Electromagnetic properties of random material

Abstract

This work addresses the relationship between grain properties and the permeability and permittivity spectra of non-crystalline materials or aerosols.

The scattered multipolar fields about a single sphere are related to the polarizability of a random collection of such spheres. Using the Clausius–Mossotti relation the effective permeability and permittivity spectra of an amorphous material is determined for arbitrary permittivity and permeability of the individual spheres, packing density, and sphere size. Although the author considers the spectra over a range where the product of the external wavevector and sphere radius is kept small, typically less than one-tenth, the product of the internal wavevector and sphere radius is unconstrained and seen to have a large effect on predicted spectra.

The result is a variety of possible spectral types which include resonances, relaxations and certain complex. conglomerate spectra that have been measured and far which no direct explanation is otherwise available.     

An acoustic shadowgraph trial to detect convection in the Arctic

The EU Framework 5 project CONVECTION aims to understand convection processes in the Greenland Sea. By studying water motion close to the surface we hope to determine how convection is linked to atmospheric conditions and local surface features.

The usual methods of studying such processes in the ocean are by taking multiple soundings of conductivity, temperature and pressure or towing a large chain measuring temperature and salinity through a cross-section of ocean. These have the disadvantage of yielding information only while the research vessel is in the area. We have employed an alternative acoustic method that can provide data for long periods using semi-permanent moorings.

The acoustic shadowgraph method relies on the fact that when an acoustic signal propagates through a region containing convective irregularities the temperature variations along the path cause the signal amplitude to fluctuate. Unlike tomography, the shadowgraph does not require travel times to be measured and so the equipment can be much cheaper.

This paper describes the experimental apparatus, its testing and deployment on Vesteris Bank in the Greenland Sea in October 2001 and its recovery in April 2002. It also gives an overview of some of the acoustic intensity results and shows how they can be interpreted to yield estimates of sub-surface convection velocities.     

Theoretical and computational aspects of scattering from periodic surfaces: two-dimensional perfectly reflecting surfaces using the spectral-coordinate method

We consider the scattering from a two-dimensional periodic surface. From our previous work on scattering from one-dimensional surfaces (1998 Waves Random Media 8 385) we have learned that the spectral-coordinate (SC) method was the fastest method we have available. Most computational studies of scattering from two-dimensional surfaces require a large memory and a long calculation time unless some approximations are used in the theoretical development. By using the SC method here we are able to solve exact theoretical equations with a minimum of calculation time.

We first derive in detail (part I) the SC equations for scattering from two-dimensional infinite surfaces. Equations for the boundary unknowns (surface field and/or its normal derivative) result as well as an equation to evaluate the scattered field once we have solved for the boundary unknowns. Special cases for the perfectly reflecting Dirichlet and Neumann boundary value problems are presented as is the flux-conservation relation.

The equations are reduced to those for a two-dimensional periodic surface in part II and we discuss the numerical methods for their solution. The two-dimensional coordinate and spectral samples are arranged in one-dimensional strings in order to define the matrix system to be solved.

The SC equations for the two-dimensional periodic surfaces are solved in part III. Computations are performed for both Dirichlet and Neumann problems for various periodic sinusoidal surface examples. The surfaces vary in roughness as well as period and are investigated when the incident field is far from grazing incidence ('no grazing') and when it is near-grazing. Extensive computations are included in terms of the maximum roughness slope which can be computed using the method with a fixed maximum error as a function of the azimuthal angle of incidence, the polar angle of incidence and the wavelength-to-period ratio.

The results show that the SC method is highly robust. This is demonstrated with extensive computations. Furthermore, the SC method is found to be computationally efficient and accurate for near-grazing incidence. Computations are presented for grazing angles as low as 0.01°. In general, we conclude that the SC method is a very fast, reliable and robust computational method to describe scattering from two-dimensional periodic surfaces. Its major limiting factor is high slopes and we quantify this limitation.     

Dependent scattering effects in latex-sphere suspensions and scattering powders

The dependent scattering effects in ideal latex-sphere suspensions and beds of irregularly shaped powder grains are theoretically described by means of a coherent addition formalism together with the statistical Percus-Yevic hard sphere model for the particle separation.

Measurements are performed with a light scattering apparatus and a linear photo diode array. The latter allows scattered and directly transmitted radiation to be separated and thus the scattering cross section of the spheres in dependence of their volume fraction to be derived. For high volume fractions, a decrease of scattering efficiency occurs in the calculated as well as the measured cross sections.

For TiO₂ powders a similar behaviour of the effective scattering and absorption cross section is derived for the near- and mid-infrared region. The relevant quantities are obtained from directional-hemispherical transmission and reflection measurements using a three-flux model. Due to the irregular shape of the powder grains Mie scattering theory has to be modified for each powder to fit the experimental data.     

Electromagnetic-wave scattering from chiral spheres in chiral media

Summary The scattering of electromagnetic waves in chiral (optically active) media from chiral spheres is studied. Mie-scattering techniques are used to find the exact solution for plane-electromagnetic-wave scattering from a chiral sphere of arbitrary size in an infinitely extended chiral medium of arbitrarily different permeability, permittivity, and chirality, and the scattering and extinction efficiencies for chiral spheres in chiral media are derived. Special cases of achiral exterior medium-chiral sphere and achiral exterior medium-achiral scatterer are considered and in the latter case well-known results of Mie scattering are recovered. Simplified results for small spheres are also found for the limit of Rayleigh scattering.     

Efficiency and optical feedback of traveling-wave semiconductor laser amplifier to single-mode fiber coupling: Theory and experiment

This paper analyzes the coupling efficiency and optical feedback of the tapered fiber end with a high-index hemiellipsoidal microlens. Such a device has been used as a coupler of traveling-wave semiconductor laser amplifier (TW-SLA) to single mode fiber (SMF).

A theory of the calculation of coupling efficiency and optical feedback is presented including the effects of spherical aberration and Fresnel reflection of thick lens. In consideration of the large beam divergency of the TW-SLA chip, the finite transmission aperture is introduced.

The calculations are in agreement with experiment results and a group of optimum structure parameters of the coupler are given.     

Channel reduction schemes for fiber-optic angle encoders

Three fiber-optic sensor systems designed to remotely determine angular position that achieve high angular resolution with fewer channels than comparable Gray code encoders are described. Two of the Systems use a sheet polarizer affixed to a “codewheel” and the third system uses a two-channel digital shaft encoder style “codewheel.”

The first polarization scheme uses four optical channels, two of which are analog and two digital. The ratio of the two analog channel intensities yields tan²θ. The fourfold quadrant ambiguity is resolved by the two digital channels that are transected by two semicircular masks on the polarizer codewheel (Ref. U.S. Patent No. 4,577,414, 25 Mar 1986). The second polarization scheme again uses quadrant ambiguity masks but employs only one analog channel that simulates a polarization vector that oscillates through 90°. The oscillating vector is produced by the superposition of two sine-wave-modulated beams at the polarizer codewheel. The modulations of the two beams have a phase difference that is created by time delaying one of the beams in a fiber delay loop. The phase difference between the generated composite signal and a reference signal then determines the angle of the codewheel. We have demonstrated experimentally that this type of split analog-digital scheme has a resolution equivalent to a 10-bit digital system (i.e., ±0.35°) independent of codewheel diameter.

The serial digital shaft encoder scheme uses only two digital channels and a codewheel that has two concentric masks with 48 equally spaced windows offset with respect to each other by one-half window width. At 0° there is a unique mask that initializes an up/down decoder chip (Hewlett-Packard HCTL-2000). This system has a resolution better than 7 bits using a 5-cm diameter code wheel and 1-mm Selfoc^TM lenses.

The supporting electro-optical systems including sources, fibers, lenses, mirrors, couplers, WDMs, polarizers, detectors, and signal processing for all schemes are described and the relative merits of each are compared.     

Form factor for large quantum graphs: evaluating orbits with time reversal

It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time τ using periodic-orbit theory. Two types of contributing pairs of orbits were identified: those which require time-reversal symmetry and those which do not. We present a new technique of dealing with contributions from the former type of orbits.

The technique allows us to derive the third-order term of the expansion for general graphs. Although the derivation is rather technical, the advantages of the technique are obvious: it makes the derivation tractable, it identifies explicitly the orbit configurations which give the correct contribution and it is more algorithmic and more system-independent, making possible future applications of the technique to systems other than quantum graphs.

(Some figures in this article are in colour only in the electronic version)     

Development of proposed federal standard 1070: 62.5/125-μm graded-index, multimode optical fiber waveguides for on-premises applications

This paper describes a process that has been successful in generating a specification to guide the user community in the procurement of single-size, multimode optical fiber for on-premises applications. This process began with an attempt to adopt an industry standard as a federal standard that would eliminate a multiplicity of choices available from the marketplace. The initial EIA-458-A Standard contained four “preferred” sizes. Discussions both in a government standards committee and in an applications-oriented industry (EIA) working group indicated the desirability of recommending a single fiber size. The process by which the industry committee selected the 62.5-μm core diameter/125-μm cladding diameter multimode fiber is presented.

The next element of the process was that of selecting the appropriate standard performance measures and attributes that would assure minimum performance of graded parameters such as attenuation and bandwidth, as well as a uniform specification of the product. The vehicle selected for this specification was the EIA 492-Series Generic, Sectional, and Blank Detail Specifications. Inputs were solicited from all of the identified U.S. manufacturers of this fiber size. Those inputs were coordinated and integrated into a detail specification, which is now being circulated by the EIA on a standards proposal ballot. After ballot approval, it will be published as an ANSIIEIA standard specification. Similar work has been initiated to develop a detail specification for fiber optic cables based on a related set (472-Series) of EIA specifications.

The process of developing a detail specification that assures conformance of the product to dimensional and strength tolerances as well as performance measures requires considerable coordination and iteration. No proprietary information or processes are contained in the specification so that the industry participants are free to compete on price and performance as long as compliance with the specification can be demonstrated.     

Operational and strategic implications of powering the fiber loop

The purpose of this paper is to highlight operational and strategic implications associated with the powering of digital-line-carrier/fiber-optic systems in the loop and in future fiber-to-the-home (FTTH) systems.

The powering of existing feeder plant and future FTTH systems is discussed. Technologies are examined, major issues identified, and a series of recommendations proposed in conclusion.     

Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum

We propose an artificial three-dimensional material that exhibits a strong resonance in the effective permeability in the visible spectral domain. This material may be implemented in a two-step procedure. First, a metamaterial made of densely packed metallic nanoparticles is fabricated that shows a Lorentz-type resonance in the permittivity at the collective plasmon frequency. Second, spheres are formed out of this material and arranged in a cubic lattice. This meta-metamaterial exhibits a strong resonance in the permeability which is caused by a Mie resonance associated with the magnetic mode of a single metamaterial sphere. Realization of this material based on self-organization in liquid crystals and the limitations of the approach are discussed.     

Estimation of maximum measurable distance in optical time domain reflectometry

The dependence of the maximum measurable distance (MMD) in optical time domain reflectormetry (OTDR) upon fiber and receiver parameters, number of averaging times, signal pulse width, and input power launched into the fiber has been investigated for both 1.3- and 1.5-μm wavelengths.

The calculations have been performed for both Ge- and InGaAs/InP-APD receivers. As a result it is found that (1) the (MMD) is larger for the InGaAs/InP-APD receiver and (2) a further increase in the MMD can be achieved by cooling the InGaAs/InP-APD receiver.     

A new method for determining hydrodynamic effects on the collision of two spheres

A sphere falling in a fluid may collide with another sphere falling more slowly if, when the spheres are far apart vertically, the horizontal distance between their centers is less than or equal to a critical radius. Accurate prediction of aerosol particle coagulation requires a good understanding of this process. Previously reported optical techniques for measuring hydrodynamic effects on this phenomenon have inherent difficulties detecting grazing collisions and hence in determining the critical radius. In this work, a novel detection technique is demonstrated and it is shown that the critical radius may be determined from the sound generated by the collision of two spheres in a viscous liquid. The technique is shown to provide a more precise and decisive indication of when hard spheres collide.     

Effective material parameters,resonance, and polarization properties of a magnetophotonic crystal

For mutually perpendicular orientations of the periodicity axis, the wavevector, and the magnetic bias, the expressions for the effective material parameters of the magnet-dielectric periodic structure are obtained in the fine-layered medium approximation. The allowance for corrections proportional to (L/λ)² leads to the dependence of the effective permittivity and permeability on the permittivity and permeability of the layers. The resonance and polarization properties, as well as the conductance of the magnetophotonic structure under consideration, are investigated.     

Cell model calculations of dynamic drag parameters in packings of spheres

An external flow approach is used to predict the viscous drag due to oscillating flow in an air-filled stack of fixed identical rigid spheres. Analytical expressions for dynamic and direct current (dc) permeability, high-frequency limit of tortuosity, and the characteristic viscous dimension are derived using a cell model with an adjustable cell radius which allows for hydrodynamic interactions between the spherical particles. The resulting theory requires knowledge of two fixed parameters: the volume porosity and the particle radius. The theory also requires a value for the cell radius. Use of the cell radius corresponding to that of the sphere circumscribing a unit cell of a cubic lattice arrangement is proposed. This is found to enable good agreement between predictions of the new theory and both published data and numerical results for simple cubic and random spherical packings.     

Integrated optical fiber data link transmitter/receiver for local area network application

Optical fiber data link transmitters and receivers have been developed for local area network applications. The features are of wide-bit-rate range and wide dynamic range as well as compact and of highly reliable construction. State-of-the-art LSI technology has been applied for the circuit electronics integration. Design emphasis was also placed on the optical connector development for ease of operation as well as reliable connection and compact size.

The data link transmitter and receiver developed utilize an AlGaAs light-emitting diode and a Si PIN photodiode as the light source and detector, respectively. Performance data were obtained for a bit rate range of dc to 35 Mbps and an 18-dB dynamic range.     

Three-sphere low-Reynolds-number swimmer with a cargo container

A recently introduced model for an autonomous swimmer at low Reynolds number that is comprised of three spheres connected by two arms is considered when one of the spheres has a large radius. The Stokes hydrodynamic flow associated with the swimming strokes and net motion of this system can be studied analytically using the Stokes Green's function of a point force in front of a sphere of arbitrary radius R provided by Oseen. The swimming velocity is calculated, and shown to scale as 1/R ³ with the radius of the sphere.     

Non compact single-layers of dielectric spheres electromagnetc behaviour

Single layer of dielectric spheres is a recognized model for the basic understanding of some aspects of photonic crystals. Here we present a systematic study of the effect of compacting in the electromagnetic transmission of dielectric spheres monolayers. Experiments were performed in the microwave domain (from 10 GHz to 30 GHz) with glass spheres of high dielectric permittivity ε = 7. Time Domain Finite Integration (TDFI) calculations were also accomplished. Experimental data and TDFI calculations agreement provides a double check on the lack of experimental artefacts and the correctness of simulation settings. Following the evolution of the lower frequency spectral peak with layer compacting ratio, we established three different electromagnetic regimes. For the higher and lower compacting ratio regimes, the peak frequency matches isolated sphere pure resonances, while for intermediate values of compacting, some transition between these two modes takes place. Extending the study to the complete frequency range, we find that sphere single layers transmission spectra become closer to isolated sphere scattering calculations as the compacting ratio is decreased. However as the agreement remains imperfect even for our lowest compacting measurable layer, we conclude that some structure contribution cannot be neglected even for low compact layers.     

Minimization of Cross-Gain Saturation in Wavelength Division Multiplexing by Optimizing Differential Gain in Semiconductor Optical Amplifiers

We successfully simulated the 10 × 40 Gbit/s soliton RZ-DPSK WDM signals over 1050 km with spectral efficiency approaching 0.4 bit/s/Hz using semiconductor optical amplifiers (SOAs) as in-line amplifier. The cross-gain saturation of SOA can be minimized by settling crosstalk at a lower level by decreasing the differential gain. This decrease in differential gain is in such a way that we get nil power penalty. The maximum transmission distance of 1050 km is possible with differential gain 210 atto cm² of SOA.

The impact of amplification factor, ASE noise power, crosstalk, quality factor and bit error rate for different differential gain has been investigated. It has been shown that with the increase in differential gain of SOA, the transmission distance goes on decreasing. At high value of differential gain 2.5 × 10^-16 cm² for the transmission distance 1050 km, all channels produce inter channel crosstalk with bit error rate greater than 10^-6. But for lower differential gain 190 atto cm², the quality of all channel increases at the cost of large power penalty.

With slight increase in differential gain 200 atto cm², the maximum transmission distance observed is 4550 km with quality of received signal more than 15 dB and having nil power penalty. We observed clear eye diagrams and optical power spectra for received signal with transmission distance 1050 km and 4550 km using soliton RZ-DPSK system. The bit error rate for all channels increase more than 10^-10 with the increase in launched input power that is due to power saturation.