Abstract

Space variant beams are of great importance for a variety of applications that have emerged in recent years. As such, manipulation of their degrees of freedom is highly desired. Here, we study the general interaction of space variant beams with a magnetically influenced Rb medium exploiting the atoms versatile properties in terms of frequency and intensity dependent circular dichroism and circular birefringence. We present the particular cases of radially polarized and hybrid polarized beams where the control of the polarization states is demonstrated experimentally. Moreover, we show that such an atomic system can be used as a tunable analyzer for space variant beams. Finally, exploiting the non-linear properties of Rb vapor, we show that we can control the circular birefringence all optically, and thus modulate the polarization of the radial polarized beam.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Measurements of spin properties of atomic systems in and out of equilibrium via noise spectroscopy

Maheswar Swar, Dibyendu Roy, Dhanalakshmi D, Saptarishi Chaudhuri, Sanjukta Roy, and Hema Ramachandran
Opt. Express 26(24) 32168-32183 (2018)

Coherent control of group index and magneto-optical anisotropy in a multilevel atomic vapor

Andreas Lampis, Robert Culver, Balázs Megyeri, and Jon Goldwin
Opt. Express 24(14) 15494-15505 (2016)

Manipulating the transmission of vector beam with spatially polarized atomic ensemble

Xin Yang, Aiping Fang, Jinwen Wang, Yunke Li, Xiyuan Chen, Xinqi Zhang, Mingtao Cao, Dong Wei, Klaus Müller-Dethlefs, Hong Gao, and Fuli Li
Opt. Express 27(4) 3900-3908 (2019)

References

  • View by:
  • |
  • |
  • |

  1. G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
    [Crossref] [PubMed]
  2. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [Crossref] [PubMed]
  3. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon., AOP 1, 1–57 (2009).
  4. G. M. Lerman, A. Yanai, N. Ben-Yosef, and U. Levy, “Demonstration of an elliptical plasmonic lens illuminated with radially-like polarized field,” Opt. Express 18(10), 10871–10877 (2010).
    [Crossref] [PubMed]
  5. P. R. Dolan, X. Li, J. Storteboom, and M. Gu, “Complete determination of the orientation of NV centers with radially polarized beams,” Opt. Express 22(4), 4379–4387 (2014).
    [Crossref] [PubMed]
  6. I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
    [Crossref]
  7. O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5(9), 665–668 (2009).
    [Crossref]
  8. F. K. Fatemi, “Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems,” Opt. Express 19(25), 25143–25150 (2011).
    [Crossref] [PubMed]
  9. L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, I. G. Hughes, and C. S. Adams, “Optical isolator using an atomic vapor in the hyperfine Paschen-Back regime,” Opt. Lett. 37(16), 3405–3407 (2012).
    [Crossref] [PubMed]
  10. R. M. Camacho, M. V. Pack, and J. C. Howell, “Slow light with large fractional delays by spectral hole-burning in rubidium vapor,” Phys. Rev. A 74(3), 033801 (2006).
    [Crossref]
  11. A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-Optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005).
    [Crossref] [PubMed]
  12. N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101(14), 147401 (2008).
    [Crossref] [PubMed]
  13. S. Knappe, P. Schwindt, V. Shah, L. Hollberg, J. Kitching, L. Liew, and J. Moreland, “A chip-scale atomic clock based on 87Rb with improved frequency stability,” Opt. Express 13(4), 1249–1253 (2005).
    [Crossref] [PubMed]
  14. D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007).
    [Crossref]
  15. M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
    [Crossref] [PubMed]
  16. S. Krishnamurthy, Y. Wang, Y. Tu, S. Tseng, and M. S. Shahriar, “High-speed modulation in ladder transitions in Rb atoms using high-pressure buffer gas,” Opt. Express 23(9), 11470–11482 (2015).
    [Crossref] [PubMed]
  17. P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. At. Mol. Opt. Phys. 41(15), 155004 (2008).
    [Crossref]
  18. B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
    [Crossref]
  19. G. M. Lerman, L. Stern, and U. Levy, “Generation and tight focusing of hybridly polarized vector beams,” Opt. Express 18(26), 27650–27657 (2010).
    [Crossref] [PubMed]

2015 (1)

2014 (2)

P. R. Dolan, X. Li, J. Storteboom, and M. Gu, “Complete determination of the orientation of NV centers with radially polarized beams,” Opt. Express 22(4), 4379–4387 (2014).
[Crossref] [PubMed]

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

2012 (1)

2011 (2)

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

F. K. Fatemi, “Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems,” Opt. Express 19(25), 25143–25150 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon., AOP 1, 1–57 (2009).

O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5(9), 665–668 (2009).
[Crossref]

2008 (3)

G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
[Crossref] [PubMed]

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. At. Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101(14), 147401 (2008).
[Crossref] [PubMed]

2007 (2)

D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007).
[Crossref]

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[Crossref]

2006 (1)

R. M. Camacho, M. V. Pack, and J. C. Howell, “Slow light with large fractional delays by spectral hole-burning in rubidium vapor,” Phys. Rev. A 74(3), 033801 (2006).
[Crossref]

2005 (2)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Adams, C. S.

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, I. G. Hughes, and C. S. Adams, “Optical isolator using an atomic vapor in the hyperfine Paschen-Back regime,” Opt. Lett. 37(16), 3405–3407 (2012).
[Crossref] [PubMed]

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. At. Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Ben-Yosef, N.

Buchler, B. C.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Budker, D.

D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007).
[Crossref]

Camacho, R. M.

R. M. Camacho, M. V. Pack, and J. C. Howell, “Slow light with large fractional delays by spectral hole-burning in rubidium vapor,” Phys. Rev. A 74(3), 033801 (2006).
[Crossref]

Campbell, G.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Clark, S. M.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-Optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005).
[Crossref] [PubMed]

Cui, Y.

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

Davidson, N.

O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5(9), 665–668 (2009).
[Crossref]

Dawes, A. M. C.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-Optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005).
[Crossref] [PubMed]

Dolan, P. R.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Fatemi, F. K.

Firstenberg, O.

O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5(9), 665–668 (2009).
[Crossref]

Gauthier, D. J.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-Optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005).
[Crossref] [PubMed]

Ge, C.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. At. Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Green, J. T.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101(14), 147401 (2008).
[Crossref] [PubMed]

Gu, B.

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

Gu, M.

Hollberg, L.

Hosseini, M.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Howell, J. C.

R. M. Camacho, M. V. Pack, and J. C. Howell, “Slow light with large fractional delays by spectral hole-burning in rubidium vapor,” Phys. Rev. A 74(3), 033801 (2006).
[Crossref]

Hughes, I. G.

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, I. G. Hughes, and C. S. Adams, “Optical isolator using an atomic vapor in the hyperfine Paschen-Back regime,” Opt. Lett. 37(16), 3405–3407 (2012).
[Crossref] [PubMed]

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. At. Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Illing, L.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-Optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005).
[Crossref] [PubMed]

Kitching, J.

Kleinbach, K. S.

Knappe, S.

Krishnamurthy, S.

Lam, P. K.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Levy, U.

Li, X.

Liew, L.

London, P.

O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5(9), 665–668 (2009).
[Crossref]

Moreland, J.

Nishiyama, I.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[Crossref]

Otani, Y.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[Crossref]

Pack, M. V.

R. M. Camacho, M. V. Pack, and J. C. Howell, “Slow light with large fractional delays by spectral hole-burning in rubidium vapor,” Phys. Rev. A 74(3), 033801 (2006).
[Crossref]

Pan, Y.

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

Proite, N. A.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101(14), 147401 (2008).
[Crossref] [PubMed]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Romalis, M.

D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007).
[Crossref]

Ron, A.

O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5(9), 665–668 (2009).
[Crossref]

Rui, G.

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

Schwindt, P.

Shah, V.

Shahriar, M. S.

Shuker, M.

O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5(9), 665–668 (2009).
[Crossref]

Siddons, P.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. At. Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Sparkes, B. M.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Stern, L.

Storteboom, J.

Tseng, S.

Tu, Y.

Umeda, N.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[Crossref]

Unks, B. E.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101(14), 147401 (2008).
[Crossref] [PubMed]

Wang, Y.

Weller, L.

Xu, D.

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

Yanai, A.

Yavuz, D. D.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101(14), 147401 (2008).
[Crossref] [PubMed]

Yoshida, N.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[Crossref]

Zentile, M. A.

Zhan, Q.

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon., AOP 1, 1–57 (2009).

Adv. Opt. Photon., AOP (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon., AOP 1, 1–57 (2009).

Appl. Phys. B (1)

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

J. Phys. At. Mol. Opt. Phys. (1)

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. At. Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Meas. Sci. Technol. (1)

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[Crossref]

Nat. Commun. (1)

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Nat. Phys. (2)

D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007).
[Crossref]

O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5(9), 665–668 (2009).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Phys. Rev. A (1)

R. M. Camacho, M. V. Pack, and J. C. Howell, “Slow light with large fractional delays by spectral hole-burning in rubidium vapor,” Phys. Rev. A 74(3), 033801 (2006).
[Crossref]

Phys. Rev. Lett. (2)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101(14), 147401 (2008).
[Crossref] [PubMed]

Science (1)

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-Optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005).
[Crossref] [PubMed]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 (a) 85Rb F = 2 to F’ = 2 schematic level diagram and a sketch showing space-variant polarized beams interacting with Rb atoms in the presence of magnetic field. (b-e) Calculated frequency dependent (b) Attenuation coefficient and (c) Refractive index of Zeeman-shifted D1 F = 2 to F' = 2 and F' = 3 Doppler broadened transitions for RHC (red) and LHC (black) in a magnetic field of B = 180G. (d) the ratio between RHC and LHC (and the inverse ratio) electric field transmission (e) The difference between LHP and RHP refractive index.
Fig. 2
Fig. 2 Numerical calculations of the polarization and intensity distribution for three different space-variant beams after propagating through CB, CD and combined media. (a-d) radially polarized beam (e-h) hybrid polarized beam with m = 1, n = 0 and (i-l) hybrid polarized beam with m = 2, n = 0. The top panel of each type of beam represents the polarization distribution while the intensity distribution (obtained by projecting the beam onto a horizontally aligned analyzer) is given in the bottom panel. The colors represent the polarization orientation - red and black correspond to RHP and LHP respectively and blue to linear polarization.
Fig. 3
Fig. 3 (a) Schematic sketch of experimental arrangement (b) Single shot measurements of radially polarized beam intensity projected on a horizontally aligned analyzer (top) and polarization map (bottom) without (left) and with (right) the applied magnetic field (c) Measured polarization distribution obtained from full Stokes parameters of a HPB transmitted through the Rb medium at different wavelengths. Red is for RHP and black is for LHP. Top left shows the absorption spectrum of the reference cell and the measured points.
Fig. 4
Fig. 4 (a,1) Measured transmission spectra of a magnetically controlled 85Rb transition manifold for RHP and LHP (red and black, respectively). (a,2-4) measured transmission of the HPB at various wavelengths (a,2) in the regime of RHP resonance (a,3) in the regime of equivalent absorption between RHP and LHP (a,4) regime of LHP resonance. b) measured transmission of radialy polarized light in the regime of CB: (b,1) at low intensity and no magnetic field, (b,2) low intensity and magnetic field (b,3) at high intensity and no magnetic field, (b,4) high intensity and magnetic field.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

E(θ,ϕ,a)~[a e i(θ+ϕ) σ ^ + + e iθ σ ^ ],
E(δ,ϕ,a)~[a e iϕ ( e iδ i e iδ ) σ ^ + +( e iδ +i e iδ ) σ ^ ],

Metrics