Large-effective-area dispersion-compensating fiber design based on dual-core microstructure Gautam Prabhakar,1 Akshit Peer,2 Vipul Rastogi,3,* and Ajeet Kumar4 1 2 3
Department of Electrical Engineering, Delhi Technological University, Delhi 110 042, India
Department of Computer Engineering, Delhi Technological University, Delhi 110 042, India
Department of Physics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247 667, India 4
Department of Applied Physics, Delhi Technological University, Delhi 110 042, India *Corresponding author:
[email protected] Received 11 March 2013; revised 22 May 2013; accepted 30 May 2013; posted 4 June 2013 (Doc. ID 186750); published 24 June 2013
We present a microstructure-based dual-core dispersion-compensating fiber (DCF) design for dispersion compensation in long-haul optical communication links. The design has been conceptualized by combining the all-solid dual-core DCF and dispersion-compensating photonic crystal fiber. The fiber design has been analyzed numerically by using a full vectorial finite difference time domain method. We propose a fiber design for narrowband as well as broadband dispersion compensation. In the narrowband DCF design, the fiber exhibits very large negative dispersion of around −42;000 ps nm−1 km−1 and a large mode area of 67 μm2 . The effects of varying different structural parameters on the dispersion characteristics as well as on the trade-off between full width at half-maximum and dispersion have been investigated. For broadband DCF design, a dispersion value between −860 ps nm−1 km−1 and −200 ps nm−1 km−1 is obtained for the entire spectral range of the C band. © 2013 Optical Society of America OCIS codes: (060.2270) Fiber characterization; (060.2280) Fiber design and fabrication; (060.2310) Fiber optics; (060.4005) Microstructured fibers. http://dx.doi.org/10.1364/AO.52.004505
1. Introduction
Dispersion-compensating fibers (DCFs) have been effectively employed to compensate for the accumulated dispersion in long-haul optical communication links operating near the 1.55 μm wavelength. The typical value of the dispersion coefficient for such communication links lies in the range of 10 –20 ps nm−1 km−1 . It is essential to compensate for this accumulated dispersion, since it limits the bandwidth of the communication channel and prevents faithful reproduction of the signal at the receiver end. Various structures such as all-solid dual-core fibers [1–7], dispersion-compensating photonic crystal fibers (DC-PCFs) [8–15], Bragg fibers [16–18], and 1559-128X/13/194505-05$15.00/0 © 2013 Optical Society of America
higher-order-mode DCFs [19–23] have been studied in the literature to achieve dispersion compensation. In all-solid dual-core fibers, a maximum dispersion of −14;500 ps nm−1 km−1 and large mode area of 86 μm2 has been predicted by numerical calculations [7]. The designs based on PCFs and Bragg fibers exhibit much larger dispersion values of up to −23;000 ps nm−1 km−1 [14] and −500;000 ps nm−1 km−1 [17], respectively. However, these designs have either small mode areas or involve complex fabrication techniques. For instance, the typical mode area associated with DC-PCF is 30 μm2 for a dispersion value of −19;000 ps nm−1 km−1 [12]. The small mode area inhibits the power transmitted through the fiber because of the introduction of nonlinear effects. Moreover, it also leads to high splice loss when the fiber is joined to a standard optical fiber. On the other hand, designs based on Bragg fiber require stringent 1 July 2013 / Vol. 52, No. 19 / APPLIED OPTICS
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fabrication conditions and exhibit high splice loss due to the presence of a hollow core as opposed to a silica core in standard fiber. For higher-order-mode DCFs, the maximum dispersion coefficient achieved is lower than −1200 ps nm−1 km−1 [23]. In this paper, a novel fiber structure has been proposed combining the conventional all-solid dualcore DCF and DC-PCF. With this design, a narrowband DCF with a high negative dispersion of −42;000 ps nm−1 km−1 and large mode area of 67 μm2 has been achieved. To the best of our knowledge, this is the largest mode area that has been obtained at a dispersion value of −42;000 ps nm−1 km−1. We have investigated the effect of varying different design parameters on the dispersion characteristics as well as on the trade-off between full width at half-maximum (FWHM) and dispersion for the proposed structure. A short length of the fiber, owing to its large negative dispersion, would efficiently compensate for the accumulated dispersion in an optical fiber communication link. Because of its largemode-area, the fiber will have low splice loss and reduced nonlinear effects. In addition, the dispersion characteristics for a broadband DCF design have also been reported. In this paper, we have extended the work reporting a large-mode-area dual-core microstructured fiber design for dispersion compensation in optical communication systems [24]. 2. Fiber Design
The proposed fiber has been designed by utilizing the properties of all-solid dual-core DCF and DC-PCF. The transverse cross section of the proposed fiber is shown in Fig. 1. The radius of the inner core is a, the width of the inner cladding is d1 , and the width of outer core is d2 . The inner core is formed by Ge-doped glass with a relative index difference Δ . The outer core is also Ge-doped and is surrounded by outer cladding made of pure silica. The inner cladding consists of pure silica with microstructured air holes of radius r arranged in concentric circular rings. The air holes are equally spaced in each concentric ring with the number of air holes in the nth concentric ring equal to 8n, where n 1;2;3…. The nth concentric ring of air holes is
Fig. 1. Transverse cross section of the proposed fiber design. The dark gray region shows Ge-doped inner and outer cores of the fiber. The light gray region shows inner and outer cladding made of pure silica. The circularly distributed air holes are shown in white. 4506
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at a distance of ln from the center of the inner core. Similar structures with circularly distributed air holes have been proposed in the literature [25–27]. The proposed fiber can be fabricated by modifying the stack-and-draw technique to assemble the present structure [27]. In addition, the slurry casting method [28] also provides the flexibility to fabricate the present geometry. In Fig. 1, the fiber design with two concentric circular rings of air holes is shown. The proposed fiber design has distinct merits in terms of dispersion management. The structural parameters, viz., a, d1 , d2 , r, l1 , and l2 , provide immense flexibility in tailoring the dispersion characteristics effectively. 3. Numerical Results A. Narrowband Dispersion-Compensating Fiber
In the proposed design, we study the effect of a, d1 , r, l1 , and l2 on resonant coupling and dispersion characteristics. In this study, we have considered r 0.3 μm, d2 1 μm, and Δ 1%. Dispersion characteristics and mode area of the fiber have been calculated by using a full-vectorial finite-difference time-domain method [29]. For the dual-core structure, resonant coupling between the inner and the outer cores is achieved by tuning the various structural parameters. We have carried out numerical calculations for a 1.6 μm, d1 26 μm, l1 6 μm, and l2 12 μm. Figure 2 illustrates the mode field pattern of the symmetric and antisymmetric supermodes for the fiber design at a resonance wavelength of 1544 nm. The variation of effective index neff with wavelength for both symmetric and antisymmetric
Fig. 2. (a) Modal field intensity of the symmetric mode at the resonance wavelength. (b) One-dimensional modal field amplitude of the symmetric and the antisymmetric supermodes at resonance wavelength.
Fig. 3. Spectral variation of effective indices of both symmetric and antisymmetric supermodes.
supermodes has been plotted in Fig. 3. At shorter wavelengths, the symmetric mode is confined in the inner core, and it gradually shifts toward the outer core as wavelength is increased. Because of the highly asymmetric nature of inner and outer cores, there is a sharp change in the slope of the effective index near resonance wavelength λres , which leads to the negative value of dispersion. The dispersion coefficient D is calculated as [30] D−
λ d2 neff ; c dλ2
(1)
where λ is the wavelength and c is the speed of light in free space. The dispersion curve of the present design can typically be characterized by the minimum value of dispersion coefficient D, resonance wavelength λres , and the FWHM. These characteristics can be effectively controlled by the structural parameters a, d1 , r, l1 , and l2 . To illustrate the effect of d1 on dispersion characteristics, the dispersion curve has been plotted in Fig. 4 at different values of d1. With an increase in d1 , the magnitude of dispersion increases with a slight blueshift in resonance wavelength. A dispersion of −7400 ps nm−1 km−1 has been obtained for d1 20 μm. With d1 26 μm, a very high negative dispersion of −42;000 ps nm−1 km−1 has been obtained. With such high negative dispersion, ∼40 m of the fiber will be needed to compensate for the accumulated dispersion in a 100 km conventional single-mode fiber, which is a substantial reduction in fiber length required for dispersion compensation in comparison to previous results [7]. The trade-off between FWHM and dispersion has been illustrated in Fig. 5 by varying the value of d1
Fig. 4. Dispersion curves of the proposed fiber for three different values of inner cladding thickness d1 .
Fig. 5. FWHM versus dispersion curve of the proposed fiber design for a 1.6 μm, l1 6 μm, and l2 12 μm. The curve has been obtained by varying the inner cladding width d1 .
while keeping other parameters constant. For large values of d1, the magnitude of dispersion becomes large, and the corresponding FWHM obtained is of the order of few nanometers; however, smaller values of d1 result in relatively smaller magnitudes of dispersion, but the corresponding FWHM obtained can extend up to tens of nanometers. This property of the fiber design can be beneficial, since, by varying a single parameter d1, one can effectively use this design to tune the FWHM according to the requirements of the optical communication system. The size and arrangement of air holes play an important role in tailoring the dispersion characteristics of the fiber. In fact, the high negative dispersion value of −42;000 ps nm−1 km−1 has been obtained because of air holes that introduce a large index difference between the air holes and silica. In the proposed fiber design, air holes are arranged in the form of two concentric circular rings. If the number of rings is held at one, then it is not possible to obtain such a high value of negative dispersion as in the proposed design. Further, it has been verified that increasing the number of rings to a large value does not affect the dispersion characteristics much. For instance, on increasing the number of rings to three (at d1 20 μm), the value of dispersion changed by 4%. Thus, to keep the structure simple, two concentric circular rings have been employed. Moreover, it is to be noted that if the number of air holes in the nth concentric ring is 6n instead of the present 8n, the magnitude of dispersion decreases by about 33% (at d1 26 μm). The effect of varying l1 on dispersion characteristics and resonance wavelength has been illustrated in Fig. 6. It is evident from Fig. 6 that keeping d1 19 μm and bringing the air holes closer to the
Fig. 6. Dispersion curves of the proposed fiber design with (a) l1 8 μm, (b) l1 6 μm, and (c) l1 4 μm. 1 July 2013 / Vol. 52, No. 19 / APPLIED OPTICS
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−15;000 ps nm−1 km−1 have considerably smaller mode areas, in the range of 1–30 μm2 [11,12,14]. This mismatch in the mode area results in high splice losses and significant nonlinear effects [1,4]. The mode area of the fiber has been calculated by using the following relation [30]: hR i2 2π 0∞ jψrj2 rdr R∞ : (2) Aeff 4 0 jψrj rdr
Fig. 7. FWHM versus dispersion curves of the proposed fiber design for varying values of (a) inner core radius a and (b) inner ring radius l1 .
inner core increases the dispersion significantly with a considerable blueshift in resonance wavelength. It can be seen that for l1 8 μm, a dispersion of −3500 ps nm−1 km−1 has been obtained at λres 1594 nm, while the dispersion increases to −42;000 ps nm−1 km−1 for l1 4 μm and the corresponding λres 1399 nm. Similarly, increasing the core radius a and decreasing the air hole radius r decreases the magnitude of dispersion, but there is a corresponding redshift in the resonance wavelength λres . To observe the effect of varying a and l1 on the FWHM-dispersion trade-off, the curves in Figs. 7(a) and 7(b) have been plotted by varying the value of d1 for a given value of a and l1 , respectively. It can be observed from Fig. 7 that increasing a and decreasing l1 results in an increase in FWHM at the same value of dispersion. It is to be noted that the effect of varying l2 is similar to that of varying l1, but the extent of change in dispersion characteristics is less in the former case. One of the key merits of the proposed fiber design is the large mode area associated with it. The mode effective area of a standard Corning SMF-28 fiber is 85 μm2 . However, the DCFs reported in the literature with high negative dispersion in excess of
Fig. 8. Variation of mode effective area and corresponding dispersion with wavelength for a 1.6 μm, d1 26 μm, and l1 6 μm. 4508
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For the proposed design with a 1.6 μm, d1 26 μm, and l1 6 μm, a mode area of 67 μm2 has been obtained at the resonance wavelength of 1544 nm, and the corresponding dispersion value is −42;000 ps nm−1 km−1 . To the best of our knowledge, this is the largest mode area that has been obtained at a high negative dispersion value of −42;000 ps nm−1 km−1 . Notice that the value of the mode area obtained is very close to that of the standard Corning LEAF and SMF-28 fibers, resulting in low splice losses and negligible nonlinear effects. We have estimated the mode-shape-mismatch loss of the proposed fiber with SMF-28 fiber by calculating the overlap of the modal fields of the two fibers. The value of mode-shape-mismatch loss comes out to be 0.3 dB. Figure 8 shows the spectral variation of mode-effective-area of the fundamental mode of the fiber. For the proposed narrowband DCF design, the bending loss has been calculated to be 0.0133 dB∕m at a bending radius of 3 cm. In most optical communication systems, the spectral linewidth of the laser source used is of the order of 0.1 nm. For the proposed design, the mode area increases by 58% due to a deviation of 0.1 nm from resonance wavelength while a deviation of −0.1 nm decreases the mode area by 24%. B. Broadband Dispersion-Compensating Fiber
Using the proposed design, broadband dispersion compensation can be achieved by tuning the parameters a, d1 , l1 , l2 , and Δ suitably. A dispersion of −450 ps nm−1 km−1 is obtained at 1550 nm for a 2.7 μm, d1 8 μm, l1 4 μm, l2 8 μm, and Δ 0.48%. The parameters have been optimized to obtain maximum dispersion in the C band. The resultant dispersion curve is illustrated in Fig. 9 with the dispersion varying between −860 ps nm−1 km−1 and −200 ps nm−1 km−1 in the spectral range 1530– 1560 nm. The value of bending loss for the proposed
Fig. 9. Dispersion curve of the proposed broadband DCF design.
broadband DCF has been calculated to be 0.9 dB∕m at a bending radius of 8 cm. 4. Conclusion
We have presented a novel microstructured dualcore DCF by combining the designs of all-solid dual-core DCF and DC-PCF. The structure has been implemented by introducing two concentric rings of air holes in the inner cladding of the fiber. The dispersion characteristics of the present fiber design have been analyzed by full-vectorial finite-difference time-domain method. The narrowband DCF exhibits very large negative dispersion of around −42;000 ps nm−1 km−1 , and the corresponding mode effective area is 67 μm2 . The effects of varying various structural parameters on the dispersion characteristics as well as on the FWHM-dispersion trade-off have also been investigated. For broadband DCF design, a dispersion value between −860 ps nm−1 km−1 and −200 ps nm−1 km−1 has been reported in the wavelength range of 1530–1560 nm. The fiber design should be useful for providing dispersion compensation in long-haul optical communication links. G. Prabhakar and A. Peer acknowledge support from the Indian Institute of Technology Roorkee, India, for carrying out this work as a part of their summer project. References 1. K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8, 1510–1512 (1996). 2. J.-L. Auguste, R. Jindal, J.-M. Blondy, M. Clapeau, J. Marcou, B. Dussardier, G. Monnom, D. B. Ostrowsky, B. P. Pal, and K. Thyagarajan, “−1800 psnm km chromatic dispersion at 1.55 μm in dual concentric core fibre,” Electron. Lett. 36, 1689–1691 (2000). 3. J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002). 4. K. Pande and B. P. Pal, “Design optimization of a dual-core dispersion-compensating fiber with a high figure of merit and a large effective area for dense wavelength-division multiplexed transmission through standard G.655 fibers,” Appl. Opt. 42, 3785–3791 (2003). 5. L. Grüner-Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. Jorgensen, B. Edvold, B. Pálsdóttir, and D. Jakobsen, “Dispersion-compensating fibers,” J. Lightwave Technol. 23, 3566–3579 (2005). 6. F. Gérôme, J. Auguste, J. Maury, J. Blondy, and J. Marcou, “Theoretical and experimental analysis of a chromatic dispersion compensating module using a dual concentric core fiber,” J. Lightwave Technol. 24, 442–448 (2006). 7. V. Rastogi, R. Kumar, and A. Kumar, “Large effective area all-solid dispersion compensating fiber,” J. Opt. 13, 125707 (2011). 8. T. A. Birks, D. Mogilevtsev, J. C. Knight, P. St, and J. Russel, “Dispersion compensation using single material fibers,” IEEE Photon. Technol. Lett. 11, 674–676 (1999). 9. L. P. Shen, W.-P. Huang, and S. S. Jian, “Design of photonic crystal fibers for dispersion-related applications,” J. Lightwave Technol. 21, 1644–1651 (2003). 10. R. K. Sinha and S. K. Varshney, “Dispersion properties of photonic crystal fibers,” Microw. Opt. Technol. Lett. 37, 129–132 (2003).
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