Abstract

We present a novel approach to directly measure the bend loss of individual modes in few-mode fibers based on the correlation filter technique. This technique benefits from a computer-generated hologram performing a modal decomposition, yielding the optical power of all propagating modes in the bent fiber. Results are compared with rigorous loss simulations and with common loss formulas for step-index fibers revealing high measurement fidelity. To the best of our knowledge, we demonstrate for the first time an experimental loss discrimination between index-degenerated modes.

© 2013 OSA

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References

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    [CrossRef]

2012

2011

2010

2009

2008

2007

2006

2005

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, S. N. Khonina, M. Duparré, B. Luedge, and J. Turunen, “Transverse mode multiplexing by diffractive optical elements,” Proc. SPIE 5854, Optical Technologies for Telecommunications, 1 (2005), doi:.
[CrossRef]

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

2002

2000

1997

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol.15, 671–679 (1997).
[CrossRef]

1994

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114, 185–200 (1994).
[CrossRef]

1992

H. Renner, “Bending losses of coated single-mode fibers: a simple approach,” J. Lightwave Technol.10, 544–551 (1992).
[CrossRef]

1986

A. Harris and P. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol.4, 34–40 (1986).
[CrossRef]

1985

N. Shibata and M. Tsubokawa, “Bending loss measurement of LP11 mode in quasi-single-mode operation region,” Electron. Lett.21, 1042–1043 (1985).
[CrossRef]

1984

1982

D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt.21, 4208–4213 (1982).
[CrossRef] [PubMed]

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

1980

1979

1976

1975

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quant. Electron.11, 75–83 (1975).
[CrossRef]

1972

1959

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys.30, 779 –788 (1959).
[CrossRef]

1902

F. Pockels, “Über die Änderung des optischen Verhaltens verschiedener Gläser durch elastische Deformation,” Ann. Phys.312, 745–771 (1902).
[CrossRef]

Barankov, R. A.

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114, 185–200 (1994).
[CrossRef]

Borchardt, J.

Brüning, R.

Castle, P.

A. Harris and P. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol.4, 34–40 (1986).
[CrossRef]

Cole, J.

R. Schermer and J. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quant. Electron.43, 899–909 (2007).
[CrossRef]

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 polarizations,” Opt. Commun.252, 12–21 (2005).
[CrossRef]

Doskolovich, L. L.

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, L. L. Doskolovich, M. R. Duparré, and B. Luedge, “Mode multiplexing by diffractive optical elements in optical telecommunication,” Proc. SPIE 5480, Laser Optics 2003: Diode Lasers and Telecommunication Systems, 153 (2004), doi:.
[CrossRef]

Duparré, M.

Duparré, M. R.

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, L. L. Doskolovich, M. R. Duparré, and B. Luedge, “Mode multiplexing by diffractive optical elements in optical telecommunication,” Proc. SPIE 5480, Laser Optics 2003: Diode Lasers and Telecommunication Systems, 153 (2004), doi:.
[CrossRef]

Eickhoff, W.

Faustini, L.

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol.15, 671–679 (1997).
[CrossRef]

Fini, J. M.

Flamm, D.

Fleming, J. W.

Forbes, A.

Ghalmi, S.

Gloge, D.

Goldberg, L.

Golub, M. A.

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

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 polarizations,” Opt. Commun.252, 12–21 (2005).
[CrossRef]

Harris, A.

A. Harris and P. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol.4, 34–40 (1986).
[CrossRef]

Harris, J.

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quant. Electron.11, 75–83 (1975).
[CrossRef]

Heiblum, M.

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quant. Electron.11, 75–83 (1975).
[CrossRef]

Kaiser, T.

Karpeev, S. V.

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, S. N. Khonina, M. Duparré, B. Luedge, and J. Turunen, “Transverse mode multiplexing by diffractive optical elements,” Proc. SPIE 5854, Optical Technologies for Telecommunications, 1 (2005), doi:.
[CrossRef]

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, L. L. Doskolovich, M. R. Duparré, and B. Luedge, “Mode multiplexing by diffractive optical elements in optical telecommunication,” Proc. SPIE 5480, Laser Optics 2003: Diode Lasers and Telecommunication Systems, 153 (2004), doi:.
[CrossRef]

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings (Optics and Photonics) (Academic Press, 1999).

Khonina, S. N.

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, S. N. Khonina, M. Duparré, B. Luedge, and J. Turunen, “Transverse mode multiplexing by diffractive optical elements,” Proc. SPIE 5854, Optical Technologies for Telecommunications, 1 (2005), doi:.
[CrossRef]

Kliner, D. A. V.

Koplow, J. P.

Lee, W.-H.

Love, J. D.

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

Luedge, B.

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, S. N. Khonina, M. Duparré, B. Luedge, and J. Turunen, “Transverse mode multiplexing by diffractive optical elements,” Proc. SPIE 5854, Optical Technologies for Telecommunications, 1 (2005), doi:.
[CrossRef]

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, L. L. Doskolovich, M. R. Duparré, and B. Luedge, “Mode multiplexing by diffractive optical elements in optical telecommunication,” Proc. SPIE 5480, Laser Optics 2003: Diode Lasers and Telecommunication Systems, 153 (2004), doi:.
[CrossRef]

Marcuse, D.

Martini, G.

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol.15, 671–679 (1997).
[CrossRef]

Moore, S. W.

Naidoo, D.

Nicholson, J. W.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides, Second Edition (Optics and Photonics Series) (Academic Press, 2005).

Pavelyev, V. S.

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, S. N. Khonina, M. Duparré, B. Luedge, and J. Turunen, “Transverse mode multiplexing by diffractive optical elements,” Proc. SPIE 5854, Optical Technologies for Telecommunications, 1 (2005), doi:.
[CrossRef]

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, L. L. Doskolovich, M. R. Duparré, and B. Luedge, “Mode multiplexing by diffractive optical elements in optical telecommunication,” Proc. SPIE 5480, Laser Optics 2003: Diode Lasers and Telecommunication Systems, 153 (2004), doi:.
[CrossRef]

Pockels, F.

F. Pockels, “Über die Änderung des optischen Verhaltens verschiedener Gläser durch elastische Deformation,” Ann. Phys.312, 745–771 (1902).
[CrossRef]

Post, D.

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys.30, 779 –788 (1959).
[CrossRef]

Primak, W.

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys.30, 779 –788 (1959).
[CrossRef]

Prokhorov, A. M.

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

Ramachandran, S.

Rashleigh, S. C.

Renner, H.

H. Renner, “Bending losses of coated single-mode fibers: a simple approach,” J. Lightwave Technol.10, 544–551 (1992).
[CrossRef]

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 polarizations,” Opt. Commun.252, 12–21 (2005).
[CrossRef]

Sakai, J.

Scherer, G. W.

Schermer, R.

R. Schermer and J. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quant. Electron.43, 899–909 (2007).
[CrossRef]

Schermer, R. T.

Schimpf, D. N.

Schmidt, O. A.

Schröter, S.

Schulze, C.

Shibata, N.

N. Shibata and M. Tsubokawa, “Bending loss measurement of LP11 mode in quasi-single-mode operation region,” Electron. Lett.21, 1042–1043 (1985).
[CrossRef]

Sisakian, I. N.

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

Snyder, A. W.

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

Soifer, V. A.

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, S. N. Khonina, M. Duparré, B. Luedge, and J. Turunen, “Transverse mode multiplexing by diffractive optical elements,” Proc. SPIE 5854, Optical Technologies for Telecommunications, 1 (2005), doi:.
[CrossRef]

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

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, L. L. Doskolovich, M. R. Duparré, and B. Luedge, “Mode multiplexing by diffractive optical elements in optical telecommunication,” Proc. SPIE 5480, Laser Optics 2003: Diode Lasers and Telecommunication Systems, 153 (2004), doi:.
[CrossRef]

Teodoro, F. D.

Tsubokawa, M.

N. Shibata and M. Tsubokawa, “Bending loss measurement of LP11 mode in quasi-single-mode operation region,” Electron. Lett.21, 1042–1043 (1985).
[CrossRef]

Turunen, J.

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, S. N. Khonina, M. Duparré, B. Luedge, and J. Turunen, “Transverse mode multiplexing by diffractive optical elements,” Proc. SPIE 5854, Optical Technologies for Telecommunications, 1 (2005), doi:.
[CrossRef]

Ulrich, R.

Wang, Z.

Yablon, A. D.

Yuan, X.-C.

Zhang, N.

Ann. Phys.

F. Pockels, “Über die Änderung des optischen Verhaltens verschiedener Gläser durch elastische Deformation,” Ann. Phys.312, 745–771 (1902).
[CrossRef]

Appl. Opt.

Electron. Lett.

N. Shibata and M. Tsubokawa, “Bending loss measurement of LP11 mode in quasi-single-mode operation region,” Electron. Lett.21, 1042–1043 (1985).
[CrossRef]

IEEE J. Quant. Electron.

R. Schermer and J. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quant. Electron.43, 899–909 (2007).
[CrossRef]

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quant. Electron.11, 75–83 (1975).
[CrossRef]

J. Appl. Phys.

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys.30, 779 –788 (1959).
[CrossRef]

J. Comput. Phys.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114, 185–200 (1994).
[CrossRef]

J. Lightwave Technol.

H. Renner, “Bending losses of coated single-mode fibers: a simple approach,” J. Lightwave Technol.10, 544–551 (1992).
[CrossRef]

A. Harris and P. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol.4, 34–40 (1986).
[CrossRef]

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol.15, 671–679 (1997).
[CrossRef]

J. Opt. Soc. Am.

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 polarizations,” Opt. Commun.252, 12–21 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE 5854, Optical Technologies for Telecommunications

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, S. N. Khonina, M. Duparré, B. Luedge, and J. Turunen, “Transverse mode multiplexing by diffractive optical elements,” Proc. SPIE 5854, Optical Technologies for Telecommunications, 1 (2005), doi:.
[CrossRef]

Sov. J. Quantum Electron.

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

Other

K. Okamoto, Fundamentals of Optical Waveguides, Second Edition (Optics and Photonics Series) (Academic Press, 2005).

S. V. Karpeev, V. S. Pavelyev, V. A. Soifer, L. L. Doskolovich, M. R. Duparré, and B. Luedge, “Mode multiplexing by diffractive optical elements in optical telecommunication,” Proc. SPIE 5480, Laser Optics 2003: Diode Lasers and Telecommunication Systems, 153 (2004), doi:.
[CrossRef]

IEC, “Optical fibres - Part 1-44: Measurement methods and test procedures - Cut-off wavelength (IEC 60793-1-44:2011),” (2012).

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

R. Kashyap, Fiber Bragg Gratings (Optics and Photonics) (Academic Press, 1999).

Supplementary Material (1)

» Media 1: MPEG (174 KB)     

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Figures (6)

Fig. 1
Fig. 1

Section of the refractive index profile in the radial direction for (a) a straight fiber and (b) a bent fiber using conformal mapping. The horizontal red line corresponds to the fundamental mode’s effective mode index. The blue curve illustrates its intensity distribution.

Fig. 2
Fig. 2

(a) Difference of transmission spectra of the investigated fiber with and without a bend around a mandrel yielding an LP11 mode cut-off at λc = 1209 nm. (b) The reflection spectrum from the fiber Bragg grating with peaks at λLP01 = 1079.86 nm and λLP11 = 1077.96 nm. Additionally the plots include (blue) the material refractive indices ncore, nclad including dispersion [28], as well as the effective mode indices nLP01, nLP11, and (black) the Bragg condition Eq. (9).

Fig. 3
Fig. 3

Hologram illumination with pure modes and resulting correlation signals for the LP01, LP11e, and LP11o modes (dots and arrows mark the position of the intensity signals ILP01, ILP11e, and ILP11o being proportional to the mode powers ρ LP 01 2, ρ LP 11 e 2, and ρ LP 11 o 2). (a) Measured near field of a pure LP01 mode beam. (b) Corresponding measured correlation signals. (c) Simulation of the diffraction of a LP01 mode beam illuminating a hologram encoding the LP11e mode only, and propagation through a 2f -setup. (d) Measured near field of a pure LP11e mode beam. (e) Corresponding measured correlation signals. (f) Simulation of the diffraction of a LP11e mode beam illuminating a hologram encoding the LP11e mode only, and propagation through a 2f -setup. Intensities are normalized.

Fig. 4
Fig. 4

Experimental setup. (a) LS - laser source, MO1,2 - microscope objectives, DB -bending diameter, P - polarizer, L1,2 - lenses, BS - beam splitter, CGH - computer-generated hologram, CCD1,2 - cameras. (b) Scheme of the metal plate with half-circle grooves. (c) Scheme of the fiber coiled around a mandrel with a stable loop at the end.

Fig. 5
Fig. 5

Relative modal powers as a function of bending diameter DB (dashed lines to guide the eye). The mode intensity distributions are depicted on the right for the straight and bent fiber (DB = 1.5cm, bending in x-z-plane with bending center in direction of −x). The corresponding measured beam intensities (CCD1 in Fig. 4) as a function of bending diameter are shown in Media 1.

Fig. 6
Fig. 6

Modal power loss 2α as a function of bending diameter DB for (a) the fundamental mode LP01 and (b) the higher-order modes LP11e and LP11o. (CGH) modal decomposition measurements, (FEM) rigorous loss simulations by FEM, (ana) analytically calculated loss after Eq. (6).

Equations (14)

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n equ ( x , y ) = n mat ( x , y ) exp ( x R ) n mat ( x , y ) ( 1 + x R )
Δ n i = n i n 0 = B 2 σ i B 1 ( σ j + σ k )
n mat ( x , y ) = n 0 + Δ n x , y = n 0 + x R [ B 2 C 12 B 1 ( C 12 + C 11 ) ]
R eff = R 1 1 n [ B 2 C 12 + B 1 ( C 12 + C 11 ) ] 1.40 R
n equ = n mat ( 1 + x R ) = n 0 ( 1 + x R eff )
2 α [ dB m ] = 10 ln ( 10 ) π 1 2 κ 2 exp [ 2 γ 3 ( R + R core ) eff 3 β 2 2 γ R core ] e m ( R + R core ) eff 1 2 γ 3 2 V 2 K m 1 ( γ R core ) K m + 1 ( γ R core )
2 α = 20 ln ( 10 ) 2 π λ Im ( n eff )
λ c = 2 π R core NA 2.405 .
λ LPmn = 2 n LPmn Λ
λ LP 01 λ LP1 1 = n LP 01 n LP 11
U ( r ) = l = 1 N c l ψ l ( r ) ,
C ( r ) = A 0 d 2 r T ˜ [ 2 π λ f r ] U ˜ [ 2 π λ f ( r r ) ]
T ( r ) = l = 1 N ψ l * ( r ) e i K l r .
2 α l = 10 L log 10 ( ρ l 2 ( D B = 30 cm ) ρ l 2 ( D B ) ) .

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