Introduction

The conventional media of magneto-optical data storage, the rare earth-transition metal alloys, are generally produced by radio frequency (rf) sputtering from an alloy target onto a plastic or glass substrate. For protection against the environment as well as for optical and thermal enhancement, the RE–TM alloy films are sandwiched between two dielectric layers (such as SiNx or AINx) and covered with a metallic reflecting and heat-sinking layer, before finally being coated with several microns of protective lacquer. The properties of the MO layer are determined not only by the composition of the alloy, but also by the sputtering environment and by the condition of the substrate's surface. The temperature at which the film grows, the sputtering gas pressure, the substrate bias voltage (self or applied), the rate of deposition, the surface roughness of the substrate, the quality of underlayer and overlayer can all affect the properties of the final product. It is therefore necessary to have accurate characterization tools with which to measure the various properties of the media and to establish their suitability for application as the media of erasable optical data storage.

The most widely used method of characterization for magnetic materials is vibrating sample magnetometry (VSM). With VSM it is possible to measure the component of net magnetization Ms along the direction of the applied field. For MO media, one obtains the hysteresis loop when the field is perpendicular to the plane of the sample.

Introduction

In a digital system, the so-called “user-data” is typically an unconstrained sequence of binary digits 0 and 1. In such devices it is the responsibility of the information storage subsystem to record the data and to reproduce it faithfully and reliably upon request. To achieve high densities and fast data rates, storage systems are usually pushed to the limit at which the strength of the readout signal is of the same order of magnitude as that of the noise. Operating under these circumstances, it should come as no surprise that errors of misinterpretation do indeed occur at the time of retrieval. Also, because individual bits are recorded on microscopic areas, the presence of small media imperfections and defects, dust particles, fingerprints, scratches, and the like, results in imperfect reconstruction of the recorded binary sequences. For these and other reasons to be described below, the stream of user-data typically undergoes an encoding process before it finally arrives on the storage medium. The encoding not only adds some measure of protection against noise and other sources of error, but also introduces certain useful features in the recorded bit-pattern that help in signal processing and future data recovery operations. These features might be designed to allow the generation of a clocking signal from the readout waveform, or to maintain the balance of charge in the electronic circuitry, or to enable more efficient packing of data on the storage medium, or to provide some degree of control over the spectral content of the recorded waveform, and so on.

Introduction

The process of magnetization reversal in thin magnetic films is of considerable importance in erasable optical data storage. The success of thermomagnetic recording and erasure depends on the reliable and repeatable reversal of magnetization in micron-sized areas within the storage medium. A major factor usually encountered in descriptions of the thermomagnetic write and erase processes is the coercivity of the magnetic material. Technically, the coercivity Hc is defined for a hysteresis loop as the value of the applied field at which the net magnetization becomes zero. Coercivity, however, is an ill-defined concept which may be useful in the phenomenology of bulk reversal, but its relevance to the phenomena occuring on the spatial and temporal scales of thermomagnetic recording must be seriously questioned. To begin with, there is the problem of distinguishing the nucleation coercivity from the coercivity of wall motion. Then there is the question of speed and uniformity of motion as the wall expands beyond the site of its origination. Finally one must address issues of stability and erasability, which are intimately related to coercivity, in a framework wide enough to allow the consideration of local instabilities and partial erasure. It is fair to say that the existing theories of coercivity are generally incapable of handling the problems associated with thermomagnetic recording and erasure. In our view, the natural vehicle for conducting theoretical investigations in this area is computer simulation based on the fundamental equations of micromagnetics, the basis for which was laid down in the preceding chapter.

Introduction

Magneto-optical recording is an important mode of optical data storage; it is also the most viable technique for erasable optical recording at the present time. The MO read and write processes are both dependent on the interaction between the laser beam and the magnetic medium. In the preceding chapters we described the readout process with the aid of the dielectric tensor of the storage medium, without paying much attention to the underlying magnetism. Understanding the write and erase processes, on the other hand, requires a certain degree of familiarity with the concepts of magnetism in general, and with the micromagnetics of thin-film media in particular. The purpose of the present chapter is to give an elementary account of the basic magnetic phenomena, and to introduce the reader to certain aspects of the theory of magnetism and magnetic materials that will be encountered throughout the rest of the book.

After defining the various magnetic fields (H, B, and A) in section 12.1, we turn our attention in section 12.2 to small current loops, and show the equivalence between the properties of these loops and those of magnetic dipoles. The magnetization M of magnetic materials is also introduced in this section. Larmor diamagnetism is the subject of section 12.3. In section 12.4 the magnetic ground state of free atoms (ions) is described, and Hund's rules (which apply to this ground state) are presented.

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.