temporal dispersion, have been studied primarily in the frequency domain. In this case temporal derivative and integral operations produce complex constitutive parameters. It is becoming equally important to characterize these effects directly in the time domain for use with direct time-domain field solving techniques such as the finite-difference time domain(FDTD)method. We shall cover the very basic properties of dispersive media in this section. A detailed description of frequency-domain fields(and a discussion of complex constitutive parameters)is deferred until later in this book It is difficult to find a simple and consistent means for classifying materials by their ectromagnetic effects. One way is to separate linear and nonlinear materials, then cate- gorize linear materials by the way in which the fields are coupled through the constitutive 1. Isotropic materials are those in which D is related to E, B is related to H the secondary source current J is related to E, with the field direction in each 2. In anisotropic materials the pairings are the same, but the fields in each pair are generally not aligned 3. In biisotropic materials(such as chiral media)the fields D and B depend on both E and H, but with no realignment of E or H; for instance, D is given by the addition of a scalar times E plus a second scalar times H. Thus the contributions o d involve no changes to the directions of E and H 4. Bianisotropic materials exhibit the most general behavior: D and H depend on both E and B, with an arbitrary realignment of either or both of these fields In 1888, Roentgen showed experimentally that a material isotropic in its own station ry reference frame exhibits bianisotropic properties when observed from a moving frame Only recently have materials bianisotropic in their own rest frame been discovered. In 1894 Curie predicted that in a stationary material, based on symmetry, an electric field might produce magnetic effects and a magnetic field might produce electric effects. These effects, coined magnetoelectric by Landau and Lifshitz in 1957, were sought unsuccess- fully by many experimentalists during the first half of the twentieth century. In 1959 the Soviet scientist I. E. Dzyaloshinskii predicted that, theoretically, the antiferromagnetic material chromium oxide(Cr2O3)should display magnetoelectric effects. The magneto- electric effect was finally observed soon after by D N. Astrov in a single crystal of Cr2O3 using a 10 kHz electric field. Since then the effect has been observed in many different materials. Recently, highly exotic materials with useful electromagnetic properties have been proposed and studied in depth, including chiroplasmas and chiroferrites 211. As the technology of materials synthesis advances, a host of new and intriguing media will The most general forms of the constitutive relations between the fields may be written in symbolic form as D=DE, B (214) HE, BI That is, D and H have some mathematically descriptive relationship to E and B. The specific forms of the relationships may be written in terms of dyadics as [102 cD=P·E+L H=M·E+Q·(cB),temporal dispersion, have been studied primarily in the frequency domain. In this case temporal derivative and integral operations produce complex constitutive parameters. It is becoming equally important to characterize these effects directly in the time domain for use with direct time-domain field solving techniques such as the finite-difference time￾domain (FDTD) method. We shall cover the very basic properties of dispersive media in this section. A detailed description of frequency-domain fields (and a discussion of complex constitutive parameters) is deferred until later in this book. It is difficult to find a simple and consistent means for classifying materials by their electromagnetic effects. One way is to separate linear and nonlinear materials, then cate￾gorize linear materials by the way in which the fields are coupled through the constitutive relations: 1. Isotropic materials are those in which D is related to E, B is related to H, and the secondary source current J is related to E, with the field direction in each pair aligned. 2 . In anisotropic materials the pairings are the same, but the fields in each pair are generally not aligned. 3. In biisotropic materials (such as chiral media) the fields D and B depend on both E and H, but with no realignment of E or H; for instance, D is given by the addition of a scalar times E plus a second scalar times H. Thus the contributions to D involve no changes to the directions of E and H. 4. Bianisotropic materials exhibit the most general behavior: D and H depend on both E and B, with an arbitrary realignment of either or both of these fields. In 1888, Roentgen showed experimentally that a material isotropic in its own station￾ary reference frame exhibits bianisotropic properties when observed from a moving frame. Only recently have materials bianisotropic in their own rest frame been discovered. In 1894 Curie predicted that in a stationary material, based on symmetry, an electric field might produce magnetic effects and a magnetic field might produce electric effects. These effects, coined magnetoelectric by Landau and Lifshitz in 1957, were sought unsuccess￾fully by many experimentalists during the first half of the twentieth century. In 1959 the Soviet scientist I.E. Dzyaloshinskii predicted that, theoretically, the antiferromagnetic material chromium oxide (Cr2O3) should display magnetoelectric effects. The magneto￾electric effect was finally observed soon after by D.N. Astrov in a single crystal of Cr2O3 using a 10 kHz electric field. Since then the effect has been observed in many different materials. Recently, highly exotic materials with useful electromagnetic properties have been proposed and studied in depth, including chiroplasmas and chiroferrites [211]. As the technology of materials synthesis advances, a host of new and intriguing media will certainly be created. The most general forms of the constitutive relations between the fields may be written in symbolic form as D = D[E,B], (2.14) H = H[E,B]. (2.15) That is, D and H have some mathematically descriptive relationship to E and B. The specific forms of the relationships may be written in terms of dyadics as [102] cD = P¯ · E + L¯ · (cB), (2.16) H = M¯ · E + Q¯ · (cB), (2.17)