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

Physics of Solid-State Lasers

Fig. 1.20 a) sequence of spectrograms of the integral spectrum of lasing of TEMmnq modes of an aleksandrite laser (diameter 4 mm, length 70 mm) with flat mirrors (L = 1.6 m) illustrating the diagram of tuning the radiation wavelength, Ep = 8Et; b) dependence of the lasing energy Eg (J) (1) and threshhold pumping energy Et (J)

(2) of an aleksandrite laser in a dispersion resonator on the wavelength of radiation λ (nm).

gradually disappeared and at a temperature of approximately 70°C lasing took place only in the vicinity of the wavelength of 750 nm (Fig. 1.21b). In the absence of spurious selection of the longitudinal waves, the maximum of the concentration of radiation energy after this wavelength was displaced to the short-wave region of the spectrum with increasing pumping energy, Fig. 1.22b.

In the temperature range of the alexandrite crystal of 10–50°C, the mean speed of the thermal drift of the gain line was 0.01 nm/ deg. The speed rapidly increased to 0.13 nm/deg at temperatures higher than 50°C (Fig. 1.23) [18, 20]. This displacement of the lasing spectrum of the laser on electronic–vibrational transitions is associated with the dependence of the gain factor α (ω ) of the active media on temperature:

where σ is the radiation cross-section of the induced transition; n* is the number of excited chromium ions of the level 4T2; no is the number of chromium ions in the ground state 4A2; ω o is the frequency of the effective phonon-less transition.

1.4.2 Energy parameters of lasing

Figure 1.33 shows the dependences for the lasing energy density of the alexandrite laser with a diameter of 5.5 mm × 80 mm, with the ends under the Brewster angle and Vg = 1.42 cm3. Pumping of the crystal was carried out using IPF-800 lamp with a pumping pulse

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Solid-state chromium lasers in free lasing regime

Fig. 1.21 Spectrograms of radiation of TEMmnq modes of an aleksandrite laser (5 mm diameter, length 70 mm) with flat mirrors (L = 0.4 m) with slight spurious selection of the longitudinal mode: a) at a constant temperature of the crystal (T = 10 °C) and different pumping energies Ep = 2, 4, 5, 6 and 8Et; b) at a constant pumping energy (Ep = 8Et) and different temperatures of the crystal T = 15, 25, 35 and 45 °C.

Fig. 1.22 Spectrograms of radiation of TEMmnq modes of an aleksandrite laser (diameter 5.5 mm, length 80 mm) with flat mirrors (L = 1.5 m) with complete exclusion of spurious selection of longitudinal modes: a) at a constant temperature of the crystal (T = 10 °C) and different pumping energies Ep = 2, 4, 5, 6 and 8Et; b) at a crystal temperature of T = 70 °C and pumping energies of Ep = 3, 4, 5, 6, 7, and 8Et.

time of 250 µs in the experimental equipment described previously. The short-wave pumping radiation (≤ 300 nm) was cut-off by a liquid filter.

Increase of the resonator length from 0.4 to 1.6 m with other resonator and pumping parameters constant resulted in a decrease of the density of lasing energy of the alexandrite laser by a factor of 4 (Fig. 1.33a)

(2) [18,20]. At a constant pumping energy and with heating of the crystal from 10 to 90°C, the density of the lasing energy of the alexandrite laser increased three times (Fig. 1.33b) (2) [18]. At a pumping energy of 0.5 kJ, the optimum transmission factor of the output mirror of the alexandrite laser resonator was 25% (Fig. 1.33c) (2) and the density

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Physics of Solid-State Lasers

Fig. 1.23 a) spectrograms of the integral spectrum of the lasing of TEMmnq modes of an aleksandrite laser (diameter 5.5 mm, length 80 mm) with flat mirrors (L = 1.6 m) without spurious selection of longitudinal modes, with constant pumping energy (Ep–3Et ) and different crystal temperatures T = 15, 30, 45, 75, 85 and 15 °C; b) dependence of the position of the maximum of the lasing spectrum of TEMmnq modes of an aleksandrite laser at wavelength λ = 750 nm on crystal temperature

T.

of lasing energy was Eg/Vg = 1.5 J/cm3. The density of lasing energy of the alexandrite laser depended in a linear manner on the pumping energy at low values of this energy (Fig. 1.33d) (2). Increasing pumping energy (≥ 0.4 kJ) resulted in a deviation from the linear dependence associated with the increase of the fraction of the energy of the pumping pulse, radiating in the ultraviolet region of the spectrum, which was cut-off by the liquid filter [18].

1.5 EMERALD LASERS

The lasing of trivalent chromium ions in an emerald crystal at the electronic–vibrational transitions 4T2 → 4A2 was examined for the first time in Ref. 35. The adjustable lasing of the laser on an emerald crystal at the transition 4T2 → 4A2 during laser pumping was investigated in Ref. 52–54, and of R-lines of chromium ions in Ref. 54, 55. The energy characteristics of lasing of an emerald laser, with the crystal grown by the flux method, with valve pumping, was investigated in Ref. 56.

The emerald crystal (Cr3+:Be3Al2(SiO3)6) is a chromium beryll, uniaxial, negative, has refractive indices no = 1.58 and ne = 1.575. With a chromium ions concentration of 0.01–1%, the crystal is green. Its melting point is 1470 °C which is 400 degrees lower than the melting point of the alexandrite crystal. The heat conductivity of the emerald crystal is almost six times lower than that of alexandrite and equals 4 W/m grad, and the thermal expansion coefficient is 2.6(2.9)×

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Solid-state chromium lasers in free lasing regime

10–6 deg–1. The Moose hardness of the emerald crystal is 8.0, density 2.68 g/cm3. The emerald crystals are grown by two methods: hydrothermal and flux. The emerald crystals grown by the flux method have better optical quality and contain a smaller content of secondary impurities. Non-selective losses of the emerald crystals, grown by the hydrothermal methods, are of the order of 0.1 cm–1.

Lasing of the electronic–vibrational transitions 4T2 → 4A2 in the emerald crystal takes place in the wavelength range 700–850 nm. The energy gap in the levels 4T2 and 2E of the chromium ions in the crystal is 400 cm–1, which is half the value in the alexandrite crystal. At room temperature, the lifetime of the excited state of the chromium ion in the beryll crystal is 65 µs, and the transition cross-section is σ = 3.3 × 10 –20 cm2. The optical absorption spectra of the emerald crystal (Fig. 1.24) are typical of the matrixes containing the Cr3+ ions in the octahedral environment of the oxygen ions. The wide bands in the blue and red regions (Y,U) of the spectrum belong to the permitted transitions 4A2 → 4T1, 4T2 respectively. The triplet levels in the emerald crystal are split by the trigonal component of the crystal field leading to differences of the π and σ components in absorption. The narrow absorption lines at 681 and 684 nm are associated with the transitions 4A2 → 2E (R1 and R2-lines) forbidden with respect to spin. The fine structure of the U line is determined by the electronphonon interaction. The emerald crystal is characterised by a more complicated structure and, as indicated by the position of the U band, by a weaker crystal field Dq = 1600 cm–1 (for alexandrite Dq = 7040 cm–1).

In the emerald crystals, strong ultraviolet absorption starts at shorter wavelengths than in the case of the alexandrite, in the range 300 nm for the crystals prepared by the flux method and 360 nm in the crystals prepared by the hydrothermal method; in the latter case, additional bands exist in the range 380–450 nm. The short-wave absorption of emerald is determined mainly by secondary impurities, especially iron, whose concentration reaches 0.001 wt% in the flux specimens and 0.1 wt% in the hydrothermal specimens.

The luminescence spectra of the chromium ions in the emerald crystal (Fig. 1.25) are characterised by the dominance of a wide band with the maximum at a wavelength of 770 nm, corresponding to the

4T2 → 4A2 transition.

The intensity of the R1 and R2 lines in the emerald crystal is lower. This associated with the lower energy gap ∆ E between the levels 2E and 4T2. In the emerald crystal, these levels are close to the thermal equilibrium (kT = 208 cm–1) already at room temperature, and the metastable level 2E is sufficiently clear through the short-life level

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Physics of Solid-State Lasers

Fig. 1.24 Dependence of the absorption coefficients α (cm–1) (1,2) and the quantum yield of luminesence η on the wavelength λ (µm) for flux (a) and hydrothermal (b) emerald at T = 300 K, 1) E || C, 2) E C.

4T2. In alexandrite as a result of a higher value of ∆ E = 800 cm–1, this takes place at higher temperatures.

The absolute quantum yield of the luminescence of the chromium ions in the emerald crystal is 0.7 for the crystal produced by the flux method, and approximately 0.01 for the crystal produced by the hydrothermal methods. The constant quantum yield in the range of absorption of chromium ions and its decrease in the range smaller than 380 nm indicated that the short-wave absorption, observed in the crystals, is associated with the chromium ions.

Difficulties in producing the emerald crystals with the dimensions standard for the lasers are associated with the very low growth rate of the crystals which is an order of magnitude lower than the growth rate of the alexandrite crystals, and the toxicity of the component, i.e. beryllium, prevents the extensive application of the emerald lasers

1.5.1 Spectral–time parameters of lasing

The spectral and energy parameters of lasing of the emerald laser were investigated by the authors of this book in Ref. 30. The lasing spectrum TEMmnq of the emerald laser (Fig. 1.26) is almost identical with the similar lasing spectra of the alexandrite laser. In the presence of even weak spurious selection of the longitudinal modes, introduced by the ends of the crystal, the lasing spectra of the emerald laser,

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Solid-state chromium lasers in free lasing regime

Fig. 1.25 Dependence of the intentsity of luminesence I (rel.units) of the emerald crystal on the wavelength λ (µm) at T = 300 K, 1) E || C, 2) E C.

Fig. 1.26 Spectrograms of radiation of TEMmnq modes of an emerald laser at T = 20 °C in relation to pumping energy Ep = 3, 4, 6, 8Et.

like the lasing spectra of the alexandrite laser, are characterised by a fine discrete structure. At room temperature and low pumping levels, the lasing of the emerald laser takes place in a wide spectrum range with the maximum wavelength of 770 nm. With increase of the pumping energy the lasing spectrum was broadened into the short-wave range, and when the pumping energy was eight times higher than the threshold energy, the width of the lasing spectrum of the emerald laser was approximately 30 nm. The width of the lasing spectrum depended in a linear manner on the pumping energy.

The rearrangement of the wavelength of lasing of the emerald laser was carried out in a dispersion resonator using three dispersion prisms produced from TF-5 glass with a general angular dispersion of the order of 3 ang.min/nm. The wavelength of lasing was rearranged in the range 710–830 nm, with the stabilisation of the wavelength of radiation in the range ~1 nm.

Experiments shows that the lasing of the TEMooq and TEMmmq modes in the emerald laser, like the all other active media with the chromium

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Physics of Solid-State Lasers

ions, always took place in the energy of non-attenuating pulsations of the radiation intensity. The nature of development of the lasing spectrum with time for the emerald laser depended, as in the case of the alexandrite laser, on the physical state of the emerald crystals and the presence of spurious discrimination of the longitudinal modes in the laser resonator. In the conditions with incomplete cut-off of ultraviolet pumping radiation, the nature of development of the lasing spectrum of the emerald laser with time changed greatly.

1.5.2 Energy parameters of lasing

The investigations were carried out on an emerald crystal with a diameter of 3 mm, 35 mm long, the volume Vg = 0.21 cm3, groaned by the flux method with the concentration of chromium ions of the 0.7 wt%. The ends of the crystal are cut under an angle of 1º. Pumping was carried out with an ISP-250 lamp in a quartz single-unit illuminator with the pumping pulse time of 250 µs. Ultraviolet radiation was cut-off with a liquid filter.

Figure 1.33 shows the dependence of the density of lasing energy Eg/Vg (J/cm3) of an emerald crystal laser (5) on the parameters of the resonator and crystal temperature. The heat conductivity of the emerald crystal is considerably lower than the heat conductivity of the alexandrite crystal and this resulted in a stronger dependence of the energy of lasing of the emerald laser on the length of the resonator (Fig. 1.33a) (5). In contrast to the alexandrite laser, the emerald laser did not show any distinctive dependence of the lasing energy on the temperature of the active medium (Fig. 1.33b) (5). This was caused by the fact that the energy gap between the metastable level 2E and the upper working level 4T2 of the chromium ions in the emerald laser is considerably smaller and its effective population already takes place at room temperature. At a pumping energy of 0.5 J, the maximum lasing energy in the emerald laser is obtained at the maximum transmission factor of the output mirror of the resonator being 40% (Fig. 1.33c) (5). The threshold energy of pumping in the emerald laser was considerably lower than in the alexandrite laser in the entire range of radiation coefficients T2. At the optimum transmission factor of the output power, the lasing energy of the emerald laser increased in a linear manner in the range of low pumping energies (Fig. 1.33d) (5), and at higher pumping energies the linear dependence was disrupted.

1.6 CHROMIUM LASERS IN RARE-EARTH–GALLIUM GARNETS

Depending on the strength of the crystal field of the active medium, the energy position of the level 4T2 of the chromium ion Cr3+ changes

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Solid-state chromium lasers in free lasing regime

greatly, whereas the position of the level 2E remains almost constant. To obtain a small difference in the energy ∆ E between the levels 4T2 and 2E, the strength of the crystal field should be ~1500 cm–1. Decrease of the energy ∆ E increases the population of the level 4T2 and the lasing efficiency. This condition in satisfied by the crystals of rare earth–gallium garnets (REGG) [36, 37] in which the ions Cr3+ are in a weaker crystal field in comparison with the alexandrite and aluminium garnets. This is associated with the higher value of the lattice constant in the case of the REGG.

The REGG crystals are characterised by higher isomorphous capacity, have higher technological properties, the lower melting point, and do not contain toxic components, like alexandrite or emerald. The general formula of the gallium garnets A3B2B3O12 makes it possible to change in a wide range the chemical composition and produce a laser matrix with the required spectral characteristics. The similarity of the ion radii of Ga3+ and Cr3+ makes it possible to add large numbers of the chromium ions to the gallium garnets. The lasing of the chromium ions in the REGG crystals, like in the chryzoberyll, takes place at the electronic–vibrational transitions 4T2 → 4A2, so that it is possible to carry out rearrangement of the lasing wavelength of these crystals in the range 700–900 nm.

Important shortcomings of the gallium garments, which inhibit their extensive applications, are: 1. low heat conductivity which in the case of R4 valve pumping resulted in high deformation of the resonator and the losses of radiation energy; 2. susceptibility to the formation of stable dye centres even in pumping with the radiation of the visible range with absorption on the lasing wavelength. This also results in large losses of radiation energy and in instability of this energy during operation. In contrast to dynamic dye centres, the stable dye centres the breakdown only after a high temperature of the crystals. This requires regular annealing of the crystals in a high-temperature furnace.

1.6.1 Spectral–time parameters of lasing

The spectral–time and energy characteristics of the free lasing of chromium lasers on the crystals of REGG have been investigated by the authors of this book in Ref. 17, 19, 20, 21–29.

The free lasing of the chromium ions in REGG crystals in lasers with flat mirrors under normal conditions was also observed in the regime of non-attenuating pulsations of radiation intensity, as in lasers based on ruby and alexandrite. Figure 1.27 shows the typical parameters of the free lasing of a Cr laser in a crystal of the gadolinium- scandium–gallium garnet (Cr3+:GSGG). In the absence of the selection of longitudinal modes, the vibrational structure of the spectrum was

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