Abstract

A new measurement technique, capable of quantifying the number and type of modes propagating in large-mode-area fibers is both proposed and demonstrated. The measurement is based on both spatially and spectrally resolving the image of the output of the fiber under test. The measurement provides high quality images of the modes that can be used to identify the mode order, while at the same time returning the power levels of the higher-order modes relative to the fundamental mode. Alternatively the data can be used to provide statistics on the level of beam pointing instability and mode shape changes due to random uncontrolled fluctuations of the phases between the coherent modes propagating in the fiber. An added advantage of the measurement is that is requires no prior detailed knowledge of the fiber properties in order to identify the modes and quantify their relative power levels. Because of the coherent nature of the measurement, it is far more sensitive to changes in beam properties due to the mode content in the beam than is the more traditional M2 measurement for characterizing beam quality. We refer to the measurement as Spatially and Spectrally resolved imaging of mode content in fibers, or more simply as S2 imaging.

©2008 Optical Society of America

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References

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2007 (3)

S. Wielandy, “Implications of Higher-Order Mode Content in LargeMode Area Fibers with Good Beam Quality,” Opt. Express 15, 15,402–15,409 (2007).
[Crossref]

C. Rydberg and J. Bengtsson, “Numerical Algorithm for the Retrieval of Spatial Coherence Properties of Partially Coherent Beams from Transverse Intensity Measurements,” Opt. Express 15, 13,613–13,623 (2007).
[Crossref]

J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headley, “Demonstration of Bend-Induced Nonlinearities in Large-Mode-Area Fibers,” Opt. Lett. 32, 2562–2564 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (2)

S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, and L. L. Buhl, “Evolution and Systems Impact of Coherent Distributed Multipath Interference,” IEEE Photon. Technol. Lett. 17, 238–240 (2005).
[Crossref]

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete Modal Decomposition for Optical Waveguides,” Phys. Rev. Lett. 94, 143,902 (2005).
[Crossref]

2004 (1)

2003 (2)

M. Skorobogatiy, C. Anastassiou, S. G. Johnson, O. Weisberg, T. D. Engeness, S. A. Jacobs, R. U. Ahmad, and Y. Fink, “Quantitative Characterization of Higher-Order Mode Converters in Weakly Multi-Moded Fibers,” Opt. Express 11, 2838–2847 (2003).
[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, 1171–1173 (2003).
[Crossref]

2001 (1)

1998 (2)

1982 (1)

Abouraddy, A. F.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete Modal Decomposition for Optical Waveguides,” Phys. Rev. Lett. 94, 143,902 (2005).
[Crossref]

Ahmad, R. U.

Anastassiou, C.

Baek, S.

Bengtsson, J.

C. Rydberg and J. Bengtsson, “Numerical Algorithm for the Retrieval of Spatial Coherence Properties of Partially Coherent Beams from Transverse Intensity Measurements,” Opt. Express 15, 13,613–13,623 (2007).
[Crossref]

Borghi, R.

Bromage, J.

S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, and L. L. Buhl, “Evolution and Systems Impact of Coherent Distributed Multipath Interference,” IEEE Photon. Technol. Lett. 17, 238–240 (2005).
[Crossref]

Buhl, L. L.

S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, and L. L. Buhl, “Evolution and Systems Impact of Coherent Distributed Multipath Interference,” IEEE Photon. Technol. Lett. 17, 238–240 (2005).
[Crossref]

Chandrasekhar, S.

S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, and L. L. Buhl, “Evolution and Systems Impact of Coherent Distributed Multipath Interference,” IEEE Photon. Technol. Lett. 17, 238–240 (2005).
[Crossref]

Codemard, C.

Engeness, T. D.

Feder, K.

Fermann, M. E.

Fienup, J. R.

Fini, J. M.

Fink, Y.

Fludger, C. R. S.

Ghalmi, S.

S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, and L. L. Buhl, “Evolution and Systems Impact of Coherent Distributed Multipath Interference,” IEEE Photon. Technol. Lett. 17, 238–240 (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, 1171–1173 (2003).
[Crossref]

Gori, F.

Guattari, G.

Headley, C.

Jacobs, S. A.

Jeong, Y. C.

Joannopoulos, J. D.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete Modal Decomposition for Optical Waveguides,” Phys. Rev. Lett. 94, 143,902 (2005).
[Crossref]

Johnson, S. G.

Mansuripur, M.

Mears, R. J.

Nicholson, J. W.

J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headley, “Demonstration of Bend-Induced Nonlinearities in Large-Mode-Area Fibers,” Opt. Lett. 32, 2562–2564 (2007).
[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, 1171–1173 (2003).
[Crossref]

Nilsson, J.

Philippov, V.

Polynkin, O.

Ramachandran, S.

S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, and L. L. Buhl, “Evolution and Systems Impact of Coherent Distributed Multipath Interference,” IEEE Photon. Technol. Lett. 17, 238–240 (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, 1171–1173 (2003).
[Crossref]

Rydberg, C.

C. Rydberg and J. Bengtsson, “Numerical Algorithm for the Retrieval of Spatial Coherence Properties of Partially Coherent Beams from Transverse Intensity Measurements,” Opt. Express 15, 13,613–13,623 (2007).
[Crossref]

Santarsiero, M.

Shapira, O.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete Modal Decomposition for Optical Waveguides,” Phys. Rev. Lett. 94, 143,902 (2005).
[Crossref]

Siegman, A. E.

A. E. Siegman, “Defining, Measuring, and Optimizing Laser Beam Quality,” in Proc. SPIE, 2 (1993).

Skorobogatiy, M.

Soh, D. B. S.

Weisberg, O.

Westbrook, P. S.

Wielandy, S.

S. Wielandy, “Implications of Higher-Order Mode Content in LargeMode Area Fibers with Good Beam Quality,” Opt. Express 15, 15,402–15,409 (2007).
[Crossref]

Yablon, A. D.

Yan, M. F.

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, 1171–1173 (2003).
[Crossref]

Yoda, H.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (2)

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, 1171–1173 (2003).
[Crossref]

S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, and L. L. Buhl, “Evolution and Systems Impact of Coherent Distributed Multipath Interference,” IEEE Photon. Technol. Lett. 17, 238–240 (2005).
[Crossref]

J. Lightwave Technol. (2)

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

Opt. Express (4)

C. Rydberg and J. Bengtsson, “Numerical Algorithm for the Retrieval of Spatial Coherence Properties of Partially Coherent Beams from Transverse Intensity Measurements,” Opt. Express 15, 13,613–13,623 (2007).
[Crossref]

M. Skorobogatiy, C. Anastassiou, S. G. Johnson, O. Weisberg, T. D. Engeness, S. A. Jacobs, R. U. Ahmad, and Y. Fink, “Quantitative Characterization of Higher-Order Mode Converters in Weakly Multi-Moded Fibers,” Opt. Express 11, 2838–2847 (2003).
[Crossref] [PubMed]

J. M. Fini, “Bend-Resistant Design of Conventional and Microstructure Fibers with Very Large Mode Area,” Opt. Express 14, 69–81 (2006).
[Crossref] [PubMed]

S. Wielandy, “Implications of Higher-Order Mode Content in LargeMode Area Fibers with Good Beam Quality,” Opt. Express 15, 15,402–15,409 (2007).
[Crossref]

Opt. Lett. (3)

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, 143,902 (2005).
[Crossref]

Other (1)

A. E. Siegman, “Defining, Measuring, and Optimizing Laser Beam Quality,” in Proc. SPIE, 2 (1993).

Supplementary Material (3)

» Media 1: AVI (3058 KB)     
» Media 2: AVI (3066 KB)     
» Media 3: AVI (3093 KB)     

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Figures (7)

Fig. 1.
Fig. 1. Calculated mode profiles from a step-index, low NA fiber for the (a) LP01 mode and (b) the LP11 mode. (c) The spatial pattern of the fringe visibility when the LP01 mode and LP11 modes interfere. The LP11 mode was 10 times weaker than the LP01 mode in this calculation.

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Fig. 2.
Fig. 2. (a) Schematic of the S2 imaging setup. (b) Typical optical spectrum measured at an arbitrary (x,y) point and (c) the Fourier transform of the optical spectrum in (b) showing multiple beat frequencies. Fourier filtering is used to pick out different peaks of interest. The horizontal axis of the Fourier transform is normalized to the fiber length to obtain group delay difference in units of ps/m.

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Fig. 3.
Fig. 3. Measurement results on a 20m length of 27 µm core diameter fiber with 0.065 NA. (a) The beam profile obtained by integrating the optical spectrum at each pixel. (b) The Fourier transform of the optical spectra showing the beat frequencies of interest. Also shown as dashed lines are group delay differences between the higher order modes and the LP01 obtained from a calculation based on the measured index profile. (c)–(f) The results of the calculation to obtain the higher-order modes images and MPI levels corresponding to the indicated peaks in (b).

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Fig. 4.
Fig. 4. (a) MPI due to an LPG measured via the transmission loss of the LP01 through the LPG. (b) Beam profile out of the HOM fiber. (c) Fourier transform of the optical spectra, modes associated with the Fourier peaks, and their MPI levels, measured at 1050 nm.

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Fig. 5.
Fig. 5. (a) (3.6 MB) and (b) (3.9 MB) Movies of the beam profile vs. wavelength for two different 27 µm core diameter fibers. (c) and (d) Change in beam center of mass and beam diameter vs. wavelength obtained from the data in (a) and (b). For comparison the center of mass movement and beam diameter change for a single mode fiber was also measured. Curves in (c) and (d) have been offset horizontally for clarity. [Media 1][Media 2]

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Fig. 6.
Fig. 6. S2 imaging of a 44 µm core diameter fiber. (a) Beam profile. (b) Fourier transform of the optical spectrum. (c)–(j) Mode images and MPI levels corresponding to the various peaks in the Fourier transform of the optical spectrum in (b).

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Fig. 7.
Fig. 7. Beam profile changes due to the higher order modes in Fig. 6. (a) (2.7 MB) Movie of the beam profile variation vs. wavelength. (b) Movement of the beam COM obtained from (a). (c) Change in beam diameter vs. wavelength obtained from (a). For comparison the results from the 27 µm core diameter fiber are also shown. [Media 3]

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Equations (7)

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

I 2 ( x , y , ω ) = α 2 ( x , y ) I 1 ( x , y , ω ) ,
I ( x , y , ω ) = I 1 ( x , y , ω ) [ 1 + α 2 ( x , y ) + 2 α ( x , y ) cos ⁡ ( τ b ω ) ] ,
B ( x , y , τ ) = [ 1 + α 2 ( x , y ) ] B 1 ( x , y , τ ) + α ( x , y ) + [ B 1 ( x , y , τ − τ b ) + B 1 ( x , y , τ + τ b ) ] ,
f ( x , y ) = B ( x , y , τ = τ b ) B ( x , y , τ = 0 ) = α ( x , y ) 1 + α 2 ( x , y ) .
α ( x , y ) = 1 − 1 − 4 f 2 ( x , y ) 2 f ( x , y ) .
I 1 ( x , y ) = I T ( x , y ) 1 1 + α 2 ( x , y ) , and I 2 ( x , y ) = I T ( x , y ) α 2 ( x , y ) 1 + α 2 ( x , y ) ,
MPI = 10 log ⁡ [ ∫ ∫ I 2 ( x , y ) dx dy ∫ ∫ I 1 ( x , y ) dx dy ] .

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