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Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 12 — Jun. 16, 2003
  • pp: 1400–1405
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High-index-core Bragg fibers: dispersion properties

Juan A. Monsoriu, Enrique Silvestre, Albert Ferrando, Pedro Andrés, and Juan J. Miret  »View Author Affiliations


Optics Express, Vol. 11, Issue 12, pp. 1400-1405 (2003)
http://dx.doi.org/10.1364/OE.11.001400


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Abstract

We study the group-velocity-dispersion properties of a novel type of Bragg fibers. These new structures are cylindrically symmetric microstructured fibers having a high-index core (silica in our case), like in conventional photonic crystal fibers, surrounded by a multilayered cladding, which is formed by a set of alternating layers of silica and a lower refractive-index dielectric. The combination of the unusual geometric dispersion behavior shown by the multilayered structure and the material dispersion corresponding to the silica core allows us to design nearly-constant chromatic dispersion profiles. In this work we focus our attention on flattened dispersion fibers in the 0.8 µm wavelength window and even on ultraflattened dispersion structures about the 1.55 µm point. We include configurations owning positive, negative, and nearly-zero dispersion in both wavelength ranges.

© 2003 Optical Society of America

1. Introduction

The presence of a periodic, or almost periodic, structure as a cladding in such microstructured fibers determines the existence of photonic band gaps in the visible or in the near infrared region for some specific configurations. The dispersion relations of the guided modes lie on the forbidden (band gap) regions and, of course, are affected by the microstructure of the cladding.

The above photonic-band-gap guiding principle results in a wide variety of appealing features that clearly surpass that of traditional step-refractive-index fibers. In this paper we focus our attention on the group-velocity-dispersion properties of a particular type of these structures. The characteristics of the dispersion relations of the guided modes in fibers using photonic band gaps are explicitly reflected on the qualitatively different behavior of the chromatic dispersion, D. In this way, a suitable design of the geometric parameters in PCF’s leads to nearly-zero ultraflattened dispersion [9

9. A. Ferrando, E. Silvestre, J.J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, pp. 790–792 (2000). [CrossRef]

11

11. K. Saitoh, M. Koshiba, H. University, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11, 843–852 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843 [CrossRef] [PubMed]

] or results in new tunable flattened dispersion properties [12

12. A. Ferrando, E. Silvestre, P. Andrés, J.J. Miret, and M.V. Andrés, “Designing the properties of dispersion flattened photonic crystal fibers,” Opt. Express 9, 687–697 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687 [CrossRef] [PubMed]

]. Likewise, a zero-dispersion wavelength [13

13. F. Brechet, P. Roy, J. Marcau, and D. Pagnoux, “Single propagation into depressed-core-index photonic bandgap fibre designed for zero-dispersion propagation at short wavelengths,” Elec. Lett. 36, 514–515 (2000). [CrossRef]

, 14

14. G. Ouyang, Y. Xu, and A. Yariv, “Comparative study of air-core and coaxial Bragg fibers: singlemode transmission and dispersion characteristics,” Opt. Express 9, 733–747 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-733 [CrossRef] [PubMed]

] or very large negative dispersion values [15

15. G. Ouyang, Y. Xu, and A. Yariv, “Theoretical study on dispersion compensation in air-core Bragg fibers,” Opt. Express 10, 899–908 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-899 [CrossRef] [PubMed]

] can be achieved in single-mode cylindrically symmetric layered fibers.

Our interest in this work is to propose a new cylindrical multilayered fiber that can be regarded as a high-index-core Bragg fiber. It is a cylindrically symmetric microstructured fiber having a high-index core (silica in our case) surrounded by a multilayered cladding made of alternating layers of silica and a lower refractive-index dielectric. In contrast to standard Bragg fibers, guidance is not given in the low-index core, but in the silica core like in central-hole-missing PCF’s. Because the dispersion produced by the fiber geometry exists in all cases (even guiding light in air), the aim of our scheme is to compensate for the geometric fiber dispersion by means of the material dispersion corresponding to the material where the mode is propagating (silica in our case). Accordingly, using the remarkable dispersion properties due to the Bragg fiber geometry, we can properly compensate the material dispersion of the silica and, then, to achieve a very nice control of the dispersion behavior.

Fig. 1. Schematic diagram of a high-index-core Bragg fiber.

2. The high-index-core Bragg fiber

The multilayered structure geometry is characterized by the radial multilayer period, Λ, and the low-index-layer thickness, a, as illustrated in Fig. 1. The refractive indices are alternately n I and n II, where n II<n I. In fact, we have selected the refractive indices of silica and air as n I and n II, respectively. Of course, our treatment can be easily adapted to other materials. Needless to say that, in order to provide structural support to the fiber, air should be replaced by some dielectric with a low refractive index, but the main results of this work would still apply. We have simulated different fiber configurations. For simplicity we restrict ourselves to vary only two independent structural parameters that define the Bragg geometry, Λ and a. Note that with this selection the core radius coincides with the thickness of the high index layer of the cladding. In any case, the structure is, strictly speaking, not periodic.

Fig. 2. Band-gap structure and modal dispersion relation curves for two angular sectors: (a) ν=1 (HE modes), and (b) ν=0 (only TE modes). In both cases, Λ=1.190 µm and a=0.248 µm. Conduction bands are represented by the shaded regions.
Fig. 3. Transverse intensity distribution for: (a) the fundamental guided mode HE11 in Fig. 2, and (b) the first intraband guided mode TE01 in Fig. 2. In both cases, λ=0.8 µm.

3. Dispersion results

Dg(λ)=(λc)d2ngdλ2.
(1)

The evaluation of ng is carried out by considering that the material refractive indices are wavelength independent. Therefore, its dependence on the wavelength arises from the fiber geometry exclusively. The interplay between the fixed silica dispersion and the tunable geometric dispersion allows us to control the dispersion properties of this new structure. For this reason we have systematically studied the dependence of Dg in terms of the geometric parameters, Λ and a. Following a design procedure similar to that described in Ref. [12

12. A. Ferrando, E. Silvestre, P. Andrés, J.J. Miret, and M.V. Andrés, “Designing the properties of dispersion flattened photonic crystal fibers,” Opt. Express 9, 687–697 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687 [CrossRef] [PubMed]

], which is based on the above approximate expression for D, one can obtain approximate values for Λ and a providing a desired constant dispersion profile. This part defines the design phase. Of course, we can evaluate D in an exact manner, including the material dispersion, as

D(λ)=(λc)d2ndλ2,
(2)

and, then, starting from the approximate values for Λ and a, we can fine tune these parameters to obtain the expected dispersion behavior.

Fig. 4. Positive (Λ=1.170 µm and a=0.266 µm), nearly-zero (Λ=1.190 µm and a=0.248 µm), and negative (Λ=1.210 µm and a=0.232 µm) flattened dispersion curves near 0.8 µm.
Fig. 5. Positive (Λ=4.900 µm and a=0.115 µm), nearly-zero (Λ=4.210 µm and a=0.094 µm), and negative (Λ=3.600 µm and a=0.082 µm) ultraflattened dispersion curves near 1.55 µm.

In Fig. 4 we present some examples of positive (anomalous), nearly-zero, and negative (normal) flattened dispersion designs at 0.8 µm. All of them show a zero third-ordered dispersion point. Note that the geometric parameters of the blue curve in Fig. 4 just correspond to that of the plots in Figs. 2 and 3. It is pretty clear the tunability of the structure, even in the region well below the critical silica zero-dispersion wavelength (1.3 µm). It is specially remarkable the possibility of obtaining a flattened positive dispersion profile centered around 0.8 µm (red curve) that can facilitate the stabilization of ultrashort soliton pulses generated at this wavelength (for example with a Ti:Sapphire laser) by a more effective suppression of higher-order dispersion terms.

High-index-core Bragg fibers can also be designed to achieve an ultraflattened dispersion behavior around 1.55 µm. Figure 5 shows the curves for the dispersion coefficient D corresponding to three different Bragg configurations. Note that this ultraflattened behavior is preserved in a large wavelength window that extends over several hundreds of nanometers and, unlike flattened dispersion, permits to obtain a point with zero fourth-order dispersion. The tunability of the structure is also clearly demonstrated by the fact that these designs own positive, negative, and zero D.

Fig. 6. Dispersion (solid curves) and relative dispersion slope (broken curves), defined as RDS=(dD/dλ)/D, corresponding to three different selections of the structural parameters to achieve zero four-ordered dispersion at 1.55 µm: red curve (Λ=4.710 µm and a=0.090 µm), blue curve (Λ=4.570 µm and a=0.094 µm), and green curve (Λ=4.465 µm and a=0.096 µm).

If we go one step further, we can also recognize diverse intermediate situations in which D has a low value and at the same time the four-ordered dispersion coefficient is null at 1.55 µm. Some solutions for such a challenging task are plotted in Fig. 6. In particular, we would like to point out that the examination of the blue curves in Fig. 6 reveals a fiber design with an ultraflattened dispersion regime and a low dispersion value around 1.55 µm presenting a point of zero third- and fourth-ordered dispersion at this wavelength simultaneously. This is a fascinating result. However, one has to take into account that in our approach light is guided in silica, not in air, and consequently, in principle, it suffers from residual absorption loss and nonlinear effects as four-wave mixing. The performances of our optical proposal finally depend on the particular application.

4. Conclusions

In this paper we have discussed the dispersion properties of high-index-core Bragg fibers. We have numerically demonstrated the ability of these structures to show, for some specific designs, a flattened dispersion behavior (one point of zero third-order dispersion) around 0.8 µm and even an ultraflattened behavior (one point of zero fourth-order dispersion) around 1.55 µm. Moreover, we have recognized some configurations exhibiting positive, negative, or nearly-zero constant dispersion in both wavelength windows. Finally, a noteworthy fiber design that combines low and nearly-constant chromatic dispersion about 1.55 µm with zero third- and fourth-order dispersion at 1.55 µm has been identified.

Acknowledgements

References and Links

1.

J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed]

2.

A. Ferrando, E. Silvestre, J.J. Miret, P. Andrés, and M.V. Andrés, “Donor and acceptor guided modes in photonic crystal fibers,” Opt. Lett. 25, 1328–1330 (2000). [CrossRef]

3.

P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68, 1196–1201 (1978). [CrossRef]

4.

Y. Xu, G.X. Ouyang, R.K. Lee, and A. Yariv, “Asymptotic Matrix Theory of Bragg Fibers,” J. Lightwave Technol. 20, 428–440 (2002). [CrossRef]

5.

M. Ibanescu, Y. Fink, S. Fan, E.L. Thomas, and J.D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419 (2000). [CrossRef] [PubMed]

6.

S.G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T.D. Engness, M. Soljacic, S.A. Jacobs, J.D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748 [CrossRef] [PubMed]

7.

J. Xu, J. Song, C. Li, and K. Ueda, “Cylindrically symmetrical hollow fiber,” Opt. Commun. 182, 343–348 (2000). [CrossRef]

8.

A. Argyros, I. Bassett, M. van Eijkelenborg, M.C.J. Large, J. Zagari, N.A.P. Nicorovici, R.C. McPhedran, and C.M. de Sterke, “Ring structures in microstructured polymer optical fibres,” Opt. Express 9, 813–820 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-813 [CrossRef] [PubMed]

9.

A. Ferrando, E. Silvestre, J.J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, pp. 790–792 (2000). [CrossRef]

10.

W.H. Reeves, J.C. Knight, P.St.J. Russell, and P.J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609 [CrossRef] [PubMed]

11.

K. Saitoh, M. Koshiba, H. University, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11, 843–852 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843 [CrossRef] [PubMed]

12.

A. Ferrando, E. Silvestre, P. Andrés, J.J. Miret, and M.V. Andrés, “Designing the properties of dispersion flattened photonic crystal fibers,” Opt. Express 9, 687–697 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687 [CrossRef] [PubMed]

13.

F. Brechet, P. Roy, J. Marcau, and D. Pagnoux, “Single propagation into depressed-core-index photonic bandgap fibre designed for zero-dispersion propagation at short wavelengths,” Elec. Lett. 36, 514–515 (2000). [CrossRef]

14.

G. Ouyang, Y. Xu, and A. Yariv, “Comparative study of air-core and coaxial Bragg fibers: singlemode transmission and dispersion characteristics,” Opt. Express 9, 733–747 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-733 [CrossRef] [PubMed]

15.

G. Ouyang, Y. Xu, and A. Yariv, “Theoretical study on dispersion compensation in air-core Bragg fibers,” Opt. Express 10, 899–908 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-899 [CrossRef] [PubMed]

16.

E. Silvestre, M.V. Andrés, and P. Andrés, “Biorthonormal-basis method for the vector description of optical-fiber mode,” J. Lightwave Technol. 16, 923–928 (1998). [CrossRef]

17.

A.W. Snyder and J.D. Love, Optical Waveguide Theory (Chapman & Hall, 1983), p. 248.

18.

D. Davidson, Optical-Fiber Transmission (E.E. Bert Basch, ed., Howard W. Sams & Co, 1987), pp. 27–64.

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2430) Fiber optics and optical communications : Fibers, single-mode

ToC Category:
Research Papers

History
Original Manuscript: May 20, 2003
Revised Manuscript: June 5, 2003
Published: June 16, 2003

Citation
Juan Monsoriu, Enrique Silvestre, Albert Ferrando, Pedro Andrés, and Juan Miret, "High-index-core Bragg fibers: dispersion properties," Opt. Express 11, 1400-1405 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-12-1400


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References

  1. J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, "Photonic band gap guidance in optical fibers,??? Science 282, 1476-1478 (1998). [CrossRef] [PubMed]
  2. A. Ferrando, E. Silvestre, J.J. Miret, P. Andrés, and M.V. Andrés, ???Donor and acceptor guided modes in photonic crystal fibers,??? Opt. Lett. 25, 1328-1330 (2000). [CrossRef]
  3. P. Yeh, A. Yariv, and E. Marom, ???Theory of Bragg fiber,??? J. Opt. Soc. Am. 68, 1196-1201 (1978). [CrossRef]
  4. Y. Xu, G.X. Ouyang, R.K. Lee, and A. Yariv, ???Asymptotic Matrix Theory of Bragg Fibers,??? J. Lightwave Technol. 20, 428-440 (2002). [CrossRef]
  5. M. Ibanescu, Y. Fink, S. Fan, E.L. Thomas, and J.D. Joannopoulos, ???An all-dielectric coaxial waveguide,??? Science 289, 415-419 (2000). [CrossRef] [PubMed]
  6. S.G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T.D. Engness, M. Soljacic, S.A. Jacobs, J.D. Joannopoulos, and Y. Fink, ???Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,??? Opt. Express 9, 748-779 (2001),<a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748</A> [CrossRef] [PubMed]
  7. J. Xu, J. Song, C. Li, and K. Ueda, ???Cylindrically symmetrical hollow fiber,??? Opt. Commun. 182, 343-348 (2000). [CrossRef]
  8. A. Argyros, I. Bassett, M. van Eijkelenborg, M.C.J. Large, J. Zagari, N.A.P. Nicorovici, R.C. McPhedran, and C.M. de Sterke, ???Ring structures in microstructured polymer optical fibres,??? Opt. Express 9, 813-820 (2001),<a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-813 ">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-813 </a> [CrossRef] [PubMed]
  9. A. Ferrando, E. Silvestre, J.J. Miret, and P. Andrés, ???Nearly zero ultraflattened dispersion in photonic crystal fibers,??? Opt. Lett. 25, pp. 790-792 (2000). [CrossRef]
  10. W.H. Reeves, J.C. Knight, P.St.J. Russell, and P.J. Roberts, ???Demonstration of ultra-flattened dispersion in photonic crystal fibers,??? Opt. Express 10, 609-613 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609</a>. [CrossRef] [PubMed]
  11. K. Saitoh, M. Koshiba, H. University; T. Hasegawa, and E. Sasaoka, ???Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,??? Opt. Express 11, 843-852 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843</a> [CrossRef] [PubMed]
  12. A. Ferrando, E. Silvestre, P. Andrés, J.J. Miret, and M.V. Andrés, ???Designing the properties of dispersion flattened photonic crystal fibers,??? Opt. Express 9, 687-697 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687</a> [CrossRef] [PubMed]
  13. F. Brechet, P. Roy, J. Marcau, and D. Pagnoux, ???Single propagation into depressed-core-index photonic bandgap fibre designed for zero-dispersion propagation at short wavelengths,??? Elec. Lett. 36, 514-515 (2000). [CrossRef]
  14. G. Ouyang, Y. Xu, and A. Yariv, ???Comparative study of air-core and coaxial Bragg fibers: singlemode transmission and dispersion characteristics,??? Opt. Express 9, 733-747 (2001),<a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-733">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-733</a> [CrossRef] [PubMed]
  15. G. Ouyang, Y. Xu, and A. Yariv, ???Theoretical study on dispersion compensation in air-core Bragg fibers,??? Opt. Express 10, 899-908 (2002),<a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-899">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-899</a> [CrossRef] [PubMed]
  16. E. Silvestre, M.V. Andrés, and P. Andrés, ???Biorthonormal-basis method for the vector description of optical-fiber mode,??? J. Lightwave Technol. 16, 923-928 (1998). [CrossRef]
  17. A.W. Snyder and J.D. Love, Optical Waveguide Theory (Chapman & Hall, 1983), p. 248.
  18. D. Davidson, Optical-Fiber Transmission (E.E. Bert Basch, ed., Howard W. Sams & Co, 1987) , pp. 27- 64.

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