Introduction

The present chapter is devoted to the analysis of the various sources of noise commonly encountered in magneto-optical readout. Although the focus will be on magneto-optics, most of these sources are known to occur in other optical recording systems as well; the arguments of the present discussion, therefore, may be adapted and applied to various other media and systems.

The MO readout scheme considered in this chapter is briefly reviewed below, followed by a description of the standard methods of signal and noise measurement, and the predominant terminology in this area. After these preliminary considerations, the characteristics of thermal noise, which originates in the electronic circuitry of the readout, are described in section 9.1. Section 9.2 considers a fundamental type of noise, shot noise, and gives a detailed account of its statistical properties. Shot noise, which in semiclassical terms arises from the random fluctuations in photon arrival times, is an ever-present noise in optical detection. Since the performance of MO media and systems is approaching the limit imposed by shot noise, it is imperative to have a good grasp of this particular source of noise. In section 9.3 we describe a model for laser noise; here we present measurement results that yield numerical values for the strength of laser power fluctuations. Spatial variations of disk reflectivity and random depolarization phenomena also contribute to the overall level of noise in readout; these and related issues are treated in section 9.4.

Introduction

The diffraction of light plays an important role in optical data storage systems. The rapid divergence of the beam as it emerges from the front facet of the diode laser is due to diffraction, as is the finite size of the focused spot at the focal plane of the objective lens. Diffraction of light from the edges of the grooves on an optical disk surface is used to generate the tracking-error signal. Some of the schemes for readout of the recorded data also utilize diffraction from the edges of pits and magnetic domains. A deep understanding of the theory of diffraction is therefore essential for the design and optimization of optical data storage systems.

Diffraction and related phenomena have been the subject of investigation for many years, and one can find many excellent books and papers on the subject. The purpose of the present chapter is to give an overview of the basic principles of diffraction, and to derive those equations that are of particular interest in optical data storage. We begin by introducing in section 3.1 the concept of the stationary-phase approximation as applied to two-dimensional integrals. Then in section 3.2 we approximate two integrals that appear frequently in diffraction problems using the stationary-phase method.

An arbitrary light amplitude distribution in a plane can be decomposed into a spectrum of plane waves. These plane waves propagate independently in space and, at the final destination, are superimposed to form a diffraction pattern.

This book has grown out of a course that I have taught at the Optical Sciences Center of the University of Arizona over the past five years. The idea has been to introduce graduate students from various backgrounds, either in physics or in one of the engineering disciplines, to the physical principles of magneto-optical (MO) recording. The topics selected for this course were of general interest, since both optics and magnetism are very broad and have many applications in modern science and technology. Each topic was treated in a self-contained and comprehensive manner. The students were first motivated by being told the relevance of a subject to optical data storage, then the subject was developed from basic principles, and examples were given along the way to show its application in quantitative detail. At the end of each chapter homework problems were assigned, so that students could learn certain details that were left out of the lectures or find out new directions in which their newly acquired knowledge could be applied.

The book essentially follows the format of the lectures, albeit with the addition of several chapters whose classroom coverage has usually been inhibited by the finite length of a semester. My primary goal in writing the book is to open the field to graduate students in physical sciences. Most college courses these days are based on single-issue topics that can be covered fairly comprehensively in the course of one or two semesters.

Introduction

Magnetostatics is the study of stationary patterns of magnetization in magnetic media. The central role in these studies is played by domains and domain walls. Domains are regions of uniform magnetization that are large on the atomic scale, but may be small in comparison with the dimensions of the medium under consideration. The walls are narrow regions that separate adjacent domains. In uniform media, the primary source of the spontaneous breakdown of magnetization into domains is the long-range dipole–dipole interaction, commonly referred to as the demagnetizing effect. Breakdown into domains provides a means of lowering the energy of demagnetization at the expense of increased exchange and anisotropy energies. Since within the domains the magnetization is fairly uniform and often aligned with an easy axis, it is at the site of the domain walls that the excess energies of exchange and anisotropy accumulate, as though the walls were endowed with an energy of their own. This chapter is devoted to the study of domains and domain walls and their structure and energy, as well as their magnetostatic interactions.

The basic tenets of magnetism were reviewed in Chapter 12, and the fundamental notions of magnetic field, magnetization, exchange and anisotropy were introduced. In the present chapter we shall confine attention to homogeneous thin-film media, where the magnetization M is treated as a continuous function of position r over the volume of the material (see Fig. 13.1).

Introduction

All media in use today for laser-assisted recording rely on the associated rise in temperature to achieve a local change in some physical property of the material. Therefore the first step in analyzing the write and erase processes is the computation of temperature profiles. Except in very simple situations, these calculations are done numerically using either the finite difference method or the finite element technique. Generally speaking, the two methods produce similar results in comparable CPU times. Most often one assumes a flat surface for the disk and circular symmetry for the beam, which then allows one to proceed with solving the heat diffusion equation in two spatial dimensions (r and z in cylindrical coordinates). For more realistic calculations when the disk is grooved and Preformatted, or when the beam has asymmetry due to aberrations or otherwise, the heat absorption and diffusion equations must be solved in three-dimensional space.

A problem with the existing thermal models is that the optical and thermal parameters of the media are assumed to be independent of the local temperature. In practice, as the temperature changes, these parameters vary (some appreciably). While it is rather straightforward to incorporate such variations in the numerical models, at the present time it is difficult to obtain reliable data on the values of thermal parameters at a fixed temperature, let alone their temperature dependences. It is hoped that some effort in the future will be directed towards the accurate thermal characterization of thin-film media.

Introduction

In this chapter, as a first application of the mathematical results derived in Chapter 3, we describe the far-field pattern obtained when a Gaussian beam is reflected from (or transmitted through) a surface with a sharp discontinuity in its reflection (or transmission) function. A good example of situations in which such phenomena occur is the knife-edge method of focus-error detection in optical disk systems; here a knife-edge partially blocks the column of light, allowing a split detector in the far field to sense the sign of the beam's curvature. Another example is the diffraction of the focused spot from the sharp edge of a groove. The far-field pattern in this case is used to derive the track-error signal, which drives the actuator responsible for track-following. Readback of the embossed pattern of information on the disk surface (e.g., data marks on CD and CD-ROM, Preformat marks on WORM and magneto-optical media) also involves diffraction from the edges of small bumps and/or pits.

This chapter begins with a general description of the problem and a derivation of all relevant formulas in section 4.1. In subsequent sections several specific cases of the general problem are treated; the emphasis will be on those instances where diffraction from a sharp edge finds application in optical-disk data storage systems.

Introduction

The optical theory of laser disk recording and readout as well as that of the various focus-error and track-error detection schemes have been developed over the past several years. Generally speaking, these theories describe the propagation of the laser beam in the optical head, its interaction with the storage medium, and its return to the photodetectors for final analysis and signal extraction. The work in this area has been based primarily on geometrical optics and the scalar theory of diffraction, an approach that has proven successful in describing a wide variety of observed phenomena.

The lasers for future generations of optical disk drives are expected to operate at shorter wavelengths; at the same time, the numerical aperture of the objective lens is likely to increase and the track-pitch will decrease. These developments will result in very small focused spots and shallow depths of focus. However, under these conditions the interaction between the light and the disk surface roughness increases, polarization-dependent effects (especially those for the marginal rays) gain significance, maintaining tight focus and accurate track position becomes exceedingly difficult, and, finally, small aberrations and/or misalignments deteriorate the quality of the readout and servo signals. Thus, attaining acceptable levels of performance and reliability in practice requires a thorough understanding of the details of operation of the system. In this respect, accurate modeling of the optical path is indispensable.

Introduction

In Chapter 12 we described the mean-field theory of magnetization for ferromagnetic materials, which consist of only one type of magnetic species. The atoms (or ions) comprising a simple ferromagnet are coupled via exchange interactions to their neighbors, and the sign of the exchange integral ℐ is positive everywhere. In this chapter we develop the mean-field model of magnetization for amorphous ferrimagnetic materials, of which the rare earth–transition metal (RE–TM) alloys are the media of choice for thermomagnetic recording applications. Ferrimagnets are composed of at least two types of magnetic species; while the exchange integral for some pairs of ions is positive, there are other pairs for which the integral is negative. This leads to the formation of two or more subnetworks of magnetic species. When the ferrimagnet has a uniform temperature, each of its subnetworks will be uniformly magnetized, but the direction of magnetization will vary among the subnetworks. In simple ferrimagnets consisting of only two subnetworks, the magnetization directions of the two are antiparallel.

In thin-film form, amorphous RE–TM alloys exhibit perpendicular magnetic anisotropy, which makes them particularly useful for polar Kerr (or Faraday) effect readout. Being ferrimagnetic, they possess a compensation point temperature, Tcomp, at which the net moment of the material becomes zero. Tcomp can be brought to the vicinity of the ambient temperature by proper choice of composition. This feature preserves uniform magnetic alignment in the perpendicular direction by preventing the magnetization from breaking up into domains.

Introduction

It has been suggested that a focused beam in the neighborhood of the focal point behaves just like a plane wave. This misconception is based on the fact that the focused beam at its waist has a flat wave-front. The finite size of the beam, however, causes the plane-wave analogy to fail: Fourier analysis shows that a focused light spot is the superposition of a multitude of plane waves with varying directions of propagation. At the high values of numerical aperture typically used in optical recording, the fraction of light having a sizeable obliquity factor is simply too large to be ignored. The reflection coefficients and magneto-optical conversion factors of optical disks are rather strong functions of the angle of incidence; thus the presence of oblique rays within the angular spectrum of the focused light must influence the outcome of the readout process. The goal of the present chapter is to investigate the consequences of sharp focus in optical disk systems, and to clarify the extent of departure of the readout signals from those predicted in the preceding chapter.

The vector diffraction theory of Chapter 3 and the methods of Chapter 5 for computing multilayer reflection coefficients are used here to analyze the effects of high-NA focusing. The focused incident beam is decomposed into its spectrum of plane waves, and the reflected beam is obtained by the superposition of these plane waves after they are independently reflected from the multilayer surface.

Introduction

In magneto-optical (MO) data storage systems the readout of recorded information is achieved by means of a focused beam of polarized light. Conventional systems today utilize a linearly polarized beam, whereas some suggested alternative methods rely instead on circular or elliptical polarization for readout.

Although the Jones calculus is the standard vehicle for analyzing the polarization properties of optical systems, we believe the alternative approach used in this chapter provides a better, more intuitive explanation for the operation of the readout system. The chapter begins by introducing the two basic states of circular polarization: right (RCP) and left (LCP). It then proceeds to show that the other two polarization states, linear (LP) and elliptical (EP), may be constructed by superposition of the two circular states. The sections that follow describe the actions of a quarter-wave plate (QWP) and a polarizing beam-splitter (PBS) on the various states of polarization. These two optical elements are of primary importance in detection schemes aimed at probing the state of polarization of a beam.

The classical scheme of differential detection for MO readout will be analyzed in section 6.4, first in its simple form for detecting the polarization rotation angle and then, with the addition of phase-compensating elements, for detecting ellipticity as well. In section 6.5 we describe an extension of the differential detection scheme. This extended scheme is used for spectral characterization (i.e., measurement of the wavelength-dependence of the Kerr angle and the ellipticity) of MO media.

Introduction

Since the early 1940s, magnetic recording has been the mainstay of electronic information storage worldwide. Audio tapes provided the first major application for the storage of information on magnetic media. Magnetic tape has been used extensively in consumer products such as audio tapes and video cassette recorders (VCRs); it has also found application in the backup or archival storage of computer files, satellite images, medical records, etc. Large volumetric capacity and low cost are the hallmarks of tape data storage, although sequential access to the recorded information is perhaps the main drawback of this technology. Magnetic hard-disk drives have been used as mass-storage devices in the computer industry ever since their inception in 1957. With an areal density that has doubled roughly every other year, hard disks have been and remain the medium of choice for secondary storage in computers. Another magnetic data storage device, the floppy disk, has been successful in areas where compactness, removability, and fairly rapid access to recorded information have been of prime concern. In addition to providing backup and safe storage, the inexpensive floppies with their moderate capacities (2 Mbyte on a 3.5″-diameter platter is typical) and reasonable transfer rates have provided the crucial function of file/data transfer between isolated machines. All in all, it has been a great half-century of progress and market dominance for magnetic recording devices which only now are beginning to face a potentially serious challenge from the technology of optical recording.

Introduction

Thermomagnetic recording involves the laser-assisted nucleation and growth of reverse-magnetized domains under the influence of external and/or internal magnetic fields. The nature of nucleation, the speed and uniformity of growth, and the local pinning of domain boundaries due to structural inhomogeneities of the material are among the factors that determine the final shape and size of recorded domains. Since it is important to control domain size, while avoiding nonuniformities and jagged boundaries, and since it is important to create stable domains, a knowledge of magnetization-reversal dynamics, including the effects of the nanostructure within the “amorphous” material, is desirable.

The observed magnetization reversal in RE–TM films is a nucleation and growth process. During bulk reversal (at temperatures not too close to the Curie point Tc) the nucleation sites are mostly reproducible. Rather than being driven by thermal fluctuations, nucleation is believed to be rooted in the nonuniform spatial distribution of the structural and magnetic properties of the media. The measured hysteresis loops generally have high squareness, which indicates that the coercivity of wall motion is less than the nucleation coercivity. In other words, once the nuclei are created at a certain applied field, they continue to grow without further hindrance. The recording and erasure processes rely on the creation and annihilation of reverse-magnetized domains. High densities are achieved when the recorded domains are small and uniform, have smooth boundaries, and are precisely positioned.

Introduction

The reflection and refraction of light at plane surfaces and interfaces, and the absorption of light by thin-film media play important roles in optical data storage. The reflection of polarized light from the surface of a magnetic material, for instance, is accompanied by a change of the state of polarization, thus carrying information about the state of magnetization of the material. The interaction is known as the magneto-optical (MO) Kerr effect and is generally used in MO data storage systems. The absorption of light by the storage medium and the subsequent creation of a hot spot is another common occurrence in optical recording. Such hot spots are typically needed for effecting the recording process, be it ablation in WORM-type media, structural phase transformation in phase-change media, or thermomagnetic recording in MO media.

Both read and write processes can benefit from the incorporation of the storage layer in a multilayer (optical-interference-type) structure. In the case of readout, the multilayer enhances the signal contrast (or the signal-to-noise ratio) by utilizing constructive interference among the various information-carrying beams reflected at the interfaces. In the case of writing and erasure, antireflection structures improve the sensitivity of the medium and promote efficient utilization of the available laser power. These benefits are not mutually exclusive and, in fact, the multilayers in use today are designed to have good recording sensitivity as well as enhanced readout signal-to-noise ratio.

Introduction

In thermomagnetic recording a focused laser beam creates a hot spot and allows an external magnetic field to reverse the direction of local magnetization. Erasure is similar to recording, except for a reversing of the external field, which enables the magnetization within the heated region to return to its original state. The technology of high-density magneto-optical data storage owes a large measure of its success to the accuracy, reliability, and repeatability of the thermomagnetic process. The recorded domains are highly regular and uniform, fully reversed, and free from instabilities. What is more, a given area of the storage medium can be erased and rewritten several million times without any degradation.

The present chapter is devoted to the analysis of the thermomagnetic process based on the physical principles of micromagnetics and domain dynamics. In section 17.1 we review some of the facts and experimental observations concerning the storage media and the recording process. This will help familiarize the reader with the variety of phenomena and the order of magnitude of the parameters involved, and will set the stage for in-depth analyses of thermomagnetic recording in subsequent sections. The discussion in section 17.2 revolves around the energetics of domain formation and the forces acting on the domain wall in its formative stages. This treatment of the problem, being based on the arguments described in section 13.3, is essentially a quasi-static treatment that ignores the dynamics of wall motion; moreover, it fails to properly account for the role of coercivity in the recording process.

We know now how alignment and orientation of angular momenta arise in the excited state as a result of optical excitation from the primarily isotropic distribution of the ensemble of angular momenta. This phenomenon reflects, in essence, the anisotropy of absorption probability G(θ,ϕ). Since spatial structures of the type shown in Fig. 2.2 appear in the excited state the same structure must be ‘eaten out’ from the angular momentum distribution in the ground (initial) state. If the gap created is not closed quickly enough, the ensemble of the remaining angular momenta of the absorbing molecules in the ground state must necessarily also be polarized.

If, from another point of view, fluorescent decay leads to a considerable population of the ground state level c, (see, e.g., Fig. 1.2), then molecules on this level may exhibit angular momenta polarization, being particularly noticeable for thermally unpopulated, high lying levels.

In the present chapter we intend to discuss the conditions necessary for the creation of ground state angular momenta polarization, the possibilities of its experimental observation, and to develop the theoretical description of broad line radiation interaction with molecules further.

Angular momenta polarization via depopulation

For many years there existed the widespread opinion that in molecules we obtain an anisotropic distribution of angular momenta only in the excited state in the absorption process, whilst in the ground state isotropy is conserved [124]. This conjecture is based essentially on the assumption of the existence of a so-called ‘weak’ excitation. At first sight it may appear, for instance, from Eq. (2.20) that, as is usual in non-linear spectroscopy, such an admission is correct if condition Γp/Γ ≫ 1 is valid.

Some atomic bound states have simple structure in the sense that a straightforward calculation obtains correct energy levels. In some cases optical oscillator strengths probe further detail. Collision theory has reached the stage where experimental observables for electron collisions involving such states can be calculated within experimental error. Observables whose calculation is sensitive to structure details constitute a probe for structure which verifies the details in more-difficult cases.

Scattering experiments are usually not very sensitive to structure. On the other hand the differential cross section for ionisation in a kinematic region where the plane-wave impulse approximation is valid gives a direct representation (10.31) of the structure of simple targets in the form of the momentum-space orbital of a target electron.

Electron momentum spectroscopy (McCarthy and Weigold, 1991) is based on ionisation experiments at incident energies of the order of 1000 eV, where the plane-wave impulse approximation is roughly valid. The differential cross section is measured for each ion state over a range of ion recoil momentum p from about 0 to 2.5 a.u. Noncoplanar-symmetric kinematics is the usual mode. In such experiments the distorted-wave impulse approximation turns out to be a sufficiently-refined theory. Checks of this based on a generally-valid sum rule will be described.

The reaction depends as much on the observed state |f〉 of the residual ion as on the ground state |0〉 of the target. Not only the single-particle structure but electron correlations in each state are sensitively probed in different circumstances.

Anisotropy of angular momenta: ideas and methods

The fundamental idea forming the basis of early quantum theory was the quantization of the angular momentum of the atom, which, at a later stage, assumed the form of the Bohr–Sommerfeld quantization rule [360], namely ∲ pdq = nℏ where p and q are the generalized momentum and coordinate. This concept has retained its physical meaning in modern-day quantum mechanics [371, 372]. In the course of the further development of quantum mechanical concepts it became increasingly clear that in the theory of atoms and molecules the angular momentum is a ‘dominant’ notion, the fundamental significance of which is in no small degree connected with its dimension of action, which coincides with that of Planck's constant ℏ.

In the interaction between particles and a directed beam of photons the angular momentum of the system is conserved, thus forming the basis for the optical method of producing spatial anisotropy of the distribution of the angular momenta of the ensemble of particles, i.e. its optical polarization. In terms of quantum concepts, spatial anisotropy means that in an ensemble of particles a non-equilibrium population of magnetic sublevels mj of angular momenta is created. We make a distinction between the alignment of momenta, for instance in the absorption of linear polarized light, when there is no difference between the population of ±mj-sublevels, and orientation, when such a difference exists. Anisotropic distribution of angular momenta in an excited state, as produced in absorption, manifests itself directly in the polarization of fluorescence.

It is rather likely that understanding of the anisotropic distribution of the angular momenta of atoms was enhanced by Hanle's [184] discovery in 1924.