Coherent manipulation of giant birefringent Goos–Hänchen shifts by compton scattering using chiral atomic medium

A four level chiral medium is considered to analyze and investigate theoretically the reflection/transmission coefficients of right circularly polarized (RCP) beam and left circularly polarized (LCP) beam as well as their corresponding GH-shifts under the effect of compton scattering. Density matrix formalism is used for calculation of electric and magnetic probe fields coherence. The polarization and magnetization are calculated from probes coherence terms in the chiral medium. The electric and magnetic susceptibilities as well as chiral coefficients are related with polarization and magnetization. The refractive indices of RCP and LCP beams under compton scattering effect is modified from the electric/magnetic susceptibilities, chiral coefficients, mass and charge of electron as well as compton scattering angle. The giant positive and negative birefringent Goos-Hänchen (GH) shifts in reflection and transmission beams are investigated in this manuscript under Compton scattering effect. The RCP and LCP beams obey the normalization condition <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mo>|</mml:mo></mml:mrow> <mml:msup><mml:mi>R</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:mo>+</mml:mo> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mo>)</mml:mo></mml:mrow> </mml:msup> <mml:mrow><mml:mo>|</mml:mo> <mml:mo>+</mml:mo> <mml:mo>|</mml:mo></mml:mrow> <mml:msup><mml:mi>T</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:mo>+</mml:mo> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mo>)</mml:mo></mml:mrow> </mml:msup> <mml:mrow><mml:mo>|</mml:mo> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn></mml:mrow> </mml:mrow> </mml:math> at the interface of a lossy chiral medium of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mo>|</mml:mo></mml:mrow> <mml:msup><mml:mi>A</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:mo>+</mml:mo> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mo>)</mml:mo></mml:mrow> </mml:msup> <mml:mrow><mml:mo>|</mml:mo> <mml:mo>≃</mml:mo> <mml:mn>0</mml:mn></mml:mrow> </mml:mrow> </mml:math> and a thin sheet of balsa wood under the effect of compton scattering angle, incident angle, probe field detuning, control field Rabi frequency, phases of electric and magnetic fields and phase of superposition states. Significant positive/negative giant GH-shifts in reflection and transmission beams are investigated. The results show potential applications in modification of cloaking devices, image coding, polarizing filters and LCD displays.