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

Physics of Solid-State Lasers

Fig. 1.7 Oscillograms of intensity of radiation of TEMooq modes of a ruby laser with flat mirrors (L = 1.6 m, diameter1.4 mm) with application of CPM (a) in the lasing process and without CPM (b), the voltage of the modulating field on the CPM is supplied to the second beam of the oscilloscope; Ep = 2Et.

1.3.2 Single-frequency adjustable quasistationary lasing in a laser with flat mirrors

The efficiency of selection of longitudinal modes rapidly increases in the conditions of the quasistationary regime. At the same parameters of the selector as those shown in Fig. 1.4e, the application of the CPM after the transition process and establishment of the quasistationary regime resulted in the narrowing of the lasing spectrum to a single longitudinal mode and in stabilisation within the limits of the single inter-mode range (Fig. 1.6d).

The efficiency of selection of the longitudinal modes increased even further in smoothing of the longitudinal heterogeneity of the field in the active medium and the conditions of the passive negative feedback in which a KS-14 dimming filter (Fig 1.8d) was placed in the laser resonator under the Brewster angle. The time evolvement of the lasing spectrum (fig 1.8E), obtained at a high spectral resolution of the recording Fabry–Perot interferometer showed that in this case there was a periodic change of modes (with a period of ~40 µs), determined by retuning of the natural modes of the resonator as a result of the decrease of the length of the active rod due to its heating. The number of these transitions during the lasing pulse time can be evaluated using equation (1.1) from the following equation

A single longitudinal mode was generated in the period between the change of the modes, and its displacement in the spectrum during the lasing pulse time was of the order of one inter-mode interval [12],

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Solid-state chromium lasers in free lasing regime

Fig. 1.8 Parameters of the lasing of TEMooq modes of a ruby laser (PL2B 8×120/ 180 mm) with flat mirrors (L = 1.6 m, diameter 1.4 mm) with smoothing of the longitudinal heterogeneity of the field in ruby using CPM in the conditions of passive negative feedback, Ep = 3Et: a) oscillogram of radiation intensity, 20 µs markers; b) evolvement of the distribution of the radiation intensity in the long range zone; c-e) the time evolvement of the lasing spectrum without selection of longitudinal modes (c) and with selection (d,e), range of dispersion of the interferometers 12 pm (c), 8 pm (d) and 1.4 pm (e).

as clearly indicated by the interferogram of the integral spectrum of radiation (Fig. 1.9a). The rearrangement of the wavelength of the single-frequency radiation of a laser continuous ruby laser was obtained within the limits of the half width of the R1-line of amplification of the ruby (~ 0.5 nm) (Fig. 1.9b). The reproducibility of the wavelength of radiation from pulse to pulse was approximately 0.5 pm with stabilisation of the temperature of the ruby and the selector-standard in the range 1°C. Divergence of laser radiation was of the diffraction type (1.5 mrad), and radiation energy was 0.1 J.

Forced sweep of the wavelength in the process of ruby laser lasing was ensured using a Fabry–Perot scanning interferometer with the dispersion range 0.24 nm in the speed range 0.01–0.4 nm/ms. Radiation intensity was stabilised using the CPM and a passive negative feedback. At low speeds (≤ 15 pm/ms) the sweep of the wavelength took place in the quasistationary regime with the size of the spectral transition between the modes equal to 1 inter-mode interval (Fig. 1.10a).

With increasing sweep speed, the change of the modes during the lasing process was accompanied by peaks of radiation intensity whose amplitude depended on the band of the dispersion resonator. As the selectivity of the dispersion resonator increased, the sweep rate at which pulsations of radiation intensity formed during mode change decrease. In the case of high sweep speeds (≥ 0.2 nm/ms) the nature of lasing was determined mainly by the sweep process and the change of the modes during the lasing process was accompanied by 100% pulsations of radiation intensity (Fig. 1.10b, c); the spectral interval between the adjacent peaks increased to ∆λ qL/l, where ∆λ = λ 2/2L is the spectral interval between the adjacent longitudinal modes.

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Physics of Solid-State Lasers

1.3.3 Energy parameters of lasing

The energy characteristics of ruby laser radiation were investigated using a ruby crystal with a diameter of 5 mm, 75 mm long, with the ends bevelled under an angle of 1º, with the ends illuminated in a resonator with flat mirrors. Pumping was carried out using an ISP250 lamp in a quartz single-unit illuminator with a pumping pulse time of 250 µs. The volume of the active medium Vg, excited by the pumping lamp and providing a contribution to the lasing energy, was 0.78 cm3. Cooling of the crystal and the pumping lamp was carried out using distilled water whose temperature was maintained with a thermostat with an accuracy of 0.1°C.

For correct comparison of the energy characteristics of the radiation of Cr lasers in the examined solid-state media, all graphs of the dependences of the lasing energy on the parameters of the resonator and the active media are presented in Fig. 1.31. The main adequate parameter of comparison is the density of lasing energy Eg/Vg (J/cm3).

The density of the lasing energy of the ruby laser is halved with increase of the resonator length from 0.4 to 1.6 m (Fig. 1.33a) (1). It should be noted that the resonator length L = 1.6 m is optimum for chromium lasers with flat mirrors for obtaining quasistationary lasing during the removal of the spatial heterogeneity of the field in the active medium. During heating of a ruby crystal from 20 to 60°C, the density of the lasing energy of the ruby laser decreased six times (Fig. 1.33b) (1), and at a constant pumping energy of 0.5 kJ the lasing threshold increased so much that lasing was interrupted.

At a pumping energy of 0.5 kJ, the optimum transmission factor

Fig. 1.9 a) interferrogram of the integral lasing spectrum of TEMooq modes of a ruby laser with smoothing of the longitudinal heterogeneity of the field in ruby using CPM in the conditions of passive negative feedback and selection of longitudinal modes, the range of dispersion of the interferrometer 8 pm; b) sequence of interferrogramsof the radiation spectra of a ruby laser with change of the radiation wavelength, the range of dispersion of the interferrometer 770 pm.

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Solid-state chromium lasers in free lasing regime

Fig. 1.10 Parameters of lasing of TEMooq modes of a ruby laser in sweeping the wavelength in the lasing process in the conditions of smoothing the longitudinal heterogeneity of the field using CPM and passive negative feedback, Ep = 3Et; sweep right 15 (a), 150 (b) and 380 pm/ms (c).

of the output m of the resonator at which the maximum density of lasing energy was obtained (0.4 E/cm3) for a ruby laser was 40% (Fig. 1.33c) (1). In the examined range of the pumping energy, the density of the lasing energy of the ruby laser depended in a linear manner on pumping energy (Fig. 1.33d) (1).

1.3.4 Lasing parameters of TEMmnq modes in a laser with spherical mirrors

The nature of free lasing TEMmnq in a ruby laser with spherical mirrors with a non-critical configuration of the resonators (Fig. 1.11) differed only slightly from that of the lasing of a laser with flat mirrors: in both cases, there were nonregular non-attenuating pulsations of radiation intensity. Several transverse modes were excited in every lasing peak and the index of these modes was higher than in the laser with flat mirrors; these modes alternated during the lasing process (Fig. 1.11b). Lasing started with modes with a low transverse index which may have a higher attenuation coefficient as a result of the focusing of pumping energy on the axis of the rod. The first peak was characterised by the excitation of a large number of longitudinal modes with the width of the lasing spectrum of approximately 50 pm which decreased to 2.5 pm within several peaks (Fig. 1.11c); this is associated with the formation of a spatial heterogeneity of inversion in the active medium leading to the appearance of a large dispersion of the gain coefficient for different modes.

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Physics of Solid-State Lasers

During smoothing of of the spatial heterogeneity in the ruby crystal using compensated phase modulation and the same experimental conditions, the lasing always took place in the quasistationary regime with a wide and uncontrollable spectrum (Fig. 1.12) [5]. Lasing with identical parameters was also detected in lasers with spherical resonators of critical configuration (L = R, 2R) with the spatial heterogeneity of the field in the resonator self-smoothed, as a result of the excitation of a large number of degenerate modes with a high transverse index.

Modes with low transverse indices were excited at the beginning of the pulse. The threshold lasing conditions were at least one rapidly for these modes (Fig. 1.12b). When the conditions of excitation for the modes was high transverse indices were fulfilled the, the crosssection of the lasing region gradually increased, and at the end of the pumping pulse it slightly decrease with decrease in pulse. This time dependence of the transverse distribution of radiation intensity also resulted in the corresponding development of the lasing spectrum with time (Fig. 1.12c).

In the first half of lasing the maximum of the radiation spectrum drifted into the short-wave range, whereas in the second half it drifted into the long-wave range of the spectrum. The short-wave drift of the maximum of the radiation spectrum during the lasing process is possible because of two reasons. Firstly, because of the presence of the temperature gradient between the centre and edges of the active rod, the modes with a high transverse index are excited later than the modes with a low index, and their lasing starts at a lower mean temperature of the active medium. Consequently, the maximum of the effective gain curve and, the correspondingly, the maximum of the lasing spectrum were displaced to the short-wave range during lasing. Secondly, during lasing, the focus fT of the induced thermal positive lens in the ruby crystal decreases. Assuming that the crystal is situated in the centre of a confocal resonator and the lens is ideally thin, we obtained the following equation for the rate of variation of the lasing wavelength [10]:

For the modes with the indices m = n ~ 100, fT ~ 1 m, ∂ fT/∂ t ~ 1 m/ms, we have ∂λ /∂ t ~ –0.6 nm/ms, which greatly exceeds the thermal drift of the gain line to the long-wave region of the spectrum. It should

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Solid-state chromium lasers in free lasing regime

Fig. 1.11 Parameters of lasing of TEMmnq modes of a ruby laser (diameter 12 mm, length 120 mm) with spherical mirrors ???(R1 = R2 = 1 m, L = 0.6 m) in normal conditions and in the absence of mode selection, Ep = 3Et; a) oscillogram of radiation intensity, 20 µs markers; b) evolvement of the distribution of the intensity in the near-zone; c) time evolvement of lasing spectrum, the range of dispersion of the interferometer 24 pm.

be noted that in the case of quasistationary lasing of TEMmnq modes in a laser with spherical mirrors, the narrowing of the lasing spectrum did not take place to a single longitudinal mode as in the case of the quasistationary lasing of TEMooq modes, but it took place in the value determined by the broadening of the tip of the curve of the gain line determined by thermal gradients in the cross-section of the active rod.

The nature of lasing of the ruby laser with spherical mirrors and the direction of displacement of the maximum of the radiation spectrum depend greatly on the cross-section of the active rod taking part in lasing. At a ruby diameter of ≥ 12 mm, the maximum of the radiation spectrum was displaced to the short-wave range throughout the entire lasing pulse (Fig.1.13a). With a decrease of the cross-section of the excitation range of the ruby to 8 mm using two diaphragms, located in the vicinity of the edges of the ruby crystal, the rate of shortwave displacement of the lasing spectrum decreased (Fig. 1.13b). At a diaphragm diameter of 6 mm, the speed of the thermal drift of the gain line exceeded the influence of the effects leading to the shortwave displacement of the maximum of the lasing spectrum (Fig. 1.13c). With a decrease of the aperture of the resonator to 4 mm quasistationary lasing was not achieved even when using compensated phase modulation (Fig. 1.13d) because in this case only transverse modes with low transverse indices were excited and the transverse heterogeneity of the field in the active medium could not be eliminated even using the CPM [10].

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Physics of Solid-State Lasers

Fig. 1.12 Parameters of the lasing of TEMmnq modes of a ruby laser with spherical mirrors in smoothing of the spatial heterogeneity of the field in ruby using CPM. Laser parameters are the same as those in Fig. 1.11.

Fig. 1.13 Time evolvement of the lasing spectrum of TEMmnq modes of a ruby laser (diameter 12 mm, length 120 mm) with CPM with spherical mirrors (R12 = R2 = 1 m, L = 0.6 m) without diaphragm (a) and with two diaphragms in the resonator, diameter 8 mm (b), 6 (c) and 4 mm (d). The range of dispersion of the interferrometer 24 pm; Ep = 3Et.

The inertia of the lasing regime

In contrast to the case of lasing of a laser with flat mirrors where the interaction of the CPM during the lasing process resulted immediately in the transition from the quasistationary regime to the regime of non-attenuating pulsations of radiation intensity (Fig. 1.7b), in the laser with spherical mirrors even short-term smoothing of the spatial heterogeneity of the field at the start of the pulse caused quasistationary lasing after the end of the pulse (Fig. 1.14a) [8]. This switching of the conditions can be carried out at any moment of lasing (Fig. 1.14b).

The reproducibility of this ‘inertia of the regime’ was 100% in the range of variation of the radius of curvature of the mirrors and the length of the resonator from the minimum possible to 1.5 mm, excluding unstable and critical configurations of the resonator [13]. In this range of variation of the resonator parameters, the quasistationary

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