Skip to main content

Controlling Spatial Shift and Spltting of Four-Wave Mixing

  • Chapter
  • 724 Accesses

Abstract

When multiple laser beams interact with multi-level atomic systems, interesting spatial effects for the probe beam, such as the pattern formation, spatial displacement, and spatial soliton, can occur, controlled by stronger coupling or pumping laser beams. In this chapter, spatial dispersion properties of the probe and generated four-waving mixing (FWM) beams are presented, which can lead to spatial shift and splitting of these weak laser beams. Such beam displacement and splitting can be controlled by the story coupling/pumping laser beams via enhanced cross-Kerr nonlinearity in the multi-level atomic systems near electromagnetically induced transparency (EIT) resonance. Such enhanced spatial dispersion behaviors follow closely to the traditional linear and nonlinear dispersion properties in a frequency domain for multi-level EIT systems. By controlling the spatial displacements of the weak probe and FWM beams with coupling/pumping beams, spatial optical switching and routing of one beam or multiple optical beams can be achieved. Such controllable spatial beam displacement and splitting effects are illustrated in two- and three-level atomic system.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Wang H, Goorskey D, Xiao M. Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system. Phys Rev Lett, 2001, 87: 073601.

    Article  ADS  Google Scholar 

  2. Agrawal G P. Induced focusing of optical beams in self-defocusing nonlinear media. Phys Rev Lett, 1990, 64: 2487–2490.

    Article  ADS  Google Scholar 

  3. Stentz A J, Kauranen M, Maki J J, et al. Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium. Opt Lett, 1992, 17: 19–21

    Article  ADS  Google Scholar 

  4. Hickmann J M, Gomes A S L, de Araújo C B. Observation of Spatial Cross-Phase Modulation Effects in a Self-Defocusing Nonlinear Medium. Phys Rev Lett, 1992, 68: 3547–3550.

    Article  ADS  Google Scholar 

  5. Desyatnikov A S, Sukhorukov A A, Kivshar Y S. Azimuthons: spatially modulated vortex solitons. Phys Rev Lett, 2005, 95: 203904.

    Article  ADS  Google Scholar 

  6. Bennink R S, Wong V, Marino A M, et al. Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor. Phys Rev Lett, 2002, 88: 113901.

    Article  ADS  Google Scholar 

  7. Harris S E. Electromagnetically induced transparency. Phys Today, 1997, 50: 36–42.

    Article  Google Scholar 

  8. Harris S H, Yamamoto Y. Photon switching by quantum interference. Phys Rev Lett, 1998, 81: 3611–3614.

    Article  ADS  Google Scholar 

  9. Truscott A G, Friese M E G, Heckenberg N R, et al. Optically written waveguide in an atomic vapor. Phys Rev Lett, 1999, 82: 1438–1441.

    Article  ADS  Google Scholar 

  10. Jain M, Merriam A J, Xia H, et al. Efficient nonlinear frequency conversion with maximal atomic coherence. Phys Rev Lett, 1996, 77: 4326–4329.

    Article  ADS  Google Scholar 

  11. Firstenberg O, Shuker M, Davidson N, et al. Elimination of the diffraction of arbitrary images imprinted on slow light. Phys Rev Lett, 2009, 102: 043601.

    Article  ADS  Google Scholar 

  12. Dawes A M C, Illing L, Clark S M, et al. All-optical switching in rubidium vapor. Science, 2005, 308: 672–674.

    Article  ADS  Google Scholar 

  13. Li Y, Xiao M. Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms. Opt Lett, 1996, 21: 1064–1066.

    Article  ADS  Google Scholar 

  14. Boyer V, Marino A M, Lett P D. Generation of spatially broadband twin beams for quantum imaging. Phys Rev Lett, 2008, 100: 143601.

    Article  ADS  Google Scholar 

  15. Boyer V, Marino A M, Pooser R C, et al. Entangled images from four-wave mixing. Science, 2008, 321: 544–547.

    Article  ADS  Google Scholar 

  16. Xiao M, Li Y Q, Jin S Z, et al. Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms. Phys Rev Lett, 1995, 74: 666–669.

    Article  ADS  Google Scholar 

  17. Zheng H B, Zhang Y P, Nie Z Q, et al. Interplay among multidressed fourwave mixing processes. Appl Phys Lett, 2008, 93: 241101; Zhang Y P, Anderson B, Brown A W, et al. Competition between two four-wave mixing channels via atomic coherence. Appl Phys Lett, 2007, 91: 061113.

    Article  ADS  Google Scholar 

  18. Nie Z Q, Zheng H B, Li P Z, et al. Interacting multiwave mixing in a five-level atomic system. Phys Rev A, 2008 77: 063829.

    Article  ADS  Google Scholar 

  19. Zhang Y P, Nie Z Q, Zheng H B, et al. Electromagnetically induced spatial nonlinear dispersion of four-wave mixing. Phys Rev A, 2009, 80: 013835.

    Article  ADS  Google Scholar 

  20. Krolikowski W, Bang O. Solitons in nonlocal nonlinear media: Exact solutions. Phys Rev E, 2001, 63: 016610.

    Article  ADS  Google Scholar 

  21. ZhangY P, Khadka U, Anderson B, et al. Temporal and spatial interference between four-wave mixing and six-wave mixing channels. Phys Rev Lett, 2009, 102: 01360.

    Google Scholar 

  22. Brown A M, Xiao M. All-optical switching and routing based on an electromagnetically induced absorption grating. Opt Lett, 2005, 30: 699–701.

    Article  ADS  Google Scholar 

  23. Yan M, Rickey E G, Zhu Y F. Observation of absorptive photon switching by quantum interference. Phys Rev A, 2001, 64: 041801.

    Article  ADS  Google Scholar 

  24. Nie Z Q, Zheng H B, Zhang Y P, et al. Experimental demonstration of optical switching and routing via four-wave mixing spatial shift. Opt Express, 2010, 18: 899–905.

    Article  ADS  Google Scholar 

  25. Ham B S, Hemmer P R. Coherence switching in a four-level system: quantum switching. Phys Rev Lett, 2000, 84: 4080–4083.

    Article  ADS  Google Scholar 

  26. Zhang J P, Hernandez G, Zhu Y F. Optical switching mediated by quantum interference of Raman transitions. Opt Express, 2008, 16: 19112–19117.

    Article  ADS  Google Scholar 

  27. Camacho R M, Vudyasetu P K, Howell J C. Four-wave-mixing stopped light in hot atomic rubidium vapour. Nature Photonics, 2009, 3: 103–106.

    Article  ADS  Google Scholar 

  28. Boyd R W. Nonlinear optics. New York: Academic Press, 1992.

    Google Scholar 

  29. Du S W, Wen J M, Rubin M H, et al. Four-wave mixing and biphoton generation in a two-level system. Phys Rev Lett, 2007, 98: 053601.

    Article  ADS  Google Scholar 

  30. Krolikowski W, Saffman M, Luther-Davies B, et al. Anomalous interaction of spatial solitons in photorefractive media. Phys Rev Lett, 1998, 80: 3240–3243.

    Article  ADS  Google Scholar 

  31. Garanovich I L, Sukhorukov A A, Kivshar Y S, et al. Surface multi-gap vector solitons. Opt Exp, 2006, 14: 4780–4785.

    Article  ADS  Google Scholar 

  32. Rosberg C R, Neshev D N, Krolikowski W, et al. Observation of surface gap solitons in semi-infinite waveguide arrays. Phys Rev Lett, 2006, 97: 083901.

    Article  ADS  Google Scholar 

  33. Swartzlander G A, Law C T. Optical vortex solitons observed in Kerr nonlinear media. Phys Rev Lett, 1992, 69: 2503–2506.

    Article  ADS  Google Scholar 

  34. Xiao Y H, Klein M, Hohensee M, et al. Slow light beam splitter. Phys Rev Lett, 2008, 101: 043601.

    Article  ADS  Google Scholar 

  35. Zhang Y P, Zuo C C, Zheng H B, et al. Controlled spatial beam splitter using four-wave-mixing images. Phys Rev A, 2009, 80: 055804.

    Article  ADS  Google Scholar 

  36. Qi Y R, Gao H, Zhang S G. Enhanced spin depolarization and storage time in a Rb vapor. Chin Phys Lett, 2009, 26: 114211.

    Article  ADS  Google Scholar 

  37. Lu X S, Chen Q F, Shi B S, et al. Generation of a non-classical correlated photon pair via spontaneous four-wave mixing in a cold atomic ensemble. Chin Phys Lett, 2009, 26: 064204.

    Article  ADS  Google Scholar 

  38. Shuker M, Firstenberg O, Pugatch R, et al. Storing images in warm atomic vapor. Phys Rev Lett, 2008, 100: 223601.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Zhang, Y., Nie, Z., Xiao, M. (2011). Controlling Spatial Shift and Spltting of Four-Wave Mixing. In: Coherent Control of Four-Wave Mixing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19115-2_7

Download citation

Publish with us

Policies and ethics