Abstract

We report on a method for estimation of angle-dependent mode coupling and attenuation in step-index plastic optical fibers (SI-POFs) from the shapes of impulse responses at two different fiber lengths. While alternating the fiber lengths, deviations between simulated and reference impulse responses are minimized by optimizing both mode coupling and attenuation parameters using pattern-search routines. Applying a matrix-based finite-difference approach to Gloge’s time-dependent power flow equation fast computation of simulated impulse responses is enabled. We demonstrate that mode-dependent coupling and attenuation parameters converge to values that reconstruct fiber characteristics reported by other authors. We show that our results can be used for prediction of impulse responses, yielding determination of frequency responses, fiber bandwidths and coupling lengths. We conclude that our method enables characterization of SI-POFs from fiber impulse response measurements.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF Handbook(Springer, 2008).
  2. C. M. Okonkwo, E. Tangdiongga, H. Yang, D. Visani, S. Loquai, R. Kruglov, B. Charbonnier, M. Ouzzif, I. Greiss, O. Ziemann, R. Gaudino, and A. M. J. Koonen, “Recent results from the EU POF-PLUS project: multi-gigabit transmission over 1 mm core diameter plastic optical fibers,” J. Lightwave Technol.29, 186–193 (2011).
    [CrossRef]
  3. D. Gloge, “Impulse response of clad optical multimode fibers,” AT&T Tech. J.52, 801–816 (1973).
  4. W. A. Gambling, D. N. Payne, and H. Matsumura, “Mode conversion coefficients in optical fibers,” Appl. Opt.14, 1538–1542 (1975).
    [CrossRef] [PubMed]
  5. J. Zubia, G. Durana, G. Aldabaldetreku, J. Arrue, M. A. Losada, and M. Lopez-Higuera, “New method to calculate mode conversion coefficients in SI multimode optical fibers,” J. Lightwave Technol.21, 776–781 (2003).
    [CrossRef]
  6. S. Savović and A. Djordjevich, “Method for calculating the coupling coefficient in step-index optical fibers,” Appl. Opt.46, 1477–1481 (2007).
    [CrossRef]
  7. R. Olshansky and S. M. Oaks, “Differential mode attenuation measurements in graded-index fibers,” Appl. Opt.47, 1830–1835 (1978).
    [CrossRef]
  8. T. Ishigure, M. Kano, and Y. Koike, “Which is a more serious factor to the bandwidth of GI POF: differential mode attenuation or mode coupling,” J. Lightwave Technol.18, 959–965 (2000).
    [CrossRef]
  9. J. Mateo, M. A. Losada, and I. Garcés, “Global characterization of optical power propagation in step-index plastic optical fibers,” Opt. Express14, 9028–9035 (2006).
    [CrossRef] [PubMed]
  10. S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode-coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol.44, 180–184 (2012).
    [CrossRef]
  11. J. Mateo, M. A. Losada, and J. Zubia, “Frequency response in step index plastic optical fibers obtained from the generalized power flow equation,” Opt. Express17, 2850–2860 (2009).
    [CrossRef] [PubMed]
  12. J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7, 308–313 (1965).
    [CrossRef]
  13. D. Gloge, “Optical power flow in multimode fibers,” AT&T Tech. J.51, 1767–1783 (1972).
  14. B. Drljača, S. Savović, and A. Djordjevich, “Calculation of frequency response in step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Laser Eng.49, 618–622 (2011).
    [CrossRef]
  15. M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step-index optical fibers,” IEEE T. Microw. Theory25, 577–585 (1977).
    [CrossRef]
  16. F. Breyer, N. Hanik, J. Lee, and S. Randel, “Getting impulse response of SI-POF by solving the time-dependent power flow equation using Crank-Nicholson scheme,” in POF Modelling: Theory, Measurement and Application,C. A. Bunge and H. Poisel, eds. (Books on Demand GmbH, 2007), pp. 111–120.
  17. David E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley Professional, 1989).
  18. A. Djordjevich and S. Savović, “Numerical solution of the power flow equation in step-index plastic optical fibers,” J. Opt. Soc. Am. B21, 1437–1442 (2004).
    [CrossRef]
  19. R. Olshansky, “Mode coupling effects in graded-index optical fibers,” Appl. Opt.14, 935–945 (1975).
    [CrossRef] [PubMed]

2012 (1)

S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode-coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol.44, 180–184 (2012).
[CrossRef]

2011 (2)

2009 (1)

2007 (2)

S. Savović and A. Djordjevich, “Method for calculating the coupling coefficient in step-index optical fibers,” Appl. Opt.46, 1477–1481 (2007).
[CrossRef]

F. Breyer, N. Hanik, J. Lee, and S. Randel, “Getting impulse response of SI-POF by solving the time-dependent power flow equation using Crank-Nicholson scheme,” in POF Modelling: Theory, Measurement and Application,C. A. Bunge and H. Poisel, eds. (Books on Demand GmbH, 2007), pp. 111–120.

2006 (1)

2004 (1)

2003 (1)

2000 (1)

1978 (1)

R. Olshansky and S. M. Oaks, “Differential mode attenuation measurements in graded-index fibers,” Appl. Opt.47, 1830–1835 (1978).
[CrossRef]

1977 (1)

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step-index optical fibers,” IEEE T. Microw. Theory25, 577–585 (1977).
[CrossRef]

1975 (2)

1973 (1)

D. Gloge, “Impulse response of clad optical multimode fibers,” AT&T Tech. J.52, 801–816 (1973).

1972 (1)

D. Gloge, “Optical power flow in multimode fibers,” AT&T Tech. J.51, 1767–1783 (1972).

1965 (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7, 308–313 (1965).
[CrossRef]

Aldabaldetreku, G.

Arrue, J.

Breyer, F.

F. Breyer, N. Hanik, J. Lee, and S. Randel, “Getting impulse response of SI-POF by solving the time-dependent power flow equation using Crank-Nicholson scheme,” in POF Modelling: Theory, Measurement and Application,C. A. Bunge and H. Poisel, eds. (Books on Demand GmbH, 2007), pp. 111–120.

Charbonnier, B.

Daum, W.

O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF Handbook(Springer, 2008).

Djordjevich, A.

S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode-coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol.44, 180–184 (2012).
[CrossRef]

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of frequency response in step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Laser Eng.49, 618–622 (2011).
[CrossRef]

S. Savović and A. Djordjevich, “Method for calculating the coupling coefficient in step-index optical fibers,” Appl. Opt.46, 1477–1481 (2007).
[CrossRef]

A. Djordjevich and S. Savović, “Numerical solution of the power flow equation in step-index plastic optical fibers,” J. Opt. Soc. Am. B21, 1437–1442 (2004).
[CrossRef]

Drljaca, B.

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of frequency response in step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Laser Eng.49, 618–622 (2011).
[CrossRef]

Durana, G.

Gambling, W. A.

Garcés, I.

Gaudino, R.

Gloge, D.

D. Gloge, “Impulse response of clad optical multimode fibers,” AT&T Tech. J.52, 801–816 (1973).

D. Gloge, “Optical power flow in multimode fibers,” AT&T Tech. J.51, 1767–1783 (1972).

Goldberg, David E.

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

Greiss, I.

Hanik, N.

F. Breyer, N. Hanik, J. Lee, and S. Randel, “Getting impulse response of SI-POF by solving the time-dependent power flow equation using Crank-Nicholson scheme,” in POF Modelling: Theory, Measurement and Application,C. A. Bunge and H. Poisel, eds. (Books on Demand GmbH, 2007), pp. 111–120.

Ishigure, T.

Jeunhomme, L.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step-index optical fibers,” IEEE T. Microw. Theory25, 577–585 (1977).
[CrossRef]

Kano, M.

Koike, Y.

Koonen, A. M. J.

Krauser, J.

O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF Handbook(Springer, 2008).

Kruglov, R.

Lee, J.

F. Breyer, N. Hanik, J. Lee, and S. Randel, “Getting impulse response of SI-POF by solving the time-dependent power flow equation using Crank-Nicholson scheme,” in POF Modelling: Theory, Measurement and Application,C. A. Bunge and H. Poisel, eds. (Books on Demand GmbH, 2007), pp. 111–120.

Lopez-Higuera, M.

Loquai, S.

Losada, M. A.

Mateo, J.

Matsumura, H.

Mead, R.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7, 308–313 (1965).
[CrossRef]

Nelder, J. A.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7, 308–313 (1965).
[CrossRef]

Oaks, S. M.

R. Olshansky and S. M. Oaks, “Differential mode attenuation measurements in graded-index fibers,” Appl. Opt.47, 1830–1835 (1978).
[CrossRef]

Okonkwo, C. M.

Olshansky, R.

R. Olshansky and S. M. Oaks, “Differential mode attenuation measurements in graded-index fibers,” Appl. Opt.47, 1830–1835 (1978).
[CrossRef]

R. Olshansky, “Mode coupling effects in graded-index optical fibers,” Appl. Opt.14, 935–945 (1975).
[CrossRef] [PubMed]

Ouzzif, M.

Payne, D. N.

Randel, S.

F. Breyer, N. Hanik, J. Lee, and S. Randel, “Getting impulse response of SI-POF by solving the time-dependent power flow equation using Crank-Nicholson scheme,” in POF Modelling: Theory, Measurement and Application,C. A. Bunge and H. Poisel, eds. (Books on Demand GmbH, 2007), pp. 111–120.

Rousseau, M.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step-index optical fibers,” IEEE T. Microw. Theory25, 577–585 (1977).
[CrossRef]

Savovic, S.

S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode-coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol.44, 180–184 (2012).
[CrossRef]

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of frequency response in step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Laser Eng.49, 618–622 (2011).
[CrossRef]

S. Savović and A. Djordjevich, “Method for calculating the coupling coefficient in step-index optical fibers,” Appl. Opt.46, 1477–1481 (2007).
[CrossRef]

A. Djordjevich and S. Savović, “Numerical solution of the power flow equation in step-index plastic optical fibers,” J. Opt. Soc. Am. B21, 1437–1442 (2004).
[CrossRef]

Tangdiongga, E.

Visani, D.

Yang, H.

Zamzow, P. E.

O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF Handbook(Springer, 2008).

Ziemann, O.

Zubia, J.

Appl. Opt. (4)

AT&T Tech. J. (2)

D. Gloge, “Impulse response of clad optical multimode fibers,” AT&T Tech. J.52, 801–816 (1973).

D. Gloge, “Optical power flow in multimode fibers,” AT&T Tech. J.51, 1767–1783 (1972).

Comput. J. (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J.7, 308–313 (1965).
[CrossRef]

IEEE T. Microw. Theory (1)

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step-index optical fibers,” IEEE T. Microw. Theory25, 577–585 (1977).
[CrossRef]

J. Lightwave Technol. (3)

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

Opt. Express (2)

Opt. Laser Eng. (1)

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of frequency response in step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Laser Eng.49, 618–622 (2011).
[CrossRef]

Opt. Laser Technol. (1)

S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode-coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol.44, 180–184 (2012).
[CrossRef]

POF Modelling: Theory, Measurement and Application (1)

F. Breyer, N. Hanik, J. Lee, and S. Randel, “Getting impulse response of SI-POF by solving the time-dependent power flow equation using Crank-Nicholson scheme,” in POF Modelling: Theory, Measurement and Application,C. A. Bunge and H. Poisel, eds. (Books on Demand GmbH, 2007), pp. 111–120.

Other (2)

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

O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF Handbook(Springer, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Program flow of optimization algorithm

Fig. 2
Fig. 2

Simplex initialization for attenuation (a) and diffusion (b) DS algorithms

Fig. 3
Fig. 3

Evolution of impulse responses of 100 m PGU fiber (left plot), modal attenuation (top right) and modal diffusion (bottom right) over iteration steps of the proposed method. Simulated data is shown as red lines, reference data from [9] in blue lines.

Fig. 4
Fig. 4

Diffusion (left) and attenuation (right) functions for GH (top row) and PGU fiber (bottom row). Blue lines represent reference data from [9], simulation results are shown as solid red lines. Dashed red lines are least squares fits of Eqs. (9)(11) to the reference characteristics for θθc.

Fig. 5
Fig. 5

Impulse (left) and frequency responses (right) at varying lengths of the PGU fiber. Blue lines represent reference data from [9], simulation results are shown as red lines.

Fig. 6
Fig. 6

Bandwidths and RMS pulse durations over lengths of GH (a) and PGU (b) fiber. Reference data from [9] is given by blue symbols, simulation results are given in red (dashed) lines. Black symbols denote measured bandwidths for two samples of each fiber (filled circles and open squares, respectively) from [11]. The arrows indicate which vertical axis the data refers to.

Tables (1)

Tables Icon

Table 1 Fiber parameters for modal diffusion and attenuation

Equations (12)

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

P ( θ , z , t ) z = a ( θ ) P ( θ , z , t ) n c 0 cos ( θ ) P ( θ , z , t ) t + 1 θ θ ( θ d ( θ ) P ( θ , z , t ) θ )
p ( θ , z , ω ) z = ( a ( θ ) + n c 0 cos ( θ ) i ω ) p ( θ , z , ω ) + 1 θ θ ( θ d ( θ ) p ( θ , z , ω ) θ ) .
p ( θ , z + Δ z , ω ) = ( 1 ( a ( θ ) + n c 0 cos ( θ ) i ω ) Δ z ) p ( θ , z , ω ) + Δ z 2 Δ θ ( d ( θ ) θ + d ( θ ) ) ( p ( θ + Δ θ , z , ω ) p ( θ Δ θ , z , ω ) ) 2 d ( θ ) Δ z Δ θ 2 p ( θ , z , ω ) + d ( θ ) Δ z Δ θ 2 ( p ( θ + Δ θ , z , ω + p ( θ Δ θ , z , ω ) ) .
p ( z 2 , ω ) = ( A ( ω ) + D ) m p ( z 1 , ω ) ,
A k , k ( ω ) = exp ( Δ z a ( k Δ θ ) Δ z n c 0 i ω ( 1 cos ( k Δ θ ) 1 ) ) .
D k , k 1 = ( d ( k Δ θ ) 1 2 d ( k Δ θ ) k 1 2 d ( k Δ θ ) Δ θ ) Δ z Δ θ 2 D k , k = 2 d ( k Δ θ ) Δ z Δ θ 2 D k , k + 1 = ( d ( k Δ θ ) + 1 2 d ( k Δ θ ) k + 1 2 d ( k Δ θ ) Δ θ ) Δ z Δ θ 2 ,
D 0 , 0 = 4 d ( 0 ) Δ z Δ θ 2 D 0 , 1 = 4 d ( 0 ) Δ z Δ θ 2 D N , N 1 = 2 d ( N ) Δ z Δ θ 2 D N , N = 2 d ( N ) Δ z Δ θ 2 ,
h ( L , ω ) = 0 π / 2 sin ( θ ) p ( L , θ , ω ) d θ .
d ( θ ) = { d 0 ( θ c | θ | ) 2 d q , if θ 0 d ( Δ θ ) Δ θ | d ( θ ) θ | θ = Δ θ , if θ = 0
a ( θ ) = a 0 + a 1 θ 2 + a 2 θ 4 .
a 0 = γ k = 0 k c ( a 1 ( k Δ θ ) 2 + a 2 ( k Δ θ ) 4 ) ( k c + 1 ) , with k c θ c / Δ θ .
P ( L = 0 , θ , t ) = δ ( t ) exp ( 4 ln ( 2 ) ( θ θ 0 ) 2 ) , with θ 0 = arcsin ( NA 0 / n ) ,

Metrics