DISPERSION PROPERTIES OF ANNULAR HOLLOW FIBER

P OZNA N U N IV ER S IT Y O F T EC HN O LO G Y A C A DE M IC J O UR N A LS

No 54 Electrical Engineering 2007

Grzegorz Żegliński*

Jerzy GAJDA*

DISPERSION PROPERTIES OF

ANNULAR HOLLOW FIBER

In this paper, the annular hollow fiber, based on the right-angle guiding mechanism, is put forward and analyzed by the FEM method. The cross section of this kind of hollow fiber is shown in fig. 1. Effective refractive index, first-order dispersion, second-order dispersion, dispersion parameter, and transverse electric field distribution of the fundamental mode are numerically calculated and discussed. Material dispersion is not included here.

.

Keywords: hollow fiber, ring fiber, dispersion

1. INTRODUCTION

Theoretical studies of guided modes in holey fibers give information about optimalization of geometrical structure. The important parameters and frequency characteristic can be study by wave expansion method, the effective index approach, the localized basis function method, fully-vector biorthonormal basis modal method, the finite element method (FEM) , the finite difference time-domain method (FDTD) and the beam propagation method (BPM). The FEM and FDTD methods are more efficient but avoids difficulties such computation time and memory.

The annular fibers are difficult geometries and the results can be obtain by FEM or FDTD methods. One of them the ring fiber with three air sections is analyzed by FEM method in this work. The material dispersion is not include in this model. This type of fiber was presented by two optical groups in papers [1-4] in 2003-2004 year. The model is presented on figure 1. The practical construction was developed by Monro group [4]. The numerical calculations for one construction were presented in Hoekstra paper [1]. The results of calculations were obtained for one setup of

2007

Poznań 6 - 7 grudnia 2007 POZNAN UNIVERSITY OF TECHNOLOGY ACADEMIC JOURNALS

parameters (r1= 1µm, r2= 2µm, r3= 2.5µm, na=1, nf for SiO2). The exact calculations

shows existing of two degenerate modes HE11 [1].

Fig.1. The structure of annular hollow fiber (na- air area).

2. MODELLING AND RESULTS

The Finite element method (FEM) was used to analyze choisen structure of annular holey fibers. The method and its application for analyzing of photonic crystal fibers and holey fiber is used by group of Professor Massanouri Koshiba and presented in many optical and communication papers [5-7]. In all of the numerical simulations presented in this paper, a total of 34110-37251 elements used to analyze holey fiber. The calculation procedure started from propagation constant calculation. We can get the first-order dispersion β1 and the effective

refractive index, the second-order dispersion β2 and parameter D as follow:

λ π β 2 = Neff (1)

λ

β

π

λ

β

d

d

c

2

=

−

( )





+





=

2

2

λ

β

λ

λ

β

π

λ

β

d

d

d

d

c









₊

−

=

₂

2

λ

β

λ

λ

β

π

λ

d

d

d

d

c

D

The calculation parameters were: na=1, nf=1.45, angle of air element: 1000, 800,

600_{, r1: 0.5µm, 0.6µm, 0.75µm, r2=2µm, r3=2.5µm. The boundary conditions}

were taken the perfect electric conductor (PEC). The wavelength range was from 600nm to 1600nm. The fiber structure has multimode properties. Two HE11 modes

are characteristic for single mode propagation in the third optical window. The results of calculations for various structure are shown on figures 2-3 (dispersion relations) and on figure 4 (modes of calculated fiber).

Fig. 2. The dispersion plots for HE11 mode :

Fig. 3. The dispersion plots for HE11 mode an various angles of air section:

a) 1000 _{(1), b) 80}0 _{(2), c) 60}0 _(3).

The attenuation can be obtained on the low level only for HE11 modes. For

example for the case when r1=0.75µm, the angle equals 1000, λ=1550nm, the

attenuation of HE11 mode is 1.3 dB/cm, for HE21 mode is 300 dB/cm. The

fundamental two fold degenerate modes are observed after small propagation distance for calculated structures. The non-propagation process is for the plot 3 on figure 2 when wavelength is more than 1.3µm. The decreasing process of mode area includes on dispersion relation and loss characteristics. The tuning of zero dispersion is possible by changing of the mode field area or the angle of air section.

a) b)

Fig.4. The modes of the annular holey fiber: a) HE11 (2 fold degenerate) , b) HE21 (2- fold

degenerate).

3. CONCLUSIONS

The annular hollow fiber has potential applications in optical communication, sensing process (two degenerate modes), nonlinear optic [2], dispersion compensators. The calculation results shows that dispersion relation can be designing by changing air holes (angle, radius). The attenuation can be obtain less than 1 dB/cm for the fundamental mode. The dispersion parameters such zero dispersion can be tuning by changing the cross section of structure (radius, angles). The FEM method is powerful for this kind of calculation. The wide wavelength range and single mode work is interesting for future applications of this fiber. The high value of attenuation excludes some of transmission applications. The cross section designing will be the subject of future works.

REFERENCES

[1] Uranus H.P and Hoekstra H.J.W.M. : Modelling of microstructured waveguides using a finite-element based vectorial mode solver with transparent boundary conditions, Optics Express, Vol. 12, No. 12, pp. 2795-2809, 2004.

[2] Nader A. Issa, Poladian L.: Vector Wave Expansion Method for Leaky Modes of Microstructured Optical Fibers, JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 4, APRIL 2003.

[3] Ebendor.-Heidepriem H.: Journal of Non-Crystalline Solids 345&346 (2004), pp. 293–296.

[4] Petropoulos P., Ebendorff-Heidepriem H., Finazzi V., Moore M., Frampton K., Richardson D.J., Monro T.M.: Highly nonlinear and anomalously dispersivelead silicate glass holey fibers, OE, voL.11, No.26, 2003.

[5] Fujisawa T., Koshiba M.: Finite element characterization of chromatic dispersion in nonlinear holey fibers, Optics Express, Vol. 11, No 13. pp. 1481, 2003..

[6] Saitoh K., Koshiba M. : Approximate Scalar Finite-Element Beam-Propagation Method with Perfectly Matched Layers for Anisotropic Optical Waveguides, Journal of Lightwave Technology, Vol. 19, Issue 5, pp. 786

[7] Koshiba M., Saitoh K.: Finite-Element Analysis of Birefringence and Dispersion Properties in Actual and Idealized Holey-Fiber Structures, Applied Optics, Vol. 42, Issue 31, pp. 6267-6275.