Skip to main content
Log in

Nonlinear optical holograms for spatial and spectral shaping of light waves

  • Review
  • Physics & Astronomy
  • Published:
Science Bulletin

Abstract

Shaping either the spatial or the spectral output of a nonlinear interaction is accomplished by introducing basic concepts of computer-generated holography into the nonlinear optics regime. The possibilities of arbitrarily spatially shaping the result of a nonlinear interaction are presented for different phase-matching schemes allowing for both one- and two-dimensional shaping. Shaping the spectrum of a beam in nonlinear interaction is also possible by utilizing similar holographic techniques. The novel and complete control of the output of a nonlinear interaction opens exciting options in the fields of particle manipulation, optical communications, spectroscopy and quantum information.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Dolev I, Ellenbogen T, Arie A (2010) Switching the acceleration direction of Airy beams by a nonlinear optical process. Opt Lett 35:1581–1583

    Article  Google Scholar 

  2. Chong A, Renninger WH, Christodoulides DN et al (2010) Airy–Bessel wave packets as versatile linear light bullets. Nat Photonics 4:103–106

    Article  Google Scholar 

  3. Imeshev G, Proctor M, Fejer MM (1998) Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings. Opt Lett 23:673–675

    Article  Google Scholar 

  4. Ellenbogen T, Ganany-Padowicz A, Arie A (2008) Nonlinear photonic structures for all-optical deflection. Opt Express 16:3077–3082

    Article  Google Scholar 

  5. Kurz JR, Schober AM, Hum DS et al (2002) Nonlinear physical optics with transversly patterned quasi-phase-matching gratings. IEEE J Sel Top Quantum Electron 8:660–664

    Article  Google Scholar 

  6. Ellenbogen T, Voloch-Bloch N, Ganany-Padowicz A et al (2009) Nonlinear generation and manipulation of Airy beams. Nat Photonics 3:395–398

    Article  Google Scholar 

  7. Siviloglou GA, Broky J, Dogariu A et al (2007) Observation of accelerating Airy beams. Phys Rev Lett 99:213901

    Article  Google Scholar 

  8. Qin Y, Zhang C, Zhu Y et al (2008) Wave-front engineering by Huygens–Fresnel principle for nonlinear optical interactions in domain engineered structures. Phys Rev Lett 100:063903

    Article  Google Scholar 

  9. Bahabad A, Arie A (2007) Generation of optical vortex beams by nonlinear wave mixing. Opt Express 15:17619–17624

    Article  Google Scholar 

  10. Yamada M, Nada N, Saitoh M et al (1993) First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation. Appl Phys Lett 62:435–436

    Article  Google Scholar 

  11. Shapira A, Juwiler I, Arie A (2011) Nonlinear computer generated holograms. Opt Lett 36:3015–3017

    Article  Google Scholar 

  12. Shapira A, Shiloh R, Juwiler I et al (2012) Two-dimensional nonlinear beam shaping. Opt Lett 37:2136–2138

    Article  Google Scholar 

  13. Shapira A, Juwiler I, Arie A (2013) Tunable nonlinear beam shaping in a non-collinear interaction. Laser Photon Rev 7:L25–L29

    Article  Google Scholar 

  14. Shiloh R, Arie A (2012) Spectral and temporal holograms with nonlinear optics. Opt Lett 37:3591–3593

    Article  Google Scholar 

  15. Leshem A, Shiloh R, Arie A (2014) Experimental realization of spectral shaping using nonlinear optical holograms. Opt Lett 39:5370–5373

    Article  Google Scholar 

  16. Boyd RW (2008) Nonlinear optics, 3rd edn. Academic Press, Orlando

    Google Scholar 

  17. Armstrong JA, Bloembergen N, Ducuing J et al (1962) Interaction between light waves in a nonlinear dielectric. Phys Rev 127:1918–1939

    Article  Google Scholar 

  18. Boyd GD, Kleinman DA (1968) Parametric interaction of focused Gaussian light beams. J Appl Phys 39:3597

    Article  Google Scholar 

  19. Saltiel SM, Neshev DN, Krolikowski W et al (2009) Mulitorder nonlinear diffraction in frequency doubling processes. Opt Lett 34:848–850

    Article  Google Scholar 

  20. Saltiel SM, Sheng Y, Voloch-Bloch N et al (2009) Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures. IEEE J Quantum Electron 45:1465–1472

    Article  Google Scholar 

  21. Freund I (1968) Nonlinear diffraction. Phys Rev Lett 21:1404

    Article  Google Scholar 

  22. Saltiel SM, Neshev DN, Fischer R et al (2008) Generation of the second-harmonic conical waves via nonlinear Bragg diffraction. Phys Rev Lett 100:103902

    Article  Google Scholar 

  23. Saltiel SM, Neshev DN, Krolikowski W et al (2010) Nonlinear diffraction from a virtual beam. Phys Rev Lett 104:083902

    Article  Google Scholar 

  24. Shapira A, Arie A (2011) Phase-matched nonlinear diffraction. Opt Lett 36:1933–1935

    Article  Google Scholar 

  25. Gabor DA (1948) A new microscopic principle. Nature 161:777–778

    Article  Google Scholar 

  26. Brown BR, Lohmann AW (1966) Complex spatial filtering with binary masks. Appl Opt 5:967–969

    Article  Google Scholar 

  27. Burch JJ (1967) A computer algorithm for the synthesis of spatial frequency filters. IEEE Proc 55:599–601

    Article  Google Scholar 

  28. Saleh BEA, Teich MC (1991) Fundamentals of photonics. Wiley, New York

    Book  Google Scholar 

  29. Lee WH (1979) Binary computer-generated holograms. Appl Opt 18:3661–3669

    Article  Google Scholar 

  30. Shoji I, Kondo T, Kitamoto A et al (1997) Absolute scale of second-order nonlinear-optical coefficients. J Opt Soc Am B: Opt Phys 14:2268–2294

    Article  Google Scholar 

  31. Arlt J, Dholakia K, Allen L et al (1998) The production of multiringed Laguerre–Gaussian modes by computer-generated holograms. J Mod Opt 45:1231–1237

    Article  Google Scholar 

  32. Voloch-Bloch N, Shemer K, Shapira A et al (2012) Twisting of light by nonlinear photonic crystals. Phys Rev Lett 108:233902

    Article  Google Scholar 

  33. Shemer K, Volovh-Bloch N, Shapira A et al (2013) Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals. Opt Lett 38:5470–5473

    Article  Google Scholar 

  34. Lu LL, Xu P, Zhong ML et al (2015) Orbital angular momentum entanglement via fork-poling nonlinear photonic crystals. Opt Express 23:1203–1212

    Article  Google Scholar 

  35. Dolev I, Ganany-Padowicz A, Gayer O et al (2009) Linear and nonlinear optical properties of MgO:LiTaO3. Appl Phys B 96:423–432

    Article  Google Scholar 

  36. Hong XH, Yang B, Zhang C et al (2014) Nonlinear volume holography for wave-front engineering. Phys Rev Lett 113:163902

    Article  Google Scholar 

  37. Shapira A, Libster A, Lilach Y et al (2013) Functional facets for nonlinear crystals. Opt Comm 300:244–248

    Article  Google Scholar 

  38. Bandres MA (2008) Accelerating parabolic beams. Opt Lett 33:1678–1680

    Article  Google Scholar 

  39. Ellenbogen T, Dolev I, Arie A (2008) Mode conversion in quadratic nonlinear crystals. Opt Lett 33:1207–1209

    Article  Google Scholar 

  40. Zhou ZY, Li Y, Ding DS et al (2014) Generation of light with controllable spatial patterns via the sum frequency in quasi-phase matching crystals. Sci Rep 4:5650

    Google Scholar 

  41. Libster-Hershko A, Trajtenberg-Mills S, Arie A (2015) Dynamic control of light beams in second harmonic generation. Opt Lett 40:1944–1947

    Article  Google Scholar 

  42. Remez R, Arie A (2015) Super-narrow frequency conversion. Optica 2:472–475

    Article  Google Scholar 

  43. Berry M (1994) Quantum coherence and reality. World Scientific, Singapore, pp 55–65

    Google Scholar 

Download references

Acknowledgments

This work was supported by the Israel Science Foundation (1310/13) and by the Israeli Ministry of Science, Technology and Space in the framework of the Israel–Italy bi-national collaboration program. The authors would like to acknowledge HC Photonics Corporation for the manufacture of the poled MgO:CLN crystals according to our customized designs.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Asia Shapira.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shapira, A., Naor, L. & Arie, A. Nonlinear optical holograms for spatial and spectral shaping of light waves. Sci. Bull. 60, 1403–1415 (2015). https://doi.org/10.1007/s11434-015-0855-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11434-015-0855-3

Keywords

Navigation