Abstract

Numerical modal decomposition (MD) is an effective approach to reveal modal characteristics in high power fiber lasers. The main challenge is to find a suitable multi-dimensional optimization algorithm to reveal exact superposition of eigenmodes, especially for multimode fiber. A novel hybrid genetic global optimization algorithm, named GA-SPGD, which combines the advantages of genetic algorithm (GA) and stochastic parallel gradient descent (SPGD) algorithm, is firstly proposed to reduce local minima possibilities caused by sensitivity to initial values. Firstly, GA is applied to search the rough global optimization position based on near- and far-field intensity distribution with high accuracy. Upon those initial values, SPGD algorithm is afterwards used to find the exact optimization values based on near-field intensity distribution with fast convergence speed. Numerical simulations validate the feasibility and reliability.

© 2017 Optical Society of America

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References

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2015 (2)

2014 (2)

2013 (3)

2012 (2)

2011 (1)

2009 (3)

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]

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]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 1106 (2009).
[Crossref]

2008 (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]

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]

2007 (2)

P. Yang, S. Hu, B. Xu, and W. Jiang, “An adaptive laser beam shaping technique based on a genetic algorithm,” Chi. Opt. Lett. 5(9), 497–500 (2007).

P. Yang, M. Ao, Y. Liu, B. Xu, and W. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15(25), 17051–17062 (2007).
[Crossref] [PubMed]

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]

2000 (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(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]

Ao, M.

Bartelt, H.

Brüning, R.

Carhart, G. W.

Cauwenberghs, G.

Cheng, X.

Cohen, M.

Demas, J.

Duparré, M.

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.

Gaida, C.

Gelszinnis, P.

Ghalmi, S.

Grimm, S.

Guo, S.

Hartung, A.

Hu, S.

P. Yang, S. Hu, B. Xu, and W. Jiang, “An adaptive laser beam shaping technique based on a genetic algorithm,” Chi. Opt. Lett. 5(9), 497–500 (2007).

Huang, L.

Jansen, F.

Jauregui, C.

Jiang, W.

P. Yang, M. Ao, Y. Liu, B. Xu, and W. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15(25), 17051–17062 (2007).
[Crossref] [PubMed]

P. Yang, S. Hu, B. Xu, and W. Jiang, “An adaptive laser beam shaping technique based on a genetic algorithm,” Chi. Opt. Lett. 5(9), 497–500 (2007).

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.

Kaiser, T.

Leng, J.

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.

Liu, Y.

Liu, Z.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 1106 (2009).
[Crossref]

Lorenz, A.

Lü, H.

Ma, H.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 1106 (2009).
[Crossref]

Ma, Y.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 1106 (2009).
[Crossref]

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.

Naidoo, D.

Nicholson, J. W.

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.

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]

Ramachandran, S.

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.

Schuster, K.

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]

Stutzki, F.

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(2–3), 345–353 (2009).
[Crossref]

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]

Tünnermann, A.

Vorontsov, M. A.

Wang, X.

H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Fast and accurate modal decomposition of multimode fiber based on stochastic parallel gradient descent algorithm,” Appl. Opt. 52(12), 2905–2908 (2013).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 1106 (2009).
[Crossref]

Xu, B.

P. Yang, M. Ao, Y. Liu, B. Xu, and W. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15(25), 17051–17062 (2007).
[Crossref] [PubMed]

P. Yang, S. Hu, B. Xu, and W. Jiang, “An adaptive laser beam shaping technique based on a genetic algorithm,” Chi. Opt. Lett. 5(9), 497–500 (2007).

Xu, X.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 1106 (2009).
[Crossref]

Yablon, A. D.

Yang, P.

P. Yang, M. Ao, Y. Liu, B. Xu, and W. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15(25), 17051–17062 (2007).
[Crossref] [PubMed]

P. Yang, S. Hu, B. Xu, and W. Jiang, “An adaptive laser beam shaping technique based on a genetic algorithm,” Chi. Opt. Lett. 5(9), 497–500 (2007).

Zhou, P.

Appl. Opt. (3)

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. 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]

Appl. Phys. Lett. (1)

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 1106 (2009).
[Crossref]

Chi. Opt. Lett. (1)

P. Yang, S. Hu, B. Xu, and W. Jiang, “An adaptive laser beam shaping technique based on a genetic algorithm,” Chi. Opt. Lett. 5(9), 497–500 (2007).

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

Opt. Express (9)

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]

P. Yang, M. Ao, Y. Liu, B. Xu, and W. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15(25), 17051–17062 (2007).
[Crossref] [PubMed]

L. Huang, J. Leng, P. Zhou, S. Guo, H. Lü, and X. Cheng, “Adaptive mode control of a few-mode fiber by real-time mode decomposition,” Opt. Express 23(21), 28082–28090 (2015).
[Crossref] [PubMed]

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]

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[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]

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

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]

Opt. Lett. (1)

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)

J. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975).

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).

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Figures (9)

Fig. 1
Fig. 1 The iteration scheme of genetic algorithm.
Fig. 2
Fig. 2 The iteration scheme of GA-SPGD algorithm
Fig. 3
Fig. 3 Ambiguity in the situation of numerical MD based on near-field intensity distribution due to modal interference: (a) shows initial near-field intensity distribution; (b) depicts the convergence merit function; (c) shows reconstructed near-field; (d) and (e) are the corresponding given and reconstructed far-field intensity, respectively.
Fig. 4
Fig. 4 Merit function as a function of iteration numbers (GA searches the rough global optimization position based on near- and far-field intensity distribution).
Fig. 5
Fig. 5 Global optimization of numerical MD with GA-SPGD algorithm: (a) shows initial near-field intensity distribution; (b) depicts the convergence merit function; (c) shows reconstructed near-field; (d) and (e) are the corresponding given and reconstructed far-field intensity, respectively.
Fig. 6
Fig. 6 Outliner numbers for each mode in continuing 100-times numerical MD with GA-SPGD algorithm: (a) initial population number = 250; (b) initial population number = 300.
Fig. 7
Fig. 7 Given near- and far-field intensity distribution for complete different mode combinations of Group 1, 2 and 3.
Fig. 8
Fig. 8 The results of near- and far-field merit functions in continuing 30-times-operation with GA-SPGD algorithm for Group 1, 2 and 3.
Fig. 9
Fig. 9 Corresponding searching time for each operation of Group 1, 2 and 3.

Tables (5)

Tables Icon

Table 1 Given and convergence modal weights and phase differences

Tables Icon

Table 2 Modal weights and phase differences of the rough global optimization position

Tables Icon

Table 3 Modal weights and phase differences revealing from GA-SPGD algorithm

Tables Icon

Table 4 Complete different mode combinations

Tables Icon

Table 5 Average modal weights and phase differences

Equations (10)

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

U NF (x, y) = n=1 N ρ n e i θ n ψ n (x,y) ψ m (x,y)| ψ n (x,y)= δ mn
n=1 N ρ n 2 =1 θ n (π,π)
U FF ( x 2 , y 2 )= exp(ikf)exp( ik( x 2 2 + y 2 2 ) 2f ) iλf + + U NF ( x 1 , y 1 ) exp( ik( x 2 x 1 + y 2 y 1 ) f )d x 1 d y 1
I NF = | U NF (x, y) | 2
I FF = | U FF (x, y) | 2
J 1 =Δ J NF +Δ J FF max
J 2 =Δ J NF max
ΔJ = | Δ I me (x,y)Δ I re (x,y)dxdy Δ I me 2 (x,y)dxdy Δ I re 2 (x,y)dxdy |
F i ={ J i / i=1 N J i ( J i F C ) 0 ( J i < F C )
P i = F i / i=1 N C F i

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