Abstract

Today a specific attention has been paid to look into the modal characteristics of the high-power laser beam. And the instantaneous monitoring and analyzing on modal content via the mode decomposition technique will provide a novel route. We implement the first-ever experimental investigation on the real-time mode decomposition technique for few-mode laser beam based on stochastic parallel gradient descent algorithm. It will reduce the cost and the complexity of the mode decomposition system. We have succeeded to decompose the mode spectra as well as calculating the beam quality factor at about 9 Hz monitoring rate, while the high agreement between the measured and reconstructed intensity profiles in each frame indicating the high accuracy and stability during the process. By employing a fiber-squeezing-based polarization controller, the modal content under test can be time-varying automatically.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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2015 (1)

C. Jollivet, B. Samson, L. Leick, L. Shah, M. Richardson, and A. Schülzgen, “Comparative study of light propagation and single-mode operation in large-mode area fibers designed for 2-μm laser applications,” Opt. Eng. 54(1), 011006 (2015).
[Crossref]

2014 (4)

D. Jain, C. Baskiotis, T. C. May-Smith, K. Jaesun, and J. K. Sahu, “Large mode area multi-trench fiber with delocalization of higher order modes,” IEEE J. Sel. Top. Quantum Electron. 20(5), 242–250 (2014).
[Crossref]

M. N. Zervas and C. A. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014).
[Crossref]

C. Jollivet, A. Mafi, D. Flamm, M. Duparré, K. Schuster, S. Grimm, and A. Schülzgen, “Mode-resolved gain analysis and lasing in multi-supermode multi-core fiber laser,” Opt. Express 22(24), 30377–30386 (2014).
[Crossref] [PubMed]

J. Demas and S. Ramachandran, “Sub-second mode measurement of fibers using C2 imaging,” Opt. Express 22(19), 23043–23056 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (4)

2011 (2)

F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Real-time characterisation of modal content in monolithic few-mode fibre lasers,” Electron. Lett. 47(4), 274–275 (2011).
[Crossref]

F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
[Crossref] [PubMed]

2009 (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(2-3), 345–353 (2009).
[Crossref]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009).
[Crossref] [PubMed]

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]

2006 (1)

2005 (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]

2004 (1)

1998 (1)

1990 (1)

S.-Y. Huang, J. N. Blake, and B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8(1), 23–33 (1990).
[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]

Bartelt, H.

Baskiotis, C.

D. Jain, C. Baskiotis, T. C. May-Smith, K. Jaesun, and J. K. Sahu, “Large mode area multi-trench fiber with delocalization of higher order modes,” IEEE J. Sel. Top. Quantum Electron. 20(5), 242–250 (2014).
[Crossref]

Blake, J. N.

S.-Y. Huang, J. N. Blake, and B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8(1), 23–33 (1990).
[Crossref]

Brüning, R.

Chen, R.

I. Giles, A. Obeysekara, R. Chen, D. Giles, F. Poletti, and D. Richardson, “Fiber LPG mode converters and mode selection technique for multimode SDM,” IEEE Photon. Technol. Lett. 24(21), 1922–1925 (2012).
[Crossref]

Codemard, C. A.

M. N. Zervas and C. A. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014).
[Crossref]

Demas, J.

Duparré, M.

C. Jollivet, A. Mafi, D. Flamm, M. Duparré, K. Schuster, S. Grimm, and A. Schülzgen, “Mode-resolved gain analysis and lasing in multi-supermode multi-core fiber laser,” Opt. Express 22(24), 30377–30386 (2014).
[Crossref] [PubMed]

C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21(3), 3170–3181 (2013).
[Crossref] [PubMed]

D. Flamm, K.-C. Hou, P. Gelszinnis, C. Schulze, S. Schröter, and M. Duparré, “Modal characterization of fiber-to-fiber coupling processes,” Opt. Lett. 38(12), 2128–2130 (2013).
[Crossref] [PubMed]

R. Brüning, P. Gelszinnis, C. Schulze, D. Flamm, and M. Duparré, “Comparative analysis of numerical methods for the mode analysis of laser beams,” Appl. Opt. 52(32), 7769–7777 (2013).
[Crossref] [PubMed]

D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37(13), 2478–2480 (2012).
[Crossref] [PubMed]

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, “Fast M2 measurement for fiber beams based on modal analysis,” Appl. Opt. 51(7), 987–993 (2012).
[Crossref] [PubMed]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009).
[Crossref] [PubMed]

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.

C. Jollivet, A. Mafi, D. Flamm, M. Duparré, K. Schuster, S. Grimm, and A. Schülzgen, “Mode-resolved gain analysis and lasing in multi-supermode multi-core fiber laser,” Opt. Express 22(24), 30377–30386 (2014).
[Crossref] [PubMed]

D. Flamm, K.-C. Hou, P. Gelszinnis, C. Schulze, S. Schröter, and M. Duparré, “Modal characterization of fiber-to-fiber coupling processes,” Opt. Lett. 38(12), 2128–2130 (2013).
[Crossref] [PubMed]

C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21(3), 3170–3181 (2013).
[Crossref] [PubMed]

R. Brüning, P. Gelszinnis, C. Schulze, D. Flamm, and M. Duparré, “Comparative analysis of numerical methods for the mode analysis of laser beams,” Appl. Opt. 52(32), 7769–7777 (2013).
[Crossref] [PubMed]

D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37(13), 2478–2480 (2012).
[Crossref] [PubMed]

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, “Fast M2 measurement for fiber beams based on modal analysis,” Appl. Opt. 51(7), 987–993 (2012).
[Crossref] [PubMed]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009).
[Crossref] [PubMed]

Forbes, A.

Gaida, C.

Gelszinnis, P.

Ghalmi, S.

Giles, D.

I. Giles, A. Obeysekara, R. Chen, D. Giles, F. Poletti, and D. Richardson, “Fiber LPG mode converters and mode selection technique for multimode SDM,” IEEE Photon. Technol. Lett. 24(21), 1922–1925 (2012).
[Crossref]

Giles, I.

I. Giles, A. Obeysekara, R. Chen, D. Giles, F. Poletti, and D. Richardson, “Fiber LPG mode converters and mode selection technique for multimode SDM,” IEEE Photon. Technol. Lett. 24(21), 1922–1925 (2012).
[Crossref]

Grimm, S.

Hartung, A.

Hou, K.-C.

Huang, S.-Y.

S.-Y. Huang, J. N. Blake, and B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8(1), 23–33 (1990).
[Crossref]

Jaesun, K.

D. Jain, C. Baskiotis, T. C. May-Smith, K. Jaesun, and J. K. Sahu, “Large mode area multi-trench fiber with delocalization of higher order modes,” IEEE J. Sel. Top. Quantum Electron. 20(5), 242–250 (2014).
[Crossref]

Jain, D.

D. Jain, C. Baskiotis, T. C. May-Smith, K. Jaesun, and J. K. Sahu, “Large mode area multi-trench fiber with delocalization of higher order modes,” IEEE J. Sel. Top. Quantum Electron. 20(5), 242–250 (2014).
[Crossref]

Jansen, F.

Jauregui, C.

F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
[Crossref] [PubMed]

F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Real-time characterisation of modal content in monolithic few-mode fibre lasers,” Electron. Lett. 47(4), 274–275 (2011).
[Crossref]

Jeong, Y.

Jiang, Z.

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]

Jollivet, C.

C. Jollivet, B. Samson, L. Leick, L. Shah, M. Richardson, and A. Schülzgen, “Comparative study of light propagation and single-mode operation in large-mode area fibers designed for 2-μm laser applications,” Opt. Eng. 54(1), 011006 (2015).
[Crossref]

C. Jollivet, A. Mafi, D. Flamm, M. Duparré, K. Schuster, S. Grimm, and A. Schülzgen, “Mode-resolved gain analysis and lasing in multi-supermode multi-core fiber laser,” Opt. Express 22(24), 30377–30386 (2014).
[Crossref] [PubMed]

Kaiser, T.

Kim, B. Y.

S.-Y. Huang, J. N. Blake, and B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8(1), 23–33 (1990).
[Crossref]

Leick, L.

C. Jollivet, B. Samson, L. Leick, L. Shah, M. Richardson, and A. Schülzgen, “Comparative study of light propagation and single-mode operation in large-mode area fibers designed for 2-μm laser applications,” Opt. Eng. 54(1), 011006 (2015).
[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(2-3), 345–353 (2009).
[Crossref]

Limpert, J.

F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Real-time characterisation of modal content in monolithic few-mode fibre lasers,” Electron. Lett. 47(4), 274–275 (2011).
[Crossref]

F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
[Crossref] [PubMed]

Lorenz, A.

Lü, H.

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(2-3), 345–353 (2009).
[Crossref]

Mafi, A.

Mansuripur, M.

May-Smith, T. C.

D. Jain, C. Baskiotis, T. C. May-Smith, K. Jaesun, and J. K. Sahu, “Large mode area multi-trench fiber with delocalization of higher order modes,” IEEE J. Sel. Top. Quantum Electron. 20(5), 242–250 (2014).
[Crossref]

Naidoo, D.

Nicholson, J. W.

Nilsson, J.

Obeysekara, A.

I. Giles, A. Obeysekara, R. Chen, D. Giles, F. Poletti, and D. Richardson, “Fiber LPG mode converters and mode selection technique for multimode SDM,” IEEE Photon. Technol. Lett. 24(21), 1922–1925 (2012).
[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(2-3), 345–353 (2009).
[Crossref]

Otto, H.-J.

Payne, D. N.

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(2-3), 345–353 (2009).
[Crossref]

Poletti, F.

I. Giles, A. Obeysekara, R. Chen, D. Giles, F. Poletti, and D. Richardson, “Fiber LPG mode converters and mode selection technique for multimode SDM,” IEEE Photon. Technol. Lett. 24(21), 1922–1925 (2012).
[Crossref]

Polynkin, P.

Ramachandran, S.

Richardson, D.

I. Giles, A. Obeysekara, R. Chen, D. Giles, F. Poletti, and D. Richardson, “Fiber LPG mode converters and mode selection technique for multimode SDM,” IEEE Photon. Technol. Lett. 24(21), 1922–1925 (2012).
[Crossref]

Richardson, M.

C. Jollivet, B. Samson, L. Leick, L. Shah, M. Richardson, and A. Schülzgen, “Comparative study of light propagation and single-mode operation in large-mode area fibers designed for 2-μm laser applications,” Opt. Eng. 54(1), 011006 (2015).
[Crossref]

Sahu, J. K.

D. Jain, C. Baskiotis, T. C. May-Smith, K. Jaesun, and J. K. Sahu, “Large mode area multi-trench fiber with delocalization of higher order modes,” IEEE J. Sel. Top. Quantum Electron. 20(5), 242–250 (2014).
[Crossref]

Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12(25), 6088–6092 (2004).
[Crossref] [PubMed]

Samson, B.

C. Jollivet, B. Samson, L. Leick, L. Shah, M. Richardson, and A. Schülzgen, “Comparative study of light propagation and single-mode operation in large-mode area fibers designed for 2-μm laser applications,” Opt. Eng. 54(1), 011006 (2015).
[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(2-3), 345–353 (2009).
[Crossref]

Schmidt, O. A.

Schröter, S.

Schulze, C.

Schülzgen, A.

C. Jollivet, B. Samson, L. Leick, L. Shah, M. Richardson, and A. Schülzgen, “Comparative study of light propagation and single-mode operation in large-mode area fibers designed for 2-μm laser applications,” Opt. Eng. 54(1), 011006 (2015).
[Crossref]

C. Jollivet, A. Mafi, D. Flamm, M. Duparré, K. Schuster, S. Grimm, and A. Schülzgen, “Mode-resolved gain analysis and lasing in multi-supermode multi-core fiber laser,” Opt. Express 22(24), 30377–30386 (2014).
[Crossref] [PubMed]

Schuster, K.

Shah, L.

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[Crossref]

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Supplementary Material (1)

Media 1: MOV (4455 KB)     

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Figures (7)
Fig. 1
Fig. 1 Scheme of the real-time modal decomposition of per frame.

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Fig. 2
Fig. 2 (a) Scheme of the experimental setup. SMF, single mode fiber; AFG, arbitrary function generator; PC, polarization controller; L, lens; HWP, half-wave plate; PBS, polarization beam splitter; NDF, neutral density filter;f1/2, focal length of L1/2; (b) The Eigen modes in the fiber.

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Fig. 3
Fig. 3 Excerpt from Media 1, showing a measurement process. The measured and reconstructed near-field intensity, the merit function of per frame and the total, as well as the corresponding M2 value and correction between the measured and reconstructed beam intensities are presented.

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Fig. 4
Fig. 4 The correction between the measured and the reconstructed intensity pattern defined by Eq. (2) of every frame. The insets depict measured (up) and reconstructed (down) intensity of the frame denoted with letters.

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Fig. 5
Fig. 5 (a) The modal weights of LP01, LP11e and LP11o and the input voltage as a function of the frame or the time. The time scale is 11.3 s. (b) The relative phases of LP11e and LP11o with respect to the LP01 as a function of frame. The dash lines in both figures are to denote the symmetry point of the modal weights and voltage.

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Fig. 6
Fig. 6 The normalized power of beam after the PBS and the modal weight of fundamental mode as a function of frame.

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Fig. 7
Fig. 7 The beam quality factor of x and y direction as a function of frame.

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Equations (2)

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

U(r,φ)= ∑ n=1 N ρ n e i θ n ψ n (r,φ)
J=| ∬ Δ I re (r,φ)Δ I me (r,φ)rdrdφ ∬ Δ I re 2 (r,φ)rdrdφ ∬ Δ I me 2 (r,φ)rdrdφ |

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