Q-switching of an erbium-doped fibre laser modulated by a Bragg grating fixed to a piezoelectric

Erbium-doped fibre lasers (EDFLs) have a variety of potential applications, as sources for wavelength division multiplexing (WDM) and soliton communications systems, and in sensor devices, optical time domain reflectometry, non-linear phenomena studies and applications, etc. Continuous-wave, Q-switching and mode-locking laser systems constructed by using doped fibres have been demonstrated. High continuouswave powers (>100 W) have been achieved with fibre lasers by using the cladding pump technique. In the pulsed operation regime (the Q-switched mode), the energy storage that can be achieved within conventional single-mode erbium-doped fibre limits the maximum energy. The use of fibre Bragg gratings to develop the laser cavity allows one to operate the laser with a narrow linewidth because of the frequency-selective reflectivity of such gratings. They act as high-reflectivity mirrors for the laser emission wavelength, but are transparent to the pump radiation, allowing the obtaining of very low loss resonators. This has the additional advantage that an all-fibrein-line laser system can be developed [1 5]. Recently, we reported the performance of a Q-switched erbium-doped fibre laser operating with two fibre Bragg gratings as cavity mirrors where the temporal modulation is performed fixing one of the gratings to a piezoelectric (PZT: Pb(Zr^Tii_x)03) element [6, 7]. Applying voltage pulses to the PZT, the laser cavity was modulated. By using this simple scheme, a Q-switched laser output has been generated with high laser efficiency of energy conversion. Q-switched laser pulses of 0.5 W peak powers were obtained pumping at 76 mW at 18.5 kHz and an energy conversion efficiency of 26% was obtained. Typical laser emission had temporal widths of 2 3 f i s and an optical bandwidth of 0.1 nm. The results depend on the pumping level of the active medium. In particular, exciting the medium at pump powers larger than six times Ppj , where PPth is the pump power of the laser threshold, produces not an increase in the laser output but the generation of additional laser peaks. A similar scheme has been reported before, but its performance was quite poor [8]. In view of the importance of fibre lasers and of the necessity of having perfect knowledge of the device operation, it is important to obtain a correct description of the laser evolution. So, we analyse here the behaviour of the Q switched laser by using a general theoretical model based on a homogeneous, three-level approximation of amplification in erbium and compare the results with the behaviour of our Q


T h eoretical m od el and results
The system is shown schematically in figure 1 When a modulated voltage is applied to the PZT, the temporal distribution of R 2 shifts in wavelength as given by equation ( 6), overlapping periodically with the reflectivity distribution of R i (figure 2).The amplitude of this displacement is, in principle, dependent on the PZT voltage input.The overlap time depends on this amplitude, the PZT frequency modulation and the spectral widths of the two gratings.The evolution of the cavity factor (/?j R 2 ) determines the laser operation.Figure 3 shows the wavelength dependence on the temporal evolution of this product.As can be observed, the cavity behaves differently for each laser component, shifting in time (in this case), for the positive edge of the distribution, from lower to larger-wavelength components.The direction depends on the initial spectral positions of the two gratings.The influence of these temporal differences depends on the modulation amplitude and frequency.Figure 5 shows the behaviours obtained for the laser operation under different continuous pumping conditions.By using the above mentioned parameters in the model resolution, we have observed that: at values larger than Pp<h and smaller than 2PPjh, lasing occurs in an unstable regime with a frequency / < /0; at 2PPih < Pp < 6Pp k, PZT governs the laser oscillation and we had a stable regime with / /o; and when the pump excitation increases to above 6Pp<h, the laser output does not increase and the laser operation becomes unstable with the appearance of additional laser peaks (/ > /o).The experimental limit for stable operation was found to be lower (Pp 5Ppj,) than the theoretical one.The general characteristics described using this model are in agreement with the experimental behaviour of the Q switched laser described in [7].
For comparison, figure 6 shows typical experimental pulsed laser emission, obtained with the laser system described in [7], as well as the modulating signal at 18.5 kHz repetition rate measured for the PZT.Theoretical values of the temporal pulse width obtained from the model at 18.5 kHz (~1 fis) are close to the experimental ones.This value is approximately constant in the region of stable operation.
Figure 7 shows the spectral evolution of one of the pulses when the laser operates at 18.At larger frequencies (/ /o ), the frequency shift starts to become more important and the pulses are chirped, due to the faster frequency oscillation of the cavity.A complementary experimental study of the spectro temporal behaviour will be carried out in the near future.Figure 8 shows the agreement between the theoretical and the experimental spectral distributions obtained in the 1540 nm region for the emission of the Q switched laser.The asymmetry observed in both curves appears also when the laser system operates at 1530 and 1554 nm.The spectral pulse width depends on the spectral characteristics of both gratings and, particularly, on that of the grating with the narrow spectral width.Differences between theoretical and experimental curves are due to imperfections of the spectral grating distributions used in the experimental system.
In [7], the PZT was modulated by a square or sinusoidal voltage wave.In both cases, the laser system was always modulated at /o 18.5 kHz, because PZT works better at its resonance frequency.Also, other frequencies have harmonics coincident with this value (18.5 kHz).Because of this, under continuous optical excitation and with square voltage pulses applied to the PZT, the laser behaves similarly for frequencies f f o / n (where n is an integer).When the pump excitation was also modulated, the excitation time could only be increased by 10 15% due to the PZT resonance.In these conditions, the laser output was increased by a factor 2 and the temporal width was reduced by the same factor.

C o n c lu s io n s
A Q switched fibre laser system actively modulated by using a Bragg grating fixed to PZT was theoretically analysed employing a three-level scheme for the erbium-doped fibre and In our model, we assume that the cavity length is large enough (some metres) that thousands of modes are simultaneously excited.Therefore the wave patterns between different waves can become sufficiently complex that many of the cross coupling effects tend to be washed out on average, with the result that only the averaged intensity of all the waves is significant [11].Results obtained with this scheme show several characteristics of the laser operation and they are in good agreement with experimental data previously reported [7].
laser based on a modulation produced by a Bragg grating fixed to PZT.The laser cavity was simulated assuming that its wavelength (frequency) distribution has a different temporal modulation for each component.

7 m 7 1. 4 x
photon flux spectral density, n o , n \ , n 2 are the ion populations corresponding to the 4Iis /2 , 4Ii3 /2 4Ii 1/2 levels normalized to the total Er3+ population and An is the population inversion between the 4I15 /2 and 4Ib /2 levels, also normalized; P represents the pumping rate normalized to 2tj 1 ; a% Ti (cre m ± cro m) with cre, a a the emission and absorption cross sections of the gain medium (constants within the Bragg grating influence range); b I N / T where/is the gain medium length, N the total ion concentration and T the time taken for the light to make one cavity round trip.The decay rate of the laser light in the cavity is given by y," (r) yo ln(Ri R i i r ) ) , where yo x \ / T is a dimensionless constant, R \ and R i are the mirror reflectivities (Bragg gratings) of the optical cavity and m is the frequency index.When the PZT is excited, the wavelength distribution of the reflecting grating fixed to it ( R 2 ) starts to oscillate in the spectrum with an amplitude depending of the applied voltage.In order to correlate the experimental behaviour o f [7] with theoretical results obtained with this model, we have simulated the reflectivity of the practical gratings (which were characterized in that work by using an optical spectrum analyser) with a Gaussian distribution for the reflectivity of R 1 and a super-Gaussian for /?2 Mathematically we express this as

Figure 2 .
Figure 2. The spectral dependence o f the temporal modulation.

Figure 4
Figure 4 shows: (a) the PZT modulation voltage with a frequency /o 18.5 kHz, (b) the population inversion for the laser transition, (c) the population of the 4In/2 level (n2) and (d) the laser output, for a pump power Pp 4Pp<h.Figure5shows the behaviours obtained for the laser operation under different continuous pumping conditions.By using the above mentioned parameters in the model resolution, we have observed that: at values larger than Pp<h and 5 kHz.A very small frequency shift of the maximum occurs before a 'broadband' distribution is achieved.The temporal distributions (a), (b), (c), (d) and (e) correspond to the wavelengths 1540.20,1540.23,1540.26,1540.30and 1540.34 nm, respectively.

Figure 6 .
Figure 6.The experimental PZT modulation voltage and laser intensity evolution.

Figure 8 .
Figure 8. Spectral distributions o f the laser emission: theoretical (dashed curve) and experimental (solid curve).