Passive Q-switching dynamics in SBS/Er fiber laser at low pump power

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a Ioffe Physico- Technical Institute of Russian Academy of Sciences 194021 Politekhnicheskaya 26, St.Petersburg, Russia a Ioffe Physico- Technical Institute of Russian Academy of Sciences 194021 Politekhnicheskaya 26, St.Petersburg, Russia ~ ~ ~ Recently a new mechanism for passive Q-switching in fiber lasers based on cooperative dynamics of linear Rayleigh backscattering (RS) and Stimulated Brillouin Scattering (SBS) has been reported in Yb- and Er-doped fiber lasers with high pump powers (> 2 W).1.2 At such high pump levels, the intensity of the light generated inside the fiber laser cavity exceeds considerably the SBS threshold, so that the conditions for passive Q-switching due to nonlinear backscattering are easily achieved and, for this reason, no special optimization of the laser configuration is required. Here, we report on experiments in Er-doped fiber lasers with low pump power levels. The Q-switching operational mode of Er;.doped fiber lasers was observed at pump power levels in the range of 30 -100 mW. Throughout the experiments, we traced in details different stages of Q-switching pulse formation process: growth of the spontaneous radiation, lasing due to Rayleigh backscattering, appearance and groWth of the fIrst order SBS Stokes radiation and the second order Stokes radiation, lasing suppression due to saturation of the population inversion in Er-doped fiber by the SBS Stokes radiation. In general, the process was slower in comparison with previous experiments at high pump power level. The output pulse duration was in the range of 10 - 20 ns and the peak power of the pulses was less than -100- 200 W. For this reason, all nonlinear processes except SBS did not influence the pulse formation process. The experimental results are well explained by a theoretical model based on RS-SBS dynamics. ~ II Q-switching dynamics in SBS/Er fiber laser with low-power pump .J Andrei A. Fotiadi a, Aris lkiades b,Nikos Vainos b, Olivier Deparis c, Roman Kiyan c ~ aloffe Physico-Te~hnica1.lnstitute of Russian Academy of~ciences ~ 194021 Pohtekhnicheskaya 26, St.Petersburg, RussIa bInstitute of Electronic Structure and Laser (FO R TH) P.O.Box 1527, Heraklion, Greece c Advanced Research in Optics, Faculte Polytechnique de Mons, 31 boulevard Dolez, B-7000 Mons, Belgium ABSTRACT ' I ! " i ! II ! i ! 1 , j I ! ! Keywords: Q-switched fiber lasers, Er-doped fiber lasers, stimulated Brillouin scattering, nonlinearities in fibers. Nowadays rare-earth-doped fiber lasers are widely used. 3 Erbium doped fiber lasers operating at 1.5 ~m are among the most successful fiber lasers. There is an evident interest for further developments of fiber lasers. Apart from the use of the population inversion mechanism for light amplification, other mechanisms such as linear and non-linear light scattering processes, which are very effective in fibers , 4-6 can be used in order to expand the possible applications of fiber lasers and to create new light sources. Recently a new mechanism for passive Q-switching in fiber I~ers based on cooperative dynamics of linear Rayleigh backscattering (RS) and Stimulated Brillouin Scattering (SBS) has been described. 7-9The mechanism is the following. Rayleigh backscattering of the light propagating in the laser cavity creates additional distributed feedback in the fiber cavity leading to a very effective linewidth narrowing. This in turn creates the conditions for SBS in the fiber. The growth of SBS then causes a series of avalanche processes leading to Q-switching. Until now, passive Q-switching caused by the above-mentioned mechanism has been realized experimentally but only with pump powers higher than 2 W. I, 2 Under this condition, the laser dynamics depends only slightly on the laser Correspondence: Andrei A. Fotiadi, e-maiI: [email protected], Tel.: +7 (812) 515-6660, Fax.: +7 (812) 515-6747. Olivier Deparis and Roman Kiyan are supported by the Interuniversity Attraction Pole lAP 1V/07 of the Belgian Government (SSTC).

Transcript of Passive Q-switching dynamics in SBS/Er fiber laser at low pump power

a Ioffe Physico- Technical Institute of Russian Academy of Sciences

194021 Politekhnicheskaya 26, St.Petersburg, Russia

a Ioffe Physico- Technical Institute of Russian Academy of Sciences

194021 Politekhnicheskaya 26, St.Petersburg, Russia

~~~

Recently a new mechanism for passive Q-switching in fiber lasers based on cooperative dynamics of linear Rayleigh

backscattering (RS) and Stimulated Brillouin Scattering (SBS) has been reported in Yb- and Er-doped fiber lasers with highpump powers (> 2 W).1.2 At such high pump levels, the intensity of the light generated inside the fiber laser cavity exceedsconsiderably the SBS threshold, so that the conditions for passive Q-switching due to nonlinear backscattering are easilyachieved and, for this reason, no special optimization of the laser configuration is required. Here, we report on experimentsin Er-doped fiber lasers with low pump power levels. The Q-switching operational mode of Er;.doped fiber lasers was

observed at pump power levels in the range of 30 -100 mW. Throughout the experiments, we traced in details differentstages of Q-switching pulse formation process: growth of the spontaneous radiation, lasing due to Rayleigh backscattering,

appearance and groWth of the fIrst order SBS Stokes radiation and the second order Stokes radiation, lasing suppression dueto saturation of the population inversion in Er-doped fiber by the SBS Stokes radiation. In general, the process was slowerin comparison with previous experiments at high pump power level. The output pulse duration was in the range of 10 -20 ns and the peak power of the pulses was less than -100- 200 W. For this reason, all nonlinear processes except SBS

did not influence the pulse formation process. The experimental results are well explained by a theoretical model based on

RS-SBS dynamics.

~

II

Q-switching dynamics in SBS/Er fiber laser with low-power pump

.J Andrei A. Fotiadi a, Aris lkiades b, Nikos Vainos b, Olivier Deparis c, Roman Kiyan c

~ aloffe Physico-Te~hnica1.lnstitute of Russian Academy of~ciences~ 194021 Pohtekhnicheskaya 26, St.Petersburg, RussIa

b Institute of Electronic Structure and Laser (FO R TH)

P.O.Box 1527, Heraklion, Greece

c Advanced Research in Optics, Faculte Polytechnique de Mons,

31 boulevard Dolez, B-7000 Mons, Belgium

ABSTRACT

'

I !" i

!

II

! i

!1,j

I

!

! Keywords: Q-switched fiber lasers, Er-doped fiber lasers, stimulated Brillouin scattering, nonlinearities in fibers.

Nowadays rare-earth-doped fiber lasers are widely used. 3 Erbium doped fiber lasers operating at 1.5 ~m are among the

most successful fiber lasers. There is an evident interest for further developments of fiber lasers. Apart from the use of the

population inversion mechanism for light amplification, other mechanisms such as linear and non-linear light scatteringprocesses, which are very effective in fibers , 4-6 can be used in order to expand the possible applications of fiber lasers and

to create new light sources.

Recently a new mechanism for passive Q-switching in fiber I~ers based on cooperative dynamics of linear Rayleigh

backscattering (RS) and Stimulated Brillouin Scattering (SBS) has been described. 7-9 The mechanism is the following.

Rayleigh backscattering of the light propagating in the laser cavity creates additional distributed feedback in the fiber cavityleading to a very effective linewidth narrowing. This in turn creates the conditions for SBS in the fiber. The growth of SBSthen causes a series of avalanche processes leading to Q-switching.

Until now, passive Q-switching caused by the above-mentioned mechanism has been realized experimentally but onlywith pump powers higher than 2 W. I, 2 Under this condition, the laser dynamics depends only slightly on the laser

Correspondence: Andrei A. Fotiadi, e-maiI: [email protected], Tel.: +7 (812) 515-6660, Fax.: +7 (812) 515-6747.Olivier Deparis and Roman Kiyan are supported by the Interuniversity Attraction Pole lAP 1V/07 of the Belgian Government (SSTC).

configuration. In a self-Q-switched Yb-doped fiber laser, generation of short, 2- 15 ns pulses was observed at a repetitionrate in the range of 1-20 kHz, which is remarkably different from relaxation oscil;ation pulsation commonly observed infiber lasers. I A prelasing pulse with duration about -50 ns and peak power -40 W followed by gigantic 2-ns pulses with

record high peak powers exceeding 10 kW were produced from a single-mode fiber laser with the use of 2-3 W diodepumping. Such extremely high peak powers in single-mode fiber, followed -20 ns later by the secondary echo pulse,produced extreme spectral broadening from 0.8 to 2.3 J.lm with the involvement of literally all possible nonlinear processesin silica optical fibers, including four-wave mixing, Raman scattering, etc. Such a rich laser dynamics at high pump powerwhich is caused by a multiplicity of competing effects impeded both the recognition of initial process leading to Q-switching and direct comparison of experimental and theoretical results.

In this paper, we report on our preliminary experiments of passive Q-switching in Er-doped fiber lasers with the use of

low-power pump laser diode. Pulsation operational mode of the laser which is caused by RS-SBS mechanism was observedat pump power levels of30 -100 mW. The main aim of our experiments was the detailed analysis of the laser dynamics. In

contrast with previous experiments, the laser dynamics was much more simple and slower. Commonly we observed a

prelasing pulse with duration of 50- 200 ns and peak power of 1 -5 W. It was followed by the main Q-switched pulse withduration of 10- 50 ns and peak power less than loo W. No extra echo pulses following the main pulse were observed. We

concluded that no nonlinear effect except SBS influenced on the laser dynamics. Therefore, we had a unique possibility to

compare qualitatively the experimentally observed laser dynamics with the theoretical behavior as predicted by the RS-SBSmodel. Excellent agreement was found between theory and experiment. We could recognize different stages of the Q-

switching pulse formation process and we could investigate each of them experimentally in details.

2. EXPERIMENT

2.1, Experimental setup

In our experiment, the laser configuration employed in refs. 1-2 was realized with the use of an Er-doped fiber pumped by

980 nrn laser diode with maximal output power of loo mW. The basic experimental setup is shown in Fig.l. The laserconsists of a linear fiber cavity, comprising 90% reflecting fiber Bragg grating (FBG), Er-doped fiber, piece of single-mode

fiber (SMF), and a single-mode fiber ring resonator (RR) attached to the cavity through a 10/90 single-mode fiber coupler.The laser is pumped by a laser diode through a WDM coupler, which is inserted between Er-doped fiber and SMF .Typically, a piece of exn-a single-mode fiber (EF) is spliced with the free end of the-1 0/90 coupler. If the output end of theextra fiber is protected from backreflection, feedback in the linear fiber cavity occurs due to reflection from FBG and

backreflection caused by RS or SBS in the fiber ring resonator. The laser output radiation from both cavity ends (output Iand output 2) is detected simultaneously by two photodiodes. The signals from photodiodes are digitized and recorded by

oscilloscope for further comparison and analysis. The temporal resolution of the detection system is less than -1 ns. An

optical spectrum analyzer was used for analysis of radiation spectra at the output 2.

~Er-doped fiber

-7m

n

Single mode fiber

-1m

~

l' "' Extra fiber-1m

r

\Fiber ringresonator

-2m

\Output 1

..

Output 2

.

/

10/90 CouplerWDM90% Fiber Bragg

/grating~

"'--c=J Pump laser diode

.-fiber splicing

Figure I. Experimental setup (lengths of fibers are indicated for the basic configuration).

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2.2. Laser operating in the basic configuration

In a fIrst experiment, we investigated the laser behavior in the basic" configuration shown in Fig.l. The lengths of all fibersare indicated in Fig. I. At pump power level in the range of 10 -100 m W, the lasing caused by backretlection from the freefiber end (2-4%) of the extra fiber takes place. The central wavelength of the laser radiation was 1532 nm. No regularpulsation, except relaxation oscillations, was observed in oscilloscope traces above the noise level.

When the free end of the extra fiber (EF) was cut at angle to eliminate backreflection from this fiber end, the laser couldoperate in pulsation mode. At pump power of 90 roW, self-starting generation of pulses occurred (Fig. 2) at a quite stablerepetition rate in the range of300-500 J.ls and peak power estimated to 10 W with -50% fluctuation. There was a correlationbetween the amplitude of pulse and its delay time. Pulses with higher delay were generally more powerful. Besides, thedouble-pass amplified pulses from output 2 demonstrated higher stability of their amplitude than single-pass amplifiedpulses recorded from output I. The characteristic duration of the pulse was -40-50 ns and was much more stable than otherpulse characteristics. Similar self-starting behavior of the laser could be observed at pump powers lower than 90 roW. Wefound that two factors influenced the pump power threshold at which repeating pulsation became self-starting. The first isthe coefficient of backreflection from the angled fiber end. Careful angled cutting of the fiber end allowed us to reducebackreflection from the fiber end and to decrease the threshold down to 70 mW. A second factor affected the threshold ofself-starting pulsation more dramatically. It was found that the environmental noise, unavoidably present in the room, coulddecrease the threshold. When the laser was entirely protected from environmental perturbations by a foam plastic box thethreshold of self-starting process could not be attained for pump power less than 100 roW. However, the self-starting pulsegeneration was achieved with threshold pump power as low as 30 m W when the laser was affected by a weak acousticsignal. It is important to note that the method of starting did not influence on the pulsation behavior and its parameters

(peak power, repetition rate, pulse duration), which were mainly determined by the laser configuration and pump powerlevel.

Output 1Output 2

-::Jro-

'-Q)~o

0-

-:Jro-

'-0)~o

0-

100 ~/divTime 100 ).1s/divTime

Figure 2. Typical oscilloscope traces recorded at 90 roW pump power (basic cavity configuration).

2.3. Specific features of laser dynamic behavior in basic configuration

Typical oscilloscope traces of laser pulses recorded from both laser outputs are shown in Fig. 3. They were recorded atpump power level of 80 mW. Oscilloscope traces with expanded y-axis scale are shown in Fig. 3(b). At the output I, a

gigantic pulse of -50 ns FWHM duration is seen on a CW background. At the output 2, an additional small hump precedesa gigantic pulse of -40 ns FWHM duration. From the CW background estimated to about 10 m W, the peak power of the

gigantic pulse at the output 1 is estimated to -10 -20 W from average output power measurements.

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Output 1a.OUtDUt 2

-

::J

ca-

0.>

~O

0-

-:J

rn-

'-Q)~O

0-

100 ns/divTime 100 ns/divTime

b. Output 1 Output 2

-.:Jro-

'-Q);:o

0..

-:Jro'--'

'-Q)3o

0,.'"=""'f= ,~:;= l , ~..~~~-;-~

Time 100 ns/div 100 ns/divTime

Figure 3. Typical oscilloscope traces recorded at 80 mW pump power (basic cavity configuration).

Several stages of the pulse formation can be clearly recognized in the oscilloscope traces of the output 2. Initially, the

power grows exponentially with a characteristic time of -70 ns (between points 1 and 2). Then inflection in the curvehappens (point 2) and the growth becomes slower. At point 3, a small pulse is generated before the gigantic pulse appears atpoint 4.

It is important to note that all the above-mentioned stages were always present in all traces that were recorded at pump

power of 80 m W. The growth time of the exponential part in the temporal behavior of output 2 (between points I and 2) didnot change in all the recorded traces. Point 2 where curve inflection happens, point 3 where small pulse starts and point 4

where gigantic pulse starts were always equidistant in time with the delay between pulses exactly equal to -80 ns, that is

the time that light takes to travel a round trip through SMF and Er-doped fiber.

2.4. Laser configuration with long linear part of the cavity

In a second experiment, the length of the linear part of the cavity was increased up to 44 m. We used 12.5 m of Er-doped

fiber and 32 m of single-roode fiber (SMF), instead of 7 m and 1 m in the basic configuration respectively. Self-starting

pulsation in this long cavity configuration was observed at pump power level in the range of 50 -80 roW. We found that the

output pulse from the laser became much more intense and shorter than in the previous experiment. The characteristicduration of the gigantic pulse was -10 -20 ns. The peak power was estimated to -lOO -200 W. Typical oscilloscope

traces recorded at pump power of 80 roW are shown in Fig.4. In general, they reproduce the temporal behavior weobserved in the basic configuration. Fig; 4 (a) shows the general behavior of the gigantic pulse. In contrast with previous

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experiment (see Fig. 3), the pulse shape at the output 2 is considerably different from that at the output I. The fIrst pulse hasa FWHM duration of- 50 ns while the second has a FWHM duration of -15 ns. It is surprising because the signal fromoutput 2 should be the same as the signal from output 1, the former being the same as the later but only reflected frommirror and amplified in Er-doped fiber. The reason of this disparity could be the saturation of the population inversion inamplifier, which could lead to the sharp trailing edge of the pulse from output 2. However, this pulse demonstrates alsosome specific features on its leading edge, which can not be connected with saturation effect. Fig. 4 (b ) shows that severalstages are present in the temporal behavior of output 2 (slowly growing part, small pulse and gigantic pulse), which arelikely the same as those shown in Fig. 3(b). Starting points of small and gigantic pulses (points 3 and 4 respectively) areseparated in time by -400 ns, which is smaller than the time that light takes to travel a round trip through SMF and Er-doped fiber (- 440 ns).

Output 1a.9utput 2

-:Jrn-

'-0)3o

0-

-:J

m-

'-(1):5:o

0..

, ...,

Time 100 ns!div100 ns/divTime

b. Output 1Output 2

-

:J

ro-

...:Q)

~O

C-

-~ro--

'-Q)~O

0-

34

~

, ., , , .., ,

Time 100 ns/div100 ns/divTime

Figure 4. Typical oscilloscope traces recorded at pump power of 80 mW (configuration with long linear part of the cavity).

2.5. Laser configuration with long extra fiber

In this experiment 2.5 km of extra fiber (EF) were attached to the basic configuration (see Fig.l). When the free end of theextra fiber was angled to eliminate back reflection from fiber end, the laser operated in pulsation mode. The pulses weresufficiently powerful to cause stimulated Raman scattering (SRS) process in the extra fiber. The SRS process led toeffective energy conversion from the main laser radiation near -1532 nm to the fIrst Raman Stokes component near-1645 nm. Optical spectrum of the radiation at the output 2 is shown in Fig. 5. One can see that the intensity of the RamanStokes component exceeds the intensity of the main laser radiation.

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>:0-aJ""0

O~

Center: 1625 nm 25 nm/div

Figure 5. Optical spectrum of the laser output 2 at pump power of 80 m W ( configuration with long extra fiber).

-::Jro'---'

Q);:0

(1.

-~ro

'-0)~o

Q.

20 ns/div20 ns/divTime Time

Figure 6. Oscilloscope traces of (a) the pump pulse (1532 nm) and (b) the Raman Stokes pulse (1645 nm) from the laser output 2, atpump power of 80 m W (configuration with long extra fiber).

The pump (1532 nm) and Raman Stokes (1645 nm) components were selected by diffraction grating and they

oscilloscope traces were recorded. Typical oscilloscope traces are s~own in Fig.6. One can see that the main laser

component is strongly depleted in the central part of the pulse, while Stokes pulse concentrated in the central part.

II

f

!!t

f

I[tl

3. DISCUSSION OF THE RESULTS

In our experiments, we observed the Q-switching behavior of the Er-doped fiber las~r shown in Fig. J. This Q-switchingbehavior of the laser and the observed fme temporal structure of the pulses can be explained by a mechanism that involves a

cascaded stimulated Brillouin scattering process in the laser cavity .The cascaded SBS process is initiated by the lasing due

to Rayleigh backscattering in the laser cavity .For the experiment in the basic configuration this mechanism is following.

At the beginning of thy-cycle, the population inversion in the Er-doped fiber builds up and laser radiation builds up

exponentially in the cavity. Feedback caused by reflection from the fiber end at the laser output is suppressed by angledcutting of the fiber end. The lasing is actually caused by feedback due to Rayleigh scattering in the ring resonator that isenhanced at the resonator resonance frequencies. Although the Rayleigh scattering coefficient of the ring resonator is low,

the double-pass gain of the Er-doped fiber is sufficiently high to provide lasing. The lasing wavelength coincidessimultaneously with one of the resonance modes of the ring resonator and one of the resonance modes of the complete

cavity (formed by FBG mirror and Rayleigh backscattering from ring resonator). Thanks to the high spectral selectivity ofRayleigh scattering, the linewidth of laser radiation is very narrow. Laser radiation circulates in the ring in both directions.

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However, the intensity of the clockwise circulating radiation is much lower than intensity of the counterclockwisecirculating radiation because the fomler results from Rayleigh backscattering of the latter.

At a certain intensity level of the growing counterclockwise radiation, the threshold of SBS is reached and a first orderStokes pulse of hundreds nanosecond duration is generated in the ring resonator. The frequency of the pulse is downshiftedbyabout II GHz and it should be coincident with one of the resonance frequencies of the ring resonator. This SBS processcauses the depletion of the counterclockwise radiation in the ring resonator which leads to the reduction of Rayleighreflection from the ring resonator and, eventually, to the suppression of lasing. The Stokes pulse propagates in theclockwise direction in the ring resonator. It is partly extracted from the ring through the coupler and experiences strongamplification through double pass the linear part of the cavity. Then, the amplified Stokes pulse is again injected into thering resonator and circulates in the counterclockwise direction. Part of this amplified Stokes pulse is extracted from thecavity through the coupler ( cf. small hump observed at output 2).

A new SBS process can be initiated by this Stokes pulse that propagates in the counterclockwise direction in the ring. Asecond order Stokes is generated in the ring while the initiating fIrst order Stokes pulse is depleted. The second order Stokespulse propagates in the clockwise direction in the ring resonator and is extracted from the ring through the coupler. Then itexperiences strong double-pass amplification in the Er-doped fiber, depleting the population inversion and extracting mostof the energy stored in the cavity .This last stage of the process results in a gigantic pulse at the output of the laser and turnsthe system back to the initial state.

In the experiment with a long linear part of the cavity, the third stage of the Q-switching process (i.e. generation of thesecond Stokes pulse) is modified. In this case, due to the long length of the linear part of the cavity, generation of thesecond order Stokes occurs in the linear part of the cavity before the fIrSt order Stokes reaches the coupler after round-tripin linear cavity and is injected into the ring. For this reason, the delay between the small hump and the gigantic pulse (points3 and 4, Fig. 5) is smaller than the time that light takes to make a round-trip through the linear part of the cavity .

Computer simulation of the RS/SBS process for the basic configuration of the laser were performed. The calculatedradiation at the output 2 is shown in Fig. 7. There is a very good qualitative agreement with experimental oscilloscopetraces. The components that form the output radiation are shown separately in Fig. 8. Fig. 8(a) demonstrates the mutualdynamics of the lasing radiation and the first order Stokes radiation at the fIrSt and second stages of the process. One cansee that the threshold of SBS in the ring resonator is reached at a very small lasing intensir:y of- 4 m W .Therefore, we didnot see lasing due to Rayleigh feedback in the experiment, simply because it was below the noise level ( -10 m W). Whatwe observed in the experiment were the first and the second order Stokes pulses. Their mutual dynamics is shown in

Fig.8(b). Starting points of small hump and gigantic pulse (points 3 and 4 respectively) are separated in time by -80 ns,which is exactly the time that light takes to travel a round trip through SMF and Er-doped fiber.

3

s

'-Q)~O

(1.

s 2~tt

1

'-Q)~o

0-

0

Figure 7. Computer simulated traces of the radiation from output 2 (a -lage scale, b -zoom on y-axis).

8

8 32-nd order Stokes

-st order Stokes -; ""b.

s 6

E-4'-

<1>$:o 2

0..

s,-0)~0

(1.

2

~1

14

0 00 100 200

Time,

300 400

ns

, .L : J\"J'-,0 100 200 300 400

Time, ns

Figure 8. Computer simulated traces of (a) the lasing radiation and the first order Stokes radiation and of (b) the first-order Stokes andthe second-order Stokes radia~ion, calculated for output 2.

4. CONCLUSION

In conclusion we have successfully demonstrated passive Q-switching in a Er-doped fiber laser configuration at very lowpump power. We have investigated the laser dynamics and described a number of specific features of the temporal behavior

that accompanied the generation of gigantic pulse. The direct comparison of experimental oscilloscope traces with

theoretically predicted ones allowed us to recognize different stages of pulse formation process and to obtain importantinformation about its key parameters. We proved that pulsation was caused by the RS-SBS Q-switching mechanism thatwas exploited early but only with high-power fiber lasers. More than 100 W peak power pulses with duration of -10nshave been observed in Er-doped fiber laser at pump power of only 80 m W .Thanks to stimulated Raman scattering initiatedin a configuration with a long extra fiber, the laser could operate in pulsed mode both at 1532 nm and at 1645 nm. Such a

light source, which could be very flexible, may be useful for many applications. Of course, these are preliminaryexperiments and some important issues such as laser instabilities, influence of polarization, noise fluctuations and backreflection fi"om cleaved fiber end, were not yet investigated. We are planning to investigate these issues in future works.

ACKNOWLEDG:MENT

Financial support of the NATO Linkage Grant HTECH.LG 970314 is gratefully acknowledged.

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pp.52-57,1998.

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