Chromatic dispersion management of high-index glass photonic

crystal fiber

Arismar Cerqueira S. Jr.* and K. Z. Nobregat ·Visiting researcher from the Department of Physics - University of Bath (UK)

and PhD student from Scuola Superiore Sant' Anna di Studi Universitari e di Perfezionamento (Italy)

Email: arismar.cerqueira@cnit.it. t CEFET-MA, Sao Luis-Ma, Brazil

E-mail:bzuzal @Yahoo.com.br.

Abstr..,cl-Chromatic dispersion engineering is one of the most promising advantages provided by the photonic crystal fibers, PCFs. Their two-dimensional photonic crystal permits to manage the waveguide dispersion as a function of the their design parameters: inter-hole spacing, hole diameter, number of air rings and dadding refractive index. Most PCFs are silica-based and has a honeycomb dadding. This paper presents a dispersion design methodology of high-index glass photonic crystal fibers, based on a new-geometry. Its numerical results pOint out positive or nearly zero ultra­Battened dispersion in a wide wavelength range. The nearly zero case presents chromatic dispersion at ..\=1.55",m equal to -0.352 psjkmjnm and a quite low slope equal to 1.10-3 psjnm2 jkm at 1.5-1.6",m window. The lowest obtained slope was 5.10-4 psjnm2 jkm.

Index Terms- U1tra-llat dispersion, photonic crystal fiber and high-index glass.

I. INTRODUCTION

Photonic Crystal Fibers (PCFs), also known as Holey Fibers, were proposed by Russell and his team, from University of Bath, in 1992. The first prototype was produced in 1995 and reported in 1996 [I]. Since then, this new kind of fiber has been extensively studied and investigated. There are many kinds of PCFs with different geometries and propagation mechanisms, which have been proposed in accordance to the desired application, such as endlessly single-mode [2], birefringent, ultrahigh nonlin­ear, large mode-area, dispersion flattened and hollow-core PCFs [3] [4) [5]. Most reported research on photonic crystal fibers has concerned fibers made of silica using a stack-and-draw process, although fibers drawn from other glasses [6) and even polymers [7] have also been reported. Feng and Monro have been recently fabricated a high-idex (n= 1.8) glass based monomode holey fiber [8].

Their applications are not limited to optical commu­nications; it is also possible to improve optical coher­ence tomography, frequency metrology and spectroscopy with their remarkable properties. PCFs have multiple air holes periodically arranged around the core. This periodic structure is called photonic crystal and it is similar to normal crystals present in semiconductor materials. In other words, photons in a PCF have similar behavior as

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electrons have in a semiconductor crystal. Initially, the photonic band gap, PBG, had been considered the only guiding mechanism for trus kind of optic fiber. Later, researches have discovered that these fibers could similarly provide revolutionary features using the simplest and most conventional principle of total internal reflection.

Index-guiding PCFs possess the especially attractive property of great controllability in chromatic dispersion by varying their photonic crystal. Control of chromatic dispersion is an extremely important problem for practical applications to optical communication systems, dispersion compensation, and nonlinear optics. The dispersion slope of standard step-index fibers is on the order of 4.0· 10-2

ps/nm2/km. With the use of traditional PCFs, it can be reduced to 4 . 10-3 ps/nm2/km by using sub-micron air hole [9) and to 1.6.10-3 ps/nm2/km by varying the air hole diameters along the fiber radius in hexagonal PCFs (10). This paper presents a dispersion management of PCFs based on a new geometry that has been proposed in a previous work [11]. Additionally, a nearly zero and a positive ultra-flattened dispersion in a high-index non­silica glass photonic crystal fiber is proposed. A design tool [11) based on a full-vectorial finite element method has been applied for design and optimization of PCFs fibers. It provides very accurate predictions of modal and dispersion properties.

II. CHROMATIC DISPERSION MANAGEMENT

Standard fiber technology is mainly limited by how small and well-controlled can be the refractive index step between core and cladding. Its conventional structure is based on a simple concentric core-cladding geometry that confines the light in the core by total internal reflection. On the other hand, index-guiding PCFs possess the especially attractive property of great controllability in chromatic dispersion.

In comparison to traditional optical fibers, it is evident that of photonic crystal fibers have a more complex geometrical structure because of their two dimensional photonic crystal. Their unusual properties result from the structure in the cladding can be designed on the same

physical scale as the light wavelength. In order to model the optical properties of a peF, it is necessary to describe accurately the transverse refractive index profile.

The total dispersion D consist of the sum of the geo­metrical dispersion, Dg, and the material dispersion, Dm. Dm is mostly determined by wavelength dependence of the fiber material, considered through Sellmeir equation, and, therefore, cannot be very much altered in the dispersion design. On the other hand, Dg of peF is strongly related to the structure, so it can be significantly changed to achieve the desired dispersion characteristics. Through properly scaling Dg, the optimized peF structure for some desired dispersion at some specific wavelengths can be obtained considering Dm [12].

In traditional peFs, the air holes are arranged in a hexagonal honeycomb pattern across their cross section, as shown in figure lea). Here it is being proposed a new and simple geometry for designing solid-core peF, figure I (b). peF can be understood by viewing the array of holes as a modal filter or sieve [5]. This novel structure follows this idea, or in other words, it has been intuitively created for taking advantage of the air holes in order confine the light in the peF core. So that, light must be evanescent in the air and unable to escape between their gaps.

(a) Hexagonal pattern. (b) New pattern.

Fig. I. Traditional and new geometries.

In order to investigate the effects of geometrical per­turbations, the peF design parameters have been initially studied with only two layers of air holes in two different ways: varying d, maintaining A; and varying d and A, maintaining the ratio d/ A. The first case has been analyzed for two different A: A = 25p.m and A = 5J1.m, as shown respectively in figs. 2(a) and 2(b). It is easy to see that in this novel approach the periodicity represents an extremely important design parameter, because for larger values of A, the peF chromatic dispersion profile does not change, independently of the ratio d/ A, as shown in 2(a). On the other hand, peFs with in the same order of magnitude of the wavelength range, the group-velocity dispersion, GVD, can be increased by increasing the air hole size as shown in Fig. 2(b).

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(a) A = 25J.1m.

(b) A = 5J.1m.

Fig. 2. Dispersion curves of PCFs with the same inter-hole spacing.

The second case is shown in Fig. 3 for peFs with d/ A =0.6. It illustrates how the dispersion properties can be changed as a function of A. If the inter-hole spacing is increased, the Zero-Dispersion-wavelength is also in­creased [13] [14], so it is possible to accurately design this parameter as a function of A. Nevertheless, it is very important to realize that the peF chromatic dispersion varies slowly as a function of the pitch size when it is much larger than the wavelength, as shown in Fig. 3(b) for A larger than 20 m.

The dispersion control is enhanced when the number of layers is increased. It makes necessary to design not only the inter-hole spacing and the air hole diameter d, but also the number of layers required to satisfy the ultra-flattened dispersion conditions. In addition, different glasses can also be exploited, since in this way both Dg and Dm can be tailored. Fig 4(a) presents a comparison between two PCFs with the same geometric parameters, or in other words, 02 layers, d=2.025p.m and A = 4.5J1.m, but with different cladding materials: silica (n=1.45) and glass (n=1.80).

Fig. 3. Dispersion curves of PCFs with d/ A = 0.6.

The parameters of the Sellmeir equation for the high­index glass have been obtained from the datasheet of S­LAM66 fiber, from OHARA GmbH, which has a refractive index n=1.8 [15]. It is easy to realize that the higher refractive index step of the glass case provides a steeper slope when compared to the silica case. Since the group­velocity dispersion depends on the group index, if the ef­fective index is increased the waveguide dispersion will be reduced. Particularly in this case, this component mirrors the material dispersion, giving a flat resultant dispersion. Since the main goal is to find a nearly zero dispersion PCF, it has been increased the number of air rings in order to decrease the dispersion, as shown in figure 4(b). In fact, the waveguide dispersion is decreased of approximately 50% as one more layer is added in both cases, A = 4.5j.tm and A = 10.0j.tm.

Moreover, this figure shows that the waveguide disper­sion converges to a limit when the number of rings is increased. These phenomena can be understood by the following way: Since losses are reduced and the magnetic field confinement is increased by increasing the number of layers [16], when losses are weak, a supplementary

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layer will not strongly change the mode. On the other hand, if the mode is not well confined in the PCF core, a supplementary layer will significantly modify the field pattern. It is important to point out that for pitches much larger than the wavelength rage, for example 1O.0j.tm, the dispersion decreases monolithically with the increase of the number of layers, because in these cases the PCF core is too large and, consequently, the waveguide effects on dispersion are weak; thus the material dispersion domi­nates. It is fundamental to realize that in this approach for the same relation d/ A , the dispersion can also be reduced by increasing the inter-hole spacing.

(a) Dispersion for PCFs with d=2.025ILm and A><4.5 ILm

(b) Waveguide dispersion for PCFS with dJA =0.45 at A=1200nm.

Fig. 4.

Figure 5 shows the curves characterized for having positive and nearly zero ultra-dispersion. The positive case presents dispersion between 16 and 17 ps/nm/km and an incredible slope equal to 5· 10-4 ps/nm2/km between 1.24 and 1.4j.tm. Whereas, the nearly zero one provides a ultra-flattened dispersion in a quite wide wavelength range, from 1.24 to 1.64 m, in which the dispersion varies from -

1.30 to - 0.22 ps/nm/km, giving a slope equal to 2.7.10-3 ps/nm2/km. It is fundamental to highlight that at the telecommunications windows from 1.5 to 1.6J1-m, this PCF provides dispersion equal to -0.352 pslkmlnrn at 1.55J1-m and a slope of 1 . 10-3 ps/nm2/km that represents an improvement of 40 times compared to traditional optical

fibers and a reduction of ate least 37.5% with respect to other PCFs. This design principle can be also applied to

control the dispersion properties of high nonlinear and

dispersion compensating PCFs.

Fig. 5. Nearly zero and positive ultra-flattened dispersion curves.

III. CONCLUSIONS AND FUTURE WORK

It has been proposed a new way to design positive and nearly zero ultra-flattened dispersion photonic crystal fibers, based on a new geometry and a high refractive

index step profile. The optimized PCFs have been designed taking into account the effects provided by the increase

of refractive index step and the suitable choice of PCF

design parameters (number of air holes rings, hole sizes and inter-hole spacing). It has been proposed a twelve­

ring PCF, which provides nearly zero ultra-flattened dis­

persion in a quite wide wavelength range, from 1.24 to

1.64J1-m, in which the dispersion varies from -1.30 to -

0.22 ps/nm/km, providing a slope equal to 2.7· 10-3 ps/nm2/km and, at the same time, it has dispersion equal to - 0.352 ps/km/nm at 1.55I-Lm and a slope of 1. 10-3 ps/nm2/km at the telecommunications windows from 1.5 to 1.6J1-m that represents an improvement of 40 times compared to traditional optical fibers and a reduction of ate

least 37.5% with respect to other PCFs. Additionally, it has been shown that it is possible to design an eight-ring PCF

that presents a positive ultra-flattened dispersion ( between 16 and 17 ps/nm/km) over wide spectral range, from

1.24 to 1.64J1-m, and an incredible slope equal to 5 . 10-4

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ps/nm2/km between 1.24 and 1.41-Lm. The fabrication

facilities from the University of Bath have been adapted in order to fabricate these new geometry-based ultra-flattened

dispersion PCFs in a near future.

REFERENCES

[lJ J.C. Knight, T.A. Birks, P.SJ. Russell, and D.M. Atkin, "All-silica single-mode fiber with photonic crystal cladding," Opt. Letters, vol. 21, pp. 1547-1549, 1996.

[2] E. Silvestre, P.SJ. Russell, T.A. Birks, and J.C. Knight, "Endlessly single-mode heat-sink waveguide," CLEO, p. 428, 1998.

[3] A. P eyri\loux, T. Chartier, A. Hideur, L. Berthelot, G. Miin, S. Lem­pereur, D. P agnoux, and P. Roy, "Theoretical and experimental study of the birefringence of a photonic crystal fiber," Journal of lightwave technology, vol. 21, pp. 536-539,2003.

[4] J. C. Knight, T. A. Birks, P. St J. Russell, and 1. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," Journal of Optical Society of America A, vol. 15, pp. 748-752, 1998.

[5] P. SI. J. Russell, " P botonic crystal fibers," Science, vol. 229, pp. 358-362, 2003. V. V. R. K. Kumar, A. K. George, W. H. Reeves, J. C. Knight, and P. S. 1. Russell, "Extruded soft glass pbotonic crystal fiber for ultrabroad supercontinuum generation," Optics express, vol. 10, pp. 1520-1525, 2002.

[7] Martunjn et ai, "Microstructured polymer optical fiber," Optics express, vol. 9, pp. 319-327, 2001. D. W. Hewak X. Feng, A. K. Mairaj, and T. M. Monro, "Towards high-index glass based monomode boley fiber with large mode area," Electronics Leiters, vol. 40, 2004. W. H. Reeves, J. C. Knight, P. S. l Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Optics express, vol. 10, pp. 609-6\3,2002. K. Saitoh. M. Koshiba, T. Hasegawa, and E. Sasaoka, "Chromatic dispersion control in pbotonic crystal fibers: application to ultra­flattened dispersion," Optics express, vol. II, pp. 843-852, 2003.

[II] Arismar Cerqueira S. Jr., K. Z. Nobrega, H. E. Hernandez-Figueroa, and F. Di Pasquale, "A powerful tool based on finite element method for designing photonic crystal devices," IEEE International Conference on Telecommunications, August 2004.

[12] L. P. Shen, W.-P. Huang, G. X. Cben, and S. S. Jian, " Design and optimization of photonic crystal fibers for broad-band dispersion compensation," Transactions on magnetics, vol. 15, pp. 540-542, 2003.

[13] lC. Knight, J. Arriaga, T.A. Birks, Ortigosa-Blancb, W. J. Wadsworth, and P.S.J. Russell, "Anomalous dispersion in ph.otonic crystal fibers," Photonics Technology Lellers, vol. 12, pp. 807-809, 2000.

[14] lincbae Kim, Un-Chul Paek, Dug Young Kim, and Youngjoo Chung, "Analysis of dispersion properties of holey optical fibers using normalized dispersion," Opt. Leiters, 2000.

[15] Ohara Gmbh, "Datasheet of s-lam66:' hltp:llwww.ohara-gmbh.com. 2004.

[16] Boris Kuhlmey, Gilles Renversez, and Daniel Mastre, " Dispersion and losses of microstructured optical fibers," Applied optics, vol. 42, pp. 634-639, 2003.