In an ionic crystal , the coupling of the transverse optical phonon with the electromagnetic wave leads to polariton with the dispersion relation

In an ionic crystal, the coupling of the transverse optical photon

In an ionic crystal , the coupling of the transverse optical phonon with the electromagneticwave leads to polariton with the dispersion relation given as :"K ? C 2 / 0 2 = E ( W ) = $ ( 00 ) + [ { ( 0 ) – $ (00) ] WOT ? / ( WOT ? _ W 2 ), where IT is the frequency of the transverse*phonon mode , & is the wave vector of the polariton . ( a ) ( 10pts ) Find the solutions for w near k = 0and k being very large ; ( b ) ( 10 pts ) Discuss if the polariton wave can propagate in the frequencyrange (T < W < WL , where we ( the frequency of the longitudinal mode ) is related to cut through the[ST relation ( eq . 62 , ch . 14 ) .E-E ( 0 )E ( 00( 62)