Low dispersion fiber system for high speed communication system over the entire S- to L- bands of EDFA R. K. Varshney*, I. C. Goyal and A. K. Ghatak Department of Physics, Indian Institute of Technology New Delhi - 110 016, INDIA Telephone: + 91-11- 659 1357, Fax: + 91-11-686 5039 * E-mail:
[email protected] ABSTRACT We have given designs for a small residual dispersion fiber system consisting of a small dispersion fiber (SDF) and the corresponding dispersion compensating fiber (DCF). The SDF has flat modal field over the central part of the core, which provides a large mode field diameter (MFD = 9.4 µm at λ0 = 1.55 µm) leading to the large effective area (Aeff ≈ 80 µm2) required to reduce nonlinear effects. The DCF, which is based on the dual core coaxial configuration, has large negative dispersion (≈ -210 ps/km/nm at λ0 = 1.55 µm). Dispersion slopes of these fibers are so adjusted that a small length of DCF will nearly compensate the accumulated dispersion in SDF simultaneously at all wavelengths in the range of 1480 -1610 nm, which covers the entire S- to L- bands of EDFA. The maximum values of the effective dispersion of the fiber system and its slope are ± 0.21 ps/km/nm and ± 0.02 ps/km/nm2, respectively in the entire S- to L- bands. Keywords: Small Dispersion Fiber, Dispersion Compensating Fiber, Non-zero Dispersion Shifted Fiber, Small Residual Dispersion Fiber, Large Effective Area Fiber, Flat Modal Field Fiber, Dispersion Compensation over S- to L- bands, Dual Core Coaxial Fiber.
1. INTRODUCTION Due to the drastic increase in the internet traffic, tremendous amount of efforts are being made to develop a high speed DWDM transmission system 1, 2. In such systems, the nonzero dispersion shifted fibers having small dispersion over the entire gain window of EDFA, are used to reduce nonlinear effects like four wave mixing (FWM), which arises due to simultaneous transmission at many closely spaced wavelengths and high optical gain from EDFA. Nonlinear effects like cross phase modulation (XPM), which limits the numbers of different wavelength signals, can be reduced by increasing the mode field diameter (MFD) and hence effective area of the nonzero dispersion shifted fiber. Therefore large effective area nonzero dispersion shifted fibers have been designed and developed 3, 4. However, if one wants repeaterless transmission over very large distances, the residual dispersion in these fibers will go on accumulating and will limit the number of bits one can send at each wavelength. Therefore high speed DWDM transmission system demands the compensation of not only dispersion but also the dispersion slope so that the residual dispersion over the entire wavelength range is very small. Amongst various techniques proposed for this purpose, DCF’s are more promising for broadband compensation of the accumulated dispersion 5-8. The design of DCF is, therefore, has to be compatible with the small dispersion fiber. In this paper, we have given designs for a small residual dispersion fiber system consisting of a small dispersion fiber and the corresponding dispersion compensating fiber. The SDF is designed to have flat modal field over the central part of the core leading to large mode field diameter and hence the large effective area required to reduce nonlinear effects. The DCF, which is based on the dual core coaxial configuration, has large negative dispersion. Dispersion slope of these fibers are so adjusted that a small length of DCF will compensate the accumulated dispersion in SDF simultaneously at all wavelengths covering the entire S- to L- bands.
2. DESIGN CONSIDERATION For a small dispersion fiber, we have considered a fiber consisting of a central dip, core, depressed inner cladding and outer cladding. The refractive index profile of the SDF is shown by solid curve in Fig. 1(a). Since this fiber structure is a 4 region configuration, modal characteristics (e.g., propagation constant, dispersion, mode field profile, etc.) of the fiber can be studied by following any method associated with the multilayer structure. We have obtained the dispersion characteristics of the proposed fiber by using the software based on the Runge-Kutta method discussed in the appendix of Ref. 9. In order to obtain the flat modal field over the entire central dip region, the
n2
n1
n(r)
n (r)
effective index (neff) of the mode should be equal to the refractive index of the central dip (i.e., neff = n1). The dispersion coefficient (D) is obtained as 2 λ d neff D = − (1) c dλ2 where, c is the velocity of light in free space and λ is the wavelength of light. Design of the SDF is optimized to achieve large effective area and appropriate dispersion. The refractive index profile of the dispersion compensating fiber is shown schematically by solid curve in Fig. 1(b). It consists of a coaxial configuration of very high dissimilar cores (inner core and outer core). The inner core has a relatively larger value of the relative index difference (∆) as compared to the outer core. Since this fiber structure is also a 4 region configuration, we have obtained the modal characteristics of the fundamental mode by using the same software. The DCF is designed for obtaining large negative dispersion and appropriate dispersion slope so that accumulated dispersion in SDF will be compensate simultaneously over the entire S- to L- bands.
n1
n4
n3
n3
(a)
a
n4
n2 b
r
a
d
b
(b)
r
d
Figure1: The refractive index profile of the actual (solid curve) and perturbed (dotted curve) fiber corresponding to (a): small dispersion fiber and (b): dispersion compensating fiber.
3. RESULTS AND DISCUSSIONS In order to obtain the various modal characteristics of the proposed fibers (SDF and DCF), we have used the software based on the Runge-Kutta method. The optimized values of various parameters used in design of the dispersion characteristics of the SDF are tabulated in Table 1. Here, the relative index difference ∆i = (ni 2- n4 2)/2ni2, (i =1, 2, 3), and the outer cladding (4th region) is assumed to be made of pure silica. Table 1: The values of various parameters used in design of the SDF and DCF.
Fiber SDF DCF
a (µm) 2.0 1.1
b (µm) 4.2 4.6
d (µm) 7.3 6.7
∆1 (%)
∆2 (%)
∆3 (%)
0.06 2.0
0.40 -0.32
- 0.30 0.30
With these values of parameters, we obtain neff - n1 = 1.6×10-4, which indicates that the modal field ψ (r) in the central dip region would be flat. The normalized mode field (ψ (r)/ψ (r = 0)) profile of the fundamental mode calculated at λ0=1550 nm is shown by solid curve in Fig.2. Dashed curve in this figure corresponds to the normalized refractive index profile ({n2(r) – n32}/{n22 – n32}) of the fiber. This figure clearly shows that the modal field is almost constant over the central dip region. The values of the MFD and Aeff associated with the modal field of the proposed design are 9.4 µm and ~ 80 µm2, respectively. The total dispersion coefficient (DS), which includes both waveguide and material dispersion of the fiber, is calculated using Eq. (1) in the wavelength range of 1480 to 1610 nm, which covers the entire S- to L- bands. In order to study the tolerance of the various characteristics of the proposed fiber design, we have randomly changed the values of thickness and ∆ of each region by 2%; the actual and the corresponding perturbed refractive index profiles are shown schematically in Fig. 1(a) by the solid and dotted curves, respectively. Figure 3 shows the variation of the total dispersion (DS) with wavelength. The solid and dotted curves correspond to the actual and the perturbed refractive index profiles, respectively. This figure indicates that over the entire wavelength range of 1480 to 1610 nm, the dispersion value is within 8-12 ps/km/nm desirable to avoid four wave mixing (FWM).
Normalized Modal Field
1 0.8 0.6 0.4 0.2 0
0
0.5
1
1.5
2
2.5
3
r/b Figure2: The normalized mode field (ψ (r)/ψ (r = 0)) profile of the fundamental mode of SDF at λ0=1550 nm. The dashed curve corresponds to the normalized refractive index profile.
DS (ps/km/nm)
12
11
10
9 8 1.48
1.52
1.56
1.6
Wavelength (µm) Figure3: Variation of the total dispersion (DS) of the SDF as a function wavelength. The solid and dotted curves correspond to the proposed and the perturbed refractive index profiles (shown in Fig. 1(a)), respectively.
The values of various parameters used in the design of DCF are tabulated in Table 1. Spectral response of the dispersion (DC) of the DCF is shown in Fig.4, where the solid and dotted curves correspond to the actual and the perturbed DCF’s, respectively. Dispersion values of the DCF vary between ≈ -170 to -240 ps/km/nm in the wavelength range from 1480 to 1610 nm. The slopes of the dispersion curves shown in Figs. 3 and 4 are such that the accumulated dispersion in SDF is compensated simultaneously at all wavelengths between 1480 to 1610 nm if LS ≅ 19.73 LC, where LS and LC are the length of the SDF and DCF, respectively. Spectral response of the effective dispersion DE {= (LSDS + LCDC) / (LS + LC)} of the proposed fiber system (with LS ≅ 19.73 LC) is shown in Fig. 5. The solid and dotted curves correspond to the actual and perturbed system, respectively. The dotted curve corresponds to LS ≅ 19.13 LC. The maximum value of the effective dispersion of the proposed fiber system is ± 0.21 ps/km/nm. We have also calculated the slope of the effective dispersion, and its maximum value is less than ± 0.015 ps/km/nm2. The maximum length L (in km) of a repeaterless transmission link using DFB laser diodes, with bit rate B (in Gb/s) and the effective dispersion DE (in ps/km/nm) should be ≤ 105/( B2.DE). In our case, it comes out to be more than 4,700 km for 10 Gb/s DWDM system.
DC (ps/km/nm)
-1 5 0 -1 7 0 -1 9 0 -2 1 0 -2 3 0 -2 5 0 1 .4 8
1 .5 2
1 .5 6
1 .6
Wavelength (µm) Figure 4: Variation of the total dispersion (DC) of the DCF as a function wavelength. The solid and dotted curves correspond to the proposed and the perturbed refractive index profiles (shown in Fig. 1(b)), respectively.
DE (ps/km/nm)
0 .2 1 0 .1 4 0 .0 7 0 -0 .0 7 -0 .1 4 -0 .2 1 1 .4 8
1 .5 2
1 .5 6
1 .6
Wavelength (µm) Figure 5: Variation of the total effective dispersion (DE) of the system as a function wavelength. The solid and dotted curves correspond to the proposed and the perturbed refractive index profiles (shown in Figs. 1(a) & (b)), respectively.
4. CONCLUSION We have given designs for a very small residual dispersion fiber system consisting of a small dispersion fiber (SDF) and the corresponding dispersion compensating fiber (DCF). The SDF has a flat modal field over the central part of the core, which provides large mode field diameter (MFD = 9.4 µm at λ0 = 1.55 µm) leading to the large effective area (Aeff ≅ 80 µm2). The DCF, which is based on the dual core coaxial configuration, has large negative dispersion (-210 ps/km/nm at λ0 = 1.55 µm). The maximum values of the effective dispersion of the fiber system and its slope are ± 0.21 ps/km/nm and ± 0.015 ps/km/nm2, respectively in the entire S- to L- bands. Thus, the proposed fiber system can provide more than 4,700 km long repeaterless transmission at 10 Gb/s DWDM system over the entire S- to L- bands. The study shows that 2% random variation in the refractive index profiles does not make significant change in effective dispersion of the link.
ACKNOWLEDGEMENT This work was partially supported by the Department of Science and Technology (Govt. of India) sponsored research project “R & D on side polished fiber based devices”, and also by All India Council of Technical Education.
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