Coherent manipulation of Goos–Hänchen shifts by forward and backward currents of complex conductivity in chiral medium

The birefringence of reflection and transmission as well as their corresponding Goos-Hänchen shifts are investigated with complex conductivity in a four level chiral atomic medium. The left circularly polarized (LCP) beam and right circularly polarized (RCP) beam 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:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <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:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <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> with forward and backward currents as well as coupled driving fields parameters 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:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <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 polystyrene. For the birefringent transmission, the positive GH-shifts are reported while for the birefringent reflection, the negative GH-shifts are measured. The maximum GH-shift in reflections of RCP and LCP beams is measured to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msubsup><mml:mi>S</mml:mi> <mml:mi>r</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo></mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>10</mml:mn> <mml:mi>λ</mml:mi></mml:mrow> </mml:math> and that in the transmission is measured to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msubsup><mml:mi>S</mml:mi> <mml:mi>t</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo></mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>10</mml:mn> <mml:mi>λ</mml:mi></mml:mrow> </mml:math> with forward and backward currents of complex conductivity. Furthermore, maximum values of GH-shifts in reflection and transmission of LCP beams are calculated to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>±</mml:mo> <mml:mn>40</mml:mn> <mml:mi>λ</mml:mi></mml:mrow> </mml:math> and RCP beams are calculated to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>±</mml:mo> <mml:mn>10</mml:mn> <mml:mi>λ</mml:mi></mml:mrow> </mml:math> with control field Rabi frequency and backward current variation. The results indicate possible uses in the designing of optical and conductive sensors.