Lasing dynamics of tunable single-frequency fiber-optic and waveguide lasersV. A. Pilipovich, A. K. Esman, I. A. Goncharenko, and V. K. Kuleshov

GNU Institute of Electronics, National Academy of Sciences of Belarus, Minsk, Belarus~Submitted July 1, 2002!Opticheski� Zhurnal70, 34–38~March 2003!

The dynamics of the wavelength tuning of the radiation of fiber-optic and waveguide lasers witha short linear cavity are analyzed. It is shown that the tuning time is minimized in lasers inwhich the output diffraction grating has a reflectance of about 95% and which possess themaximum lasing efficiency. The additional losses that appear when the optical fiber iscoupled with a controllable diffraction grating written on a waveguide electrooptic modulatorreduce the tuning time of the laser radiation, but its lasing efficiency is also reduced inthis case. ©2003 Optical Society of America

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INTRODUCTION

Single-frequency tunable lasers with a short cavity baon optical fibers doped with erbium ions are widely usedfiber-optic communication systems, fiber-optic sensors,other devices.1–4 A single-frequency lasing regime iachieved in such lasers by using a short cavity, as well ausing a selective element, which can be a fiber-optic~Bragg!diffraction grating ~FOBDG!.1–3 As is well known, themodes propagating in the forward and reverse directionsFOBDG become coupled at a definite wavelength, andreflectance reaches a maximum in a narrow spectral inte~of the order of fractions of nanometers!. The wavelength atwhich the reflection is a maximum~the Bragg wavelength!depends on the parameters of the FOBDG. The regionmaximum reflection can be displaced over the spectrumchanging the grating parameters, and the lasing can thebe tuned in frequency.

However, not much of the pump radiation can be asorbed in the short section of fiber that makes up the caand the output power of such a laser will consequentlysmall.2,5 Increasing the erbium-ion concentration makespossible to increase the absorption of pump photons,ion–ion interactions at concentrations greater than (3 –31024 ion/m3 produce degeneracy of the metastable leveerbium, and this reduces the lasing efficiency.2 A solution ofthis problem is to use optical fibers co-doped with erbiuand ytterbium ions with the optimum concentrations.1–4,6

One more drawback of lasers with a short cavity is that iimpossible to continuously tune the radiation over walength in them, since the spectral distribution of the cavmodes is large. By altering the FOBDG parameters, it is opossible to transfer the lasing from one mode to another wa step that is inversely proportional to the linear size ofcavity. The switching time of such systems usually reacseveral milliseconds, since the radiation is tuned in walength by changing the FOBDG parameters eithmechanically4 or by using the piezoelectric effect.1

In our earlier papers,7,8 for rapid wavelength tuning olaser generation, we proposed that the mirror of its extecavity and the selective element should consist of a diffrtion grating written on one part of a waveguide or a fibelectrooptic modulator. The second part of the modulato

173 J. Opt. Technol. 70 (3), March 2003 1070-9762/2003/030

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inside the cavity and is used as an electrooptic cell. Whevoltage is supplied to the electrodes of the intracavity eltrooptic cell, the optical length of the cavity varies, and thleads to continuous tuning of the lasing wavelength withthe reflection band of the FOBDG. The tuning range iscreased when a voltage is supplied to the electrodes ofdiffraction grating, because this displaces its reflection baand thus tunes the lasing range. The calculated spectral cacteristics of the radiation of such a laser device insteady-state lasing regime when a voltage is applied toelectrodes of both the electrooptic cell and the controllagrating are shown in Fig. 1. The calculation was carriedusing the well-known formula that describes the transmissof a Fabry–Perot cavity filled with an amplifying mediummodified for our case.7,8

The lasing wavelength can be tuned continuously bying such a layout. It can therefore be used as a basiscreating fiber-optic lasers with frequency modulation of tradiation. In this case, there is significance in the ratewhich the lasing can be tuned to another frequency. Sincwaveguide electrooptic modulator with a low control voltais used in the proposed scheme~the time to vary the refrac-tive index in a lithium niobate crystal under the action of

FIG. 1. Lasing lines of a fiber-optic laser in which the electrodes ofFOBDG and the intracavity cell are simultaneously supplied with a voltaof 0 ~1! and 5 V~2!. The dotted curves show the spectral distribution of treflectance of the controllable FOBDG.

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electric field is of the order of picoseconds!, it can be as-sumed in first approximation that the time to tune the laseanother wavelength is limited by the time to establish steastate lasing. Thus, in order to estimate the tuning rate,necessary to analyze the lasing dynamics of the laser.

THE DYNAMICS OF ESTABLISHING LASING

The dynamics of establishing lasing was calculateding the theoretical model for a fiber laser doped with erbiuytterbium with a linear cavity based on the rate equationsRefs. 2 and 9. The variation of the pump powerPp(z,np)and the power of the laser radiationPs j

6(z,ns j) over thelength of the laser cavity is described by the system offerential equations

dPp~z,np!

dz52Gp@sEr13n̄11sYb56n̄52sYb65n̄6#

3Pp~z,np!2 l pPp~z,np!, ~1!

dPs j6~z,n j !

dz56Gs j@sEr21~n j !n̄22sEr12~n j !n̄1#

3Ps j6~z,n j !62hn jDn jGs jsEr21~n j !n̄2

7 l s jPs j6~z,n j !

Pp~0,np!5Pp0 ,~2!

Ps j~0,n j !50,

R2~n j !Ps j1~L,n j !5Ps j

2~L,n j !,~3!

R1~n j !Ps j2~0,n j !5Ps j

1~0,n j !,

where j 51,...,M ; M is the number of longitudinal modethat can be generated by the laser;np , n j and l p , l s j are,respectively, the frequencies of the radiation and the optlosses of the pump wave and the generated wave;R1(n j ) andR2(n j ) are the reflectances of the cavity mirrors~Bragg grat-ings!, L is the length of the cavity, andsEri j andsYbi j are theabsorption and emission cross sections of erbium and ybium. The plus sign in the notationPs j

6(z,ns j), as well as theupper signs on the right-hand side of the second equatiothe system of Eqs.~1!, describe optical radiation propagatinthrough the cavity in the forward direction; the minus siand the lower signs in Eqs.~1! correspond to optical radiation in the reverse direction. The overlap integrals betwethe cross section of the radiation fields and the active regof the waveguideGp andGs j , assuming a Gaussian intensidistribution of the fields of the pump radiation and the sigradiation, can be determined from

Gm512exp~ad2/vm

2 !, ~4!

where ad is the active radius of the fiber, andvm is thetransverse size of the radiation field, withm5p for the pumpwave and m5s j for the signal wave. The term2hn jDn jGs jsEr21(n j )n̄2 in the second equation of the systeof Eqs.~1! describes the input noise equivalent power andincluded in the equation for initiation of the lasing processthe absence of start-up radiation.

174 J. Opt. Technol. 70 (3), March 2003

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The averaged populationsn̄i of the levels are determineby means of the rate equations2

]n1

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~7!

n11n21n31n45NEr , ~8!

]n5

]t52W56n51A65n61W65n61Ccrn1n6 , ~9!

n51n65NYb , ~10!

where n1 , n2 , n3 , and n4 are the populations of energlevels4I 15/2, 4I 13/2, 4I 11/2, and4I 9/2 of the Er31 ions, andn5

andn6 are the populations of the2F7/2 and2F5/2 levels of theYb31 ions. TheWi j terms determine the stimulated transtion probabilities, theA21 andA65 terms determine the spontaneous transition probabilities, andA32 and A43 determinethe nonradiative relaxation probabilities;Cup, Ccr14, andCcr

are the transformation coefficients with increased frequeand cross-relaxation; andNEr and NYb are the Er31 andYb31 concentrations. It should be pointed out that this moneglects various mechanisms that broaden the energy leas well as the temperature instability.

The system of Eqs.~1! was solved numerically by theRunge–Kutta method. The averaged populations of theels at each step alongz were determined by means of Eq~5!–~10!. The spontaneous- and stimulated-transition prabilities, as well as the conversion coefficients with ancrease of the frequency and the cross-relaxation coefficiused in the calculations, are analogous to the values useRef. 2. Apodized fiber and waveguide Bragg gratingsused as cavity mirrors. The spectral dependence of theirflectancesR1(n j ) andR2(n j ) at various values of the applieexternal electric field were calculated by means ofmethod of lines.11,12A broad-band FOBDG with a maximumreflectance of 100%, written on a doped optical fiber, seras the input mirror of the cavity. A refractive-index changeabout 231023 can be created in a photosensitive fiber dopwith erbium and ytterbium ions.3 The calculated width of theprincipal maximum of the reflection spectrum of the outpcontrollable waveguide grating with a bell-shaped apodition function equals 0.1 nm.7 To ensure a single-frequenclasing regime, the length of the laser cavity with such a gring must equal 1 cm.

As the first step, we analyzed how the time to establisstable lasing regime depends on the reflectanceR of the out-put mirror of the cavity. For the device considered here, tdependence is represented by curve1 in Fig. 2. Curve2 in

174Pilipovich et al.

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this figure shows the dependence onR of the lasing effi-ciency h5Ps /Pp0 , where Ps is the power of the outpuradiation of the laser in the steady-state lasing regime. Asbe seen from the figure, the minimum time to establish lascorresponds to the maximum effective lasing and forgiven laser parameters is reached when the reflectance ooutput mirror equals about 95%.

It is obvious that the time to establish lasing at a definwavelength strongly depends on the residual or start-upnal at this wavelength. As can be seen from Fig. 1, besradiation at the fundamental wavelength, a small amounradiation at other wavelengths is also present in the lasspectrum of the laser under consideration. The presencthis radiation is explained by the presence of side peakthe reflection functions of the Bragg gratings~the dottedcurves in Fig. 1!, with the gain of an erbium fiber in thenarrow spectral interval of interest being virtually constaAt the same time, when such a laser is used for frequemodulation of radiation, it is sufficient to constantly vary ilasing over the spectrum by a small amount within the baof the principal lasing peak.

The lasing dynamics of the laser in the presence ofsidual radiation are calculated by means of the systemEqs.~1!–~3!, where the second of the initial conditions giveby Eq. ~2! is replaced byPs j(0,np)5Ps0 . As shown by thecalculations, when the wavelength varies within the limitsthe principal lasing line, the steady-state lasing regimevirtually established in one pass of the radiation throughcavity. For a cavity 1 cm long, the minimum possible timeestablish lasing is about 0.045 ns. When the lasing maktransition to a wavelength where there is no residual ration, the time to switch the laser is a maximum and,example, reaches 1.19 ns when the concentrations areNEr

5231026 ion/m3 and NYb52.531027 ion/m3, the reflec-tance of the controllable FOBDG isR595%, and the pumppower is Pp0540 mW. The relative power of the residuradiation Pres5Ps0 /Ps outside the principal lasing maximum is about 0.025~Fig. 1!. The switching time for a lase

FIG. 2. Time to establish a stable lasing regime~1! and the lasing efficiencyof the laser~2! vs the reflectance of the output mirror of the cavity;NEr

5431025 ion/m3, NYb5531026 ion/m3, andPp0540 mW.

175 J. Opt. Technol. 70 (3), March 2003

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with the indicated parameters at this level of residual radtion lies within the limits of 0.6 ns.

LASING DYNAMICS OF THE LASER, TAKING INTOACCOUNT LOSSES AT THE JOINT

When an optical fiber is coupled with an FOBDG writen on a waveguide electrooptic modulator, additional loscan occur that substantially affect the efficiency and lasdynamics of the laser and thereby affect the tuning rate oradiation. To estimate the effect of these losses, we calated the lasing dynamics of the laser by means of the mematical model of Eqs.~1!–~3!, replacing the first of theboundary conditions given in Eq.~3! with

Rl~n j !R2~n j !Ps j1~L,n j !5Ps j

2~L,n j !,

where Rl(n j ) is the loss factor at the joint of the opticawaveguide and the fiber lightguide.

As expected, the lasing efficiency of the laser decreasubstantially because of the additional losses. However,switching time of a laser with additional losses at anothlasing wavelength also decreases. For example, the mmum switching time equals about 1.06 ns in the absencresidual radiation, whereas, when there is residual radiawith a relative power ofPrel50.025, the laser’s switchingtime decreases to 0.4 ns. This can be explained by meanFig. 3, which shows the dynamics of the establishmentlasing when the power of the residual signal isPs0

50.1 mW. As can be seen from this figure, the additionlosses reduce the growth rate of the laser radiation powHowever, the steady-state lasing power itself also decrein this case and is therefore reached much faster. The mmum switching time of lasing does not vary and is limitedthe time for a single pass of the radiation through the cav

CONCLUSION

Thus, the dynamics of the establishment of lasing habeen studied for a single-frequency laser based on an opfiber doped with erbium and ytterbium ions with a contro

FIG. 3. Power of the output radiation vs time, neglecting the losses atjoint ~1! and taking these losses into account~2!. NEr5231026 ion/m3,NYb52.531027 ion/m3, R595%, andPp0540 mW.

175Pilipovich et al.

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lable waveguide Bragg grating and an electrooptic cell. Tdependence of the lasing efficiency and the wavelenswitching time on the parameters of the laser componehas been analyzed. As shown by the calculations, the mmum lasing efficiency and the minimum switching time aachieved when the reflectance of the output mirror oflaser cavity equals about 95%. The switching time astrongly depends on the concentration of resonance impties, the pump power, and the initial signal level at the nwavelength. With the optimum choice of parameters,switching time of a laser with a cavity about 1 cm lonvaries from 0.045 to 1.19 ns.

The additional losses that arise when the optical fibecoupled with an FOBDG written on a waveguide electrootic modulator reduce the radiation-switching time of theser, but its lasing efficiency also decreases in this case.

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