Abstract

A procedure for the μltiplexing and deμltiplexing of modes in optical fibers with digital holograms is presented. By using a spatial light modulator (SLM) to encode a digital hologram, the desired complex field is shaped and injected into the fiber. The SLM's ability to rapidly refresh the encoded transmission function enables one to excite pure single modes, as well as arbitrary coherent mode superpositions, in real-time. The modes from the output of the fiber are subsequently deμltipexed by applying a correlation filter for modal decomposition, thus allowing for an all-digital-hologram approach to modal analysis of fibers. The working principle is tested using conventional step-index large mode area fibers being excited with higher-order single modes and superpositions.

© 2013 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. C. Xia, N. Bai, I. Ozdur, X. Zhou, G. Li, "Supermodes for optical transmission," Opt. Exp. 19, 16 653-16 664 (2011).
  2. C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, G. Charlet, "Two mode transmission at 2 × 100 gb/s, over 40 km-long prototype few-mode fiber, using LCoS-based programmable mode μltiplexer and deμltiplexer," Opt. Exp. 19, 16 593-16 600 (2011).
  3. A. A. Amin, A. Li, S. Chen, X. Chen, G. Gao, W. Shieh, "Dual-LP11 mode 4 × 4 mimo-ofdm transmission over a two-mode fiber," Opt. Exp. 19, 16 672-16 679 (2011).
  4. N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. L. nares, 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, T. Wang, "Mode-division μltiplexed transmission with inline few-mode fiber amplifier," Opt. Exp. 20, 2668-2680 (2012).
  5. N. Bozinovic, S. Golowich, P. Kristensen, S. Ramachandran, "Control of orbital angular momentum of light with optical fibers," Opt. Lett. 37, 2451-2453 (2012).
  6. C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, A. Tünnermann, "Fiber based polarization filter for radially and aziμthally polarized light," Opt. Exp. 19, 19 582-19 590 (2011).
  7. P. Hofmann, A. Mafi, C. Jollivet-Salvin, N. Peyghambarian, A. Schülzgen, "Detailed investigation of mode-field adapters utilizing μltimode-interference in graded index fibers," J. Lightw. Technol. 30, 2289-2298 (2012).
  8. S. V. Karpeev, V. S. Pavelyev, S. N. Khonina, N. L. Kazanskiy, A. V. Gavrilov, V. A. Eropolov, "Fibre sensors based on transverse mode selection," J. Mod. Opt. 54, 833-844 (2007).
  9. X. Zhu, A. Schülzgen, H. Li, H. Wei, J. V. Moloney, N. Peyghambarian, "Coherent beam transformations using μltimode waveguides," Opt. Exp. 18, 7506-7520 (2010).
  10. S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, M. Yan, "Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers," Laser Photon. Rev. 2, 429-448 (2008).
  11. F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, A. Tünnermann, "Non-hexagonal large-pitch fibers for enhanced mode discrimination," Opt. Exp. 19, 12 081-12 086 (2011).
  12. B. Ward, C. Robin, I. Dajani, "Origin of thermal modal instabilities in large mode area fiber amplifiers," Opt. Exp. 20, 11 407-11 422 (2012).
  13. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, A. Tünnermann, "Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers," Opt. Exp. 20, 15 710-15 722 (2012).
  14. F. Dubois, P. Emplit, O. Hugon, "Selective mode excitation in graded-index μltimode fiber by a computer-generated optical mask," Opt. Lett. 19, 433-435 (1994).
  15. G. Stepniak, L. Maksymiuk, J. Siuzdak, "Binary-phase spatial light filters for mode-selective excitation of μltimode fibers," J. Lightw. Technol. 29, 1980-1987 (2011).
  16. J. Carpenter, T. D. Wilkinson, "Characterization of μltimode fiber by selective mode excitation," J. Lightw. Technol. 30, 1386-1392 (2012).
  17. A. D. Galea, F. Couny, S. Coupland, P. J. Roberts, H. Sabert, J. C. Knight, T. A. Birks, P. S. J. Russell, "Selective mode excitation in hollow-core photonic crystal fiber," Opt. Lett. 30, 717-719 (2005).
  18. T. Grosjean, A. Sabac, D. Courjon, "A versatile and stable device allowing the efficient generation of beams with radial, aziμthal or hybrid polarizations," Opt. Comμn. 252, 12-21 (2005).
  19. S. B. Shaklan, "Selective mode injection and observation for few-mode fiber optics," Appl. Opt. 30, 4379+ (1991).
  20. S. Barcelos, M. Zervas, P. Russell, "Selective excitation of fibre-modes using surface plasmons," IEEE Photon. Technol. Lett. 7, 1051-1053 (1995).
  21. O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, Y. Fink, "Complete modal decomposition for optical waveguides," Phys. Rev. Lett. 94, 143902 (2005).
  22. N. Andermahr, T. Theeg, C. Fallnich, "Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers," Appl. Phys. B 91, 353-357 (2008).
  23. J. W. Nicholson, A. D. Yablon, S. Ramachandran, S. Ghalmi, "Spatially and spectrally resolved imaging of modal content in large-mode-area fibers," Opt. Exp. 16, 7233-7243 (2008).
  24. D. N. Schimpf, R. A. Barankov, S. Ramachandran, "Cross-correlated (c2) imaging of fiber and waveguide modes," Opt. Exp. 19, 13 008-13 019 (2011).
  25. O. A. Schmidt, C. Schulze, D. Flamm, R. Brüning, T. Kaiser, S. Schröter, M. Duparré, "Real-time determination of laser beam quality by modal decomposition," Opt. Exp. 19, 6741-6748 (2011).
  26. D. Naidoo, K. Aït-Ameur, M. Brunel, A. Forbes, "Intra-cavity generation of superpositions of Laguerre-Gaussian beams," Appl. Physics B: Lasers and Optics 106, 683-690 (2012).
  27. T. Kaiser, D. Flamm, S. Schröter, M. Duparré, "Complete modal decomposition for optical fibers using CGH-based correlation filters," Opt. Exp. 17, 9347-9356 (2009).
  28. D. Flamm, D. Naidoo, C. Schulze, A. Forbes, M. Duparré, "Mode analysis with a spatial light modulator as a correlation filter," Opt. Lett. 37, 2478-2480 (2012).
  29. D. Flamm, O. A. Schmidt, C. Schulze, J. Borchardt, T. Kaiser, S. Schröter, M. Duparré, "Measuring the spatial polarization distribution of μltimode beams emerging from passive step-index large-mode-area fibers," Opt. Lett. 35, 3429-3431 (2010).
  30. C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, M. Duparré, "Wavefront reconstruction by modal decomposition," Opt. Exp. 20, 19 714-19 725 (2012).
  31. A. Dudley, I. A. Litvin, A. Forbes, "Quantitative measurement of the orbital angular momentum density of light," Appl. Opt. 51, 823-833 (2012).
  32. I. A. Litvin, A. Dudley, F. S. Roux, A. Forbes, "Aziμthal decomposition with digital holograms," Opt. Exp. 20, 10 996-11 004 (2012).
  33. D. Gloge, "Weakly guiding fibers," Appl. Opt. 10, 2252-2258 (1971).
  34. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  35. M. A. Golub, A. M. Prokhorov, I. N. Sisakian, V. A. Soifer, "Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation," Soviet J. Quantum Electron. 9, 1866-1868 (1982).
  36. M. Born, E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999).
  37. J. Nicholson, A. Yablon, J. Fini, M. Mermelstein, "Measuring the modal content of large-mode-area fibers," IEEE J. Sel. Topics Quantum Electron. 15, 61-70 (2009).
  38. H.-J. Otto, F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, A. Tünnermann, "Improved modal reconstruction for spatially and spectrally resolved imaging (${\rm S}^{2}$)," J. Lightw. Technol. (2012).
  39. J. P. Kirk, A. L. Jones, "Phase-only complex-valued spatial filter," J. Opt. Soc. Amer. 61, 1023-1028 (1971).
  40. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, "Encoding amplitude information onto phase-only filters," Appl. Opt. 38, 5004-5013 (1999).
  41. V. Arrizón, U. Ruiz, R. Carrada, L. A. González, "Pixelated phase computer holograms for the accurate encoding of scalar complex fields," J. Opt. Soc. Amer. A 24, 3500-3507 (2007).
  42. W. H. Lee, "Sampled Fourier transform hologram generated by computer," Appl. Opt. 9, 639-643 (1970).
  43. C. B. Burckhardt, "A simplification of Lee's method of generating holograms by computer," Appl. Opt. 9, 1949-1949 (1970).
  44. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1996).
  45. M. Padgett, J. Courtial, L. Allen, "Light's orbital angular momentum," Phys. Today 57, 35-40 (2004).
  46. S. Franke-Arnold, L. Allen, M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299-313 (2008).
  47. S. Wielandy, "Implications of higher-order mode content in large mode area fibers with good beam quality," Opt. Exp. 15, 15 402-15 409 (2007).
  48. D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, M. Duparré, "Fast M2 measurement for fiber beams based on modal analysis," Appl. Opt. 51, 987-993 (2012).
  49. R. Olshansky, "Mode coupling effects in graded-index optical fibers," Appl. Opt. 14, 935-945 (1975).
  50. R. Schermer, J. Cole, "Improved bend loss forμla verified for optical fiber by siμlation and experiment," IEEE J. Quantum Electron. 43, 899-909 (2007).
  51. T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, N. Fukuchi, "Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators," Opt. Lett. 34, 34-36 (2009).

2012 (13)

N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. L. nares, 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, T. Wang, "Mode-division μltiplexed transmission with inline few-mode fiber amplifier," Opt. Exp. 20, 2668-2680 (2012).

N. Bozinovic, S. Golowich, P. Kristensen, S. Ramachandran, "Control of orbital angular momentum of light with optical fibers," Opt. Lett. 37, 2451-2453 (2012).

P. Hofmann, A. Mafi, C. Jollivet-Salvin, N. Peyghambarian, A. Schülzgen, "Detailed investigation of mode-field adapters utilizing μltimode-interference in graded index fibers," J. Lightw. Technol. 30, 2289-2298 (2012).

B. Ward, C. Robin, I. Dajani, "Origin of thermal modal instabilities in large mode area fiber amplifiers," Opt. Exp. 20, 11 407-11 422 (2012).

H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, A. Tünnermann, "Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers," Opt. Exp. 20, 15 710-15 722 (2012).

J. Carpenter, T. D. Wilkinson, "Characterization of μltimode fiber by selective mode excitation," J. Lightw. Technol. 30, 1386-1392 (2012).

D. Naidoo, K. Aït-Ameur, M. Brunel, A. Forbes, "Intra-cavity generation of superpositions of Laguerre-Gaussian beams," Appl. Physics B: Lasers and Optics 106, 683-690 (2012).

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, M. Duparré, "Wavefront reconstruction by modal decomposition," Opt. Exp. 20, 19 714-19 725 (2012).

A. Dudley, I. A. Litvin, A. Forbes, "Quantitative measurement of the orbital angular momentum density of light," Appl. Opt. 51, 823-833 (2012).

I. A. Litvin, A. Dudley, F. S. Roux, A. Forbes, "Aziμthal decomposition with digital holograms," Opt. Exp. 20, 10 996-11 004 (2012).

D. Flamm, D. Naidoo, C. Schulze, A. Forbes, M. Duparré, "Mode analysis with a spatial light modulator as a correlation filter," Opt. Lett. 37, 2478-2480 (2012).

H.-J. Otto, F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, A. Tünnermann, "Improved modal reconstruction for spatially and spectrally resolved imaging (${\rm S}^{2}$)," J. Lightw. Technol. (2012).

D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, M. Duparré, "Fast M2 measurement for fiber beams based on modal analysis," Appl. Opt. 51, 987-993 (2012).

2011 (8)

D. N. Schimpf, R. A. Barankov, S. Ramachandran, "Cross-correlated (c2) imaging of fiber and waveguide modes," Opt. Exp. 19, 13 008-13 019 (2011).

O. A. Schmidt, C. Schulze, D. Flamm, R. Brüning, T. Kaiser, S. Schröter, M. Duparré, "Real-time determination of laser beam quality by modal decomposition," Opt. Exp. 19, 6741-6748 (2011).

F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, A. Tünnermann, "Non-hexagonal large-pitch fibers for enhanced mode discrimination," Opt. Exp. 19, 12 081-12 086 (2011).

G. Stepniak, L. Maksymiuk, J. Siuzdak, "Binary-phase spatial light filters for mode-selective excitation of μltimode fibers," J. Lightw. Technol. 29, 1980-1987 (2011).

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, A. Tünnermann, "Fiber based polarization filter for radially and aziμthally polarized light," Opt. Exp. 19, 19 582-19 590 (2011).

C. Xia, N. Bai, I. Ozdur, X. Zhou, G. Li, "Supermodes for optical transmission," Opt. Exp. 19, 16 653-16 664 (2011).

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, G. Charlet, "Two mode transmission at 2 × 100 gb/s, over 40 km-long prototype few-mode fiber, using LCoS-based programmable mode μltiplexer and deμltiplexer," Opt. Exp. 19, 16 593-16 600 (2011).

A. A. Amin, A. Li, S. Chen, X. Chen, G. Gao, W. Shieh, "Dual-LP11 mode 4 × 4 mimo-ofdm transmission over a two-mode fiber," Opt. Exp. 19, 16 672-16 679 (2011).

2010 (2)

X. Zhu, A. Schülzgen, H. Li, H. Wei, J. V. Moloney, N. Peyghambarian, "Coherent beam transformations using μltimode waveguides," Opt. Exp. 18, 7506-7520 (2010).

D. Flamm, O. A. Schmidt, C. Schulze, J. Borchardt, T. Kaiser, S. Schröter, M. Duparré, "Measuring the spatial polarization distribution of μltimode beams emerging from passive step-index large-mode-area fibers," Opt. Lett. 35, 3429-3431 (2010).

2009 (3)

J. Nicholson, A. Yablon, J. Fini, M. Mermelstein, "Measuring the modal content of large-mode-area fibers," IEEE J. Sel. Topics Quantum Electron. 15, 61-70 (2009).

T. Kaiser, D. Flamm, S. Schröter, M. Duparré, "Complete modal decomposition for optical fibers using CGH-based correlation filters," Opt. Exp. 17, 9347-9356 (2009).

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, N. Fukuchi, "Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators," Opt. Lett. 34, 34-36 (2009).

2008 (4)

S. Franke-Arnold, L. Allen, M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299-313 (2008).

N. Andermahr, T. Theeg, C. Fallnich, "Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers," Appl. Phys. B 91, 353-357 (2008).

J. W. Nicholson, A. D. Yablon, S. Ramachandran, S. Ghalmi, "Spatially and spectrally resolved imaging of modal content in large-mode-area fibers," Opt. Exp. 16, 7233-7243 (2008).

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, M. Yan, "Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers," Laser Photon. Rev. 2, 429-448 (2008).

2007 (4)

S. V. Karpeev, V. S. Pavelyev, S. N. Khonina, N. L. Kazanskiy, A. V. Gavrilov, V. A. Eropolov, "Fibre sensors based on transverse mode selection," J. Mod. Opt. 54, 833-844 (2007).

S. Wielandy, "Implications of higher-order mode content in large mode area fibers with good beam quality," Opt. Exp. 15, 15 402-15 409 (2007).

V. Arrizón, U. Ruiz, R. Carrada, L. A. González, "Pixelated phase computer holograms for the accurate encoding of scalar complex fields," J. Opt. Soc. Amer. A 24, 3500-3507 (2007).

R. Schermer, J. Cole, "Improved bend loss forμla verified for optical fiber by siμlation and experiment," IEEE J. Quantum Electron. 43, 899-909 (2007).

2005 (3)

A. D. Galea, F. Couny, S. Coupland, P. J. Roberts, H. Sabert, J. C. Knight, T. A. Birks, P. S. J. Russell, "Selective mode excitation in hollow-core photonic crystal fiber," Opt. Lett. 30, 717-719 (2005).

T. Grosjean, A. Sabac, D. Courjon, "A versatile and stable device allowing the efficient generation of beams with radial, aziμthal or hybrid polarizations," Opt. Comμn. 252, 12-21 (2005).

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, Y. Fink, "Complete modal decomposition for optical waveguides," Phys. Rev. Lett. 94, 143902 (2005).

2004 (1)

M. Padgett, J. Courtial, L. Allen, "Light's orbital angular momentum," Phys. Today 57, 35-40 (2004).

1999 (1)

1995 (1)

S. Barcelos, M. Zervas, P. Russell, "Selective excitation of fibre-modes using surface plasmons," IEEE Photon. Technol. Lett. 7, 1051-1053 (1995).

1994 (1)

1991 (1)

S. B. Shaklan, "Selective mode injection and observation for few-mode fiber optics," Appl. Opt. 30, 4379+ (1991).

1982 (1)

M. A. Golub, A. M. Prokhorov, I. N. Sisakian, V. A. Soifer, "Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation," Soviet J. Quantum Electron. 9, 1866-1868 (1982).

1975 (1)

1971 (2)

J. P. Kirk, A. L. Jones, "Phase-only complex-valued spatial filter," J. Opt. Soc. Amer. 61, 1023-1028 (1971).

D. Gloge, "Weakly guiding fibers," Appl. Opt. 10, 2252-2258 (1971).

1970 (2)

Appl. Opt. (8)

Appl. Phys. B (1)

N. Andermahr, T. Theeg, C. Fallnich, "Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers," Appl. Phys. B 91, 353-357 (2008).

Appl. Physics B: Lasers and Optics (1)

D. Naidoo, K. Aït-Ameur, M. Brunel, A. Forbes, "Intra-cavity generation of superpositions of Laguerre-Gaussian beams," Appl. Physics B: Lasers and Optics 106, 683-690 (2012).

IEEE J. Quantum Electron. (1)

R. Schermer, J. Cole, "Improved bend loss forμla verified for optical fiber by siμlation and experiment," IEEE J. Quantum Electron. 43, 899-909 (2007).

IEEE J. Sel. Topics Quantum Electron. (1)

J. Nicholson, A. Yablon, J. Fini, M. Mermelstein, "Measuring the modal content of large-mode-area fibers," IEEE J. Sel. Topics Quantum Electron. 15, 61-70 (2009).

IEEE Photon. Technol. Lett. (1)

S. Barcelos, M. Zervas, P. Russell, "Selective excitation of fibre-modes using surface plasmons," IEEE Photon. Technol. Lett. 7, 1051-1053 (1995).

J. Lightw. Technol. (4)

P. Hofmann, A. Mafi, C. Jollivet-Salvin, N. Peyghambarian, A. Schülzgen, "Detailed investigation of mode-field adapters utilizing μltimode-interference in graded index fibers," J. Lightw. Technol. 30, 2289-2298 (2012).

G. Stepniak, L. Maksymiuk, J. Siuzdak, "Binary-phase spatial light filters for mode-selective excitation of μltimode fibers," J. Lightw. Technol. 29, 1980-1987 (2011).

J. Carpenter, T. D. Wilkinson, "Characterization of μltimode fiber by selective mode excitation," J. Lightw. Technol. 30, 1386-1392 (2012).

H.-J. Otto, F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, A. Tünnermann, "Improved modal reconstruction for spatially and spectrally resolved imaging (${\rm S}^{2}$)," J. Lightw. Technol. (2012).

J. Mod. Opt. (1)

S. V. Karpeev, V. S. Pavelyev, S. N. Khonina, N. L. Kazanskiy, A. V. Gavrilov, V. A. Eropolov, "Fibre sensors based on transverse mode selection," J. Mod. Opt. 54, 833-844 (2007).

J. Opt. Soc. Amer. (1)

J. P. Kirk, A. L. Jones, "Phase-only complex-valued spatial filter," J. Opt. Soc. Amer. 61, 1023-1028 (1971).

J. Opt. Soc. Amer. A (1)

V. Arrizón, U. Ruiz, R. Carrada, L. A. González, "Pixelated phase computer holograms for the accurate encoding of scalar complex fields," J. Opt. Soc. Amer. A 24, 3500-3507 (2007).

Laser Photon. Rev. (2)

S. Franke-Arnold, L. Allen, M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299-313 (2008).

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, M. Yan, "Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers," Laser Photon. Rev. 2, 429-448 (2008).

Opt. Comµn. (1)

T. Grosjean, A. Sabac, D. Courjon, "A versatile and stable device allowing the efficient generation of beams with radial, aziμthal or hybrid polarizations," Opt. Comμn. 252, 12-21 (2005).

Opt. Exp. (16)

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, A. Tünnermann, "Fiber based polarization filter for radially and aziμthally polarized light," Opt. Exp. 19, 19 582-19 590 (2011).

X. Zhu, A. Schülzgen, H. Li, H. Wei, J. V. Moloney, N. Peyghambarian, "Coherent beam transformations using μltimode waveguides," Opt. Exp. 18, 7506-7520 (2010).

F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, A. Tünnermann, "Non-hexagonal large-pitch fibers for enhanced mode discrimination," Opt. Exp. 19, 12 081-12 086 (2011).

B. Ward, C. Robin, I. Dajani, "Origin of thermal modal instabilities in large mode area fiber amplifiers," Opt. Exp. 20, 11 407-11 422 (2012).

H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, A. Tünnermann, "Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers," Opt. Exp. 20, 15 710-15 722 (2012).

C. Xia, N. Bai, I. Ozdur, X. Zhou, G. Li, "Supermodes for optical transmission," Opt. Exp. 19, 16 653-16 664 (2011).

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, G. Charlet, "Two mode transmission at 2 × 100 gb/s, over 40 km-long prototype few-mode fiber, using LCoS-based programmable mode μltiplexer and deμltiplexer," Opt. Exp. 19, 16 593-16 600 (2011).

A. A. Amin, A. Li, S. Chen, X. Chen, G. Gao, W. Shieh, "Dual-LP11 mode 4 × 4 mimo-ofdm transmission over a two-mode fiber," Opt. Exp. 19, 16 672-16 679 (2011).

N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. L. nares, 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, T. Wang, "Mode-division μltiplexed transmission with inline few-mode fiber amplifier," Opt. Exp. 20, 2668-2680 (2012).

I. A. Litvin, A. Dudley, F. S. Roux, A. Forbes, "Aziμthal decomposition with digital holograms," Opt. Exp. 20, 10 996-11 004 (2012).

T. Kaiser, D. Flamm, S. Schröter, M. Duparré, "Complete modal decomposition for optical fibers using CGH-based correlation filters," Opt. Exp. 17, 9347-9356 (2009).

J. W. Nicholson, A. D. Yablon, S. Ramachandran, S. Ghalmi, "Spatially and spectrally resolved imaging of modal content in large-mode-area fibers," Opt. Exp. 16, 7233-7243 (2008).

D. N. Schimpf, R. A. Barankov, S. Ramachandran, "Cross-correlated (c2) imaging of fiber and waveguide modes," Opt. Exp. 19, 13 008-13 019 (2011).

O. A. Schmidt, C. Schulze, D. Flamm, R. Brüning, T. Kaiser, S. Schröter, M. Duparré, "Real-time determination of laser beam quality by modal decomposition," Opt. Exp. 19, 6741-6748 (2011).

S. Wielandy, "Implications of higher-order mode content in large mode area fibers with good beam quality," Opt. Exp. 15, 15 402-15 409 (2007).

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, M. Duparré, "Wavefront reconstruction by modal decomposition," Opt. Exp. 20, 19 714-19 725 (2012).

Opt. Lett. (6)

Phys. Rev. Lett. (1)

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, Y. Fink, "Complete modal decomposition for optical waveguides," Phys. Rev. Lett. 94, 143902 (2005).

Phys. Today (1)

M. Padgett, J. Courtial, L. Allen, "Light's orbital angular momentum," Phys. Today 57, 35-40 (2004).

Soviet J. Quantum Electron. (1)

M. A. Golub, A. M. Prokhorov, I. N. Sisakian, V. A. Soifer, "Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation," Soviet J. Quantum Electron. 9, 1866-1868 (1982).

Other (3)

M. Born, E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.