Abstract

We demonstrate a method that enables reconstruction of waveguide or fiber modes without assuming any optical properties of the test waveguide. The optical low-coherence interferometric technique accounts for the impact of dispersion on the cross-correlation signal. This approach reveals modal content even at small intermodal delays, thus providing a universally applicable method for determining the modal weights, profiles, relative group-delays and dispersion of all guided or quasi-guided (leaky) modes. Our current implementation allows us to measure delays on a femtosecond time-scale, mode discrimination down to about – 30 dB, and dispersion values as high as 500 ps/nm/km. We expect this technique to be especially useful in testing fundamental mode operation of multi-mode structures, prevalent in high-power fiber lasers.

©2011 Optical Society of America

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References

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  1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [Invited],” J. Opt. Soc. Am. B 27, B63–B92 (2010). http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-11-B63
    [Crossref]
  2. D. N. Schimpf, J. Limpert, and A. Tünnermann, “Optimization of high performance ultra-fast fiber laser systems to >10GW peak power,” J. Opt. Soc. Am. B 27, 2051–2060 (2010). http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-10-2051
    [Crossref]
  3. L. Dong, H. A. Mckay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending effective area of fundamental mode in optical fibers,” J. Lightwave Technol. 27, 1565–1570 (2009). http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-27-11-1565
    [Crossref]
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    [Crossref]
  9. S. Blin, D. M. Nguyen, T. N. Nguyen, M. Thual, T. Chartier, and L. Provino, “Simple modal analysis method for multi-mode fibers,” European Conference on Optical Communication (ECOC) (2009), P1.16.
  10. Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
    [Crossref]
  11. P. Nandi, Z. Chen, A. Witkowska, W. J. Wadsworth, T. A. Birks, and J. C. Knight, “Characterization of a photonic crystal fiber mode converter using low coherence interferometry,” Opt. Lett. 34, 1123–1125 (2009). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-7-1123
    [Crossref] [PubMed]
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    [Crossref]
  14. M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12, 2404–2422 (2004). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-11-2404
    [Crossref] [PubMed]
  15. J. F. de Boer, C. E. Saxer, and J. S. Nelson, “Stable carrier generation and phase-resolved digital data processing in optical coherence tomography,” Appl. Opt. 40, 5787–5790 (2001). http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-31-5787 .
    [Crossref]
  16. X. Luo, P. Chen, and Y. Wang, “Power content M2-values smaller than one,” Appl. Phys. B 98, 181185 (2010).
  17. S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15, 15402–15409 (2007). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-23-15402
    [Crossref] [PubMed]
  18. K. G. Jespersen, T. Le, L. Grner-Nielsen, D. Jakobsen, M. E. V. Pederesen, M. B. Smedemand, S. R. Keiding, and B. Palsdottir, “A higher-order-mode fiber delivery for Ti:sapphire femtosecond lasers,” Opt. Express 18, 7798–7806 (2010). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-7798
    [Crossref] [PubMed]
  19. S. Golowich and S. Ramachandran, “Impact of fiber design on polarization dependence in microbend gratings,” Opt. Express 13, 6870–6877 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-18-6870
    [Crossref] [PubMed]

2011 (1)

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. Express 36, 689–691 (2011). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689

2010 (3)

2009 (4)

L. Dong, H. A. Mckay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending effective area of fundamental mode in optical fibers,” J. Lightwave Technol. 27, 1565–1570 (2009). http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-27-11-1565
[Crossref]

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]

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
[Crossref]

P. Nandi, Z. Chen, A. Witkowska, W. J. Wadsworth, T. A. Birks, and J. C. Knight, “Characterization of a photonic crystal fiber mode converter using low coherence interferometry,” Opt. Lett. 34, 1123–1125 (2009). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-7-1123
[Crossref] [PubMed]

2007 (2)

2006 (1)

2005 (2)

2004 (1)

2001 (1)

2000 (1)

1811 (1)

X. Luo, P. Chen, and Y. Wang, “Power content M2-values smaller than one,” Appl. Phys. B 98, 181185 (2010).

Birks, T. A.

Blin, S.

S. Blin, D. M. Nguyen, T. N. Nguyen, M. Thual, T. Chartier, and L. Provino, “Simple modal analysis method for multi-mode fibers,” European Conference on Optical Communication (ECOC) (2009), P1.16.

Chartier, T.

S. Blin, D. M. Nguyen, T. N. Nguyen, M. Thual, T. Chartier, and L. Provino, “Simple modal analysis method for multi-mode fibers,” European Conference on Optical Communication (ECOC) (2009), P1.16.

Chen, P.

X. Luo, P. Chen, and Y. Wang, “Power content M2-values smaller than one,” Appl. Phys. B 98, 181185 (2010).

Chen, Z.

Clarkson, W. A.

de Boer, J. F.

Dimarcello, F. V.

Dong, L.

Duker, J.

Eidam, T.

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. Express 36, 689–691 (2011). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689

Fermann, M. E.

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]

Fu, L.

Fujimoto, J.

Gabet, R.

Galvanauskas, A.

A. Galvanauskas, M. C. Swan, and C.-H. Liu, “Effectively single-mode large core passive and active fibers with chirally coupled-core structures,” paper CMB1, CLEO/QELS, San Jose (2008).

Ghalmi, S.

Goldberg, L.

Golowich, S.

Grner-Nielsen, L.

Hamel, P.

Jakobsen, D.

Jansen, F.

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. Express 36, 689–691 (2011). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689

Jaoun, Y.

Jauregui, C.

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. Express 36, 689–691 (2011). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689

Jespersen, K. G.

Keiding, S. R.

Kliner, D. A. V.

Knight, J. C.

Ko, T.

Koplow, J. P.

Kowalczyk, A.

Le, T.

Leuchs, G.

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
[Crossref]

Li, J.

Limpert, J.

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. Express 36, 689–691 (2011). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689

D. N. Schimpf, J. Limpert, and A. Tünnermann, “Optimization of high performance ultra-fast fiber laser systems to >10GW peak power,” J. Opt. Soc. Am. B 27, 2051–2060 (2010). http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-10-2051
[Crossref]

Liu, C.-H.

A. Galvanauskas, M. C. Swan, and C.-H. Liu, “Effectively single-mode large core passive and active fibers with chirally coupled-core structures,” paper CMB1, CLEO/QELS, San Jose (2008).

Luo, X.

X. Luo, P. Chen, and Y. Wang, “Power content M2-values smaller than one,” Appl. Phys. B 98, 181185 (2010).

Ma, Y. Z.

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
[Crossref]

Marcinkevicius, A.

Mckay, H. A.

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]

Monberg, E.

Nandi, P.

Nelson, J. S.

Nguyen, D. M.

S. Blin, D. M. Nguyen, T. N. Nguyen, M. Thual, T. Chartier, and L. Provino, “Simple modal analysis method for multi-mode fibers,” European Conference on Optical Communication (ECOC) (2009), P1.16.

Nguyen, T. N.

S. Blin, D. M. Nguyen, T. N. Nguyen, M. Thual, T. Chartier, and L. Provino, “Simple modal analysis method for multi-mode fibers,” European Conference on Optical Communication (ECOC) (2009), P1.16.

Nicholson, J. W.

Nilsson, J.

Onishchukov, G.

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
[Crossref]

Palsdottir, B.

Pederesen, M. E. V.

Peschel, U.

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
[Crossref]

Provino, L.

S. Blin, D. M. Nguyen, T. N. Nguyen, M. Thual, T. Chartier, and L. Provino, “Simple modal analysis method for multi-mode fibers,” European Conference on Optical Communication (ECOC) (2009), P1.16.

Ramachandran, S.

Richardson, D. J.

Saxer, C. E.

Schimpf, D. N.

Schmauss, B.

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
[Crossref]

Smedemand, M. B.

Srinivasan, V.

Steinmetz, A.

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. Express 36, 689–691 (2011). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689

Stutzki, F.

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. Express 36, 689–691 (2011). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689

Swan, M. C.

A. Galvanauskas, M. C. Swan, and C.-H. Liu, “Effectively single-mode large core passive and active fibers with chirally coupled-core structures,” paper CMB1, CLEO/QELS, San Jose (2008).

Sych, Y.

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
[Crossref]

Thomas, B. K.

Thual, M.

S. Blin, D. M. Nguyen, T. N. Nguyen, M. Thual, T. Chartier, and L. Provino, “Simple modal analysis method for multi-mode fibers,” European Conference on Optical Communication (ECOC) (2009), P1.16.

Tünnermann, A.

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. Express 36, 689–691 (2011). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689

D. N. Schimpf, J. Limpert, and A. Tünnermann, “Optimization of high performance ultra-fast fiber laser systems to >10GW peak power,” J. Opt. Soc. Am. B 27, 2051–2060 (2010). http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-10-2051
[Crossref]

Wadsworth, W. J.

Wang, Y.

X. Luo, P. Chen, and Y. Wang, “Power content M2-values smaller than one,” Appl. Phys. B 98, 181185 (2010).

Wielandy, S.

Wisk, P.

Witkowska, A.

Wojtkowski, M.

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]

Yan, M. F.

Appl. Opt. (1)

Appl. Phys. B (2)

X. Luo, P. Chen, and Y. Wang, “Power content M2-values smaller than one,” Appl. Phys. B 98, 181185 (2010).

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry, ” Appl. Phys. B 96, 345–353 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

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. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Opt. Express (5)

Opt. Lett. (4)

Other (2)

A. Galvanauskas, M. C. Swan, and C.-H. Liu, “Effectively single-mode large core passive and active fibers with chirally coupled-core structures,” paper CMB1, CLEO/QELS, San Jose (2008).

S. Blin, D. M. Nguyen, T. N. Nguyen, M. Thual, T. Chartier, and L. Provino, “Simple modal analysis method for multi-mode fibers,” European Conference on Optical Communication (ECOC) (2009), P1.16.

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Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental setup (SLD: superluminescent diode), and illustration of the cross-correlation trace expected at one pixel of the stack of images.

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Fig. 2
Fig. 2

(a) Temporal resolution as a function of the FWHM spectral bandwidth of a Gaussian spectrum (for GVD value of ϕ (2) = 0.1ps 2), (b) and as a function of both FWHM bandwidth and GVD.

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Fig. 3
Fig. 3

(a) Cross-correlation trace for the entire image (data is offset corrected) for the bandpass at λcenter =780 nm. (b) and (c), fit of the model to the envelope of the experimental data, for the first and second peak, corresponding to LP01 and LP02, respectively.

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Fig. 4
Fig. 4

(a) Group-delays, and (b) Dispersion values of the two modes as a function of center wavelength of the bandpass.

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Fig. 5
Fig. 5

(a) and (b), reconstructed LP 01 and LP 02-mode (gamma-adjusted) at a center wavelength of 780 nm, (c) multi-path interference (MPI) values as a function of center wavelength of the bandpass.

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Fig. 6
Fig. 6

(a) Spectrum without and after filtering with the 5-nm bandpass, (b) corresponding envelopes of the cross-correlation traces.

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Fig. 7
Fig. 7

Reconstructed mode profiles in order of temporal delay as shown in the cross-correlation trace of Fig. 6(b) for the case of the full spectrum.

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Fig. 8
Fig. 8

(a–c) Output of the fiber under test (near-field images) for different excitations, and corresponding changes in the cross-correlation trace.

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Equations (13)

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

I ( x , y )   =   ∫ − Δ T / 2 + Δ T / 2 d t | E ( x , y , t ) | 2   =   ∫ − ∞ + ∞ d ω 2 π   | E ( x , y , ω ) | 2 ,
E ( x , y , ω )   =   ∑ m α m e m   ( x , y , ω ) A m   ( ω ) e i ϕ m   +   e r   ( x , y , ω ) A r ( ω ) e i ϕ r .
ϕ m   =   β m   ( ω )   ⋅   L .
ϕ r   =   β r   ( ω )   ⋅   L r   +   ω c d ,
I ( x , y )   =   I 0   ( x , y )   +   I int   ( x , y ) ,
I 0   =   ∫ − ∞ + ∞ d ω 2 π ( | e r A r   ( ω ) | 2   +   ∑ m | α m e m A m   ( ω ) | 2   +   ∑ ( m ≠ m ′ ) 2 Re [ α m ′ e m ′ * A m ′ *   ( ω )   α m e m A m   ( ω )   e i ( ϕ m   −   ϕ m ′ ) ] )
I int   =   ∑ m ∫ − ∞ + ∞ d ω 2 π 2 Re [ e r *   ( x , y , ω ) A r *   ( ω )   α m e m   ( x , y ,   ω ) A m   ( ω ) e i ( ϕ m − ϕ r ) ] .
Δ ϕ mr   =   Θ mr   −   ( τ   −   τ mr )   ⋅   Ω   +   Δ ϕ mr   ( Ω ) ,
I int   ( x , y )   =   ∑ m I m ( x , y ,   τ )   =   ∑ m 2 α m Re [ e r *   ( x , y , ω 0 ) ⋅   e m ( x , y ,   ω 0 )   c mr ( τ   −   τ mr )   exp   ( i Θ mr ) ] ,
c mr   ( t )   =   1 2 π   ∫ d Ω   S ( Ω )   exp   ( i Δ ϕ mr   ( Ω ) )   exp ( − i Ω   ⋅   t ) .
I ( x , y )   =   I 0   ( x , y )   +   ∑ m 2 α m   i r   ( x , y ) i m ( x , y )   | c mr   ( τ   −   τ mr ) |   cos   ( ψ ) .
I m   ( x , y ,   τ )   =   α m | e m   ( x , y )   ⋅   e r ( x , y ) | S 0 Δ Ω π   1 ( 1   +   d m 2 ) 1 / 4   exp [ − ( τ   −   τ m r ) 2   Δ Ω 2 4 ( 1   +   d m 2 ) ]   cos   ( ψ ) ,
ψ   =   ϕ m   ( x , y )   +   Θ m r   +   ( τ   −   τ m r ) 2   Δ Ω 2 4 ( 1   +   d m 2 ) d m   +   const ,

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