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

Physics of Solid-State Lasers

In continuous lamp pumping, the active rod shows the formation of strong thermal-optical deformations with the formation of a thermal lens. This resulted in extensive deformation of the optical resonator and the wave front of radiation of TEMmnq modes (Fig. 2.13, b–d). In this case, when using standard spherical optics, it is not possible to carry out correction of the radiation front and efficient focusing of radiation.

The focusing distance of the thermal lens fT, induced in the crystal, can be approximately calculated [45], knowing the characteristics of the YAG crystal and the pumping power, absorbed in the crystal

where h is the heat transfer coefficient; l is the length of the crystal; κ is the heat conductivity coefficient; α is the coefficient of linear expansion; C is the photoelasticity coefficient; n is the refractive index; ∂ n/∂ T is the thermo-optical coefficient. The experimental focusing distance fT was measured using the Fabry–Yudin method in two planes: the crystal–lamp plane and in the plane orthogonal to this plane, at various points along the radius of the crystal. In a quantron with an elliptical illuminator, spherical aberrations of the thermal lens are more marked (Fig. 2. 14a) than in the case of a cylindrical illuminator (Fig. 2.14b).

The distribution of temperature in the crystal along its radius was determined from the variation of the distribution of the refractive index ∆ n (r) in the cross-section of the rod which was determined on Mach– Zender interferograms (Fig. 2.15) from the equation

here N(r) is the number of the interference ring. The anisotropy of the variation of the refractive index in the cross-section of the rod at dif-

Fig.2.13 Distribution of intensity of radiation of a powerful continuous Nd:YAG laser (diameter 6.3 mm, length 100 mm) in the near-range zone for transverse modes TEMooq (a), TEMo1q (b), TEM11q (c) and TEMmnq (d); Pp = 6 kW.

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Solid-state neodymium lasers in free lasing regime

Fig.2.14 Dependences of the Foci of the thermal length fT (m) on pumping power Pp (kW) in the crystal-lamp plane (2) and in the plane normal to the former (1) for a garnet crystal (6.3 mm diameter, 100 mm length) in an eliptical illuminator at r/ r0 = 0.2 (1) and for a crystal (diameter 5 mm, length 100 mm) in a cylindrical illuminator at r/r0 = 0.5 (b).

Fig.2.15 Mach–Zender interferograms obtained in a garnet crystal (diameter 6.3 mm, length 100 mm) in an eliptical illuminator. Pp = 0 (a), 1.5 (b), 3.0 (c) and 5 kW (d).

ferent pumping powers is associated with both the physical properties of the garnet crystal and with the parameters of the illuminator. The dependence of the distribution of temperature T(r) in the crystal on the radius r, calculated from the equation

is shown in Fig. 2.16. On the graph, the temperature dependence can be approximated with sufficient accuracy by the parabola:

where r0 is the radius of the crystal.

The thermal lens, formed in the garnet crystal, transform the flat laser resonator to a spherical one with equivalent parameters (1.13). The maximum power of laser radiation was obtained when fulfilling the coefficient of

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Physics of Solid-State Lasers

Fig.2.16 Dependence of the radial distribution of temperature T in a garnet crystal (diameter 6.3 mm, length 100 mm) at Pp = 5 kW.

the stability of the equivalent resonator (1.40) at respectively the optimisation of the resonator length L (2.17a) and the transmission factor of the output mirror of the resonator T2 (Fig. 2.17b). The power Pg (Fig. 2.17c) and divergence θ (Fig. 2.17d) of laser radiation depended in a linear manner on pumping power Pp. For a Nd:YAG crystal with a diameter of 6.3 mm, 100 mm long, at a pumping power of 6 kW, the lasing power was 150 W, with the divergence of radiation of 20 mrad. The increase of the divergence of radiation took place as a result of both the increase of the number and indices of the transverse modes and the increase of the divergence of every individual mode, due to the decrease of the focusing distance of the thermal lens.

2.4 Nd LASERS ON GADOLINIUM–SCANDIUM–GALLIUM GARNET WITH CHROMIUM

Significant advances in the physics and technology of solid-state lasers are associated with the development of crystals of gadolinium-scandium– gallium garnets, activated by Nd ions and sensitised by chromium ions (Nd3+:Cr3+3+:GSGG). The application of chromium ions as a joint activator of the Nd ions has made it possible to decrease greatly the efficiency of the GSGG crystal.

The chromium ions, characterised by wide absorption bands, can absorb more efficiently pumping radiation and transfer excitation to the upper working level of Nd ions 4F3/2 without radiation from the excited level 4T2 by the multipole-resonance regime. This rapid transfer of excitation (in comparison with the rate of deactivation of the 4F3/2 level) is possible because of the fact that the energy gap between the levels 2E and 4T2 of the chromium ions is equal to 0 and there is no luminescence of the R-line of the chromium crystals.

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Fig.2.17 Dependence of the lasing power Pg (W) (a,b,c) and the angle of convergence of radiation θ (mrad) (d) on the length of the flat resonator L (m) (a), the coefficient of transmission of the output mirror T2 (b) and pumping power Pp (kW) (c,d): a) Pp = 3.5 (1) and 6 kW (2), T2 = 0.2; b) Pp = 3 (1), 4 (2), 5 (3) and 6 kW (4), L = 0.55 (1), 0.53 (2), 0.35 (3) and 0.33 m (4); c) crystal, 5 mm diameter, 100 mm long (1) and 6.3 mm diameter, 100 mm long (2); d) in the crystal–lamp plane (2) and in the plane normal to it (1).

The decay of the excited level of the chromium ions in the GSGG crystal in the absence of Nd ions takes place exponentially with a decay time of 180 µs and does not depend on the concentration of chromium ions up to 6 × 10 20 cm–3 (without concentrational decay of luminescence). When adding Nd ions to the crystal, the decay time of the 4T2 level rapidly decreases as a result of the transfer of excitation energy by the levels of the Nd ions, and decay becomes non-exponential.

The optimum concentrations of the ions of chromium and Nd in GSGG are approximately 1020 cm–3. In the Nd:Cr: GSGG crystal it is possible to ensure the effective lasing of Nd ions at a wavelength of

the resonance losses as a result of absorption on the 4I9/2 – 4F3/2 transition do not exceed the permissible value of ~0.01 cm–1. This is comparable with the losses in the active element.

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The efficiency of build-up of energy in the Nd:Cr: GSGG crystal is 1.7 times higher [46], and the efficiency factor is twice the value [47] in the Nd:YAG crystal. However, the widening of the absorption bands of pumping results in a larger increase of heat lasing in the Nd:Cr:GSGG the crystal and, consequently, this crystal is characterised by considerably stronger effects of induced birefringence, the thermal lens and thermoelastic stresses. At the same pumping power, the focusing distance of the thermal lens in the Nd:Cr:GSGG crystal is 4.5 times shorter than in the Nd:YAG crystal [46]. In the Nd:Cr:GSGG crystal, it is possible to obtain a specific power of free lasing in the pulsed regime of 7 kW/ cm2 [48] and in the continuous regime 0.15 kW/cm2 [49].

The Nd:Cr:GSGG crystal has a cubic structure, and its main spectral and physical characteristics are: melting point 1850 °C, density 6.5 g/ cm3, the refractive index of the crystal at a wavelength of 1060 nm 1.94, heat conductivity 6.02 W/m deg, the thermo-optical constant 13 10–6 deg–1, the lifetime of the chromium ions 120 µs, the width of the

gain line at the 4F3/2→ 4I11/2 transition 1.4 nm, the cross-section of this transition 1.5 10–19 cm2.

2.4.1 Spectral–time characteristics of radiation

The spectral–time, angular and energy parameters of lasing of the Nd:Cr:GSGG laser were investigated by the authors of this book in Ref. 11,12,16,18–20,22–28, with the non-optimum length of the flat resonator of 1.6 m for the Nd ions. This is determined by high thermo-optical deformation of the active rod and the laser resonator. A further increase of the resonator length resulted in a large decrease of the radiation energy due to a rapid increase of the losses of the equivalent spherical resonator. The high level of thermo-optical deformation of the crystal did not make it possible to obtain, in the Nd:Cr:GSGG crystal, the quasistationary

lasing of TEMmnq modes which was achieved only for the TEMooq modes (Fig. 2.18). In this case, the quasistationary regime of lasing was highly

unstable in relation to the smallest perturbations of the resonator and, consequently, this required careful tuning of all elements of the resonator.

In the absence of the selection of the longitudinal modes, the width of the instantaneous spectrum of quasistationary lasing was 70 pm (Fig. 2.18c). This parameter reached saturation when the pumping was three times higher than the threshold value. The single-frequency tunable quasistationary lasing of the TEMooq modes (Fig. 2.18d) was obtained using a complex dispersion resonator, consisting of two Fabry–Perot selectors-etalons with the transmission factors of the mirrors of 20% and the dispersion ranges of 1.88 and 0.56 nm. The general range of retuning of the radiation wavelength at the 4F3/2→ 4I11/2 transition between the Stark sublevels R2→ Y3 (1064 nm) and R1→ Y1 (1060 nm) was ap-

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Solid-state neodymium lasers in free lasing regime

Fig.2.18 Parameters of the lasing of TEMooq modes of the Nd:CR:GSGG laser (diameter 4 mm, length 90 mm) with flat mirrors (L = 1.6 m, diameter 1.6 mm), Ep = 5Et; a) oscillogram of radiation intensity, scale 50 µs/div; b) evolvement of the distribution of the intensity in the near-range zone; c,d) time evolvements of the lasing spectrum without selection of longitudinal modes (c) and with selection (d), the range of dispersion of the interferometer is 110 pm (c) and 20 pm (d).

Fig.2.19 Dependence of the energy of one-particle lasing Eg (J) of Nd:Cr:GSGG laser on the lasing wavelength λ (nm) in a dispersion resonator; Ep = 0.3 kJ.

proximately 3 nm (Fig. 2.19).

In a non-selective resonator, the lasing threshold at a wavelength of 1061 nm at room temperature was 6 times higher than the lasing threshold at a wavelength of 1064 nm. At a temperature of 80 °C, the lasing threshold at a wavelength of 1061 nm decreased three times (Fig. 2.20a). The thermal drift of the gain line in the Nd:Cr:GSGG crystal was measured during heating of the crystal from the displacement of the maximum of the spectrum of quasistationary lasing from pulsed pulse on the interferograms of the spectrum (Fig. 2.20a). The mean speed of the thermal drift of the gain line in the examined temperature range was 4.0 pm/deg (Fig. 2.10b).

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Physics of Solid-State Lasers

Fig.2.20 Interferograms of the spectra of quasi-stationary lasing of Nd:Cr:GSGG

(a) and Nd:BLN (b) lasers at different crystal temperatures: a) T = 10, 30, 40, 50, 60, 70, 80 and 90 °C; b) T = 10, 30, 40, 50, 60, 70, 80 °C. The range of dispersion of the interferometers 560 pm (a) and 280 pm (b); Ep = 2Et (a) and 4Et (b).

2.4.2 Energy parameters of lasing

The energy characteristics of the radiation of a Nd:Cr:GSGG laser with flat mirrors was investigated using a crystal 4 mm × 90 mm long, with bevelled and illuminated ends. The concentration of the Nd ions in the crystal was 2 1020 cm–3, and the concentration of the chromium ions was 3 1020 cm–3. Pumping of the crystal was carried out with an ISP-250 lamp, pumping pulse time was 250 µs. The volume of the active medium, contributing to lasing energy, was Vg = 0.5 cm3. The ultraviolet radiation of pumping was cut off with a liquid filter.

The lasing energy of the Nd:Cr:GSGG laser decreased 1.75 times when the resonator length was increased from 0.3 to 1.6 m (Fig. 2.29a)

(1). Heating the crystal from 10 to 90°C resulted in a linear decrease of the lasing energy of the examined laser by a factor of 1.2 (Fig. 2.29b)

(1). The maximum density of the lasing energy of the Nd:Cr:GSGG laser of 4.5 J/cm3 at a pumping energy of 300 J was obtained at a transmission factor of the output mirror of T2 = 96%, i.e. when the output mirror of the resonator was represented by a non-sprayed wedge-shaped substrate made of K-8 glass (Fig. 2.29c) (1). The transmission factor of the output mirror T2 was saturated to its maximum value of 96% already at a pumping energy of 100 J (Fig. 2.30a) (1). The dependence of the lasing energy of the Nd:Cr:GSGG laser on pumping energy was non-linear almost in the entire examined pumping energy range (Fig. 2.29d) (1). At a pumping energy of 500 J the density of the lasing energy of the Nd:Cr:GSGG laser was Eg/Vg = 4.8 J/cm3. At a constant resonator length and with the pumping energy changing from 100 to 500 J, the divergence of radiation of the Nd:Cr:GSGG laser was doubled (Fig. 2.30b) (1). Thus, the radiation luminosity of 6 107 W/cm2 ster was obtained in the examined laser.

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Solid-state neodymium lasers in free lasing regime

2.5 Nd-DOPED LANTHANUM BERYLLATE LASERS

The single crystals of lanthanum beryllate (La2Be2O5) are characterised by monoclinic symmetry. This results in a considerable anisotropy of the thermophysical and spectral–luminescence characteristics of these crystals. The heat conductivity coefficients of the Nd:BLN crystal at room temperature in the main axes are 4.6 (4.7 and 4.7) W/m deg. The refractive index of the BLN the crystal in the axes is: na = 1.96, nb = 1.99, nc = 2.03. Its coefficients of thermal expansion in the axes are 7.0 (7.9 and 9.5) 10–6 deg–1. The density of the Nd:BLN crystal is 6.06 g/cm3, the melting point of the Nd:BLN crystals is 1361°C.

The Nd ions in the La beryllate crystal (Nd:BLN) are characterised by a wide uniformly broadened gain line (3.4 nm) so that it is possible to change the wavelength of radiation in a relatively wide region of the spectrum.

The cross-section of the transition 4F3/2→ 4I11/2 at room temperature is 1.5 × 10 –19 cm2. The optimum concentration of the Nd ions in the

BLN crystal, resulting in the maximum intensity of luminescence, is 1.8%. At this concentration, the lifetime of the upper working level of the Nd ions is 110 µs. The technology of growth of these crystals has been sufficiently developed and active elements of standard dimensions are being grown.

Some integral parameters of free lasing have been investigated in lamp [50] and laser [51] pumping.

2.5.1 Spectral–time parameters of lasing

The spectral–time, spatial, angular and energy characteristics of radiation of lasers on Nd ions in crystals of La beryllate (La2Be2O5) were examined in detail by the authors of this work in [8, 10, 11, 13, 18, 19, 22–28].

With the optimum parameters of the flat resonator after eliminating the effect of technical perturbations of the resonator in the Nd: BLN laser it is possible to obtain stable quasistationary lasing of the TEMooq (Fig. 2.21b, c) and TEMmnq modes (Fig. 2.21d,e). The Nd: BLN crystals are inferior in their heat conductivity and homogeneity to the Nd: YAG crystals and, consequently, the quasistationary lasing of the TEMooq modes of the Nd:BLN laser is more sensitive to weak perturbations of the resonator and requires more careful adjustment of the elements of the resonator. In the absence of the selection of the longitudinal modes, a radiation spectrum 250 pm is excited in the first peak, and within several peaks its width decreases to the stationary value determined by the pumping level (Fig. 2.21c) [8]. When the pumping level is 10 times higher than its threshold volume, the stationary instantaneous with of the spectrum of lasing was 120 pm. The process of lasing was accompanied by the

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