Focusing characteristics of a planar solid-immersion mirror

The focusing characteristics of a planar waveguide solid-immersion mirror with parabolic design have been investigated. The solid-immersion mirror is integrated into an optical waveguide, and light focusing is achieved with a parabolic mirror parallel to the waveguide plane and waveguide mode confinement normal to the waveguide plane. Optical-quality tantala silica planar waveguides can be obtained by evaporation. The parabolic sidewall reflects over 50% of the incident waveguide mode and generates a diffraction-limited focus. The measured spot size for the solid-immersion mirror described here is less than one third of the wavelength. Polarization analysis shows that the electric field near the focal region has components parallel and normal to the polarization state of the incident beam. The planar solid-immersion mirror is essentially free of chromatic aberration, and the alignment of the illumination beam is within a fraction of degrees.     

Structures in superconducting YBa2Cu3O7−δ thin films investigated by magneto-optic technique

Using a reflection magneto-optic technique we have investigated natural inhomogeneities and artificial structures in YBCO thin films exposed to an external magnetic field. The artificial structures were mechanically scratched by scanning a diamond tip with different loading over the film surface. Alternatively planar structures with reduced oxygen content could be patterned by heating the YBCO film with a focused laser beam in nitrogen atmosphere. Depending on the laser annealing parameters different screening properties concerning the applied magnetic field could be achieved.As a magneto-optically active layer we used EuS films evaporated on glass as well as bismuth- and gallium-doped lutetium-iron-garnet films grown onto (111) oriented gadolinium-gal lium-gar net substrates by liquid phase epitaxy. In contrast to measurements with EuS films that show only weak faraday rotation for temperatures higher than 20 K the magneto-optic studies have been expanded to about 60 K by using the garnet films.     

Magnetophotonic crystals: nonreciprocity, birefringence and confinement

Photonic crystals in magnetic materials open up a number of interesting possibilities for the study of nonreciprocal effects in confined geometries, including enhanced Faraday rotation and optical unidirectionality. The development of integrated devices based on nonreciprocal magneto-optic phenomena requires understanding the effects of geometrical confinement on light propagation and magnetization in these systems. This article introduces a model for controlling the band gap by exploiting the birefringence in film-based planar magneto-optic structures. It also presents a study of magnetic remanence control through magnetization confinement in the resonant microcavity of one-dimensional planar magnetophotonic crystals.     

Magnetophotonic crystals: nonreciprocity,birefringence and confinement

Photonic crystals in magnetic materials open up a number of interesting possibilities for the study of nonreciprocal effects in confined geometries, including enhanced Faraday rotation and optical unidirectionality. The development of integrated devices based on nonreciprocal magneto-optic phenomena requires understanding the effects of geometrical confinement on light propagation and magnetization in these systems. This article introduces a model for controlling the band gap by exploiting the birefringence in film-based planar magneto-optic structures. It also presents a study of magnetic remanence control through magnetization confinement in the resonant microcavity of one-dimensional planar magnetophotonic crystals.     

Optical nonreciprocal devices with a silicon guiding layer fabricated by wafer bonding

Optical nonreciprocal devices with a silicon guiding layer fabricated by wafer bonding are proposed. The optical nonreciprocal devices are composed of a magneto-optic waveguide with a magnetic garnet/Si/SiO2 structure. Nonreciprocal characteristics are obtained by an evanescent field penetrating into the upper magnetic garnet cladding layer. Several kinds of the optical nonreciprocal device are investigated with the magneto-optic waveguide and designed at a wavelength of 1.55 microm. As a preliminary experiment, wafer bonding between Gd3Ga5O12 and Si was studied. Wafer bonding was successfully achieved with heat treatment at 220 degrees C in H2 ambient.     

Magnetometry in dense coherent media

The rotation of the polarization direction of linearly polarized light produced by the nonlinear magneto-optic effect has been proposed as a sensitive measure of small magnetic fields. In this paper, the advantages of this technique in optically thick media for precision magnetometry are discussed. Results are presented for measurements of this rotation for resonant light in optically dense Rb vapour under various conditions, with and without buffer gas. The sensitivity of the measurements of small magnetic field is investigated as a function of laser frequency, laser power, beam diameter and atomic density for D ₁ line of ⁸⁷Rb.     

Reflection of light at structured chiral interfaces

Modified boundary conditions and general surface constitutive equations are derived for a very thin interface with some internal structure that separates two different media. The modified boundary conditions are reduced to the standard ones for an idealized steplike sharp interface without additional structure. These modified boundary conditions together with surface constitutive equations and Maxwell equations in the bulk form a complete set of macroscopic equations to describe optical properties of planar interfaces with thicknesses much less then the wavelength of light. In particular, two-dimensional chiral surfaces are considered that are characterized by surface gyrotropic coefficients even if the two different bulk media and the interface are made of nonchiral materials. It is shown that the rotation of the polarization state should occur for the light reflected from such a surface. This result is supported by recent experimental data.     

Permanent magnets for Faraday rotators inspired by the design of the magic sphere

Faraday polarization rotators are commonly used in laser experiments. Most Faraday materials have a nonnegligible absorption, which is a limiting factor for high power laser optical isolators or for intracavity optical diodes. By using a stronger magnetic field and a shorter length of Faraday material, one can obtain the same polarization rotation and a reduced absorption. In this paper, we describe two permanent magnet arrangements that are easy to build and produce magnetic fields up to 1.7 T, substantially more than commonly used. The field homogeneity is largely sufficient for a 30 dB isolation ratio. We finally discuss the prospects for producing even larger fields with permanent magnets.     

Magneto-optic sensor by use of time-division-multiplexed orthogonal linearly polarized light

A magneto-optic sensor is proposed and experimentally demonstrated. The sensing unit is mainly composed of an electro-optic modulator, a Faraday magneto-optic glass, and two polarizers. Different from the conventional magneto-optic sensors, this sensor utilizes a time-division-multiplexed and alternately polarized light carrier whose azimuthal angle is periodically alterable between two orthogonal linear polarization states. In particular, this sensing scheme is suitable for dc magnetic field or current measurement, and the measurement result is free from the influences of light intensity fluctuation and environmental electromagnetic interference, due to the applications of square-wave modulation and lock-in amplification techniques. The dc magnetic field in the range of +/-(0.067 approximately 20) mT has been remotely measured and the nonlinear error is less than 1.0%.     

Frequency response of a thin cobalt film magnetooptic sensor

The magnetooptic effect is due to a change in the polarization of the light when it is reflected or passes through a magnetized material. The rotation of the polarization plane is proportional to the magnetic field. The great advantage of using a magnetooptic sensor to measure intensity or magnetic fields is its wide bandwidth. This fact is widely known; however, no effective measurements have been taken. In this paper, we present the frequency response of a cobalt thin film used as magnetooptic material. It was first excited by several sinusoidal magnetic fields at different frequencies. The range of frequencies studied in the first experiment reached 179 Hz, which is suitable for measuring power line intensity or magnetic fields. Because the coil that creates the magnetic field has a great impedance at higher frequencies, an alternative method based on magnetic impulses has been designed to obtain high-frequency data. With the latest experiments we have been able to measure frequencies as high as 2 MHz, obtaining a flat frequency response.     

Polarization eccentricity of the transverse field for modes in chiral core planar waveguides.

The general solution for modes in an asymmetric planar waveguide with a homogeneous and isotropic chiral core is given in terms of a pair of parameters related to the eccentricity of the polarization ellipse for the transverse electric field. This formulation provides insight into the transition, with increasing chirality of the core, from TE/TM modes to right-handed and left-handed circular polarization modes. Mode polarization as a function of waveguide thickness and of frequency is discussed in detail. Beyond a mode-dependent maximum thickness (or frequency), the left-handed elliptical modes consist of a slow-wave component whose cutoff properties are examined. The limiting case of a symmetric waveguide is also discussed.     

Analysis of planar superconducting waveguides in DC magnetic field

A theoretical analysis of microwave properties of planar superconducting waveguides of finite thickness in the presence of an external dc magnetic field is presented in this article. Some analytical formulas are derived for determining the attenuation and dispersion properties of the superconducting waveguide, which may account for the effects of the dc magnetic field, the electrodynamic properties of type-II superconductors, the thickness of superconducting films, and the dielectric loss in the waveguide. Numerical results are then given to show quantitatively how the dc magnetic field influences the propagation properties of the planar superconducting waveguide. Some analysis are also given to study the effect of dc magnetic field on the quality factorQ and the resonant frequency of planar superconducting waveguide resonators.     

Single-crystal magneto-optic sensor with electrically adjustable sensitivity

A novel magneto-optic sensor with electrically adjustable sensitivity is proposed that is based on the approximate multiplication correlation between the linear electro-optic phase retardation and the Faraday magneto-optic rotation angle in a single bismuth germanate crystal. The measurement sensitivity and its temperature stability, linear and monotonic measurement ranges of the proposed sensor can be controlled in real time by adjusting the modulating voltage applied to the sensing crystal. In particular, the proposed sensor can be used for the precise measurement of dc magnetic field or dc current. The basic sensing performance is theoretically analyzed and experimentally demonstrated by dc current measurement.     

Application of zeeman modulation faraday spectroscopy to the measurement of a magnetic field

We report what is to our knowledge the first possibility of a NO(2) molecular magnetometer based on the Zeeman modulation magnetic rotation spectroscopic (ZM MRS) technique and the magneto-optic activity of NO(2). The linear dependence of the ZM MRS signal intensity on the modulating magnetic field is theoretically analyzed and experimentally measured. The design concept of the magnetometer and its main features are discussed.     

Manipulation of polarization-dependent effects by magnetostrictive stress on silicon-on-insulator rib waveguides

Polarization dependent loss (PDL) can cause deterioration in optical network performance owing to the resultant fluctuation in received power because of random changes in fiber polarization. We describe the use of a magnetostrictive layer integrated on a planar light-wave circuit that can offer the functionality of modifying the variable PDL or differential group delay produced within the typical tolerances of volume manufacturing. This approach provides an alternative to the sizable delay lines and splitters that were previously employed for polarization compensation. We demonstrate adjustment of polarization-dependent parameters by the application of an external magnetic field to a ferromagnetic layer adjacent to the waveguide.     

Analyzing combinations of circular birefringence,linear birefringence,and elliptical dichroism in magneto-optical rotators

We derive analytic expressions for the polarization characteristics of light emerging from a magneto-optical medium possessing arbitrary contributions from linear and circular birefringence as well as magnetic circular dichroism. The medium is placed inside a static magnetic field. The rotation of the plane of polarization and the ellipticity of the resultant light exhibit interesting characteristics that can be a useful guide in the design and analysis of new photonic devices. Furthermore, the Jones matrices are derived in all cases, including for elliptical dichroism, indicating the role of hyperbolic trigonometric functions in modeling the effects of dichroism. Finally, implications for experimental detection of the polarization state and the limits on the performance of optical isolators are discussed.     

Singular polarization eigenstates in anisotropic stratified structures

A new optical element that displays singular polarization eigenstates is proposed. It consists of a planar stratified structure composed of alternate gyrotropic and birefringent layers. The orthogonality of the polarization eigenstates is lost because of anisotropic reflections at the interfaces, which are enhanced by the special condition chosen for the multiple-beam interference. First we show that the anisotropic reflection at the interface between the layers with linear and circular symmetries does produce strong enough dichroism to break the orthogonality of polarization eigenstates. Second, we investigate the behavior of these eigenstates with respect to their linearity and orthogonality as a function of the width of the layers. Our results concretely demonstrate that it is possible to control the effective optical parameters of such stratified structures by adjusting the thickness of each anisotropic layer. Finally, we obtain the necessary conditions for designing a double-layer system with singular eigenstates of linear polarization.     

A photorefractive effect accompanying the acoustooptical interaction in gyrotropic cubic crystals in the presence of an alternating electric field

A photorefractive effect in gyrotropic cubic crystals is considered. The effect accompanies the Bragg diffraction of light by an ultrasound in the presence of an alternating electric field. The possibility of recording holographic gratings with the help of the light waves diffracted by traveling ultrasonic waves is demonstrated. The amplitude of the index phase grating is studied as a function of the intensity of the recording ultrasound, the length of the region of acoustooptical interaction, and the specific rotation of the crystal.     

Theory of Non-linear Longitudinal Kerr Magneto-optic Effect in a Ferromagnetic Metallic Thin Film

A theory of the non-linear longitudinal Kerr magneto-optic effect, previously developed for bulk materials [1], is now applied to a magnetic thin film. The material model is based on the classical equation of motion for a free electron with a finite relaxation frequency under the action of a Lorentz force. A second harmonic current density, dependent upon three non-linear conductivity tensors, reduces to results obtained by Jha [2] in the limit of vanishing ferromagnetic state. The second harmonic reflection coefficients are approximated and are given in terms of the first harmonic reflection coefficients as derived by Smith [3].     

Generalized far-infrared magneto-optic ellipsometry for semiconductor layer structures: determination of free-carrier effective-mass,mobility, and concentration parameters in n-type GaAs

We report for the first time on the application of generalized ellipsometry at far-infrared wavelengths (wave numbers from 150 cm(-1) to 600 cm(-1)) for measurement of the anisotropic dielectric response of doped polar semiconductors in layered structures within an external magnetic field. Upon determination of normalized Mueller matrix elements and subsequent derivation of the normalized complex Jones reflection matrix r of an n-type doped GaAs substrate covered by a highly resistive GaAs layer, the spectral dependence of the room-temperature magneto-optic dielectric function tensor of n-type GaAs with free-electron concentration of 1.6 x 10(18) cm(-3) at the magnetic field strength of 2.3 T is obtained on a wavelength-by-wavelength basis. These data are in excellent agreement with values predicted by the Drude model. From the magneto-optic generalized ellipsometry measurements of the layered structure, the free-carrier concentration, their optical mobility, the effective-mass parameters, and the sign of the charge carriers can be determined independently, which will be demonstrated. We propose magneto-optic generalized ellipsometry as a novel approach for exploration of free-carrier parameters in complex organic or inorganic semiconducting material heterostructures, regardless of the anisotropic properties of the individual constituents.