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

Solid-state neodymium lasers in free lasing regime

The optimum concentration of the Nd ions in the Nd:YAG crystal is approximately 1%, which corresponds to the concentration of Nd ions

of 1.38 × 10 20 cm–3. The cross-section of the transition 4F3/2 → 4I11/2 (λ = 1064 nm) is 3.3 × 10 –19 cm2, the width of the gain line is

0.62 nm, and the lifetime of the upper working level is 250 µs [33]. The main absorption bands of the Nd ions in the YAG crystal correspond to the transition from the ground to the following levels: 4F3/2

(880 nm), (4F5/2 + 2H9/2)(810 nm), (4F7/2 + 4S3/4)(750 nm), (4G7/2 + 2G5/2) (580 nm) and (2K13/2 + 4G7/2 + 4G9/2) (520 nm). In the absence of dispersion elements in the resonator, the lasing of the Nd:YAG laser takes

place only on the transition 4F3/2 → 4I11/2(1064 nm), characterised by the maximum value of the cross-section of induced transition. The spectroscopic

and time characteristics of radiation of Nd:YAG lasers under different regimes have been examined quite extensively in Ref. 34.

2.3.1 Spectral–time parameters of free lasing in pulsed regime

The spectral–time, angular and energy characteristics of free lasing of Nd:YAG lasers have been investigated by the authors of this book in detail in Ref. 4,5,11,18,19,22–28.

The stable quasistationary lasing of TEMooq modes (Fig. 2.5) in a Nd:YAG laser with a flat resonator with the optimum parameters (length 2 m, the diameter of the diaphragms 2 mm) was achieved without forced smoothing of the longitudinal heterogeneity of the field in the crystal during the removal of the effect of technical perturbations of the resonator using the method described previously. Under normal conditions in the transition regime the relaxation pulsations of radiation intensity were regular with respect to the repetition frequency and slightly irregular with respect to amplitude (Fig. 2.5a). They became completely irregular (Fig. 2.6a) in forced smoothing of the longitudinal heterogeneity of the field in the garnet crystal by means of compensated phase modulation (CPM). The width of the instantaneous spectrum of the quasistationary lasing of the Nd:YAG laser in the normal conditions and with the pumping level considerably higher than the threshold level was 30 pm (Fig. 2.5c). The width remained almost completely constant during smoothing of the longitudinal heterogeneity of the field at inversion in the active medium (Fig. 2.6c), in contrast to the ruby laser in which the smoothing of the heterogeneity of inversion always leads to single-frequency quasistationary lasing of TEMooq modes (Fig. 1.6c) [4,5].

The experimental value of the instantaneous width of the lasing spectrum (∆λ g) is in relatively good agreement with the calculated value, obtained from the rate equations in the case in which the active medium with the length l completely fills the resonator (l/L = 1) [43]:

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Physics of Solid-State Lasers

where ∆λ is the width of the gain line; δλ q is the spectral range between the longitudinal modes; x = Ep/Et is the amount by which the pumping level exceeds the threshold value. In a general case in which l/L << 1, accurate analytical calculations of the width of the lasing spectrum are almost impossible because of the additional discrimination of the longitudinal waves which depends not only on the ratio l/L but also on the position of the active rod in the resonator.

In the quasistationary regime, it was relatively easy to obtain the singlefrequency lasing of the TEMooq modes (Fig. 2.5d) using the Fabry–Perot selector-etalon with a transmission band of of 25 pm (the base of the etalon 1 mm, the transmission coefficient of the mirrors 0.15).

In the Nd:YAG laser with flat mirrors in the same experimental conditions it was considerably easier to obtain the quasistationary lasing of the TEMmnq modes (Fig. 2.7) in a wide pumping range [4,5]. In this case, the values of the indices of the transverse modes must be low (m, n < 10). Consequently, the transition pulsations of the radiation intensity were irregular not only with respect to the amplitude but also the repetition frequency. This is associated with the alternation of the transverse modes (Fig. 2.7b and 2.8), with a different excitation volumes and, consequently, the gain and the duration of linear development of lasing. The width

Fig.2.5 Parameters of the lasing of TEMooq modes of Nd:YAG laser with flat mirrors (L = 2 m, diameter 2 mm) in normal conditions with elimination of the effect of technical interference of the resonator without selection of the longitudinal modes (a–c) and with selection (d), Ep = 20Et; a) oscillograms of radiation intensity, 20 µs marks; b) evolvement of the distribution of radiation intensity in the near-range zone; c) time evolvement of radiation spectrum, the region of dispersion of the interferometers 56 pm (c) and 20 pm (d).

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Solid-state neodymium lasers in free lasing regime

of the instantaneous spectral of quasistationary lasing (Fig. 2.7c) did not differ from the lasing spectrum of the longitudinal modes and reached saturation when the pumping was four times higher than the threshold level. Increase of the indices of the transverse waves, with a decrease of the resonator length, was accompanied by the alternation of the transverse modes during the entire lasing pulse, associated with the increase in the competition of the modes, as a result of the greater overlapping of their excitation volumes. At high pumping, this resulted in the appearance of a low-level of non-attenuating pulsations of radiation intensity with the retention of a high level of the constant component of the integral

Fig.2.6 Parameters of the lasing of TEMooq modes of the Nd:YAG laser with flat mirrors in smoothing the longitudinal heterogeneity of the field in the active medium using compensated phase modulation. The laser parameters are the same as those shown in Fig. 2.5.

Fig.2.7 Parameters of the lasing of TEMmnq modes of Nd:YAG laser (diameter 5 mm, length 100 mm) with flat mirrors (L = 2 m) in normal conditions with elimination of the effect of technical interference of the resonator without selection of the longitudinal modes (a–c) and with selection (d), Ep = 40Et; a) oscillograms of radiation intensity, 20 µs marks; b) evolvement of the distribution of radiation intensity in the nearrange zone; c) time evolvement of radiation spectrum, the region of dispersion of the interferometers 70 pm (c) and 20 pm (d).

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Fig.2.8 Time evolvement of the distribution of radiation intensity of TEMmnq modes of Nd:YAG laser in the near-range zone; Ep/Et = 1.5 (a), 2 (b), 4 (c) and 20 (d).

Fig.2.9 Dependence of the energy of one-particle lasing Eg (J) (1) and threshhold pumping Et (kJ) (2) of Nd:YAG laser (diameter 5 mm, length 50 mm) on the lasing wavelength λ (nm) in the dispersion resonator.

intensity of radiation. In the conditions of stable quasistationary regime of the Nd:YAG laser it was quite easy to ensure single-frequency lasing of the TEMmnq modes (Fig. 2.7d) when using a Fabry–Perot selectoretalon, with a transmission band of 25 pm. This was accompanied by a smooth change of the wavelength of radiation within the limits of the width of the gain line (Fig. 2.9).

In a non-selective resonator with a low level of pumping, lasing at

the 4F3/2 → 4I11/2 transition took place at a radiation wavelength of 1064 nm (transition between the Stark sublevels R2 → Y3). When the pumping

was four times higher than the threshold value, the second radiation line also reached lasing at a wavelength of 1061 nm (transition R1 → Y1), and the threshold of appearance of this lasing was almost completely independent of the temperature of the crystal.

The thermal drift of the gain line of the Nd:YAG crystal was measured from the displacement of the spectrum of quasistationary lasing during heating a crystal with pumping slightly higher than the threshold value

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Solid-state neodymium lasers in free lasing regime

Fig.2.10 a) Sequence of interferograms of the spectrum of quasi-stationary lasing of Nd:YAG laser at different temperatures of the crystal T = 10, 30, 40, 60, 70, 80 and 90 °C. The region of dispersion of the interferometer 570 nm, L = 2 m; b) dependence of the displacement of the lasing wavelength ∆λ (nm) on the temperature of active media of Nd lasers on crystals of YAG (4), GSGG:Cr (3) BLN (1), KGW (2).

(Ep ~ 2Et), Fig. 2.10. With completely removal of the spurious selection of the longitudinal modes, the centre of gravity of the spectrum of quasistationary lasing coincided, according to the measurements, with high accuracy with the maximum of the gain line. The measured main velocity of the thermal drift of the gain line on the interferograms of the radiation spectrum (Fig. 2.10a) in the examined temperature range reached the value dλ /dT = 4.3 pm/deg (Fig. 2.10b) [11], and its value was in excellent agreement with the value obtained in Ref. 44 in the analysis of luminescence spectra.

In a Nd:YAG laser with a spherical resonator of critical configuration, the lasing of TEMmnq modes also took place in the quasistationary regime. The width of the instantaneous spectrum of the quasistationary lasing decreased to 8 pm, as a result of smoothing of the spatial heterogeneity of the inversion, which basically determines the width of the spectrum. The centre of gravity of the radiation spectrum was displaced to the long-wave range with a mean speed of 20 pm/ms, indicating the heating of the garnet crystal by 3°C during the lasing pulse.

In the case of a smaller detuning of the setting of the resonator from the critical configuration there was alternation of both the transverse and longitudinal modes during lasing. When pumping was considerably higher than the threshold level, this process was accompanied by pulsations of integral radiation intensity.

2.3.2 Energy parameters of lasing in pulsed regime

Investigations were carried out on a crystal of yttrium–aluminium garnet with Nd (Nd:YAG) with the ends machined to the same angle, with

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illumination, diameter 6.3 mm, length 100 mm. The volume of the active medium, contributing to the lasing energy, was Vg = 2.5 cm3. The concentration of the Nd ions in the crystal was 1%. The crystal was selected from a large batch of crystals on the basis of optical and the thermo-optical homogeneity and, consequently, was capable of operation with continuous lamp pumping. Pumping in the pulsed regime was carried out using an IFP-800 lamp, with the pumping pulse time of 250 µs. Ultraviolet radiation was cut off with a liquid filter.

With decrease of the resonator length of a flat resonator from 0.3 to 1.6 m at constant pumping, the lasing energy of the Nd:YAG laser decreased by only a factor of 1.1 (Fig. 2.29a) (3). Heating of the garnet crystal in the temperature range from 10 to 90 °C resulted in a very small decrease of the lasing energy by a factor of 1.06 (Fig. 2.29b) (3). The maximum lasing energy of the Nd:YAG laser at a pumping energy of 300 J was obtained in a relatively wide range of the radiation of the transmission factor of the output mirror of the resonator from 30 to 70% (Fig. 2.29c) (3). At a high pumping energy, the values of the optimum transmission factor reached saturation at a factor of approximately 40% (Fig. 2.30a) (3). The lasing energy of the Nd:YAG laser depended in a linear manner on the pumping energy at low levels of this energy, and with increase of the pumping energy this linearity of the dependence was disrupted (Fig. 2.29d) (3). At a pumping energy of 500 J, the density of lasing energy of the Nd:YAG laser was Eg/Vg = 2.8 J/cm3. The divergence of radiation of the Nd:YAG laser with respect to a level of 0.1 at a pumping energy of 300 J was 1.2×10 –4 rad (Fig. 2.30b) (3), and the lasing energy was 5 J, radiation luminosity 5.3 × 10 8 W/cm2 ster.

2.3.3 Spectral–time and energy characteristics of lasing in continuous regime

From the large number of the active media, activated by the Nd ions, only the Nd:YAG crystals can operate efficiently during continuous lamp pumping. At the same time, the application of laser, especially diode pumping, makes it possible to achieve efficient lasing of the Nd lasers in the majority of active media. The parameters of the Nd:YAG laser in the continuous regime were investigated by the authors of this book in Ref. 6,7,11,14,27.

The presence of even weak spurious selection of the longitudinal modes, induced by the illuminated edges of the crystals, resulted in the formation of non-attenuating pulsations of radiation intensity, especially in the case of lasing of the TEMooq modes (Fig. 2.11a). In this case, the spectrum of stationary lasing widened to 12 pm (Fig. 2.11b). The complete elimination of the spurious selection of the longitudinal modes resulted in the stable stationary lasing without pulsations of radiation intensity (Fig. 2.11c),

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Solid-state neodymium lasers in free lasing regime

and the width of the radiation spectrum decrease to 5 pm (Fig. 2.11d). The simultaneous stationary lasing on several longitudinal modes was observed in this case.

In the case of lasing of TEMmnq modes and with pumping considerably higher than the threshold level, the radiation intensity depended only a very slightly on the effect of the spurious selection of the longitudinal modes. However, in this case also, the effect of external perturbations of the resonator on the nature of lasing was very strong (Fig. 2.12 a), and the width of the lasing spectrum increased to 30 pm (Fig. 2. 12b). With the elimination of external perturbations, lasing took place with a very low (≤ 1%) level of the residual pulsations of radiation intensity (Fig. 2.12c). The complete elimination of the spurious selection of the longitudinal modes increased the stability of the stationary regime in relation to external perturbations and the use the width of the lasing spectrum to 8 pm (Fig. 2.12d).

Fig.2.11 Parameters of lasing of TEMooq modes of a continuous neodymium laser (diameter 6.3 mm, length 100 mm) with flat mirrors (L = 0.3 m) in the presence of spurious selection of longitudinal modes (a,b) and its absence (c,d), Pp = 4Pt; a,c) oscillograms of radiation intensity, scale 100 µs/division, for better reading of the zero level of intensity radiation was modulated by an external modulator; b,d) interferograms of the lasing spectrum, the range of dispersion of the interferometer 20 pm.

Fig.2.12 Parameters of the lasing of TEMmnq modes of a continuous neodymium laser (diameter 6.3 mm, length 100 mm) with flat mirrors (L = 0.3 m) in the presence of spurious selection of longitudinal modes (a,b) and its absence (c,d), Pp = 4Pt; a,c) oscillograms of radiation intensity, scale 500 µs/division, b,d) interferograms of the lasing spectrum, the range of dispersion of the interferometer 56 pm.

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