Abstract

Wavefront characterization for orbital angular momentum (OAM) modes is demonstrated using quadrature phase-shift interference. The phase fronts and intensity profiles of OAM2, OAM4, OAM6, and OAM8 are measured. Wavefront correlations between the experimental results and the pure Laguerre–Gaussian modes are calculated to evaluate the measurement. The measured results are in reasonable agreement with the anticipated results based on simulations.

© 2013 Optical Society of America

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References

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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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A. Lizana, A. Marquez, L. Lobato, Y. Rodange, I. Moreno, C. Iemmi, and J. Campos, Opt. Express 18, 10581 (2010).
[CrossRef]

T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, J. Opt Soc. Am. A 27, 2602 (2010).
[CrossRef]

2009 (1)

2007 (1)

2004 (3)

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[CrossRef]

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M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
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Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

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M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

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Barnett, S.

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H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

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M. Padgett and R. Bowman, Nat. Photonics 5, 343 (2011).
[CrossRef]

Bozovich, A.

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Campos, J.

Choi, J.

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

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M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

Courtial, J.

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K. Creath, in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), 26, 357–373.

Dändliker, R.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dändliker, Opt. Commun. 242, 163 (2004).
[CrossRef]

Dholakia, K.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Erkmen, B.

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Franke-Arnold, S.

Gavel, D. T.

Gibson, G.

Herzig, H. P.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dändliker, Opt. Commun. 242, 163 (2004).
[CrossRef]

Huang, H.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Iemmi, C.

Ina, H.

Inoue, T.

T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, J. Opt Soc. Am. A 27, 2602 (2010).
[CrossRef]

Ivanovskyy, A. A.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dändliker, Opt. Commun. 242, 163 (2004).
[CrossRef]

Izmailov, I. V.

Joenathan, C.

Kanev, F. Yu.

Kobayashi, S.

Kochemasov, G. G.

Koltygin, M. O.

Kulikov, S. M.

Lizana, A.

Lobato, L.

Löffler, W.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Manachinsky, A. N.

Marquez, A.

Maslov, N. V.

Matsumoto, N.

T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, J. Opt Soc. Am. A 27, 2602 (2010).
[CrossRef]

Moreno, I.

Ogorodnikov, A. V.

Ohtake, Y.

T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, J. Opt Soc. Am. A 27, 2602 (2010).
[CrossRef]

Olivier, S. S.

Padgett, M.

Pas’ko, V.

Ren, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Ricci, F.

Rockstuhl, C.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dändliker, Opt. Commun. 242, 163 (2004).
[CrossRef]

Rodange, Y.

Salt, M. G.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dändliker, Opt. Commun. 242, 163 (2004).
[CrossRef]

Silva, D. A.

Soldatenkov, I. S.

Soskin, M. S.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dändliker, Opt. Commun. 242, 163 (2004).
[CrossRef]

Stappaerts, E. A.

Starikov, F. A.

Sukharev, S. A.

Takeda, M.

Takiguchi, Y.

T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, J. Opt Soc. Am. A 27, 2602 (2010).
[CrossRef]

Tucker, J. W.

Tur, M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

van Exter, M. P.

Vasnetsov, M.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Wang, J.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Wilks, S. C.

Willner, A.

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Willner, A. E.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yan, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yang, J.-Y.

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Yao, A.

Young, P. E.

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

J. Opt Soc. Am. A (1)

T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, J. Opt Soc. Am. A 27, 2602 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

Nat. Photonics (2)

M. Padgett and R. Bowman, Nat. Photonics 5, 343 (2011).
[CrossRef]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Opt. Commun. (2)

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dändliker, Opt. Commun. 242, 163 (2004).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Other (2)

H. Huang, Y. Ren, N. Ahmed, Y. Yan, Y. Yue, A. Bozovich, J.-Y. Yang, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, M. Tur, and A. Willner, in CLEO: 2011-Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CF3C.4.

K. Creath, in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), 26, 357–373.

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Figures (5)

Fig. 1.
Fig. 1.

Principle of OAM beam phase reconstruction based on the quadrature phase-shift interference.

Fig. 2.
Fig. 2.

Experiment setup. SLM, spatial light modulator; BS, beam splitter; HWP, half-wave plane; Col., collimator; LCR, liquid crystal retarder; CL, convex lens; MR, mirror. A forked phase hologram for generating OAM4 is inserted.

Fig. 3.
Fig. 3.

Measured intensity profiles (a) OAM-4 beam. (b) Reference beam. (c) and (d) Fringe patterns without and with a π/2 phase shift.

Fig. 4.
Fig. 4.

Measured and simulated wavefronts of generated OAM beams. (a1)–(a4) Measured intensity profiles of OAM2, OAM4, OAM6, and OAM8. (b1)–(b4) Measured phase profiles of OAM2, OAM4, OAM6, and OAM8. (c1)–(c4) Simulated phase profiles.

Fig. 5.
Fig. 5.

Wavefront correlation between the generated OAM modes and the theoretical LG modes as functions of azimuthal index.

Equations (3)

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

|A+B|2=|A|2+|B|2+2|A||B|cos(ΦAΦB),
|A+Bexp(jπ/2)|2=|A|2+|B|2+2|A||B|sin(ΦAΦB).
ΦA=ΦB+arctan[|A+Bexp(jπ/2)|2|A|2|B|2|A+B|2|A|2|B|2],

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