The two eigenmodes of light propagation through the magnetooptic medium can be expressed as a right circular polarized(RCP) light wave E1(2)=exp[ j or- 2rn,2 (57.5a) and a left circular polarized(LCP) light wave 2兀t -Expl J where n,2=E, +fMj; o and no are the angular frequency and the wavelength of the incident light, respectively n, and n are the refractive indices of the RCP and LCP modes, respectively. These modes correspond to two counterrotating circularly polarized light waves. The superposition of these two waves produces a linearly polarized wave. The plane of polarization of the resultant wave rotates as one circular wave overtakes the other The rate of rotation is given by 6≡M rad/m B is known as the Faraday rotation(FR)coefficient. When the direction of the magnetization is reversed, the gle of rotation changes its sign. Since two counterrotating circular polarized optical waves are used to explain FR. the effect also known as optical magnetic circular birefringence(MCB ). Furthermore, since the senses of polarization rotation of forward traveling and backward traveling light waves are opposite, FR is a nonreciprocal optical effect. Optical devices such as optical isolators and optical circulators use the Faraday effect to achieve their nonreciprocal functions For ferromagnetic and ferrimagnetic media, the FR is charac terized under a magnetically saturated condition, i.e., M,= Ms the saturation magnetization of the medium. For paramagnetic or diamagnetic materials, the magnetization is proportional to the external applied magnetic field Ho. Therefore, the FR is proportional to the external field or AF= VHo where V=Xof/o ve, )is called the Verdet constant and %o is the magnetic susceptibility of free space Cotton. Mouton effect or magnetic linear birefringence When transmitted light is propagating perpendicular to the magnetization direction, the first-order isotropic R effect will vanish and the second-order anisotropic Cotton-Mouton(CM)effect will dominate. For example, if the direction of magnetization is along the Z axis and the light wave is propagating along the X axis, the E,+fu,M 0 0 0E,+f12M30 Er+fMi c 2000 by CRC Press LLC© 2000 by CRC Press LLC The two eigenmodes of light propagation through the magnetooptic medium can be expressed as a right circular polarized (RCP) light wave (57.5a) and a left circular polarized (LCP) light wave (57.5b) where n± 2 @ er ± f1M3; w and l0 are the angular frequency and the wavelength of the incident light, respectively. n+ and n– are the refractive indices of the RCP and LCP modes, respectively. These modes correspond to two counterrotating circularly polarized light waves. The superposition of these two waves produces a linearly polarized wave. The plane of polarization of the resultant wave rotates as one circular wave overtakes the other. The rate of rotation is given by (57.6) qF is known as the Faraday rotation (FR) coefficient. When the direction of the magnetization is reversed, the angle of rotation changes its sign. Since two counterrotating circular polarized optical waves are used to explain FR, the effect is thus also known as optical magnetic circular birefringence (MCB). Furthermore, since the senses of polarization rotation of forward traveling and backward traveling light waves are opposite, FR is a nonreciprocal optical effect. Optical devices such as optical isolators and optical circulators use the Faraday effect to achieve their nonreciprocal functions. For ferromagnetic and ferrimagnetic media, the FR is charac￾terized under a magnetically saturated condition, i.e., M3 = MS, the saturation magnetization of the medium. For paramagnetic or diamagnetic materials, the magnetization is proportional to the external applied magnetic field H0. Therefore, the FR is proportional to the external field or qF = VH0 where V = c0f1p/(l0 ) is called the Verdet constant and c0 is the magnetic susceptibility of free space. Cotton-Mouton Effect or Magnetic Linear Birefringence When transmitted light is propagating perpendicular to the magnetization direction, the first-order isotropic FR effect will vanish and the second-order anisotropic Cotton-Mouton (CM) effect will dominate. For example, if the direction of magnetization is along the Z axis and the light wave is propagating along the X axis, the permittivity tensor becomes (57.7) ˜ E Z j exp j t n 1 Z 0 1 0 2 ( ) = È Î Í Í Í ˘ ˚ ˙ ˙ ˙ - Ê Ë Á ˆ ¯ ˜ È Î Í Í ˘ ˚ ˙ ˙ + w p l ˜ E Z j exp j t n 2 Z 0 1 0 2 ( ) = - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ - Ê Ë Á ˆ ¯ ˜ È Î Í Í ˘ ˚ ˙ ˙ - w p l q p l e l e F r r f M f M @ = 1 3 0 1 3 0 1 8 rad/m degree/cm . er ´ = + + + È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ e e e e e 0 12 3 2 12 3 2 11 3 2 0 0 0 0 0 0 r r r f M f M f M