Abstract

A Mach-Zehnder interferometer (MZI) that includes in an arm either a reflective image inverter or a Gouy phase shifter (RGPS) can (de)multiplex many types of modes of a few mode fiber without fundamental loss. The use of RGPSs in combination with binary phase plates for multiplexing purposes is studied for the first time, showing that the particular RGPS that shifts π the odd modes only multiplexes accurately low order modes. To overcome such a restriction, we present a new exact refractive image inverter, more compact and flexible than its reflective counterpart. Moreover, we show that these interferometers remove or reduce the crosstalk that the binary phase plates could introduce between the multiplexed modes. Finally, an experimental analysis of a MZI with both an approximated and an exact refractive image inverter is presented for the case of a bimodal multiplexing. Likewise, it is proven experimentally that a RGPS that shifts π/2 demultiplexes two odd modes which can not be achieved by any image inverter.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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2017 (1)

2016 (1)

Y. Weng, E. Ip, Z. Pan, and T. Wang, “Advanced spatial-division multiplexed measurement systems propositions—from telecommunication to sensing applications: A review,” Sensors 16, 1387 (2016).
[Crossref]

2015 (3)

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

K. Igarashi, D. Souma, K. Takeshima, and T. Tsuritani, “Selective mode multiplexer based on phase plates and Mach-Zehnder interferometer with image inversion function,” Opt. Express 23, 183–194 (2015).
[Crossref] [PubMed]

R. Brüning, Y. Zhang, M. McLaren, M. Duparré, and A. Forbes, “Overlap relation between free-space Laguerre Gaussian modes and step-index fiber modes,” J. Opt. Soc. Am. A 32, 1678–1682 (2015).
[Crossref]

2014 (1)

2013 (3)

2012 (1)

2003 (1)

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

2000 (1)

A. Belafhal and L. Dalil-Essakali, “Collins formula and propagation of Bessel-modulated Gaussian light beams through an ABCD optical system,” Opt. Commun. 177, 181–188 (2000).
[Crossref]

1994 (1)

1993 (2)

I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron. 29, 2562–2567 (1993).
[Crossref]

M. Beijersbergen, L. Allen, H. van der Veen, and J. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

1991 (1)

J. Liñares and C. Gómez-Reino, “Diffraction-limited coupling efficiency between SMF connected by GRIN fibre lens,” J. Mod. Opt 38, 597–604 (1991).
[Crossref]

Ahmed, N.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Alfano, R. R.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Allen, L.

M. Beijersbergen, L. Allen, H. van der Veen, and J. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

Bai, N.

Barnett, S. M.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Beijersbergen, M.

M. Beijersbergen, L. Allen, H. van der Veen, and J. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

Belafhal, A.

A. Belafhal and L. Dalil-Essakali, “Collins formula and propagation of Bessel-modulated Gaussian light beams through an ABCD optical system,” Opt. Commun. 177, 181–188 (2000).
[Crossref]

Bickham, S.

Boffi, P.

P. Boffi, P. Martelli, A. Gatto, and M. Martinelli, “Mode-division multiplexing in fibre-optic communications based on orbital angular momentum,” Journal of Optics 15, 075403 (2013).
[Crossref]

Brüning, R.

Cao, Y.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Casperson, L. W.

Chung, K. M.

Courtial, J.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Crespo, J.

Dalil-Essakali, L.

A. Belafhal and L. Dalil-Essakali, “Collins formula and propagation of Bessel-modulated Gaussian light beams through an ABCD optical system,” Opt. Commun. 177, 181–188 (2000).
[Crossref]

Duparré, M.

Elias, L. R.

I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron. 29, 2562–2567 (1993).
[Crossref]

Forbes, A.

Franke-Arnold, S.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Gatto, A.

P. Boffi, P. Martelli, A. Gatto, and M. Martinelli, “Mode-division multiplexing in fibre-optic communications based on orbital angular momentum,” Journal of Optics 15, 075403 (2013).
[Crossref]

Gómez-Reino, C.

J. Liñares and C. Gómez-Reino, “Diffraction-limited coupling efficiency between SMF connected by GRIN fibre lens,” J. Mod. Opt 38, 597–604 (1991).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005), 3rd ed.

Huang, H.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Huang, Y.-K.

Igarashi, K.

K. Igarashi, D. Souma, K. Takeshima, and T. Tsuritani, “Selective mode multiplexer based on phase plates and Mach-Zehnder interferometer with image inversion function,” Opt. Express 23, 183–194 (2015).
[Crossref] [PubMed]

D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Ip, E.

Kawaguchi, Y.

D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Kimel, I.

I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron. 29, 2562–2567 (1993).
[Crossref]

Lau, A. P. T.

Lavery, M. P. J.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Leach, J.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Li, G.

Li, M.-J.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. P. T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20, 2668–2680 (2012).
[Crossref] [PubMed]

Liñares, J.

Lu, C.

Luo, Y.

Martelli, P.

P. Boffi, P. Martelli, A. Gatto, and M. Martinelli, “Mode-division multiplexing in fibre-optic communications based on orbital angular momentum,” Journal of Optics 15, 075403 (2013).
[Crossref]

Martinelli, M.

P. Boffi, P. Martelli, A. Gatto, and M. Martinelli, “Mode-division multiplexing in fibre-optic communications based on orbital angular momentum,” Journal of Optics 15, 075403 (2013).
[Crossref]

Mateo, E.

Mateo, E. F.

C. Montero-Orille, V. Moreno, X. Prieto-Blanco, E. F. Mateo, E. Ip, J. Crespo, and J. Liñares, “Ion-exchanged glass binary phase plates for mode-division multiplexing,” Appl. Opt. 52, 2332–2339 (2013).
[Crossref] [PubMed]

J. Liñares, X. Prieto-Blanco, C. Montero, V. Moreno, E. F. Mateo, M. D. Mouriz, and M. C. Nistal, “Mode-division multiplexing by Mach-Zehnder interferometers with graded-index elements,” in “Proceedings of IX Optoelectronics Spanish Meeting,” (Salamanca, 2015), pp. PO–SII–07.

McLaren, M.

Milione, G.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Montero, C.

N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. P. T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20, 2668–2680 (2012).
[Crossref] [PubMed]

J. Liñares, X. Prieto-Blanco, C. Montero, V. Moreno, E. F. Mateo, M. D. Mouriz, and M. C. Nistal, “Mode-division multiplexing by Mach-Zehnder interferometers with graded-index elements,” in “Proceedings of IX Optoelectronics Spanish Meeting,” (Salamanca, 2015), pp. PO–SII–07.

Montero-Orille, C.

Moreno, V.

Morita, I.

D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Mouriz, M. D.

J. Liñares, X. Prieto-Blanco, C. Montero, V. Moreno, E. F. Mateo, M. D. Mouriz, and M. C. Nistal, “Mode-division multiplexing by Mach-Zehnder interferometers with graded-index elements,” in “Proceedings of IX Optoelectronics Spanish Meeting,” (Salamanca, 2015), pp. PO–SII–07.

Nguyen, T. An

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Nistal, M. C.

J. Liñares, X. Prieto-Blanco, C. Montero, V. Moreno, E. F. Mateo, M. D. Mouriz, and M. C. Nistal, “Mode-division multiplexing by Mach-Zehnder interferometers with graded-index elements,” in “Proceedings of IX Optoelectronics Spanish Meeting,” (Salamanca, 2015), pp. PO–SII–07.

Nolan, D. A.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Padgett, M. J.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Pan, Z.

Y. Weng, E. Ip, Z. Pan, and T. Wang, “Advanced spatial-division multiplexed measurement systems propositions—from telecommunication to sensing applications: A review,” Sensors 16, 1387 (2016).
[Crossref]

Peng, G.-D.

Prieto, X.

Prieto-Blanco, X.

J. Liñares, X. Prieto-Blanco, C. Montero-Orille, and V. Moreno, “Spatial mode multiplexing/demultiplexing by Gouy phase interferometry,” Opt. Lett. 42, 93–96 (2017).
[Crossref] [PubMed]

C. Montero-Orille, V. Moreno, X. Prieto-Blanco, E. F. Mateo, E. Ip, J. Crespo, and J. Liñares, “Ion-exchanged glass binary phase plates for mode-division multiplexing,” Appl. Opt. 52, 2332–2339 (2013).
[Crossref] [PubMed]

J. Liñares, X. Prieto-Blanco, C. Montero, V. Moreno, E. F. Mateo, M. D. Mouriz, and M. C. Nistal, “Mode-division multiplexing by Mach-Zehnder interferometers with graded-index elements,” in “Proceedings of IX Optoelectronics Spanish Meeting,” (Salamanca, 2015), pp. PO–SII–07.

Ren, Y.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Ryf, R.

Soma, D.

D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Souma, D.

Suzuki, M.

D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Takeshima, K.

K. Igarashi, D. Souma, K. Takeshima, and T. Tsuritani, “Selective mode multiplexer based on phase plates and Mach-Zehnder interferometer with image inversion function,” Opt. Express 23, 183–194 (2015).
[Crossref] [PubMed]

D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Tam, H.-Y.

Ten, S.

Tovar, A. A.

Tse, V.

Tsuritani, T.

K. Igarashi, D. Souma, K. Takeshima, and T. Tsuritani, “Selective mode multiplexer based on phase plates and Mach-Zehnder interferometer with image inversion function,” Opt. Express 23, 183–194 (2015).
[Crossref] [PubMed]

D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Tur, M.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

van der Veen, H.

M. Beijersbergen, L. Allen, H. van der Veen, and J. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

von Hoyningen-Huene, J.

Wakayama, Y.

D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Wang, T.

Wei, H.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Weng, Y.

Y. Weng, E. Ip, Z. Pan, and T. Wang, “Advanced spatial-division multiplexed measurement systems propositions—from telecommunication to sensing applications: A review,” Sensors 16, 1387 (2016).
[Crossref]

Willner, A. E.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

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Woerdman, J.

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[Crossref]

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H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Xue, X.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Yaman, F.

Yao, E.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

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D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

Zhang, Y.

Zhao, N.

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P. Boffi, P. Martelli, A. Gatto, and M. Martinelli, “Mode-division multiplexing in fibre-optic communications based on orbital angular momentum,” Journal of Optics 15, 075403 (2013).
[Crossref]

Opt. Commun. (3)

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

M. Beijersbergen, L. Allen, H. van der Veen, and J. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

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[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Sci. Rep. (1)

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An 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] [PubMed]

Sensors (1)

Y. Weng, E. Ip, Z. Pan, and T. Wang, “Advanced spatial-division multiplexed measurement systems propositions—from telecommunication to sensing applications: A review,” Sensors 16, 1387 (2016).
[Crossref]

Other (3)

J. Liñares, X. Prieto-Blanco, C. Montero, V. Moreno, E. F. Mateo, M. D. Mouriz, and M. C. Nistal, “Mode-division multiplexing by Mach-Zehnder interferometers with graded-index elements,” in “Proceedings of IX Optoelectronics Spanish Meeting,” (Salamanca, 2015), pp. PO–SII–07.

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D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in “2015 European Conference on Optical Communication (ECOC),” (2015), pp. 1–3.

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Figures (7)

Fig. 1
Fig. 1 MZI for implementing relative Gouy phases and multiplexing.
Fig. 2
Fig. 2 Protocol of nine space mode multiplexing.
Fig. 3
Fig. 3 Sketch of the refractive image inverter and ray-tracing.
Fig. 4
Fig. 4 Sketch of the MZI with refractive inverter L0L1L2.
Fig. 5
Fig. 5 Photography of the MZI used in the experiment.
Fig. 6
Fig. 6 Images of the modes at outputs v (left) and h (right) for a RIIS (top and middle) and a RGPS G(∼ π) (bottom).
Fig. 7
Fig. 7 Images of the outputs v (left) and h (right) for a G(π/2) RGPS.

Tables (1)

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Table 1 Optical power values at h and v outputs of the MZI.

Equations (22)

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ϒ m n i ( ρ ) = K i ( ρ , ρ 0 ) ϒ m n ( ρ 0 ) d ρ 0 ,
K i ( ρ , ρ 0 ) = i k 0 2 π B i exp { i k 0 2 B i [ D i ( x 2 + y 2 ) + A i ( x 0 2 + y 0 2 ) 2 x x 0 2 y y 0 ] } ,
ϒ m n i ( x , y ) = C m n i w i H m ( x 2 w i ) H n ( y 2 w i ) exp ( x 2 + y 2 w i 2 ) exp ( i k 0 x 2 + y 2 2 R i ) exp ( i ϕ m n i ) ,
w i 2 = w o i 2 z R i 2 ( z R i 2 A i 2 + B i 2 ) , 1 R i = w o i 2 w i 2 [ A i C i + B i D i z R i 2 ] ,
ϕ m n i = ( m + n + 1 ) arctan ( B i z R i A i ) ,
Ψ ν μ ( c , s ) ( x , y ) = ( j even , j odd ) ν + μ i ( j , j 1 ) 2 C ν μ , j ϒ μ + ν j , j ( x , y ) ,
Φ m n = ( m + n + 1 ) 2 arctan [ ( z R 2 z R 1 ) d z R 2 z R 1 + d 2 ] .
Φ m n = ( m + n + 1 ) Δ ϕ with Δ ϕ = 2 arcsin ( d / f ) .
Φ m n ( m + n + 1 ) ( π ) with = 4 z R 1 / d .
Φ q = ( q + 1 2 ) Δ ϕ ,
M = ( cos α 1 a sin α a sin α cos α ) ,
M = ( 1 2 d / f 2 d ( 2 / f ) ( 1 d / f ) 1 2 d / f ) .
a = 2 ( f / d 1 ) 1 / 2 / f , cos α = 1 2 d / f .
sin 2 ( g 0 l / 2 ) = sin ( Δ ϕ / 2 ) .
Ψ 11 ϒ 20 + ϒ 02 ; Ψ 22 ϒ 40 + 2 ϒ 22 + ϒ 04 ,
3 Δ ϕ θ = ( 2 s 1 + 1 ) π ; 7 Δ ϕ θ = 2 s 2 π ,
Ψ e ( ρ ) = K ( ρ , ρ 0 ) Ψ 0 ( ρ 0 ) d ρ 0
( A 1 B 1 C 1 D 1 ) = ( 1 d e 0 1 ) ( A ˜ 1 B ˜ 1 C ˜ 1 D ˜ 1 ) ( 1 d 0 0 1 ) ,
lim Δ 0 1 π Δ exp [ ( x + x 0 ) 2 + ( y + y 0 ) 2 Δ ] = δ ( x + x 0 , y + y 0 ) ,
( A 1 B 1 C 1 D 1 ) = ( 1 2 f d 0 d e 0 1 ) .
K ( 1 ) ( ρ , ρ 0 ) = i k 0 2 π d exp [ i k 0 2 d ( ρ + ρ 0 ) 2 ]
K ( 2 ) ( ρ , ρ 0 ) = i k 0 2 π d exp [ i k 0 2 d ( ρ ρ 0 ) 2 ]

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