Abstract

Optical aspects of space-division multiplexing with orthogonal modes of coherent light were considered in theory and experiments with the coherent optical correlator. We resorted to the mathematical tool of generating functions and technologies of diffractive optical elements to implement complex spatial filters matched to rotationally symmetrical transverse modes. Successful multiplexing and demultiplexing in free-space transmission of low-frequency temporally modulated signals through different spatial modes was demonstrated. Experimental results show low cross talk between different mode channels and feasibility of further applications in multimode fiber optical communication data links.

© 2013 Optical Society of America

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2012 (3)

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

S. Shwartz, M. A. Golub, and S. Ruschin, “Generating function approach for creation of coherent multimode beams by diffractive optics,” J. Mod. Opt. 59, 83–89 (2012).
[CrossRef]

D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37, 2478–2480 (2012).
[CrossRef]

2011 (5)

2010 (2)

2009 (1)

2008 (3)

2007 (1)

2006 (1)

M. R. Duparre, B. Luedge, and S. Schroeter, “Etalons for pure and composite transversal modes,” Proc. SPIE 6101, 61011C (2006).
[CrossRef]

2005 (1)

2001 (3)

S. Makki and J. Leger, “Mode shaping of a graded-reflectivity-mirror unstable resonator with an intracavity phase element,” IEEE J. Quant. Electron. 37, 80–86 (2001).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, and E. Wolf, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).

2000 (2)

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000).
[CrossRef]

U. W. Krackhardt, R. Klug, and K.-H. Brenner, “Broadband parallel-fiber optical link for short-distance interconnection with multimode fibers,” Appl. Opt. 39, 690–697 (2000).
[CrossRef]

1994 (1)

1982 (2)

S. Berdagué and P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt. 21, 1950–1955 (1982).
[CrossRef]

M. A. Golub, A. M. Prokhorov, I. N. Sissakian, and V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

1981 (1)

U. Levy, H. Kobrinsky, and A. A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron 17, 2215–2224 (1981).
[CrossRef]

1979 (1)

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Anguita, J. A.

Arabaci, M. T.

Barros, D. J. F.

Berdagué, S.

Biswas, R.

S. H. Murshid, A. Chakravarty, and R. Biswas, “Attenuation and modal dispersion models for spatially multiplexed co-propagating helical optical channels in step index fibers,” Opt. Laser Technol. 43, 430–436 (2011).
[CrossRef]

Boffil, P.

A. Gatto, M. Tacca, P. Martelli, P. Boffil, and M. Martinelli, “Free-space orbital angular momentum division multiplexing with Bessel beams,” J. Opt. 13, 064018 (2011).
[CrossRef]

Bolle, C. A.

Brenner, K.-H.

Chakravarty, A.

S. H. Murshid, A. Chakravarty, and R. Biswas, “Attenuation and modal dispersion models for spatially multiplexed co-propagating helical optical channels in step index fibers,” Opt. Laser Technol. 43, 430–436 (2011).
[CrossRef]

Chiu, Y.-J.

Davidson, N.

M. A. Golub, L. Shimshi, N. Davidson, and A. A. Friesem, “Mode-matched phase diffractive optical element for detecting laser modes with spiral phases,” Appl. Opt. 46, 7823–7828 (2007).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, and E. Wolf, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[CrossRef]

Djordjevic, I. B.

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Dubois, F.

Duparre, M. R.

M. R. Duparre, B. Luedge, and S. Schroeter, “Etalons for pure and composite transversal modes,” Proc. SPIE 6101, 61011C (2006).
[CrossRef]

Duparré, M.

Emplit, P.

Essiambre, R.-J.

Facq, P.

Fan, S.

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Flamm, D.

Forbes, A.

Friesem, A. A.

M. A. Golub, L. Shimshi, N. Davidson, and A. A. Friesem, “Mode-matched phase diffractive optical element for detecting laser modes with spiral phases,” Appl. Opt. 46, 7823–7828 (2007).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, and E. Wolf, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[CrossRef]

U. Levy, H. Kobrinsky, and A. A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron 17, 2215–2224 (1981).
[CrossRef]

Gatto, A.

A. Gatto, M. Tacca, P. Martelli, P. Boffil, and M. Martinelli, “Free-space orbital angular momentum division multiplexing with Bessel beams,” J. Opt. 13, 064018 (2011).
[CrossRef]

Gnauck, A. H.

Golub, M. A.

S. Shwartz, M. A. Golub, and S. Ruschin, “Generating function approach for creation of coherent multimode beams by diffractive optics,” J. Mod. Opt. 59, 83–89 (2012).
[CrossRef]

M. A. Golub, L. Shimshi, N. Davidson, and A. A. Friesem, “Mode-matched phase diffractive optical element for detecting laser modes with spiral phases,” Appl. Opt. 46, 7823–7828 (2007).
[CrossRef]

M. A. Golub, A. M. Prokhorov, I. N. Sissakian, and V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

V. A. Soifer and M. A. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC, 1994).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1998).

Grossman, B.

S. Murshid, B. Grossman, and P. Narakorn, “Spatial domain multiplexing: a new dimension in fiber optic multiplexing,” Opt. Laser Technol. 40, 1030–1036 (2008).
[CrossRef]

Hasman, E.

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, and E. Wolf, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Hugon, O.

Ip, E.

Kahn, J. M.

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000).
[CrossRef]

Klug, R.

Kobrinsky, H.

U. Levy, H. Kobrinsky, and A. A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron 17, 2215–2224 (1981).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000).
[CrossRef]

Krackhardt, U. W.

Kurihara, K.

Laakonen, P.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000).
[CrossRef]

Lau, A. P. T.

Lee, W. H.

Leger, J.

S. Makki and J. Leger, “Mode shaping of a graded-reflectivity-mirror unstable resonator with an intracavity phase element,” IEEE J. Quant. Electron. 37, 80–86 (2001).
[CrossRef]

Levy, U.

U. Levy, H. Kobrinsky, and A. A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron 17, 2215–2224 (1981).
[CrossRef]

Lingle, R.

Liou, J.-H.

Luedge, B.

M. R. Duparre, B. Luedge, and S. Schroeter, “Etalons for pure and composite transversal modes,” Proc. SPIE 6101, 61011C (2006).
[CrossRef]

Makki, S.

S. Makki and J. Leger, “Mode shaping of a graded-reflectivity-mirror unstable resonator with an intracavity phase element,” IEEE J. Quant. Electron. 37, 80–86 (2001).
[CrossRef]

Mao, W.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides(Academic, 1974).

Martelli, P.

A. Gatto, M. Tacca, P. Martelli, P. Boffil, and M. Martinelli, “Free-space orbital angular momentum division multiplexing with Bessel beams,” J. Opt. 13, 064018 (2011).
[CrossRef]

Martinelli, M.

A. Gatto, M. Tacca, P. Martelli, P. Boffil, and M. Martinelli, “Free-space orbital angular momentum division multiplexing with Bessel beams,” J. Opt. 13, 064018 (2011).
[CrossRef]

McCurdy, A.

Murshid, S.

S. Murshid, B. Grossman, and P. Narakorn, “Spatial domain multiplexing: a new dimension in fiber optic multiplexing,” Opt. Laser Technol. 40, 1030–1036 (2008).
[CrossRef]

Murshid, S. H.

S. H. Murshid, A. Chakravarty, and R. Biswas, “Attenuation and modal dispersion models for spatially multiplexed co-propagating helical optical channels in step index fibers,” Opt. Laser Technol. 43, 430–436 (2011).
[CrossRef]

Naidoo, D.

Narakorn, P.

S. Murshid, B. Grossman, and P. Narakorn, “Spatial domain multiplexing: a new dimension in fiber optic multiplexing,” Opt. Laser Technol. 40, 1030–1036 (2008).
[CrossRef]

Neifeld, M. A.

Oron, R.

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, and E. Wolf, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[CrossRef]

Otomo, A.

Panicker, R. A.

Peckham, D. W.

Prokhorov, A. M.

M. A. Golub, A. M. Prokhorov, I. N. Sissakian, and V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

Randel, S.

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Ruschin, S.

S. Shwartz, M. A. Golub, and S. Ruschin, “Generating function approach for creation of coherent multimode beams by diffractive optics,” J. Mod. Opt. 59, 83–89 (2012).
[CrossRef]

Ryf, R.

Saito, S.

Schroeter, S.

M. R. Duparre, B. Luedge, and S. Schroeter, “Etalons for pure and composite transversal modes,” Proc. SPIE 6101, 61011C (2006).
[CrossRef]

Schulze, C.

Shemirani, M. B.

Shimshi, L.

Shwartz, S.

S. Shwartz, M. A. Golub, and S. Ruschin, “Generating function approach for creation of coherent multimode beams by diffractive optics,” J. Mod. Opt. 59, 83–89 (2012).
[CrossRef]

Sierra, A.

Sissakian, I. N.

M. A. Golub, A. M. Prokhorov, I. N. Sissakian, and V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

Skidanov, R. V.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000).
[CrossRef]

M. A. Golub, A. M. Prokhorov, I. N. Sissakian, and V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

V. A. Soifer and M. A. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC, 1994).

Syouji, A.

Tacca, M.

A. Gatto, M. Tacca, P. Martelli, P. Boffil, and M. Martinelli, “Free-space orbital angular momentum division multiplexing with Bessel beams,” J. Opt. 13, 064018 (2011).
[CrossRef]

Taga, H.

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Turunen, J.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000).
[CrossRef]

Vasic, B. V.

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Wang, Z.

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Winzer, P. J.

Wolf, E.

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, and E. Wolf, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Yu, C.-P.

Yuan, X.-C.

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Zhang, N.

Appl. Opt. (6)

IEEE J. Quant. Electron. (1)

S. Makki and J. Leger, “Mode shaping of a graded-reflectivity-mirror unstable resonator with an intracavity phase element,” IEEE J. Quant. Electron. 37, 80–86 (2001).
[CrossRef]

IEEE J. Quantum Electron (1)

U. Levy, H. Kobrinsky, and A. A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron 17, 2215–2224 (1981).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (2)

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).

S. Shwartz, M. A. Golub, and S. Ruschin, “Generating function approach for creation of coherent multimode beams by diffractive optics,” J. Mod. Opt. 59, 83–89 (2012).
[CrossRef]

J. Opt. (1)

A. Gatto, M. Tacca, P. Martelli, P. Boffil, and M. Martinelli, “Free-space orbital angular momentum division multiplexing with Bessel beams,” J. Opt. 13, 064018 (2011).
[CrossRef]

Nat. Photonics (1)

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, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 138, 1–9 (2012).

Opt. Commun. (1)

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000).
[CrossRef]

Opt. Express (5)

Opt. Laser Technol. (2)

S. Murshid, B. Grossman, and P. Narakorn, “Spatial domain multiplexing: a new dimension in fiber optic multiplexing,” Opt. Laser Technol. 40, 1030–1036 (2008).
[CrossRef]

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Supplementary Material (2)

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