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Optics Communications 281 (2008) 2073–2076

New nonlinear and dispersion flattened photonic crystal fiberwith low confinement loss

Ming Chen a,b,*, Shizhong Xie a

a Department of Electronic Engineering, Tsinghua University, Beijing 100084, PR Chinab Information & Communication College, Guilin University of Electronic Technology, Guilin 541004, Guangxi Province, PR China

Received 28 September 2007; received in revised form 5 December 2007; accepted 5 December 2007

Abstract

A new nonlinear dispersion flattened photonic crystal fiber with low confinement loss is proposed. This fiber has threefold symmetrycore. The doped region in the core and the big air-holes in the 1st ring can make high nonlinearity in the PCF. And the small air-holes inthe 1st ring and the radial increasing diameters air-holes rings in cladding can be used to achieve the dispersion properties of the PCF. Wecan achieve the optimized optical properties by carefully selecting the PCFs structure parameters. A PCF with flattened dispersion isobtained. The dispersion is less than 0.8 ps/(nm km) and is larger than �0.7 ps/(nm km) from 1.515 lm to 1.622 lm. The nonlinear coef-ficient is about 12.6456 W�1 km�1, the fundamental mode area is about 10.2579 lm2. The confinement loss is 0.30641 dB/km. This workmay be useful for effective design and fabrication of dispersion flattened photonic crystal fibers with high nonlinearities.� 2007 Elsevier B.V. All rights reserved.

PACS: 42.81.�i; 42.81.Bm; 42.81.Qb; 42.79.Gn

Keywords: Photonic crystal fiber; Dispersion flattened; Fiber nonlinearity; Optical telecommunication

1. Introduction

Broadband optical transmission with a wavelength-divi-sion-multiplexing technology is effective for large capacitynetworks, the single mode fiber with 1.30 lm zero-disper-sion wavelength and dispersion-shifted fiber are widelyused as optical data transmission media. However, chro-matic dispersion restricts the wavelength region availablewith these fibers. Dispersion flattened fiber (DFF) is effec-tive solution for high speed optical communication overbroadband wavelength range [1]. Recently, photoniccrystal fibers (PCFs) consisting of a central defect regionsurrounded by multiple air-holes those run along the fiberlength have received increasing attention because of its

0030-4018/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2007.12.006

* Corresponding author. Address: Department of Electronic Engineer-ing, Tsinghua University, Beijing 100084, PR China. Tel.: +86 1062784784.

E-mail address: m_chen@126.com (M. Chen).

novel optical characteristics [2–4]. Dispersion flattenedPCFs, with high nonlinearities, may have various potentialapplications, such as supercontinuum generation [5] andall-optical signal processing [2–4,6]. So control of chro-matic dispersion in PCFs in very important problem forpractical applications in optical communication systems,dispersion compensation and nonlinear optics. So far,many novel works have been reported on using PCFs forDFFs design and manufacture [7–11]. However, in conven-tional PCFs, the chromatic dispersion is controlled byusing air-holes with same diameter in cladding region, itis difficult to control the dispersion slope in wide wave-length range in those conventional PCFs. In order to con-trol dispersion and dispersion slope, Saitoh et al. havereported a new design based on the radially increaseddiameter air-holes in fiber cladding [12]. In this paper, wepropose a new chromatic dispersion flattened photoniccrystal fiber with high nonlinearity simultaneously alsousing the radially increased diameter cladding air-holes.

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We will show this fiber in detail in the following. This workmay be a replaceable method for design and manufactureof chromatic dispersion flatten photonic crystal fibers.

2. Cross-section and fundamental mode profile

Consider the schematic cross-section structure of thePCF as shown in Fig. 1. It is composed of circular air-holesin the cladding arranged in a triangular array with latticeconstant K. The diameter of the circular doped region inthe fiber core is d1 and the diameters of the 2nd to 4th ringair-holes around the fiber core are denoted by d4, d5 and d6,respectively. There d4, d5 and d6 are radially varied, goingfrom small air-holes in the 2nd ring to large air-holes inthe last ring. The 1st ring air-holes surrounded the PCFscore have three small holes and three big holes with diam-eter d2 and d3, respectively, as shown in Fig. 1. The diam-eters of 1st ring air-holes become the key design parameterswill be shown in following. The circled high refractive indexregion is germanium-doped in the fiber core. The refractiveindex ncore = 1.487 [13]. The other region is the triangularair/pure silica optical lattice structure as shown in Fig. 1.The validation of the design is done by using an efficientfull vector finite element method with anisotropic perfectlymatched layers for accurate modeling of PCFs [14].

The dispersion coefficient is proportional to the secondderivatives of the mode effective index with respect to thewavelength. The exact definition of dispersion coefficientD(k) is expressed as

DðkÞ ¼ � kc

d2ReðneffÞdk2

; ð1Þ

where c is the velocity of light in vacuum, Re(� � �) stands forthe real part of a physical quantity, neff is the effective indexand k denotes the wavelength. The total dispersion is sum ofthe material dispersion and the waveguide dispersion. It ispossible to alter the balance between the two dispersionmechanisms and one can achieve desired dispersion profile.

Fig. 1. Cross-section and the fundamental mode field profile (inset) of thePCF with K = 1.50 lm, d1 = 1.20 lm, d2 = 0.24 lm, d3 = 0.54 lm,d4 = 0.32 lm, d5 = 0.36 lm and d6 = 0.40 lm.

The material dispersion given by Sellmeier’s formula[3,4,14] is directly included in the calculation. As shown inRefs. [10], [14], the rings air-holes with incremental diame-ters in cladding can make dispersion profile flatten [10,15].We use this principle combined other techniques to designour PCF with flattened dispersion profile and high nonlin-earity. The fundamental mode field is mainly in the dopedcore as shown in the inset of Fig. 1. There K = 1.50 lm,d1 = 1.20 lm, d2 = 0.24 lm, d3 = 0.54 lm, d4 = 0.32 lm,d5 = 0.36 lm and d6 = 0.40 lm. As we can see from this fig-ure, the energy of the fundamental mode is mainly boundedin the fiber core region, so we can obtain high nonlinearityin the PCF. The fundamental mode area is about10.2579 lm2. And we can conclude that the fundamentalmode has threefold symmetry due to the symmetric prop-erty of the core. The three big air-holes surrounded the fibercore can make the mode bounded in the core area and thethree small air-holes surrounded the fiber core can makethe mode extended into the cladding region. There are someoptimized structural parameters must be searched out inPCF design process and we will show them in tail infollowing.

3. Design the optimized structure parameters

The diameter of the germanium-doped region in PCFcore is very important in PCF design process. Fig. 2 showsthe calculated dispersion curves with K = 1.50 lm, d2 =0.24 lm, d3 = 0.54 lm, d4 = 0.32 lm, d5 = 0.36 lm andd6 = 0.40 lm. The diameters d1 of the circular doped regionin the fiber core are chosen 1.10 lm (dashed line), 1.20 lm(solid line), and 1.30 lm (dashed-dot line). We can con-clude that all the dispersion curves have minimal valuesand the minimal dispersion value of the curve is shiftedtoward short wavelength side and the whole dispersioncurve has descended lightly with the d1 increasing. The dis-persion is less than 0.8 ps/(nm km) and is larger than�0.7 ps/(nm km) from 1.515 lm to 1.622 lm for

Fig. 2. Calculated dispersion curves with different diameters d1.

Fig. 4. Calculated dispersion curves with different diameters d3.

M. Chen, S. Xie / Optics Communications 281 (2008) 2073–2076 2075

d1 = 1.20 lm. This will be shown again in detail in the fol-lowing parts. For 1.55 lm, the dispersion decreases whend1 become from 1.10 lm to 1.30 lm and the nonlinear coef-ficients are 10.7523 W�1 km�1, 12.6456 W�1 km�1 and14.5958 W�1 km�1, the confinement losses are 0.535104dB/km, 0.306411 dB/km and 0.250575 dB/km at 1.55 lm,respectively. Big doped region can make the PCF had highnonlinearity and low confinement loss. On the contrary,small doped region can make the PCF had low nonlinearityand high confinement loss. As we can see, the doped regionis also the decided the PCFs chromatic dispersion proper-ties, so we must carefully select this parameter in practice.

The calculated dispersion curves, with K = 1.50 lm,d1 = 1.20 lm, d3 = 0.54 lm, d4 = 0.32 lm, d5 = 0.36 lmand d6 = 0.40 lm, are shown in Fig. 3. The diameters ofthe three small holes d2 are 0.20 lm (dashed line),0.24 lm (solid line) and 0.28 lm (dashed-dot line), respec-tively. The dispersion curve is whole decreasing with thediameters d2 increasing, that is to say that the dispersionare decreased for all wavelength (between 1.42 and1.65 nm as show in Fig. 3) when d2 increased. But the min-imal dispersion values of the curve are not shifted with thed1 increasing and they are all at about 1.57 lm. The nonlin-ear coefficients are 12.6016 W�1 km�1, 12.6456 W�1 km�1

and 12.662 W�1 km�1, the confinement losses are0.446771 dB/km, 0.306411 dB/km and 0.243983 dB/km at1.55 lm, respectively. As we can see, the nonlinearity ofthe PCF increases and the confinement loss decreases withd2 increasing because that the big air-holes can make themode bounded in the core region.

Fig. 4 shows the calculated dispersion curves withK = 1.50 lm, d1 = 1.20 lm, d2 = 0.24 lm, d4 = 0.32 lm,d5 = 0.36 lm and d6 = 0.40 lm. The diameters of the threebig holes d3 are chosen as 0.52 lm, 0.54 lm and 0.56 lm,respectively. In the figure, the dashed line and solid lineand dashed-dot line are denoted the 0.52 lm, 0.54 lmand 0.56 lm, respectively. The whole dispersion curve is

Fig. 3. Dispersion curves with different diameters d2.

decreasing with the diameters d3 increasing and the maxi-mal dispersion values of the curve are shifted toward longwavelength side with the d3 increasing. The nonlinear coef-ficients are 12.6367 W�1 km�1, 12.6456 W�1 km�1 and12.6579 W�1 km�1, the confinement losses are0.373446 dB/km, 0.306411 dB/km and 0.280506 dB/km at1.55 lm, respectively. The nonlinearity is increasing withd3 increase.

Now, we can see that the PCF with high nonlinearityand flatten dispersion profile by careful selecting the struc-tural parameter d1, d2 and d3 and associating with the func-tion of the radial varying size air-holes in the cladding. Fordispersion flattened PCF at wavelength between 1.515 lmand 1.622 lm, the optimized structural parameters d1, d2

and d3 are 1.20 lm, 0.24 lm and 0.54 lm, respectively.Finally, we investigate the optical lattices pitch K-depen-

dence of the optical properties. When d1 = 1.20 lm, d2 =0.24 lm, d3 = 0.54 lm, d4 = 0.32 lm, d5 = 0.36 lm and

Fig. 5. Dispersion curves with different lattice pitch K 1.48 lm, 1.50 lmand 1.52 lm.

Fig. 6. Dispersion curves with K = 1.50 lm, d1 = 1.20 lm, d2 = 0.24 lm,d3 = 0.54 lm, d4 = 0.32 lm, d5 = 0.36 lm and d6 = 0.40 lm.

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d6 = 0.40 lm, the dispersion curves are shown in Fig. 5with the optical lattice pitch 1.48 lm (dashed line),1.50 lm (solid line) and 1.52 lm (dashed-dot line), respec-tively. As shown in figure, with K = 1.48 lm orK = 1.52 lm, the dispersion of the PCFs are lower thanthat of the PCF with K = 1.50 lm at 1.55 lm. The nonlin-ear coefficients are 12.5131 W�1 km�1 (K = 1.48 lm),12.6456 W�1 km�1 (K = 1.50 lm) and 12.3967 W�1 km�1

(K = 1.52 lm) and the confinement losses are0.363164 dB/km, 0.306411 dB/km and 0.330137 dB/km,respectively. For dispersion flattened PCF at wavelengthbetween 1.515 lm and 1.622 lm, the optimized structuralparameter K is 1.50 lm.

Fig. 6 shows the dispersion curves with K = 1.50 lm,d1 = 1.20 lm, d2 = 0.24 lm, d3 = 0.54 lm, d4 = 0.32 lm,d5 = 0.36 lm and d6 = 0.40 lm. We can see that the disper-sion of the designed PCF is less than 0.8 ps/(nm km) and islarger than �0.7 ps/(nm km) from 1.515 lm to 1.622 lm.

4. Conclusion

Summarized mentioned previously, we must select struc-ture parameters carefully to simultaneously achieve desireddispersion profile, high nonlinearities and low confinementloss in the PCF design process. The diameters of the 1string air-holes around the core in PCF cladding are alsothe key parameters to balance the dispersion characteristicsand nonlinearities. The three big air-holes can make themode bound in the core area then PCF has high nonlinear-ity and low confinement losses, and the three small air-holes make the mode extended into PCF cladding areaand then we can achieve desired dispersion flatten profiles.Due to high nonlinearity is mainly determined by thedoped core, however the dispersion flatten profile is deter-mined by the cladding structure. So we must balance the

structural parameters to achieve our desired PCF in design.We have obtain the dispersion flattened PCF with opti-mized structure parameters. The dispersion of the designedPCF is less than 0.8 ps/(nm km) and is larger than �0.7 ps/(nm km) from 1.515 lm to 1.622 lm with d1 = 1.20 lm,d2 = 0.24 lm, d3 = 0.54 lm, d4 = 0.32 lm, d5 = 0.36 lm,d6 = 0.40 lm and K = 1.50 lm. At 1.55 lm, the nonlinearcoefficient is about 12.6456 W�1 km�1, the fundamentalmode area is about 10.2579 lm2. The confinement loss is0.306411 dB/km. This PCF may have various potentialapplications, such as supercontinuum generation and all-optical signal processing and other research and applica-tion areas. This work may be a useful selectionable solutionfor effective design and fabrication of dispersion flattenedphotonic crystal with high nonlinearities.

Acknowledgements

The authors thank the National Basic Research Pro-gram of China (973 Program) under Contract2003CB314907, the China Postdoctoral Science Founda-tion of under Contract 20060400059, the National ScienceFoundation Council of China under Contract 90604026and 60310174, the Open Fund of Key Laboratory ofOptical Communication and Lightwave Technologies,Beijing University of Posts and Telecommunications,Ministry of Education, China, for their supports. Theauthors would like to thank the reviewers for their impor-tant comments and consideration. Ming Chen’s e-mail ad-dresses are m_chen@126.com and mchen2006@tsinghua.edu.cn.

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