Файл: Antsiferov V.V., Smirnov G.I. Physics of solid-state lasers (ISBN 1898326177) (CISP, 2005)(179s).pdf

Physics of Solid-State Lasers

is slightly higher than nanoJoule. This is explained by the fact that the intensity of saturation of the gain of the active media of the solid-state lasers is three orders of magnitude higher than the intensity of saturation of the dye lasers. Consequently, the mechanism of synchronisation of the modes of the solid-state lasers greatly differs from the mechanism of the dye lasers.

In the solid-state lasers, the active medium has only a slightly effect on the formation of the SRP and the mechanism of compression of the produced pulse is completely determined by the saturating absorber. Consequently, the method of synchronisation of pumping, which is highly effective in the dye lasers, does not operate in the solid-state lasers.

4.1 METHODS OF PRODUCTION OF STABLE SUPERSHORT RADIATION PULSES

In most cases, the supershort radiation pulses in solid-state lasers are generated by the passive and active synchronisation of the modes and by the combination of these methods. The method of active synchronisation of the longitudinal modes of the laser is characterised by high reproducibility of the SRP but it is very difficult to obtain the duration of generated light pulses shorter than 50 picosecond because of the high inertia of the currently available modulators [18]. These lasers with stable SRP parameters are used widely for the pumping of dye lasers in order to produce the SRP of the femtosecond range of duration in the synchronous pumping regime.

In passive synchronisation of the modes, the compression of the produced pulse is carried out mainly as a result of undercutting of its leading and near edges during passage through the saturating absorber. The typical values of the relaxation time of the saturating absorbers are 10–50 picoseconds, so that the duration of the supershort pulses does not exceed several picoseconds.

Recently, work has been carried out with the passive synchronisation of the longitudinal modes with almost inertialess gates based on the Kerr effect [17] and the intra-resonator conversion to second harmonics [19, 20]. In this case, the duration of the generated light pulses is determined mainly by the width of the band of the amplifier of the active medium which in laser media such as alexandrite or sapphire with titanium is comparable or greater than the width of the band of the gain of the dye lasers. The removal of the non-reproducibility of the SRP of the light, associated with the fluctuation of the formation of pulses during the passive synchronisation of the modes in solid-state lasers, makes it possible to develop reliable and technologically efficient high-power sources of light picosecond and femtosecond pulses.

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To improve the reproducibility of the SRP of the solid-state lasers and decrease their duration, a number of methods have been proposed:

1.The decrease of the number of generated modes [21];

2.Injection of an external signal [27];

3.The regime of the second threshold [22,23];

4.Self-stabilisation regime [24];

5.Introduction of additional losses [26].

The lasing of stable supershort radiation pulses in lasers on the ions of Cr and Nd has been examined by the authors of this book in Ref. 27–30.

4.1.1 The method of decreasing the number of lasing modes

The probability of the appearance of a transient whose intensity is considerably higher than that of other transients, is inversely proportional to the number and, consequently, the width of the lasing spectrum. The increase of the probability of realisation of the regime of the single pulse in the axial period is achieved by decreasing the number of lasing modes [21]. For this purpose, it is necessary to place a selecting element in the resonator of the laser with passive synchronisation of the modes. This element stabilizes and extends the length of the lasing pulses. In Ref. 21, it was proposed to ‘thin out’ the lasing spectrum. The width of the lasing spectrum and, consequently, the pulse time remained unchanged. In addition, the ‘thinning out’ of the lasing spectrum decreases the repetition period of the SRP.

4.1.2 The method of injection of the external signal

The authors of Ref. 27 proposed a method of injection of a short highly coherent light pulse into the laser resonator with the passive synchronisation of the modes in the initial moment of the linear development of lasing. This makes it possible to eliminate the effect of fluctuations of the intensity of initial noise emission. The power of the injected pulse is considerably higher than the level of the spontaneous radiation noise in the laser resonator. In this case, together with 100 percent realisation of the single pulse in the axial period, the reproducibility of the form of the SRP is improved.

4.1.3 The method of the regime of the second threshold

When the saturation of the absorber and the amplifier takes place simultaneously, the regime of the so-called second threshold is realised. In this case, if the noise field does not contain transients greatly higher than other transients, the small difference in their intensity causes that the pulses with lower intensity appear with higher probability below the gain threshold [22, 23]. Therefore, in order to ensure more efficient

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synchronisation of the modes, it is necessary to operate in the vicinity of the lasing threshold. For example, to apply this approach in an Nd laser, it is necessary to ensure that the gain is approximately 0.03 higher than the threshold. This imposes very stringent requirements on the stability of the pumping source of the laser and the resonator parameters.

4.1.4 The method of the self-stabilisation regime

The reproducibility of the SRP in lasers with passive synchronisation of the longitudinal modes greatly increases in the self-stabilisation regime [24]. The expansion of the light beam in the saturating absorber using the intra-resonator telescope decreases the efficiency of the positive feedback, caused by clarification of the absorber. Thus, the mechanism of ‘swinging’ of inversion–field self-oscillations weakens. Free lasing starts to develop at the start of the transition process.

At the start of lasing, the spectrum of intra-resonator radiation is relatively wide and the number of transients with the intensity considerably higher than the general noise level is not large. The probability of appearance of a high-intensity transient increases with lasing when due to the dispersion of the gain line and the effect of the spatial heterogeneity of the inversion, formed in the field of the standing waves, the width of the spectrum decreases.

The dependence of the probability of appearance of a single pulse in the axial period on the width of the spectrum was confirmed by experiments. If no transient was detected in the noise initial field club with the intensity of the transient considerably higher than the general level, the peak of free lasing was observed. In the following peak of the same lasing transient, the process is repeated until an intensive noise transient forms in some of the peaks and is capable of causing saturation of the absorber and does not lead to the display of the sequence of the single light pulses in the axial period, with the envelope in the form of a giant pulse.

Thus, the increase of the reproducibility of lasing with single SRP in the axial period is obtained as a result of increasing the number of different realisations of the initial conditions of passive synchronisation of the modes and different peaks of the single laser pulse. Without taking special measures in the solid-state lasers during passive synchronisation of the modes in the regime of the giant pulse, the absorber is initially saturated and this is followed by saturation of the amplifier. On the other hand, in the self-stabilisation regime, the amplifier is the first to be saturated and this is followed by the absorber.

The problem of effective realisation of the method of self-stabilisation is manifested in the accurate correspondence of the levels of the density of intensity in the active medium and the saturating absorber, and

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also the stabilisation of the pumping power and losses in the resonator.

4.1.5 The method of introducing additional losses

The passive synchronisation of the modes in solid-state lasers takes place in the regime of the giant pulse. Because of the short duration of the effective interaction of radiation with the saturating absorber, the process of the formation of the SRP from the initial noise field appears to be incomplete. To increase the duration of interaction of the field in the non-linear medium, it has been proposed to add additional losses to the laser resonator at the moment of lasing when the saturating absorber is being clarified. Consequently, it is possible to maintain the intensity of intra-resonator radiation on a constant level during the given period of time [26].

The SRP can also be stabilised by suppressing instabilities characteristic of solid-state lasers. Consequently, the passive synchronisation of the modes of the solid-state lasers becomes identical with the passive synchronisation of the modes of dye lasers. In this case, after the transition period, the lasing of a single stable stationary pulse on the axial period is set in the laser. The parameters of this pulse are determined by the properties of the laser system and are independent of the initial lasing conditions. This regime operates without changes up to the end of the pumping pulse.

As regards the reproducibility and duration of the resultant SRP, the solid-state lasers in this regime are similar to the dye lasers. To stabilise the passive synchronisation of the modes of solid-state lasers, it is initially necessary to suppress the instability associated with the oscillating of relaxation self-oscillations of intensity and inversion which in the case of sufficiently dense saturating absorbers is manifested as the clarification of the giant pulse. This type of instability is suppressed by the application of the electronic-optical negative feedback.

Another type of instability, formed at times of the order of 100 µs, is associated with the formation of a random transverse distribution of the generated radiation. In movement to the subpicosend range of duration, the instability associated with the phase modulation of the formed pulses starts to appear.

4.2 LASING OF STABLE SUPERSHORT PULSES OF RADIATION BY THE METHOD OF INJECTION OF THE EXTERNAL SIGNAL

In examination of the method of injection of the external signal in a ruby laser with a ring-shaped resonator (Fig. 3.4), we realised the regime of lasing of stable supershort radiation pulses [27–29] in cases in which the duration of the pulse of external radiation, injected into the resonator

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of a powerful laser, was considerably shorter than the duration of passage through the resonator of the ring-shaped laser (τ s << L/c). The length of the resonator of the ring-shaped laser was 1.5 m, and longitudinal modes were separated by a diaphragm with a diameter of 1.7 mm.

The pulse of external radiation with a duration of approximately 1 ns was separated from the radiation of the single-frequency quasicontinuous master laser (Fig. 1.8d) using an electro-optical gate placed between the lasers. The external pulse was introduced into the resonator of the powerful laser after fulfilling the threshold conditions of lasing of the giant radiation pulse. To reduce the duration of the introduced pulse of external radiation, a passive gate was placed in the resonator of the powerful laser. The gate contained a solution of cryptocyanine in methyl alcohol with an initial transmittance of 40%.

Figure 4.1 shows the fragments of time evolution of the spatial distribution of the radiation intensity of the powerful laser with a passive gate with injection of the external pulse (a, b) and without injection (c, d). In the conditions of absence of the external pulse of radiation in passive synchronisation of the modes with the passive gate, in 10% of cases we observed the lasing of a single pulse in the axial period with a duration of the order of 300 ps, with strong background illumination (Fig. 4.1c). The width of the integral spectrum of radiation was 2 pm and the product of the duration of the supershort pulse τ p by the width of the spectrum ∆ν was τ p ∆ν = 4.5. In the majority of cases (~90%), lasing took place in the regime of several pulses on the period (Fig. 4.1d).

When an external radiation pulse with the duration τ s << L/c was introduced into the resonator of the powerful laser, a single radiation pulse was detected in the period with a high contrast and 100% reproducibility (Fig. 4.1a, b). The width of the integral radiation spectrum was 2.9 pm and the relationship τ p ∆ν = 1.8 indicates the high coherence of supershort radiation pulses. The density graph of the time evolution

Fig. 4.1 Parameters of the lasing of a ruby laser with a ring resonator in the regime of passive synchronisation of modes in injection of the external signal with τ s < L/ c (a,b) and in its absence (c,d): a,cd) fragments of time evolution of the spatial distribution of radiation, obtained using a photochronograph; b) density pattern of the fragment of time evolution (a).

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(Fig. 4.1b) shows that the duration of the SRP remained almost constant in lasing. This is caused by a large difference of the shape of the envelope of the introduced light pulse from the Gaussian shape, and this is associated with the flattening of the tip of the external light pulse as a result of the small curvature of the modulated function of the electrooptical gate.

In injection of the external radiation pulse into the ring resonator of a powerful laser, the reversed radiation wave was completely suppressed (Fig. 4.2a). In this case, the laser resonator did not contain any non-mutual elements. In the absence of the external radiation pulse, lasing included both waves with almost identical amplitudes, Fig. 4.2b.

For the pulse with the Gaussian shape, the estimates indicate a decrease of the duration of the SRP by a factor of 5 for the same experimental conditions. The parameters of the ultra-short radiation pulses in the injection regime are determined by the parameters of the external light pulse. The high coherence of the introduced light pulse, formed from the monochromatic radiation of the master laser, results in complete synchronisation of the phases of the generated modes. When fulfilling the corresponding conditions, it is possible to obtain reproducible SRP with a very short duration.

The addition of losses to the resonator of the powerful laser with a ring-shaped resonator (Fig. 3.4) in the stage of non-linear development of the giant radiation pulse made it possible to reduce 50 times the width of the introduced external pulse in the ruby laser (Fig. 4.3a). The additional losses in the resonator of the powerful laser were generated using the two-stage supply of the voltage pulse, opening the electrooptical gate. The duration of the pulses, measured on the basis of twophoton fluorescence, was approximately 30 ps (Fig. 4.3b).

The method of injection of the external nanosecond pulse without the application of the negative feedback was used in Ref. 31, 32. In Ref.

Fig. 4.2 Oscillograms of the radiation intensity of direct and reversed waves of the ruby laser in injection of the external signals with τ s < L/c (a) and without the external signal (b).

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Fig. 4.3 Parameters of supershort radiation pulses of a ruby laser in the regime of a giant pulse with passive synchronisation of modes in injection of the external signal and introduction of a negative feedback: a) oscillogram of supershort radiation pulses; b) density of the track of a pulse in two-photon fluoresence.

31, the width of the injected external pulse in the Nd:YAG laser was reduced 8 times.

4.3 LASING OF STABLE SUPERSHORT RADIATION PULSES BY THE METHOD OF INTRODUCING INTRA-RESONATOR LOSSES

The regime of stable stationary supershort radiation pulses in the solidstate lasers with the passive synchronisation of the modes in the stationary regime is realised when suppressing the instability associated with the illumination of the saturating absorber, by means of a negative feedback [26]. The regime of the negative feedback was used for producing stable supershort radiation pulses in ruby lasers [30,33–35], in Nd-doped lasers in phosphate glass [16,30,33,36–39,44], yttriumaluminium garnet [13,30,33,40–42], potassium–gadolinium tungstate [33, 43], yttrium aluminate [11,40] and other active media.

Experimental investigations of the stabilisation of the passive synchronisation of the modes of solid-state lasers indicate new possibilities of developing stable sources of SRP with unique parameters as regards the pulse time, their reproducibility and radiation power. Consecutive suppression of the instabilities, formed during passive synchronisation of the modes for solid-state lasers, makes it possible to realise longterm non-linear self-effect of radiation in these systems, determine the fine details of the self-organisation of radiation in the self-effect, and examine the physical mechanisms of the formation of instabilities and special features of their suppression.

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To obtain the maximum power of the supershort radiation pulses, a number of authors [11,37,38,40] selected the configuration of the laser resonator for which the application of negative feedback resulted in a small increase of the duration of the giant pulse, sufficient for the formation of a single pulse on the axial period. In this circuit, the radiation inside the resonator is not focused in a cuvette with the saturating absorber and the strength of the field in the active medium is relatively high. In this case, there is no equilibrium between ‘dumping’ of inversion in the active medium and pumping. This leads to a rapid removal of the inversion resulting in a reduction of the duration of lasing to several microseconds, and the formation of SRP takes place in the conditions of the nonequilibrium process. In this case, the value of the inverse population in the active medium continuously changes and this results in a change of the equilibrium duration of the SRP. Consequently, the SRP parameters change in the lasing process.

To accelerate the process of formation of the single pulse in the axial period, additional activation of synchronisation of the modes was carried out [12,13,39,45]. In Ref. 14,41,44, the inertia negative feedback was represented by a non-linearly absorbing semiconductors sheet made of gallium arsenide placed in the laser resonator. SIB with a duration of 4.5 picosecond were obtained in a Nd doped laser yttrium aluminate [41].

4.3.1 Experimental equipment

Investigations were carried out into the lasing of stationary supershort radiation pulses with a relatively long time of formation of the SRP with interaction with the saturating absorber. In this case, the lasing time was determined by the duration of the pumping pulse which is considerably longer than the transition process, and the main intensity of radiation in the active media was close to the free lasing level. This was achieved by focusing radiation in a cuvette with a solution of the saturating absorber; in this case, the requirements on the parameters of the negative feedback system were greatly reduced.

The diagram of experimental equipment is shown in Fig. 4.4 [30]. A hemispherical resonator with a solid spherical mirror with a radius of curvature of 30 cm (1) and a flat output wedge-shaped mirror (8) were used; the transmittance factor of the mirror was selected by experiments in relation to the active medium. The length of the laser resonator of the ruby laser was 1.5 m, and that of the Nd-doped laser 2.0 m. The cuvette with the saturating absorber with a thickness of 0.2 mm (2) was placed at the focus of the spherical mirror and the spherical lens (3), with a focusing distance of 10 cm. The lasing conditions were optimised by changing the density of radiation power in the saturating absorber.

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