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

Journal name:
Nature Photonics
Year published:
Published online


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


  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.


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Author information


  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


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.

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