Abstract

This study demonstrates a self-referenced interferometric method to estimate the magnitude and sign of a high-order topological charge (TC) carried by incoming optical vortex beams. The proposed method uses a right-angle prism in a Mach–Zehnder interferometer setup with controlled lateral shift and tilt between the wavefronts of interfering beams. The in-line interference with its conjugate results in a petal-shaped fringe pattern, where the number of petals reveals the magnitude of the TC. When the direction of one of the interfering beams is laterally displaced and rotated to emerge at a small angle for off-axis interference such that the vortices overlap at the output plane, then a fork-like interference pattern with better visibility is obtained, which can be used for estimating the magnitude as well as the sign of the TC. Through numerical simulation and optical experiment, it is shown that the technique is capable of estimating the TC of Laguerre–Gaussian beams even with a nonzero radial index.

© 2019 Optical Society of America

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References

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2019 (4)

E. Fedorov, K. Gavril’eva, A. Gorelaya, A. Sevryugin, I. Tursunov, D. Venediktov, and V. Venediktov, “Reference beam lacking measurement of topological charge of incoming vortex beam,” Proc. SPIE 11030, 1103002 (2019).
[Crossref]

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[Crossref]

H. Ma, X. Li, H. Zhang, J. Tang, H. Li, M. Tang, J. Wang, and Y. Cai, “Optical vortex shaping via a phase jump factor,” Opt. Lett. 44, 1379–1382 (2019).
[Crossref]

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[Crossref]

2018 (4)

2017 (3)

2016 (3)

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
[Crossref]

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
[Crossref]

S. N. Alperin, R. D. Niederriter, J. T. Gopinath, and M. E. Siemens, “Quantitative measurement of the orbital angular momentum of light with a single, stationary lens,” Opt. Lett. 41, 5019–5022 (2016).
[Crossref]

2015 (5)

2014 (2)

2013 (2)

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padagett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

2011 (3)

2010 (1)

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

2008 (3)

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Detection of phase singularity using a lateral shear interferometer,” Opt. Lasers Eng. 46, 419–423 (2008).
[Crossref]

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Shearograms of an optical phase singularity,” Opt. Commun. 281, 1315–1322 (2008).
[Crossref]

J. Vickers, M. Burch, R. Vyas, and S. Singh, “Phase and interference properties of optical vortex beams,” J. Opt. Soc. Am. A 25, 823–827 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

2004 (2)

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

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

1996 (1)

1994 (2)

M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, “Laser modes with helical wave fronts,” Phys. Rev. A 49, 3119–3122 (1994).
[Crossref]

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

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. 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]

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]

1991 (1)

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[Crossref]

1990 (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beam with screw dislocations in their wavefronts,” Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

Ahmed, N.

Alfano, R. R.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. 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]

Alperin, S. N.

Ando, T.

Ashrafi, N.

Ashrafi, S.

Banerji, J.

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).
[Crossref]

Bao, C.

Barnett, S.

Barnett, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padagett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

Bazhenov, V. Y.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beam with screw dislocations in their wavefronts,” Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

Beijersbergen, M. W.

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

L. Allen, M. W. Beijersbergen, R. J. 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. C. G.

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[Crossref]

Bernet, S.

Bhattacharya, M.

Boyd, R. W.

G. Kulkarni, R. Sahu, O. S. Magana-Loaiza, R. W. Boyd, and A. Jha, “Single-shot measurement of the orbital-angular-momentum spectrum of light,” Nat. Commun. 8, 1054 (2017).
[Crossref]

Burch, M.

Cai, Y.

Cai, Z.

Cao, Y.

Chaudhary, S.

Chávez-Cerda, S.

S. Cui, B. Xu, S. Luo, H. Xu, Z. Cai, Z. Luo, J. Pu, and S. Chávez-Cerda, “Determining topological charge based on an improved Fizeau interferometer,” Opt. Express 27, 12774–12779 (2019).
[Crossref]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Chen, L.

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
[Crossref]

Chen, M.

B. Lan, C. Liu, D. Rui, M. Chen, F. Shen, and H. Xian, “The topological charge measurement of the vortex beam based on dislocation self-reference interferometry,” Phys. Scripta 94, 055502 (2019).
[Crossref]

Chen, Q.

F. Lv, X. Li, Y. Tai, L. Zhang, Z. Nie, and Q. Chen, “High-order topological charges measurement of LG vortex beams with a modified Mach–Zehnder interferometer,” Optik 126, 4378–4381 (2015).
[Crossref]

Chen, Z.

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 phase plate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Courtial, J.

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

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

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

Cui, S.

Fan, R.

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
[Crossref]

Fang, Z.

Fedorov, E.

E. Fedorov, K. Gavril’eva, A. Gorelaya, A. Sevryugin, I. Tursunov, D. Venediktov, and V. Venediktov, “Reference beam lacking measurement of topological charge of incoming vortex beam,” Proc. SPIE 11030, 1103002 (2019).
[Crossref]

Ferreira, Q. S.

Fonseca, E. J.

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Franke-Arnold, S.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

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

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

Fukuchi, N.

Fürhapter, S.

Gahagan, K. T.

Galvez, E.

Gavril’eva, K.

E. Fedorov, K. Gavril’eva, A. Gorelaya, A. Sevryugin, I. Tursunov, D. Venediktov, and V. Venediktov, “Reference beam lacking measurement of topological charge of incoming vortex beam,” Proc. SPIE 11030, 1103002 (2019).
[Crossref]

Gezhi, Z.

Ghai, D. P.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Detection of phase singularity using a lateral shear interferometer,” Opt. Lasers Eng. 46, 419–423 (2008).
[Crossref]

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Shearograms of an optical phase singularity,” Opt. Commun. 281, 1315–1322 (2008).
[Crossref]

Gibson, G.

Gopinath, J. T.

Gorelaya, A.

E. Fedorov, K. Gavril’eva, A. Gorelaya, A. Sevryugin, I. Tursunov, D. Venediktov, and V. Venediktov, “Reference beam lacking measurement of topological charge of incoming vortex beam,” Proc. SPIE 11030, 1103002 (2019).
[Crossref]

Gou, F.

Guo, B.

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
[Crossref]

Guo, J.

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
[Crossref]

Hara, T.

Harris, M.

M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, “Laser modes with helical wave fronts,” Phys. Rev. A 49, 3119–3122 (1994).
[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]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[Crossref]

Hickmann, J. M.

Q. S. Ferreira, A. J. Jesus-Silva, E. J. Fonseca, and J. M. Hickmann, “Fraunhofer diffraction of light with orbital angular momentum by a slit,” Opt. Lett. 36, 3106–3108 (2011).
[Crossref]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Hill, C.

M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, “Laser modes with helical wave fronts,” Phys. Rev. A 49, 3119–3122 (1994).
[Crossref]

Hu, X.

Huang, H.

Ito, H.

Jesacher, A.

Jesus-Silva, A. J.

Jha, A.

G. Kulkarni, R. Sahu, O. S. Magana-Loaiza, R. W. Boyd, and A. Jha, “Single-shot measurement of the orbital-angular-momentum spectrum of light,” Nat. Commun. 8, 1054 (2017).
[Crossref]

Jha, A. K.

Johansson, P.

Käll, M.

Khajavi, B.

Khare, K.

Kim, D. J.

Kim, J. W.

Kristensen, M.

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

Kulkarni, G.

G. Kulkarni, R. Sahu, O. S. Magana-Loaiza, R. W. Boyd, and A. Jha, “Single-shot measurement of the orbital-angular-momentum spectrum of light,” Nat. Commun. 8, 1054 (2017).
[Crossref]

Lan, B.

B. Lan, C. Liu, D. Rui, M. Chen, F. Shen, and H. Xian, “The topological charge measurement of the vortex beam based on dislocation self-reference interferometry,” Phys. Scripta 94, 055502 (2019).
[Crossref]

Lavery, M. P. J.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padagett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[Crossref]

Leach, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

Lee, Y.

Lehmuskero, A.

Li, H.

Li, J.

Li, L.

Li, P.

Li, X.

H. Ma, X. Li, H. Zhang, J. Tang, H. Li, M. Tang, J. Wang, and Y. Cai, “Optical vortex shaping via a phase jump factor,” Opt. Lett. 44, 1379–1382 (2019).
[Crossref]

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42, 135–138 (2017).
[Crossref]

F. Lv, X. Li, Y. Tai, L. Zhang, Z. Nie, and Q. Chen, “High-order topological charges measurement of LG vortex beams with a modified Mach–Zehnder interferometer,” Optik 126, 4378–4381 (2015).
[Crossref]

X. Li, Y. Tai, F. Lv, and Z. Nie, “Measuring the fractional topological charge of LG beams by using interference intensity analysis,” Opt. Commun. 334, 235–239 (2015).
[Crossref]

Li, Y.

Liu, C.

B. Lan, C. Liu, D. Rui, M. Chen, F. Shen, and H. Xian, “The topological charge measurement of the vortex beam based on dislocation self-reference interferometry,” Phys. Scripta 94, 055502 (2019).
[Crossref]

Liu, G.

Liu, S.

Liu, Z.

Luo, S.

Luo, Z.

Lv, F.

X. Li, Y. Tai, F. Lv, and Z. Nie, “Measuring the fractional topological charge of LG beams by using interference intensity analysis,” Opt. Commun. 334, 235–239 (2015).
[Crossref]

F. Lv, X. Li, Y. Tai, L. Zhang, Z. Nie, and Q. Chen, “High-order topological charges measurement of LG vortex beams with a modified Mach–Zehnder interferometer,” Optik 126, 4378–4381 (2015).
[Crossref]

Ma, H.

Magana-Loaiza, O. S.

G. Kulkarni, R. Sahu, O. S. Magana-Loaiza, R. W. Boyd, and A. Jha, “Single-shot measurement of the orbital-angular-momentum spectrum of light,” Nat. Commun. 8, 1054 (2017).
[Crossref]

Massari, M.

Matsumoto, N.

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]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[Crossref]

Molisch, A. F.

Nie, Z.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42, 135–138 (2017).
[Crossref]

F. Lv, X. Li, Y. Tai, L. Zhang, Z. Nie, and Q. Chen, “High-order topological charges measurement of LG vortex beams with a modified Mach–Zehnder interferometer,” Optik 126, 4378–4381 (2015).
[Crossref]

X. Li, Y. Tai, F. Lv, and Z. Nie, “Measuring the fractional topological charge of LG beams by using interference intensity analysis,” Opt. Commun. 334, 235–239 (2015).
[Crossref]

Niederriter, R. D.

Ohtake, Y.

Padagett, M. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padagett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

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A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
[Crossref]

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

Pan, S.

Pas’ko, V. P.

Pei, C.

Pu, J.

Ramachandran, S.

Ren, Y.

Ritsch-Marte, M.

Romanato, F.

Rubinsztein-Dunlop, H.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[Crossref]

Ruffato, G.

Rui, D.

B. Lan, C. Liu, D. Rui, M. Chen, F. Shen, and H. Xian, “The topological charge measurement of the vortex beam based on dislocation self-reference interferometry,” Phys. Scripta 94, 055502 (2019).
[Crossref]

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R. Sahu, S. Chaudhary, K. Khare, M. Bhattacharya, H. Wanare, and A. K. Jha, “Angular lens,” Opt. Express 26, 8709–8718 (2018).
[Crossref]

G. Kulkarni, R. Sahu, O. S. Magana-Loaiza, R. W. Boyd, and A. Jha, “Single-shot measurement of the orbital-angular-momentum spectrum of light,” Nat. Commun. 8, 1054 (2017).
[Crossref]

Sasaki, O.

Senthilkumaran, P.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Detection of phase singularity using a lateral shear interferometer,” Opt. Lasers Eng. 46, 419–423 (2008).
[Crossref]

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Shearograms of an optical phase singularity,” Opt. Commun. 281, 1315–1322 (2008).
[Crossref]

Sevryugin, A.

E. Fedorov, K. Gavril’eva, A. Gorelaya, A. Sevryugin, I. Tursunov, D. Venediktov, and V. Venediktov, “Reference beam lacking measurement of topological charge of incoming vortex beam,” Proc. SPIE 11030, 1103002 (2019).
[Crossref]

Shen, F.

B. Lan, C. Liu, D. Rui, M. Chen, F. Shen, and H. Xian, “The topological charge measurement of the vortex beam based on dislocation self-reference interferometry,” Phys. Scripta 94, 055502 (2019).
[Crossref]

Siemens, M. E.

Singh, R. P.

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).
[Crossref]

Singh, S.

Sirohi, R. S.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Detection of phase singularity using a lateral shear interferometer,” Opt. Lasers Eng. 46, 419–423 (2008).
[Crossref]

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Shearograms of an optical phase singularity,” Opt. Commun. 281, 1315–1322 (2008).
[Crossref]

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[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]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[Crossref]

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

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V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beam with screw dislocations in their wavefronts,” Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

Speirits, F. C.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padagett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

Spreeuw, R. J.

L. Allen, M. W. Beijersbergen, R. J. 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]

Swartzlander, G. A.

Sztul, H. I.

Tai, Y.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42, 135–138 (2017).
[Crossref]

F. Lv, X. Li, Y. Tai, L. Zhang, Z. Nie, and Q. Chen, “High-order topological charges measurement of LG vortex beams with a modified Mach–Zehnder interferometer,” Optik 126, 4378–4381 (2015).
[Crossref]

X. Li, Y. Tai, F. Lv, and Z. Nie, “Measuring the fractional topological charge of LG beams by using interference intensity analysis,” Opt. Commun. 334, 235–239 (2015).
[Crossref]

Tamm, C.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[Crossref]

Tang, J.

Tang, M.

Tapster, P.

M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, “Laser modes with helical wave fronts,” Phys. Rev. A 49, 3119–3122 (1994).
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Tu, C.

Tur, M.

Tursunov, I.

E. Fedorov, K. Gavril’eva, A. Gorelaya, A. Sevryugin, I. Tursunov, D. Venediktov, and V. Venediktov, “Reference beam lacking measurement of topological charge of incoming vortex beam,” Proc. SPIE 11030, 1103002 (2019).
[Crossref]

Vaity, P.

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).
[Crossref]

Vasnetsov, M.

Vasnetsov, M. V.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beam with screw dislocations in their wavefronts,” Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

Vaughan, J. M.

M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, “Laser modes with helical wave fronts,” Phys. Rev. A 49, 3119–3122 (1994).
[Crossref]

Venediktov, D.

E. Fedorov, K. Gavril’eva, A. Gorelaya, A. Sevryugin, I. Tursunov, D. Venediktov, and V. Venediktov, “Reference beam lacking measurement of topological charge of incoming vortex beam,” Proc. SPIE 11030, 1103002 (2019).
[Crossref]

Venediktov, V.

E. Fedorov, K. Gavril’eva, A. Gorelaya, A. Sevryugin, I. Tursunov, D. Venediktov, and V. Venediktov, “Reference beam lacking measurement of topological charge of incoming vortex beam,” Proc. SPIE 11030, 1103002 (2019).
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Voelz, D. G.

D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial (SPIE, 2011), p. TT89.

Vyas, R.

Vyas, S.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Detection of phase singularity using a lateral shear interferometer,” Opt. Lasers Eng. 46, 419–423 (2008).
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Wanare, H.

Wang, D.

Wang, H.

Wang, J.

Wang, K.

Wang, Y.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42, 135–138 (2017).
[Crossref]

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
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Wei, J.

Weiss, C. O.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[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]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[Crossref]

Willner, A. E.

Woerdman, J. P.

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

L. Allen, M. W. Beijersbergen, R. J. 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).
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Wu, D.

Wu, S.

Xia, K.

Xia, Y.

Xian, H.

B. Lan, C. Liu, D. Rui, M. Chen, F. Shen, and H. Xian, “The topological charge measurement of the vortex beam based on dislocation self-reference interferometry,” Phys. Scripta 94, 055502 (2019).
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Xu, H.

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Yao, Y.

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Zhang, L.

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
[Crossref]

F. Lv, X. Li, Y. Tai, L. Zhang, Z. Nie, and Q. Chen, “High-order topological charges measurement of LG vortex beams with a modified Mach–Zehnder interferometer,” Optik 126, 4378–4381 (2015).
[Crossref]

Zhang, P.

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
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Zhang, W.

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
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J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
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Zhou, J.

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
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Adv. Opt. Photon. (2)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
[Crossref]

Chin. Opt. Lett. (1)

J. Mod. Opt. (1)

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and C. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[Crossref]

J. Opt. (1)

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[Crossref]

J. Opt. Soc. Am. A (1)

Nat. Commun. (1)

G. Kulkarni, R. Sahu, O. S. Magana-Loaiza, R. W. Boyd, and A. Jha, “Single-shot measurement of the orbital-angular-momentum spectrum of light,” Nat. Commun. 8, 1054 (2017).
[Crossref]

Opt. Commun. (3)

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Shearograms of an optical phase singularity,” Opt. Commun. 281, 1315–1322 (2008).
[Crossref]

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

X. Li, Y. Tai, F. Lv, and Z. Nie, “Measuring the fractional topological charge of LG beams by using interference intensity analysis,” Opt. Commun. 334, 235–239 (2015).
[Crossref]

Opt. Eng. (1)

J. Guo, B. Guo, R. Fan, W. Zhang, Y. Wang, L. Zhang, and P. Zhang, “Measuring topological charges of Laguerre–Gaussian vortex beams using two improved Mach–Zehnder interferometers,” Opt. Eng. 55, 035104 (2016).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (1)

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Detection of phase singularity using a lateral shear interferometer,” Opt. Lasers Eng. 46, 419–423 (2008).
[Crossref]

Opt. Lett. (13)

B. Khajavi and E. Galvez, “Determining topological charge of an optical beam using a wedged optical flat,” Opt. Lett. 42, 1516–1519 (2017).
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H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42, 135–138 (2017).
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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]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral interferometry,” Opt. Lett. 30, 1953–1955 (2005).
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K. T. Gahagan and G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
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H. Ma, X. Li, H. Zhang, J. Tang, H. Li, M. Tang, J. Wang, and Y. Cai, “Optical vortex shaping via a phase jump factor,” Opt. Lett. 44, 1379–1382 (2019).
[Crossref]

Q. S. Ferreira, A. J. Jesus-Silva, E. J. Fonseca, and J. M. Hickmann, “Fraunhofer diffraction of light with orbital angular momentum by a slit,” Opt. Lett. 36, 3106–3108 (2011).
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H. I. Sztul and R. R. Alfano, “Double-slit interference with Laguerre–Gaussian beams,” Opt. Lett. 31, 999–1001 (2006).
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G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre–Gaussian modes by means of spiral phase plates,” Opt. Lett. 39, 5094–5097 (2014).
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Y. Ohtake, T. Ando, N. Fukuchi, N. Matsumoto, H. Ito, and T. Hara, “Universal generation of higher-order multi-ringed Laguerre–Gaussian beams by using a spatial light modulator,” Opt. Lett. 32, 1411–1413 (2007).
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Optik (1)

F. Lv, X. Li, Y. Tai, L. Zhang, Z. Nie, and Q. Chen, “High-order topological charges measurement of LG vortex beams with a modified Mach–Zehnder interferometer,” Optik 126, 4378–4381 (2015).
[Crossref]

OSA Continuum (1)

Phys. Lett. A (1)

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).
[Crossref]

Phys. Rev. A (2)

M. Harris, C. Hill, P. Tapster, and J. M. Vaughan, “Laser modes with helical wave fronts,” Phys. Rev. A 49, 3119–3122 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. 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).
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Phys. Rev. Lett. (3)

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Figures (7)

Fig. 1.
Fig. 1. Schematic of the proposed method. L, laser; BE, beam expander; SLM, reflective spatial light modulator; BS1, BS2, and BS3, nonpolarizing beam splitters; M1 and M2, reflecting mirrors; RAP, right-angle prism; CMOS, camera.
Fig. 2.
Fig. 2. In-line interference patterns of a vortex beam with its conjugate copy using the proposed interferometer. Column (i) denotes the intensity distribution of fringes recorded by a camera for input beams with TC=1, 3, 6, and 10, and are presented in rows (a), (b), (c), and (d), respectively. Column (ii) shows the simulation results corresponding to column (i). Similarly, the column (iii) presents the experimental results of interference fringes when beams with TC=1, 3, 6, and 10 each presented in rows (a), (b), (c), and (d), respectively. Column (iv) shows the corresponding simulation results.
Fig. 3.
Fig. 3. In-line interference of a high-order vortex beam with its conjugate. Column (i) denotes the intensity distribution of obtained fringes, for input vortex beams with TC=50, and 130 presented in rows (a) and (b), respectively. Column (ii) shows the corresponding simulation results. Row (c) presents the enlarged images of selected region of figures of row (d) for better visualization.
Fig. 4.
Fig. 4. In-line interference of the LG vortex beam with its conjugate. Column (i) denotes the intensity distribution of fringes recorded by a camera for incoming LG beams with indices l=20, p=1 and l=20, p=2 presented in rows (a) and (b), respectively. Column (ii) shows the corresponding simulation results.
Fig. 5.
Fig. 5. Interference patterns of vortex beams with their displaced and tilted conjugate copies. Column (i) denotes the intensity distribution of fringes registered by the camera for incoming vortex beams with TC=1, 3, 6, and 10 presented in rows (a), (b), (c), and (d), respectively. Column (ii) shows the corresponding simulation results. Similarly, the column (iii) presents the experimental results of interference fringes for vortex beams with TC=1, 3, 6, and 10, each presented in rows (a), (b), (c), and (d), respectively. Column (iv) contains simulated results.
Fig. 6.
Fig. 6. Interference patterns of high-order vortex beams with its displaced and tilted conjugate copies. (i) Intensity profile of fringe patterns resulting from a beam with (a) TC=25 and (b) TC=50 obtained through the experiment, and column (ii) shows the corresponding simulation results.
Fig. 7.
Fig. 7. Interference patterns of LG beams carrying TC=6 with their displaced and tilted conjugate copies using the proposed interferometer. Column (i) denotes obtained intensity distribution of fringes for incoming beams with radial indices p=1, 2, 3, and 4, presented in rows (a), (b), (c), and (d), respectively, and column (ii) shows the corresponding simulation results.

Equations (6)

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E1(x,y)=exp(ilϕ)·sign[Lp|l|(2r2wo2)],
E1c(x,y+Δy)=exp(ilϕ(x,y+Δy))·sign[Lp|l|(2r(x,y+Δy)2wo2)].
T(x,y)=exp(i2πλytan(θ)),
E2(x,y+Δy)=E1c(x,y+Δy)T(x,y+Δy).
E1z(x,y)=exp(ikz)iλzE1(xo,yo)exp(ik2z((xxo)2+(yyo)2))dxodyo,E2z(x,y)=exp(ikz)iλzE2(xo,yo)exp(ik2z((xxo)2+(yyo)2))dxodyo,
I(x,y)=|E1z(x,y)+E2z(x,y+Δy)exp(iδ)|2,