In the principal crystal axes [100] coordinate system, the magnetooptic permittivity reduces to the following E where*denotes complex conjugate operation. The elements are given by paramagnetic state E=Elo E. O 00￡ Faraday rotation jfM -ifM, +ifM, -jf,M Cotton-Mouton effect fM+f, M3+f 2M4,, 2MMM,M, 2/4M,M f12M2+f1M2+f12M2 MMM,M, (57.3) 2MM,M, 2M. frMi +fnMS+MMM In order to keep the discussion simple, analytic complexities due to optical absorption of the magnetic mediu have been ignored. Such absorption can give rise to magnetic circular dichroism(MCD)and magnetic linear dichroism(MLD). Interested readers can refer to Hellwege[ 1978] and Arecchi and Schulz-DuBois [1972] for more in-depth discussions on MCD and MLD 57.2 Classification of Magnetooptic Effects Faraday Rotation or Magnetic Circular Birefringence The classic Faraday rotation takes place in a cubic or isotropic transparent medium where the propagation direction of transmitted light is parallel to the direction of applied magnetization within the medium. For example, if the direction of magnetization and the propagation of light is taken as Z, the permittivity tensor becomes(assuming second-order effect is insignificantly small) Er jfM, 0 E≡-ifMe,0 c 2000 by CRC Press LLC© 2000 by CRC Press LLC In the principal crystal axes [100] coordinate system, the magnetooptic permittivity reduces to the following forms: where * denotes complex conjugate operation. The elements are given by paramagnetic state Faraday rotation Cotton-Mouton effect (57.3) In order to keep the discussion simple, analytic complexities due to optical absorption of the magnetic medium have been ignored. Such absorption can give rise to magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD). Interested readers can refer to Hellwege [1978] and Arecchi and Schulz-DuBois [1972] for more in-depth discussions on MCD and MLD. 57.2 Classification of Magnetooptic Effects Faraday Rotation or Magnetic Circular Birefringence The classic Faraday rotation takes place in a cubic or isotropic transparent medium where the propagation direction of transmitted light is parallel to the direction of applied magnetization within the medium. For example, if the direction of magnetization and the propagation of light is taken as Z, the permittivity tensor becomes (assuming second-order effect is insignificantly small): (57.4) ´ = È Î Í Í Í ˘ ˚ ˙ ˙ ˙ e e e e e e e e e e e 0 11 12 13 12 22 23 13 23 33 * * * ´ = È Î Í Í Í ˘ ˚ ˙ ˙ ˙ e e e e e 0 0 0 0 0 0 0 r r r + + - - + + - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ e0 1 3 1 2 1 3 1 1 1 2 1 1 0 0 0 j f M j f M j f M j f M j f M j f M + + + + + + + È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ e0 11 1 2 12 2 2 12 3 2 44 1 2 44 1 3 44 1 2 12 1 2 11 2 2 12 3 2 44 2 3 44 1 3 44 2 3 12 1 2 12 2 2 11 3 2 2 2 2 2 2 2 f M f M f M f M M f M M f M M f M f M f M f M M f M M f M M f M f M f M ´ @ - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ e e e e e 0 1 3 1 3 0 0 0 0 r r r j f M j f M