Abstract

We experimentally demonstrate an adaptive-optics-based approach that allows selective excitation of waveguide modes and their mixtures in a two-mode fiber (TMF). A phase-only spatial light modulator is used for wavefront control, using feedback signals provided by the correlation between the experimentally measured field distribution and the desired mode profiles. Experimental results show the optical field within the TMF can be shaped to be pure linearly polarized (LP) modes or their combinations. Analysis shows selective mode excitation can be achieved using only 5 × 5 independent phase blocks. With proper feedback signals, this method should enable one to precisely control the optical field within any multimode fiber or other types of waveguides in real time.

© 2014 Optical Society of America

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  1. P. J. Winzer, “Optical networking beyond WDM,” IEEE Photonics J. 4(2), 647–651 (2012).
    [Crossref]
  2. R.-J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013).
    [Crossref]
  3. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
    [Crossref]
  4. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
    [Crossref] [PubMed]
  5. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
    [Crossref]
  6. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s COOFDM signal over a two-mode fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’11) (2011), PDPB8.
  7. R. Ryf, N. K. Fontaine, and R.-J. Essiambre, “Spot-based mode coupler for mode-multiplexed transmission in few mode fiber,” in Proc. IEEE Summer Topical (2012), TuC3.2.
    [Crossref]
  8. H. Bulow, H. Al Hashimi, and B. Schmauss, “Spatial-mode multiplexers and MIMO processing,” in Proc. Opto-Electronics and Communication Conference (OECC 2012) (2012), 5E4–1.
    [Crossref]
  9. S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: A study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010).
    [Crossref] [PubMed]
  10. N. K. Fontaine, R. Ryf, S. G. Leon-Saval, and J. Bland-Hawthorn, “Evaluation of photonic lanterns for lossless mode-multiplexing,” in Proc. European Conference on Optical Communication (ECOC’12) (2012), Th.2.D.6.
    [Crossref]
  11. R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, A. H. Gnauck, S. Chandrasekhar, X. Liu, B. Guan, R.-J. Essiambre, P. J. Winzer, S. Leon-Saval, J. Bland-Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R. V. Jensen, and R. Lingle, “12 x 12 MIMO transmission over 130-km few-mode fiber,” in Proc. Frontiers in Optics Conference (FiO’12) (2012), FW6C.4.
    [Crossref]
  12. S. Berdagué and P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt. 21(11), 1950–1955 (1982).
    [Crossref] [PubMed]
  13. 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. Man 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(3), 2668–2680 (2012).
    [Crossref] [PubMed]
  14. D. Sperti, M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, A. Boutin, P. Sillard, and G. Charlet, “Experimental investigation of modal crosstalk using LCOS-based spatial light modulator for mode conversion,” in Proc. European Conference on Optical Communications 2011 (ECOC 2011) (2011), Th.12.B.2.
    [Crossref]
  15. J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49(9), 095801 (2010).
    [Crossref]
  16. J. Carpenter and T. D. Wilkinson, “All-optical mode multiplexing using holography and multimode fiber couplers,” J. Lightwave Technol. 30(12), 1978–1984 (2012).
    [Crossref]
  17. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012).
    [Crossref]
  18. J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013).
    [Crossref] [PubMed]
  19. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007).
    [Crossref] [PubMed]
  20. I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
    [Crossref]
  21. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
    [Crossref] [PubMed]
  22. M. Cui, “Parallel wavefront optimization method for focusing light through random scattering media,” Opt. Lett. 36(6), 870–872 (2011).
    [Crossref] [PubMed]
  23. R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19(1), 247–254 (2011).
    [Crossref] [PubMed]
  24. D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012).
    [Crossref] [PubMed]
  25. R. N. Mahalati, D. Askarov, J. P. Wilde, and J. M. Kahn, “Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling,” Opt. Express 20(13), 14321–14337 (2012).
    [Crossref] [PubMed]
  26. C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20(14), 15086–15092 (2012).
    [Crossref] [PubMed]
  27. A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013).
    [Crossref] [PubMed]
  28. I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35(8), 1245–1247 (2010).
    [Crossref] [PubMed]
  29. G. Ghielmetti and C. M. Aegerter, “Scattered light fluorescence microscopy in three dimensions,” Opt. Express 20(4), 3744–3752 (2012).
    [Crossref] [PubMed]
  30. T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nat. Commun. 3, 1027 (2012).
    [Crossref]
  31. R. N. Mahalati, R. Y. Gu, and J. M. Kahn, “Resolution limits for imaging through multi-mode fiber,” Opt. Express 21(2), 1656–1668 (2013).
    [Crossref] [PubMed]
  32. T. Čižmár and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19(20), 18871–18884 (2011).
    [Crossref] [PubMed]

2013 (5)

R.-J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013).
[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

R. N. Mahalati, R. Y. Gu, and J. M. Kahn, “Resolution limits for imaging through multi-mode fiber,” Opt. Express 21(2), 1656–1668 (2013).
[Crossref] [PubMed]

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013).
[Crossref] [PubMed]

J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013).
[Crossref] [PubMed]

2012 (9)

P. J. Winzer, “Optical networking beyond WDM,” IEEE Photonics J. 4(2), 647–651 (2012).
[Crossref]

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref]

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012).
[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. Man 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(3), 2668–2680 (2012).
[Crossref] [PubMed]

G. Ghielmetti and C. M. Aegerter, “Scattered light fluorescence microscopy in three dimensions,” Opt. Express 20(4), 3744–3752 (2012).
[Crossref] [PubMed]

R. N. Mahalati, D. Askarov, J. P. Wilde, and J. M. Kahn, “Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling,” Opt. Express 20(13), 14321–14337 (2012).
[Crossref] [PubMed]

C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20(14), 15086–15092 (2012).
[Crossref] [PubMed]

J. Carpenter and T. D. Wilkinson, “All-optical mode multiplexing using holography and multimode fiber couplers,” J. Lightwave Technol. 30(12), 1978–1984 (2012).
[Crossref]

J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012).
[Crossref]

2011 (3)

2010 (5)

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: A study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010).
[Crossref] [PubMed]

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35(8), 1245–1247 (2010).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49(9), 095801 (2010).
[Crossref]

2008 (1)

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
[Crossref]

2007 (1)

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

1982 (1)

Aegerter, C. M.

Argyros, A.

Askarov, D.

Bai, N.

Berdagué, S.

Bianchi, S.

Bickham, S.

Bifano, T.

Bland-Hawthorn, J.

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

Caravaca-Aguirre, A. M.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

Carpenter, J.

Cižmár, T.

Conkey, D. B.

Cui, M.

Dholakia, K.

Di Leonardo, R.

Essiambre, R.-J.

R.-J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013).
[Crossref]

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

Facq, P.

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

Fontaine, N. K.

R.-J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013).
[Crossref]

Foschini, G. J.

Ghielmetti, G.

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

Goebel, B.

Gu, R. Y.

Hoffman, S.

Huang, Y.-K.

Ip, E.

Kahn, J. M.

Kramer, G.

Lau, A. P. T.

Leon-Saval, S. G.

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

Li, G.

Li, M.-J.

Liñares, J.

Lu, C.

Lu, Y.

Luo, Y.

Mahalati, R. N.

Man Chung, K.

Mateo, E.

Mitra, P. P.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Montero, C.

Moore, J.

Moreno, V.

Mosk, A. P.

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
[Crossref]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007).
[Crossref] [PubMed]

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Niv, E.

Paxman, R.

Peng, G.-D.

Piestun, R.

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

Prieto, X.

Randel, S.

R.-J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013).
[Crossref]

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Ryf, R.

R.-J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013).
[Crossref]

J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013).
[Crossref] [PubMed]

Stark, J. B.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Stockbridge, C.

Tam, H.-Y.

Ten, S.

Thomsen, B. C.

Toussaint, K.

Tse, V.

Vellekoop, I. M.

von Hoyningen-Huene, J.

Wang, T.

Wilde, J. P.

Wilkinson, T. D.

Winzer, P.

Winzer, P. J.

Yaman, F.

Appl. Opt. (1)

IEEE Photonics J. (2)

P. J. Winzer, “Optical networking beyond WDM,” IEEE Photonics J. 4(2), 647–651 (2012).
[Crossref]

R.-J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013).
[Crossref]

J. Lightwave Technol. (3)

Nat. Commun. (1)

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref]

Nat. Photonics (1)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Nature (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref] [PubMed]

Opt. Commun. (1)

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
[Crossref]

Opt. Eng. (1)

J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49(9), 095801 (2010).
[Crossref]

Opt. Express (11)

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19(1), 247–254 (2011).
[Crossref] [PubMed]

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012).
[Crossref] [PubMed]

R. N. Mahalati, D. Askarov, J. P. Wilde, and J. M. Kahn, “Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling,” Opt. Express 20(13), 14321–14337 (2012).
[Crossref] [PubMed]

C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20(14), 15086–15092 (2012).
[Crossref] [PubMed]

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013).
[Crossref] [PubMed]

R. N. Mahalati, R. Y. Gu, and J. M. Kahn, “Resolution limits for imaging through multi-mode fiber,” Opt. Express 21(2), 1656–1668 (2013).
[Crossref] [PubMed]

T. Čižmár and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19(20), 18871–18884 (2011).
[Crossref] [PubMed]

G. Ghielmetti and C. M. Aegerter, “Scattered light fluorescence microscopy in three dimensions,” Opt. Express 20(4), 3744–3752 (2012).
[Crossref] [PubMed]

J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013).
[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. Man 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(3), 2668–2680 (2012).
[Crossref] [PubMed]

S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: A study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

Other (6)

N. K. Fontaine, R. Ryf, S. G. Leon-Saval, and J. Bland-Hawthorn, “Evaluation of photonic lanterns for lossless mode-multiplexing,” in Proc. European Conference on Optical Communication (ECOC’12) (2012), Th.2.D.6.
[Crossref]

R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, A. H. Gnauck, S. Chandrasekhar, X. Liu, B. Guan, R.-J. Essiambre, P. J. Winzer, S. Leon-Saval, J. Bland-Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R. V. Jensen, and R. Lingle, “12 x 12 MIMO transmission over 130-km few-mode fiber,” in Proc. Frontiers in Optics Conference (FiO’12) (2012), FW6C.4.
[Crossref]

D. Sperti, M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, A. Boutin, P. Sillard, and G. Charlet, “Experimental investigation of modal crosstalk using LCOS-based spatial light modulator for mode conversion,” in Proc. European Conference on Optical Communications 2011 (ECOC 2011) (2011), Th.12.B.2.
[Crossref]

A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s COOFDM signal over a two-mode fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’11) (2011), PDPB8.

R. Ryf, N. K. Fontaine, and R.-J. Essiambre, “Spot-based mode coupler for mode-multiplexed transmission in few mode fiber,” in Proc. IEEE Summer Topical (2012), TuC3.2.
[Crossref]

H. Bulow, H. Al Hashimi, and B. Schmauss, “Spatial-mode multiplexers and MIMO processing,” in Proc. Opto-Electronics and Communication Conference (OECC 2012) (2012), 5E4–1.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 (a) Principle of AO-based mode control. (b) Schematic of the setup: λ/2, half-wave plate; Expander, 1:5 beam expander comprise of two lenses; M, mirror; SLM, phase-only spatial light modulator; P1, P2 and P3, polarizers; L1, 20 × objective lens, NA = 0.40; Fiber, Thorlabs 980HP, ~1.5m; L2, 100 × objective lens, NA = 0.70; CCD, CCD camera. (c) Optimization sequence of SLM blocks (N = 13).

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Fig. 2
Fig. 2 Selective excitation of the LP01 mode. Images in (a) are the initial field distributions. Results in (b) are the images captured after the optimization process. Figures with the same sequence number belong to the same optimization process; (c) and (d) show the horizontal and the vertical cross-section of the intensity profiles (along the dashed blue line in the inset) of both the theoretical target (solid line) and the experiment results (dots), respectively.

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Fig. 3
Fig. 3 Selective excitation of the LP11 mode. Intensity profiles in (a) and (b) denotes the “before” and “after” optimization of four different optimization processes; (c) and (d) show the horizontal and the vertical cross-section (along the dashed blue line in the inset) of the intensity profiles for both the theoretical target (solid line) and the experiment results (dots), respectively.

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Fig. 4
Fig. 4 Converting the LP01 mode (shown as the initial distributions in (a)) to the LP11 mode (shown as the optimized intensity profiles in (b)). Figures labeled as the same sequence number belong to the same optimization process.

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Fig. 5
Fig. 5 Excitation of a specific mixture of the LP01 and the LP11 modes. Targets in (a) to (d) are obtained through theoretical calculations, with specific amplitude ratios (AR = A01/A11) and phase differences β, as defined in Eq. (1). (a) AR = 0.5, β = π/2. (b) AR = 0.5, β = π/4 (c) AR = 0.2, β = π/2. (d) AR = 0.2, β = π/4. In (e)-(f), we choose four representative CCD camera images, captured experimentally, as the targets used in the optimization process.

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Fig. 6
Fig. 6 The variation of the objective function obtained during the optimization process: (a) Optimize the mode to LP01 mode; (b) Optimize the mode to LP11 mode; (c) Optimize towards a mixed LP01/LP11 mode.

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Fig. 7
Fig. 7 The variations of mode ratio A012/A112 during the optimization cycles. Mode is shaping to (a) LP01 mode, (b) LP11 mode, and (c) mixed modes. The legend in (c) shows the mode ratios A012/A112 of the targets used in optimization.

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Fig. 8
Fig. 8 Results of selective mode excitation using 5 × 5 blocks with different initial and target intensity profiles. The initial intensity distributions, the target intensity distributions, and the optimized images are labelled accordingly in (a)-(c). The optical output field is shape to (a) the LP01 mode, (b) the LP11 mode and (c) a mixture of the LP01/LP11 modes (the target is an experimentally captured CCD camera image). The objective functions obtained during the optimization process are also shown in (a)-(c).

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Fig. 9
Fig. 9 Results of selective mode excitation using 3 × 3 blocks with different target intensity profiles. The initial intensity distributions, the target intensity distributions, and the optimized images are labelled accordingly in (a)-(b). The optical output field is shape to (a) the LP01 mode, (b) the LP11 mode. The objective functions obtained during the optimization process are also shown in (a) and (b).

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Equations (2)

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I(r,φ)= | A 01 E 01 (r,φ) e −jβ + A 11 E 11 (r,φ) | 2 = A 01 2 E 01 2 (r,φ)+ A 11 2 E 11 2 (r,φ)+2 A 01 A 11 cosβ E 01 (r,φ) E 11 (r,φ)
f(k)=1− ∑ ( I 0 (x,y)− I 0 ¯ )( I k (x,y)− I k ¯ ) ∑ ( I 0 (x,y)− I 0 ¯ ) 2 ∑ ( I k (x,y)− I k ¯ ) 2

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