Phase-sensitive optical low-coherence reflectometrytechnique applied to
the characterization of photonic crystal fiber properties
Carlos Palavicini, Yves Jaouën, and Guy Debarge
Centre National de la Recherche Scientifique, Unité Mixte de Recherche 4151, GET–Telecom Paris, 75634 Paris, France
Emmanuel Kerrinckx, Yves Quiquempois, Marc Douay, and Catherine Lepers*
Laboratoire de Physique des Lasers, Atomes et Molécules, Centre National de la Recherche Scientifique, Unité Mixte de Recherche8523, Université des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq, France
Anne-Françoise Obaton
Bureau National de Métrologie, Laboratoire National d’Essais, 78197 Trappes, France
Gilles Melin
Alcatel Research and Innovation Center, 91461 Marcoussis, France
A photonic crystal f iber (PCF) consists of an all-silicacore surrounded by a periodic lattice of airholesrunning along its propagation axis. The air–silicastructure exhibits an effective cladding refractiveindex that is lower than the pure-silica core’s index,making possible the confinement of light by totalinternal ref lection as in conventional fibers.1 As thePCF may exhibit variations of waveguide propertiesalong the fiber axis that are artifacts of the fabrica-tion process, an unexpected birefringence (B) can beinduced, and the group-velocity dispersion (GVD) canexhibit polarization dependence.2 – 4 In that context,phase-sensitive optical low-coherence ref lectometry(OLCR) is proposed here as an accurate methodfor characterization of the GVD and B parameters.Moreover, unlike in the conventional phase-modulationtechnique, to produce accurate local values of the GVDthe OLCR method requires only short samples of PCF(i.e., ,1 m).
A phase-sensitive OLCR is basically a Michelson in-terferometer illuminated with a broadband source witha translating mirror in one arm and the fiber undertest in the other, as shown in Fig. 1.5,6 An Er31 su-perf luorescent source with a f lat-topped spectrum al-lows one to characterize the PCF over the entire C 1 Lband (i.e., 1525–1605 nm). A rotatable polarizer isplaced in front of the OLCR photodetector to character-ize each polarization mode separately. One obtains aref lectogram by varying the optical path difference be-tween the two arms of the interferometer at a constantvelocity (�0.2 mm�s). To keep track of the absoluteposition of the reference mirror we use a coherent in-
terferometer signal as a zero-crossing trigger to per-mit �80-nm periodic sampling of OLCR ref lectogramI �t� as a function of optical path difference t:
I �t� ~14p
�
∑Z 1`
2`
S�v�r̃�v�exp�ivt�dv
∏, (1)
where S�v� and r̃�v� � jr̃�v�jexp� jf�v�� are thepower spectrum of the OLCR source and the complexref lectivity, respectively.7 It can be seen that theref lectogram is essentially a Fourier transform of thecomplex ref lectivity weighted by the source spectrum.Scanning the entire length of the f iber yields tworef lectograms that are due to the ref lections at thefront and rear cleaved faces of the f iber. Both ref lec-tograms are numerically isolated, and a fast-Fourier-transform algorithm is applied to each ref lectogram.PCF group delay tg that results from the differencebetween the frear�v� and ffront�v� phases of the
Fig. 1. Phase-sensitive OLCR setup. Inset, SEM of thecleaved end face of the PCF.
ref lectivities of the rear and front faces of the fiber,respectively, is
tg �ddv
�frear�v� 2 ffront�v�� . (2)
We then straightforwardly obtain the GVD parameterby calculating the group-delay slope and scaling it tothe fiber length (i.e., GVD � 1�2Ldtg�dl).
A scanning-electron micrograph (SEM) of the PCFinvestigated here is shown in the inset of Fig. 1. Thisimage allows us to determine the airhole arrange-ment. The basic lattice of the PCF is a hexagonalarray of airholes whose parameters are hole diameterd � 1.89 mm and hole pitch L � 2.13 mm. Re-f lectograms of the front and the rear faces of the81.4-cm-long PCF are outlined in Fig. 2. The ref lec-togram of the rear face is broadened by the inf luenceof chromatic dispersion of the characterized fiber.Birefringence effects are clearly noticeable, as anumber of beat lobes appear in the ref lectogram.Nevertheless, birefringence cannot be evaluated froma ref lectogram because of the strong inf luence ofdispersion effects. Adjusting the polarizer allowssignificant reduction in beating by isolating a singlepolarization state, thus confirming the existenceof birefringence. By rotating the polarizer in 45±
increments it is possible to select a ref lectogram thatcorresponds to a given polarization state, i.e., theHE11x or the HE11y polarization mode, and thus toobtain the GVD for each polarization mode. Theref lectogram that corresponds to 0± polarization isspatially delayed with respect to the 90± polarization,which corresponds to different values of group delay.
Beat lobes caused by birefringence are thus ob-served only in the region where the two modes overlap,i.e., when the polarizer is set at 45± with respect tothe orthogonal axes of the polarization modes.8 Thespectrum of the PCF’s rear face ref lection is depictedin Fig. 3 and compared with the spectrum of theC 1 L band OLCR source. Beat lobes that are dueto birefringence are visible. Group birefringence isevaluated from the spectrum by use of the relationB � l2�Dl�2L�, where Dl is the spectral intervalbetween consecutive minima and 2L is the roundtrip over the PCF’s length.9 In this manner theminimum value of birefringence that can be measuredcorresponds to a maximum Dl equal to the sourcebandwidth (80 nm): For a fiber length of 1 m, Bminis of the order of 2 3 1025 at 1550 nm. For thecharacterized PCF, Dl was equal to 1.81 nm and thebirefringence was B1550nm � 8.1 3 1024.
A small asymmetry of the ref lectogram envelopewith respect to the position of the scanning mirroris related to the weak inf luence of higher-orderchromatic dispersion. This fact is conf irmed fromthe group-delay curve for both polarization modes ofthe f iber, as it varies almost linearly as a functionof wavelength, thus verifying the predominance offirst-order GVD (Fig. 4). We determined the GVDby calculating the slope of the group-delay curve,using a third-order polynomial function. The GVDof the PCF exhibits a large positive value for both
polarization modes [GVD0± � 152.4 �ps�nm��kmand GVD90± � 155.1 �ps�nm��km] at 1550 nm. Alow GVD slope value of 0.016 �ps�nm2��km wasdetermined. The accuracy of the GVD value wasevaluated to be 60.3 �ps�nm��km from multiple con-secutive measurements (ref lectogram acquisitions).
We calculated the theoretical B and GVD valuesof the PCF under test to compare the experimentaldata with the theoretical data and to determine theorigin of the f iber’s birefringence. A finite-elementmethod was applied to the SEM to provide a fullvectorial analysis of the electromagnetic f ield of
Fig. 2. Ref lectograms of PCF front and rear faces. Therear face was measured with a linear polarizer at OLCRoutputs set at 0±, 45±, and 90±.
Fig. 3. Spectrum of the PCF rear face ref lection com-pared with the OLCR source for 45± rotatable polarizeradjustment.
Fig. 4. Group delay of the characterized PCF for a singlepolarization mode. GVD values for both polarizationmodes are indicated.
the fiber structure.10,11 The simulation reveals theexistence of two orthogonal linearly polarized modes.By computing the effective indices neffx and neffy forthe two orthogonal polarization modes as a functionof wavelength we could straightforwardly obtain thePCF’s phase and group birefringence. The calcu-lated values of the group birefringence at 1300- and1550-nm wavelengths were B1300nm � 5.8 3 1024 andB1550nm � 8.2 3 1024, respectively. The waveguideGVD was then calculated from the effective indexneff from the relation GVD � 2l�c�d2neff�dl2�. Thevariation in material index as a function of wave-length was taken into account by use of the Sellmeierformula.12 The evolution of the GVD was calculatedfor both orthogonal polarization modes as a functionof wavelength, as shown in Fig. 5. The curves areincreasing functions with a zero-dispersion wave-length near 770 nm. A significant GVD differencecan be observed. At 1550 nm the GVD values were151.2 and 154.2 (ps�nm)�km for the two polarizationmodes. These high GVD values are due to predomi-nant waveguide dispersion. Because of the �1%imprecision of the dimension scale of the fiber’s profileSEM, the uncertainty in GVD was evaluated to be61.8 �ps�nm��km.
Table 1 summarizes both the measured and thecalculated GVD values for the two polarization modes.The model takes into account only the birefringencethat is due to asymmetry of the fiber core (geometrical-shape birefringence). The good agreement betweenthe theoretical and the experimental results showsthat the effect of stress on the birefringence isnegligible in the f iber under test. Note that the ex-perimental results were included in the unreliabilityinterval of the theoretical GVD values. In addition,the f iber GVD was measured near 1300 nm. A60-nm Gaussian-shaped super-LED source was usedto produce GVD1300nm � 142.5 �ps�nm��km.
The phase-sensitive OLCR is a high-resolution tech-nique used for direct and accurate measurements ofGVD and birefringence of PCFs. It is possible to mea-sure precisely the GVD value for both polarizationmodes as well as the birefringence. The experimen-tal results are in good agreement with the theoreticalresults calculated from the real structure of the fibersample. The application of phase-sensitive OLCR tothe characterization of fibers less than 1 m long con-firmed its performance as a major investigation tool inevery stage of the design and manufacture of specialtyfibers.
This study was supported in part by the ConseilRégional Nord Pas de Calais Picardie and the FondsEuropéen de Développement Economique des Régions,France. Carlos Palavicini was financially supportedby the National Council of Science and Technology,Mexico. Y. Jaouën’s e-mail address is [email protected].
*Present address, Laboratoire Centre National dela Recherche Scientif ique, Laboratoire Traitement etCommunication de l’Information, Unité Mixte de laRecherche 4151, GET–Telecom, 75634 Paris, France.
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