Abstract

An efficient numerical strategy to compute the higher-order dispersion parameters of optical waveguides is presented. For the first time to our knowledge, a systematic study of the errors involved in the higher-order dispersions’ numerical calculation process is made, showing that the present strategy can accurately model those parameters. Such strategy combines a full-vectorial finite element modal solver and a proper finite difference differentiation algorithm. Its performance has been carefully assessed through the analysis of several key geometries. In addition, the optimization of those higher-order dispersion parameters can also be carried out by coupling to the present scheme a genetic algorithm, as shown here through the design of a photonic crystal fiber suitable for parametric amplification applications.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed (Academic Press, 1995).
  2. L. Valor and J. Zapata, “Efficient finite element analysis of waveguides with lossy inhomogeneous anisotropic materials characterized by arbitrary permittivity and permeability tensors,” IEEE Trans. Microw. Theory Tech. 43(10), 2452–2459 (1995).
    [CrossRef]
  3. M. Koshiba and Y. Tsuji, “Curvilinear Hybrid Edge/Nodal Elements with Triangular Shape for Guided-Wave Problems,” J. Lightwave Technol. 18(5), 737–743 (2000).
    [CrossRef]
  4. F. L. Teixeira and W. C. Chew, “General Closed-Form PML Constitutive Tensors to Match Arbitrary Bianisotropic and Dispersive Linear Media,” IEEE Microwave Guided Wave Lett. 8(6), 223–230 (1998).
    [CrossRef]
  5. Finite Difference Schemes of One Variable - Wolfram Demonstrations, http://demonstrations.wolfram.com/FiniteDifferenceSchemesOfOneVariable/
  6. L. H. Gabrielli, H. E. Hernández-Figueroa, and H. L. Fragnito, “Robustness Optimization of Fiber Index Profiles for Optical Parametric Amplifiers,” J. Lightwave Technol. 27(24), 5571–5579 (2009).
    [CrossRef]
  7. S. Arismar Cerqueira., “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73(2), 024401 (2010).
    [CrossRef]
  8. E. Kerrinckx, L. Bigot, M. Douay, and Y. Quiquempois, “Photonic crystal fiber design by means of a genetic algorithm,” Opt. Express 12(9), 1990–1995 (2004).
    [CrossRef] [PubMed]
  9. J. M. Chavéz Boggio, J. D. Marconi, S. R. Bickham, and H. L. Fragnito, “Spectrally flat and broadband double-pumped fiber optical parametric amplifiers,” Opt. Express 15(9), 5288–5309 (2007).
    [CrossRef] [PubMed]
  10. Schott Corporation, North America, http://www.us.schott.com .
  11. X. Feng, A. K. Mairaj, D. W. Hewak, and T. M. Monro, “Nonsilica Glasses for Holey Fibers,” J. Lightwave Technol. 23(6), 2046–2054 (2005).
    [CrossRef]

2010

S. Arismar Cerqueira., “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73(2), 024401 (2010).
[CrossRef]

2009

2007

2005

2004

2000

1998

F. L. Teixeira and W. C. Chew, “General Closed-Form PML Constitutive Tensors to Match Arbitrary Bianisotropic and Dispersive Linear Media,” IEEE Microwave Guided Wave Lett. 8(6), 223–230 (1998).
[CrossRef]

1995

L. Valor and J. Zapata, “Efficient finite element analysis of waveguides with lossy inhomogeneous anisotropic materials characterized by arbitrary permittivity and permeability tensors,” IEEE Trans. Microw. Theory Tech. 43(10), 2452–2459 (1995).
[CrossRef]

Arismar Cerqueira, S.

S. Arismar Cerqueira., “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73(2), 024401 (2010).
[CrossRef]

Bickham, S. R.

Bigot, L.

Chavéz Boggio, J. M.

Chew, W. C.

F. L. Teixeira and W. C. Chew, “General Closed-Form PML Constitutive Tensors to Match Arbitrary Bianisotropic and Dispersive Linear Media,” IEEE Microwave Guided Wave Lett. 8(6), 223–230 (1998).
[CrossRef]

Douay, M.

Feng, X.

Fragnito, H. L.

Gabrielli, L. H.

Hernández-Figueroa, H. E.

Hewak, D. W.

Kerrinckx, E.

Koshiba, M.

Mairaj, A. K.

Marconi, J. D.

Monro, T. M.

Quiquempois, Y.

Teixeira, F. L.

F. L. Teixeira and W. C. Chew, “General Closed-Form PML Constitutive Tensors to Match Arbitrary Bianisotropic and Dispersive Linear Media,” IEEE Microwave Guided Wave Lett. 8(6), 223–230 (1998).
[CrossRef]

Tsuji, Y.

Valor, L.

L. Valor and J. Zapata, “Efficient finite element analysis of waveguides with lossy inhomogeneous anisotropic materials characterized by arbitrary permittivity and permeability tensors,” IEEE Trans. Microw. Theory Tech. 43(10), 2452–2459 (1995).
[CrossRef]

Zapata, J.

L. Valor and J. Zapata, “Efficient finite element analysis of waveguides with lossy inhomogeneous anisotropic materials characterized by arbitrary permittivity and permeability tensors,” IEEE Trans. Microw. Theory Tech. 43(10), 2452–2459 (1995).
[CrossRef]

IEEE Microwave Guided Wave Lett.

F. L. Teixeira and W. C. Chew, “General Closed-Form PML Constitutive Tensors to Match Arbitrary Bianisotropic and Dispersive Linear Media,” IEEE Microwave Guided Wave Lett. 8(6), 223–230 (1998).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

L. Valor and J. Zapata, “Efficient finite element analysis of waveguides with lossy inhomogeneous anisotropic materials characterized by arbitrary permittivity and permeability tensors,” IEEE Trans. Microw. Theory Tech. 43(10), 2452–2459 (1995).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Rep. Prog. Phys.

S. Arismar Cerqueira., “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73(2), 024401 (2010).
[CrossRef]

Other

Schott Corporation, North America, http://www.us.schott.com .

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed (Academic Press, 1995).

Finite Difference Schemes of One Variable - Wolfram Demonstrations, http://demonstrations.wolfram.com/FiniteDifferenceSchemesOfOneVariable/

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 (5)

Fig. 1
Fig. 1

Diagram of the developed numerical strategy.

Fig. 2
Fig. 2

Analysis of the rectangular waveguide. (a) Geometry of the guide; (b) RE versus Degrees of Freedom for 1299.41 nm; (c) RE versus Degrees of Freedom for 1702.33 nm; (d) RE versus wavelength for 75191 DOF.

Fig. 3
Fig. 3

Analysis of the Fiber F3. (a) Geometry of the W-profile fiber analyzed in [6]; (b) RE versus Degrees of Freedom for 1299.41 nm; (c) RE versus Degrees of Freedom for 1702.33 nm; (d) RE versus wavelength for 75099 DOF.

Fig. 4
Fig. 4

Solver automation for the treatment of inverse problems.

Fig. 5
Fig. 5

The inverse problem solved. (a) PCF obtained by GA; (b) β(1) and β(2) versus wavelength; (c) β(3) and β(4) versus wavelength; (d) β(5) and β(6) versus wavelength.

Tables (4)

Tables Icon

Table 1 HOD parameters of the rectangular waveguide at λ = 1299.41 nm. They were used 7 sample points in the derivatives calculation and 75191 DOF in the mesh

Tables Icon

Table 2 HOD parameters of the rectangular waveguide at λ = 1702.33 nm. They were used 7 sample points in the derivatives calculation and 75191 DOF in the mesh

Tables Icon

Table 3 HOD parameters of the step index fiber at λ = 1299.41 nm. They were used 7 sample points in the derivatives calculation and 75099 DOF in the mesh

Tables Icon

Table 4 HOD parameters of the step index fiber at λ = 1702.33 nm. They were used 7 sample points in the derivatives calculation and 75099 DOF in the mesh

Equations (7)

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

β ( ω ) = β ( 0 ) + β ( 1 ) ( ω ω 0 ) + 1 2 β ( 2 ) ( ω ω 0 ) 2 + 1 6 β ( 3 ) ( ω ω 0 ) 3 +
β ( i ) = ( i β ω i ) ω = ω 0 ( i = 0 , 1 , 2 , 3 , )
β ( i ) ( ω 0 ) = ( i β ( 0 ) ω i ) ω = ω 0
β ( i ) ( λ 0 ) = f [ ( i β ( 0 ) λ i ) λ = λ 0 , ( i 1 β ( 0 ) λ i 1 ) λ = λ 0 , ... , ( β ( 0 ) λ ) λ = λ 0 ]
R E = L o g 10 | β f e m ( i ) β r e f ( i ) β r e f ( i ) |
D = 2 π c λ 2 β ( 2 )
F = | β ( 4 ) β a i m ( 4 ) | / σ + | D D a i m |

Metrics