Abstract

We implement cross-correlated imaging in the frequency domain (fC2) in order to reconstruct different modes propagating in a multi-mode optical fiber, and measure their relative powers. Our system can complete measurements in under a second (950 ms), with a maximum signal to noise ratio of 25 dB. The system is capable of group-delay temporal resolution as high as 720 fs, and this number can be tailored for a variety of modal discrimination levels by choice of apodization functions and effective bandwidths of the tunable source we use. Measurements are made on a double-clad test fiber to demonstrate simultaneous reconstruction of six guided modes. Finally, the system is used to optimize alignment into the fiber under test and achieve mono-mode purity > 95%, underscoring the utility of fC2 imaging for near-real-time modal content analysis.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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2014 (3)

2012 (2)

2011 (1)

2010 (1)

2009 (1)

Y. 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(2-3), 345–353 (2009).
[Crossref]

2008 (2)

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

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

2007 (2)

2006 (2)

2005 (2)

S. Ramachandran, “Dispersion Tailored Few-Mode Fibers: A Versatile Platform for In-Fiber Photonic Devices,” J. Lightwave Technol. 23(11), 3426–3443 (2005).
[Crossref]

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]

2004 (1)

2003 (1)

S. Ramachandran, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Measurement of Multipath Interference in the Coherent Crosstalk Regime,” IEEE Photon. Technol. Lett. 15(8), 1171–1173 (2003).
[Crossref]

1998 (1)

1994 (1)

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical Fiber-Based Dispersion Compensation Using Higher Order Modes Near Cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994).
[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(14), 143902 (2005).
[Crossref] [PubMed]

Andermahr, N.

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Baek, S.

Barankov, R. A.

Baskiotis, C.

D. Jain, C. Baskiotis, T. C. May-Smith, J. Kim, and J. K. Sahu, “Large Mode Area Multi-Trench Fiber With Delocalization of Higher Order Modes,” IEEE J. Quantum Electron. 20, 0902909–0902917 (2014).

Bolle, C.

Borghi, R.

Burrows, E. C.

Carpenter, J.

Chen, Y.

Clarkson, W. A.

Codemard, C.

Demas, J.

DiGiovanni, D. J.

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical Fiber-Based Dispersion Compensation Using Higher Order Modes Near Cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994).
[Crossref]

Dimarcello, F. V.

Duparré, M.

Eggleton, B. J.

Esmaeelpour, M.

Essiambre, R. J.

Fallnich, C.

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

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.

Fujimoto, J. G.

Ghalmi, S.

Gnauck, A. H.

Gori, F.

Guattari, G.

Huber, R.

Jain, D.

D. Jain, C. Baskiotis, T. C. May-Smith, J. Kim, and J. K. Sahu, “Large Mode Area Multi-Trench Fiber With Delocalization of Higher Order Modes,” IEEE J. Quantum Electron. 20, 0902909–0902917 (2014).

Jeong, Y.

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]

Kim, J.

D. Jain, C. Baskiotis, T. C. May-Smith, J. Kim, and J. K. Sahu, “Large Mode Area Multi-Trench Fiber With Delocalization of Higher Order Modes,” IEEE J. Quantum Electron. 20, 0902909–0902917 (2014).

Leuchs, G.

Y. 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(2-3), 345–353 (2009).
[Crossref]

N. Lindlein, G. Leuchs, and S. Ramachandran, “Achieving Gaussian outputs from large-mode-area higher-order-mode fibers,” Appl. Opt. 46(22), 5147–5157 (2007).
[Crossref] [PubMed]

Lindlein, N.

Lingle, R.

Ma, Y.

Y. 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(2-3), 345–353 (2009).
[Crossref]

May-Smith, T. C.

D. Jain, C. Baskiotis, T. C. May-Smith, J. Kim, and J. K. Sahu, “Large Mode Area Multi-Trench Fiber With Delocalization of Higher Order Modes,” IEEE J. Quantum Electron. 20, 0902909–0902917 (2014).

McCurdy, A. H.

Monberg, E.

Mumtaz, S.

Naidoo, D.

Nicholson, J. W.

Nilsson, J.

Onishchukov, G.

Y. 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(2-3), 345–353 (2009).
[Crossref]

Peckham, D. W.

Peschel, U.

Y. 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(2-3), 345–353 (2009).
[Crossref]

Philippov, V.

Poole, C. D.

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical Fiber-Based Dispersion Compensation Using Higher Order Modes Near Cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994).
[Crossref]

Ramachandran, S.

P. Steinvurzel, J. Demas, B. Tai, Y. Chen, L. Yan, and S. Ramachandran, “Broadband parametric wavelength conversion at 1 μm with large mode area fibers,” Opt. Lett. 39(4), 743–746 (2014).
[Crossref] [PubMed]

D. N. Schimpf, R. A. Barankov, and S. Ramachandran, “Cross-correlated imaging of fiber and waveguide modes,” Opt. Express 19(14), 13008–13019 (2011).
[Crossref] [PubMed]

Y. 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(2-3), 345–353 (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(10), 7233–7243 (2008).
[Crossref] [PubMed]

N. Lindlein, G. Leuchs, and S. Ramachandran, “Achieving Gaussian outputs from large-mode-area higher-order-mode fibers,” Appl. Opt. 46(22), 5147–5157 (2007).
[Crossref] [PubMed]

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31(12), 1797–1799 (2006).
[Crossref] [PubMed]

S. Ramachandran, “Dispersion Tailored Few-Mode Fibers: A Versatile Platform for In-Fiber Photonic Devices,” J. Lightwave Technol. 23(11), 3426–3443 (2005).
[Crossref]

S. Ramachandran, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Measurement of Multipath Interference in the Coherent Crosstalk Regime,” IEEE Photon. Technol. Lett. 15(8), 1171–1173 (2003).
[Crossref]

Randel, S.

Richardson, D. J.

Ryf, R.

Sahu, J. K.

D. Jain, C. Baskiotis, T. C. May-Smith, J. Kim, and J. K. Sahu, “Large Mode Area Multi-Trench Fiber With Delocalization of Higher Order Modes,” IEEE J. Quantum Electron. 20, 0902909–0902917 (2014).

Santarsiero, M.

Schimpf, D. N.

Schmauss, B.

Y. 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(2-3), 345–353 (2009).
[Crossref]

Schröder, J.

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]

Sierra, A.

Soh, D. B. S.

Steinvurzel, P.

Sych, Y.

Y. 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(2-3), 345–353 (2009).
[Crossref]

Tai, B.

Theeg, T.

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Vengsarkar, A. M.

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical Fiber-Based Dispersion Compensation Using Higher Order Modes Near Cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994).
[Crossref]

Wielandy, S.

Wiesenfeld, J. M.

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical Fiber-Based Dispersion Compensation Using Higher Order Modes Near Cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994).
[Crossref]

Winzer, P. J.

Wisk, P.

Wojtkowski, M.

Yablon, A. D.

Yan, L.

Yan, M. F.

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31(12), 1797–1799 (2006).
[Crossref] [PubMed]

S. Ramachandran, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Measurement of Multipath Interference in the Coherent Crosstalk Regime,” IEEE Photon. Technol. Lett. 15(8), 1171–1173 (2003).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (2)

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Y. 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(2-3), 345–353 (2009).
[Crossref]

IEEE J. Quantum Electron. (1)

D. Jain, C. Baskiotis, T. C. May-Smith, J. Kim, and J. K. Sahu, “Large Mode Area Multi-Trench Fiber With Delocalization of Higher Order Modes,” IEEE J. Quantum Electron. 20, 0902909–0902917 (2014).

IEEE Photon. Technol. Lett. (1)

S. Ramachandran, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Measurement of Multipath Interference in the Coherent Crosstalk Regime,” IEEE Photon. Technol. Lett. 15(8), 1171–1173 (2003).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Express (5)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

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]

Other (4)

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (John Wiley & Sons, Inc., 1999).

R. Kashyap, Fiber Bragg Gratings Ch. 5 (Acad. Press1999).

Y. Chen, P. Gregg, and S. Ramachandran, “Fiber Mode Excitation via Free-Space Beam Shaping,” in Conference on Lasers and Electro-optics 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper CTu3K.4.
[Crossref]

R. A. Barankov, “Cross-correlation (C2) imaging for waveguide characterization,” M.S. Thesis, Boston University (2012).

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Figures (6)

Fig. 1
Fig. 1 (a) Various apodized input spectra including: Gaussian (blue), 4th (green), 6th (yellow), and 12th (orange) order super-Gaussians, and the un-apodized case (red); (b) |C(t)|2 for all cases (offset for clarity); (c) the envelopes of the functions in (b) shown for t>0; the −15 dB point is marked with a dashed line – above the line the un-apodized case is narrowest, below it the Gaussian-apodized function is narrowest; (d) Group delay resolution as a function of MPI between a dominant and parasitic C2 signal for each apodization function.
Fig. 2
Fig. 2 (a) The effect of GVD times length mismatch on |C(t)|2 with no apodization; (b) the effect of GVD times length mismatch on |C(t)|2 with Gaussian apodization; note that the legends for (a) and (b) describe different GVD times length values.
Fig. 3
Fig. 3 (a) Experimental setup for fC2 imaging facilitated by a tunable external cavity laser split into three arms: monitor (orange), reference (green), and fiber under test (FUT, red), all combined on a CMOS camera; (b) Sample image frame showing the monitor beam (orange) spatially decorrelated from the interfering reference (green) and fiber under test (FUT, red) beams.
Fig. 4
Fig. 4 (a) Average of 5 S(t) traces, each measured in 950 ms, used for the calculation of signal to noise ratio (SNR); blue-shaded region corresponds to DC, red-shaded region is anticipated C2 peak, green-shaded region is noise; (b) Maximum SNR for our system as a function of measurement time – all subsequent measurements are performed with a speed of 950 ms/measurement.
Fig. 5
Fig. 5 (a) Facet image of the double-clad FUT used for multi-mode experiments with the core (I), inner cladding (II), and outer-cladding (III) marked; (b) S(t) trace for a mixture of modes excited in the test fiber (output of the fiber under this excitation condition inset in trace), images (i) through (vi) are points of interest in the S(t) trace reconstructed with gamma correction for visibility; (c) Comparison of simulated and measured relative delays for the excited modes in 1.13 meters of test fiber.
Fig. 6
Fig. 6 (a); (b) S(t) traces as a function of the alignment of the FUT with respect to the coupling lens; the red shaded portion of each trace corresponds to signal in the LP0,5 mode; (c) Reconstruction of the dominant parasitic mode LP1,4; (c) Reconstruction of the desired LP0,5 mode for worst case alignment; significant power is coupled in to the LP2,4 mode which is near-degenerate in group delay with the LP0,5 mode – thus the reconstruction at this delay value (shown above the −2 μm trace) is a coherent superposition of the two.

Equations (13)

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I ( x , y , ω ) = α r 2 I r A ˜ ( ω ) + m α m 2 I m A ˜ ( ω ) + m α r α m Φ r Φ m * A ˜ ( ω ) e i ( β r L r β m L f ) e i ω τ + m n n α m α n Φ m Φ n * A ˜ ( ω ) e i ( β m β n ) L f ,
I ( x , y , t ) = 1 2 π ( α r 2 I r + m α m 2 I m ) A ( t ) + m α r α m Φ r Φ m * C m r ( t τ τ m r ) + c . c . + m n m α m α n Φ m Φ n * C m n ( t τ m n ) + c . c .
C m r ( t τ τ m r ) = 1 2 π e i Θ m r d Δ ω A ˜ ( Δ ω ) e i Δ φ m r e i Δ ω ( t τ τ m r )
Θ m r ω 0 t ω 0 τ + β r ( 0 ) L r β m ( 0 ) L f
τ m r β m ( 1 ) L f β r ( 1 ) L r
Δ φ m r k 2 Δ ω k k ! ( β r ( k ) L r β m ( k ) L f )
s ( x , y , t ) = I ( x , y , t ) α r Φ r = 1 2 π ψ D C ( x , y ) A ( t ) + m α m Φ m * C m r ( t τ τ m r ) + c . c . + m n m ψ m n ( x , y ) C m n ( t τ m n ) + c . c .
ψ D C ( x , y ) = α r Φ r + m α m 2 I m α r Φ r
ψ m n ( x , y ) = α m α n α r Φ m Φ n * Φ r
S ( x , y , t ) = | s ( x , y , t ) | 2 = | s D C | 2 + | s C 2 | 2 + | s B G | 2 + s D C s C 2 * + c . c . + s D C s B G * + c . c . + s C 2 s B G * + c . c . | s D C | 2 + | s C 2 | 2 + | s B G | 2
S ( x , y , t ) = | ψ D C A ( t ) | 2 2 π + m α m 2 I m | C m r ( t τ τ m r ) | 2 + c . c . + m n m | ψ m n C m n ( t τ m n ) | 2 + c . c .
A ˜ ( ω ) = A 0 r e c t ( Δ ω Δ Ω ) e ( Δ ω Δ Ω N ) N A 0 e ( Δ ω Δ Ω N ) N
t F W H M = 5.56 Δ Ω = 5.56 λ 0 2 2 π Δ λ c

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