Abstract

We study the propagation of orbital angular momentum (OAM) modes in rectangular multimode waveguides. Due to the multimode interference effect, an OAM mode input forms self-images at certain propagation distances. As OAM modes can be decomposed as the superposition of a pair of quarter-wave phase-shifted even and odd modes, their symmetry properties lead to two different self-imaging categories – forming the OAM-maintaining and the field-splitting self-images. We analyze these phenomena using multimode interference theory, and establish the rules governing the OAM-maintaining self-imaging, which allows the multi-mode interference waveguides to be used as OAM mode splitters and couplers.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  4. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
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  6. Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  17. P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2014 (1)

2013 (3)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

2012 (3)

Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, M. Watanabe, and J. Sakaguchi, “Space division multiplexed transmission of 109-Tb/s data signals using homogeneous,” J. Lightwave Technol. 30(4), 658–665 (2012).
[Crossref]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

2011 (1)

P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011).
[Crossref]

2006 (1)

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

2005 (1)

H. Chen and D. T. K. Tong, “Two dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
[Crossref]

2004 (2)

D. Khalil and A. Yehia, “Two-dimensional multimode interference in integrated optical structures,” J. Opt. A 6(1), 137–145 (2004).
[Crossref]

A. Yehia, K. Madkour, H. Maaty, and D. Khalil, “Multiple-imaging in 2-D MMI silicon hollow waveguides,” IEEE Photon. Technol. Lett. 16(9), 2072–2074 (2004).
[Crossref]

2003 (1)

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(25), 257901 (2002).
[Crossref] [PubMed]

1995 (2)

M. Bachmann, P. A. Besse, and H. Melchior, “Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting,” Appl. Opt. 34(30), 6898–6910 (1995).
[Crossref] [PubMed]

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Ahmed, N.

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Alhassen, F.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Ao, X.

Awaji, Y.

Bachmann, M.

Barnett, S. M.

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(25), 257901 (2002).
[Crossref] [PubMed]

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Besse, P. A.

Boffi, P.

P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011).
[Crossref]

Boyd, R. W.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Chen, H.

H. Chen and D. T. K. Tong, “Two dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
[Crossref]

Coolbaugh, D.

Courtial, J.

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(25), 257901 (2002).
[Crossref] [PubMed]

Dashti, P. Z.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Dolinar, S.

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Fazal, I. M.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Franke-Arnold, S.

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(25), 257901 (2002).
[Crossref] [PubMed]

Gatto, A.

P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011).
[Crossref]

Hayashi, T.

He, S.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Kanno, A.

Kawanishi, T.

Khalil, D.

D. Khalil and A. Yehia, “Two-dimensional multimode interference in integrated optical structures,” J. Opt. A 6(1), 137–145 (2004).
[Crossref]

A. Yehia, K. Madkour, H. Maaty, and D. Khalil, “Multiple-imaging in 2-D MMI silicon hollow waveguides,” IEEE Photon. Technol. Lett. 16(9), 2072–2074 (2004).
[Crossref]

Kobayashi, T.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Leach, J.

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(25), 257901 (2002).
[Crossref] [PubMed]

Leake, G.

Lee, H. P.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Maaty, H.

A. Yehia, K. Madkour, H. Maaty, and D. Khalil, “Multiple-imaging in 2-D MMI silicon hollow waveguides,” IEEE Photon. Technol. Lett. 16(9), 2072–2074 (2004).
[Crossref]

Madkour, K.

A. Yehia, K. Madkour, H. Maaty, and D. Khalil, “Multiple-imaging in 2-D MMI silicon hollow waveguides,” IEEE Photon. Technol. Lett. 16(9), 2072–2074 (2004).
[Crossref]

Malik, M.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

Martelli, P.

P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011).
[Crossref]

Martinelli, M.

P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011).
[Crossref]

Melchior, H.

Mirhosseini, M.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

Moresco, M.

O’Brien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Padgett, M. J.

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(25), 257901 (2002).
[Crossref] [PubMed]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Romanov, V.

Sakaguchi, J.

Shi, Z.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Sun, J.

Taru, T.

Thompson, M. G.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Tong, D. T. K.

H. Chen and D. T. K. Tong, “Two dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
[Crossref]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wada, N.

Wang, J.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Watanabe, M.

Watts, M. R.

Willner, A. E.

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Yan, Y.

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, J.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yehia, A.

D. Khalil and A. Yehia, “Two-dimensional multimode interference in integrated optical structures,” J. Opt. A 6(1), 137–145 (2004).
[Crossref]

A. Yehia, K. Madkour, H. Maaty, and D. Khalil, “Multiple-imaging in 2-D MMI silicon hollow waveguides,” IEEE Photon. Technol. Lett. 16(9), 2072–2074 (2004).
[Crossref]

Yu, S.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. E. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum,” Opt. Lett. 38(19), 3930–3933 (2013).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Zhu, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Appl. Opt. (3)

Electron. Lett. (1)

P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (2)

A. Yehia, K. Madkour, H. Maaty, and D. Khalil, “Multiple-imaging in 2-D MMI silicon hollow waveguides,” IEEE Photon. Technol. Lett. 16(9), 2072–2074 (2004).
[Crossref]

H. Chen and D. T. K. Tong, “Two dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
[Crossref]

J. Lightwave Technol. (2)

Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, M. Watanabe, and J. Sakaguchi, “Space division multiplexed transmission of 109-Tb/s data signals using homogeneous,” J. Lightwave Technol. 30(4), 658–665 (2012).
[Crossref]

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

J. Opt. A (1)

D. Khalil and A. Yehia, “Two-dimensional multimode interference in integrated optical structures,” J. Opt. A 6(1), 137–145 (2004).
[Crossref]

Nat. Commun. (1)

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Opt. Lett. (2)

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

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(25), 257901 (2002).
[Crossref] [PubMed]

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Science (2)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Other (1)

OptiBPM, http://optiwave.com/category/products/component-design/optibpm/

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Figures (7)

Fig. 1
Fig. 1 Schematic of central inputs into a square cross-section MMI waveguide. (a) Gaussian mode input forming single image at propagation lengths of 3Lc/4 and 3Lc/2. (b) Decomposition of λ = 1 OAM mode into odd and even modes, each of them symmetric in one direction and anti-symmetric in the other. (c) Decomposition of λ = 2 OAM mode into odd and even modes, the odd mode is anti-symmetric in both directions and the even mode is symmetric in both directions. Both λ = 1 and λ = 2 central OAM mode inputs exhibit field-splitting at 3Lc/4 and OAM-maintaining image at 3Lc/2.
Fig. 2
Fig. 2 The amplitude and phase distributions with a central OAM input with λ = 1 in rectangular MMI waveguide. (a) z = 0, (b) z = 3Lcy/2 = 3Lcx/10.
Fig. 3
Fig. 3 The amplitude and phase distributions at various z-position with a central OAM input with λ = 1 in square MMI waveguide. (a)Z = 0, (b)Z = 1/12, (c)Z = 1/8, (d)Z = 1/6, (e)Z = 1/4, (f)Z = 1/3, (g)Z = 3/8, (h)Z = 1/2.
Fig. 4
Fig. 4 The amplitude and phase distributions at 3Lc/4, with a central OAM input with (a) λ = 1, (b) λ = 2, (c) λ = 3, (d) λ = 4 in square MMI waveguide.
Fig. 5
Fig. 5 The amplitude and phase distributions for an OAM input with λ = 1 in square MMI waveguide. The input locates at position of (W/6, W/6). (a) z = 0, (b) z = 3Lc/2.
Fig. 6
Fig. 6 Interferences between Gaussian mode and OAM mode with different orders in a square MMI waveguide. (a) the input pattern of Gaussian mode at the lower left and OAM mode at the upper right. The other three are interference intensity patterns at z = 3Lc/2 for (b) λ = 3, (c) λ = 2, and (d) λ = 1.
Fig. 7
Fig. 7 The amplitude and phase distributions of OAM distortion and synthesis. (a) Input of OAM mode with l = 1 at (-W/6,0), (b) Output pattern at 3Lc/2, (c) Input of two diagonal odd and even modes with a π/2 phase shift at (-W/6,0) and (W/6,0), (d) Output pattern of an λ = −1 OAM mode at (-W/6,0).

Tables (1)

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Table 1 self-image analysis of OAM modes

Equations (22)

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ψ(x,L)= 1 C p=0 N1 [ψ(x x p ,0)exp(j Φ p )] ,
x p =(2pN) M N W,
Φ p =p(Np) M N π.
ψ(x, 3 L c 2K )= 1 C p=0 K1 [ψ(x x p+K ,0)( exp(j Φ p+K )±exp(j Φ p ) )] .
ψ(x, 3 L c 2K )= 2 C p=0 K1 [f(x x p )exp(j φ p )] ,
x Sp = x Ap = x p ={ p K W, for 0p[K/2] p K WW, for [K/2]+1pK1 ,
φ Sp ={ ( K 2 p 2 2K +a 1 4 )π, for 0p[K/2] ( K 2 p 2 2K +a 1 4 +1 )π, for [K/2]+1pK1 ,
φ Ap =( K 2 p 2 2K a 1 4 )π.
s={ p+[K/2] 0p[K/2] p[K/2]1 [K/2]+1pK1 .
x ' Ap =x ' Sp + W K .
W x W y = N x N y = 2K 2J .
ψ(x,y,L)= 1 C x C y p=0 K1 q=0 J1 f X (x x p ) f Y (y y q )exp[ j( φ p + θ q ) ],
f OAM (x,y)= f o (x,y)±i f e (x,y)= f o (x,y)± e jπ/2 f e (x,y),
f 1 (x,y)= f S (x) f A (y)± e jπ/2 f A (x) f S (y).
f 2 (x,y)= f A (x) f A (y)± e jπ/2 f S (x) f S (y).
ψ(x,y,L)= 1 C x C y p=0 K1 q=0 J1 { f S (x x Sp ) f A (y y Aq )exp[ j( φ Sp + θ Aq ) ] ± e jπ/2 f A (x x Ap ) f S (y y Sq )exp[ j( φ Ap + θ Sq ) ]},
ψ(x,y,L)= 1 C x C y p=0 K1 q=0 J1 { f A (x x Ap ) f A (y y Aq )exp[ j( φ Ap + θ Aq ) ] ± e jπ/2 f S (x x Sp ) f S (y y Sq )exp[ j( φ Sp + θ Sq ) ]}.
( φ Ap + θ Sq )( φ Sp + θ Aq )=( φ Ap φ Sp )+( θ Sq θ Aq ) ={ a 2 π, 0p[K/2] ( a 2 1 )π, [K/2]+1pK1 +{ b 2 π, 0q[J/2] ( b 2 +1 )π, [J/2]+1qJ1 ,
( φ Sp + θ Sq )( φ Ap + θ Aq )=( φ Sp φ Ap )+( θ Sq θ Aq ) ={ a 2 π, 0p[K/2] ( a 2 +1 )π, [K/2]+1pK1 +{ b 2 π, 0q[J/2] ( b 2 +1 )π, [J/2]+1qJ1 .
f A 1/3 (x, 3 L c 2 )= 1 C [ f A 1/3 (x)exp(j π 2 )+ f A 1/3 (Wx)],
f S 1/3 (x, 3 L c 2 )= 1 C [ f S 1/3 (x)exp(j π 2 )+ f S 1/3 (Wx)exp(jπ)].
( φ A 1/3 + θ S 1/2 )( φ S 1/3 + θ A 1/2 )=( φ A 1/3 φ S 1/3 )+( θ S 1/2 θ A 1/2 )={ 0 π + π/2={ π/2 left π/2 right ,

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