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

Physics of Solid-State Lasers

Fig.2.28 Dependence of the specific energy of lasing Eg/Vg (J/cm3) of the laser on a self-activated crystal of rubydium–neodymium tungstate on pumping energy Ep (kJ) at room temperature and the resonator length L = 0.2 m.

is very similar to the parameters of the crystals of potassium–gadolinium tungstate (Nd:KGW). Some characteristics of radiation of the laser on the crystal of Rb–Nd tungstate were investigated in Ref. 73.

The authors of this book investigated a laser on a crystal of Rb– Nd tungstate with the crystal size of 3 mm diameter, 30 mm2 long, in experimental equipment described previously [29].

Figure 2.28 shows the graph of the dependence of the specific lasing energy of the laser on the pumping energy, which shows that the differential efficiency of the laser on the self-activated crystal of the Rb– Nd tungstate corresponds almost completely to the differential efficiency of the Nd:YAG laser, irrespective of the considerably shorter lifetime of the working upper level and the cross-section of the forced transition. It is likely that these losses are compensated by a considerably higher concentration of the Nd ions in the self-activated crystal. At low pumping energies, the dependence of the lasing energy of the laser was almost linear, and with increasing pumping energy, it deviated from the linear dependence. This is associated with the fact that increase of the radiation energy of the pumping lamp increases the fraction of ultraviolet radiation of pumping which does not agree with the absorption spectrum of the Nd ions in the self-activated crystal.

When technical perturbations of the resonator were eliminated, it was possible to obtain stable quasistationary lasing of the TEMmnq and TEMooq modes of the laser on the crystal of Rb–Nd tungstate, as in other widely used Nd media. The decay time of the transition pulsations of the radiation intensity of the laser on the self-activated crystal rapidly decreased in comparison with the Nd:YAG laser in accordance with the lifetime of the upper working level.

The shorter lifetime of the upper working level of the laser on the

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Solid-state neodymium lasers in free lasing regime

self-activated crystal of Rb–Nd tungstate results in a considerably lower sensitivity of this laser to technical perturbations in the laser resonator. Consequently, it is far easier to obtain the quasistationary lasing of the laser on the self-activated crystal in comparison with other Nd media.

2.9 OPTIMISATION OF THE ENERGY CHARACTERISTICS OF RADIATION OF PULSED Nd LASERS

The maximum energy characteristics of radiation of Nd lasers are the same as in the case of the Cr lasers, and are obtained as a result of optimisation of the parameters of the resonators and the temperature of the active medium (Fig. 2.29 and 2.30). At a constant pumping energy, an increase of the resonator length (Fig. 2.29a) and of the temperature of the active medium (Fig. 2.29b) reduces the radiation energy of all

Fig.2.29 Dependence of the densities of lasing energy Eg/Vg (J/cm3) on the length of the resonator L (m) (a), the temperature of active media T (b), the coefficients of transmission of the output mirror of the resonator T2 (c) at a constant pumping energy Ep = 0.3 kJ (a,b,c) and pumping energy Ep (kJ) (d) for lasers: Nd:Cr:GSGG (1), Nd:BLN (2), Nd:YAG (3), Nd:KNFS (4), Nd:LNA (5), Nd:GLS-22 (6) and Nd:KGW

(7). Generated volumes of the active media Vg = 0.5 (Cr:GSGG), 0.56 (BLN), 2.5 (YAG, GLS-22), 2 (KNFS), 0.28 (LNA) and 1.57 cm3 (KGW).

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Nd lasers, with the exception of the Nd:YAG laser. The values of the optimum transmission factors of the output mirror of the laser resonator characterised by the highest lasing energy reach saturation at pumping levels of Ep ≥ 0.4 kJ (Fig. 2.30a).

At low pumping levels, the radiation energy of the Nd lasers was usually characterised by a linear dependence on pumping energy (Fig. 2.29d). Increasing pumping energy resulted in the saturation of the radiation energy of the lasers as a result of a decrease of the efficiency of pumping due to the increase of the fraction of short-wave radiation in the pumping spectrum which was cut off by a liquid filter.

The smallest divergence of radiation was recorded in the case of the Nd:KGW laser (2.30b) as a result of the high homogeneity of the crystal and good heat conductivity. Therefore, the highest luminosity of radiation from the unit volume of the active medium was obtained in the case of the Nd:KGW laser regardless of the fact that the Nd:Cr:GSGG laser was characterised by higher efficiency and specific energy of lasing.

2.10 PROBLEM OF NON-ATTENUATING PULSATIONS OF RADIATION IN SOLID-STATE LASERS

The experimental results presented above indicate that the free lasing of the Cr lasers with flat mirrors always takes place in the regime of non-attenuating pulsations of radiation intensity, in contrast to the Nd lasers. The reasons for the formation of non-attenuating pulsations of radiation in solid-state lasers have been discussed for more than 30 years in a large number of studies and dissertations. In the majority of investigations lasing was presented in a quasi-classic description characterised by the classic examination of the electromagnetic field and the quantum-me- chanics analysis of the active medium. The balance equations, describing

Fig.2.30 Dependence of the optimum coefficient of transmission of the output mirror T2 (a) and the angle of divergence of laser radiation Θ (mrad) (b) of the pumping energy Ep (kJ) for lasers: Nd:Cr:GSGG (1), Nd:BLN (2), Nd:YAG (3), Nd:KNFS (4), Nd:LNA (5), Nd:GLS-22 (6) and Nd:KGW (7).

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Solid-state neodymium lasers in free lasing regime

the lasing and linking together the energy of the field in the resonator and the difference of the populations of the working levels, were obtained in the conditions of a large number of simplifying assumptions and in a limited range of the variation of the laser parameters.

The formation of automodulation and non-attenuating pulsations of radiation intensity in solid-state lasers have been explained by a large number of reasons in many investigations: 1) the process of establishment of the stationary lasing regime [57]; 2) the anisotropy of the gain curve [58]; 3) the effect of different non-linear effects of interaction of the radiation field with the active medium [59–61]; 4) the multimode lasing regime [62); 5) the heterogeneity of pumping [63]; 6) the effect of spontaneous noise [64]; 7) the effect of saturated absorption in the active medium above the critical level [65]; 8) the effect of instabilities of the resonator parameters [66]; 9) the effect of fluctuations of intensity with respect to the amplitude above the attenuation decrement [67]; 7) the non-uniform nature of broadening of the gain line [68]; 11) the effect of focusing of radiation [69]; 12) the effect of the periodic structure of inverse population [70]; 13) the effect of the thermal drift of the gain line [71].

All the proposed mechanisms, causing the non-attenuating pulsations of the radiation intensity of solid-state lasers, can be divided into physical, determined by internal physical processes and not associated with the specific equipment, and technical, determined by external factors (instability of the parameters of the resonator and pumping). The effect of the technical factors on the free lasing dynamics is eliminated by a relatively simple means, as shown previously, even in the conditions of the pulsed lasing regime. Analysis of the experimental results, presented in the study, indicates that none of the previously described physical mechanisms explains the reasons for the formation of the non-attenuating pulsations of the radiation intensity in Cr lasers. The experiments with a ruby laser showed clearly the effect of the physical mechanisms causing such pulsations.

Comparison of the lasing characteristics of radiation of the TEMooq modes of the lasers on the chromium and Nd ions in the crystal of the gadolinium–scandium–gallium garnet, having the same matrix of the active medium and, consequently, identical non-linearities, excludes the physical mechanisms associated with the spatial interaction of the modes in the active medium. Under the same experimental conditions, the Cr:GSGG laser generates in the regime of non-attenuating pulsations of radiation, and the Nd:GSGG laser in the quasistationary regime.

This quantitative difference in the dynamics of free lasing of these lasers is determined by large differences in the structures of their working levels. If irradiation of the chromium ions is determined by the elec-

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Physics of Solid-State Lasers

trons of the outer 3d-shell, the irradiation of the Nd ions is determined by the electrons of the 4f-shell, which is highly screened. Consequently, the generated electric field of laser radiation in the active medium affects only the chromium ions, leading to additional splitting of its working levels as a result of the dynamic Stark effect.

In the conditions of the spatially non-uniform field in the active medium, generated by the standing wave whose spatial structure changes during the lasing process (Fig. 1.4), the dynamic Stark effect leads to the modulation of the gain factor of the active media with time and the non-attenuating pulsations of radiation intensity. The forced smoothing of the spatial heterogeneity of the field in the active media eliminates the induced modulation of the gain factor with time and leads to quasistationary lasing (Fig. 1.6).

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Generation of powerful single-frequency giant radiation pulses

Chapter 3

Generation of powerful single-frequency giant radiation pulses in solid-state lasers

The large number of investigations using powerful solid-state lasers in superhigh resolution spectroscopy in the selective ionisation and excitation of atoms and molecules, plasma diagnostics and beams of atoms and ions, etc., imposes more and more stringent requirements on the laser radiation parameters: power, the width of the spectrum and its tuning, the time and spatial distribution of intensity, the stability of the spectrum and the time of appearance of the pulse. The solid-state lasers with Q- factor modulation (active and passive) in the giant pulse regime are used widely in various areas of science, investigations and technology.

3.1 METHODS OF PRODUCING SINGLE-FREQUENCY LASING IN LASERS WITH Q-FACTOR MODULATION

In lasers with the passive Q-factor modulation of the resonator (Q- modulation), the efficiency of selection of longitudinal modes is considerably higher than in lasers with active Q-modulation. This is determined by the fact that in the lasers with passive Q-modulation, the duration of the linear development of the giant pulse is approximately 1 microsecond, whereas in the lasers with active Q-modulation, it is an order of magnitude shorter.

During linear development, various modes increase from the level of spontaneous noise independently of each other, and the ratio of the amplitude of the modes at the moment of non-linear development of the giant pulse determines the modes that are included in lasing. In the case of passive Q-modulation, the number of passages of photons through the resonator is of the order of 1000. Consequently, the necessary difference in the losses for the two modes, after which the intensities of these modes at the end of linear development will differ by an order of magnitude, is approximately 10–3 (1.4). In a laser with passive Q-modulation, singlefrequency lasing is achieved in the conditions of slight discrimination

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of the longitudinal modes. In the lasers with active Q-modulation, the number of passages through the resonator is reduced to several tens. Consequently, it is not possible to carry out sufficiently strong discrimination of the longitudinal modes when using the conventional selection methods, in order to obtain lasing on a single longitudinal mode.

1.Dispersion prisms, diffraction gratings and interference-polarisation filters are used as the dispersion elements, characterised by not too high frequency selectivity for the separation of individual modes. However, because of a wide dispersion range, these elements are used in the lasers with a wide gain band of the active medium. In the laser on Nd in glass with passive Q-modulation and the prism dispersion resonator, the radiation wavelength of the giant pulse is modified in the range 5.6 nm, with the spectrum 0.1 nm wide [1].

When using the complex dispersion resonator, consisting of a holographic diffraction grating and a non-sprayed resonance reflector, it is possible to achieve single-frequency lasing of the giant pulse with the retuning of the radiation wavelength in the regime of passive Q-modulation in the ruby lasers [3], in the Nd:YAG lasers [4], and in lasers on Nd glass

[5].The retuning of the radiation wavelength is carried out by the smooth change of the total thickness of the crystal wedges, and its range in the laser on the Nd glass is 13.4 nm, and the spectral width 4.5 pm [5].

2.The higher efficiency of the selection of longitudinal modes in the lasers with passive Q-modulation is obtained when using a resonance reflector, consisting of two or more plane-parallel sheets, separated by air gaps. Using the resonance reflector as the output mirror the resonator, it is quite easy to achieve single-frequency lasing in a ruby laser [6,7] and in the vicinity of the threshold in a Nd glass laser [8,9]. The retuning of the radiation wavelength of the giant pulse is carried out by changing the pressure of the air gap. However, the resonance reflector without mirror coatings is characterised by reduced selectivity and does not make it possible to obtain single-frequency lasing in lasers with active Q-modulation even in the vicinity of the threshold.

3.The duration of the linear development of the giant pulse can be artificially increased in lasers with active Q-modulation as a result of slow [10, 11] or two-stage [12,13] application of the Q-factor. In this case, as in the regime with passive Q-modulation, single-frequency lasing of the giant pulse is achieved in the conditions of slight discrimination of the longitudinal waves in the ruby laser [11,12] and in the Nd laser on potassium tungstate [30]. However, with slow activation of the Q- factor of the resonator, intra-resonator losses rapidly increase and the power of the giant pulse decreases. In addition, with slow activation of the Q-factor, it is necessary to work only the vicinity of the threshold, otherwise lasing will involve several pulses with different spectral char-

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Generation of powerful single-frequency giant radiation pulses

acteristics, and this also restricts the power of the giant pulse. These restrictions are eliminated when activating the Q-factor of the resonator in two stages. In the first stage of activation of the Q-factor, the gate is partially opened and a weak single-frequency radiation pulse forms during the period of linear development. At the moment corresponding to the maximum volume of the pulse intensity, the second voltage pulse is supplied to the gate and completely opens the latter, and a singlefrequency giant pulse is irradiated without any loss of power.

4. Lasers with the electro-optical Q-modulation of the resonator are used when accurate synchronization of the time of appearance of the giant pulse with the examined process is required. The most efficient method of ensuring single-frequency lasing in these lasers is the method of injection of the external signal [14]. After activating the Q-factor, single-frequency radiation from a low-power master laser is injected into the resonator of the high-power laser. Since the duration of linear development of the giant pulse is inversely proportional to the logarithm of radiation intensity in the laser resonator, the radiation in the giant pulse will not form from the spontaneous noise with a wide spectrum but it will form from external single-frequency radiation whose intensity is an order of magnitude higher than that of spontaneous noise. In the case of capture of the wavelength, the spectrum of the giant pulse is identical to that of the external signal. The absence of selecting elements in the resonator of the high-power laser makes it possible to generate high power of the giant pulse of radiation in the single-frequency regime. The gain factor of a weak monochromatic signal may reach ~1010. The method of injection of the external signal was used in ruby lasers with electro-optical Q-modulation [15] and in Nd glass lasers [16–18]. In addition to solidstate lasers, the method of injection of the external signal is used widely in liquid [19, 20] and gas [21, 22] lasers.

The lasing of Cr and Nd lasers in the regime with active and passive Q-modulation was examined by the authors of this book in Ref. 33– 38,51,53.

3.2 POWERFUL SINGLE-FREQUENCY TUNABLE RUBY LASER WITH INJECTION OF THE EXTERNAL SIGNAL

The method of injection of the external signal was examined in detail by the authors of the book in a ruby laser with electro-optical Q-modulation of the resonator in [23–28, 34–38]. In a three-mirror variant of the injection system of the external signal, the output mirror of the master laser was represented by a dense mirror of a high-power laser (Fig. 3.1). The master laser was represented by a single-frequency ruby laser in the quasistationary regime with the parameters shown in Fig. 1.8. In this case, there was no need for additional synchronization of the operation of the two lasers,

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Physics of Solid-State Lasers

Fig.3.1 Diagram of a three-mirror single-frequency ruby laser with electro-optical modulation of the Q-factor: I – single-frequency master quasi-continuous laser (Fig. 1.1); II – powerful laser: 10, 13 – mirrors (T10 = 0.02 T10 = 0.02 T13 = 0.7); 11) electro-optical gate; 12) ruby.

in addition to the simultaneous activation of pumping lamps. The electrooptical gate of the master laser was opened when the maximum inversion was reached 0.3–0.5 ms after the start of lasing of the master laser.

At the edge of the retuning range, the width of the radiation spectrum of the master laser in the absence of capture of the radiation wavelength of the master laser was 15 pm (Fig. 3.2a). In the spectral range 180 pm wide the wavelength of external single-frequency radiation was captured, and the lasing spectrum of the giant pulse completely coincided with the spectrum of the external signal (Fig. 3.2b). However, in this case, the powerful laser generated a split radiation pulse (Fig. 3.2c). This is associated with a decrease of the reflection factor of the general mirror 10 (Fig. 3.1) as a result of the increase of the energy stored in the resonator of the master laser in the process of increase of the intensity of the giant pulse. This increases the losses and the self-excitation threshold in the powerful laser. The power of the giant radiation pulse of the executive laser on a level of approximately 1 MW in this circuit was restricted by the failure of the mirror coatings of the Fabry–Perot selector-etalon in the master laser.

The power of the giant radiation pulse was increased as a result of the application of a four-mirror system for the injection of the external signal (Fig. 3.3). The master laser 1 remained unchanged, and the resonator of the powerful laser was formed by one of the ends of the ruby rod 5 and by the dense mirror 8. The lasers were separated by the electro-optical gate, consisting of two Archard–Taylor prisms 2 a 4 and the Pockels cell 3 which was activated for the passage of radiation of the master laser for a period of approximately 50 ns several nanoseconds prior to opening the electro-optical gate of the powerful laser. The radiation of the giant pulse with a power of ≥ 10 MW was transferred through the side face of the polarisation prism 2 which was often damaged at very high powers of the giant pulse.

To eliminate this shortcoming, investigations were carried out into

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