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OpticsOptikOptikOptik 121 (2010) 867–871

0030-4026/$ - se

doi:10.1016/j.ijl

�CorrespondE-mail addr

www.elsevier.de/ijleo

New high negative dispersion photonic crystal fiber

Ming Chen�, Qing Yang, Tiansong Li, Mingsong Chen, Ning He

School of Information and Communication Engineering, Guilin University of Electronic Technology, Guilin 541004,

Guangxi Province of China, China

Received 30 May 2008; accepted 24 September 2008

Abstract

A new high negative dispersion photonic crystal fiber is proposed. It has double-core structure. The inner corehas a circle germanium-doped region. The outer core is formed by removing the 3rd ring air-holes around the core.There are two ring air-holes between the two cores, Diameter of the 1st ring air holes is bigger than that of the2nd ring air-holes, this can make mode coupling between inner mode and outer mode and showed that the highnegative PCF is the result of this structure characteristics. There are honeycomb photonic lattice in the PCF’s cladding.The influence of the structure parameters deviated from the design those on the chromatic dispersion are evaluated.When the structure parameters L ¼ 1.50 mm, dcore ¼ 2.10 mm, d1 ¼ 0.90 mm, d2 ¼ 0.44 mm and d3 ¼ 1.04 mm,the dispersion coefficient D is �1320 ps/(nm � km) at 1550 nm. This is a new kind of chromatic dispersioncompensation PCF.r 2009 Elsevier GmbH. All rights reserved.

Keywords: Negative chromatic dispersion; PCF; Double-core; Optical communication

1. Introduction

It is low-cost and efficient to broaden the transmissioncapacity by increasing the data rate and channel countsbased on the established G.652 optical fiber networks soas to meet the ever increasing demand for communica-tion bandwidth. However, in those systems the chro-matic dispersion of transmission optical fiber is one ofthe primary impediments. One of the best approaches tominimize the penalty of chromatic dispersion is to usedispersion compensating fibers which have negativechromatic dispersion used to periodically balance thepositive chromatic dispersion from the G.652 optical

e front matter r 2009 Elsevier GmbH. All rights reserved.

eo.2008.09.039

ing author.

ess: m_chen@126.com (M. Chen).

fibers [1,2]. In designing chromatic dispersion compen-sation optical fibers, one must use an asymmetrical dual-concentric-core structure that can propagate two super-modes. This dual-core is widely used in design of thedispersion compensation fibers [3,4].

Photonic crystal fibers have received increasing atten-tion because of its novel optical characteristics recently.It has been reported that PCFs can realize endlesslysingle mode operation [5], controllable nonlinearity [6],large birefringence [7,8], flexible chromatic dispersionover a wide wavelength range [9,10], and have been usedin other research areas [11,12]. In the PCFs, there have aclass of PCFs with honeycomb lattice in their claddings[13,14]. Generally speaking, for structures with same air-filling fraction, honeycomb structures support largerphotonic band gaps than triangular structures.

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To this day, the PCFs with honeycomb latticecladding were mainly used in air-guiding fibers bymeans of the photonic bandgap effect. Few worksare reported on the index-guiding PCFs with honey-comb lattice cladding. In this paper, we use the PCFwith honeycomb lattice in cladding to design largenegative chromatic dispersion fibers for dispersioncompensation in optical telecommunication systems.To our knowledge, this is a new negative chromaticdispersion compensation PCF based on the honeycomblattice.

2. Cross structure of the PCF

Our proposed high negative chromatic dispersionPCF structure considered the schematic cross section ofthe PCF structure as shown in Fig. 1. It is composed ofcircular air-holes in the cladding arranged in ahoneycomb array with lattice constant L, where L isthe centre-to-centre spacing between two nearest air-holes. The diameter of the circular doped region in thefiber core is dcore and the diameters of the 1st and 2ndring air-holes around the fiber core are denoted by d1and d2, respectively, and the d1 is bigger than d2(This structure characteristic can make the inner modeand the outer mode of the super-mode coupled andthen the high negative chromatic dispersion obtained.).The diameter of the air-holes in the cladding is d3. Thecircular doped region forms the fiber’s inner core. Theouter core is formed between the 2nd air-holes ring andthe fiber cladding by deleting some air-holes, as shownin the figure. The circled high refractive index region isgermanium-doped in the fiber core. The refractive indexncore ¼ 1.487 at 1.55 mm [15].

Fig. 1. Illustration of the cross structure of the high negativedispersion PCF.

3. Mathematical method

The validation of the design is done by using anefficient finite-difference frequency-domain method withuniaxial anisotropic perfectly matched layers (UPML-FDFD) for accurate modeling of PCFs [16,17]. In linearand isotropic medium, the Maxwell’s curl equations canbe expressed as

r � E*¼ �jomH

*(1)

r �H*¼ jo�E

*, (2)

where E*

and H*

denote the electric field and magneticfield, e and m are the electrical permittivity and themagnetic permeability respectively, j ¼

ffiffiffiffiffiffiffi�1p

, and o isthe angular frequency of the light.

To improve the accuracy of the calculation, UPMLabsorbing boundary condition is used, and then the Eqs.(1) and (2) can be rewritten as:

r � E*¼ �joms H

*(3)

r �H*¼ jo�s E

*, (4)

where s is defined as

s ¼

sy=sx

sx=sy

sxsy

264

375, (5)

and sx ¼ 1�sx/joe0, sy ¼ 1�sy/joe0, s is conductivity ofthe medium, e0 is the free-space permittivity.

Using the Yee’s mesh [18], Eqs. (3) and (4) can bewritten in a matrix forms and the mode propagationconstant b and mode field distribution can be obtained.Then, the mode effective refractive index can beobtained as neff ¼ b/k0, where k0 is the free-space wavevector. The mode effective refractive index is calculatedas a function of the wavelength, then the GVD D(l) ofPCF can be numerically calculated. The exact definitionof dispersion D(l) is expressed as:

DðlÞ ¼ �lc

d2 Reðneff Þ

dl2, (6)

where c is the velocity of light in vacuum and Re(y)stands for the real part of a physical quantity. neff is theeffective index and l denotes the wavelength. The totaldispersion is sum of the material dispersion and thewaveguide dispersion. It is possible to alter the balancebetween the two dispersion mechanisms and one canachieve desired dispersion profile by designing thewaveguide dispersion through changing the structureparameters. The material dispersion given by Sellmeier’sformula [10] is directly included in the calculation.

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Fig. 3. Dispersion curves with different lattice pitch L 1.450,

1.500 and 1.550 mm.

Fig. 4. Dispersion curves with different diameters dcore.

M. Chen et al. / Optik 121 (2010) 867–871 869

4. Design the optimized structure parameters

There is supermode in the high negative chromaticdispersion fiber, this is an important property which isthe cause of the high negative chromatic dispersion[3,4,10,19]. So firstly, we study the property of thesupermode. The super mode field profile is shown inFig. 2 at 1.55 mm (inset figure A). There, the crossstructure parameters are as follows: the diameter of thecircular doped region in the fiber core dcore ¼ 2.10 mm,the optical lattice constant L ¼ 1.50 mm, the structureparameters d1, d2 and d3 are 0.90, 0.44 and 1.04 mm,respectively. The inset figure B and the inset figure C areshown the inner mode profile and the outer modeprofile, respectively. We can see that the supermode hastwo parts distributed in the inner fiber core and theouter fiber core regions. That is to say that the innermode field is in the inner core region and the outer modefield is in the outer field area. To obtain high negativechromatic dispersion, we must make the inner mode andthe outer mode coupled by carefully design the structureparameters [3,4,19].

The optical lattice constant L in PCF cladding is veryimportant in PCF design process. In honeycomboptical lattice PCF, the constant L is the centre-to-centre spacing between two nearest air-holes, as shownin Fig. 1. Fig. 3 shows the calculated dispersion curveswith dcore ¼ 2.10 mm, d1 ¼ 0.90 mm, d2 ¼ 0.44 mm, d3 ¼

1.04 mm. The optical lattice constant L in PCF claddingare chosen 1.450 mm (dashed line), 1.500 mm (solid line)and 1.550 mm (dashed-dot line). We can conclude thatall the dispersion curves have minimal values at certainwavelengths and the minimal dispersion value of the

Fig. 2. Super mode field profile (A) at 1.55 mm and the innermode profile (B) and the outer mode profile (C).

curve is shifted toward long wavelength side and thewhole dispersion curve has increased with the Lincreasing. The minimal dispersion D is �2300 ps/(nm � km) at 1.442 mm when lattice constant L is1.450 mm, it is �1320 ps/(nm � km) at 1.550 mm when Lis 1.500 mm, but it is about �1020 ps/(nm � km) at1.625 mm when L is 1.550 mm.

Bigger optical lattice L can make the PCF hasnegative chromatic dispersion in long wavelength side,but the minimal negative dispersion increase as shown inFig. 3. On the contrary, small L can make the PCF asnegative chromatic dispersion in short wavelength side,and the decreased minimal negative dispersion.

The diameter of the germanium-doped region inPCF core is very important in PCF design process.Fig. 4 shows the calculated dispersion curves withL ¼ 1.50 mm, d1 ¼ 0.90 mm, d2 ¼ 0.44 mm, d3 ¼ 1.04 mm.The diameters dcore of the circular doped region in thefiber core are chosen 2.00 mm (dashed line), 2.10 mm(solid line), and 2.20 mm (dashed-dot line). We canconclude that all the dispersion curves also haveminimal values and be similar with those in Fig. 3,and the minimal dispersion value of the curve is shifted

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Fig. 6. Dispersion curves with different diameters d2.

Fig. 7. Dispersion curves with different diameters d3.

M. Chen et al. / Optik 121 (2010) 867–871870

toward long wavelength side and the whole dispersioncurve has increased lightly with the dcore increasing.

The minimal dispersion D is �1500 ps/(nm � km) at1.523 mm when dcore is 2.00 mm, it is �1320 ps/(nm � km)at 1.550 mm when dcore is 2.10 mm, but it is about�1175 ps/(nm � km) at 1.575 mm when dcore is 2.20 mm.

The 1st and the 2nd rings air-holes around the dopedPCF core are situated between the doped inner core andthe outer core, they can be used to control the couplingeffect of the inner mode and the outer mode of thesupermode. And then the high negative chromaticdispersion of the PCF can be achieved and controlledby changing those air-holes structure parameters.

Firstly, we study the influence for chromatic disper-sion property of the 1st air-holes around the dopedcore. Fig. 5 shows the calculated dispersion curveswith L ¼ 1.50 mm, dcore ¼ 2.10 mm, d2 ¼ 0.44 mm,d3 ¼ 1.04 mm. The diameters d1 of the 1st air-holes arechosen 1.10 mm (dashed line), 1.20 mm (solid line), and1.30 mm (dashed-dot line), respectively. We can see thatthe minimal dispersion value of the curve is shiftedtoward long wavelength side and the whole dispersioncurve has increased sharply with the d1 increasing. Bigdoped region can make the PCF had high nonlinearitybut dispersion become low. On the contrary, smalldoped region can make the PCF had low nonlinearitybut dispersion become high. The minimal dispersion D

is �3150 ps/(nm � km) at 1.440 mm when d1 is 0.850 mm, itis �1320 ps/(nm � km) at 1.550 mm when d1 is 0.900 mm,but it is about �750 ps/(nm � km) at 1.640 mm when d1 is0.960 mm. As we can see, the diameters of the 1st air-holes can influence the negative chromatic dispersionsharply.

Secondly, we study the influence for chromaticdispersion property of the 2nd air-holes around thedoped core. Fig. 6 shows the calculated dispersioncurves with L ¼ 1.50 mm, dcore ¼ 2.10 mm, d1 ¼ 0.90 mm,d3 ¼ 1.04 mm. The diameters d2 of the 2nd air-holes arechosen 0.40 mm (dashed line), 0.44 mm (solid line), and0.48 mm (dashed-dot line). We can conclude that all thedispersion curves have minimal values which are similar

Fig. 5. Dispersion curves with different diameters d1.

with those in above mentioned figures and the minimaldispersion value of the curve is shifted toward longwavelength side and the whole dispersion curve hasincreased lightly with the d2 increasing. The minimaldispersion D is �1340 ps/(nm � km) at 1.540 mm when d2is 0.400mm, it is �1320 ps/(nm � km) at 1.550 mm when d2is 0.440 mm, and it is about �1315 ps/(nm � km) at1.565 mm when d2 is 0.480 mm. As we can see, theinfluence for the negative chromatic dispersion of ismore minimal than that of the 1st air-holes diameter.

Finally, we investigate the influence for chromaticdispersion property of the diameters of air-holes in thehoneycomb optical lattice cladding. It is also veryimportant in PCF design process. Fig. 7 shows thecalculated dispersion curves with L ¼ 1.50 mm, dcore ¼

2.10 mm, d1 ¼ 0.90 mm, d2 ¼ 0.44 mm. The diameters d3of the air-holes in the honeycomb optical latticecladding are chosen 1.000 mm (dashed line), 1.040 mm(solid line), and 1.100 mm (dashed-dot line). We canconclude that all the dispersion curves also haveminimal values which are similar with those in abovementioned figures. The minimal dispersion value of thecurve is shifted toward long wavelength side and thewhole dispersion curve has increased lightly with the d3increasing. The minimal dispersion D is �1420 ps/(nm � km) at 1.535mm when d3 is 1.000mm, it is �1320ps/

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(nm � km) at 1.550mm when d3 is 1.040mm, and it is about�1230ps/(nm � km) at 1.560mm when d3 is 1.100mm.

Summarized mentioned previously, the optimal struc-ture parameters is as follows: the optical lattice constantL ¼ 1.50 mm, the diameter of the circular doped regionin the fiber core dcore ¼ 2.10 mm, the structure para-meters d1, d2 and d3 are 0.90, 0.44 and 1.04 mm,respectively.

5. Conclusion and discussion

A new high negative dispersion photonic crystal fiberis proposed in this paper. This PCF has double-corestructure. The inner core has a circle germanium-dopedregion. The outer core is formed by removing the 3rdring air-holes around the core. There is honeycomboptical lattice in the PCF’s cladding. Diameter of the 1string air holes is bigger than that of the 2nd ring air-holes,this can make mode coupling between inner mode andouter mode and the high negative PCF is the result ofthis structure character. The field of the supermode hastwo parts which mainly been localized in the inner coreregion and the outer core region, respectively. Theinfluence of the structure parameters deviated from thedesign those on the chromatic dispersion are evaluated.We can conclude that the diameter of the 1st ring air-holes around the doped core and the optical pitch L caninfluence sharply the dispersion property that those otherstructure parameters, as shown in Figs. 3–7. We obtainthe optimal structure parameters: there the optical latticeconstant L ¼ 1.50mm, the diameter of the circular dopedregion in the fiber core dcore ¼ 2.10mm, the structureparameters d1, d2 and d3 are 0.90, 0.44 and 1.04mm. Thedispersion coefficient of this high negative chromaticdispersion D is �1320ps/nm � km at 1550nm. This is anew kind of chromatic dispersion compensation PCF.

Acknowledgements

The authors thank the Foundation of Guangxi KeyLaboratory of Information and Communication, theOpen Fund of Key Laboratory of Optical Communicationand Lightwave Technologies, Beijing University of Postsand Telecommunications, Ministry of Education of China,and the Guangxi Provincial Natural Science Foundationfor youth, for their supports. Ming Chen’s e-mailaddresses are m_chen@126.com and mchen@guet.edu.cn.

References

[1] I.P. Kaminow, T.Y. Li, Optical Fiber Telecommunication

IV B Systems and Impairments, Academic Press, SanDiego, 2002.

[2] M. Chen, L.N. He, S.G. Yang, Y.J. Zhang, H.W. Chen,

S.Z. Xie, Chromatic dispersion and PMD monitoring and

compensation techniques studies in optical communica-

tion systems with single channel speed 40Gbit/s andCSRZ format, Optics Express 15 (2007) 7667–7676.

[3] L.G. Nielsen, S.N. Knudsen, B. Edvold, T. Veng, D.

Magnussen, C.C. Larsen, H. Damsgaard, Dispersion

compensating fibers, Optical Fiber Technology 6 (2000)

164–180.

[4] L. Auguste, J.M. Blondy, J. Maury, J. Marcou, B.

Dussardier, R. Jindal, K. Thyagarajan, B.P. Pal, Con-

ception, realization, and characterization of a very high

negative chromatic dispersion fiber, Optical Fiber Tech-

nology 8 (2002) 89–105.[5] T.A. Birks, J.C. Knight, P.St.J. Russell, Endlessly single

mode photonic crystal fiber, Optics Letters 22 (1997)

961–963.

[6] J.C. Knight, T.A. Birks, R. Cregan, P.St.J. Russel, J.

Sandro, Large mode area photonic crystal, Electronics

Letters 34 (1998) 1347–1348.

[7] D. Chen, L. Shen, Ultrahigh birefringent photonic crystal

fiber with ultralow confinement loss, IEEE Photonics

Technology Letters 19 (2007) 185–187.[8] T.P. Hansen, J. Broeng, S.E.B. Liori, E. Knudsen, A.

Bjarklev, J.R. Jensen, H. Simonsen, Highly birefringent

index-guiding photonic crystal fibers, IEEE Photonics

Technology Letters 13 (2001) 588–590.

[9] A. Ferrando, E. Silvestre, P. Andres, Designing the

properties of dispersion-flattened photonic crystal fibers,

Optics Express 9 (1997) 961–963.

[10] A. Bjarklev, J. Broeng, A.S. Bjarklev, Photonic Crystal

Fibers, Kluwer Academic Publishers, Dordrecht, 2003.

[11] P.St.J. Russell, Photonic-crystal fibers, IEEE Journal ofLightwave Technology 24 (2006) 4729–4749.

[12] S. Saitoh, M. Koshiba, Numerical modeling of photonic

crystal fibers, IEEE Journal of Lightwave Technology 23

(2005) 3580–3590.

[13] M. Yan, P. Shum, Guiding with honeycomb photonic

bandgap fiber, IEEE Photonics Technology Letters 17

(2005) 64–66.

[14] L. Vincetti, F. Poli, S. Selleri, Confinement loss and

nonlinearity analysis of air-guiding modified honeycombphotonic bandgap fibers, IEEE Photonics Technology

Letters 18 (2006) 508–510.

[15] K.P. Hansen, Dispersion flatten hybrid-core nonlinear

photonic crystal fiber, Optics Express 11 (2003)

1503–1509.

[16] S.P. Guo, F. Wu, S. Albin, H. Tai, R.S. Rogowski,

Loss and dispersion analysis of microstructured fibers by

finite-difference method, Optics Express 12 (2004)

3341–3352.

[17] Z.M. Zhu, T.G. Brown, Full-vectorial finite-differenceanalysis of microstructured optical fibers, Optics Express

10 (2004) 853–864.

[18] A. Taflove, S.C. Hagness, Computational Electrody-

namics: The Finite-Difference Time-Domain Method,

second ed., Artech House, Boston, 2000.

[19] S.G. Yang, L.N. He, Y.J. Zhang, S.Z. Xie, Broadband

dispersion-compensating photonic crystal fiber, Optics

Letters 31 (2006) 2830–2832.