1926 OPTICS LETTERS / Vol. 30, No. 15 / August 1, 2005

Observation of spatial migration of excitation inEr-doped optical fibers by means of a

population grating technique

Serguei Stepanov and Eliseo HernándezCentro de Investigación Centífica y de Educación Superior de Ensenada, km. 107 Carretera Tijuana-Ensenada,

Ensenada 22860, México

Received February 8, 2005

The influence of spatial migration of excitation among neighboring Er3+ ions on the dynamics of populationgrating formation in Er-doped optical fibers is reported. The effect manifests itself in an additional incre-ment in the grating formation rate compared with the fluorescence growth rate observed for the same spa-tially uniform average light power. The experiments, performed at �=1549 nm in the configuration of tran-sient two-wave mixing with two similar single-mode Er-doped fibers with significantly different erbiumconcentrations (�640 and �5600 parts in 106), demonstrated the essential contribution of this effect to thegrating formation rate in the latter fiber. The evaluated diffusion coefficient proved to be �2.3� 10−9 cm2/s, which ensures effective migration of the excitation by �48 nm, i.e., by �18 average inter-iondistances in this fiber. © 2005 Optical Society of America

OCIS codes: 060.2410, 190.7070.

Spatial migration of an excited state among neigh-boring active ions by means of nonradiative reso-nance interaction is well known in various lasermedia,1 but to the best of our knowledge no experi-mental data on observation of this effect in erbium-doped fibers (EDFs) appear in the current literature.The excitation migration can, however, influence theperformance of some important EDF-based devices.In particular, it can ensure effective transport of theexcitation to the Er3+ pairs characterized by effectivecooperative upconversion,2 in this way enhancingconcentration quenching of fluorescence in erbium-doped fibers.3 It can also influence spatial holeburning,4 which is the effect that is in charge of theinstability of single-frequency operation of standing-wave lasers, and, in particular, those based onEDFs.5

In general, observation of excitation migrationneeds an experimental technique with a submicrome-ter spatial resolution that is comparable with charac-teristic excitation diffusion length LD. In bulk lasermaterials such measurements are usually performedby use of the dynamic population grating configura-tion (see, e.g., Ref. 6), and excitation diffusion coeffi-cient D is evaluated from the spatial-frequency de-pendence of grating relaxation time �g�K�. Similarpopulation gratings recorded in a spectral range ofEr3+ absorption, from approximately 1500 to 1560nm, have been investigated in Er-doped fibers since1992.7 But they are usually recorded in the reflec-tance configuration only, which does not allow us tovary the spatial frequency of the grating significantly�K=4�n /��12 �m−1�.

We report the first experimental observation, toour knowledge, of the influence of excitation migra-tion on the dynamics of the population gratings in Er-doped fibers. The excitation diffusion coefficient andthe corresponding diffusion length are evaluated by

comparison of the population grating formation rate

0146-9592/05/151926-3/$15.00 ©

with the fluorescence signal decay–growth rate underuniform fiber illumination.

The experiments were performed in two similarAl, Ge, Er codoped single-mode fibers, Er103 andEr123 (referred to below as fibers 1 and 2), with sig-nificantly different erbium concentrations and withmaximal attenuations of 4 ± 1 and 35 ± 1 dB/m, re-spectively, at 1531 nm. In accordance with the datasheet of the provider (http://www.ino.ca), the fibershave similar core diameters �4 ± 1 �m� and numeri-cal apertures �N.A.eff�0.16 ± 10% �. To ensure simi-lar conditions for grating recording we used signifi-cantly different fiber lengths (L=8.8, 1.0 m), whichwere characterized, however, by approximately equalinitial, i.e., not saturated, optical densities�0L�4.0, 4.5 at the utilized wavelength, �=1549 nm. Typical transmittances of the saturatedfibers reached in our experiments were 4% to 2%.

In the first experiment an input power Pin of the in-cident wave at �=1549 nm was modulated by a chop-per, and the fluorescence signal from the whole spec-tral region of the Er3+ fundamental transition (1500–1560 nm) was detected transversally by a photodiodelocated near the input fiber end. The decay time ofthe fluorescence was practically independent of thelight power and was approximately equal to 10 ms(i.e., to the spontaneous relaxation time �0 of the4I13/2 excited state of Er3+ in Al, Ge codoped silica8) inboth fibers. The fluorescence growth rate (i.e., thatobserved after the light was switched on), however,proved to be strongly light-power dependent; see Fig.1. It corresponded to the predictions of a simplemodel of saturation in a two-level system4:

�−1 = �0−1�1 +

I

Isat� . �1�

Here I is the incident light’s intensity, and saturation4

intensity Isat equals �� /2�0, where �� is the photon

2005 Optical Society of America

August 1, 2005 / Vol. 30, No. 15 / OPTICS LETTERS 1927

energy and is the ion absorption cross section. Inthe optical fibers the light power is a better experi-mental parameter, and it is to be compared with thesaturation power Psat�AmodIsat, where Amod is an ef-fective mode field area. The input powerPin� �0.5±0.02 mW� that increases the fluorescencegrowth rate two times compared with �0

−1 is markedin Fig. 1 by vertical dotted lines. Note that Pin� differsfrom Psat by transmission coefficient T of the FC/FCconnection between our EDF and other fiber ele-ments of our setup. Note that fiber 2 demonstrates abit lower value of Pin� , which can be attributed to thesomewhat reduced mode field diameter in this fiber.The fluorescence amplitudes corresponded quite wellto the light-power dependence of the excited-levelpopulation �N2= �N0 /2��Pin/Pin� � / �1+Pin/Pin� �� pre-dicted by the same two-level model4; see Fig. 1, inset.The maximal (i.e., saturated at Pin Pin� ) fluores-cence signal amplitude proved to be �7 times largerin fiber 2 than in fiber 1, which corresponds approxi-mately to the ratio of the optical absorption of the fi-bers, which grows linearly with erbium concentra-tion.

The experiments on recording–detection of the dy-namic population gratings were performed by use ofthe configuration of the transient two-wave mixing(TWM) with the rectangular phase modulation de-scribed in Refs. 9–11 earlier. The unshifted grating ofan absorption type was formed by two mutually co-herent waves counterpropagating inside the Sagnacloop interferometer with an incorporated piece of theEDF (see Fig. 2) by local saturation of the fiber opti-cal absorption in bright fringes of the interferencepattern. In this TWM configuration the grating re-corded in the fiber without optical pumping wasmanifested as a negative pulse in the light power re-flected from the Sagnac interferometer (detected atterminal 1) in reply to the rapid 180° phase jump in-troduced by means of an electro-optic modulator inone of the recording waves. The transient pulses that

Fig. 1. Fluorescence decay (a) and growth (b) rates asfunctions of input light power Pin observed in fiber samples1 (dots) and 2 (squares) (modulation frequency, 15 Hz;number of chopper blades, 2). Inset, detected fluorescenceintensity versus input light power; solid curves, theoreti-cally predicted dependences calculated for Pin� =0.5 mW.

are observed in the reflected light power (Fig. 2, in-

set) relaxed to an initial level with grating formationtime �g.

The experimental dependences of �g−1 on input light

power PR,in of direct recording wave R are shown inFig. 3, where one can see a significant growth of thegrating formation rate in fiber 2. This growth was ac-companied by reduction in the detected TWM signalamplitude (Fig. 3, inset). For comparison of the grat-ing formation rates with the fluorescence growth rate(Fig. 1), one has to take into consideration that thefluorescence signal was measured at the input end ofthe fiber, where the light power is nearly equal to theincident power multiplied by T. In its turn, the de-tected transient TWM signal is averaged over thewhole fiber length, where the total input power is re-duced because of the fiber absorption. The electro-optic modulator used in our setup was characterizedby significant light attenuation ��70% �, which intro-duced additional asymmetry in the recording configu-ration. Figure 4 shows theoretical power profiles (seeRef. 10) for two recording beams obtained for thesaturated Er-doped fiber with �0L=4, input powerratio PR,in /PS,in�3/1, and PR,in=Psat.

Fig. 2. Configuration of the Sagnac interferometer utilizedfor observation of transient TWM in Er-doped fibers: PC1,PC2, polarization controllers; EOM, electro-optic lightmodulator. Inset, rectangular phase modulation and typi-cal response in the reflected light power.

Fig. 3. TWM signal decay rates as functions of input lightpower PR,in observed in fiber samples 1 (dots) and 2(squares). Solid and dashed lines represent original theo-retical and shifted theoretical curves, respectively. Inset,the TWM relative amplitudes as functions of PR,in.

1928 OPTICS LETTERS / Vol. 30, No. 15 / August 1, 2005

In spite of significantly nonuniform distribution ofthe recording powers, the evaluated gratingamplitude10 proved to be approximately uniformthroughout the fiber length (curve d in Fig. 4). As aresult, the dominating part of the diffracted signal isformed near the fiber end where direct wave R ismost powerful. The overall diffracted wave is formedfrom partial components that appear at differentcross sections of the fiber with significantly differentaverage levels of total illumination, i.e., with differ-ent grating relaxation rates [see Eq. (1)]. One canshow, however, that the overall diffracted wave ob-tained as a result of summation of all these contribu-tions demonstrates approximately exponentialgrowth–decay with the characteristic rate �g�PR,in�dependence shown in the inset of Fig. 4. In derivationof this result we also assumed an exponential profileof propagating wave R with an initial decay rate cor-responding to that of this wave at the input end ofthe fiber (curve c in Fig. 4).

The same curve plotted with the experimentallymeasured values of �0�10 ms and Pin� =0.5 mW andshown by the solid line in Fig. 3 fits the experimentalpoints obtained for fiber 1 with a low erbium concen-tration quite well. One has to take into account thatno variable fitting parameters were used but only �0,Pin� , and �0L, which were measured experimentally.One can clearly see, however, that fitting the data ob-tained for fiber 2 needs a significant vertical displace-ment of the theoretical curve by the value�32�±2� s−1; see the dashed curve in Fig. 3. We at-tribute this light-power independent contribution tothe grating formation rate to relaxation by means ofexcitation migration from the bright into the darkfringes of the recording pattern.

For the dynamic population gratings recorded inbulk laser media this effect is described by the follow-ing equation:1,6

Fig. 4. Normalized light-power profiles: a, PR�z� /Psat; b,PS�z� /Psat calculated for �0L=4, PR,in/Psat=1, andPR,in/PS,in=3/1. Curve c shows the exponential power pro-file of the forward wave used in calculations, and curve dshows the profile of the estimated recorded grating ampli-tude (plotted in arbitrary units). Inset, dependence of theevaluated effective grating formation rate as a function ofPR,in/Psat.

�g−1 = ��I0�−1 + K2D = �1 + K2LD

2 �/��I0�. �2�

From the experimental data obtained and using Eq.(2) we can evaluate the diffusion coefficient for fiber 2as D�2.3 � 10−9 cm2/s, which also gives us that forrelatively low light power �P � Psat� the excitationmigrates for a distance LDmax= �D�0�1/2�48 nm. Forthe estimated mode field and core diameters �8 and�4 �m, respectively, and maximal attenuation�35 dB/m at 1531 nm we can evaluate the Er3+ con-centration N0 as �5.6 � 1019 cm−3 (�5600 parts in106) in this fiber. This means that, on average, the ex-citation migrates for approximately 18 inter-ion dis-tances �N0

−1/3�2.6 nm� here.It is supposed1,6 that for nonradiative dipole–dipole

interactions among neighboring ions D � N04/3. For

this reason the value of the diffusion coefficient in fi-ber 1 (with �640 parts in 106 of Er) is approximately10 to 20 times lower than that in fiber 2. This ex-plains why the experimental data obtained for theformer fiber could be approximated with a theoreticalcurve, which does not take into account spatial diffu-sion of excitation: The necessary vertical displace-ment of the corresponding curve in Fig. 3 proves to becomparable with the experimental errors of our mea-surements of characteristic rates. Note that we haveperformed similar experiments with Er-doped fiberswith maximal attenuation of 9 and 17 dB/m, and theevaluated D values demonstrated continuous growthwith erbium concentration.

Summarizing, we have reported direct experimen-tal confirmation of the influence of excited-state spa-tial migration on the dynamics of population gratingformation in Er-doped fibers. Comparison of the grat-ing formation rate with the growth rate of the fluo-rescence resulted in an excitation diffusion coefficientthat proved to be �2.3 � 10−9 cm2/s in the fiber with�5600 parts in 106 of Er.

S. Stepanov’s e-mail address is steps@cicese.mx.

References

1. R. C. Powell, Physics of Solid-State Laser Materials(Springer, 1998), Chap. 5.

2. N. V. Nikonorov, A. K. Przhevuskii and A. V.Chukharev, J. Non-Cryst. Solids 324, 92 (2003).

3. E. Delavaque, T. Georges, M. Monerie, P. Lamouler,and J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73(1993).

4. A. E. Siegman, Lasers (University Science, 1986).5. M. Horowitz, R. Daisy, B. Fisher, and J. Zyskind,

Electron. Lett. 30, 648 (1994).6. V. A. French and R. C. Powell, Opt. Lett. 16, 666

(1991).7. S. J. Frisken, Opt. Lett. 17, 1776 (1992).8. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-

Doped Fiber Amplifiers: Fundamentals and Technology(Academic, 1999), Chap. 4.

9. S. Stepanov, E. Hernández, and M. Plata, Opt. Lett.29, 1327 (2004).

10. S. Stepanov and M. Plata, Ukr. J. Phys. 49, 389 (2004).11. S. Stepanov, E. Hernández, and M. Plata, J. Opt. Soc.

Am. B 22, 1161 (2005).