1. Introduction

Bragg fiber consisting of a core surrounded by alternating layers of high and low refractive index was first proposed in [1]. Light is confined in the core by the one-dimensional photonic bandgap (PBG) effect, which is caused by Bragg reflection of light from the alternating layers. Bragg fiber is a beautiful idea, but it is rather difficult to fabricate a Bragg fiber with conventional technique. It was more than 20 years later that first actual Bragg fiber was fabricated in MIT [2], which was composed of alternating layers of PES and As₂Se₃. A silica core Bragg fiber was fabricated by sputtering Si and SiO₂ alternatively on silica fiber [3], but the fiber length is only 20 cm, because the Si layers in cladding restricts the drawing of fiber.

Bragg fibers may have novel dispersion properties due to the cladding structures. The potential application of air-core Bragg fibers for dispersion compensation was discussed in [4], with refractive index contrast of 4.6:1.5 in the cladding, very large negative dispersion value (-20,000 ps/(nm.km)) was achieved. However, it is very difficult to connect this air-core Bragg fiber with conventional silica fibers, for the material in these two kinds fibers are not matched.

A new air-silica Bragg fiber design was proposed in [5], which was a cylindrically symmetric fiber with a high-index core (silica) surrounded by alternating layers of silica and air, and dispersion properties of this air-silica Bragg fiber was discussed. However, in practices, it was impossible to provide structural support to this air-silica fiber, which made this design unrealizable.

In this paper, a novel all-solid silica Bragg fiber is proposed, the core is composed of conventional silica material and the cladding are formed by alternating layers of cylindrical up-doped and down-doped silica. Technically, silica can be up-doped (for example, doped with Gemanium) or down-doped (for example, doped with Fluorine), and the index variation (Δn) of doped silica can reach about 2%. Our all-solid Bragg fiber is entirely made of silica material, which simplifies the fabrication technique and can be made by the conventional fiber drawing process. The preform of this Bragg fiber can be made by putting alternating up-doped and down-doped silica tubes on the silica core, for the melting points of the core and the two cladding materials are very close, the preform can be easily drawn in the drawing tower.

Influence of doping level and cladding parameters on chromatic dispersion (D) of this all-solid silica Bragg fiber is investigated and it is shown that zero dispersion wavelength λ ₀ around 1.55 μm with nonlinear coefficient γ (n₂/A_eff) about 50 W^-1km^-1 can be obtained in this all-solid silica Bragg fiber.

2. Fiber design and dispersion simulations

The schematic diagram of all-solid silica Bragg fiber is shown in Fig. 1. Figure 1(a) is the cross section of fiber, the centric red circle is the silica core, white and black rings are up-doped and down-doped silica layers, respectively. The index profile of this all-solid silica Bragg fiber is shown in Fig. 1(b), with core radius r₀, radial multilayer period Λ, and the down-doped-layer thickness a, the refractive indices of core, up-doped and down-doped silica layers are n_C, n₁, and n₂, respectively. According to the technical feasibility, in the following simulations, we set n₁=(1+0.015) n_S and n₂=(1–0.015) n_S, here, nS is the refractive index of pure silica.

 

Fig. 1. Schematic diagram of all-solid silica Bragg fiber (a) cross section (b) refractive index profile.

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In this paper, mode field pattern and dispersion of all-solid silica Bragg fiber are simulated with Hermite-Gaussian functions [6][7], which is an efficient model for analyzing the modes in photonic crystal fiber (PCF), it takes only 1 minute to accomplish once simulation on P4-2GHz computer and offers a convenient method for parameter optimization. We use this model to simulate the PBG in [8], our results are consistent with those obtained by the authors, then, we use this model to perform the simulations in this paper. We choose n_C= n_S=1.45, λ=1.55 μm, r₀= 0.5 μm, Λ =1.6μm and a= 0.8 μm, respectively. Model field pattern of fundamental mode (HE₁₁) is shown in Fig. 2, we can see that light is confined in the silica core due to the Bragg reflection in cladding. The effective area of modal field A_eff is about 3 μm², and γ is estimated to be about 50 W^-1km^-1. The core diameter of this all-solid silica Bragg fiber is about 1 μm, whilst that of single mode fiber (SMF) is about 9 μm, the core diameter mismatch between this Bragg fiber and SMF could be solved by connecting these two fibers with a tapered fiber. At present, splicing between high nonlinear PCF (core diameter about 1 μm) and SMF is commercially obtainable. We investigate the modal properties of this Bragg fiber, and find that it is single-mode when λ > 0.3 μm.

 

Fig. 2. Modal field pattern of the fundamental mode (HE₁₁) in all-solid silica Bragg fiber with n_C=n_S, r₀ =0.5 μm, Λ = 1.6 μm and a = 0.8 μm. Units of axes are in μm and λ = 1.55 μm.

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At present, core diameter less than 1 μm and thickness of silica webs in cladding less than 0.5 μm can be achieved in air-silica microstructured fibers [8] [9]. Since there are no air holes in the all-solid silica Bragg fiber, compared with those air-silica microstructured fibers, it is much easier to maintain the fiber shape and the proportion of fiber parameters (r₀/Λ, and a/Λ) during the fiber drawing process. The all-solid merit of this silica Bragg fiber simplifies the fabrication technique, and it is convincible that the core radius of the silica Bragg fiber can be reduced to 0.5 μm.

We calculate the primary PBG of the all-solid silica Bragg fiber with n_C=n₁, then simulate the neff (β/k) of the defect modes with both up-doped (n_C>n₁) and down-doped (n_C<n₁) cores, as shown in Fig. 3. The up-doping level is 1% (n_C=1.01n₁), and the down-doping level are 0.5%, 1%, and 1.5%, respectively.

Figure 3 shows that n_eff of up-doped defect mode is above the PBG, which means the index-guiding effect is the guiding mechanism of up-doped defect mode; in contrast, n_eff of down-doped defect modes lie inside the PBG, which implies that PBG effect is the guiding mechanism of the down-doped defect modes.

In order to investigate the dispersion properties of all-solid silica Bragg fibers thoroughly, in the following dispersion simulations, material dispersion of silica is taken into account through the Sellmeier equation.

 

Fig. 3. Effective indices (n_eff = β/k) for defect modes in all-solid silica Bragg fiber with a/Λ=0.50. The down-doped defect modes from top are for down-doping level of 0.5%, 1%, and 1.5%, respectively.

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Fig. 4. Dispersion of all-solid silica Bragg fiber with r₀= 0.5 μm, Λ= 1.6μm and a/Λ=0.50 for different down-doped levels: 0.5% (black), 1% (red), and 1.5% (green).

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Chromatic dispersion D is composed of waveguide dispersion and material dispersion. Firstly, we investigate the influence of down-doping levels on the material dispersion of all-solid silica Bragg fibers with identical geometrical parameters, wherein the waveguide dispersion is the same. Figure 4 is the dispersion of all-solid silica Bragg fibers with r₀=0.5 μm, Λ=1.6 μm, a/Λ=0.5, and the down-doping levels as 0.5%, 1% and 1.5%, respectively. We can see that D increases with λ, but D values of different down-doping levels vary little, which indicates that down-doping levels of the core have little influence on the dispersion of defect modes. The trend of D increasing with λ is dominated by material dispersion, which is the second-order derivative of the refractive index of doped silica $\left(D=-\frac{c}{\lambda }\frac{d^{2}n}{d{\lambda }^2}\right),$ if down-doping level keeping unvaried, relative variation of D between different curves equal their relative variation of Δn (about 1% in our simulation), therefore, material dispersion is almost identical for different doping levels and D of three curves vary little.

Since doping level has little influence on dispersion, in the following simulations, the down-doping level is set as 1.5%, i.e., n_C= n_S (refractive index of pure silica), the aim of choosing pure silica as the core is to reduce the transmitting loss. Then we investigate the influence of cladding parameters (a and Λ) on the D of all-solid silica Bragg fiber further.

We fix Λ=1.6 μm, dispersion of all-solid silica Bragg fiber with a/Λ=0.4, 0.5, and 0.6, are shown in Fig. 5(a). Then, we fix a/Λ=0.5, dispersion of all-solid silica Bragg fiber with Λ =1.2 μm, 1.6 μm, and 2 μm are shown in Fig. 5(b). Both figures show that D increases with λ, and three lines almost parallel. Zero dispersion wavelength λ ₀ of defect mode increases with a/Λ (when Λ fixed, Fig. 5(a)) or Λ ( when a/Λ fixed, Fig. 5(b)), and λ ₀ can be easily tuned to desired wavelength by adjusting cladding parameters (Λ, a/Λ). For example, we choose r₀=0.5 μm, Λ=1.66 μm, and a/Λ=0.5, dispersion of all-solid silica Bragg fiber is shown in Fig. 6, we can see that λ ₀ is around 1.55 μm. Compared with the shifting of λ ₀ in SMF, that in all-solid silica Bragg fiber can be achieved much easier, for the latter has more flexible waveguide dispersion due to the Bragg cladding.

 

Fig. 5. Dispersion of all-solid silica Bragg fiber (a) Λ= 1.6μm with a/Λ=0.40 (black), a/Λ=0.50 (red), and a/Λ=0.60 (green), (b) a/Λ=0.50 with Λ= 1.2μm (black), Λ= 1.6μm (red), and Λ= 2μm (green).

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The normalized frequency V of step-index fiber is: $V=\frac{2\pi }{\lambda }\rho n_1\sqrt{2\Delta },$ wherein, ρ is the core radius, n₁ is the core index, and Δ is the index contrast between the core and cladding. The index contrast in the cladding of this all-solid silica Bragg fiber is 3%, if the index contrast in step-index fiber is also increased to 3%, to preserve single mode propagation, the fiber radius ρ must decrease. In order to compare the A_eff of this all-solid silica Bragg fiber with that of the step-index fiber, we design a step-index fiber with index contrast of 3% and V=1.5 at 1550nm, then its ρ is about 1.05 μm. The A_eff of this step-index fiber is calculated to be about 7 μm², and γ of this step-index fiber is about 20 W^-1km^-1, it shows that in step-index fiber, small A_eff can be achieved due to the high index contrast. The A_eff of the all-solid silica Bragg fiber is about a half of that of step-index fiber with equal index contrast. This comparation indicates that small A_eff in this all-solid silica Bragg fiber is associated with both the high index contrast and the fiber design. The high nonlinearity of this all-solid silica Bragg fiber can be used in some nonlinear applications, for examples, parametric amplification and wavelength conversion.

The major disadvantage of this Bragg fiber is the high loss, for the low index contrast in cladding results in a large confinement loss, and much more layers are required to reduce the confinement loss to acceptable level. This problem could be solved with large index contrast glasses [11], wherein the index contrast is 1.76:1.53. When index contrast reaches 15%, about 20 layers in cladding can reduce the confinement loss to acceptable level.

 

Fig. 6. Dispersion of high nonlinear all-solid silica Bragg fiber with λ ₀ around 1.55 μm.

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3. Conclusion

In conclusion, we propose a novel all-solid silica Bragg fiber with cladding composed of a set of alternating layers of up-doped and down-doped silica. This all-solid silica Bragg fiber is technically feasible, and it is much easier to maintain the fiber shape and the proportion of fiber parameters (r₀/Λ, and a/Λ) during the fiber drawing process. Besides simplifying the fabrication technique, the all-solid merit makes it easy to connect this silica Bragg fiber with conventional fiber. We investigate the dispersion of this all-solid silica Bragg fiber thoroughly, and show that high nonlinear all-solid silica Bragg fiber with γ about 50 W^-1km^-1 and λ ₀ near 1.55 μm and can be obtained.