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

Solid-state chromium lasers in free lasing regime

Fig. 1.14 Oscillograms of the intensity of radiation of TEMmnq modes of a ruby laser (diameter 12 mm, length 120 mm) with spherical mirrors (L = 0.7 m, R1 = R2 = 1 m (a-d) and 1.8 m (e) and without CPM lasing; Ep = 3Et.

lasing regime was resistant to relatively strong external perturbations. When inversion in the ruby crystal was eliminated using a gigantic pulse with a power of 10 MW from another laser, its effect was followed by the formation of relaxation radiation pulses which rapidly attenuated to the stationary level (Fig. 1.14c). Only in the case in which the lasing was artificially interrupted using an electro-optical gate for a period of ~ 20 µs, sufficient for the attenuation of the fields of the generating modes, there was a reverse transition from the quasistationary regime to the regime of non-attenuating pulsations of radiation (Fig. 1.40d). With an increase of the radius of curvature of the mirrors to R > 1.5 m, a similar transition was observed spontaneously at any moment of time after switching off the CPM (Fig. 1.14 e), and in the limiting case of the flat mirrors this switching off the regimes took place simultaneously with the disconnection of

the CPM.

The spectrum inertia regime

In lasers with spherical mirrors it is almost impossible to carry out the forced selection of longitudinal modes. However, in a ruby laser with spherical mirrors with strong degeneration of the modes under

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specific conditions there may be a spontaneous effect of stabilisation of the radiation wavelength (‘inertia of the spectrum’) [13]. In this case, in the absence of external and spurious selection of the longitudinal waves a very narrow (~ 0.05 pm) and stable (with respect to spectrum and time) radiation line generates (Fig. 1.15 and 1.16). This effect is achieved in the conditions of the thermal drift of the gain line of the order of 30 pm, the thermal rearrangement of the natural modes of the resonator (~5 pm) and the thermal broadening of the tip of the curve of the gain line (~10 pm). The stable regime of inertia of the spectrum is established when the threshold conditions are fulfilled only for the modes with a high transverse index (m, n > 100), and the degree of degeneration of the modes is sufficient for the longterm alternation of the modes in lasing without any change of the radiation wavelength. The reproducibility of the inertia regime of the spectrum increased during an artificial decrease of the Q-factor of the modes with the low transverse index. This is achieved by overlapping the centre of the ruby crystal by a non-transparent screen with a diameter of ~1 mm.

Depending on experimental conditions, spectrum inertia was obtained in both peak (Fig. 1.15) and quasi-continuous (Fig. 1.16) regimes, in the range of radiation of the radius of curvature of the mirrors 20 ≤ R ≤ 110 cm and the resonator length 30 ≤ L ≤ 100 cm. In the quasistationary regime, spectrum inertia was achieved at considerable de-tuning of the mirrors of the resonator with respect to the angle (~ 30') which resulted in the appearance of a small transverse ‘running’ of the field, increasing the intensity of the parametrically scattered radiation priming. The latter decreases the time of the linear development of the radiation peaks to such an extent that the pulsations of the radiation intensity overlap in time (Fig. 1.16c).

Fig. 1.15 Parameters of the lasing of TEMmnq modes of a ruby laser (diameter 12 mm, length 120 mm) with spherical mirrors (R1 = R2 = 0.5 m, L = 0.4 m) in the regime of ‘inertia of the spectrum’, Ep = 3Et; a) oscillogram of intensity, 20 µs markers; b) evolvement of the distribution of intensity of radiation in the near-zone; c) time evolvement of lasing spectra, the range of dispersion of the interferometer 24 pm.

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Solid-state chromium lasers in free lasing regime

Fig. 1.16 Parameters of the lasing of TEMmnq modes in a ruby laser (diameter 12 mm, length 120 mm) with spherical mirrors (R1 = R2 = 1.1 m, L = 0.9 m) in the regime of "inertia of the spectra" with a high constant component of the integral intensity of radiation, Ep = 3Et: a) oscillogram of radiation intensity, 20 µs marker; b) time evolvement of the lasing spectrum, the range of dispersion of the interferrometer 24 pm; c) the fragment of the time evolvement of the distribution of intensity of radiation in the near zone, obtained with high spatial and time resolution.

The simultaneous excitation of the modes with a high transverse index and the establishment of quasistationary lasing are prevented by the spatial heterogeneity of the inversion developed by the modes with low transverse indices at the beginning of lasing (Fig. 1.15b). After establishment of the spectrum inertia regime a single transfer mode with a high index was generated in every peak, as clearly indicated by the time evolvement of the spatial distribution of the radiation intensity in the near zone (Fig. 1.15b and Fig. 1.16c) on the basis of the presence of the distinctive structure of the field. Numerical estimates indicates that after lasing of some mode, the effective gain coefficient with the spatial heterogeneity of inversion taken into account will be maximum for the mode whose frequency is close to or identical with the frequency of the generated mode. The lasing in the subsequent peak starts to develop not from the level of spontaneous noise but from the intensity of priming radiation, formed by the generated mode with its parametric scattering on the spatial heterogeneity of inversion. According to the estimates, the intensity of the priming is several orders of magnitude higher than the intensity of spontaneous noise.

In cases in which the spatial heterogeneity of inversion was smoothed out using compensated phase modulation with some delay from the start of lasing, there was always a transition in the lasing process from the regime of spectrum inertia to the quasistationary lasing with a wide spectrum drifting in time. With complete removal of the selection of the longitudinal modes in which the ends of the ruby crystal were

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Physics of Solid-State Lasers

cut under the Brewster angle, the moment of establishment of the regime of spectrum inertia was extended by approximately ~100 µs in relation to the start of lasing. The decrease of the indices of the transverse modes by means of a diaphragm resulted in jumps of the radiation wavelength during the lasing process as a result of a decrease of the number of generated transverse waves with the same radiation frequency.

The rearrangement of the wavelength of single-frequency radiation within the limits of the maximum of the curve of the gain line in the regime of spectrum inertia was carried out by angular rotation of one of the mirrors of the resonator. In the case of a ruby crystal with a diameter of 12 mm and 120 mm long, when the pumping was three times higher than the laser threshold value, the energy of singlefrequency radiation was 5 J.

1.4 ALEXANDRITE LASERS

The lasing of trivalent chromium ions in a chryzoberyll crystal

crystal, part of the Al3+ ions is isomorphously substituted by Cr3+ ions. Alexandrite is characterised by high heat conductivity (23 W/m deg) which is still only half the heat conductivity of the ruby crystal, and the optical resistance to radiation of alexandrite is not inferior to that of the ruby crystal. Alexandrite is a biaxial crystal with a rhombic structure and its refractive index in the individual axes is: na = 1.796, nb = 1.738 and nc = 1.746. The Moose hardness is 8.5, density 3.7 g/cm4. The coefficients of thermal expansion of alexandrite are 7.0 (7.9; 9.5)×10 –6 deg–1, and the thermo-optical constant is dn/dT = 9.4 (8.3)×10 –6 deg–1. The melting point of alexandrite is 1870°C, and the crystal is characterised by isotropic expansion with increasing temperature. A wider application of the alexandrite crystal is prevented by both the toxicity of beryllium (i.e. the component of alexandrite) and by the relatively complicated technology of crystal growth.

The excited state of alexandrite is represented by a superposition of two states of the chromium ions 2E and 4T2 (Fig. 1.17), with the relaxation time between them being 10–11 s. The energy range between these states is ∆ E ~ 800 cm–1, which is almost four times higher than the value of kT at room temperature (208 cm–1), resulting in the thermal instability of the energy characteristics of radiation. The transition cross-section increases from 0.7×10 –20 at 300 K to 2×10 –20 cm–2 at T = 470 K. The transition from the level 2E to the ground state 4A2 is forbidden in respect of spin and consequently, the lifetime is long,

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Solid-state chromium lasers in free lasing regime

Fig. 1.17 Diagram of energy levels E (eV) of chromium ions Cr3+ in chryzoberyll (aleksandrite).

1.54 ms. The relatively short-lived state 4T2, with the transition from the state being forbidden as intra-configuration, but permitted with respect to spin, has a lifetime of 6.6 µs. Therefore, the effective lifetime of the total upper laser level (2E, 4T2), determined by the relationship

is 300 µs. Here W1 and W2 are the rates of deactivation of the states 2E and 4T2, respectively. In optical pumping, the excited ions buildup on the metastable level 2E and are transferred, as a result of thermal excitation, through the energy gap ∆ E to the level 4T2, and the population of the state 4T2 is only ~5% of the population of the level 2E. A relatively high gain factor on the upper laser level in the alexandrite crystal

lasing, Q-factor modulation and mode synchronization, in pulsed, pulsedperiodic and continuous regimes.

1.4.1 Spectral–time lasing parameters

The spectral–time, spatial and energy characteristics of free lasing of alexandrite lasers have been investigated by the authors of the book

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in [15,16,18–29]. Free lasing of TEMooq (Fig. 1.18) and TEMmnq (Fig. 1.19) modes in an alexandrite laser with flat mirrors under normal conditions and with the elimination of the effect of technical perturbations of the resonator, as in the case of the ruby laser, took place in the regime of non-attenuating pulsations of radiation intensity.

The nature of development of the lasing spectrum with time depends on the physical state of alexandrite crystals, on the temperature and the existence of discrimination of modes in the resonator. In the case of separation of TEMooq modes the width of the instantaneous lasing spectrum decreased in individual peaks to ~1 nm (Fig. 1.18c) [50], but the width of the integral radiation spectrum did not differ from the lasing spectrum of TEMmnq modes.

In long-term operation of alexandrite in the conditions of incomplete cut-off of ultraviolet radiation the lasing threshold at a radiation wavelength of 734 nm increased and with time the lasing on this wavelength completely disappeared even at low temperatures (~10°C) of the crystals and high pumping levels (Fig. 1.19a). The lasing on this wavelength did not appear also in the case of non-irradiated crystal at a crystal temperature of ≥ 70°C (Fig. 1.19e). In the case of the low discrimination of the longitudinal waves, introduced by the illuminated ends of the crystals, the radiation spectrum contained a fine discrete structure (Fig. 1.19b), which disappeared after complete removal of the spurious selection of longitudinal waves when the ends of the crystals were cut under the Brewster angle (Fig. 1.19c-e). Only in this case the lasing spectrum showed clearly the vibrational structure (Fig. 1.22). In this case, the duration of the peaks of free lasing increased

Fig. 1.18 Parameters of lasing of TEMooq of a Aleksandrite laser (5 mm diameter, 80 mm long) with flat mirrors in the absence of longitudinal mode selection, EpI = 5Et; a) oscillogram of the intensity, 50 µs/div; b) evolvement of the distribution of radation in the near-zone; c) time evolvement of the spectrum.

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Solid-state chromium lasers in free lasing regime

Fig. 1.19 Time evolvement of the lasing spectrum of TEMmnq modes of an aleksandrite laser with different crystals with flat mirrors in the absence of longitudinal mode selection (c-e) and with longitudinal mode selection (f), in the conditions of weak spurious selection of modes (b). The temperature of aleksandrite crystals T = 10 (a-d) and 70 °C (e,f), L = 1.5 m, Ep = 8Et.

(Fig. 1.19c-e). The distance between the components of the vibrational structure of the spectrum was 1.5 nm and did not depend on the temperature of the alexandrite crystal [18,20].

The application of a prism dispersion resonator with an angular dispersion of ~3 angular min/nm made it possible to stabilise the lasing spectrum, reduced its width to ~1 nm (Fig. 1.19f) and rearrange the radiation wavelength in the range 700–800 nm (Fig. 1.20).

In the conditions with a low spurious selection of the longitudinal modes, the integral radiation spectrum contained a fine discrete structure of the radiation spectrum (Fig. 1.21). With the completely spurious selection of the modes where the ends of the alexandrite crystals were cut under the Brewster angle, the fine structure of the spectrum disappeared and the integral radiation spectrum showed clearly the vibrational structure of the spectrum, Fig. 1.22. With increase of the pumping energy, the width of the integral radiation spectrum increased and when the pumping energy was eight times higher than the threshold value, its width was ~40 nm (Fig. 1.21a). During heating of the alexandrite crystal the short-wave components in the radiation spectrum

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