Tunnelling based birefringent phase sensitivity through dynamic chiral medium
Syed Muhammad Arif, Bakht Amin Bacha, Umer Wahid, Arif Ullah, Muhammad Haneef
Abstract
Abstract The absorption coefficients, refractive/group indices, phase shifts and fractional change of birefringence beams through dynamic chiral atomic medium are investigated under the effect of quantum tunnelling. The birefringence of phase indices <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>+</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and group indices <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msub> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>+</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> are controlled and modified through induced dynamic chiral medium by tunnelling effect. The group indices <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>±</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mo>±</mml:mo> <mml:mn>500</mml:mn> </mml:math> and group velocities <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>±</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mo>±</mml:mo> <mml:mi>c</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>500</mml:mn> </mml:math> are reported with the tunnelling effect. The maximum change in birefringent phase shifts is calculated to 5 microradian with tunnelling frequency at a speed of v = 10 cm/s of the chiral medium in the right circularly polarized (RCP) and left circularly polarized (LCP) beams. A 60% fractional change in the phase shift of RCP and LCP beams are investigated through induced chiral medium when the medium is at rest and when it is moving with the speed of v = 10 cm/s. These results will play an important role in scatterplate phase shifting interferometry.