption properties are rarely studied. Considering the current high absorptivity of one-way absorbers has one absorption peak, and the optical constants of magnetophotonic crystals are all ideal approximation, we introduce the practical optical constants of silicon carbide (SiC) into the magnetophotonic crystals model. The optical properties are investigated in visible wavelength based on the transformation matrix method, and some parameter effects are also discussed in detail, such as the incidence angle and the thickness of defect layer. The one-dimensional (1-D) magnetophotonic crystal structure was systematically optimized. Then a multipeak one-way light absorber composed of real semiconductor and metal based on 1-D magnetophotonic crystal is further proposed, which makes the channel position of perfect nonreciprocal absorption controllable and the number increased; the influence of incident conditions on the absorption efficiency is greatly weakened and the universality and flexibility of one-way absorber in practice are greatly enhanced. The achievement provides new ideas for the study of nonreciprocal absorbers.

Enhancing the Faraday rotation in the monolayer phosphorus base of magneto-photonic crystals

We present a theoretical study on enhancing the Faraday rotation of the monolayer phosphorus in a symmetric one-dimensional defective magneto-photonic crystal. The results show that by embedding the monolayer black phosphorus in the defect layer, the Faraday rotation angle can be significantly enhanced due to the defect mode of the magneto-photonic crystal that can strongly confine the electromagnetic field in the vicinity of the black phosphorus. The enhanced Faraday rotation angle may be increased in proportion to the external magnetic field while keeping the working wavelength and transmittance basically unchanged. The enhanced Faraday rotation can reach a gain of 20.9 dB with a transmission exceeding 60% with the applied magnetic field of 5 T after introducing the defect mode. Moreover, the Faraday rotation and the operating wavelength can be tunable using the width of the thickness of the defect layer, the incident angle, and the electron doping.

Reducing the Length and Enhancing the Design Accuracy in the Synthesis of One-Dimensional Magnetophotonic Crystals

The influence of the materials that construct a one-dimensional magnetophotonic crystal (MPC) is investigated in this letter. Recently, we suggested a procedure for realizing a desirable magneto-optical performance by utilizing an MPC heterostructure. The performance to be realized consists of a desirable transmittance along with a desirable Faraday rotation angle. The synthesis procedure gives the heterostructure configuration, provided that the constituent materials have already been chosen. The heterostructure consists of dielectric Bragg gratings with a high optical contrast ratio as well as gratings with a low contrast ratio. In this letter, we show that by properly choosing the materials that compose the MPC, it is possible to reduce the length of the structure without violating the accuracy of the design. Indeed, we can reduce the length by customizing the high-contrast stacks of the MPC in such a way that they exhibit a larger contrast ratio. The length reduction is verified by two examples. In each of the examples, a desirable performance is realized by employing two different MPCs, which are composed of two different sets of materials. On the other hand, the designer can enhance the synthesis accuracy by customizing the low-contrast stacks of the MPC in such a way that they exhibit a smaller contrast ratio.

Enhancement of Faraday rotation in defect modes of one-dimensional magnetophotonic crystals

Abstract In this paper, employing of one-dimensional magnetophotonic crystals in infrared wavelengths range is considered. For this purpose, magnetophotonic multilayer structures, composed of magnetic defect layer surrounded by dielectric and MO Bragg mirrors, have been proposed. Ce:YIG with an optical thickness in the range of 0 to λs was used as a magnetic material. By using four by four transfer matrix method, the transmittance values and Faraday rotation (FR) angles of these structures were computed. The electric field distribution was obtained by Finite Element Method (FEM). By investigation of transmittance and FR angle of magnetophotonic crystals, it was possible to design the optimized structures with a rotation larger than 30 degrees and high transmittance. Such structures with a few micrometer thickness and fast magneto-optical (MO) responses have the potential to be used in MO devices like integrated photonic elements and sensors.

Existence of high Faraday rotation and transmittance in magneto photonic crystals made by silica matrix doped with magnetic nanoparticles

This paper focuses on studying the potential of CoFe2O4-doped magnetic nanoparticles SiO2 / ZrO2 matrix to produce high-performance one-dimensional magnetophotonic crystals (MPC) and to solve the problem of integrating magneto-optical devices. Given the importance of the magneto-optical Faraday effecton most non-reciprocal optical components, we studied the influence of different 1D structures on Faraday rotations.The potential of these structures offers a wide range of applications in the field of miniaturized and integrated non-reciprocal devicessuch as isolators.

Enhancement of magneto-optical responses in adjustable one-dimensional magnetophotonic crystals

We investigated the one-dimensional magnetophotonic crystals (1D − MPCs) created by magnetic defect layer sandwiched between dielectric photonic crystals (PCs) utilizing the 4×4 transfer matrix method (TMM). To simultaneously achieve high transmittance and large magneto-optical (MO) Faraday effect, we changed the repetition numbers of PCs and the thickness of defect layers. Using finite element method (FEM), we simulated the distribution of electric field in the length of structures. The efficient localization of light in the vicinity of defect layer led to MO responses enhancement and resonant transmittance inside the photonic band gap (PBG). For single cavity structure, the MO responses were enhanced for symmetric spatial configuration. By increasing the number of defect layer, the MO responses of MPCs were improved. The transmittance and Faraday rotation (FR) for MO multilayer structures having six cavities were obtained T = 0.92 and θF = 44.5° respectively. This is a proper case to design MO isolator applied in optical telecommunications.

Transmission characteristics of linearly polarized light in reflection-type one-dimensional magnetophotonic crystals

The propagation properties of linearly polarized light in reflection-type one-dimensional magnetophotonic crystals are studied by using the 4 × 4 transmission matrix method. The structure models of reflection-type one-dimensional magnetophotonic crystals are designed, the magnetic field direction control characteristics of reflection spectrum and Kerr rotation angle are discussed, and the effect of applied magnetic field direction and strength on reflection spectrum and Kerr rotation angle are analyzed. The results show that the non-diagonal elements in the dielectric constant of magneto optical materials change when the angle φ between applied magnetic field and optical path changes, the reflectivity and Kerr rotation angle decrease when the angle φ increases; when the applied magnetic field strength changes, the reflectivity and Kerr rotation angle increase when the applied magnetic field strength increases; by adjusting the angle φ and strength of the applied magnetic field, the rotation angle of Kerr can be adjusted to 45°, and a more flat reflection spectrum can be obtained by designing the appropriate structure.

Improvement of the polar magneto-optical Kerr effect in the spatial tunable one-dimensional magnetophotonic crystals

We have studied the magnetophotonic crystals (MPCs) with excellent capabilities to enhance reflection and Kerr rotation simultaneously. In order to simultaneously investigate the symmetric and nonsymmetric spatial structures, we have considered the different repetition numbers for dielectric photonic crystals around the magnetic defect layer. To construction of dielectric Bragg mirrors, we have used of Al2O3 due to low refractive index and its unique optical features. The Ce:YIG with high magneto-optical features is utilized as magnetic material to increasing the magneto-optical responses of structures. By adjusting spatial features such as repetition numbers of PCs and thickness of magnetic defect layers, we have achieved the magneto-optical Kerr rotation more than 70 degrees and reflection close to 1. We have introduced the structures with single and several cavities. For investigation of light localization at defect layer, the electric field distribution along the MPCs is simulated using finite element method (FEM). With light localization inside the cavity and multiple reflections in it, the magneto-optical (MO) responses of these MPCs are significantly increased. Our proposed structures having high MO responses, are suitable cases to design MO elements incorporated in integrated photonic devices and optical telecommunication tools.

Magneto-optical properties of asymmetric one-dimensional magneto-photonic crystals

We analytically investigate the magneto-optical properties of asymmetric one-dimensional magneto-photonic crystals (MPCs) by using our previously presented coupled mode description. We show that an MPC with one magnetic defect, placed asymmetrically, provides the same number of degrees of freedom as a symmetric double-defect MPC. Consequently, an asymmetric single-defect MPC allows arbitrary transmittance and Faraday rotation at the central frequency, just as a symmetric double-defect MPC, and hence a desired performance can be obtained by the more compact single-defect structure. However, the possible ranges of performance are more restricted than the possible ranges of a double-defect MPC. We present the synthesis relations to design the single-defect MPC. In a similar manner, we show that an asymmetric double-defect MPC provides more degrees of freedom than either a symmetric double-defect or an asymmetric single-defect MPC. The excessive degree allows us to design a more compact MPC than the symmetric double-defect MPCs for a desirable central frequency performance, in the wide possible range that double-defect structures provide.

Giant magneto-optical Kerr rotation, quality factor and figure of merit in cobalt-ferrite magnetic nanoparticles doped in silica matrix as the only defect layer embedded in magnetophotonic crystals

In this work, we report on the theoretical study of one-dimensional magnetophotonic crystals (MPC) comprising of periodic dielectric structure Si/SiO and of silica matrix doped with cobalt-ferrite (CoFe2O4) magnetic nanoparticles as the only magnetic defect layer. Such structure can be prepared by sol-gel dip coating method that controls the thickness of each layer with nanometer level, hence, can overcome the problem of integration of the magneto-optical (MO) devices. We have studied the influence of the volume fraction (concentration of magnetic nanoparticles VF%) on the optical (reflectance, transmittance and absorption) and MO (Kerr rotation) responses in reflection-type one-dimensional MPCs. During investigation of the influence of magnetic nanoparticle’s concentration, we found that giant Kerr rotations (even ≈135° for VF = 39%) can be obtained accompanied by large reflectance and low amounts for transmittance and absorption. We report on the demonstration of large MO quality factor and figure of merit in cobalt-ferrite magnetic nanoparticles in the infrared regime. Given the large Kerr rotation, high reflectance accompanied by low absorption and nearly zero transmittance of the 1D MPC containing cobalt-ferrite magnetic nanoparticles, large MO Q factor and figure of merit are obtained.

Bloch-surface-wave-induced Fano resonance in magnetophotonic crystals

We have observed the Fano-type Faraday rotation spectrum in a one-dimensional magnetophotonic crystal at the Bloch surface wave (BSW) resonance and found that it is a result of the coupling between the $s$-polarized BSW and the $p$-polarized waveguiding modes of the magnetophotonic crystal. The shape of the resonance is determined by the relative position and spectral splitting of the modes.

Highly-sensitive magneto-optical sensors based on thin transmission-type one-dimensional magnetophotonic crystals for the visualization of magnetic fields

We have performed a theoretical study on the case of thin magneto-optical (MO) sensors based on transmission-type one-dimensional magnetophotonic crystals (MPCs). We could achieve thin MPC structures having only two or three magnetic defect layers that lead to large Faraday rotations up to 30° at the wavelength 560 nm in the visible region. Since the sensitivity of a MO sensor depends on the thickness of the sensing film, these very thin MPCs can act as highly sensitive MO magnetic field sensors. We could achieve MPC-based sensors with sensitivities up to 0.057 °/G.