2764 OPTICS LETTERS / Vol. 33, No. 23 / December 1, 2008

Birefringence in microstructure fiber with ellipticalGeO2 highly doped inclusion in the core

Tadeusz Martynkien,1 Marcin Szpulak,1 Gabriela Statkiewicz-Barabach,1 Jacek Olszewski,1

Alicja Anuszkiewicz,1 Waclaw Urbanczyk,1,* Kay Schuster,2 Jens Kobelke,2 Anka Schwuchow,2

Johannes Kirchhof,2 and Hartmut Bartelt2

1Institute of Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland2Institute of Photonic Technology, Albert-Einstein-Strasse 9, D-07745 Jena, Germany

*Corresponding author: waclaw.urbanczyk@pwr.wroc.pl

Received August 25, 2008; revised October 20, 2008; accepted October 21, 2008;posted October 24, 2008 (Doc. ID 100562); published November 19, 2008

We studied both numerically and experimentally a birefringence in a microstructure fiber with elliptical in-clusion highly doped with GeO2. We demonstrate that such inclusion increases the phase modal birefrin-gence and modifies its dispersion in the short wavelength range, thus causing that group birefringencecrosses zero value at a certain wavelength. Moreover, we numerically analyzed different factors contributingto the overall fiber birefringence, including geometrical birefringence induced by holes distribution and el-lipticity of the inclusion as well as stress birefringence associated with thermal shrinkage of the doped glass.© 2008 Optical Society of America

OCIS codes: 060.4005, 060.2420, 060.2280.

Geometrical birefringence in microstructure fibers(MOFs) is typically induced by breaking hexagonalsymmetry of either the core or the cladding [1–3]. Itis also possible to induce a so-called stress birefrin-gence by placing symmetrically the stress applyinginclusions doped with B2O3 in the solid part of the fi-ber cladding [4]. In this Letter, we study the MOFwith birefringence induced simultaneously by holesdistribution in the microstructure cladding andGeO2-doped elliptical inclusion in the fiber core. TheMOFs with GeO2-doped cores become a subject ofgrowing interest because the appropriate choice ofdopant concentration facilitates splicing with conven-tional fibers and inscription of Bragg gratings [5], de-creases susceptibility to bending loss [6], enablesendlessly single-mode regime tuning [7], and in-creases nonlinearity [8]. Although potential applica-tions of GeO2-doped MOFs are very wide, to ourknowledge the birefringence in the MOFs with ellip-tical inclusions has not been studied yet. In such fi-bers, the geometrical birefringence induced by themicrostructured cladding and elliptical shape of theinclusions is combined with stress birefringence aris-ing due to different thermal expansion coefficients ofdoped and pure silica glass. We analyze an impact ofeach factor on overall fiber birefringence and com-pare the results of birefringence measurements withsimulations carried out using the finite elementmethod (FEM).

The investigated fiber was fabricated for nonlinearapplications; therefore the concentration of GeO2 inthe inclusion is very high to enhance the nonlinearcoefficient [9]. The GeO2-doped rod for the inclusionwas prepared from a modified chemical-vapor deposi-tion manufactured preform of 25 mm in diameter,drawn down to 1 mm. The germanium content of thefirst layers was continuously increased up to14 mol. %. For the last 36 layers, it was jumped to36 mol. %, which corresponds to a refractive index

−2

contrast of about 5.5�10 (Fig. 1).

0146-9592/08/232764-3/$15.00 ©

The measurements of group modal birefringence Gwere carried out in a wide wavelength range by pro-cessing the spectral interferograms arising due to in-terference between fundamental modes of ortoghonalpolarization equally excited in the investigated fiber[10]. The group modal birefringence was determinedfrom the following relation:

�G� =�2

��L, �1�

where �� is a separation of two successive interfer-ence fringes, � is an average wavelength between thefringes, and L stands for the fiber length. The spec-trogram displayed in Fig. 2 proves that group modalbirefringence changes its sign at �=880 nm. This un-usual spectral dependence of G shown in Fig. 3 is notencountered in the MOFs with purely geometrical bi-refringence and, as demonstrated by our numericalanalysis, is caused by ellipticity of the inclusion. Us-ing the lateral force method [11], we have also mea-sured at several wavelengths the phase modal bire-fringence B with a precision of about 1%. Similarly as

Fig. 1. Design of the five air ring germanium doped MOF(inset) and refractive index profile of the germanium doped

inclusion measured at �=633 nm.

2008 Optical Society of America

December 1, 2008 / Vol. 33, No. 23 / OPTICS LETTERS 2765

for the G, the effect of doped inclusion is clearly vis-ible in the short wavelength range (Fig. 3). In MOFwith purely geometrical birefringence, the phasemodal birefringence tends to zero for a decreasingwavelength while in the investigated fiber it stabi-lizes on the level of 0.58�10−4. It is worth mention-ing that measured values of B and G satisfy well thedispersion relation G=B−�dB /d�.

To better understand the effect of inclusion onoverall birefringence, we modeled the investigatedMOF using the finite-element method. The fiber ge-ometry assumed in numerical simulations was deter-mined from the scanning electron microscopy (SEM)micrographs using a special image processing proce-dure. It is clearly visible in Fig. 4(a) and 4(b) that thecentral part of doped inclusion is slightly ellipticalwith major and minor axes equal, respectively, ax=0.915 �m, ay=0.832 �m, and ellipticity ax /ay=1.1.Because of gradient doping, it was practically impos-sible to detect the outer edge of the inclusion usingSEM. Therefore, we assumed that the ellipticity ofthe outer edge is the same as of the central part ofthe inclusion. Outer dimensions of the inclusion werecalculated using data extracted from Fig. 1, assum-

Fig. 2. Registered spectrogram proving that group modalbirefringence changes its sign at �=880 nm. The length ofthe measured fiber sample is L=1.457 m.

Fig. 3. (Color online) Results of simulations of phase �B�and group �G� modal birefringence. Geometrical birefrin-gence induced by the holes microstructure (coarse dashedcurve), geometrical birefringence induced by holes micro-structure and ellipticity of the inclusions (fine dashedcurve), and overall birefringence including the stresscontribution (solid curve). Black dots indicate the experi-

mental results.

ing that the drawing process preserves the propor-tion between the outer and the inner parts of the in-clusion. These dimensions are equal to 2.90 and2.64 �m, respectively, in x and y directions. The mapof the refractive index distribution assumed in nu-merical simulations is visualized in Fig. 4(c).

In the simulations, we took into account the spec-tral dependence of refractive indices of pure andGeO2-doped glass described by corresponding Sell-meier equations [12]. It can be clearly seen in theSEM micrographs that because of the unequal sizeand different shapes of holes in the first ring sur-rounding the core, it exhibits a small ellipticity andits major axis is oriented almost in parallel with themajor axis of the inclusion. In such a case a signifi-cant part of the fiber birefringence is induced by theholes layout. We first modeled this effect by totallydisregarding the inclusion and performing the calcu-lations for purely MOF. The results of simulationspresented in Fig. 3 show a strong increase of B and Gagainst wavelength, which is typical behavior forMOFs with purely geometrical birefringence. In thesecond step, we evaluated the geometrical birefrin-gence introduced by the inclusion. In this case, wetook into account the refractive index distribution inthe inclusion; however, the material birefringence in-duced by the difference in thermal expansion coeffi-cient between pure and doped silica was still disre-garded. Because the ellipse of the inclusion and of thefiber core are almost parallel, the birefringence in-duced by these two factors have the same sign. As aconsequence, in a short wavelength range, we ob-serve an increase of the phase modal birefringence Bto the level of 0.38�10−4. In a long wavelengthrange, the effect of the inclusion is opposite, becausethe birefringence introduced by the inclusion be-comes negligible and, at the same time, the birefrin-gence induced by holes is reduced owing to increased

Fig. 4. (Color online) (a) and (b) SEM images of the inves-tigated MOF obtained after etching the fiber cleave to bet-ter visualize edges of the inclusion, (c) fiber structure re-produced from SEM images used in numerical simulations,and (d) calculated distribution of material birefringence�nyy–�nxx induced by thermal stress.

confinement of the mode in the fiber core. These

2766 OPTICS LETTERS / Vol. 33, No. 23 / December 1, 2008

simulation results match relatively well with themeasured values of birefringence.

Finally, we have evaluated the effect of the thermalstress. To do so, we first calculated the distribution ofthe normal �xx, �yy, �zz, and shear �xy components ofthe thermal stress using a plane strain model. In thesecond step, the stress-induced corrections of the re-fractive index �nxx, �nyy, �nzz, and �nxy were ar-ranged into the symmetric tensor and used to modelthe fiber birefringence using fully vectorial FEM. Inthe calculations of stress components and correctionsof refractive index, we used the following materialconstants for pure silica glass [11]: stress opticcoefficients C1=−6.9�10−13 �1/Pa�, C2=−41.9�10−13 �1/Pa�, Young modulus E=72.5�109 �Pa�,Poisson ratio ��=0.165, thermal expansion coefficient��=5.5�10−7 �1/K�, and glass transition tempera-ture Tg=1130°C. For germanium doped glass, wetook into account the dependence of E, �, �, and Tgupon dopant concentration estimated from [11]. Formaximum concentration of GeO2 in the center of theinclusion �36 mol. % �, these constants are equal, re-spectively, to E=52.2�109 �Pa�, �=0.137, �=3.95�10−6 �1/K�, and Tg=1000°C.

The results of simulations displayed in Fig. 3 showthat in the short wavelength range, thermal stressincreases B by about 50%, while in the long wave-length range the effect of stress is negligible. This isassociated with a specific distribution of material bi-refringence induced by thermal stress [see Fig. 4(d)].In the central part of the inclusion with a maximumconcentration of GeO2, the material birefringence�nyy–�nxx is almost uniform and equals 3.7�10−5.For short wavelengths, almost whole mode energy isconfined in this region, thus causing the stress con-tribution to modal birefringence to be simply equal tothe material birefringence in the central part of theinclusion. For longer wavelengths, the modal fieldspreads over the entire inclusion and surroundingsilica glass, in which the material birefringence peri-odically changes its sign between different sectors ofthe fiber cross section and gradually decays with in-creasing distance from the inclusion’s edge. As a con-sequence, a contribution of the thermal stress tooverall modal birefringence tends to zero with an in-creasing wavelength.

It is already known from earlier publications [5–9]that the addition of the germanium-doped inclusionin the core of MOFs significantly improves their se-

lected propagation and nonlinear characteristics. In

this Letter, we show that the doped inclusion of theelliptical shape provides additional degrees of free-dom in engineering the birefringence dispersion. Wedemonstrate that parallel alignment of the majoraxes of the fiber core and the inclusion increases Band simultaneously reduces its dispersion in theshort wavelength range. As a consequence, the groupbirefringence G crosses zero value at a certain wave-length that can be adjusted by tuning the geometry ofthe inclusion. It is expected that by rotating the in-clusion by 90° one can obtain the opposite effect, i.e.,enhanced G in the short wavelength range and Bcrossing zero at a certain wavelength.

This work was supported in part by the EuropeanCOST Action 299–Optical Fibres for New ChallengesFacing the Information Society–“FIDES”. J.Olszewski acknowledges support from the StartProgram of the Foundation for Polish Science FNP.References

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