1730 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO. I , JULY 1996

Optimization of Wavelength Tuning of Erbium-Doped Fiber Ring Lasers

Yew Tai Chieng, Gregory J. Cowle, and Robert A. Minasian

Abstract- The dynamics of erbium-doped fiber ring lasers undergoing wavelength tuning is examined. The relaxation oscil- lations and mode build-up time are characterized. An all-optical damping technique which is capable of complete elimination of relaxation oscillations is analyzed, and measurements on a tunable erbium-doped fiber lasers are reported. An analytical solution is derived for the mode build-up time of tunable fiber lasers. Limiting parameters for the design of a high-speed tunable fiber laser are identified. An equalization technique for obtaining uniform switching speed is described.

I. INTRODUCTION APIDLY wavelength tunable lasers at the 1.55 pm region are important for many optical communication schemes

such as wavelength-division multiplexing systems. The high- gain and broad gain spectrum of erbium doped fibers at around 1.55 pm have generated considerable interest and have resulted in extensive development of narrow linewidth tunable fiber laser sources. Several erbium-doped fiber lasers have been demonstrated with wide tuning range [ 11-[9] using different methods.

When the center wavelength of the tunable filter in a tunable erbium-doped fiber laser (EDFL) is changed, the laser will generally change to a different cavity mode, and the amplitude of the new mode exhibits slow but often large-amplitude relaxation oscillations in its evolution toward the steady state. This is significant in the erbium-glass system as well as in most solid-state lasers as a result of the recovery time of the excited state population being substantially longer than the photon life-time in the cavity [lo]. Although fast wavelength tuning elements like the electro-optic bandpass filters [ 1 1 J are capable of switching the cavity loss in nanoseconds, the relaxation oscillations ultimately limit the switching speed of the laser output, as they determine the time taken for the photon number to reach its steady-state value. This is highly undesired for practical reasons, as the full build-up time can be as long as several milliseconds.

An effective fast wavelength tuning technique not only requires a method of tuning the cavity loss, but also a method of controlling the relaxation oscillations. An optoelectronic feedback system [ 121 has recently been developed toward this end, and we have recently proposed an all-optical relaxation-

Manuscript received January 30, 1996; revised April 2, 1996. The work of Y. T. Chicng was supported by a scholarship from the Australian Photonics Cooperative Research Centre.

The authors are with the Department of Electrical Engineering and Aus- tralian Photonics Cooperative Research Centre, University of Sydney, NSW 2006, Australia.

Publisher Item Identifier S 0733-8724(96)05433-3.

oscillation damping technique using an intracavity intensity- dependent attenuator [13], which does not have the complexity of active electronic feedback. Devices such as nonlinear optical switches, couplers, and limiters could be used to provide the appropriate nonlinear attenuation.

In this paper, we investigate the dynamics of tunable fiber lasers while undergoing wavelength-switching. In Section 11, the fiber laser rate equation model is described and in Sec- tion I11 we provide analysis of the all-optical relaxation- oscillation damping technique, based on a nonlinear attenuator. Experimental results of complete elimination of relaxation oscillations will be presented.

Once the relaxation oscillations are controlled, one needs to address the question: How fast is the build-up of the lasing mode of a tunable fiber laser when the operating wavelength is tuned from one to another? Some earlier work [ I O ] , [ 141 addressed the oscillation build-up or delay time for an idealistic single transition laser. Tunable lasers however differ from the simplistic picture in terms of 1) the initial population inversion is dictated by the steady-state inversion of the previous lasing mode, 2) during the wavelength-tuning interval there is significant photon number of the previous mode present in the cavity, and 3) for a relaxation-oscillation- controlled tunable laser, the analysis is further complicated by the relaxation-oscillation damping mechanism, which needs to be taken into consideration. In Section IV, we present an analytical solution of the mode build-up time of a tunable fiber laser. From the resulting equation, one can study the characteristics and identify the limiting parameters so that new techniques can be devised to improve the speed of mode switching. Comparison between the analytical solution, numerical simulation and experimental measurements will be presented.

A new threshold equalization technique is presented in Section V to compensate for the switching speed variations of an individual mode, as well as to achieve a similar switching speed across the tuning bandwidth. This requires a customized intracavity filter which adds loss to modes with high gain.

11. FIBER LASER RATE EQUATION MODEL

Characteristic lengths of erbium-doped fiber ring lasers are typically such that the transit time of the resonator is shorter than the pulses which occur in relaxation oscillations. As a result, the laser can be modeled as consisting of “lumped elements” in which gain and loss are averaged over each element. The erbium-doped fiber in the laser can be char- acterized by three atomic levels (ignoring ESA), consisting

0733-8724/96$05.00 0 1996 IEEE

CHIENG et al.: OPTIMIZATION OF WAVELENGTH TUNING 1731

of the ground level with population density N l , an upper laser level with population density N,, and a pump level with population density N3. To study wavelength tuning we consider two modes, the starting (A,) and finishing (A,) points of the wavelength-tuning occurrence. The photon numbers of the two modes are represented by q1 and q 2 , and the modes are switched by an intracavity filter with a response represented by Tzl, which refers to the filter transmittance at A, when the center wavelength is at A,. Ion clustering effect is ignored for moderate dopant concentration Nc(:g 20 x loz4 mP3) [15]. The temporal behavior of the laser is then described by the following coupled rate equations:

where the index z = 1 or 2 refers to the old lasing mode and the new lasing mode, respectively, Wp = rlpPpcrap/Ahvp is the pump probability, Pp is the pump power, hv, is the pump photon energy, A is the fiber core area, crap is the absorption cross-section at the pump wavelength, rip and rls are proportion of the pump and signal powers withiin the fiber core, oat and ne, are the absorption and emission cross-sections of the zth mode, 732 is the nonradiative decay time from the pump level to the metastable level, 7 2 1 is the life-time of the metastable level, rc is the cavity round-trip time, and I, is the length of the active part of the cavity.

The term S,, in (4) accounts for losses of the ith mode, namely, a wavelength independent los,s a and the transmittance of the tuning filter T,,. For the lasing mode, z = j and thus the filter transmittance is T,,. The effect of the tuning element to control the wavelength of operation is contained in this parameter.

Implied in the foregoing rate equations is that only pre- dominantly homogeneously broadened systems such as the Er3+-doped aluminosilicate fibers [ 161 are considered here. However, due to fast thermalization in the metastable manifold and the presence of a narrowband filter with a bandwidth much smaller than the homogeneous and in homogeneous linewidths, the consideration of inhomogeneous broadening in typical erbium-doped fibers is not expected to lead to significant differences. For fibers with strong inhomogeneous broadening, however, additional equations are required to account for the partial accessibility of the total population inversion.

Numerical simulation can be used to examine the mode build-up during switching, as a function of time. It has been shown in [ 131 that after each wavelength-shift the laser output exhibits the characteristic large-amplitude initial spike and decaying relaxation oscillations [ 1 Z!], [ 171. The prominent initial spike depletes the population inversion at a faster rate than the pump can replenish the population inversion, and the population inversion is reduced to less than the threshold value. This process is repeated as the inversion builds up again

under constant pumping, leading to the undesired relaxation oscilhtions. The time taken for the laser to effectively switch operation to the new mode is therefore determined by the time taken for the relaxation oscillations to die out.

111. RELAXATION-OSCILLATION ELIMINATION THROUGH NONLINEAR LOSS

The interplay betweein the photon number and the pop- ulation inversion in causing relaxation oscillations indicates the path to a method for controlling the behavior and in- creasing the wavelength tuning speed. If the initial spike is supprmed, laser build-up will not lead to the population invers ion falling below the threshold level, and the photon number will quickly achieve the steady-state level. Recently we reported the incorporation of a nonlinear attenuator within a fiber laser resonator as a technique for controlling relaxation oscilldions [13], [18]. To perform the required function, the device should be transparent at low intensities, and lossy at high ntensities. A suitable device for use in a fiber laser is a nonlinear optical loop mirror (NOLM), used extensively for mode-locking as a saturalble absorber [ 191. For this application the NOLM is used either as a mirror with the characteristic of a nonlinear attenuator or as a transmission device if the NOLM is prebiased for reverse-switching operation [20]. Assuming the polarization of the light is maintained, the transmittance of the reverse-switching NOLM at A, can be written

Ri = 1 - 4k( l - k ) sin2 - (1 - 2k)n2L,Iin] (5) [ i

where k is the power coupling ratio of the coupler, n2 is the third order nonlinearity (Kerr type) of the nonlinear fiber, L, is the length of the nonlinear fiber in the NOLM loop, A, is the wavelength, and I,, is the intensity of the incident light.

In I he fiber laser model, this can be included in the cavity loss term and the total cavity loss is now given by

The inclusion of this device prevents the initial oscillation spike or pulse from growing to an excessively high level, thereby preventing the population inversion from being de- pleted below the threshold level. As the population inversion is ma ntained above thre,shold during the build-up of the new mode the requirement on the recovery time is eliminated and consequently the laser amplitude settles to the steady-state level smoothly, without relaxation oscillations.

A. Sttady-State Solutions

Tht: inclusion of this additional loss will undoubtedly affect the stcady-state solutions. Consider that the ith mode is lasing, the steady-state population densities of the three levels can be obtaired from (1)-(3) as

1132 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO. 7, JULY 1996

I , 1.4

(9)

and from (4), the cavity loss is related to the upper level population density by

(10)

where 7’ 1 ~ 2 1 / ( 1 + WP721), 6, = - I n (aT,,R,) is the total cavity loss of the lasing ith mode at steady state and is the steady-state photon number of the ith mode. From (9) and ( 1 O), the threshold or steady-state population inversion density is obtained as

A’Ytfli =

f i 2 (1 + W p 7 3 2 ) i i + r / s laaa i i vc

rlsla[aai + O e z ( l + Wp73z)]

’ (11) (2 + Wp732)s^i + %La(aa7 - 0 e i ) N c

,r/sla[Uai + a,i(l + Wp73z)]

The new steady-state photon number can be found by solving (8) and (10) and using an approximation of the intensity-dependent loss term Sdi given as

where approximations: ln(.c) E n: - 1 for n: E 1, and cos E 1 - 1/2y2 for small y, have been used. The steady- state photon number is found to be governed by a cubic

and

is t..s steady-state photon number of the undampe- case. The stcady-state photon number iz can thus be solved using standard formulae [ 2 1 1.

For a typical fiber laser, the G L characteristic is depicted in Fig. 1 as a function of the nonlinearity product n,aL, for an arbitrary wavelength. For small rI2 L,,, the nonlinear effect is negligible and therefore the remains the same as the undamped case. But as the nonlinear effect sets in, 4, decreases

1 .o

0.8

(0- 0.6

< d 0.4

0.2

0.0

.

1.2

1 .o

o.8 9 0.6 4 0.4 <d 0.2

0.0

I 10 100

n , ~ n x10-17 m 3 ~

Fig. I . Steady-state photon population and the loss of the nonlinear attenu- ator versus the nonlinearity product. Dotted line is the approximation of 6 d L from (12). Laser parameters are: N , = 3.8 x loz4 mP3, I , = 6 m, Pp = 50 mW @ 980 nm, X = 1.550 nm, cavity length = 10 rn, and cold cavity loss ~ -10 dB. -

as a result of the added loss of the nonlinear attenuator. The damping loss 8 d l obtained from (5) is also plotted in Fig. 1 to show the onset of the nonlinear effect, which is compared with the approximation (12) shown as the dotted line. The excellent agreement suggests that approximations made in the above analysis are valid.

B. Design Requirement

To implement the all-optical relaxation-oscillation damping technique, the nonlinearity requirement for the damping ele- ment needs to be assessed. Generally the standard approach of linearized small-signal perturbation can be employed [ 101. It is however not possible to derive a generic solution as the analysis will depend on the type of nonlinear device used. For the reverse-switching NOLM, suppose that in the steady- state regime the instantaneous photon number and population inversion in the laser are varied by a small amount, not too far from the steady-state value, i.e.,

If (1 8) is substituted into the rate equations, the dc or steady- state terms will automatically cancel out of the equations. In addition, higher order terms and cross products of the small fluctuations can be dropped as they will be small. By using the steady-state solutions and (12), the rate equations can then be reduced to the linearized small-signal form

CHIENC ef al.. OPTIMIZATION OF WAVELENGTH TUNING 1733

h . :I 18 16 14

1 - 8 2 6

$ 4 2 I LOSS= -7dB t 0 ' I I - 1520 1530 1540 1550 1560 1570

Wavelength, nim

Fig. 2. wavelength range. Same laser parameters as in Fig. 1.

The zero-crossing point of the nonliinearity requirement across the

Assuming that the small quantities ,?iq(t) and 6 N ( t ) vary as then this linearization leads to the secular equation

s2 + h1s + bo := 0 (21)

where the coefficients are

For nonoscillatory output, the condition

b: - 460 3 0 (24)

must be satisfied for the mode of interest. When no damping is employed, (24) will always be negative, indicating that the secular (21) has complex roots and therefore the system is os- cillatory when subjected to perturbation. By implementing the relaxation-oscillation damping techniique, (24) can be satisfied and thus relaxation oscillations can Ibe avoided if the product n z L, is above the zero-crossing point. The zero-crossing point of (24) for the range of wavelengths of interest is plotted in Fig. 2 for two loss conditions and two cavity lengths. As can be seen, the nonlinearity requirement decreases with the cavity loss as a result of the earlier onset of damping effect, and with the cavity length because of the shorter round-trip time.

It should be borne in mind that the above analysis is based on the assumption that the perturbation is small relative to the steady-state values. For large amplitude perturbations, higher order terms and cross-product terms may need to be taken into consideration. The actual required n2Ln value may therefore be slightly different from predicted in Fig. 2. Nevertheless the small-signal linearization provides a quick tool to assess the damping requirement without going into complex mathematics.

C. Numerical Results

Numerical simulation with the inclusion of the nonlinear attenuator illustrates the resulting suppression of relaxation oscillations. For the laser given in Fig. 1, n2Ln 3 1.2 x m3/W is required (Fig. 2) to cover the range 1525-1565 nm. As shown in Fig. 3, the initial overshoot of the photon

d 0 200 400 600 800 1000 1200 1400

time, pes

Fig. 3 . using n2Ln = 1.5 x IO-16 m 3 N .

The amplitude-stabilized output with a reverse-switching NOLM,

number is significantly suppressed, and therefore the pop- ulation inversion is not in any time being depleted below the tk reshold value. Consequently, relaxation oscillations are eliminated and the laser {outputs smoothly settle to the steady- state levels. The regulative action of the damping mechanism also maintains a stable laser intensity, but at the expense of a loQer intensity level determined by (13). The steady-state damping loss accounts for only -2.5% of the total cavity loss in this example.

D. Experiment and Results The principle of the relaxation-oscillation damping tech-

nique was experimentally demonstrated with an acousto- optically tuned erbium-doped fiber laser [22]. The exper- imental EDFL configuration is shown in Fig. 4 where a nonconventional reverse-switching NALM was configured as the nonlinear attenuat'or for relaxation-oscillation damping, and an acousto-optic tunable filter (AOTF) with a bandwidth of 1.5 nm and a switching speed of -3.5 ,us was employed as the wavelength selective element. The NALM consisted of -9.5 m of Er'+-doped aluminosilicate fiber, a WDM coupler to ccuple the pump light, a polarization controller, and a 30:7C coupler responsible for the intensity mismatch required betwcen the counter-propagating signals in the NALM. Since the nsmlinear refractive index 7 ~ 2 is small in silica fibers, the signal-dependent resonant-enhanced nonlinearity in the Er- doped fiber [23] was utilized in the NALM for the nonlinearity effecls. This allowed the laser cavity to be kept short, and a small signal intensity for onset of the nonlinear effect. The polarization controller biased the NALM such that all light is transmitted at low incident intensities, but at high intensities, loss is introduced via signal cancellation through the nonlinear effecl. Isolators were also included at the input and output of the hALM, providing isolation of 41 dB each, and combined inseriion loss of 2.5 dB. The cavity length of the fiber laser was -25 m, and the cold cavity loss was estimated to be arourld 15 dB.

The control circuit for the AOTF allowed the AOTF to see a single RF signal at a time and thus shifted the operating wavelength between two discrete wavelengths alternately. The laser output was monitored by an optical spectrum analyzer (OSP,) for the spectral characteristics. The filtered output from the OSA was fed to a high-speed photodetector to explore

1734 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO. 7, JULY 1996

--~.f--------

Nonlinear Amplified

Fig. 4. The experimental acousto-optic tunable erbium-doped fiber laser.

the wavelength-tuning dynamics. A polarization controller was also inserted in the cavity because of the polarization sensitivity of the AOTF.

With -55 mW of pump power from a 980 nm pump diode, the laser wavelength was tunable from 1524 to 1565 nm by varying the RF drive frequency (173-179 MHz). When X > 1560 nm was selected, however, the gain peak near 1532.5 nm tends to compete for lasing because of the poor extinction ratio of the AOTF (-12 dB). The laser exhibited a relatively large linewidth of 0.15-0.2 nm as a result of the bi- directional operation in the active medium and some frequency drifts in the RF sources.

By adjusting the polarization controllers, reverse-switching of the NALM was achieved and typical results for the temporal characteristics of the laser output are shown in Fig. 5, for an example of tuning between XI = 1550.75 nm and = 1541.56 nm. As compared to the classic large-amplitude slow- decaying relaxation oscillations observed for an EDFL (inset of Fig. 5) , by the use of damping the initial spike at switching for both wavelengths was significantly suppressed, and the subsequent relaxation oscillations eliminated. Similar damping results were obtained for other wavelengths in the tuning range, except at wavelengths near the gain peak (1532.5 nm). The lack of damping near the gain peak is consistent with the small index changes near resonance, that is a characteristic of the resonantly-enhanced nonlinearity in the erbium-doped fiber [23], [24]. The poor extinction ratio of the AOTF also resulted in some unstable operation around the gain peak because of mode competition.

It is difficult to estimate the equivalent n 2 of the erbium fiber in the 1550 nm region, as contributions of all resonant terms associated with the 56 Stark transitions may need to be considered [24]. The results of these experiments. however, clearly demonstrate the elimination of relaxation oscillations, stabilization of the laser amplitude, and the feasibility of the

Detector

development of high-speed relaxation-oscillation-free tunable fiber laser sources.

The laser was sensitive to polarization variations and the po- larization controllers often needed to be adjusted for different sets of wavelengths in order to achieve complete relaxation- oscillation damping. This problem should be reduced with a polarization maintaining implementation. In future, the advent of high n2 fibers [25] would allow the nonlinear mirror be constructed with more or less uniform nonlinear effect across the spectrum of interest, and with very short length in order to keep the resonator short. It should be possible to achieve relaxation-oscillation damping over the entire tuning range, and unidirectional operation could be configured for narrow linewidth laser output.

IV. MODE BUILD-UP TIME ANALYSIS

A. Rate Equations and Steady-State Solutions

The plane-wave lumped-circuit laser model discussed in Section I1 provides a simple but useful platform for this analysis. However, an analytical solution for the laser mode build-up time is difficult to derive without some considerable simplifications. For rare-earth systems like the erbium-doped fiber, if the chosen pump level has a fast relaxation time to the metastable level and no excited state absorption (ESA), a two-level approximation model can be adopted [26] as the population of the pump level N3 is much smaller than the metastable level population N2. Since the signal intensity in the regime of wavelength-switching is small, the constant pumping to the fiber laser means that there is a continuous increase of excited atoms in the metastable level. The omis- sion of the pump level relaxation time is therefore justified in the regime of wavelength-switching transients. The two- level approximation can be obtained by taking the difference

CHIENG et al.: OPTIMlZATlON OF WAVELENGTH TUNING 1735

a 4.d

0 ” - U‘ 2

Y

I

h -

t b , defined here as the mode build-up time or wavelength- switching time, to first reach its steady-state population. It continues to rise to a peak under the influence of the high- population inversion still existing in the system, before the damping mechanism manifests its effects. The photon number -Jib

During the next interval t , < t < t b , since there are almost

ternis need to be considered for the growth of the population inversion A N [14]. The population inversion is found to increase linearly in this interval according to

(31) r r’

2 1 v s

wp - - + ~

721 AT,

where A N = (N2 - N I ) is the population inversion density, and N, 2 N I + N2 is the dopant concentration. For the photon rate equation, the spontanelous emission term in (4) is omitted, instead an arbitrarily small number of photons qL0

- aez )qz (25) no photons in the cavity, only the pumping and relaxation 1=1

Alv(7) ANthl - E O + D’ -

v 2

0 ” - Y

,a

LI

cl

is assumed initially present in the c,avity. The photon rate (4) is then rewritten in terms of A N and N, as

where r = t - t , and GI’ = nNC - ANthl + E O . The increase of population inversion eventually leads to the growth of the

1 then settles smoothly to its steady-state value.

In a recent paper 1271, we separated the analysis into two time intervals: 0 < t < t,,, and t , < t < t b . In the first interval 0 < t < t,, the decay time constant of the old lasing mode is found as

0 1 . Time, ms

............... ..............................

(29) T C

1550.75 nm 1!541.56 nm t , = ~

, Tl 1 I I I I In ~

................................ ................

photon number of the new wavelength to the steady-state value qi. in a time given by [27]

t* z= t , + 7’

- (na2 f nei)

(26) dt 27,

The threshold or steady-state population inversion for the ith mode can now be obtained from (26), or simply from (1 1)

dYi - r l s L -~

47,In - Y2

“ ’ I s L ( f l a 2 + pe2)D’

(32)

by setting 7332 = 0,

(27)

and the steady-state photon number Gi is related to the ANthi by

26; + ‘ I S L ( C ‘ , i - n,;)N, r l sL (oa2 + O e i )

hNih,i =

where

ancl 920 is the small initial photon number of Xz. In (33), AiVthz is the threshold inversion of the new wavelength and

which is not present in the interval because of small photon number. It may be noted that the exact knowledge of the ratio q2/’y20 is not essential because the logarithm is a slow varying

where n = (Wpr21 - l)/(WPr21 + I ) . Equations (27) and (28)

By substituting (27) into (28) and rearranging the terms, iz can be shown to be given by the same cubic equation as ( I 3), and 0, as (17) except for 7 3 2 = 0.

are interdependent because of the intensity dependent term & . the is the co,rection for steady-state damping loss

function. The build-up time of an individual mode is therefore

strongly dependent not only on its own threshold inversion AIVth2, but also on the threshold population inversion of the old lasing mode ANthl. This is expected as these inversion values physically correspond to the final population inversion

B. Analysis

When the center wavelength of the tuning filter is tuned from an old lasing mode A 1 to a new mode X2, the old mode decays exponentially with a time constant oft,, while the new mode is slowly building up from noise. The new mode takes

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO. 7, JULY 1996 1736

60

m e, 30 a

10 0

1520 1530 1540 1550 1560 1570

Wavelength, nm

Fig. 6. 1525-1565 nm.

Variations of mode build-up time of Wavelengths within the range

and the initial available population inversion for the new mode, respectively. Therefore, a fast t b is expected when tuning from a mode with high-threshold population inversion to a mode with low threshold population inversion, and a slow tb when tuning in the reverse order as D// changes sign. This implies that the build-up time of a laser mode will spread over a wide range of values, depending on where switching originates. As shown in Fig. 6 is the calculated mode build- up time variations of the example laser used in Fig. 1 when tuned within the range 1525-1565 nm. The build-up time is generally small around the gain peak (1532.5 nm) because the threshold values are smallest in this range and therefore there are abundant amount of initial available inverted atoms wherever switching originates.

The influence of the cavity loss on t b is obvious: the higher the loss the smaller the gain per round-trip, and therefore the longer it takes to build-up the intensity. This is also reflected in (32) as the denominator decreases with the increase of the cavity loss. A long cavity length generally increases t b , but it is only prominent when ANttL2 5 ANthl, as the second term under the square root of (32) becomes important in this case.

Generally, for high-speed operation (32) suggests that the laser resonator should have low loss, short length, a highly doped fiber with small core and large power flow in the core for both pump and signal, and be pumped by a high-power source. Under high-power pumping condition 7’ M l /Wp, the mode build-up time (32) appears to be independent of 7 2 1 .

However, this must not be taken literally. The effect of 7 2 1

is present indirectly through the requirement for lasing on the pump probability VtTP >> 1/721. For a system with small 721,

the required pump probability W, is higher than that for a system with large ~ 2 1 , and thus a faster mode build-up time results.

C. Experimental Results

Using the acousto-optically tuned erbium-doped fiber laser as shown in Fig. 4, the amplitude-stabilized laser output was monitored with a high-speed photodetector and an oscillo- scope. By varying the RF drive frequency, mode switching characteristics of different wavelengths were measured. The

2. 8 G 7 9 a m

a

.-

30

20

10

0 30

20

10

0 1520 1530 1540 1550 1560 1570

Wavelength, nm

Fig. 7. Measured mode switching time of the acouto-optic tunable erbium fiber laser, and comparison with both analytical and numerical predictions. (a) t b of various \vave-lengths when switched from the 1550 nm mode, and (b) t b of the 1550 nm mode when switched from the various wavelengths.

measured switching time characteristics of tuning between a reference wavelength, 1550 nm, and various wavelengths within the tuning range are shown in Fig. 7(a) and (b). In Fig. 7(a), the mode switching times of the various wavelengths were measured when switched from 1550 nm, while Fig. 7(b) shows the mode switching time of the 1550 nm mode when the switching was performed in the reverse order. As it can be seen from Fig. 7(b) the mode switching time of the 1550 nm output is not constant, but follows the theoretical prediction of (32) which is shown as the solid line. Similar characteristics were also obtained in the range of 1537-1561 nm with switching time <20 ps. Because of mode competition and small nonlinearity near the gain peak [23], however, no meaningful data was obtained in this region. Nevertheless, these results show the success of the all-optical damping technique over a bandwidth of 24 nm, and the laser operates with a fast dynamic tuning speed of <20 ps across the range.

As a comparison, the numerical simulation result of the mode switching time using the full set of rate (1)-(4) is also included in Fig. 7 as dotted lines. The signal-dependent nonlinearity of n2 = 1.84 x m2PW, comparable to estimation of resonant-enhanced nonlinearity from [23], pro- duced the best fit. The analytical solution (32) shows excellent agreement with the numerical result, except in the vicinity of the gain peak (1532.5 nm) where t b is overestimated by N 10%. This results from the two-level approximation model which has a stronger effect when the difference between the threshold values are large. The overall agreement between the measurement, analytical and numerical predictions is excellent and thus validates the above analysis.

V. THRESHOLD EQUALIZATION TECHNIQUE

It was found in the previous section that the mode switching time of a lasing mode exhibits a large time delay when switched from a mode with a low threshold, and a rapid time when switched from a mode with a large threshold value. This large variation in the build-up time of any particular laser mode

CHIENG et al.: OPTlMlZATlON OF WAVELENGTH TUNING 1737

is highly undesirable for practical purpose. In this section, a threshold equalization technique is described, which is capable of eliminating the mode-switching time variations.

A. The Equalization Filter Function

To eliminate the build-up time variation experienced by an individual laser mode, the dependence on the previous lasing mode needs to be removed. In other words, the mode build-up time should be made to be dependent on the characteristics of the mode itself and not on those of any other modes. The solution is to equalize the thresholds for all wavelengths within the tuning range. One simple method to eliminate the mode- switching time variations is to insert a specially designed filter in the cavity that will introduce additional loss for modes with high-unsaturated gain [28]. As a result, all modes within the tuning range will have the same threshold inversion value.

Before proceeding to derive the transfer function of the required equalization filter, it should be recalled that the damping loss is intensity dependenl. As the additional loss will inevitably reduce the steady-state photon number, it is therefore necessary to recalculate the steady-state photon number with the equalization filter fix full compensation. By selecting the equalized threshold inversion ANe,, usually the largest threshold value within the tuning range, we can obtain the steady-state photon number of the ith mode from (28) as

Note that the cubic (13) is no longer necessary as AN,, is known in this case.

Assume that the equalization filter has a transmittance of Trnz at A,, the overall steady-state cavity loss, Se,% = -In ( ~ T , , & ~ l l , , ~ ) , of the ith mode at steady-state of the equalized system can thus be obtained from (27), and in turn the characteristic of the equalization filter can then be obtained as

(35)

where &i is the steady-state transmittance of the nonlinear attenuator and can be calculated using ( 5 ) and (34).

Since the equalization filter primarily adds loss to the system, the nonlinearity requirement for complete relaxation- oscillation suppression will be higher than the uncompensated system. Because AN,, is dependent on n2Ln, an iteration pro- cedure is therefore needed. By using (34), (35) for (22)-(24), the nonlinearity requirement for the equalized system can be determined.

B. Mode Build-up Time of the Equalized System

With the equalization installed, ANthz = ANe, for all wavelengths within the tuning range, the build-up time of the

25 CT-

rrieasured piredicted

0 0.0 0.5 1 .o 1.5 2.0

Relative cavity loss of the initial lasing mode, dB

Mode build-up time of 1561.7 nm versus the increased cavity loss Fig. 8. of previous lasing mode.

ith mode is then reduced to I

ii 4rc In -

where a high-pump power has been assumed, i.e., K M 1, r / 2: l /Wp, and EO and ta have been ignored. The positive term p2 in (36) corrects for the absence of the damping loss during the wavelength-tuning interval, and is given as

The mode build-up time of the ith mode is no longer dependent on parameters of other modes, and is therefore constant regairdless of where the :switching originates.

C. Results and Discussion

The concept of threshold equalization can be tested by looking at the dependence of mode build-up time on the cavity loss of the old lasing mode. Shown in Fig. 8 is the measured and predicted mode build-up time of A2 = 1561.7 nm when the cavity loss of the old lasing mode A 1 = 1548.6 nm was changed. The R F drive power for A 1 was varied in the experiment of Fig. 4, thus changing the cavity loss for AI, whik keeping the drive fior A2 constant. As can be seen, the t b

of thle 1561.7 nm mode decreases with the increase of cavity loss of the 1548.6 nm mode, as the threshold of the 1548.6 nm mode approaches that of the 1561.7 nm. This effect was also observed in (121 and can be explained by (32).

For the acousto-optically tunable erbium fiber laser as shown in Fig. 4, the suitable response of the equalization filter (AN,, = threshold of 1565 nm) is calculated from (35) using nzLn = 3.5 x m3W, and shown as the inset of Fig. 9. With the equalization filter, the mode build-up time is calculated for all wavelengths using (36), and as can be seen in Fig. 9, the mode switching time variation is eliminated and the rnode build-up time i:j maintained at an average of -10 ps acro'js the range 1525-1565 nm. This is a great improvement over the unequalized system in which mode switching time can vary anywhere within the shaded area in Fig. 9.

1738

Equalisation Filter, dB n-.c, 15*0 Wavelength, nm 1570 40 - 2.

d E F 30 -

F ?j 20 - m 4 1 0 -

1520 1530 1540 15850 1560 1570

Wavelength, nrn

Fig. 9. Equalized mode build-up time, shc’wn as filled circles, of the acousto-optic tunable fiber laser, as compared to the variations of the unequalized system. Inset shows the equiilization filter response for NV, , = ANth(l5(isnrn) and nzL,, = 3.5 x m3/W.

The required equalization filter for the erbium-doped fiber laser may be realized using one or several blazed gratings [29] or mode-coupled gratings [30]. These gratings have been used for gain flattening in erbium-doped fiber amplifiers [31].

VI. CONCLUSION

In this paper, the wavelength-swi tching dynamics of ho- mogeneously broadened fiber lasers have been discussed. The undesired slow decaying relaxation oscillations can be controlled by utilizing an all-optical damping technique, based on nonlinear attenuation. Theory and design requirements have been presented with experimental recjults, showing complete elimination of relaxation oscillations.

The mode-switching time of a tunable fiber laser has been derived, using a two-level plane-wave lumped-circuit approx- imation. The solution identifies the limiting parameters for high-speed operation, and also shows the inherent problem of switching time variation of any individual mode. The analytical solution shows excellent agreements with numerical simulations and experimental measuirements of a fiber laser employing Er3+-doped aluminosilicate fiber.

A threshold equalization technique has been proposed to equalize the mode switching time variation and the design requirements for the equalization filter have been established. The equalization filter can be synthesized by several blazed gratings or mode-coupled gratings. Further improvement on the mode switching time can be made by employing a pop- ulation inversion booster technique, which will be reported subsequently.

These techniques should lead to thie realization of fast-ps- rate tunable fiber lasers with no relaxation oscillations in the output, which are suitable for WDM applications.

ACKNOWLEDGMENT The authors wish to thank S. C. Guy for useful discussion.

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO. 7, JULY 1996

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Yew Tai Chieng received the B.E and M.Eng.Sc. degrees from the 1Jniversity of Melbourne, Aus- tralia, in 1986 and 1989, respectively He has been pursuing the Ph.D degree at the Department of Electrical Engineering, University of Sydney, since 1994.

From 1988 to 1990, he was with Hewlett-Packard Pte., Ltd., in Singapore as an Instrumentation Engi- neer In 1990, he joined the Department of Electrical Engineering and Optical Fibre Technology Centre, University of Sydney, Sydney, Australia, to perform

research in high-speed tuned optical receivei s and optical links His current research interestr include WDM systems, fiber lasers, fiber devices, and nonlinear fiber optics.

Robert A. Minasian received the B.E. degree from the IJniversity of Melbourne, Australia the M.Sc. degree from the University of London, University College in 1976, and the Ph.D. degree from the University of Melbourne, Australia in 1980.

He then joined the University of Melbourne. Since 1989, he has been with the University of Syd- ney and is currently Director of Photonics Research in the Department of Electrical Engineering, which takes, part in the Australian Photonics Cooperative Research Centre. He bas spent sabbatical periods at

LEP. GEC, and Cambridge University. His research has centered on wideband optical fiber systems, tunable lasers, low-noise optical receivers, microwave SCM[ systems, and optical processing. Presently, his research interests include adaptive photonic signal processors, multiwavelength sources, WDM systems, optical phased arrays, and in microwave systems. He has published over 100 photonics research publications.

Dr. Minasian is a Fellow omf the Institute of Engineers, Australia and has won the ATERB Medal for Outstanding Investigator in Telecommunications, awarded by the Australian Telecommunications and Electronics Research Board.