1758 OPTICS LETTERS / Vol. 26, No. 22 / November 15, 2001

Ultrashort-pulse investigation of the propagation properties ofthe LP11 mode in 1.55-mm communication fibers

Ilaria Cristiani, Luca Tartara, Gian Piero Banfi, and Vittorio Degiorgio

Istituto Nazionale per la Fisica della Materia and Dipartimento di Elettronica, Università di Pavia, Via Ferrata 1, I-27100 Pavia, Italy

Received June 19, 2001

The coupling of an ultrashort laser pulse into a single-mode optical communication fiber gives rise to twopropagating pulses as a result of the excitation of two guided modes, the fundamental, LP01, and the leaky,LP11. Such a phenomenon provides a new approach to the study of the propagation properties of the LP11

mode. An experiment with tunable 110-fs pulses at a wavelength near 1550 nm is described. Informationabout the group velocity, the polarization-rotation length, the attenuation coefficient, and the cutoff wave-length of the LP11 mode is obtained in a simple and direct way for various fibers. © 2001 Optical Society ofAmerica

OCIS codes: 060.2270, 060.2430, 060.5530.

Ideally, a single-mode optical fiber operating at a wave-length l should present a cutoff wavelength lc for thefirst higher-order mode LP11 smaller than l, so thatonly the fundamental mode LP01 can propagate. Inpractice, most of the so-called single-mode fibers usedin optical communication systems and other applica-tions operate at wavelengths smaller than lc but ina condition such that the mode LP11, although stillguided, suffers considerable attenuation.1 It is a com-mon practice to define an effective cutoff wavelengthleff as the wavelength above which the attenuation co-efficient exceeds a certain value.2,3 If an optical beamat a wavelength l such that lc . l . leff is coupled ina single-mode fiber, both modes LP01 and LP11 will beable to propagate. It is of considerable interest to mea-sure the propagation properties of LP11 at 1.55 mm,especially to determine the length above which thedisturbance that is due to LP11 can be considered negli-gible. In particular, in an optical communication sys-tem the LP11 mode can be excited in a pigtail, and acertain fraction of its power may couple back into theLP01 mode at the successive splice, thus giving rise tomodal noise that can degrade the system performance.Furthermore, the presence of higher-order modes maybecome relevant when one is dealing with nonlinear in-teractions.4 A few measurements of modal noise per-formed by use of broadband cw sources near 1.3 mmhave been reported in the literature,3,5,6 but experi-mental limitations were such that a satisfactory de-scription of the phenomenon is still lacking. In thisLetter we propose a characterization of the propaga-tion properties of the leaky LP11 mode that relies on theuse of tunable ultrashort pulses. We find that eachinput pulse launched into the single-mode fiber givesrise to a couple of pulses presenting a relative delayin the range 15–25 ps�m. Such an approach, besidesmaking conventional spectral analysis easier (becauseof the higher spectral brilliance of the source), permitsus to exploit the temporal separation of the two pulses.By measuring the intensity autocorrelation functionand (or) the frequency spectrum at the output of thefiber, we are able to give a quick and accurate evalua-tion of the group-velocity difference between the two

0146-9592/01/221758-03$15.00/0

modes. Furthermore, we present the direct observa-tion of the rotation of the transverse intensity patternof the LP11 mode as function of the fiber length. Infor-mation about the attenuation of the LP11 mode is alsoobtained. It is found that the attenuation coeff icientof the LP11 mode is typically in the range 0.1 0.2 cm21

at l � 1550 nm and is strongly dependent on the wave-length of the laser beam. Our data allow us to givean estimate of lc by defining lc as the wavelength atwhich the attenuation coefficient diverges.

The source used is an optical parametric oscilla-tor (Opal, Spectra-Physics) pumped by a Ti:sapphirelaser (Tsunami, Spectra-Physics) that emits a continu-ous pulse train with an 80-MHz repetition rate in thewavelength range 1300–1630 nm. The pulses have asech2 envelope and a duration TFWHM � 110 fs. Thelaser output is coupled to the fibers by means of a lenswith a focal length f � 4 mm. The lens is mounted ona high-precision translation stage that permits us tocontrol its position with submicrometer resolution.

The fibers that we tested have a length L of up to2 m. They were fixed on a V groove and preservedfrom any stress resulting from strain or bendings.The average power level inside the f ibers was alwaysless than 500 mW so that we could avoid the occurrenceof nonlinear effects. We considered the followingtypes of telecommunications fiber: single-mode re-duced (SMR) fiber, large-core f iber (LCF), dispersion-shifted (DS) fiber, and nonzero dispersion–shifted(NZDS) fiber. The effective cutoff wavelengths leff ofthe used fibers, as measured according to the recom-mended ITUT standard procedure, were leff

SMR �1230 nm, leff

NZDS � 1280 nm, leffDS � 1280 nm, and

leffLCF � 1450 nm.

We performed measurements at various laser wave-lengths. Unless otherwise specified, the reportedresults were taken at l � 1550 nm. After optimizingthe laser coupling, we studied the fiber output bymeans of an autocorrelator (based on noncollinearsecond-harmonic generation) and an optical spectrumanalyzer. A typical autocorrelation trace and therelated optical spectrum are shown in Figs. 1(a) and1(b), respectively. They were measured at the output

© 2001 Optical Society of America

November 15, 2001 / Vol. 26, No. 22 / OPTICS LETTERS 1759

Fig. 1. Autocorrelation function and optical spectrum ob-served at the output of a DSF with L � 12 cm by launchinglaser pulses at l � 1550 nm.

of a 12-cm-long DSF fiber. The autocorrelation traceclearly shows the presence of a second pulse thatpropagates along the f iber with a group velocity thatis different from that of the main pulse. The mainpulse (truncated because it is much larger than thesecond one) corresponds to the LP01 mode, and the sec-ond pulse can be ascribed to the presence of the LP11mode. Measurements performed at different fiberlengths show that both pulses maintain their durationand shape as they propagate along the fiber andthat the amplitude of the LP11 pulse is a decreasingfunction of L. As shown in Fig. 1(b), the opticalspectrum presents a marked oscillation with a periodproportional to the reciprocal of the time delay. Weobtained results similar to those of Fig. 1 with all thefibers that we tested.

In Fig. 2 we present the measured delay, t, betweenthe two pulses, as derived from the autocorrelationfunction and (or) the corresponding optical-spectrumoscillation period, plotted as a function of the fiberlength for the DSF and the SMR fiber at two differ-ent values of l. As expected, t is proportional to L,with a slope dt�dL depending on the f iber type and onl. The l dependence of the slope ref lects mainly thefact that the LP11 mode is near cutoff and thereforepresents a rather large modal dispersion. The valuesof dt�dL obtained for all the cases investigated aregiven in Table 1.

To confirm the fact that the f ield observed at thefiber output is the superposition of the two lower-order modes, we obtained images by use of an IR vidi-con camera (Hamamatsu C 2400) after magnif icationof the images by a 403 objective. In Figs. 3(a) and3(b) we show two images of the fiber output obtainedwith the LCF at two distinct values of L. The modal

structures of the LP01 and LP11 modes can be easilyrecognized. It should be noted that in our experi-ment, at variance with the case in which a cw source isused, it is easier to separate the LP11 pattern becausethe fields of the two modes are temporally delayedso that they do not interfere in the plane of the pho-todetector. By comparing Fig. 3(a) with 3(b), we mayeasily detect the rotation of the modal structure as the

Fig. 2. Delay between the LP01 pulse and the LP11 pulseplotted as a function of the propagation length L for twofibers, each at two different values of l. The straight linesare interpolating lines.

Table 1. Group-Velocity Delay per Unit Lengthbetween the LP01 Mode and the LP11 Mode for

Various Fibers and Wavelengths

Fiber Wavelength (nm) dt�dL �ps�cm�

SMR 1500 0.178SMR 1550 0.153DSF 1500 0.245DSF 1550 0.200LCF4 1500 0.146NZDS 1500 0.227

Fig. 3. Transverse distribution of the output intensity forthe LCF at two distinct values of L. To make the obser-vation of the rotation pattern easier, we present, besidesthe direct images, the contour plots. (a) 5 cm, (b) 10 cm.

1760 OPTICS LETTERS / Vol. 26, No. 22 / November 15, 2001

Fig. 4. Intensity of the LP11 mode at propagation distanceL, relative to the input intensity, plotted as a function ofl, for a SMR fiber. The straight lines are interpolatinglines.

fiber length increases. Such a behavior was indeedpredicted for the LP11 mode,4,7 together with a rotationof the linear polarization of the LP11 field. To verifythis latter aspect, we placed a half-wavelength plate atthe autocorrelator input. We observed that the rela-tive intensity of the pulses varies for different platerotations, thus indicating that the two pulses havedifferent polarization states. The length over whichthe pattern rotates by p�2 is 18 cm, in qualitativeagreement with the formulas given in Ref. 4, whichwere derived for a step-index fiber.

Since the LP11 mode near cutoff presents a largetransverse field extent and suffers large losses causedby macrobends and microbends, it is very difficult toobtain repeatable attenuation measurements becauseof the extreme sensitivity to the f iber layout condi-tions.3 We call a11 the attenuation coefficient for theLP11 mode intensity. Information on a11 can be ob-tained either from the autocorrelation trace or from thespectrum measured at various values of L. We foundit quite practical to apply an inverse fast Fourier-trans-form algorithm to extract from the spectrum the rela-tive intensity between leaky and fundamental pulses.The data obtained present a rather large spread that isdue mainly to the fact that the amplitude of the leakymode depends on the input coupling and varies greatlywith repositioning of the f iber. We can say that all thetested f ibers present at l � 1550 nm values of a11 thatlie in the range 0.1 0.2 cm21. Such values indicatethat effects that are due to the existence of the LP11mode may still be present at propagation lengths ofsome tens of centimeters in f ibers that are commonlydesignated single mode.

Particularly interesting is the measurement of theattenuation of the LP11 pulse at fixed fiber length as afunction of l, because in such an experiment the dataare collected without modification of the fiber layout.As a consequence, the internal consistency of data col-lected within a single run should be much higher than

in the case of measurements performed by varyingL. The data shown in Fig. 4 for the SMR fiber attwo different values of L indicate that the quantityexp�2a11L� is linearly decreasing with l and extrapo-lates to 0 at a wavelength value near 1615 nm. Such avalue, which should coincide with lc within the experi-mental uncertainties, is much larger than the effectivecutoff wavelength leff

SMR. The linear plots in Fig. 4suggest a logarithmic dependence of the attenuationcoefficient a11 on the difference �lc 2 l�.

As a conclusion, we have shown that, by launchingultrashort laser pulses into a single-mode fiber ata wavelength larger than the effective cutoff wave-length, one can investigate the propagation propertiesof the higher-order mode LP11. If the fiber is suffi-ciently short, two pulses are found at the output, witha relative delay owing to the different group velocitiesof the two modes. We present a direct visualizationof the rotation of the intensity pattern of the LP11mode as it propagates along the fiber. Furthermore,our data provide an estimate of the attenuation coef-ficient, a11, and show that a11 presents a logarithmicdivergence at the cutoff wavelength, thus providing amethod of measuring the cutoff wavelength of the LP11mode. As a final comment, we note that experimentsinvolving nonlinear propagation of ultrashort pulses inshort f iber stubs are performed and interpreted on theassumption that the f iber is single mode.8 For suchexperiments, it is therefore very important to knowthe extent to which higher-order modes can be ne-glected, as they strongly affect the fundamental pulsepropagation.

We thank Giulia Pietra (Pirelli Labs, Milan, Italy)and Paolo Vavassori (OTI, Corning, Milan, Italy) forthe gift of optical f ibers and for useful discussions andErica Bricchi for help in the measurements. V. De-giorgio’s e-mail address is v.degiorgio@ele.unipv.it.

References

1. E.-G. Neumann, Single-Mode Fibers (Springer-Verlag,Berlin, 1988).

2. The effective cutoff wavelength is usually measured fol-lowing a reference test method recommended by profes-sional organizations; see, for instance, Chap 6 of Ref. 1.

3. K. Abe, Y. Lacroix, L. Bonnell, and Z. Jakubczyk,J. Lightwave Technol. 10, 401 (1992).

4. S. J. Garth and C. Pask, J. Lightwave Technol. 8, 129(1990).

5. K. A. H. Van Leeuwen and H. T. Nijnuis, Opt. Lett. 9,252 (1984).

6. J. C. Goodwin and P. J. Vella, J. Lightwave Technol. 9,954 (1991).

7. A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman & Hall, London, 1983).

8. N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata,R. Morita, H. Shigekawa, and M. Yamashita, IEEE J.Quantum Electron. 37, 398 (2001).