Magneto-optical transverse Kerr effect in a film-substrate system

The problem of electromagnetic reflection at an oblique angle of incidence in a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate is studied. The magnetizations in both the film and substrate are assumed normal to the plane of incidence (transverse geometry). The results are expressed in terms of the reflection matrix. The solution includes the conditions for guided wave propagation in the system. As a special case of the general formulae the reflection matrix in a system consisting of a uniaxial film and a uniaxial substrate optical axes of which are oriented normal to the plane of incidence are obtained.     

Magneto-optical longitudinal Kerr effect in a film-substrate system

The problem of electromagnetic reflection at an arbitrary angle of incidence in a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate is considered. The magnetization in both the film and substrate is assumed parallel to the planar interfaces and to the plane of incidence. The analysis provides the dispersion relation for the guided wave propagation in the system. The obtained general formulae are applied to the special cases of (a) normal incidence, (b) oblique incidence on a uniaxial film on a uniaxial substrate, both optical axes being parallel to the interfaces and to the plane of incidence, and (c) to the case when the permittivity tensor diagonal elements are the same and the off-diagonal element is small. The possible practical applications of the present analysis are in the ellipsometry of thin-film — substrate structures displaying magnetic order and in the theory of magneto-optic thin-film devices for integrated optics.     

Magneto-optical effects in crystals at the normal incidence

We consider the interaction of a polarized electromagnetic wave in a magnetically ordered crystal plate surrounded by an isotropic ambient at the normal incidence. The crystalline medium of the plate is specified by the general non-symmetric permittivity tensor. The results are expressed in terms of the transmission and reflection matrices which relate the electric fields of the incident wave to those of transmitted and reflected waves. Their applications are illustrated by examples of an isotropic plate magnetized normal to the interface, a cubic crystal magnetized parallel to the interface and an orthorhombic crystal magnetized along the axis normal to the interface. The effect of the reflection from the interfaces and the interference effect are included. The paper treats the reflection at an interface between an isotropic ambient and an absorbing magnetic crystal at small non-zero angles of incidence. The general reflection matrix is applied to the determination of the magneto-optical effects quadratic in magnetization.     

Reflexion und Brechung des Lichtes an optisch einachsigen Medien

Reflection and Refraction of Light in Uniaxial Media The formulae for the amplitude relations for the reflection and refraction of plane monochromatic light waves at a plane interface between an isotropic and an arbitrarily anisotropic medium, derived in an earlier paper by the author, are specialized here to the case of uniaxial media. The incidence both from the isotropic and from the uniaxial medium is dealt with. A series of special cases (normal incidence, optical axis parallel or normal to the plane of incidence, transition from uniaxial to isotropic media a.o.) are considered.     

Multilayer Anisotropic Bi-periodic Diffraction Gratings

The formalism of Rokushima and Yamakita [J. Opt. Soc. Am. 73 (1983) 901] treating the diffraction on planar multilayered 1D anisotropic gratings is extended to the diffraction on anisotropic 2D multilayer grating structures bi-periodic in the plane parallel to the interfaces. In addition to the oblique incidence of plane waves, the case of normal incidence is also treated. The goal of the paper is to provide a basis for the formal analysis of 2D patterned multilayers with natural or induced anisotropies. For example, such structures are of interest in the design of new magnetic and magneto-optic devices. In view of the fact that the anisotropies have often a negligible effect on the energy distribution among diffracted modes with respect to the isotropic case the optical response is alternatively expressed in terms of the ellipsometric parameters of diffracted waves. The present analysis represents generalization of the problem of electromagnetic wave interactions in planar multilayers consisting of layers characterized by a general permittivity tensor treated by Yeh [J. Opt. Soc. Am. 69 (1979) 742].     

Polar and longitudinal magnetooptical Kerr effects in magnetic film/spacer/magnetic substrate system

The paper deals with the electromagnetic theory of longitudinal and normal incidence polar magnetooptical Kerr effects (MOKE) in sandwich structures consisting of a magnetic film on a thick magnetic substrate separated by a nonmagnetic spacer. These structures are employed in fundamental studies of magnetic exchange coupling, tunnel magnetoresistance, spin polarized current,etc., as well as in the design of the magnetoelectronic devices,e.g., magnetic random access memories. The results are expressed in terms of the Jones reflection matrix. This makes the analysis of the observed MOKE in various experimental set-ups easier. To first order in off-diagonal elements of the permittivity tensor, the analytical expressions approximate the results obtained using rigorous matrix formalisms with a little loss in accuracy, provided the magnetooptical effects quadratic in the offdiagonal elements are negligible. The total MOKE is expressed as a a sum of components originating from magnetic film and magnetic substrate, respectively. The components enter the analytical expressions with different phases and may be identified separately by a proper control of the polarization state and photon energy of the incident radiation, angle of incidence, nonmagnetic spacer thickness, and radiation wavelength. The formulae are derived without any restriction on the magnetic film thickness. However, for a rapid evaluation of the trends the MOKE response is also treated under the assumption that the thickness of the magnetic film is much smaller than the radiation wavelength. This work has been partially supported by Grant Agency of the Czech Republic (#202/97/1180 and #202/00/0761), Barrande Project and Grant Agency of Charles University.     

Analysis of electromagnetic propagation in birefringent thin film

Recently, a series of thin films with particular microstructure have been deposited successfully[1,2]. The thin films with regular microstructure give optical anisotropy in macroscopic view, i.e. birefringent feature. The theoretical analysis and deposition of birefringent thin film inject activity into traditional optical thin film[3―6]. Basing on the birefringent thin film, the researchers have successfully prepared electro-optic tunable filters[7], antireflection coatings[8], phase compens…     

Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum

A method has been proposed for determining the optical properties of a thin film layer on absorbing substrates. The film optical parameters such as thickness, refractive index, absorption coefficient, extinction coefficient and the optical energy gap of an absorbing film are retrieved from the interference fringes of the reflection spectrum at normal incidence. The envelopes of the maxima of the spectrum E_M and of the minima E_m are introduced in analytical forms to find the reflectance amplitudes at the interfaces and approximate values of the thin film refractive index. Then, the interference orders and film thickness are calculated to get accurate values of the needed optical parameters. There are no complex fitting procedures or assumed theoretical refractive index dispersion relations. The method is applied to calculate the optical properties of an epitaxial gallium nitride thin film on a silicon (1 1 1) substrate. Good agreement between our results and the published data are obtained.     

Generalized ellipsometry in unusual configurations

Most ellipsometry experiments are performed by shining polarized light onto a sample at a large angle of incidence, and the results are interpreted in terms of thin film thicknesses and isotropic optical functions of the film or substrate. However, it is possible to alter the geometrical arrangement, either by observing the sample in transmission or at normal-incidence reflection. In both cases, the experiment is fundamentally the same, but the interpretation of the results is considerably different. Both configurations can be used in conjunction with microscope optics, allowing for images to be made of the sample. The results of three examples of these different configurations using the two-modulator generalized ellipsometer (2-MGE) are reported: (1) spectroscopic birefringence measurements of ZnO, (2) electric field-induced birefringence (Pockels effect) in GaAs, and (3) normal-incidence reflection anisotropy of highly oriented pyrolytic graphite (HOPG).     

Magneto-optical Kerr effect in bilayer structures

This paper describes the magneto-optical effects and the reflectivity behaviors of bilayers based on magnetic and isotropic ()/anisotropic () layers under the condition of total internal reflection. In the framework of Green's dyadic technique, we show accurately the optical properties of anisotropic layers deposited on a substrate. We present numerical simulations which account for the variation of angle of incidence at the HeNe laser wavelength. The Kerr rotation is found to increase significantly around the optical modes in total reflection. We also discuss the importance of anisotropic effects due to the crystallization of the dielectric material () which occur in the reflectivity and Kerr rotation spectra. Received 26 January 2000     

Magnetization of the ferromagnetic-superconductor structures

The magnetization of a structure consisting of a thin superconducting film lying on a thin ferromagnetic substrate with uniaxial anisotropy is considered. It is shown that if a ferromagnet is in a multidomain state, then due to the presence of a superconducting film, the period of its domain structures decreases, which is caused by the increase of the magnetostatic energy of the system owing to Meissner currents. In a certain range of the constant of uniaxial anisotropy, under the action of a superconducting film, a domain structure may transform from a strip structure to the structure with closure domains. It is found that due to the nonuniform magnetic field of a multidomain ferromagnet, Abrikosov vortices may exist in a thin film only at certain parameters of the magnetic field.     

Zone structure and polarization properties of the stack of a metamaterial-based cholesteric liquid crystal and isotropic medium layers

The optical properties of a stack of metamaterial-based cholesteric liquid crystal (CLC) layers and isotropic medium layers are investigated. The problem is solved by a modification of Ambartsumian’s layer addition method. CLCs with two types of chiral nihility are defined. The peculiarities of the reflection spectra of this system are investigated and it is shown that the reflection spectra of the stacks of CLC layers of these two types differ from each other. Besides, in contrast to the single CLC layer case, these systems have multiple photonic band gaps. There are two types of such gaps: those selective with respect to polarization of the incident light and nonselective ones. It is shown that the system eigenpolarizations mainly coincide with the quasi-orthogonal, quasi-circular polarizations for normally incident light, except the regions of diffraction reflection selective with respect to the polarization of incident light. The influence of the CLC sublayer thick-nesses, the incidence angle, the local dielectric (magnetic) anisotropy of the CLC layers, and the refractive indices and thicknesses of the isotropic media layers on the reflection spectra and other optical characteristics of the system is investigated.     

Optical properties of thin films and the Berreman effect

The measurement of reflection and transmission of normally incident light to obtain the optical constants of a material is a usual tool in solid-state spectroscopy. If the material under investigation is a thin film, the interaction of the electromagnetic field with the sample can be enhanced by oblique incidence. If the light is p-polarized, structures in the reflection and transmission spectra are observed at the frequencies of transverse (TO) and longitudinal (LO) resonances. The LO structure — called the Berreman effect — is generated by the surface charges due to the normal component of the electric field. We discuss this effect for three cases: a free film, a film with a metallic back and a substrate with thin films on both sides. The dependence of the effect on the energy-loss function Im {–1/} and on the film thickness is discussed. For idealized systems simple formulae are derived and a characteristic parameter, called the Berreman thickness, is obtained. Films of this thickness show a maximum effect. Intuitive arguments are given to explain the effect. Examples for the application of the Berreman effect to characterize very thin films are discussed.     

Method of the ratio of envelopes of the reflection spectrum for measuring optical constants and thickness of thin films

A spectrophotometric method is proposed that uses the ratio of envelopes of minima and maxima of the interference reflection spectrum for measuring optical constants of a film on a substrate. Because this ratio does not contain the instrumental function of a spectrophotometer, there is no need in careful calibration of the spectrophotometer. In the case of a transparent isotropic film on an absorbing substrate, the inverse problem has an analytic solution. A simple method is proposed for numerical calculations of the optical constants and thickness of an absorbing film.     

Broadband,polarization-insensitive,and wide-angle microwave absorber based on resistive film

A simple design of broadband metamaterial absorber(MA) based on resistive film is numerically presented in this paper.The unit cell of this absorber is composed of crossed rectangular rings-shaped resistive film,dielectric substrate,and continuous metal film.The simulated results indicate that the absorber obtains a 12.82-GHz-wide absorption from about 4.75 GHz to 17.57 GHz with absorptivity over 90% at normal incidence.Distribution of surface power loss density is illustrated to understand the intrinsic absorption mechanism of the structure.The proposed structure can work at wide polarization angles and wide angles of incidence for both transverse electric(TE) and transverse magnetic(TM) waves.Finally,the multi-reflection interference theory is involved to analyze and explain the broadband absorption mechanism at both normal and oblique incidence.Moreover,the polarization-insensitive feature is also investigated by using the interference model.It is seen that the simulated and calculated absorption rates agree fairly well with each other for the absorber.     

晶格失配应力对单晶(BiTm)_3(GaFe)_5O_(12)膜磁畴结构的影响

利用液相外延工艺在钆镓石榴石衬底上制得了单晶(BiTm)_3(GaFe)_5O_(12)膜,研究了晶格失配应力对其磁畴结构的影响.研究发现,生长速率越快,膜的晶格常数越大;晶格失配应力可以在一定范围内调整膜的垂直各向异性;随着晶格失配应力由较大张应力逐渐转变为较大压应力,磁畴形状先由磁泡畴转变成迷宫畴,然后转变为过渡态部分弯曲的条状畴,最终转变为整齐排列的条状畴;失配应力同时对畴宽也有影响,膜受到的失配应力越大,畴宽越大.这一实验研究对基于控制晶格失配应力来调控单晶膜的各向异性和磁畴结构有指导意义.     

Magnetic and magneto-optical properties of epitaxial cobalt films grown on a corrugated CaF<Subscript>2</Subscript>/Si surface

The magnetic properties of CaF₂/Co/CaF₂(110)/Si(001) heterostructures fabricated by molecular-beam epitaxy and having a corrugated CaF₂ buffer surface were studied. The optical and magneto-optical properties of these structures reflect the C _2v symmetry of the corrugated structure surface. The studies of hysteresis loops using the longitudinal and transverse magneto-optical Kerr effects under oblique light incidence and of magneto-optical phenomena under near-normal light incidence demonstrate that the corrugated structure surface leads to optical and magneto-optical anisotropies. The magnetization of such structures occurs via coherent magnetization rotation over a wide magnetic-field range. The magnetic anisotropy of these structures is described using a Gaussian distribution of easy axes of magnetization in cobalt granules about the direction parallel to the groove direction. The asymmetry of hysteresis loops of the rotation of the plane of polarization detected under oblique and normal light incidence is shown to be related to the contributions to the effective film permittivity that are quadratic in the magnetic moment.     

Analysis of KrF excimer laser beam modification resulting from ablation under closed thick film flowing filtered water

The application of a closed thick film flowing filtered water to immerse the ablation etching mechanism of an excimer laser poses interesting possibilities concerning debris control, modification of machined feature topography and modification of the ablation rate. Furthermore, these parameters have been shown to be dependent on flow velocity; hence, offering further user control of machining characteristics. However, the impact of this technique requires investigation. This contribution offers comparison of the calculated ablation pressure and the effect on feature surface characteristics given for laser ablation of bisphenol A polycarbonate using KrF excimer laser radiation in ambient air against laser ablation of the same substrate under closed thick film flowing filtered water immersion. Also, an impact of such immersion equipment on the optical performance of the micromachining centre used is quantified and reviewed. The pressure is calculated to have risen by a magnitude of 48, when using the liquid immersed ablation technique. This increase in pressure is proposed to have an increased surface roughness, promoting the number of asperities with a surface area lower than 16 μm²; resulting in a diffuse reflection of light and an apparent darkening of features. The focal length of the optical system was accurately predicted to increase by 2.958 mm, when using the closed flowing liquid immersion equipment. This equipment is predicted to have increased the optical depth of focus via reduction in the angle of convergence of the two defining image rays; yet the perceived focus, measured discretely by mean feature wall angle, was found to be 25% smaller when using the closed thick film flowing filtered water immersion technique instead of similar laser ablation in ambient air. A compressed plume interaction is proposed as a contributing factor in this change.     

Investigation of induced parallel magnetic anisotropy at low deposition temperature in Ba-hexaferrites thin films

In this paper we present the effect of low substrate temperature on structural, morphological, magnetic and optical properties of Ba-hexaferrite thin films. Films were deposited on single crystal Silicon (1 0 0) substrate employing the Pulsed Laser Deposition (PLD) technique. The structural, morphological, magnetic and optical properties are found to be strongly dependent on substrate temperature. The low substrate temperatures (room temperature to 200 °C) restrict the formation of larger grains. For the higher substrate temperature i.e., 400 °C, the grain size of the deposited thin film are much larger. The film grown at low substrate temperature do not show any anisotropy. As the substrate temperature is increased, the easy axis of the films alinged itself in the direction parallel to the film plane whereas the hard axis remained in the perpendicular direction. The higher substrate temperature caused the uniaxial magnetic anisotropy, which is very important in magnetic recording devices. The saturation magnetization and optical band gap energy values of 62 emu/cc and 1.75 eV, respectively, were achieved for the film of thickness 500 nm deposited at 400 °C. Higher values of coercivity, squareness and films thickness are associated with the growth of larger grains at higher substrate temperature.     

Effects of oblique-incidence evaporation on magnetic properties of Fe20Ni80/Fe70Co30 bilayer film

Evaporative deposition at oblique incidence is shown to enhance the magnetic anisotropy of an Fe₂₀Ni₈₀ magnetic film and induce magnetic anisotropy in an overlying, strongly isotropic Fe₇₀Co₃₀ film. This deposition method for the formation of an underlayer of several lattice parameters in thickness and semi-hard overlayer of a few thousands Angstroms in thickness achieves a significant change in the magnetization process and strong suppression of the coercive forces of Fe₇₀Co₃₀ in the hard magnetization direction. Soft magnetization of the Fe₇₀Co₃₀ overlayer is not achieved when one of the layers is deposited at oblique incidence. It is anticipated that shape magnetic anisotropy is responsible in part for the magnetic anisotropy induced in both in Fe₂₀Ni₈₀ under- and Fe₇₀Co₃₀ overlayer by oblique incidence evaporation.