Abstract

We have used common path interferometry for rapid determination of the electric field and complex modal content of vector beams, which have spatially-varying polarization. We combine a reference beam with a signal beam prior to a polarization beam splitter for stable interferograms that preserve intermodal phase shifts even in noisy environments. Interferometric decomposition into optical modes (IDIOM) provides a direct, sensitive measure of the complete electric field, enabling rapid modal decomposition and is ideally suited to single-frequency laser sources. We apply the technique to beams exiting optical fibers that support up to 10 modes. We also use the technique to characterize the fibers by determining a scattering matrix that transforms an input superposition of modes into an output superposition. Furthermore, because interferograms are linear in the field, this technique is very sensitive and can accurately reconstruct beams with signal-to-noise << 1.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon.1(1), 1–57 (2009).
    [CrossRef]
  2. S. Tripathi and K. C. Toussaint., “Rapid Mueller matrix polarimetry based on parallelized polarization state generation and detection,” Opt. Express17(24), 21396–21407 (2009).
    [CrossRef] [PubMed]
  3. D. P. Biss, K. S. Youngworth, and T. G. Brown, “Dark-field imaging with cylindrical-vector beams,” Appl. Opt.45(3), 470–479 (2006).
    [CrossRef] [PubMed]
  4. Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express18(10), 10828–10833 (2010).
    [CrossRef] [PubMed]
  5. F. K. Fatemi, “Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems,” Opt. Express19(25), 25143–25150 (2011).
    [CrossRef] [PubMed]
  6. C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
    [CrossRef] [PubMed]
  7. J. A. Pechkis and F. K. Fatemi, “Cold atom guidance in a capillary using blue-detuned, hollow optical modes,” Opt. Express20(12), 13409–13418 (2012).
    [CrossRef] [PubMed]
  8. T. G. Euser, G. Whyte, M. Scharrer, J. S. Y. Chen, A. Abdolvand, J. Nold, C. F. Kaminski, and P. St. J. Russell, “Dynamic control of higher-order modes in hollow-core photonic crystal fibers,” Opt. Express16(22), 17972–17981 (2008).
    [CrossRef] [PubMed]
  9. S. Ravets, J. E. Hoffman, L. A. Orozco, S. L. Rolston, G. Beadie, and F. K. Fatemi, “A low-loss photonic silica nanofiber for higher-order modes,” Opt. Express21(15), 18325–18335 (2013).
    [CrossRef] [PubMed]
  10. M. C. Frawley, A. Petcu-Colan, V. G. Truong, and S. Nic Chormaic, “Higher order mode propagation in an optical nanofiber,” Opt. Commun.285(23), 4648–4654 (2012).
    [CrossRef]
  11. R. Cherif, M. Zghal, L. Tartara, and V. Degiorgio, “Supercontinuum generation by higher-order mode excitation in a photonic crystal fiber,” Opt. Express16(3), 2147–2152 (2008).
    [CrossRef] [PubMed]
  12. A. A. Ishaaya, C. J. Hensley, B. Shim, S. Schrauth, K. W. Koch, and A. L. Gaeta, “Highly-efficient coupling of linearly- and radially-polarized femtosecond pulses in hollow-core photonic band-gap fibers,” Opt. Express17(21), 18630–18637 (2009).
    [CrossRef] [PubMed]
  13. J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express21(15), 18097–18110 (2013).
    [CrossRef] [PubMed]
  14. S. Golowich, N. Bozinovic, P. Kristensen, and S. Ramachandran, “Complex mode amplitude measurement for a six-mode optical fiber,” Opt. Express21(4), 4931–4944 (2013).
    [CrossRef] [PubMed]
  15. 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(12), 2905–2908 (2013).
    [CrossRef] [PubMed]
  16. 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(23), 4572–4574 (2011).
    [CrossRef] [PubMed]
  17. O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett.94(14), 143902 (2005).
    [CrossRef] [PubMed]
  18. D. B. S. Soh, J. Nilsson, S. Baek, C. Codemard, Y. Jeong, and V. Philippov, “Modal power decomposition of beam intensity profiles into linearly polarized modes of multimode optical fibers,” J. Opt. Soc. Am. A21(7), 1241–1250 (2004).
    [CrossRef] [PubMed]
  19. T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express17(11), 9347–9356 (2009).
    [CrossRef] [PubMed]
  20. D. Flamm, C. Schulze, D. Naidoo, S. Schröter, A. Forbes, and M. Duparré, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Technol.31(7), 1023–1032 (2013).
    [CrossRef]
  21. I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express20(10), 10996–11004 (2012).
    [CrossRef] [PubMed]
  22. R. Brüning, D. Flamm, C. Schulze, O. A. Schmidt, and M. Duparré, “Comparison of two modal decomposition techniques,” Proc. SPIE Vol. 8236, Laser Resonators, Microresonators, and Beam Control XIV, eds. A. V. Kudryashov, A. H. Paxton, V. S. Ilchenko, L. Aschke, and K. Washio, 82360I (2012).
  23. 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(12), 2128–2130 (2013).
    [CrossRef] [PubMed]
  24. V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun.283(6), 861–864 (2010).
    [CrossRef]
  25. 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. Express16(10), 7233–7243 (2008).
    [CrossRef] [PubMed]
  26. J. Jasapara and A. D. Yablon, “Spectrogram approach to S2 fiber mode analysis to distinguish between dispersion and distributed scattering,” Opt. Lett.37(18), 3906–3908 (2012).
    [CrossRef] [PubMed]
  27. 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(4), 450–456 (2012).
    [CrossRef] [PubMed]
  28. D. N. Schimpf and S. Ramachandran, “Polarization-resolved imaging of an ensemble of waveguide modes,” Opt. Lett.37(15), 3069–3071 (2012).
    [CrossRef] [PubMed]
  29. M. Paurisse, M. Hanna, F. Druon, P. Georges, C. Bellanger, A. Brignon, and J. P. Huignard, “Phase and amplitude control of a multimode LMA fiber beam by use of digital holography,” Opt. Express17(15), 13000–13008 (2009).
    [CrossRef] [PubMed]
  30. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express18(10), 10777–10785 (2010).
    [CrossRef] [PubMed]
  31. T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarization,” Opt. Commun.252(1-3), 12–21 (2005).
    [CrossRef]
  32. L. Lepetit, G. Cheriaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B12(12), 2467–2474 (1995).
    [CrossRef]
  33. MATLAB R2007B, Natick, Massachusetts: The MathWorks Inc., (2007).
  34. T. Ĉiẑmár and K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nature Commun.3, 1027 (2012).

2013

2012

2011

F. K. Fatemi, “Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems,” Opt. Express19(25), 25143–25150 (2011).
[CrossRef] [PubMed]

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

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(23), 4572–4574 (2011).
[CrossRef] [PubMed]

2010

2009

2008

2006

2005

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett.94(14), 143902 (2005).
[CrossRef] [PubMed]

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarization,” Opt. Commun.252(1-3), 12–21 (2005).
[CrossRef]

2004

1995

Abdolvand, A.

Abouraddy, A. F.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett.94(14), 143902 (2005).
[CrossRef] [PubMed]

Aiello, A.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Alonso, M. A.

Andersen, U. L.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Baek, S.

Banzer, P.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Beadie, G.

Beckley, A. M.

Bellanger, C.

Biss, D. P.

Blin, S.

Bozinovic, N.

Brignon, A.

Brown, T. G.

Chartier, T.

Chen, J. S. Y.

Cheriaux, G.

Cherif, R.

Ci?már, T.

T. Ĉiẑmár and K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nature Commun.3, 1027 (2012).

Codemard, C.

Courjon, D.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarization,” Opt. Commun.252(1-3), 12–21 (2005).
[CrossRef]

Degiorgio, V.

Dholakia, K.

T. Ĉiẑmár and K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nature Commun.3, 1027 (2012).

Druon, F.

Dudley, A.

Duparré, M.

Elser, D.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Euser, T. G.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

T. G. Euser, G. Whyte, M. Scharrer, J. S. Y. Chen, A. Abdolvand, J. Nold, C. F. Kaminski, and P. St. J. Russell, “Dynamic control of higher-order modes in hollow-core photonic crystal fibers,” Opt. Express16(22), 17972–17981 (2008).
[CrossRef] [PubMed]

Fatemi, F. K.

Fink, Y.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett.94(14), 143902 (2005).
[CrossRef] [PubMed]

Flamm, D.

Forbes, A.

Förtsch, M.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Frawley, M. C.

M. C. Frawley, A. Petcu-Colan, V. G. Truong, and S. Nic Chormaic, “Higher order mode propagation in an optical nanofiber,” Opt. Commun.285(23), 4648–4654 (2012).
[CrossRef]

Gabriel, C.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Gaeta, A. L.

Gaida, C.

Gelszinnis, P.

Georges, P.

Ghalmi, S.

Golowich, S.

Grosjean, T.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarization,” Opt. Commun.252(1-3), 12–21 (2005).
[CrossRef]

Hanna, M.

Hensley, C. J.

Hoffman, J. E.

Hou, K.-C.

Huignard, J. P.

Inavalli, V. V. G. K.

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun.283(6), 861–864 (2010).
[CrossRef]

Ishaaya, A. A.

Jansen, F.

Jasapara, J.

Jauregui, C.

Jeong, Y.

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(14), 143902 (2005).
[CrossRef] [PubMed]

Joffre, M.

Joly, N. Y.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Kaiser, T.

Kaminski, C. F.

Koch, K. W.

Kozawa, Y.

Kristensen, P.

Le, S. D.

Lepetit, L.

Leuchs, G.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Limpert, J.

Litvin, I. A.

Lü, H.

Marquardt, Ch.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Naidoo, D.

Nguyen, D. M.

Nguyen, T. N.

Nic Chormaic, S.

M. C. Frawley, A. Petcu-Colan, V. G. Truong, and S. Nic Chormaic, “Higher order mode propagation in an optical nanofiber,” Opt. Commun.285(23), 4648–4654 (2012).
[CrossRef]

Nicholson, J. W.

Nilsson, J.

Nold, J.

Orozco, L. A.

Otto, H.-J.

Paurisse, M.

Pechkis, J. A.

Petcu-Colan, A.

M. C. Frawley, A. Petcu-Colan, V. G. Truong, and S. Nic Chormaic, “Higher order mode propagation in an optical nanofiber,” Opt. Commun.285(23), 4648–4654 (2012).
[CrossRef]

Philippov, V.

Provino, L.

Ramachandran, S.

Ravets, S.

Rolston, S. L.

Roux, F. S.

Russell, P. St. J.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

T. G. Euser, G. Whyte, M. Scharrer, J. S. Y. Chen, A. Abdolvand, J. Nold, C. F. Kaminski, and P. St. J. Russell, “Dynamic control of higher-order modes in hollow-core photonic crystal fibers,” Opt. Express16(22), 17972–17981 (2008).
[CrossRef] [PubMed]

Ryf, R.

Sabac, A.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarization,” Opt. Commun.252(1-3), 12–21 (2005).
[CrossRef]

Sato, S.

Scharrer, M.

Schimpf, D. N.

Schrauth, S.

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(14), 143902 (2005).
[CrossRef] [PubMed]

Shim, B.

Soh, D. B. S.

Stutzki, F.

Tartara, L.

Thual, M.

Toussaint, K. C.

Tripathi, S.

Truong, V. G.

M. C. Frawley, A. Petcu-Colan, V. G. Truong, and S. Nic Chormaic, “Higher order mode propagation in an optical nanofiber,” Opt. Commun.285(23), 4648–4654 (2012).
[CrossRef]

Tünnermann, A.

Viswanathan, N. K.

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun.283(6), 861–864 (2010).
[CrossRef]

von Hoyningen-Huene, J.

Wang, X.

Whyte, G.

Winzer, P.

Yablon, A. D.

Youngworth, K. S.

Zghal, M.

Zhan, Q.

Zhong, W.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Zhou, P.

Adv. Opt. Photon.

Appl. Opt.

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature Commun.

T. Ĉiẑmár and K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nature Commun.3, 1027 (2012).

Opt. Commun.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarization,” Opt. Commun.252(1-3), 12–21 (2005).
[CrossRef]

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun.283(6), 861–864 (2010).
[CrossRef]

M. C. Frawley, A. Petcu-Colan, V. G. Truong, and S. Nic Chormaic, “Higher order mode propagation in an optical nanofiber,” Opt. Commun.285(23), 4648–4654 (2012).
[CrossRef]

Opt. Express

R. Cherif, M. Zghal, L. Tartara, and V. Degiorgio, “Supercontinuum generation by higher-order mode excitation in a photonic crystal fiber,” Opt. Express16(3), 2147–2152 (2008).
[CrossRef] [PubMed]

A. A. Ishaaya, C. J. Hensley, B. Shim, S. Schrauth, K. W. Koch, and A. L. Gaeta, “Highly-efficient coupling of linearly- and radially-polarized femtosecond pulses in hollow-core photonic band-gap fibers,” Opt. Express17(21), 18630–18637 (2009).
[CrossRef] [PubMed]

J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express21(15), 18097–18110 (2013).
[CrossRef] [PubMed]

S. Golowich, N. Bozinovic, P. Kristensen, and S. Ramachandran, “Complex mode amplitude measurement for a six-mode optical fiber,” Opt. Express21(4), 4931–4944 (2013).
[CrossRef] [PubMed]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express17(11), 9347–9356 (2009).
[CrossRef] [PubMed]

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express18(10), 10828–10833 (2010).
[CrossRef] [PubMed]

F. K. Fatemi, “Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems,” Opt. Express19(25), 25143–25150 (2011).
[CrossRef] [PubMed]

S. Tripathi and K. C. Toussaint., “Rapid Mueller matrix polarimetry based on parallelized polarization state generation and detection,” Opt. Express17(24), 21396–21407 (2009).
[CrossRef] [PubMed]

J. A. Pechkis and F. K. Fatemi, “Cold atom guidance in a capillary using blue-detuned, hollow optical modes,” Opt. Express20(12), 13409–13418 (2012).
[CrossRef] [PubMed]

T. G. Euser, G. Whyte, M. Scharrer, J. S. Y. Chen, A. Abdolvand, J. Nold, C. F. Kaminski, and P. St. J. Russell, “Dynamic control of higher-order modes in hollow-core photonic crystal fibers,” Opt. Express16(22), 17972–17981 (2008).
[CrossRef] [PubMed]

S. Ravets, J. E. Hoffman, L. A. Orozco, S. L. Rolston, G. Beadie, and F. K. Fatemi, “A low-loss photonic silica nanofiber for higher-order modes,” Opt. Express21(15), 18325–18335 (2013).
[CrossRef] [PubMed]

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. Express16(10), 7233–7243 (2008).
[CrossRef] [PubMed]

I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express20(10), 10996–11004 (2012).
[CrossRef] [PubMed]

M. Paurisse, M. Hanna, F. Druon, P. Georges, C. Bellanger, A. Brignon, and J. P. Huignard, “Phase and amplitude control of a multimode LMA fiber beam by use of digital holography,” Opt. Express17(15), 13000–13008 (2009).
[CrossRef] [PubMed]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express18(10), 10777–10785 (2010).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett.94(14), 143902 (2005).
[CrossRef] [PubMed]

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106(6), 060502 (2011).
[CrossRef] [PubMed]

Other

MATLAB R2007B, Natick, Massachusetts: The MathWorks Inc., (2007).

R. Brüning, D. Flamm, C. Schulze, O. A. Schmidt, and M. Duparré, “Comparison of two modal decomposition techniques,” Proc. SPIE Vol. 8236, Laser Resonators, Microresonators, and Beam Control XIV, eds. A. V. Kudryashov, A. H. Paxton, V. S. Ilchenko, L. Aschke, and K. Washio, 82360I (2012).

Supplementary Material (3)

» Media 1: AVI (732 KB)     
» Media 2: AVI (710 KB)     
» Media 3: AVI (785 KB)     

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 (7)

Fig. 1
Fig. 1

(top) LP and (bottom) vector modes (HE, EH, TM, TE) used in this paper. Different angular orientations of degenerate modes are labeled with ‘e’ and ‘o.’ For the LP-modes, only the vertical polarization is shown; the horizontal polarizations have the same intensity profiles.

Fig. 2
Fig. 2

(a) Interferometer setup for scalar beams. For Gaussian input, the FFT of the interferogram has Gaussian features that are fit to extract ktilt (b) Modified setup for vector modes. The signal beam is split: One arm (black) is interfered with a reference beam (blue), and the other arm (red) is displaced vertically so that four images fit on one CCD image. Actual reflection angles are shallow to avoid differential phase and amplitude shifts between horizontal and vertical components. A sample image is shown, along with the FFT of the vertical component. One of the FFT features is digitally removed as described in the text. Apart from aspheric lenses to collimate the fiber outputs of the signal and reference arms, no other imaging lenses are used.

Fig. 3
Fig. 3

(a) Creation of a known, free-space LP11 mode. The waveplates are rotated to create different superpositions of L P 11 ye and L P 11 xe modes. Not shown is an aperture after the phase plate for mild spatial filtering. (b) (left) Measured and simulated coefficient amplitudes. The fundamental modes are strongly suppressed by the phase plate. At right are the measured and simulated phases of c3 for each waveplate orientation.

Fig. 4
Fig. 4

(a) Results for a fiber supporting only the LP01 and LP11 mode families. The input beam profile for the centered phase plate is shown at left, along with typical output interferograms for the centered phase step for horizontal and vertical polarization components. Modal powers in the LP01 family (black) and LP11 family (red) are shown, with input (solid lines) and output (points) mode powers. (b) Measured (left) and reconstructed (right) beam profiles for phase step position at −150, 0, and 150 μm (Media 1, 0.7 MB). The media file shows the horizontal and vertical interferograms. (c) Results for SMF-28 fiber, which supports up to the LP21 mode family. As in (a), mode powers for the LP01, LP11, and LP21 families are shown. (d) Measured and reconstructed images for phase step position at −150, 0, and 150 μm (Media 2, 0.7 MB). The media file shows the horizontal and vertical interferograms.

Fig. 5
Fig. 5

(a) Measured (left) and predicted (right) mode powers and phases of the LP11 output modes of the fiber over all orientations of the input half- and quarter-wave-plates. CCD images (left) and predicted (right) profiles calculated by S (Media 3, 0.8 MB).

Fig. 6
Fig. 6

(top) Two different outputs of the fiber using strain-induced birefringence. Bottom: Pure modes in both the LP and vector bases can be generated with strain-induced birefringence. The purity of each of the modes is above 90%. Profiles can be compared with Fig. 1.

Fig. 7
Fig. 7

(a) Interferograms, signal images, and reconstructed images for four different beam powers over 4 orders of magnitude. Color contrast is adjusted so that the interferograms are observed. Slight fringes on some signal images are due to other optical components but are filtered out in processing. The signal image on the bottom row has a peak SNR of ~0.1. At right are the recovered mode powers (top) and phases (bottom) for the 6 modes at 6 different powers spanning 4 orders of magnitude. The normalization is chosen so that c3 is 1.0 at full power so that the coefficients can be easily compared. In decreasing order, the normalized beam powers are 1.0 (black), 0.138 (red), 0.041 (green), 0.010 (blue), 0.0017 (dashed), and 0.00021 (magenta). The lowest power in (b) has SNR ~0.1 on the signal arm. We chose c5 as the reference mode, so its phase is always 0.

Equations (12)

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

E( r,θ )= i= 1 n c i f i ( r, θ )
L P 01 x ( r,θ )= F 01 ( r ) x ^ L P 01 y ( r,θ )= F 01 ( r ) y ^ L P 11 xe ( r,θ )= F 11 ( r )cosθ x ^ L P 11 xo ( r,θ )= F 11 ( r )sinθ x ^ L P 11 ye ( r,θ )= F 11 ( r )cosθ y ^ L P 11 yo ( r,θ )= F 11 ( r )sinθ y ^ L P 21 xe ( r,θ )= F 21 ( r )cos2θ x ^ L P 21 xo ( r,θ )= F 21 ( r )sin2θ x ^ L P 21 ye ( r,θ )= F 21 ( r )cos2θ y ^ L P 21 yo ( r,θ )= F 21 ( r )sin2θ y ^
F 01 ( r )=exp( r 2 ω 2 ) F 11 ( r )=rexp( r 2 ω 2 ) F 21 ( r )= r 2 exp( r 2 ω 2 )
I tot | E sig ( r )+ E ref ( r )exp( i k tilt r ) | 2
= I sig + I ref +2Re[ E sig * ( r ) E ref ( r )exp( i k tilt r ) ]
I tot   I sig I ref =2Re{ | E sig * ( r ) E ref ( r ) |exp[ iφ( r,θ )+i k tilt r ] }
{ 2Re[ E sig * ( r ) E ref ( r )exp( i k tilt r ) ] }= g * ( k k tilt )+g( k+ k tilt )
D= SC
( S 11 S 12 0 0 0 0 S 21 S 22 0 0 0 0 0 0 S 33 S 34 S 35 S 36 0 0 S 43 S 44 S 45 S 46 0 0 S 53 S 54 S 55 S 56 0 0 S 63 S 64 S 65 S 66 )( c 1 c 2 c 3 c 4 c 5 c 6 )=( D 1 D 2 D 3 D 4 D 5 D 6 ) e iϕ
S 11 = D 1 M1 C 1 M1  ; S 21 = D 2 M1 C 1 M1 ;    S j3 = D j M1 C 3 M1
S 12 = D 1 M2 C 2 M2 exp( i ϕ M2 ) ; S 22 = D 2 M2 C 2 M2 exp( i ϕ M2 );   S j5 = D j M2 C 5 M2 exp( i ϕ M2 )
e i ϕ M2 = C 3 M2 C 1 M3 [ S 11 D 2 M2 S 21 D 1 M3 ] C 3 M3 [ D 1 M3 D 2 M2 D 2 M3 D 1 M2 ]

Metrics