Abstract

A new approach for the complete modal decomposition of the optical fields emerging from the multimode fiber is presented in this paper. Based on the stochastic parallel gradient descent algorithm, mode coefficients for all the bound modes in the multimode fiber can be exactly calculated by utilizing one intensity profile of the beam. Numerical simulation validates the feasibility, and the reconstructed error is below 0.1%. In the case of six modes within the fiber, the running time is about 2 s.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994).
    [CrossRef]
  2. A. J. Poustie, and N. Finlayson, “Multiwavelength fiber laser using a spatial mode beating filter,” Opt. Lett. 19, 716–718 (1994).
    [CrossRef]
  3. H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
    [CrossRef]
  4. A. P. Napartovich, and D. V. Vysotsky, “Theory of spatial mode competition in a fiber amplifier,” Phys. Rev. A 76, 063801 (2007).
    [CrossRef]
  5. R. Eckhardt and R. Ulrich, “Mode‐beating spectroscopy in a few‐mode optical guide,” Appl. Phys. Lett. 63, 284–286 (1993).
    [CrossRef]
  6. H. Yoda, P. Polynkin, and M. Mansuripur, “Beam quality factor of higher order modes in a step-index fiber,” J. Lightwave Technol. 24, 1350–1355 (2006).
    [CrossRef]
  7. O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
    [CrossRef]
  8. F. Stutzki, H. 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]
  9. 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]
  10. M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A 15, 2745–2758 (1998).
    [CrossRef]

2011 (1)

2009 (1)

2007 (1)

A. P. Napartovich, and D. V. Vysotsky, “Theory of spatial mode competition in a fiber amplifier,” Phys. Rev. A 76, 063801 (2007).
[CrossRef]

2006 (1)

2005 (1)

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

1999 (1)

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

1998 (1)

1994 (2)

1993 (1)

R. Eckhardt and R. Ulrich, “Mode‐beating spectroscopy in a few‐mode optical guide,” Appl. Phys. Lett. 63, 284–286 (1993).
[CrossRef]

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]

Amano, C.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Bachmann, M.

Besse, P. A.

Duparré, M.

Eckhardt, R.

R. Eckhardt and R. Ulrich, “Mode‐beating spectroscopy in a few‐mode optical guide,” Appl. Phys. Lett. 63, 284–286 (1993).
[CrossRef]

Fink, Y.

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

Finlayson, N.

Flamm, D.

Gaida, C.

Goh, T.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Hirano, A.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Ishii, T.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Jansen, F.

Jauregui, C.

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]

Kaiser, T.

Kurokawa, T.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Limpert, J.

Mansuripur, M.

Melchior, H.

Napartovich, A. P.

A. P. Napartovich, and D. V. Vysotsky, “Theory of spatial mode competition in a fiber amplifier,” Phys. Rev. A 76, 063801 (2007).
[CrossRef]

Okamoto, K.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Otto, H.

Polynkin, P.

Poustie, A. J.

Sato, K.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Schröter, S.

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]

Sivokon, V. P.

Stutzki, F.

Takenouchi, H.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Tsuda, H.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

Tünnermann, A.

Ulrich, R.

R. Eckhardt and R. Ulrich, “Mode‐beating spectroscopy in a few‐mode optical guide,” Appl. Phys. Lett. 63, 284–286 (1993).
[CrossRef]

Vorontsov, M. A.

Vysotsky, D. V.

A. P. Napartovich, and D. V. Vysotsky, “Theory of spatial mode competition in a fiber amplifier,” Phys. Rev. A 76, 063801 (2007).
[CrossRef]

Yoda, H.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Eckhardt and R. Ulrich, “Mode‐beating spectroscopy in a few‐mode optical guide,” Appl. Phys. Lett. 63, 284–286 (1993).
[CrossRef]

Electron. Lett. (1)

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, “Spectral encoding and decoding of 10  Gbit/s femtosecond pulses using high resolution arrayed-waveguide grating,” Electron. Lett. 35, 1186–1188 (1999).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

A. P. Napartovich, and D. V. Vysotsky, “Theory of spatial mode competition in a fiber amplifier,” Phys. Rev. A 76, 063801 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

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

Cited By

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

Alert me when this article is cited.


Figures (2)

Fig. 1.
Fig. 1.

Comparisons between the reconstructed and given results for the three arbitrary chosen higher order mode beams, which are Group 1, 2, and 3, respectively. All the images in each row are plotted within the same colorbar.

Fig. 2.
Fig. 2.

Ratios of the appearance numbers for the real and conjugated fields with respect to the total operation numbers for the first group of higher mode beam above.

Tables (2)

Tables Icon

Table 1. Parameters for Numerical Computing

Tables Icon

Table 2. Changing Trends of the Reconstruction Error and Running Time Versus the Number of Modes

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ΔI(r)=j(|cj|2|dj|2)|Ψj(r)|2+lj(clcj*dldj*)Ψl(r)Ψj*(r).
|cj|=|dj|,
clcj*+cjcl*dldj*djdl*=0.
ρc,j=ρd,j,
φd,lφd,j=±(φc,lφc,j)+2mπ,
J=Ire(x,y)Ime(x,y)dxdyIre2(x,y)dxdyIme2(x,y)dxdy,
Ra=||dj|2j|dj|2|cj|2j|cj|2|.

Metrics