Abstract

q-plates are quasi-optical devices specifically designed to generate and detect the orbital angular momentum states of the light. It is possible to produce q-plates working at millimeter wavelengths by using a well-known and cheap manufacturing technique. The technique consists of creating inhomogeneous, artificial birefringent materials by machining grooves with specific geometries into normal dielectric materials. In this work, a q-plate working around 100 GHz has been designed, manufactured, and tested using a vector network analyzer. The experimental data validate the modeled intensity and phase for the transformation of an incident Gaussian beam.

© 2013 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef]
  2. S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
    [CrossRef]
  3. F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
    [CrossRef]
  4. M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597, 1266–1270 (2003).
    [CrossRef]
  5. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  6. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef]
  7. B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
    [CrossRef]
  8. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef]
  9. A. Yariv and P. Yeh, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. Am. 67, 438–755 (1977).
    [CrossRef]
  10. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [CrossRef]
  11. Eccosorb by Emerson and Cuming Microwave Products. http://www.eccosorb.eu .

2011 (1)

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[CrossRef]

2010 (1)

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

2007 (1)

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

2003 (1)

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597, 1266–1270 (2003).
[CrossRef]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

1983 (1)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

1977 (1)

A. Yariv and P. Yeh, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. Am. 67, 438–755 (1977).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Barbieri, C.

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Bergman, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Bergman, J. E. S.

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

Carozzi, T. D.

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Daldorff, L. K. S.

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

Flanders, D. C.

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Forozesh, K.

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

Harwit, M.

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597, 1266–1270 (2003).
[CrossRef]

Heckenberg, N. R.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

Ibragimov, N. H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Isham, B.

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

Istomin, Ya. N.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Karlsson, R.

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

Khamitova, R.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Mari, E.

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[CrossRef]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

Mohammadi, S. M.

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

Palmer, K.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Romanato, F.

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[CrossRef]

Sjöholm, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Tamburini, F.

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[CrossRef]

Then, H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

Thidé, B.

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[CrossRef]

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

White, A. G.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. Am. 67, 438–755 (1977).
[CrossRef]

Yeh, P.

A. Yariv and P. Yeh, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. Am. 67, 438–755 (1977).
[CrossRef]

Appl. Phys. Lett. (2)

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[CrossRef]

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Astrophys. J. (1)

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597, 1266–1270 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

A. Yariv and P. Yeh, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. Am. 67, 438–755 (1977).
[CrossRef]

Opt. Commun. (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Opt. Lett. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Phys. Rev. Lett. (2)

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Radio Sci. (1)

S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, “Orbital angular momentum in radio: measurement methods,” Radio Sci. 45, 1–14 (2010).
[CrossRef]

Other (1)

Eccosorb by Emerson and Cuming Microwave Products. http://www.eccosorb.eu .

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Figures (10)

Fig. 1.
Fig. 1.

Illustration of the birefringent grating structure. Zones with two different refractive indexes, n1 usually being equal to 1 (air), alternate with a ratio and a periodicity that determine the effective refractive indexes experienced by the two components of an incident electromagnetic wave parallel and perpendicular, respectively to the grating grooves.

Fig. 2.
Fig. 2.

Nylon q-plate prototype. The concentric 0.5 mm wide grooves giving the inhomogeneous birefringence are visible.

Fig. 3.
Fig. 3.

Beam profile HFSS simulations: the FG beam taken as a reference is compared with the same beam going through the q-plate positioned at 3, 5, and 10 cm from the horn antenna aperture.

Fig. 4.
Fig. 4.

Section of the prototype q-plate along the diameter. The grooves total depth required to make the slab of nylon birefringent was reached digging half of the depth on both sides of a central matched thickness.

Fig. 5.
Fig. 5.

Polarization of the radiation at the different stages of the experimental setup. The q-plate acts as an HWP thus rotating the circular polarization obtained with the QWR from right handed to left handed or vice versa.

Fig. 6.
Fig. 6.

Experimental set-up for far field beam pattern measurements. The source horn and the q-plate rotate together around a center located on the beamwaist of the beam at the horn aperture making possible to scan the wavefront at a certain distance with the receiver horn.

Fig. 7.
Fig. 7.

Beam intensity profile of both the FG beam produced by the source horn and the OAM beam generated by inserting the q-plate a few centimeters after the source horn are reported. Both beam patterns were measured having the two horns emitting and receiving radiation with same circular polarization [7(a)] or opposite circular polarization [7(b)] in order to confirm the q-plate is acting as an HWP.

Fig. 8.
Fig. 8.

Far-field intensity pattern of the q-plate output beam at different angles on the transverse plane obtained with the experimental setup represented in Fig. 6. For simplicity only the cuts at 0, 45, 90, and 135 deg are reported but data were taken every 5 deg and all the cuts are consistent.

Fig. 9.
Fig. 9.

Model (dashed curves) and experimental data (solid curves) of the original Gaussian beam and the beam after passing through the q-plate placed at 10 cm from the source.

Fig. 10.
Fig. 10.

Measured E field real part (c) and relative phase-shift (d) induced by the q-plate at different points on the central part of its surface. In (a) and (b) the theoretical expected ones are reported. Asymmetries in the data are possibly due to misalignments between the horns and the limited precision of the xy moving system.

Tables (1)

Tables Icon

Table 1. Nylon q-plate Prototype Parameters Calculated According to the Formulas in the Paper by Dale C. Flanders [10] and Optimized with Finite-Element Analysis HFSS

Equations (2)

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

M=[sin(2φ)cos(2φ)cos(2φ)sin(2φ)],
Eout=M·Ein=E0[sin(2φ)cos(2φ)cos(2φ)sin(2φ)]·[1i]=E0[sin(2φ)+icos(2φ)cos(2φ)+isin(2φ)]=E0[iei2φei2φ]=E0ei2φeiπ2[1i].

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