We present a systematic process of theoretical design and experimental fabrication of the large mode area and large negative dispersion photonic crystal fiber. An easily fabricated fiber structure is proposed. The influence of structure parameters deviations from the design on the chromatic dispersion are evaluated and a design rule is given. Finally our fabricated fiber and test results are demonstrated. The measured effective area of inner core mode is 40.7 μm2 which is the largest effective area of high negative dispersion photonic crystal fibers that have been experimentally fabricated. The measured peak dispersion is -666.2ps/(nm.km) and the bandwidth is 40nm.
©2006 Optical Society of America
It’s low-cost and efficient to broaden the transmission capacity by increasing the data rate and channel counts based on the established G.652 optical networks so as to meet the ever increasing demand for communication bandwidth. However, in such systems the chromatic dispersion of transmission optical fiber is one of the primary limits. One of the best approaches to minimize the penalty of chromatic dispersion is to use dispersion compensating fiber. The basic design of DCF consists of two spatially separated asymmetric concentric cores with matched cladding [1,2,3,4]. This structure supports two supermodes: fundamental supermode and second supermode. Commercially available DCF modules are based on the fundamental supermode. To achieve large negative dispersion and insure single mode transmission, the fiber core must have a high refractive index and a small diameter. As a result, the fiber mode field effective area is small. The typical effective area values are around 15-20 μm2. The small effective area has raised a concern over non-linear effects. Because of the limitation of doped concentration it can’t realize very large dispersion value in commercial DCF. The typical dispersion value is about -100~ -150 ps/(nm·km).
Photonic crystal fiber(PCF) can realize larger refractive index modulation than doped fibers .This affords more knobs to tailor PCF’s dispersion. Many works have been carried through to try to gain large waveguide dispersion in photonic crystal fibers [6,7,8,9,10,11]. F.Gerome originally uses photonic crystal fiber technology to form the coupling asymmetric dual core structure which is usually used in commercial DCF design . By introducing a ring of smaller diameter air holes in the outer ring core, he realizes the dual core asymmetry structure based on pure silica. This structure can exhibit very high negative chromatic dispersion (-2200 ps/(nm·km) at 1550 nm). However it is very hard to fabricate the fiber exactly according to the design because it adopts a ring of much smaller air holes (the diameter of the ring holes is 0.51μm) and the dimension of the smaller holes is very difficult to control. In the following chapter we will illustrate that the dispersion characteristics of this structure is sharply sensitive to the diameter of smaller holes. So the dispersion characteristics is very difficult to guaranteed in the fabrication.
The alternative scheme is to adopt the structures that have a high index inner core and a defect ring of reduced holes diameter in the cladding and similar dual core fiber geometries . The largest negative dispersion achieved in this design is -55000 ps/(nm·km) which is extremely high as compared to the other designs with similar fiber geometries. One critical reason is that very high refractive indices (1.5~2.8) in the inner core is used. However such high refractive index doping is difficult to realize in the practical fabrication. Increasing the index of inner core would lead to high order mode (HOM) occurrence . Guidance of HOM should be avoided because the HOM can interfere with the fundamental mode, leading to modal noise. Another drawback of high doping of core is the increased loss due to higher GeO2 . Furthermore high refractive index of core is not preferred because the coupling from a standard optical fiber is hard. It needs to be pointed out that the mode field effective area in reference  corresponds to the area of outer ring core mode, which is not similar to the previous studies.
Dispersion compensation photonic crystal fiber (DCPCF) research mainly stays in the stage of theory simulation and design till now. The first experimental demonstration of DCPCF is reported in reference . The implementation in that paper can realize dispersion and dispersion slope compensation simultaneously. However the mode field diameter of the DCPCF is around 3 μm. Such small mode field would lead to large nonlinear effect.
PCF can maintain single mode transmission with much larger mode area than standard single mode fiber [12,13,14]. We can utilize such characteristics of PCF to broaden the mode field area of DCPCF and maintain the single mode guidance. In this paper the whole work aims at drawing the large mode field area and large negative dispersion photonic crystal fiber experimentally. The theory design must be technically feasible and decrease the technical difficulties. Here we adopt the structure which consists of a low Germanium doped inner core and pure silica outer core that eliminates the smaller holes. The fabrication of low Germanium doped inner core preform is compatible to the traditional MCVD process. Considering the potential fluctuations of structure parameters possibly occurred in the fabrication, we analyze the influence of several parameters fluctuations on the fiber’s dispersion characteristics. This work is essential to guide the drawing process. Then we demonstrate our experimentally fabricated DCPCF and give the test results.
2. Analysis method and implementation
The fiber is simulated by a full vector Frequency Domain Finite Difference (FDFD) method [15,16] with Perfect Matched Layer (PML) absorbing boundary condition. An index average technique is used to improve the algorithm’s refractive index resolution. The mode transmission constant β and mode field distribution can be obtained using this algorithm. Then the mode effective refractive index can be obtained as neff=β/k0, where k0 is the free space wave vector. In this way the mode effective refractive index is calculated as a function of the wavelength λ. The group velocity dispersion D(λ) of PCF can be numerically calculated as 
where c is the velocity of light in vacuum. The material dispersion is not considered since the waveguide dispersion value is so high that the effect of material dispersion is small sufficiently and can be ignored.
The mode field area is another important parameter for fiber design. The effective area of fiber Aeff is defined as follows 
To validate the FDFD algorithm developed by our group, we use it to simulate and analyze the structure proposed in reference . In that structure, the effective refractive index of outer ring core can be adjusted by introducing the respective smaller diameter holes. Thus the phase matching wavelength can be controlled by adjusting the diameter of smaller holes of outer core. To couple at 1.55 μm, the diameter of smaller holes is much less than 1 μm and is decided to be 0.51 μm . The dependence of the chromatic dispersion on the radius of outer ring smaller air holes is evaluated here. The radius of outer ring holes is varied between 254 nm to 256 nm in steps of 1nm. The chromatic dispersion varies as in Fig. 1. The figure shows that chromatic dispersion of the fiber is sharply sensitive to the radius of smaller holes. When the radius of smaller holes varies as 1nm, the position of peak dispersion would have a 10 nm shift in wavelength. Increasing or decreasing the radius of outer ring holes would increase or decrease the average refractive index greatly. It denotes that the chromatic dispersion is sharply sensitive to the average refractive index of outer core. Preciously controlling the diameter of sub-micon holes of outer core is quite difficult in the practical fabrication. So this design is not suitable for the drawing fabrication. To facilitate the experimental drawing, an easily fabricated design is proposed and described in the following chapters.
3. Theoretical design
Based on the summarization of the previous works in DCPCF, our work aims at experimental fabrication of large mode field area and large negative dispersion photonic crystal fibers. To decrease the fabrication difficulty, our proposed structure consists of a low Germanium doped inner core and a solid outer ring core which eliminates the smaller holes. By including a low Germanium doped central defect and a ring of pure silica, it allows to obtain an asymmetric concentric dual core structure as that of usual DCF design. Guidance occurs in regions where defects are located. The transverse section of our proposed DCF is illustrated in Fig. 2.
To guarantee the single mode guidance of inner core, the doping concentration in the inner core should be as small as possible. The feasible refractive index of inner core is the critical parameter in this design. In our experiment, we first fabricate the low Germanium doped preform and test its refractive index at 633nm wavelength (our preform test set can only test the refractive index at 633 nm wavelength). Then we calculate the refractive index at 1550 nm wavelength according to corresponding value at 633nm. The resulting refractive index of the doped preform is 1.446724 at 1550 nm where the refractive index of pure silica is 1.444024. The value of largest negative dispersion is targeted for the wavelength λ=1.55 μm. The structure parameters are chosen as: the lattice constant or pitch Λ=6. 65μm, d/Λ=0.45, and d is the diameter of air holes. The diameter of Germanium doped region is 5.018 μm which is less than the lattice constant because only the central part of the preform can be doped during the MCVD procedure. The chromatic dispersion versus wavelength is illustrated in Fig. 3. The modeling demonstrates that it can keep single mode transmission in the whole C band. The peak dispersion is -1203 ps/(nm·km) at wavelength λ=1.55 μm.
As the complete structure of DCPCF considered, the effective area of the fundamental mode depends on the wavelength and presents an important variation around the phase matching wavelength. Before the phase matching wavelength, the power of the supermode is concentrated in the central core and is a Gaussian shape. The mode effective area of the complete fiber is defined as the inner core mode area. After the phase matching wavelength, the power is only in the ring core, and the mode field is an annular shape. The mode effective area of the complete fiber is defined as the effective area of outer ring core mode. While around the phase matching wavelength, the mode field exists in the inner core and the outer ring core simultaneously. The mode field is not a Gaussian shape yet. The effective area of the complete fiber is the total of area of inner core mode and the outer core mode. So when designing the DCPCF, we can not be limited in only considering the area of outer core mode but ignoring the area of inner core mode. Around the wavelength where the coupling between the inner core and outer core is strongest, the area of outer ring core mode is much larger than the area of the inner core mode. For example in our proposed structure the inner core fundamental mode effective area is 47 μm2 and the outer core mode effective area is 835 μm2 at the wavelength where the coupling is strongest in the FDFD simulation. The total mode field effective area is as high as 882 μm2. The mode area of outer ring core is near 18 times that of the inner core mode.
4. The behavior of chromatic dispersion with the parameters variations
During the fabrication, the values of structure parameters would have some deviations from the values of the theoretical design inevitably. So it’s very important to predict the behavior of chromatic dispersion of the fiber with the deviations of the structure parameters. In the whole paper a reference configuration is chosen as Λ=6.65 μm, d/Λ=0.45, the refractive index of the doped inner core is nD=1.446724. At first we study the dependence of chromatic dispersion on the filling fraction f by simply changing d/Λ with Λ=6.65 μm and nD= 1.446724 fixed. The result is represented in Fig. 4. The figure shows that the dispersion peak is shifted toward the shorter wavelength and the value of the peak dispersion demonstrates little variation when increasing the filling fraction, while the dispersion peak is shifted toward the longer wavelength and the value of the peak demonstrates a remarkable variation and becomes less negative when decreasing the filling fraction. When the holes diameter is increased by 5% (from d/Λ=0.45 to d/Λ=0.4725), the position of the dispersion peak is shifted by about only 5 nm toward the shorter wavelength. When the holes diameter is decreased by 5% (from d/Λ=0.45 to d/Λ=0.4275), the position of the dispersion peak is shifted by about only 5 nm toward the longer wavelength. The simulation indicates that a certain positive tolerance of the holes diameter is preferred during the fabrication.
Figure 5 shows the dependence of chromatic dispersion of the fiber on the lattice constant with d/Λ=0.45 and nD=1.446724 fixed. When Λ has a variation of 50 nm(0.75% of the reference lattice constant), the dispersion peak is shifted by about 10 nm in wavelength. This indicates that the chromatic dispersion of the fiber is more sensitive to the variation of the lattice constant than that of filling fraction. Then we keep the lattice constant Λ and filling fraction d/Λ fixed and change the refractive index of the doped inner core. The change of the dispersion characteristics of the fiber is illustrated in Fig. 6. When the refractive index of the doped inner core increases from 1.446724 to 1.44694(an increase of 0.015% of the reference refractive index value), the peak position is shifted from 1550 nm to 1610 nm. On the contrary, when the refractive index of the doped inner core decreases from 1.446724 to 1.4465(a decrease of 0.015% of the reference refractive index value), the peak position is shifted from 1550 nm to 1485 nm. This indicates that the dispersion characteristics of the fiber is sharply sensitive to the refractive index of the doped inner core. Now we arrange the parameters of the fiber in the sequence of sensitivity degree of the dispersion characteristics. They are the refractive index of the doped inner core, the lattice constant and the filling fraction. Due to the sharp sensitivity of chromatic dispersion to the refractive index of the doped inner core, the fiber design should be based on the refractive index of the doped preform when the doped preform is fabricated and the its refractive index is measured. This is the critical rule that guarantees the chromatic dispersion of fabricated fiber accords with the design. To target the negative dispersion peak for the wavelength Λ=1.55 μm, lower refractive index of doped inner core is needed and larger mode field area can be available when adopting larger lattice constant Λ and the fixed value of d/Λ=0.45, vice versa.
5. Experiment and discussion
At first we draw a pure silica dual core structure resembling to the designed structure so as to decide the technical conditions. Then the doped preform is fabricated and tested. According to the refractive index of the doped preform, the fiber is designed. Then after several drawing experiments we get the final photonic crystal fiber as illustrated in Fig. 7(a). During the drawing process the controlling parameters are adjusted gradually so as to guarantee that there is a section of fiber which has the desired structure parameters. The qualified fiber has a length of 200 meters. The mode field of the fiber is measured with Photon Kinetics 2500 Optical Fiber Analysis System. Figure 7(b) illustrates the measured near field displayed as density plot around phase matching wavelength. The measured near field distribution curve shows that the mode field of inner core is close to gaussian. The measured mode field diameter of inner core is 7.2 μm at 1550 nm wavelength and the mode field area of inner core is 40.7 μm2 which is close to the theoretical value of inner core mode field area. This is the largest mode field area of all the fabricated dispersion compensating photonic crystal fibers to our knowledge.
Figure 8(a) is the relative group delay (RGD) measured using a Photon Kinetics S18 test set. The dots are the measured values of RGD and the solid line is the fitting RGD data. By a differential calculation of RGD data by wavelength Λ, the spectral dispersion is illustrated in Fig. 8(b). The peak dispersion value is -666.2 ps/(nm.km) which is less negative than the designed. And the position of dispersion peak is at wavelength Λ= 1.586 μm which has a shift from the designed peak position. The figure also shows that the full width at half maximum (FWHM) is about 40 nm which is larger than that of design. We can give a qualitative explain to the test results. The nonuniformity of holes diameter, the abnormity of holes arrangement introduced in the fabrication and a little longitudinal nonuniformity lead to the broadening of FWHM bandwidth and the decrease of the absolute value of peak dispersion. The filling fraction of fabricated fiber is less than the designed value as illustrated in the microscope image. The compositive effects of the deviation of filling fraction, the nonuniformity of holes diameter, the abnormity of holes arrangement and the longitudinal nonuniformity lead to the shift of peak dispersion toward the longer wavelength.
We have been dedicated to the experimental fabrication of large mode field area and large negative dispersion photonic crystal fiber. Based on the summarization of the advantages and drawbacks of the previous proposed large negative dispersion photonic crystal fiber, we adopt an easily fabricated fiber structure which includes a low Germanium doped inner core and solid outer ring core.
As the potential parameters deviations from the design considered, the behaviors of chromatic dispersion on the structure parameters deviations are studied systematically. The deviations of the refractive index of the doped inner core, the lattice constant and the filling fraction are considered respectively. Finally we find that the chromatic dispersion of the fiber is most sensitive to the refractive index of the doped inner core. In the arrangement of sensitivity degree of the chromatic dispersion, they are the refractive index of the doped inner core, the lattice constant and the filling fraction. Based on this conclusion, we first fabricate the doped preform and test its refractive index. Based on this parameter, the other structure parameters are decided according to the desiring chromatic dispersion characteristics. Eventually we fabricate the large negative and large mode field area photonic crystal fiber successfully. The measurement result shows the fiber has a peak dispersion of – 666.2ps/(nm.km) and a FWHM of 40nm.
This work is supported by the National Basic Research Program of China(973 Program) under Contract 2003CB314907. Sigang Yang’s e-mail address is firstname.lastname@example.org.
References and links
1. K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photonics Technol. Lett. 8, 1510–1512 (1996). [CrossRef]
2. L. Gruner-Nielsen, S.N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C.C. Larsen, and H. Damsgaard, “Dispersion compensating fibres,” Opt. Fiber Technol. 6, 164–180 (2000). [CrossRef]
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). [CrossRef]
4. L. Grüner-Nielsen, M. Wandel, P. Kristensen, C. Jørgensen, L.V. Jørgensen, B. Edvold, B. Pälsdóttir, and D. Jakobsen, “Dispersion-Compensating Fibers,” IEEE J. Lightwave Technol. 23, 3566–3579 (2005). [CrossRef]
7. Y. Ni, L. An, and J. Peng, “Dual-core photonic crystal fiber for dispersion compensation,” IEEE Photonics Technol. Lett. 16, 1516–1518 (2004). [CrossRef]
8. B. Zsigri, J. Laegsgaard, and A. Bjarklev, “A novel photonic crystal fibre design for dispersion compensation,” J. Opt. A: Pure Appl. Opt. 6, 717–720 (2004). [CrossRef]
9. A. Huttunen and P. Torma, “Optimization of dual-core and microstructure fiber geometries for dispersion compensation and large mode area,” Opt. Express 13, 627–635 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-627. [CrossRef]
10. B.J. Mangan, F. Couny, L. Farr, A. Langford, P.J. Roberts, D.P. Williams, M. Banham, M.W. Mason, D.F. Murphy, E. A.M. Brown, H. Sabert, T.A. Birks, J.C. Knight, and P.St.J. Russell, “Slope-matched dispersion-compensating photonic crystal fibre,” Lasers and Electro-Optics , 2004. (CLEO). (Conference on Volume 2, 16-21 May 2004), pp.1069–1070.
11. Yejin Zhang, Sigang Yang, Xiaozhou Peng, Yang Lu, Xiangfei Chen, and Shizhong Xie, “Design of large effective area microstructured optical fiber for dispersion compensation,” In Optics and Optoelectronics, Proc. SPIE 5950, 43 (2005).
12. J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998). [CrossRef]
13. M.D. Nielsen, J.R. Folkenberg, and N.A. Mortensen, “Singlemode photonic crystal fibre with effective area of 600 |lm2 and low bending loss,” Electron. Lett. 39, 1802–1803 (2003). [CrossRef]
14. Martin Dybendal Nielsen, Anders Petersson, Christian Jacobsen, Harald R. Simonsen, Guillaume Vienne, Anders, and Bjarklev, “All-silica photonic crystal fiber with large mode area,” 28th European Conference on Optical Communication ECOC′02 (Copenhagen, Denmark, 2002).
15. Zhaoming Zhu and Thomas G. Brown, ”Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10, 853–864 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853. [PubMed]
16. Shangpin Guo, Feng Wu, and Sacharia Albin, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express 12, 3341–3352 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3341. [CrossRef] [PubMed]
17. Govind P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).
18. Niels Asger Mortensen, “Effective area of photonic crystal fibers,” Opt. Express10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10- 7-341. [PubMed]