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

Physics of Solid-State Lasers

displacement of the emission spectrum to the long-wave length region at a speed of 0.2 nm/ms as a result of the thermal drift of the gain line, determined by heating of the crystal. Thus, during the pumping pulse of 0.25ms, the Nd:BLN crystal was heated to approximately 60 °C [8].

The speed of the thermal drift of the gain line was measured from the displacement of the spectrum of quasistationary lasing (Fig. 2.20b) with the pumping slightly higher than the threshold level and with controlled heating of the crystal with an accuracy to 0.1 °C. In the examined range of radiation of the temperature of the Nd:BLN crystal, the speed of the thermal drift of the gain line was characterised by a linear dependence and was 0.84 pm/deg (Fig. 2.10b) [10].

The quasistationary lasing of TEMmnq modes was achieved only for the modes with a low transverse index (m, n ≤ 5) when only a small number of the modes was excited and the spatial competition of the modes was greatly weakened. This regime is more sensitive to the external perturbations and the regime of lasing of the longitudinal waves. The width of the instantaneous spectrum of lasing of TEMmnq modes (Fig. 2.21e) corresponded to the lasing spectrum of TEMooq modes. In the

Fig.2.21 Parameters of the lasing of TEM00q (b,c) and TEMmnq modes (d,e) of Nd:BLN laser (4 mm in diameter, 70 mm long) with flat mirrors (L = 2 m, T2 = 0.7) without (c,e) and with selection of the longitudinal modes (f), Ep = 10Et: b,d) evolvement of the distribution of radiation intensity in the near-range zonel; c,e,f) time evolvement of the lasing spectrum, the range of dispersion of the interferometers 280 pm (c,e) and 20 pm (f).

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complex dispersion resonator, consisting of two Fabry–Perot selectorsetalons, we achieved the single-frequency quasistationary lasing of TEMooq and TEMmnq modes (Fig. 2.21f). The change of the wavelength of the single-frequency radiation at the transition 4F3/2→ 4I11/2 approximately 6 nm (Fig. 2.22) and the width of the integral radiation spectrum was 3 pm [10].

2.5.2 Energy parameters of lasing

Investigations were carried out on the crystals of La beryllate with Nd (Nd:BLN), 4 mm in diameter, 70 mm long, with the bevelled and clarified ends in a flat mirror laser. The concentration of the Nd ions in the crystals was 2%. The pumping of active elements was conducted using an INP 5/45 lamp, in a quartz single-block illuminator, with the cutting off of the ultraviolet radiation of pumping. The lasing volume in this case was Vg = 0.56 cm3.

The lasing energy of the Nd:BLN laser decreased by a factor of 2.2 when the length of the resonator was increased from 0.3 to 1.6 m (Fig. 2.29a) (2). Heating of the La beryllate crystal in the range from 10 to 90 °C decreased the lasing energy of the Nd:BLN laser by a factor of 1.5 (Fig. 2.29b) (2). At a pumping energy of 300 J, the maximum energy of lasing of the laser was obtained at a transmission factor of the output mirror of the resonator of 70% (Fig. 2.29c) (2).

With increase of the pumping energy, the value of the optimum transmission factor T2 at which the maximum energy is obtained, tended to its limiting value of 85% (Fig. 2.30a) (2). If at a low pumping energy

Fig.2.22 Dependence of the energy of one-particle lasing Eg (J) (1) and threshhold energy Et (J) (2) of Nd:BLN laser on the wavelength λ (nm) in a dispersion resonator (L = 2 m); Ep = 200 J.

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level the efficiency of lasing of the Nd:BLN laser was comparable with the efficiency the lasing of the Nd:YAG laser, then with increasing energy of the pumping, the efficiency of lasing of the Nd:BLN laser was higher than the efficiency of lasing of the Nd:YAG laser, and at a pumping energy of 500 J the density of energy of the Nd:BLN laser was 2.8 J/ cm3, and for the Nd:YAG laser it was 2.6 J/cm3 (Fig. 2.29d) (2). The heat conductivity of the La beryllate crystal is considerably lower than that of the crystal of the yttrium–aluminium garnet. In the experiments, this was reflected in an increase of the angular divergence of radiation of the Nd:BLN laser and in a decrease of the luminosity of radiation in comparison with the Nd:YAG laser (Fig. 2.30b) (2).

2.6 Nd LASERS IN HEXA-ALUMINATES OF LANTHANUMMAGNESIUM AND LANTHANUM–BERYLLIUM

Recently, special attention has been given to the application of crystals of hexa-aluminates of La–Mg and La–Be in which the Nd ion concentration may reach tens of percent at a slight concentration decay of luminescence. Therefore, it may be expected that the efficiency of lasing on these crystals will be relatively high.

The single crystals of the hexa-aluminate of La–Mg with Nd (Nd3+:LaMgAl11O19, Nd:LNA) are characterised by a hexagonal structure and a relatively low anisotropy of properties in different crystallographic directions. Optically, these are anisotropic uniaxial crystals. They melt congruently at a temperature of 1870°C. The density of the crystals of LNA is 4.04 g/cm3, hardness (Moose) is 7.5. The heat conductivity of the LNA crystals is relatively high and equals 14 W/m deg( c) and 10 W/m deg(||c).

The Nd:LNA crystals may have a relatively high concentration of Nd ions (to 7 × 10 20 cm–3) with slight concentration decay of luminescence.

The cross-section of the laser transition 4F3/2→ 4I11/2 in the crystal is 3.2 × 10 –19 cm–3, the lifetime of the upper level is 320 µs, the half-width

of the gain line is 3 nm. The lasing of Nd ions in the crystal of the hexa-aluminate of La–Mg was recorded for the first time in Ref. 52 and 53. The integral characteristics of radiation of the Nd:LNA laser were investigated in lamp [53] and laser [56] pumping.

The lasing of Nd ions in the crystal hexa-aluminate of La–Be (Nd3+:LaBeAl11O19, Nd:GALB) was investigated in Ref. 54 and 55. The Moose hardness of the Nd:GALB crystals was ~7, density 4.15 g/cm3.

The lifetime of the upper level of the laser transition 4F3/2→ 4I11/2 is 150 µs at room temperature. The absorption spectra of the examined

Nd:GALB crystal (Fig. 2.23) contained a large number of lines determined by transitions from the ground state 4I9/2 to the excited levels 4F, 2H, 4S, 2G, 4G and other multiplets of the Nd ions. The luminescence spectra

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Fig.2.23 Dependence of the coefficient of absorption α (cm–1) of neodymium ions (Nd3+) on the wavelength λ (µm) on the crystal of lanthanum–beryllium hexa-aluminate at room temperature.

Fig.2.24 Dependence of the intensity of luminescence I (rel.units) of neodymium ions in the crystal of lanthanum–beryllium hexa-aluminate on wavelength λ (µm) in transition 4F3/2→ 4I11/2 at room temperature.

of the crystal on the transition 4F3/2→ (Fig. 2.24) are considerably wider indicating the disordered structure of the crystal.

2.6.1 Spectral and time parameters of lasing

Of all the examined Nd lasers, the quasistationary lasing with lamp pumping could not be obtained only in the Nd:LNA flat mirror laser because of high thermal strains of the crystal. In this case, it was not possible to obtain the optimum parameters of the resonator which make it possible to eliminate the effect of technical perturbations in the Nd lasers and obtain quasistationary lasing. The regime of non-attenuating pulsations of the radiation intensity was characterised by the random alternation

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Fig.2.25 a) Interferogram of the integral spectrum of lasing of TEMmnq modes of Nd:LNA laser (diameter 3 mm, length 50 mm) with flat mirrors (L = 0.4 m) in the absence of selection of longitudinal modes, range of dispersion of the interferometer 560 pm, Ep = 2Et; b) dependence of lasing energy Eq (J) (1) and the threshhold energy of pumping Et (J) (2) on wavelength λ (nm) in a dispersion resonator with a selectoretalon with a temperature range of 5.5 nm, Ep = 2Et.

of the spectral components of the spectrum, and when the a pumping level was twice as high as the threshold level and there was no selection of the longitudinal modes, the width of the integral radiation spectrum was 1 nm (Fig. 2.25a). This indicates the non-uniform nature of broadening of the gain line. When using a Fabry–Perot selector-etalon with a dispersion range of 5.6 nm, the width of the lasing spectrum decreased to 5.6 nm, and this was accompanied by the rearrangement of the radiation wavelength in the range 3.5 nm (Fig. 2.25b).

In free lasing regime with pumping slightly higher than the threshold value, the width of the integral spectrum of lasing of the Nd:GALB laser was approximately 0.3 nm, as in the Nd:LNA laser. In the absence of spurious selection of the longitudinal modes, the width of the integral spectrum of the Nd:GALB laser increased with increasing pumping energy and when the pumping value was twice the threshold level, it was approximately 1 nm and reached saturation. This large increase of the width of the lasing spectrum was evidently determined by the non-uniform nature of broadening of the gain line of the Nd:GALB crystal as in the case of the Nd:LNA crystal. The nature of lasing of the Nd:GALB laser was almost identical with the nature of lasing of the Nd:LNA laser.

The addition of the Fabry–Perot selector-etalon with a dispersion range of 5 nm into the resonator of the Nd:GALB laser reduced the width of the lasing spectrum to 0.03 nm and made it possible to change the lasing wavelength lasing in the range of the order of 3 nm in the vicinity of the centre of the maximum of the gain line.

2.6.2 Energy parameters of lasing

Investigations were carried out on lasers with flat mirrors on crystals Nd:LNA and Nd:GALB, 3 mm in diameter, 50 mm long, with bevel-

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led and clarified ends. The volumes of the active media, contributing to lasing energy, were Vg = 0.28 cm3. The concentration of the Nd ions in the crystals was 5 wt%. Pumping was carried out with an ISP-250 lamp with a pumping pulse time of 250 µs in a quartz single-unit illuminator. The ultraviolet radiation of pumping was cut-off with a liquid filter.

The nature of the dependences of the lasing energies of the Nd:LNA and Nd:GALB lasers was almost identical and, consequently, Figs. 2.29 and 2.30 show these relationships only for the laser on the Nd:LNA crystal which is a better known active medium, and the efficiency of lasing of the Nd:GALB laser was slightly higher than that of the Nd:LNA laser. With an increase of the length of the resonator from 0.2 to 1.6 m at a constant pumping energy, the lasing energy of the lasers decreased by a factor of 3 (Fig. 2.29a) (5).

The large decrease of lasing energy with increasing resonator length is caused mainly by high thermo-optical deformation of the crystals which transformed the flat resonator of the laser to an unstable equivalent spherical resonator with high losses. At a constant length of the resonator, heating of the crystals from 10 to 90 °C resulted in a decrease of lasing energy by a factor of 1.5 (Fig. 2.29b) (5).

At a pumping energy of 300 J, the maximum lasing energy of the lasers was obtained at the transmission factor of the output mirror of the resonator T2 of approximately 70% (Fig. 2.29c). With increase of the pumping energy, the optimum transmission factor T2 tended to its maximum value of 90% (Fig. 2.30a) (5). In the range of low pumping energies, the lasing energy of the lasers depended in a linear manner on the pumping energy, and with increase of pumping energy the linear form of the dependence was disrupted, and at a pumping energy of 500 J the density of the lasing energy was approximately Eg/Vg = 1.2 J cm3 (Fig. 2.29d). This is associated with both the thermal deformation of the laser resonator and with the energy losses of pumping where the short-wave part of pumping radiation was cut-off by a liquid filter.

2.7 Nd LASERS ON POTASSIUM–GADOLINIUM AND POTASSIUM– YTTRIUM TUNGSTATES

The single crystals of the binary potassium–gadolinium tungstate (KGd(WO4)2, KGW) belong to monoclinic crystals, and this results in the anisotropy of the thermophysical and spectral–luminescence characteristics of these crystals. The heat conductivity coefficient of KGW crystals is several times lower than that of YAG crystals, and the coefficients of heat conductivity of the KGW crystals are characterised by anisotropy in the three main crystallographic axes: [100] k = 2.8 W/m deg, [010] k = 2.2 W/m deg, [001] k = 3.5 W/m deg. This greatly restricts the area

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of application of these crystals in the lasing regime with continuous lamp pumping.

The thermal expansion coefficients are also characterised by the corresponding anisotropy in the direction of the axes: 4 (1.4; 8.5) × 10–6 deg–1. The refractive index of the KGW crystal at a wavelength of 1067 nm is: na = 2.03, nb = 1.94 and nc = 1.98. The thermo-optical constants of these crystals are characterised by even greater anisotropy along the axes: dna/dT = + 8×10 –7 deg–1, dnb/dT = –5.5×10 –6 deg–6, dnc / dT = +1.7×10 –6 deg–1, with the orientation of the heating region parallel to the c axis. Since the temperature coefficient has positive and negative values, at a specific orientation of the KGW crystal the thermal lens may not form in the resonator. The density of the KGW crystals is 7.27 g/cm3, hardness (Moose) 5, melting point 1075 °C, which is 900 degrees lower than in the YAG crystals. Consequently, it is possible to grow larger active specimens of KGW crystals and, as indicated by experiments, with higher optical quality.

The absorption bands of the Nd ions in the KGW almost coincide with the corresponding absorption bands in the YAG, but the absorption bands of the Nd: KGW crystal are considerably wider and less truncated resulting in more efficient absorption of radiation of the pumping lamps.

The cross-section of the 4F3/2→ 4I11/2 transition of the Nd:KGW crystal at a wavelength of 1067 nm is 3.8×10 –19 which, according to the

latest spectroscopic measurements [32], is larger than the cross-section of these transitions in the Nd:YAG crystal. The width of the gain line of the Nd:KGW crystal is 7 times greater than that of the gain line of the Nd:YAG crystal and is 4.3 nm, so that Nd:KGW crystals can be used in tunable lasers. The lifetime of the upper working level of the Nd:KGW crystal depends only slightly on the concentration of the Nd ions, and with increase of the concentration of these ions from 1 to 10 at.% the lifetime is only halved from 142 to 70 µs. This high concentration of the activator results in a high efficiency factor of the Nd:KGW crystal, but only at low pumping levels and the small dimensions of the active element.

The lasing on Nd ions in the crystals of potassium–yttrium (Nd:KYW) and potassium–gadolinium (Nd: KGW) tungstates was reported for the first time in Ref. 37.

2.7.1 Spectral–time parameters of lasing

The spectral–time, spatial and angular parameters of lasing of Nd: KGW and Nd:KYW lasers were investigated in Ref. 4,11,17–19,22–28.

At the optimum parameters of the flat resonator and as a result of eliminating the effect of technical perturbations of the resonator in the Nd:KGW laser, it was possible to obtain quite easily the stable

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quasistationary lasing of TEMooq (Fig. 2.26b, d) and TEMmnq modes (Fig. 2.26c, d). The quasistationary lasing of the TEMmnq modes was realised only at low values of the indices of the transverse modes (m, n ≤ 5). The short duration of the transition process is determined by the short lifetime of the upper working level. The instantaneous width of the structureless spectrum in the quasistationary regime was 15 pm (Fig. 2.26d), and reached saturation when the pumping value was 5 times higher than the threshold value. It is evident that this wide spectrum of lasing in the lasers with the uniformly broadened gain line without selection of the longitudinal modes is caused by their self-synchronization. This should be accompanied by the appearance of a continuous spectrum with the period (c/2L), where c is the velocity of light, L is the length of the resonator. The recording of the lasing spectrum with a time resolution of approximately 1 ns has confirmed this.

In a dispersion resonator with a Fabry–Perot selector-etalon, with a dispersion range of 5.7 nm, it was possible to obtain single-frequency quasistationary lasing of TEMooq and TEMmnq modes (Fig. 2.26e), with smooth tuning of the radiation wavelength in the range 4 nm.

The speed of the thermal drift of the gain line into the long-wave region of the spectrum in the Nd:KGW and Nd:KYW crystals during

Fig.2.26 Parameters of the lasing of TEMooq (b,d) and TEMmnq (c,d) modes of Nd:KGW laser (diameter 6 mm, length 90 mm) with flat mirrors (L = 2 m, T2 = 0.5), Ep = 10Et; a) oscillogram of radiation intensity, 20 µs marks; b,c) time evolvement of

the distribution of radiation intensity of TEMooq (b) and TEMmnq (c) modes in the near-range zone; d,e) time evolvement of the lasing spectrum of TEMmnq modes (c)

in the near-range zone; d,e) time evolvement of the lasing spectrum of TEMooq and TEMmnq modes without (d) and with selection of the longitudinal modes (e), the range of dispersion of the interferometer 190 pm (d) and 20 pm (e).

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heating, recorded on the basis of the interferograms of the lasing spectrum, was approximately 0.9 pm/deg (Fig. 2.10b).

The spectral–time parameters of lasing of Nd:KYW laser under normal conditions were almost identical with the lasing parameters of the Nd:KGW laser. An original regime was realised in the Nd:KYW laser in which the dispersion element in the resonator with flat mirrors was represented by an active rod whose ends were cut under an angle of approximately 10° in relation to each other and in relation to the axis of the rod. In this case, it is possible to ensure the self-sweep of the radiation wavelength to the short-wave range of the spectrum with a high constant of the component of the integral intensity of radiation (Fig. 2.25). The laser resonator did not contain any additional selecting elements and the maximum of the gain line was displaced to the long-wave region of the spectrum.

The displacement of the lasing wavelength (self-sweep) took place in the case in which the lasing channel, determined by the diaphragms, did not pass accurately along the axis of the rod and the induced thermal lens. The variation of the focus of the thermal lens in the process of lasing resulted in a smooth deflection of the beam in the angle and in the sweep of the radiation wavelength as a result of the dispersion of the active rod. The sweep rate of the lasing wavelength depended on the pumping energy and the dispersion of the active element. For the parameters of the Nd:KYW laser, shown in Fig. 2.27, this rate was approximately 0.4 nm/ms.

After the transition process, a single longitudinal mode was excited in every peak. The change of the modes in the lasing process was adiabatic and was not accompanied by the pulsations of the integral intensity of radiation as a result of the low sweep rate of the wavelength. The absence of the selecting elements in the resonator, which leads to significant losses of radiation intensity, has made it possible to obtain satisfactory radiation

Fig.2.27 Parameters of lasing of TEMooq modes of Nd:KYW laser (diameter 5 mm, length 80 mm) with flat mirrors (L = 2 m): a) oscillogram of radiation intensity, 20 µs marks; b,c) time evolvement of the lasing spectrum at different pumping levels Ep= 3Et (b) and I4Et (c), the range of dispersion of the interferometer 20 pm.

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energy characteristics in such a sweep-laser.

2.7.2 Energy parameters of lasing

Investigations were carried out on a laser with flat mirrors on a crystal of binary potassium–gadolinium tungstate with Nd (Nd:KGW), 5 mm diameter, 100 mm long, with bevelled and illuminated ends. The concentration of the Nd ions was 3%. The volume of the active medium, providing a contribution to the lasing energy, was Vg = 1.57 cm3. Pumping was carried out using a IPF-800 pulsed lamp, the pumping pulse time was 250 µs. The ultraviolet radiation of pumping was cut-off with the liquid filter.

The efficiency of lasing of the examined Nd:KGW crystal was slightly higher than that of Russian standard active elements produced from the Nd:YAG crystals. In the Nd:KGW laser, all energy characteristics were identical to the characteristics obtained for the majority of Nd media (Fig. 2.29 and 2.30). With increase of the length of the resonator, the lasing energy of the Nd:KGW laser decreased by a factor of 1.3 (Fig. 2.29 a, b) (7). When heating the crystal from 10 to 90 °C, the lasing energy of the Nd:KGW laser decreased only by a factor of 1.2 (Fig. 2.29b) (7).

At a pumping energy of 300 J, the maximum lasing energy was obtained at the optical coefficient of transmission of the mirror of the resonator of 50% (Fig. 2.29c) (7). The divergence of the radiation of the Nd:KGW laser was similar to the diffraction divergence (Fig. 2.30b) because of the examined active media, the Nd:KGW crystals are characterised by higher optical homogeneity.

2.8 Nd LASERS ON SELF-ACTIVATED CRYSTALS

In widely used crystal laser media, active ions represent an impurity and substitute a specific type of atoms of the matrix lattice. In the majority of cases, the ion of the activator differs from the substituted ion of the matrix by a whole number of parameters: ion radius, mass, etc. This imposes certain restrictions of the possibility of activation of the matrix with respect to concentration, and the increase of concentration results in thermal stresses causing failure of the crystal.

The self-activated crystals include the RbNd(WO4)2 crystal, whose structure and lattice parameters were determined in Ref. 72. The concentration of Nd ions in the crystal was 6 × 10 21 cm–3, the lifetime of the upper

working level was 10 µs, the cross-section of the 4F3/2→ 4I11/2 transition at room temperature was 2.5 × 10 –19 cm2, the wavelength at the maximum

of the luminescence line was 1065 nm, the width of the gain line was ~2 nm. As regards the parameters, the crystal of the Rb–Nd tungstate

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