COMUNICACIÓN MATEMÁTICAS CIUDADANÍA

On tuning the pump laser away from the wavelength of minimum tlireshold towards the absorption peak the threshold increases dramatically and a hysteresis is observed around this

threshold (hence the double points in figure 8,16). This phenomenon was evident with both 7,5 and 30m lasers (see figure 8.17), The degree of bistability was dependent on the pump wavelength, the effect increasing with tuning towards line centre and was accompanied by a

marked threshold increase. A mechanism will now be suggested for this type of bistable operation. a

I

&

Figure 8.17 Power transfer characteristic of a 30m laser for Àp=957nm. Insert: Detail of threshold region for a 7.5m laser (lp=980nm)

For a long laser pumped close to the absorption peak a large inversion is created at the beginning of the fibre, whereas the end of the fibre is unpumped and exhibits absorption at the laser wavelength. Therefore the laser can be considered as two essentially distinct parts (this

represents a gross over simplification but should not significantly alter the physical interpretation

involved). This situation of an inhomogeneously pumped laser is shown in figure 8.18. Section 1 presents large gain since it is highly pumped and hence fluoresces strongly. The fluorescence is coupled into section 2 and is reabsorbed thereby reducing the GSA.

When the gain in section 1 is increased through external pumping such that it equals the loss of the unpumped section the laser begins to oscillate. And the increase in intensity at the laser wavelength reduces the ground state absorption of section 2. The decrease in the cavity loss leads

to a further increase in the laser output which in turn reduces the loss. This avalanche process is

repeated until the saturable loss component of section 2 is bleached. As this sequence of events

occurs rapidly the output is observed to undergo a light jump from a low intensity fluorescent

8.19(b) on a plot of total cavity gain versus pump power (where the assumption that the gain is linear with pump power is used). Included in figure 8.19 is a similar plot of the characteristics of a traditional laser, and also a sketch of the (probable) loss function of section 2 versus laser

intensity. Output coupler \ — PUMP highly reflecting mirror

Large inversion Moderate GSA

Reduced GSA due to

in-band pumping

Figure 8.18 Inhomogeneously pumped fibre laser.

With increasing pump power the laser output follows the curve relating to a traditional laser witli a loss equal to Lu^sat» At threshold the process described above forces the output to jump onto the trajectory relating to that of a laser with The output is then linear with further increases in pump power. As the pump power is reduced from a high level the output decreases linearly until the intracavity intensity reaches I2 (as indicated in figure 9.19(c). At this point the avalanche process previously described is repeated but this time in reverse. That is, as

the intensity decreases the loss increases, which further reduces the intracavity flux Thus the laser is abruptly switched off.

The magnitude of the hysteresis loop can then be described in terms of the difference between the unsaturated and saturated loss components (AL) of section 2 of the laser cavity, and the value of the saturation intensity 1% (see figure 8.20). It is clear that larger regions of unpumped fibre result in larger values of AL and hence more exaggerated hysteresis, and also the light jump will be correspondingly larger. Using a simple geometric argument it can be shown for the situation described here that: Ii=r\AL, I2=T| ^ therefore implying that 1^=212 and P2= -^^^.

(a) G Putputpower Pump power G= gain L= loss 1 = saturation intensity Output power G L(unsat) L(sat) I₂ Pump power Loss L(unsat) I (b) (c)

Figure 8.19 Characteristics of (a) a traditional laser, and (b) a laser exhibiting saturable absorption optical bistability, (c) Loss characteristic for (b).

AI=f(slope efficiency, A L) I

Pump power

G=L(unsat)-L(sat) Figure 8.20 Magnitude of hysteresis.

Further work is still required to obtain the timescales involved in switching between the two output states, but due to the influence of the upper-state lifetime (-8ms) of the erbium system

8.8.3 Self Q-switching

The longest oscillation wavelengths were obtained using the 30m length of fibre in the laser. At wavelengths above 1612nm the output of the laser consisted of a sequence of pulses.

This pulse sequence was very stable as evidenced in figures 8.21(a) and (b), where the duration of the pulses was typically 8p.s (see figure 8.21(c)) with a 90ps interpulse separation. On close examination a modulation is apparent on the pulses, and the measured period was about 300ns.

This modulation can be identified as mode-beating between the longitudinal cavity modes which are separated by 3.3MHz, with this corresponding to a round-trip time of 300ns. The interpulse separation was observed to decrease with increased pumping in a similar way to the spiking

oscillations associated with laser tum-on^^.

Figure 8.21 Oscillograms of self Q-switched laser behaviour at 1616nm from a 30m erbium fibre laser. Fav=75mW.

This effect can be explained in the following way. A rapid build-up of the laser signal

occurs due to saturation of the residual giound-state absorption present at the long wavelength tail

of the gain spectrum. The optical pulse produced forces the laser to turn off due to a depletion of the inverted population. The whole process is repeated after a characteristic time when the laser has recovered sufficiently. This time constant will be similar to that which controls spiking and relaxation oscillations. With stronger pumping the pulse build-up is faster and thus the delay to the next pulse is accordingly reduced.

The CW tuning range of the erbium:fibre laser system studied here is limited by the onset of this self-driven Q-switching. Although this phenomenon may be avoided by using different cavity configuiations, and in particular those employing bidirectional pumping geometties. The enhancement in the peak power of the laser was only a factor of about ten for the situation described above. Therefore an attempt to obtain higher peak power pulses from erbium-doped fibre lasers using a more conventional form of Q-switching will now be described.