The classical harmonic oscillator equation of motion with a static magnetic field is m d7 2...

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The classical harmonic oscillator equation of motion with a static magnetic field is m d²7 2 dt² =-moor-eE-e- -x (B2), dt where damping is ignored and B is applied along the z-axis. For an incident beam with an electric field of the form Eef, we assume that the position vector is also of the form ře-it. a. Write out Equation 3.160 in terms of complex amplitudes for each Cartesian component. Show that the resultant equations can be written as a -ib ib (3.160) a 0 0 0 % 0|7=E, m (3.161) where a and b are constants dependent on parameters given in the problem. b. Use Equation 3.161 to solve for 7, and use the polarization definition P=-Ner=EoE to find the susceptibility matrix. c. Show that the eigenvectors of the susceptibility matrix are right and left cir- cularly polarized. The classical harmonic oscillator equation of motion with a static magnetic field is m d²7 2 dt² =-moor-eE-e- -x (B2), dt where damping is ignored and B is applied along the z-axis. For an incident beam with an electric field of the form Eef, we assume that the position vector is also of the form ře-it. a. Write out Equation 3.160 in terms of complex amplitudes for each Cartesian component. Show that the resultant equations can be written as a -ib ib (3.160) a 0 0 0 % 0|7=E, m (3.161) where a and b are constants dependent on parameters given in the problem. b. Use Equation 3.161 to solve for 7, and use the polarization definition P=-Ner=EoE to find the susceptibility matrix. c. Show that the eigenvectors of the susceptibility matrix are right and left cir- cularly polarized.