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Physica Scripta

Birefringence of lateral shifts in reflection and transmission based on milnor polynomial and quantum tunnelling in induced chiral medium

Hamad Ali, Abdul Basit, Fuli Li, Xiaojie Li, Xuecheng Cao

Published Dec 1, 2025• 0 citations
Publisher

Abstract

Abstract We theoretically investigate birefringence of lateral Goos-Hänchen (GH) shift in a tunnelling chiral atomic medium. The Milnor polynomial of controlled fields and tunnelling modulate the light-mater interactions. We analyze the GH shift for right- and left-circularly polarized (RCP and LCP) beams for varying incident angles. We found a lossless condition R (+) + T (+) = 1 for RCP beams at the incident angle θ i = π /3, while LCP beams shows loss R (−) + T (−) + A (−) = 1 and A (−) = 0.2. The lateral shift in reflection of RCP beam varies in range of 0 λ ≤ S r ( + ) ≤ 60 λ and transmission of RCP beam varies in the range of 0 λ ≤ S t ( + ) ≤ 100 λ at θ i = π /3, while the shift in LCP beam decreases 0 λ ≤ S r ( − ) ≤ 40 λ and transmission increases 0 λ ≤ S t ( − ) ≤ 150 λ for the same parameters. Further, for incident angle θ i = π /4, we found an increase in lateral shifts S r , t ( − ) ≤ 150 λ for RCP and 0 λ ≤ S r , t (

DOI
10.1088/1402-4896/ae2dd5

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Physica Scripta•Dec 30, 2020•25 citations
Abstract We theoretically investigate birefringence of lateral Goos-Hänchen (GH) shift in a tunnelling chiral atomic medium. The Milnor polynomial of controlled fields and tunnelling modulate the light-mater interactions. We analyze the GH shift for right- and left-circularly polarized (RCP and LCP) beams for varying incident angles. We found a lossless condition R (+) + T (+) = 1 for RCP beams at the incident angle θ i = π /3, while LCP beams shows loss R (−) + T (−) + A (−) = 1 and A (−) = 0.2. The lateral shift in reflection of RCP beam varies in range of 0 λ ≤ S r ( + ) ≤ 60 λ and transmission of RCP beam varies in the range of 0 λ ≤ S t ( + ) ≤ 100 λ at θ i = π /3, while the shift in LCP beam decreases 0 λ ≤ S r ( − ) ≤ 40 λ and transmission increases 0 λ ≤ S t ( − ) ≤ 150 λ for the same parameters. Further, for incident angle θ i = π /4, we found an increase in lateral shifts S r , t ( − ) ≤ 150 λ for RCP and 0 λ ≤ S r , t (
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 ∣R(R,L)∣+∣T(R,L)∣=1|R^{(R,L)}|+|T^{(R,L)}|=1∣R(R,L)∣+∣T(R,L)∣=1 with forward and backward currents as well as coupled driving fields parameters at the interface of a lossy chiral medium of ∣A(R,L)∣≃0|A^{(R,L)}|\simeq 0∣A(R,L)∣≃0 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 Sr(R,L)=−10λS^{(R,L)}_{r}=-10\lambdaSr(R,L)​=−10λ and that in the transmission is measured to St(R,L)=10λS^{(R,L)}_{t}=10\lambdaSt(R,L)​=10λ with forward and backward currents of complex conductivity. Furthermore, maximum values of GH-shifts in reflection and transmission of LCP beams are calculated to ±40λ\pm 40\lambda±40λ and RCP beams are calculated to ±10λ\pm 10\lambda±10λ with control field Rabi frequency and backward current variation. The results indicate possible uses in the designing of optical and conductive sensors.
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 ∣R(+,−)∣+∣T(+,−)∣=1|R^{(+,-)}|+|T^{(+,-)}|=1∣R(+,−)∣+∣T(+,−)∣=1 at the interface of a lossy chiral medium of ∣A(+,−)∣≃0|A^{(+,-)}|\simeq 0∣A(+,−)∣≃0 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.
Abstract Birefringence of lateral Goos-Hänchen (GH) shift in reflection and transmission beams are investigated through four level chiral atomic medium. Significant positive and negative shifts in reflection and transmission birefringence beams are reported under the strength of driving fields. At resonance point, positive birefringent shifts of 2.8 λ and 2 λ are noted in reflection beams. The birefringence lateral GH-shift in transmission beams show contrast behaviors of −2 λ and −2.8 λ at resonance point. A 30% fractional change in birefringent reflection and transmission beams with GH-shift are investigated. These results will play a vital role in the modification of optical heterodyne sensors technology, cloaking devices, image coding, integrated optical technologies and telecom industry.
Abstract We present a new scheme to report on the effects of a five-level chiral atomic medium on the lateral Goos–Hänchen (GH) shift in Gaussian probe beams via Kerr nonlinearity (KNL) and local field effects. The physical realization of birefringence in absorption, dispersion, reflection and transmission beams is investigated, with special emphasis on the manipulation of absolute and fractional change in lateral GH shifts in birefringence transmission and reflection beams, via local fields and Kerr nonlinearity. We have employed a semiclassical atomic density-matrix formalism so as to obtain the expression for electric and magnetic susceptibilities of the chiral medium and the corresponding chirality coefficients in conjunction with Kerr and local fields, both separately and in combination. Stationary-phase theory is used to compute GH shift from the calculated birefringent reflection and transmission coefficients of probe beams. A negative and positive GH shift is observed in reflection and transmission beams, respectively, subjected to local field and Kerr effect. In contrast, a positive GH shift is observed in both reflection and transmission beams in the presence of both local field and Kerr effects. The local and Kerr fields also alter the divergence angle between left and right circularly polarized birefringence beams. GH shift depends on incident angle and probe detuning. The anisotropy of medium is lessened by switching ON the Kerr field in the medium. We observed a positive fractional change of ±30% in the GH shift in the birefringence reflection beam in the presence of a local field without KNL, while a 20% fractional GH shift was observed in the presence of both local field and KNL effects. Our results suggest promising applications in nonlinear optical, plasmonic and biophotonic devices for the manipulation of light propagation and optical signal processing.
The role of a chiral quantum-dot molecule (QDM) system in controlling and enhancing the Goos-H\"anchen (GH) shift is revealed here. The proposed setup is a four-level atomic system excited by incoherent pump and probe fields where the electron tunneling is prominent in affecting the GH shift upon the reflection and transmission of probe beams. The GH shifts in the chiral QDM system are calculated analytically by using stationary phase theory, whereas the dynamics of the quantum-dot system are derived by the density-matrix method. It is demonstrated that the GH shifts through transmission and reflection light beams are strongly influenced due to right-circularly polarized (RCP) and left-circularly polarized light. The GH shifts through RCP light are enhanced in the presence of chiral QDM systems, and these shifts could become either highly negative or highly positive, sensitively depending on the electron tunneling and chiral coefficients. This proposal can be viewed as a theoretical approach to the potential application of GH shifts in nano-optoelectronic sensors.
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 Δ n = n r ( + ) − n r ( − ) and group indices Δ n g = n g ( + ) − n g ( − ) are controlled and modified through induced dynamic chiral medium by tunnelling effect. The group indices n g ( ± ) = ± 500 and group velocities v g ( ± ) = ± c / 500 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.