Forthcoming

Influence of magnetic field and temperature on negative refractive index in a degenerate three-level atomic system

Nguyen Huy Bang, Luong Thi Yen Nga, Nguyen Van Ai, Le Van Doai
Author affiliations

Authors

  • Nguyen Huy Bang Vinh University, 182 Le Duan Street, Vinh City, Vietnam
  • Luong Thi Yen Nga Vinh University, 182 Le Duan Street, Vinh City, Vietnam
  • Nguyen Van Ai Ha Tinh University, Ha Tinh City, Vietnam
  • Le Van Doai Vinh University, 182 Le Duan Street, Nghe An Province, Vietnam https://orcid.org/0000-0002-1850-3437

DOI:

https://doi.org/10.15625/0868-3166/22871

Abstract

This work investigates the manipulation of the negative refractive index in a degenerate three-level \( \Lambda \)-type atomic system in the presence of an external magnetic field and Doppler broadening. The results show that the bandwidth of the negative refractive index can be significantly broadened by increasing the coupling laser intensity; for example, when \( \Omega_c \) increases from \( 30\gamma \) to \( 60\gamma \), the bandwidth expands from \( [0.5\gamma, 1.5\gamma] \) to \( [1.2\gamma, 4\gamma] \). The spectral position can be flexibly tuned by adjusting the magnetic field, shifting toward lower (higher) frequencies for \( B = -1\gamma_c \) (\( B = 2\gamma_c \)). Temperature has a pronounced effect on both the range and amplitude; increasing the temperature from \( 200\,\mathrm{K} \) to \( 400\,\mathrm{K} \) narrows the range from \( [-1.6\gamma_c, -0.2\gamma_c] \) to \( [-1.1\gamma_c, -0.5\gamma_c] \). These findings may facilitate experimental realization and potential practical applications of EIT-based negative-index materials.

Downloads

Download data is not yet available.

References

[1] J. D. Jackson, Classical Electrodynamics. Wiley, New York, 3rd ed., 1999.

[2] V. G. Veselago, The electrodynamics of substances with simultaneously negative values of ε and μ, Sov. Phys. Usp. 10 (1968) 509.

[3] R. A. Shelby, D. R. Smith and S. Schultz, Experimental verification of a negative index of refraction, Science 292 (2001) 77.

[4] S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood and S. R. J. Brueck, Experimental demonstration of near-infrared negative-index metamaterials, Phys. Rev. Lett. 95 (2005) 137404.

[5] K. Aydin, I. Bulu and E. Ozbay, Subwavelength resolution with a negative-index metamaterial superlens, Appl. Phys. Lett. 90 (2007) 254102.

[6] A. Lakhtakia, Positive and negative goos-hänchen shifts and negative phase-velocity mediums (alias left-handed materials), Int. J. Electron. Commun. (AEU) 58 (2004) 229.

[7] J. B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 85 (2000) 3966.

[8] Y. P. Yang, J. P. Xu, H. Chen and S. Y. Zhu, Quantum interference enhancement with left-handed materials, Phys. Rev. Lett. 100 (2008) 043601.

[9] J. Pendry, Positively negative, Nature 423 (2003) 22.

[10] E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, Electromagnetic waves: Negative refraction by photonic crystals, Nature 423 (2003) 604.

[11] G. V. Eleftheriades, A. K. Iyer and P. C. Kremer, Planar negative refractive index media using periodically l-c loaded transmission lines, IEEE Trans. Microwave Theory Tech. 50 (2002) 2702.

[12] Z. Li, M. Mutlu and E. Ozbay, Chiral metamaterials: from optical activity and negative refractive index to asymmetric transmission, J. Opt. 15 (2013) 023001.

[13] N. H. Bang, D. X. Khoa and L. V. Doai, Controllable optical properties of multi-electromagnetically induced transparency gaseous atomic medium, Comm. Phys. 28 (2019) 1.

[14] M. O. Oktel and O. E. Mustecaplioglu, Electromagnetically induced left-handedness in a dense gas of three-level atoms, Phys. Rev. A 70 (2004) 053806.

[15] J. Q. Shen, Z. C. Ruan and S. He, How to realize a negative refractive index material at the atomic level in an optical frequency range, J. Zhejiang Univ. Science 5 (2004) 1322.

[16] C. M. Krowne and J. Q. Shen, Dressed-state mixed-parity transitions for realizing negative refractive index, Phys. Rev. A 79 (2009) 023818.

[17] S. C. Zhao, Z.-D. Liu and Q.-X. Wu, Zero absorption and a large negative refractive index in a left-handed four-level atomic medium, J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 045505.

[18] D. X. Khoa, P. V. Trong, L. V. Doai and N. H. Bang, Electromagnetically induced transparency in a five-level cascade system under doppler broadening: an analytical approach, Phys. Scr. 91 (2016) 035401.

[19] D. X. Khoa, H. M. Dong, L. V. Doai and N. H. Bang, Propagation of laser pulse in a three-level cascade inhomogeneously broadened medium under electromagnetically induced transparency conditions, Optik 131 (2017) 497.

[20] N. T. Anh, L. V. Doai, D. H. Son and N. H. Bang, Manipulating multi-frequency light in a five-level cascade eit medium under doppler broadening, Optik 171 (2018) 721.

[21] N. H. Bang, D. X. Khoa, D. H. Son and L. V. Doai, Effect of doppler broadening on giant self-kerr nonlinearity in a five-level ladder-type system, Opt. Soc. Am. B 36 (2019) 3151.

[22] N. V. Ai, N. H. Bang and L. V. Doai, Negative refractive index in a doppler broadened three-level λ-type atomic medium, Phys. Scr. 97 (2022) 025503.

[23] N. H. Bang and L. V. Doai, Controlling negative refractive index of degenerated three-level λ-type system by external light and magnetic fields, Eur. Phys. J. D 75 (2021) 261.

[24] N. H. Bang, N. V. Phu, V. N. Sau, N. T. Cong and L. V. Doai, Negative refractive index in an inhomogeneously broadened four-level inverted-y atomic medium, IEEE Photonics Journal 13 (2021) 2200407.

[25] H. G. Al-Toki and A. H. Al-Khursan, Negative refraction in the double quantum dot system, Opt. Quant. Electron. 52 (2020) 467.

[26] N. Boutabba, Controllable refractive index in a four-level left-handed medium using pulse shaping, J. Opt. 23 (2021) 075504.

[27] U. Hayat, I. Ahmad, H. Ali, R. U. Din and S. Haddadi, Enhanced negative refraction in one- and two-dimensional chiral atomic lattices, Results in Physics 56 (2024) 107277.

Published

28-11-2025

How to Cite

[1]B. Nguyen Huy, L. T. Y. Nga, A. Nguyen Van, and D. Le Van, “Influence of magnetic field and temperature on negative refractive index in a degenerate three-level atomic system”, Comm. Phys., vol. 35, no. 4, Nov. 2025.