Controlled generation of higher-order Poincaré sphere beams from a laser

Journal name:
Nature Photonics
Volume:
10,
Pages:
327–332
Year published:
DOI:
doi:10.1038/nphoton.2016.37
Received
Accepted
Published online

Abstract

The angular momentum of light can be described by positions on a higher-order Poincaré sphere, where superpositions of spin and orbital angular momentum states give rise to laser beams that have many applications, from microscopy to materials processing. Many techniques exist to create such beams but none so far allow their creation at the source. Here we report on a new class of laser that is able to generate all states on the higher-order Poincaré sphere. We exploit geometric phase control inside a laser cavity to map polarization to orbital angular momentum, demonstrating that the orbital angular momentum degeneracy of a standard laser cavity may be broken, producing pure orbital angular momentum beams, and that generalized vector vortex beams may be created with high purity at the source. This work paves the way to new lasers for structured light based on intracavity geometric phase control.

At a glance

Figures

  1. HOP sphere representation of vector vortex beams.
    Figure 1: HOP sphere representation of vector vortex beams.

    a, Local polarization vector states at various positions on the sphere. b, The intensity of the outputs are consistent beams with a central null. These beams are differentiated by the transmitted intensity from a linear polarizer oriented in the vertical, as depicted by the double-ended arrows. Expressions are provided for the states at the poles and for the special points on the equator with radial and azimuthal polarization.

  2. Laser concept.
    Figure 2: Laser concept.

    a, A standard Fabry–Pérot configuration controls the laser polarization using a PBS and a QWP. b, A q-plate is used to map the polarization to helically phased beams, with the handedness of the output depending on the incident state of the circular polarization. c, Experimental concept of the active selection of pure OAM LG0ℓ by the intracavity coupling of SAM to OAM. The coupling is achieved by selecting a pure SAM state by transmitting light that is linearly polarized in the horizontal through a QWP rotated at angle β. This LG00 shaped field is directed to a q-plate (QP) rotated at angle γ and consequently out-coupled through the FM. The two rotation angles may be varied accordingly to map out the HOP sphere. The inset illustrates the various polarization states operating in the cavity with their associated vectors.

  3. Mode purity of OAM beams.
    Figure 3: Mode purity of OAM beams.

    a, Recorded output of the laser as a function of β with the insets showing the left- and right-circularly polarized components. A pure scalar mode of left handedness is observed at β =  −45° and of right handedness at β = 45°, with superpositions of SAM states in between (for example β = 0°). b, Experimental measured (data points) and theoretical prediction (curves) for the evolution of the relative weightings of the and |R〉 states making up the final field as a function of β. c, Modal analysis of the laser output (β =  ±45°) confirms pure LG0,−1 and LG0,+1 modes, respectively, with their corresponding measurement channels (right). m, azimuthal index. d, Results of radial and azimuthal modal decomposition show that >98% of the power is contained in the desired mode (ℓ =  − 1 and p = 0). The cavity was operated at q = 1/2 and γ = 0° for these tests.

  4. Measured HOP sphere beams.
    Figure 4: Measured HOP sphere beams.

    a, The output of the laser (γ = 0, β = 0) is radially polarized (this is confirmed in b). b, A lobe structure is observed after transmission through a linear polarizer. The lobed structure is parallel to the orientation of the polarizer (indicated by double-ended arrows) on rotation. c, With γ = 90° an azimuthally polarized beam is observed, and confirmed in d. d, The lobe structure now rotates out of phase with the polarizer. These results are also confirmed by Stokes polarimetry (see Supplementary Information). e, Experimental measured beams as represented on a HOP sphere, together with their state expression and an example of the transmission through a polarizer. The values in parentheses represent the angles β and γ used to create these beams.

  5. HOP sphere beams with a larger topological charge.
    Figure 5: HOP sphere beams with a larger topological charge.

    a, For a q-plate with q = 5 we obtain annular outputs for the cavity operating under β = 45°, −45° and 0° with γ = 0. b, At β = 0°, the output leads to a rotatable lobed beam after transmission through a linear polarizer, inferring radial polarization. c, An azimuthal inner product is executed on the output of the laser operating under β =  −45° and 45° illustrating a pure LG0,−10 and LG0,+10 mode, respectively, with their corresponding measurement channels.

References

  1. Milione, G., Sztul, H. I., Nolan, D. A. & Alfano, R. R. Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light. Phys. Rev. Lett. 107, 053601 (2011).
  2. Milione, G., Evans, S., Nolan, D. A. & Alfano, R. R. Higher-order Pancharatnam–Berry phase and the angular momentum of light. Phys. Rev. Lett. 108, 190401 (2012).
  3. Holleczek, A., Aiello, A., Gabriel, C., Marquardt, C. & Leuchs, G. Classical and quantum properties of cylindrically polarized states of light. Opt. Express 19, 97149736 (2011).
  4. Bomzon, Z., Kleiner, V. & Hasman, E. Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings. Opt. Lett. 26, 14241426 (2001).
  5. Niv, A., Biener, G., Kleiner, V. & Hasman, E. Manipulation of the Pancharatnam phase in vectorial vortices. Opt. Express 14, 42084220 (2006).
  6. Gregg, P. et al. Q-plates as higher order polarization controllers for orbital angular momentum modes of fiber. Opt. Lett. 40, 17291732 (2015).
  7. Lavery, M. P. J. et al. Space division multiplexing in a basis of vector modes. in Proc. European Conf. Opt. Commun. We.3.6.1 (IEEE, 2014); http://dx.doi.org/10.1109/ECOC.2014.6964136
  8. Milione, G. et al. 4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer. Opt. Lett. 40, 19801983 (2015).
  9. Cardano, F. et al. Polarization pattern of vector vortex beams generated by q-plates with different topological charges Appl. Opt. 51, C1C6 (2012).
  10. Liu, Y. et al. Realization of polarization evolution on higher-order Poincaré sphere with metasurface. Appl. Phys. Lett. 104, 191110-1191110-4 (2014).
  11. Zhan, Q. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1, 157 (2009).
  12. Hamazaki, J. et al. Optical-vortex laser ablation. Opt. Express 18, 21442151 (2010).
  13. Toyoda, K. et al. Transfer of light helicity to nanostructures. Phys. Rev. Lett. 110, 143603 (2013).
  14. Weber, R. et al. Effects of radial and tangential polarization in laser material processing. Phys. Proc. 27, 2130 (2011).
  15. Wong, L. J. & Kartner, F. X. Direct acceleration of an electron in infinite vacuum by a pulsed radially-polarized laser beam. Opt. Express 18, 2503525051 (2010).
  16. Grier, D. G. A revolution in optical manipulation. Nature 424, 810816 (2003).
  17. Padgett, M. J. & Bowman, R. Tweezers with a twist. Nature Photon. 5, 343348 (2011).
  18. Hao, X., Kuang, C., Wang, T. & Liu, X. Effects of polarization on the de-excitation dark focal spot in STED microscopy. J. Opt. 12, 115707 (2010).
  19. Chen, R., Agarwal, K., Sheppard, C. J. R. & Chen, X. Imaging using cylindrical vector beams in a highnumerical-aperture microscopy system. Opt. Lett. 38, 31113114 (2013).
  20. Ren, H., Lin, Y.-H. & Wu, S.-T. Linear to axial or radial polarization conversion using a liquid crystal gel. Appl. Phys. Lett. 86, 051114 (2006).
  21. Bashkansky, M., Park, D. & Fatemi, F. K. Azimuthally and radially polarized light with a nematic SLM. Opt. Express 18, 212217 (2010).
  22. Machavariani, G., Lumer, Y., Moshe, I., Meir, A. & Jackel, S. Efficient extracavity generation of radially and azimuthally polarized beams. Opt. Lett. 32, 14681470 (2007).
  23. Lai, W. J. et al. Generation of radially polarized beam with a segmented spiral varying retarder. Opt. Express 16, 1569415699 (2008).
  24. Moshe, I., Jackel, S. & Meir, A. Production of radially or azimuthally polarised beams in solid-state lasers and the elimination of thermally induced birefringence effects. Opt. Lett. 28, 807809 (2003).
  25. Yonezawa, Y., Kozawa, Y. & Sato, S. Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal. Opt. Lett. 31, 21512153 (2006).
  26. Kawauchi, H., Kozawa, Y. & Sato, S. Generation of radially polarized Ti:sapphire laser beam using a c-cut crystal. Opt. Lett. 33, 19841986 (2008).
  27. Ito, A., Kozawa, Y. & Sato, S. Selective oscillation of radially and azimuthally polarised laser beam induced by thermal birefringence and lensing. J. Opt. Soc. Am. B 26, 708712 (2009).
  28. Kozawa, Y. & Sato, S. Generation of a radially polarized laser beam by use of a conical Brewster prism. Opt. Lett. 30, 30633065 (2005).
  29. Bisson, J.-F., Li, J., Ueda, K. & Senatsky, Y. Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon. Opt. Express 14, 33043311 (2006).
  30. Chang, K.-C., Lin, T. & Wei, M.-D. Generation of azimuthally and radially polarized off-axis beams with an intracavity large-apex-angle axicon. Opt. Express 21, 1603516042 (2013).
  31. Wei, M.-D., Lai, Y.-S. & Chang, K.-C. Generation of a radially polarized laser beam in a single microchip Nd:YVO4 laser. Opt. Lett. 38, 24432445 (2013).
  32. Vyas, S., Kozawa, Y. & Sato, S. Generation of radially polarized Bessel-Gaussian beams from c-cut Nd:YVO4 laser. Opt. Lett. 39, 11011104 (2014).
  33. Fang, Z., Xia, K., Yao, Y. & Li, J. Radially polarized and passively Q-switched Nd:YAG laser under annular-shaped pumping. IEEE J. Sel. Top. Quant. Elec. 21, 1600406 (2015).
  34. Padgett, M. J. & Courtial, J. Poincaré-sphere equivalent for light beams containing orbital angular momentum. Opt. Lett. 249, 430432 (1999).
  35. Yao, A. M., & Padgett, M. J. Orbital angular momentum origins, behavior and applications. Adv. Opt. Photon. 3, 161204 (2011).
  36. Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nature Photon. 6, 488496 (2012).
  37. Senatsky, Y. et al. Laguerre-Gaussian modes selection in diode-pumped solid-state lasers. Opt. Rev. 19, 201221 (2012).
  38. Lin, D., Daniel, J. M. O. & Clarkson, W. A. Controlling the handedness of directly excited Laguerre-Gaussian modes in a solid-state laser. Opt. Lett. 39, 39033906 (2014).
  39. Kim, D. J. & Kim, J. W. Direct generation of an optical vortex beam in a single-frequency Nd:YVO4 laser. Opt. Lett. 40, 399402 (2015).
  40. Lin, D. & Clarkson, W. A. Polarization-dependent transverse mode selection in an Yb-doped fiber laser. Opt. Lett. 40, 498501 (2015).
  41. Lu, T. & Wu, Y. Observation and analysis of single and multiple high-order Laguerre-Gaussian beams generated from a hemi-cylindrical cavity with general astigmatism. Opt. Express 21, 2849628506 (2013).
  42. Litvin, I. A., Ngcobo, S., Naidoo, D., Ait-Ameur, K. & Forbes, A. Doughnut laser beam as an incoherent superposition of two petal beams. Opt. Lett. 39, 704707 (2014).
  43. Li, H. et al. Orbital angular momentum vertical-cavity surface-emitting lasers. Optica 2, 547552 (2015).
  44. Cai, X. et al. Integrated compact optical vortex beam emitters. Science 338, 363336 (2012).
  45. Hodgson, N. & Weber, H. Laser Resonators and Beam Propagation Ch. 3 (Springer, 2005).
  46. Marucci, L., Manzo, C. & Paparo, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006).
  47. Flamm, D., Naidoo, D., Schulze, C., Forbes, A. & Duparre, M. Mode analysis with a spatial light modulator as a correlation filter. Opt. Lett. 37, 24782480 (2012).
  48. Naidoo, D., Ait-Ameur, K., Brunel, M. & Forbes, A. Intra-cavity generation of superpositions of Laguerre-Gaussian beams. Appl. Phys. B 106, 683690 (2012).
  49. Karimi, E., Zito, G., Piccirillo, B., Marrucci, L. & Santamato, E. Hypergeometric-Gaussian modes. Opt. Lett. 32, 30533055 (2007).
  50. Ngcobo, S., Litvin, I., Burger, L. & Forbes, A. A digital laser for on-demand laser modes. Nature Commun. 4, 2289 (2013).

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Author information

Affiliations

  1. CSIR National Laser Centre, PO Box 395, Pretoria 0001, South Africa

    • Darryl Naidoo,
    • Filippus S. Roux,
    • Angela Dudley &
    • Igor Litvin
  2. School of Physics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

    • Filippus S. Roux,
    • Angela Dudley &
    • Andrew Forbes
  3. Dipartimento di Fisica, Università di Napoli Federico II, Complesso Universitario di Monte Sant'Angelo, via Cintia, 80126 Napoli, Italy

    • Bruno Piccirillo &
    • Lorenzo Marrucci
  4. Consiglio Nazionale delle Ricerche (CNR)-SPIN, Complesso Universitario di Monte Sant'Angelo, via Cintia, 80126 Napoli, Italy

    • Lorenzo Marrucci

Contributions

A.F. conceived the idea and supervised the project; D.N. performed the experiments with assistance from I.L. and A.D.; F.S.R. and I.L. performed the mathematical analysis; D.N. performed the data analysis; B.P. and L.M. manufactured the q-plate and assisted with analysis; A.F. and D.N. wrote the paper with inputs from all co-authors.

Competing financial interests

The authors declare no competing financial interests.

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