Design and fabrication of a nonzero-dispersion fiber ... - IEEE Xplore

IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 4, APRIL 2001

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Design and Fabrication of a Nonzero-Dispersion Fiber with a Maximally Flat Dispersion Spectrum Jaedeuk Lee, G. Hugh Song, Un-Chul Paek, and Yong Gon Seo

Abstract—Using a general-purpose multivariate optimization program that we have developed for the design of the fiber-index profile for a given set of several fiber optimization parameters, we have designed and fabricated nonzero-dispersion fibers with a maximally flat chromatic dispersion spectrum, which have shown improved dispersion-spectrum curves compared to those of commercially available fibers developed for the same purpose. Index Terms—Chromatic dispersion, multivariate optimization, nonzero-dispersion fiber.

I. INTRODUCTION

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HE wavelength-division-multiplexing (WDM) scheme is being employed in the newly developed optical communication systems in that it increases the communication bandwidth of the existing and future optical links without increasing the fiber installment. In fibers for such WDM optical links, there are some well-known effects from optical nonlinearity, which adversely affect the transmission characteristics of fibers. One of the most troublesome effects in such fibers is four-wave mixing (FWM). Due to the phase-matching condition, the effect becomes quite pronounced at wavelengths where dispersion is intentionally suppressed. Fibers intentionally having a nonzero but relatively small dispersion were found advantageous because the nonlinear effects such as FWM can be reduced substantially by such a new design giving a slightly increased dispersion parameter values over the wavelength range around 1.55 m [1], [2]. Such fibers are called the nonzero dispersion fibers (NZDFs). It is the most desirable if the chromatic dispersion of an optical fiber is constant over the entire wavelength range of operation, while satisfying all other specifications of a well-designed single-mode optical fiber. Commercially available NZDFs having near-flat dispersion spectra, such as Fiber Model “TrueWave RS” made by Lucent Technologies, whose nominal dispersion is relatively flat over the so-called C-band range of 1530–1565 nm, do not appear to give sufficiently constant dispersion curves in the L-band of 1565–1620 nm. To improve the flatness of the dispersion spectrum while simultaneously satisfying all other modal characteristics of the fiber waveguide, an elaborate design process based on numerical simulation is required before fabrication. Manuscript received June 1, 2000; revised October 2, 2000. This work has been supported in part by KOSEF through the ERC (UFON) Program, by the Institute of Information Technology Assessment through the University Basic Research Fund Program, by the Ministry of Education through the BK21-IT Program, and by a generous support from Samsung Electronics Co., Ltd. The authors are with the Department of Information and Communication, Kwangju Institute of Science and Technology, Buk-gu, Kwangju, Korea. Publisher Item Identifier S 1041-1135(01)03128-7.

In this letter, we have developed a general-purpose multivariate optimization program. Using this computer program, we have investigated into an optimized index profile of a NZDF that has the absolute dispersion slope lower than 0.015 ps km nm over the C- and L-bands, while satisfying other modal characteristics such as the mode-field diameter, mode, and the bending the cutoff wavelength for the loss requirement. Based on optimized design obtained by the optimization program, we then fabricated optical fibers through a programmed process of modified chemical-vapor deposition (MCVD). The refractive-index profile of the fabricated fiber was predicted from the result of the preform index-profile measurement, and was compared with the original design. Then, the chromatic-dispersion spectrum was measured and was compared with the calculated prediction made from the predicted index profile of the fiber. II. DESIGN OF A NZDF WITH A MAXIMALLY FLAT DISPERSION SPECTRUM The design program uses a multivariate optimization technique [3], which is based on synthesis approach leading to an optimized index profile from layers of piecewise constant reis a fractive index. We recognize that any modal property . functional of the index-profile function parameterized by , Parameterizing several optimal properties as , we wish to minimize

where ’s are the weighting factors for the respective properties. In practice, we deal with the index profile using the piece, . There are sevwise-step approximation, eral physical constraints for the optimization process. First, the mode should be lower than 1.53 cutoff wavelength for the m wavelength to confirm single-mode transmission and also be longer than approximately 1 m wavelength to ensure stable guiding with a low bending loss. Second, the mode-field diameter must be as large as possible so that the nonlinear effect can be effectively minimized, as long as the designed fibers satisfy the standard specification of the bending-induced attenuation. in the opWe thus have specified four modal properties, timization program; two chromatic-dispersion values at wave-mode cutoff wavelength, lengths (1.53 and 1.62 m), the and the mode-field diameter at wavelength 1.55 m. For the calculation of the mode-field diameter, a definition known as the Petermann-I diameter was used [4]. The bending-induced

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Fig. 1. Three optimized index profiles of fibers with the maximally flat dispersion spectra. The three fibers have been designed to give different near-constant values of dispersions over the wavelength ranges shown in the horizontal axis of the inset diagram. The solid, dotted, and dash-dotted lines represent the fibers with positive dispersion, zero dispersion, and negative dispersion, respectively.

attenuation was calculated by the method proposed in [5] for the designed index profiles, and compared to standard specifications of commercial optical fibers. The layers with higher and lower refractive-index values are assumed to be realized -doping and fluorine-doping, respectively. The waveby length dependence in the refractive-index value was calculated by using the Sellmeier’s formula with a correction based on the Claussius–Mossotti relation [6]. The degrees of freedom, , for the optimization calculation was chosen to be 100 as the number of layers with almost continuously varying refractive indices. The range of values for ’s are limited to values obtainable with practical fabrication techniques of the MCVD process. We also introduced a realistic constraint for the index profile at the center as a shape of central dip. With only such constraints, quite impressively, the numerical convergence to the final result was found to be sufficiently good with resulting refractive-index profiles that are practically manufacturable. To investigate the relation between the profile and the dispersion parameter in a NZDF, we have tried to find three different optimized index profiles of fibers with maximally flat dispersion spectrum with three different values of dispersions over the transmission band: 4, 0, -4 ps km nm . The index profile of the zero-dispersion fiber was calculated for the purpose of comparison. For the three types of the fiber profiles, -mode cutoff-wavelength and the mode-field diameter the at wavelength 1.55 m was set to 1.1 m and 8.0 m in the optimization program, respectively. Fig. 1 shows the optimized index profiles and the corresponding dispersion spectrums. The solid, dotted, and dash-dotted lines indicate the NZDF with a positive dispersion, the zero-dispersion fiber, and the NZDF with a negative dispersion. The index profiles in Fig. 1 are basically a triangular-core structure with a depressed-clad section and a outer ring-core section. All three resulting curves of the

IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 4, APRIL 2001

Fig. 2. Index profile (dashed curve) obtained through optimization and the measured profile (solid curve) of the preform fabricated for a sample nonzero dispersion fiber (NZDF) with the flat positive dispersion shown as the solid curve in Fig. 1. The scale for the horizontal axis has been converted from the scale of the preform to that of the fiber.

dispersion spectrum for the designed fibers are found to be sufficiently flat within the optimization specification. The major difference among the three curves exists in the peak refractive index near the center. It has been found that the sharply depressed inner cladding inside of the outer ring-core introduces a cutoff of the fundamental mode, which effectively flattens the -versus- curve in the wavelength region around m. To obtain a lower value, the -versus- curve should be curved more from the contribution of the waveguide dispersion. This is achieved by the higher peak refractive index near the center. This increase of the refractive index near the center must be compensated by the overall shrink of the profile in the cross-sectional plane to keep all other mode parameters approximately the same. The presence of the ring core pushes the cutoff wavelength for the fundamental mode toward the wavelength sufficiently longer than 1.55 m. III. FABRICATION OF THE OPTIMIZED OPTICAL FIBER The optimized NZDF with a positive dispersion in Fig. 1 was fabricated by the MCVD technique. The refractive-index profile of the fabricated fiber was predicted from the result of preform index-profile measurement and was shown in Fig. 2 as a solid curve. The dashed curve in Fig. 2 is the designed index profile that is reproduced from the solid curve in Fig. 1. The comparison between two curves shows good agreement. In Fig. 3, the square blobs indicate the chromatic-dispersion measurement result of the fabricated NZDF, while the solid curve in the figure is the calculated prediction from predicted fiber index profile shown in Fig. 2. The dispersion measurement was performed by the well-known conventional phase-shift technique [7]. It evidently shows good agreement between the experimental measurement and the calculation result. The dispersion slope over the C-band of the measured dispersion spectrum is approximately 0.011

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listed in Table I. We can observe that the measurement results of the mode-field diameter at wavelength 1.55 m and of the cutoff wavelength agree well with the design specifications of the optimization program. The bending-induced attenuation was measured to be lower than 0.5 dB for the one turn at a 32-mm diameter mandrel, which is the standard specification of commercial single-mode fibers. IV. CONCLUSION

Fig. 3. Chromatic dispersion spectra of the NZDF with the index profile of solid line in Fig. 2 (square blobs and solid curve) and Fiber Model “TrueWave RS” (dashed line). The square blobs and the solid curve indicate the measured result and the calculation result, respectively. TABLE I OPTICAL PROPERTIES OF THE FABRICATED FIBER

A NZDF with a maximally flat dispersion spectrum has been designed and fabricated. For the design process, we have used a synthesis approach leading to an optimized index profile from layers of piecewise constant refractive index. Four design parameters have been chosen simultaneously as the convergence target specifications: 1) the value and 2) the slope of the dispersion spectrum for a given wavelength range; 3) the cutoff mode for reduced bend loss; and 4) the wavelength of the mode-field diameter for suppressed nonlinear effects. The dispersion measurement has shown that the original goal has been achieved to a satisfactory level. ACKNOWLEDGMENT We would like to thank Dr. Kitae Jeong of the WDM Research Division, Access Network Laboratory, Korea Telecom, who kindly gave us access to measurement facilities of the Laboratory. REFERENCES

ps km nm . The chromatic dispersion spectrum of the Fiber Model “TrueWave RS,” which has one of the flattest dispersion spectral curves among the commercially available NZDFs, is also shown as a dashed curve for the purpose of comparison. The comparison between the dashed curve and the solid curve shows that the proposed NZDF has a much flatter dispersion spectrum than commercially available NZDFs. The measurement results of other optical properties of fabricated fiber are

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