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 OSA

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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]
  4. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultra-large modal areas in optical fibers,” Opt. Lett. 27, 1797–1799 (2006). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-12-1797
    [CrossRef]
  5. 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).
  6. 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
  7. J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-25-7-442
    [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]
  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]
  12. P. Hamel, Y. Jaoun, R. Gabet, and S. Ramachandran, “Optical low-coherence reflectometry for complete chromatic dispersion characterization of few-mode fibers,” Opt. Lett. 32, 1029–1031 (2007). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-9-1029
    [CrossRef] [PubMed]
  13. S. Ramachandran, “Dispersion-tailored few-mode fibers: a versatile platform for in-fiber photonic devices,” J. Lightwave Technol. 23, 3426–3443 (2005).
    [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]

2009 (2)

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]

2005 (1)

1811 (1)

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

Chen, P.

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

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]

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]

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]

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]

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]

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]

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]

Ramachandran, S.

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]

S. Ramachandran, “Dispersion-tailored few-mode fibers: a versatile platform for in-fiber photonic devices,” J. Lightwave Technol. 23, 3426–3443 (2005).
[CrossRef]

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]

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]

Wang, Y.

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

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]

Appl. Phys. B (2)

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]

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

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. (1)

Other (15)

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.

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]

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]

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]

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]

P. Hamel, Y. Jaoun, R. Gabet, and S. Ramachandran, “Optical low-coherence reflectometry for complete chromatic dispersion characterization of few-mode fibers,” Opt. Lett. 32, 1029–1031 (2007). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-9-1029
[CrossRef] [PubMed]

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]

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]

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]

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]

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]

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultra-large modal areas in optical fibers,” Opt. Lett. 27, 1797–1799 (2006). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-12-1797
[CrossRef]

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).

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

J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-25-7-442
[CrossRef]

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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.

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.

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.

Fig. 4
Fig. 4

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

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.

Fig. 6
Fig. 6

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

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.

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.

Equations (13)

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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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