Abstract

We have been investigating the angular spectrum method for analysis of single-mode and multimode optical fibers. The justification is simple because the approach requires less computational time than other methods because it is heavily dependent on the fast Fourier transform. This method should become much more important as new approaches are being studied for higher data rate transmission. We examine two basic components in the application of this technique to propagation of light in optical fibers – an absorbing layer at the outer radius and design of the interface between the cord and cladding of the optical fiber.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

2018 (2)

2017 (1)

2016 (5)

2015 (1)

2014 (1)

2012 (2)

2011 (1)

J. Richardson, J. Fini, M. Yao, and M. J. Padgett, “Orbital angular momentum: origins, behavior, and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

2010 (1)

2003 (1)

1995 (1)

1993 (2)

W. P. Huang and C. L. Xu, “Simulation of three-dimensional waveguides by full vector-beam propagation method,” J. Lightwave Technol. 29(10), 2639–2649 (1993).
[Crossref]

W. P. Huang and C. L. Xu, “Simulation of three-dimensional waveguides by full vector-beam propagation method,” J. Lightwave Technol. 29(10), 2639–2649 (1993).
[Crossref]

1981 (1)

1979 (1)

1978 (1)

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high-energy laser beams through the atmosphere,” Appl. Phys. 10(2), 129–160 (1976).
[Crossref]

1971 (1)

Alfano, R. R.

Bland-Hawthon, R. J.

Brown, W. P.

Bures, J.

J. Bures, Guided Waves, (Wiley-VCH, 2009)

Chiang, K. S.

Cottrell, D. M.

Davis, J. A.

Ercan, B.

Essiambre, R.

Feigenbaum, E.

Feit, M. D.

M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17(24), 3990–3998 (1978).
[Crossref]

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high-energy laser beams through the atmosphere,” Appl. Phys. 10(2), 129–160 (1976).
[Crossref]

Fini, J.

J. Richardson, J. Fini, M. Yao, and M. J. Padgett, “Orbital angular momentum: origins, behavior, and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Fleck, J. A.

M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17(24), 3990–3998 (1978).
[Crossref]

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high-energy laser beams through the atmosphere,” Appl. Phys. 10(2), 129–160 (1976).
[Crossref]

Fontaine, N. K.

Foschini, G. J.

Frazier, R. J.

Fu, S.

Gan, L.

Gloge, D.

Goebel, B.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, (McGraw Hill, 1969)

Holzlohner, R.

Huang, H.

Huang, W. P.

W. P. Huang and C. L. Xu, “Simulation of three-dimensional waveguides by full vector-beam propagation method,” J. Lightwave Technol. 29(10), 2639–2649 (1993).
[Crossref]

W. P. Huang and C. L. Xu, “Simulation of three-dimensional waveguides by full vector-beam propagation method,” J. Lightwave Technol. 29(10), 2639–2649 (1993).
[Crossref]

Huo, L.

Ip, E.

Karabasi, S.

Karimi, E.

Koch, K. W.

Kramer, G.

Lagasse, P. E.

Lavery, M. P. J.

Learn, R.

Leon-Saval, S. G.

Li, M.-J.

Lian, Z.

Liang, J.

Liu, D.

Lou, S.

Mafi, A.

Marrucci, L.

Menyuk, C. R.

Milione, G.

Mirr, C. R.

Mo, Q.

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high-energy laser beams through the atmosphere,” Appl. Phys. 10(2), 129–160 (1976).
[Crossref]

Nguyen, T. A.

Nolan, D. A.

Padgett, M. J.

J. Richardson, J. Fini, M. Yao, and M. J. Padgett, “Orbital angular momentum: origins, behavior, and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Peng, G.

Ren, Y.

Richardson, J.

J. Richardson, J. Fini, M. Yao, and M. J. Padgett, “Orbital angular momentum: origins, behavior, and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Ryl, R.

Salazar-Gil, J. R.

Saleh, B.E.A.

B.E.A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Edition, (Wiley & Sons, 2007)

Shen, L.

Shum, P.

Sinkin, O. V.

Stone, J.

Szejn, R.

Tang, M.

Teich, M. C.

B.E.A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Edition, (Wiley & Sons, 2007)

Tong, W.

van der Donk, J.

Van Roey, J.

Wang, T.

Wang, X.

Willner, A. E.

Winzer, P. J.

Wu, Y.

Xie, G.

Xu, C. L.

W. P. Huang and C. L. Xu, “Simulation of three-dimensional waveguides by full vector-beam propagation method,” J. Lightwave Technol. 29(10), 2639–2649 (1993).
[Crossref]

W. P. Huang and C. L. Xu, “Simulation of three-dimensional waveguides by full vector-beam propagation method,” J. Lightwave Technol. 29(10), 2639–2649 (1993).
[Crossref]

Yang, C.

Yao, M.

J. Richardson, J. Fini, M. Yao, and M. J. Padgett, “Orbital angular momentum: origins, behavior, and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Yarandi, P. G.

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University, 1997)

Yeh, C.

Yevick, D.

Yu, J.

Zhao, T.

Zhou, M.

Zweck, J.

Adv. Opt. Photonics (1)

J. Richardson, J. Fini, M. Yao, and M. J. Padgett, “Orbital angular momentum: origins, behavior, and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Appl. Opt. (9)

M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17(24), 3990–3998 (1978).
[Crossref]

C. Yeh, W. P. Brown, and R. Szejn, “Multimode inhomogeneous fiber couplers,” Appl. Opt. 18(4), 489–495 (1979).
[Crossref]

J. A. Davis and D. M. Cottrell, “Ray matrix analysis of the fast Fresnel transform with applications towards liquid crystal displays,” Appl. Opt. 51(5), 644–650 (2012).
[Crossref]

D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10(10), 2252–2258 (1971).
[Crossref]

R. Learn and E. Feigenbaum, “Adaptive step-size algorithm for Fourier beam-propagation method with absorbing boundary layer of auto-determined width,” Appl. Opt. 55(16), 4402–4407 (2016).
[Crossref]

T. Zhao, S. Lou, X. Wang, M. Zhou, and Z. Lian, “Ultrabroadband polarization splitter based on three-core photonic crystal fiber with a modulation core,” Appl. Opt. 55(23), 6428–6434 (2016).
[Crossref]

D. M. Cottrell and J. A. Davis, “Simulation of optical fiber couplers using the angular spectrum algorithm,” Appl. Opt. 57(19), 5319–5327 (2018).
[Crossref]

L. Shen, L. Gan, L. Huo, C. Yang, W. Tong, S. Fu, M. Tang, and D. Liu, “Design of highly mode group selective photonic lanterns with geometric optimization,” Appl. Opt. 57(24), 7065–7069 (2018).
[Crossref]

D. M. Cottrell and J. A. Davis, “Simulation of multimode optical fibers using the angular spectrum algorithm and a Fourier analysis,” Appl. Opt. 58(17), 4585–4591, (2019)
[Crossref]

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high-energy laser beams through the atmosphere,” Appl. Phys. 10(2), 129–160 (1976).
[Crossref]

J. Lightwave Technol. (4)

W. P. Huang and C. L. Xu, “Simulation of three-dimensional waveguides by full vector-beam propagation method,” J. Lightwave Technol. 29(10), 2639–2649 (1993).
[Crossref]

W. P. Huang and C. L. Xu, “Simulation of three-dimensional waveguides by full vector-beam propagation method,” J. Lightwave Technol. 29(10), 2639–2649 (1993).
[Crossref]

R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber-communications systems,” J. Lightwave Technol. 21(1), 61–68 (2003).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

J. A. Davis and D. M. Cottrell, “Simulation of Anderson localization in a random fiber using a fast Fresnel diffraction algorithm,” Opt. Eng. 55(6), 066122 (2016).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Other (4)

J. W. Goodman, Introduction to Fourier Optics, (McGraw Hill, 1969)

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University, 1997)

B.E.A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Edition, (Wiley & Sons, 2007)

J. Bures, Guided Waves, (Wiley-VCH, 2009)

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Figures (9)

Fig. 1.
Fig. 1. Icon based program used in this computational study of optical fiber propagation.
Fig. 2.
Fig. 2. Phase function for lens in Eq. (6) having a focal length of 193 micron with pixel sizes and wavelength for our computational system.
Fig. 3.
Fig. 3. Amplitude of the electric field as a function of distance through the optical fiber where there is no absorbing layer at the boundary of the fiber.
Fig. 4.
Fig. 4. Amplitude of absorbing layer near the border of the 1024 × 1024 grid.
Fig. 5.
Fig. 5. Amplitude of the electric field as a function of distance through the optical fiber where we apply an absorbing layer. The beam retains the exact solution of the wave equation, but the amplitude slowly decays.
Fig. 6.
Fig. 6. Smoothing of the phase step boundary between the core and cladding.
Fig. 7.
Fig. 7. Phase mask for the transmission through the propagation distance with the absorbing layer shown in black. Note that the phase representing the fiber core is graded.
Fig. 8.
Fig. 8. The amplitude does not decay noticeably over the 23 cm length of fiber.
Fig. 9.
Fig. 9. Energy of the beam as a function of distance through the optical fiber comparing the case where the core-cladding interface is a step function (in red) and where we apply a smoothing function to this interface (in black).

Equations (6)

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

V = a k n 1 2 n 2 2 .
n 1 k β n 2 k .
g ( x 2 , y 2 , z 2 ) = 1 { H ( p , q , z 2 z 1 ) [ g ( x 1 , y 1 , z 1 ) ] } .
H ( p , q , z 2 z 1 ) = exp [ i π λ ( z 2 z 1 ) ( p 2 + q 2 ) N 2 Δ 4 ] .
H ( p , q , z 2 z 1 ) = exp [ i π ( p 2 + q 2 ) λ F ] .
F = ( N Δ 2 λ ) 2 1 ( z 2 z 1 ) .