Abstract

We propose a new solution for modal decomposition in multimode fibers, based on a spectral and spatial imaging technique. The appearance of spurious modes in the spectral and spatial processing of the images at the output of the fiber under test when it has more than two modes is demonstrated theoretically. The new method, which allows us to identify spurious modes, is more accurate, simpler, and faster than previously reported methods. For demonstration, measurements in a standard step-index multimode fiber and a small-core microstructured fiber are carried out successfully.

© 2012 Optical Society of America

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  1. D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
    [CrossRef]
  2. B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon. 5, 141–148 (2011).
  3. O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902–143905 (2005).
    [CrossRef]
  4. N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive characterization of transversal modes in few-mode optical fibers,” Appl. Phys. B 91, 353–357 (2008).
    [CrossRef]
  5. T.-J. Ahn and D. Y. Kim, “High-resolution differential mode delay measurement for a multimode optics fiber using a modified optical frequency domain reflectometer,” Opt. Express 13, 8256–8262 (2005).
    [CrossRef]
  6. S. Ring, D. Menashe, U. Levy, S. Steinblatt, Y. Danziger, and M. Tur, “Characterization in mode coupling in few-mode fibers using optical low-coherence reflectometry,” in Optical Fiber Communication Conference (2008), paper OWO5.
  7. 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]
  8. J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
    [CrossRef]

2011

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon. 5, 141–148 (2011).

2010

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

2009

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[CrossRef]

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]

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

2005

T.-J. Ahn and D. Y. Kim, “High-resolution differential mode delay measurement for a multimode optics fiber using a modified optical frequency domain reflectometer,” Opt. Express 13, 8256–8262 (2005).
[CrossRef]

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902–143905 (2005).
[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, 143902–143905 (2005).
[CrossRef]

Ahn, T.-J.

Andermahr, N.

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

Bramerie, L.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Brilland, L.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Chartier, T.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Coulombier, Q.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Danziger, Y.

S. Ring, D. Menashe, U. Levy, S. Steinblatt, Y. Danziger, and M. Tur, “Characterization in mode coupling in few-mode fibers using optical low-coherence reflectometry,” in Optical Fiber Communication Conference (2008), paper OWO5.

Eggleton, B. J.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon. 5, 141–148 (2011).

Fallnich, C.

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

Fini, J. M.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[CrossRef]

Fink, Y.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902–143905 (2005).
[CrossRef]

Ghalmi, S.

Joannopoulos, J. D.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902–143905 (2005).
[CrossRef]

Kim, D. Y.

Le, S. D.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Lengle, K.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Levy, U.

S. Ring, D. Menashe, U. Levy, S. Steinblatt, Y. Danziger, and M. Tur, “Characterization in mode coupling in few-mode fibers using optical low-coherence reflectometry,” in Optical Fiber Communication Conference (2008), paper OWO5.

Luther-Davies, B.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon. 5, 141–148 (2011).

Mechin, D.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Menashe, D.

S. Ring, D. Menashe, U. Levy, S. Steinblatt, Y. Danziger, and M. Tur, “Characterization in mode coupling in few-mode fibers using optical low-coherence reflectometry,” in Optical Fiber Communication Conference (2008), paper OWO5.

Mermelstein, M. D.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[CrossRef]

Nguyen, D. M.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Nicholson, J. W.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[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]

Ramachandran, S.

Richardson, K.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon. 5, 141–148 (2011).

Ring, S.

S. Ring, D. Menashe, U. Levy, S. Steinblatt, Y. Danziger, and M. Tur, “Characterization in mode coupling in few-mode fibers using optical low-coherence reflectometry,” in Optical Fiber Communication Conference (2008), paper OWO5.

Shapira, O.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902–143905 (2005).
[CrossRef]

Steinblatt, S.

S. Ring, D. Menashe, U. Levy, S. Steinblatt, Y. Danziger, and M. Tur, “Characterization in mode coupling in few-mode fibers using optical low-coherence reflectometry,” in Optical Fiber Communication Conference (2008), paper OWO5.

Theeg, T.

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

Thual, M.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Troles, J.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Tur, M.

S. Ring, D. Menashe, U. Levy, S. Steinblatt, Y. Danziger, and M. Tur, “Characterization in mode coupling in few-mode fibers using optical low-coherence reflectometry,” in Optical Fiber Communication Conference (2008), paper OWO5.

Yablon, A. D.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[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]

Appl. Phys. B

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

IEEE J. Sel. Top. Quantum Electron.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[CrossRef]

IEEE Photon. Technol. Lett.

D. M. Nguyen, S. D. Le, K. Lengle, D. Mechin, M. Thual, T. Chartier, Q. Coulombier, J. Troles, L. Bramerie, and L. Brilland, “Visual system-response functions and estimating reflectance,” IEEE Photon. Technol. Lett. 22, 1844–1846 (2010).
[CrossRef]

Nat. Photon.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon. 5, 141–148 (2011).

Opt. Express

Phys. Rev. Lett.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902–143905 (2005).
[CrossRef]

Other

S. Ring, D. Menashe, U. Levy, S. Steinblatt, Y. Danziger, and M. Tur, “Characterization in mode coupling in few-mode fibers using optical low-coherence reflectometry,” in Optical Fiber Communication Conference (2008), paper OWO5.

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Figures (7)

Fig. 1.
Fig. 1.

(a) Typical spectrum measured at an arbitrary (x,y) point and (b) its Fourier transform showing multiple beat frequencies.

Fig. 2.
Fig. 2.

The Fourier transform when (a) the fiber supports two HOMs LP11 and LP02 and (b) when three HOMs are supported: LP11, LP21, and LP02.

Fig. 3.
Fig. 3.

Experimental setup for the new technique.

Fig. 4.
Fig. 4.

(a) The Fourier transform measured by the new technique for the standard multimode fiber and (b) the HOM profiles and their relative powers.

Fig. 5.
Fig. 5.

(a) Theoretical modes and (b) modes extracted by the technique in the new measurement for the same standard step-index fiber but with the new condition of the optical injection.

Fig. 6.
Fig. 6.

Transverse section of the photonic-crystal fiber. Λ=1.5μm, d=0.75μm.

Fig. 7.
Fig. 7.

Experimental (top) and numerical (bottom) intensity profiles of transverse modes for a small-core photonic-crystal optical fiber.

Tables (1)

Tables Icon

Table 1. Relative Power Calculated by the Previously Published Algorithms and the New Algorithms

Equations (9)

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

Ei(x,y,w)=αi(x,y,w)E0(x,y,w)exp(iwτi),
I(x,y,w)=I0(x,y,w)[1+j=1nαj(x,y,w)eiwτj][1+k=1nαk(x,y,x)eiwτk]=I0(1+j=1nαj2+j=1nαj(eiwτj+eiwτj)+j>knαjαk(eiw(τjτk)+eiw(τjτk)),
B(x,y,τ)=[1+j=1nαj2(x,y)]B0(x,y,τ)+j=1nαj(x,y)[B0(x,y,ττi)+B0(x,y,τ+τi)]+j>knαj(x,y)αk(x,y)[B0(x,y,ττi+τk)+B0(x,y,τ+τiτk)],
fj(x,y)=B(x,y,τ=τj)B(x,y,τ=0)=αj(x,y)1+j=1nαj2(x,y).
fjk(x,y)=B(x,y,τ=τjτk)B(x,y,τ=0)=αj(x,y)αk(x,y)1+j=1nαj2(x,y).
fj(x,y)=αj(x,y)1+αj2(x,y),
fjk(x,y)0.
αj(x,y)=fj(1141nfk2)21nfk2.
Ij(x,y)=IT(x,y)αj2(x,y)1+k=1nαk2,

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