Abstract

Optical vortex beams can be used as carriers of information in optical communication and quantum optics applications. Owing to their spatial orthogonality, these beams can be multiplexed and demultiplexed, but up until now this was primarily achieved by bulky and large devices. In this work, a new approach is used to fabricate miniature vortex mode sorters based on three-dimensional laser printing, thereby enabling direct integration into optical systems. Mode sorters that are composed of two separate elements as well as a single integrated device are presented. These devices can handle both pure and mixed vortex beams with topological charge |l|3 and |l|2 for the dual-element device and integrated system, respectively. Mode-sorter spectral bandwidth and surface-quality effects are also discussed.

© 2017 Optical Society of America

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References

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2017 (2)

2016 (1)

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).
[Crossref]

2015 (3)

A. Selimis, V. Mironov, and M. Farsari, “Direct laser writing: principles and materials for scaffold 3D printing,” Microelectron. Eng. 132, 83–89 (2015).
[Crossref]

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

S. Lightman, R. Gvishi, G. Hurvitz, and A. Arie, “Shaping of light beams by 3D direct laser writing on facets of nonlinear crystals,” Opt. Lett. 40, 4460–4463 (2015).
[Crossref]

2014 (1)

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

2013 (3)

A. Shapira, A. Libster, Y. Lilach, and A. Arie, “Functional facets for nonlinear crystals,” Opt. Commun. 300, 244–248 (2013).
[Crossref]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

A. Zukauskas, M. Malinauskas, and E. Brasselet, “Monolithic generators of pseudo-nondiffracting optical vortex beams at the microscale,” Appl. Phys. Lett. 103, 181122 (2013).
[Crossref]

2012 (2)

2010 (4)

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18, 2144–2151 (2010).
[Crossref]

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

2008 (2)

2004 (1)

2003 (2)

O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21, 61–68 (2003).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

1994 (1)

1992 (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]

1987 (1)

W. J. Hossack, A. M. Darling, and A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[Crossref]

Abdul-Malik, R. S.

Ahmed, N.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Alfano, R. R.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[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]

Angelis, F. D.

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

Arie, A.

S. Lightman, R. Gvishi, G. Hurvitz, and A. Arie, “Shaping of light beams by 3D direct laser writing on facets of nonlinear crystals,” Opt. Lett. 40, 4460–4463 (2015).
[Crossref]

A. Shapira, A. Libster, Y. Lilach, and A. Arie, “Functional facets for nonlinear crystals,” Opt. Commun. 300, 244–248 (2013).
[Crossref]

Bao, C.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Barnett, S. M.

Beijersbergen, M.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Beijersbergen, M. W.

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]

Berkhout, G.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Berkhout, G. C. G.

Boyd, R. W.

Brasselet, E.

A. Zukauskas, M. Malinauskas, and E. Brasselet, “Monolithic generators of pseudo-nondiffracting optical vortex beams at the microscale,” Appl. Phys. Lett. 103, 181122 (2013).
[Crossref]

Candeloro, P.

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

Cao, Y.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Chamorro-Posada, P.

J. García-Escartín and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 062320 (2008).
[Crossref]

Chujo, K.

Close, L. M.

Cojoc, G.

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

Courtial, J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20, 2110–2115 (2012).
[Crossref]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

Dahdouh, A.

W. J. Hossack, A. M. Darling, and A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[Crossref]

Darling, A. M.

W. J. Hossack, A. M. Darling, and A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[Crossref]

Das, G.

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

Dholakia, K.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

Dultz, W.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

Einfeldt, S.

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

Fabrizio, E. D.

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

Farsari, M.

A. Selimis, V. Mironov, and M. Farsari, “Direct laser writing: principles and materials for scaffold 3D printing,” Microelectron. Eng. 132, 83–89 (2015).
[Crossref]

Ford, E. L.

Franke-Arnold, S.

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

García-Escartín, J.

J. García-Escartín and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 062320 (2008).
[Crossref]

Gentile, F.

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

Gibson, G.

Giessen, H.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).
[Crossref]

Gissibl, T.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).
[Crossref]

Gvishi, R.

Hamazaki, J.

Hell, S. W.

Herkommer, A.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).
[Crossref]

Hoffmann, V.

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

Holzlohner, R.

Hossack, W. J.

W. J. Hossack, A. M. Darling, and A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[Crossref]

Huang, H.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Hurvitz, G.

Knauer, A.

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

Kneissl, M.

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

Kobayashi, Y.

Kruger, O.

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

Lavery, M.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Lavery, M. P. J.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20, 2110–2115 (2012).
[Crossref]

Li, L.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Li, M. J.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Liberale, C.

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

Libster, A.

A. Shapira, A. Libster, Y. Lilach, and A. Arie, “Functional facets for nonlinear crystals,” Opt. Commun. 300, 244–248 (2013).
[Crossref]

Lightman, S.

Lilach, Y.

A. Shapira, A. Libster, Y. Lilach, and A. Arie, “Functional facets for nonlinear crystals,” Opt. Commun. 300, 244–248 (2013).
[Crossref]

Look, J.

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

Love, G. D.

Malik, M.

Malinauskas, M.

A. Zukauskas, M. Malinauskas, and E. Brasselet, “Monolithic generators of pseudo-nondiffracting optical vortex beams at the microscale,” Appl. Phys. Lett. 103, 181122 (2013).
[Crossref]

Massari, M.

McGloin, D.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

Menyuk, C. R.

Milione, G.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Mirhosseini, M.

Mironov, V.

A. Selimis, V. Mironov, and M. Farsari, “Direct laser writing: principles and materials for scaffold 3D printing,” Microelectron. Eng. 132, 83–89 (2015).
[Crossref]

Molisch, A. F.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Morita, R.

Nguyen, T. A.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Nolan, D. A.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

O’Sullivan, M. N.

Omatsu, T.

Padgett, M.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

Padgett, M. J.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20, 2110–2115 (2012).
[Crossref]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

Palacios, D. M.

Parisi, G.

Pas’ko, V.

Peters, M. A.

Ren, Y.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Robertson, D. J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20, 2110–2115 (2012).
[Crossref]

Romanato, F.

Ruffato, G.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Schmitzer, H.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

Selimis, A.

A. Selimis, V. Mironov, and M. Farsari, “Direct laser writing: principles and materials for scaffold 3D printing,” Microelectron. Eng. 132, 83–89 (2015).
[Crossref]

Shapira, A.

A. Shapira, A. Libster, Y. Lilach, and A. Arie, “Functional facets for nonlinear crystals,” Opt. Commun. 300, 244–248 (2013).
[Crossref]

Sinkin, O. V.

Sponselli, A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[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]

Steinhoff, N. K.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

Sutherland, R. L.

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).

Swartzlander, G. A.

Tanda, S.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Thiele, S.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).
[Crossref]

Tur, M.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Tyler, G. A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

Vasnetsov, M.

Vogt, P.

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

Weyers, M.

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

Wichmann, J.

Willner, A. E.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

Wilson, D. W.

Woerdman, J. P.

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]

Xie, G.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Yan, Y.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Zhao, Z.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Zukauskas, A.

A. Zukauskas, M. Malinauskas, and E. Brasselet, “Monolithic generators of pseudo-nondiffracting optical vortex beams at the microscale,” Appl. Phys. Lett. 103, 181122 (2013).
[Crossref]

Zweck, J.

Appl. Phys. Lett. (1)

A. Zukauskas, M. Malinauskas, and E. Brasselet, “Monolithic generators of pseudo-nondiffracting optical vortex beams at the microscale,” Appl. Phys. Lett. 103, 181122 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (1)

J. Look, S. Einfeldt, O. Kruger, V. Hoffmann, A. Knauer, M. Weyers, P. Vogt, and M. Kneissl, “Laser scribing for facet fabrication of InGaN MQW diode lasers on sapphire substrates,” IEEE Photon. Technol. Lett. 22, 416–418 (2010).
[Crossref]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

W. J. Hossack, A. M. Darling, and A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[Crossref]

Microelectron. Eng. (2)

A. Selimis, V. Mironov, and M. Farsari, “Direct laser writing: principles and materials for scaffold 3D printing,” Microelectron. Eng. 132, 83–89 (2015).
[Crossref]

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. D. Angelis, and E. D. Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010).
[Crossref]

Nat. Commun. (1)

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Nat. Photonics (1)

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).
[Crossref]

New J. Phys. (1)

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

Opt. Commun. (1)

A. Shapira, A. Libster, Y. Lilach, and A. Arie, “Functional facets for nonlinear crystals,” Opt. Commun. 300, 244–248 (2013).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. A (2)

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]

J. García-Escartín and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 062320 (2008).
[Crossref]

Phys. Rev. Lett. (2)

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Sci. Rep. (1)

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M. J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref]

Other (2)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).

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Figures (8)

Fig. 1.
Fig. 1.

Top: Theoretical (de)multiplexer designs of the (a) transforming and (b) correcting elements. Bottom: (c, d) SEM images of the above-fabricated elements. Scale bars are 25 μm.

Fig. 2.
Fig. 2.

Schematic design of the optical setup for testing the vortex multiplexer.

Fig. 3.
Fig. 3.

Top row: incoming vortex beams towards the mode sorter. Center row: simulated beams at detector. Bottom row: measured beams at detector. The dotted horizontal lines mark the location of the =0 beam. Upper and lower scale bars correspond to the incoming and focused demultiplexed beams, respectively.

Fig. 4.
Fig. 4.

Left column: interference of various states before entering the mode sorter. Middle column: simulated spots at detector. Right column: measurements. The bottom =0 row is for reference.

Fig. 5.
Fig. 5.

Wavelength dependency measurements of incoming =±1 interference beam. (a) Simulated and measured beams at the detector plane, when varying the beam’s wavelength from 690 to 990 nm. Left and right scale bars correspond to the incoming beam and focused demultiplexed beams, respectively. (b) Line-scans of the measured spots at various wavelengths. (c) Peak-to-peak distances of measured and calculated values between the OAM states at different wavelengths.

Fig. 6.
Fig. 6.

SEM pictures of side (top row) and top (center row) views of three printing methods, which resulted in estimated surface roughness of (a) 450, (b) 250, and (c) 50 nm. Bottom row: Simulated =2 vortex beams at the detector plane for the three samples. The dotted horizontal lines mark the location for the =2 beam. Scale bars are 10 μm.

Fig. 7.
Fig. 7.

SEM picture of a combined mode sorter. The transformer and corrector elements are integrated on a glass substrate. The relatively massive poles are needed for accurate alignment.

Fig. 8.
Fig. 8.

Top row: Input beams. Center row: simulated output beams. Bottom row: measured output beams. The dotted horizontal lines mark the location of the =0 beam. Upper and lower scale bars correspond to the incoming and focused demultiplexed beams, respectively.

Equations (6)

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

u=aln(x2+y2/b),
v=a×tan1(y/x).
Z1(x,y)=af(nmnair)[yarctan(y/x)xln(x2+y2b)+x12a(x2+y2)],
Z2(x,y)=abf(nmnair)[exp(u/a)×cos(v/a)12ab(u2+v2)],
Δx=×(fλd).
h(x,y)=φ(x,y)×λ2π(nmnair).

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