Abstract

We present a comparative study of four numerical methods to detect the mode content of a laser beam from, at most, two intensity images. The techniques are compared regarding temporal effort, stability, and accuracy, using the example of three multimode optical fibers that differ in the number of supported modes.

© 2013 Optical Society of America

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  1. M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
    [CrossRef]
  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, 1545–1548 (2013).
    [CrossRef]
  3. D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, “Fast M2 measurement for fiber beams based on modal analysis,” Appl. Opt. 51, 987–993 (2012).
    [CrossRef]
  4. C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20, 19714–19725 (2012).
    [CrossRef]
  5. F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36, 689–691 (2011).
    [CrossRef]
  6. C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21, 3170–3181 (2013).
    [CrossRef]
  7. D. Flamm, K.-C. Hou, P. Gelszinnis, C. Schulze, S. Schröter, and M. Duparré, “Modal characterization of fiber-to-fiber coupling processes,” Opt. Lett. 38, 2128–2130 (2013).
    [CrossRef]
  8. F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “Non-hexagonal large-pitch fibers for enhanced mode discrimination,” Opt. Express 19, 12081–12086 (2011).
    [CrossRef]
  9. S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
    [CrossRef]
  10. N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91, 353–357 (2008).
    [CrossRef]
  11. J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
    [CrossRef]
  12. D. N. Schimpf, R. A. Barankov, and S. Ramachandran, “Cross-correlated (c2) imaging of fiber and waveguide modes,” Opt. Express 19, 13008–13019 (2011).
    [CrossRef]
  13. J. M. O. Daniel, J. S. P. Chan, J. W. Kim, J. K. Sahu, M. Ibsen, and W. A. Clarkson, “Novel technique for mode selection in a multimode fiber laser,” Opt. Express 19, 12434–12439 (2011).
    [CrossRef]
  14. F. Stutzki, C. Jauregui, C. Voigtlaender, J. U. Thomas, S. Nolte, J. Limpert, and A. Tuennermann, “Real-time monitoring of the modal content of monolithic large-mode-area fiber lasers,” in Optical Fiber Communication Conference (Optical Society of America, 2010).
  15. V. A. Soifer and M. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).
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    [CrossRef]
  17. C. Schulze, A. Dudley, D. Flamm, M. Duparr, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15, 073025 (2013).
    [CrossRef]
  18. D. M. Nguyen, S. Blin, T. N. Nguyen, S. D. Le, L. Provino, M. Thual, and T. Chartier, “Modal decomposition technique for multimode fibers,” Appl. Opt. 51, 450–456 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36, 4572–4574 (2011).
    [CrossRef]
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    [CrossRef]
  24. M. Skorobogatiy, C. Anastassiou, S. Johnson, O. Weisberg, T. Engeness, S. Jacobs, R. Ahmad, and Y. Fink, “Quantitative characterization of higher-order mode converters in weakly multimoded fibers,” Opt. Express 11, 2838–2847 (2003).
    [CrossRef]
  25. H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Fast and accurate modal decomposition of multimode fiber based on stochastic parallel gradient descent algorithm,” Appl. Opt. 52, 2905–2908 (2013).
    [CrossRef]
  26. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1996).
  27. J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).
  28. C. Borgentun, J. Bengtsson, and A. Larsson, “Full characterization of a high-power semiconductor disk laser beam with simultaneous capture of optimally sized focus and farfield,” Appl. Opt. 50, 1640–1649 (2011).
    [CrossRef]
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    [CrossRef]
  30. T. Isernia, G. Leone, and R. Pierri, “Phaseless near field techniques: uniqueness conditions and attainment of the solution,” J. Electromagn. Wave Appl. 8, 889–908 (1994).
  31. S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15, 15402–15409 (2007).
    [CrossRef]
  32. ISO, “ISO 11146-1:2005 Test methods for laser beam widths, divergence angles and beam propagation ratios part 1: Stigmatic and simple astigmatic beams,” (2005).

2013

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

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, 1545–1548 (2013).
[CrossRef]

C. Schulze, A. Dudley, D. Flamm, M. Duparr, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15, 073025 (2013).
[CrossRef]

C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21, 3170–3181 (2013).
[CrossRef]

H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Fast and accurate modal decomposition of multimode fiber based on stochastic parallel gradient descent algorithm,” Appl. Opt. 52, 2905–2908 (2013).
[CrossRef]

D. Flamm, K.-C. Hou, P. Gelszinnis, C. Schulze, S. Schröter, and M. Duparré, “Modal characterization of fiber-to-fiber coupling processes,” Opt. Lett. 38, 2128–2130 (2013).
[CrossRef]

2012

2011

2009

2008

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
[CrossRef]

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[CrossRef]

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

2007

2005

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[CrossRef]

2003

1995

1994

T. Isernia, G. Leone, and R. Pierri, “Phaseless near field techniques: uniqueness conditions and attainment of the solution,” J. Electromagn. Wave Appl. 8, 889–908 (1994).

1992

1988

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).

1982

1972

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Abouraddy, A. F.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[CrossRef]

Ahmad, R.

Anastassiou, C.

Andermahr, N.

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

Barankov, R. A.

Bartelt, H.

Bengtsson, J.

Blin, S.

Borgentun, C.

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, 1545–1548 (2013).
[CrossRef]

Brüning, R.

Chan, J. S. P.

Chartier, T.

Clarkson, W. A.

Courtial, J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

Cutolo, A.

Daniel, J. M. O.

Dudley, A.

C. Schulze, A. Dudley, D. Flamm, M. Duparr, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15, 073025 (2013).
[CrossRef]

Duparr, M.

C. Schulze, A. Dudley, D. Flamm, M. Duparr, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15, 073025 (2013).
[CrossRef]

Duparré, M.

Eidam, T.

Engeness, T.

Esposito, A.

Fallnich, C.

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

Fienup, J. R.

Fini, J.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[CrossRef]

Fink, Y.

Flamm, D.

Forbes, A.

C. Schulze, A. Dudley, D. Flamm, M. Duparr, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15, 073025 (2013).
[CrossRef]

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20, 19714–19725 (2012).
[CrossRef]

Gaida, C.

Gelszinnis, P.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Ghalmi, S.

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
[CrossRef]

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[CrossRef]

Golub, M.

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

Hartung, A.

Hou, K.-C.

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, 1545–1548 (2013).
[CrossRef]

Ibsen, M.

Isernia, T.

Izzo, I.

Jacobs, S.

Jansen, F.

Jauregui, C.

Jiang, Z.

Joannopoulos, J. D.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[CrossRef]

Johnson, S.

Kaiser, T.

Kim, J. W.

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, 1545–1548 (2013).
[CrossRef]

Larsson, A.

Lavery, M. P. J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

Le, S. D.

Leone, G.

T. Isernia, G. Leone, and R. Pierri, “Phaseless near field techniques: uniqueness conditions and attainment of the solution,” J. Electromagn. Wave Appl. 8, 889–908 (1994).

Limpert, J.

Lorenz, A.

Love, J. D.

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

Lü, H.

Mermelstein, M.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[CrossRef]

Naidoo, D.

Nguyen, D. M.

Nguyen, T. N.

Nicewander, W. A.

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).

Nicholson, J.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[CrossRef]

Nicholson, J. W.

Nolte, S.

F. Stutzki, C. Jauregui, C. Voigtlaender, J. U. Thomas, S. Nolte, J. Limpert, and A. Tuennermann, “Real-time monitoring of the modal content of monolithic large-mode-area fiber lasers,” in Optical Fiber Communication Conference (Optical Society of America, 2010).

Otto, H.-J.

Padgett, M. J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

Pierri, R.

Provino, L.

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, 1545–1548 (2013).
[CrossRef]

D. N. Schimpf, R. A. Barankov, and S. Ramachandran, “Cross-correlated (c2) imaging of fiber and waveguide modes,” Opt. Express 19, 13008–13019 (2011).
[CrossRef]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
[CrossRef]

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[CrossRef]

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, 1545–1548 (2013).
[CrossRef]

Robertson, D. J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

Rodgers, J. L.

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).

Sahu, J. K.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Schimpf, D. N.

Schmidt, O. A.

Schröter, S.

Schulze, C.

Shapira, O.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[CrossRef]

Skorobogatiy, M.

Snyder, A. W.

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

Soifer, V. A.

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

Sponselli, A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

Steinhoff, N. K.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

Steinmetz, A.

Stutzki, F.

Theeg, T.

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

Thomas, J. U.

F. Stutzki, C. Jauregui, C. Voigtlaender, J. U. Thomas, S. Nolte, J. Limpert, and A. Tuennermann, “Real-time monitoring of the modal content of monolithic large-mode-area fiber lasers,” in Optical Fiber Communication Conference (Optical Society of America, 2010).

Thual, M.

Tuennermann, A.

F. Stutzki, C. Jauregui, C. Voigtlaender, J. U. Thomas, S. Nolte, J. Limpert, and A. Tuennermann, “Real-time monitoring of the modal content of monolithic large-mode-area fiber lasers,” in Optical Fiber Communication Conference (Optical Society of America, 2010).

Tünnermann, A.

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, 1545–1548 (2013).
[CrossRef]

Tyler, G. A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

Voigtlaender, C.

F. Stutzki, C. Jauregui, C. Voigtlaender, J. U. Thomas, S. Nolte, J. Limpert, and A. Tuennermann, “Real-time monitoring of the modal content of monolithic large-mode-area fiber lasers,” in Optical Fiber Communication Conference (Optical Society of America, 2010).

Wang, X.

Weisberg, O.

Wielandy, S.

Willner, A. E.

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, 1545–1548 (2013).
[CrossRef]

Wilner, A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

Yablon, A. D.

Yan, M.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[CrossRef]

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, 1545–1548 (2013).
[CrossRef]

Zeni, L.

Zhou, P.

Am. Stat.

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).

Appl. Opt.

Appl. Phys. B

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

J. Electromagn. Wave Appl.

T. Isernia, G. Leone, and R. Pierri, “Phaseless near field techniques: uniqueness conditions and attainment of the solution,” J. Electromagn. Wave Appl. 8, 889–908 (1994).

Laser Photon. Rev.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[CrossRef]

New J. Phys.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[CrossRef]

C. Schulze, A. Dudley, D. Flamm, M. Duparr, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15, 073025 (2013).
[CrossRef]

Opt. Express

M. Skorobogatiy, C. Anastassiou, S. Johnson, O. Weisberg, T. Engeness, S. Jacobs, R. Ahmad, and Y. Fink, “Quantitative characterization of higher-order mode converters in weakly multimoded fibers,” Opt. Express 11, 2838–2847 (2003).
[CrossRef]

S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15, 15402–15409 (2007).
[CrossRef]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
[CrossRef]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17, 9347–9356 (2009).
[CrossRef]

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20, 19714–19725 (2012).
[CrossRef]

C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21, 3170–3181 (2013).
[CrossRef]

F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “Non-hexagonal large-pitch fibers for enhanced mode discrimination,” Opt. Express 19, 12081–12086 (2011).
[CrossRef]

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