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Numerical simulation of regenerative amplification of nanosecond pulses in a CO2 laser

This content has been downloaded from IOPscience. Please scroll down to see the full text. 1982 Sov. J. Quantum Electron. 12 526 (http://iopscience.iop.org/0049-1748/12/4/L42) View the table of contents for this issue, or go to the journal homepage for more

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his interest and encouragement and to A. A. Abdullaev for his help in the experiments. *V. I. Kozlovskii, A. S. Naslbov, A. N. Pechenov, and Yu. M. Popov, Kvantovaya Elektron. (Moscow) 6, 189 (1979) [Sov. J. Quantum Electron. 9, 104 (1979)]. 2 A. Kh. Abduev, A. D. Adukov, and Β. Μ. Ataev, Abstracts of Papers presented at Tenth AU-Unlon Conf. on Nonlinear and

Coherent Optics, Kiev, 1980 [in Russian], Part 2, p. 275. V. G. Lysenko, V. I. Revenko, T. G. Tratas, and V. B. Timofeev, Zh. Eksp. Teor. Fiz. 68, 335 (1975) [Sov. Phys. JETP 41, 163 (1975)]. 4 M. S. Brodin, N. V. Volovik, V. Ya. Reznichenko, and M. I. Strashnikova, Fiz. Tverd. Tela (Leningrad) 23, 1318 (1981) [Sov. Phys. Solid State 23, 771 (1981)]. 3

Translated by A. Tybulewicz

Numerical simulation of regenerative amplification of nanosecond pulses in a CO2 laser V. V. Apollonov, F. V. Bunkin, V. R. Sorochenko, K. N. Firsov, and Yu. A. Shakir P. N. Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow (Submitted August 12,1981) Kvantovaya Elektron. (Moscow) 9, 832-835 (April 1982) The results are given of a numerical simulation of regenerative amplification of nanosecond pulses in a highpower electric-discharge CO2 laser. The finite contrast of the injected pulse is allowed for in a determination of the ranges of the injection energy and time in which regenerative amplification can be expected. It is shown that the shape of a small-signal pulse has a considerable influence on the energy and contrast of the output pulse. The optimal combinations of the parameters of a regenerative amplification system are determined so as to maximize the energy and contrast of nanosecond pulses. PACS numbers: 42.55.Dk One of the ways of generating high-power nanosecond COj laser pulses is regenerative amplification.1"4 In the process of such amplification a small-signal pulse injected into a laser resonator near the lasing threshold makes it possible to control the nature of the output radiation, which is a train of pulses of total energy equal to the free oscillation energy of the laser. Regenerative amplification makes it possible to concentrate in a single nanosecond pulse a considerable proportion of the free-lasing energy of the laser for any aperture of the beam. Therefore, high-power pulses can be generated in active media which are considerably shorter than in the traditional system comprising a master oscillator and a multistage amplifier. Inclusion in the regenerative amplification system, first applied to a COj laser in Ref. 1, of a saturable absorber made of SF 6 and of a GE plate with modulated transmission 3 · 4 has made it possible to generate single pulses of energy representing 12% of the free-lasing energy (in the case of additional double-pass amplification the output pulse contained 40% of the free-lasing energy). Numerical optimization of the parameters of the regenerative amplification system similar to that in Ref. 4 is needed to achieve the maximum output energy and contrast of nanosecond pulses. The influence of various parameters on the regenerative amplification process was considered in Refs. 5 and 6. However, the results could not be used to optimize the system producing a single pulse. Moreover, the range of injection times in which regenerative amplification is possible (this range is governed by the ratio of the powers of the injected 526

Sov. J. Quantum Electron. 12(4), April 1982

pulse and of the intrinsic radiation of the laser) was found only on the basis of a greatly simplified point model inapplicable to real conditions, and a fuller model of cells ignored the growth of intrinsic laser radiation. We carried out calculations using the model of cells in which, in contrast to Refs. 5 and 6, we allowed for intrinsic laser radiation. Our aim was to carry out several tasks: 1) to find the ranges of energy of the injected pulses Einj and of the times of injection Τ in which regenerative amplification is possible (time was measured from the beginning of a pump pulse); 2) to study the influence of the contrast of the injected pulse on the regenerative amplification process; 3) to optimize the parameters of the system in order to obtain the maximum energy in a selected pulse when the ratio of this energy to that of a preceding pulse in a train was at least 20-30 (which should ensure a contrast of 10 6 10 8 : 1 at the output of a saturable absorber 4 ). We solved numerically a system of equations for the populations of the active levels and for the photon density in the resonator (i.e., for the intrinsic laser radiation)7 by dividing the active medium and the resonator into cells. We used the following parameters of the system: the resonator length L = 20 m; the reflection coefficient of the exit mirror 0.6; the length of the active medium 1 = 50, 100, or 150 cm; the energy of the injected pulses 10' 15 -10" 10 J; the duration of the injected pulses τ = 5 nsec; the working mixture composition CO 2 : N2 : He = 1: 1: 3 at atmospheric pressure. In these calculations we used the experimental dependence of

0049-1748/82/040526-03$04.10

© 1982 American Institute of Physics

526

TABLE I.

f inj. J

/, cm

50 100 150

ΑΓ. i»ec

550 450 400

no significant weakening of the injected pulse. Therefore, region A begins from T = 0. Table I gives the r e sults of calculations of the value of ΔΤ (measure of region A along the time axis) for a fixed value of £ l n J (10- 1 0 J) but different values of I. We can see that ΔΤ decreases slowly on increase in I because of acceleration of the growth of intrinsic laser radiation. FIG. 1. Positions of regions representing various regimes of laser operation plotted in terms of the coordinates Τ and £i n j for I = 100 cm, JTinj = °° (a) and A i n j = 103 (b).

the electron density ne on the time /. The constants in the equations were selected so as to achieve the maximum agreement between the experimental and calculated shapes of the edge of the small-signal amplification pulse ao{t). For simplicity, we assumed that the beam aperture was constant throughout the resonator and that it amounted to 6 cm. The following notation was employed: a^^ is the maximum value of ao(t); a(t) is the time dependence of the gain obtained by calculations relating to the regenerative amplification process; T t h is the moment at which the gain becomes equal to the losses in the resonator; QTL is the interval between the pulses in a train; Ν is the number of a pulse in a train with a maximum energy; En is the energy of the n-th pulse in a train; Kinj is the contrast of the injected pulse (in the task 1 it was assumed that Kiaj = °°). Our calculations showed that there are three ranges of Τ and £ l n j corresponding to three operating regimes of the laser (Fig. la): 1) region A, where regenerative amplification takes place and there is practically no intrinsic laser radiation; 2) region B, where an injected pulse is being amplified and intrinsic laser radiation is observed (it is assumed that in region Β the energy of the intrinsic laser radiation during an interval 5TL exceeds by 10% the energy of the adjoining pulse in a train); 3) region C, where free lasing takes place. The existence of all these regions was established also in Ref. 6. However, in contrast to the results of Ref. 6, where in the interval 0< T< T t h there is a successive change from C, to Β and A, our results indicated that 15 in the range Elnj > 5 x 10' J, region A begins from the moment Τ = 0. This difference is due to the fact that we considered a longer resonator (L = 20 m in the present case and 1.2 m in Refs. 5 and 6), which is desirable for the attainment of the maximum energy of the selected 8 pulse. In Ref. 6, it was assumed that $TL« T, h and that if T< T t h , a pulse passes ~100 times through the resonator during the interval T< t< Ttb, when the losses exceed the gain. A considerable weakening of the pulse gives rise to regions Β and C at times Τ < T t h . In our calculations the number of passes in the interval Τ < t < T l h was assumed to be 3-4 so that there should be 527

Sov. J. Quantum Electron. 12(4), April 1982

It is of interest to study the influence of the finite contrast of the injected pulse Kini on the regenerative amplification process. Therefore, we introduced a constant external flux into the equation for the photon density in the resonator; this flux is proportional to / = EM /if,nj. Calculations carried out for different values of £ l n J in the range 10" 1 0 - 2 χ 10"15 J assuming that I = 100 cm, demonstrated that Δ Τ decreases on reduction in Klaj because of an increase in the photon flux reaching the resonator before the arrival of the injected pulse and favoring the growth of intrinsic laser radiation. There is a limiting value / l l m = 5 χ 10"16 J (practically independent of -E^j) such that if/>/ U m , then there is no regenerative amplification. Hence, it follows that contrary to the K U J = °° case, when region A is bounded in respect of the energy only from below by ^ui" = 2 x 10"15 J (Fig. la), if the contrast K lnJ is finite, then this region is bounded also from above by the value of Atm^ioi- I" the range 2· 10"15 J< £ i n J < lUmKlnl there is an optimal value of £JJ| corresponding to the maximum value of ΔΤ. Figure lb shows the distribution of regions A, B, and C for a value of the contrast Kla) = 103 encountered in practice. It should be pointed out that if Ε™* = 5 x 10" u J the value of ΔΤ is close to that for the same £ U J and ifUJ = °° (Fig. la). For the working mixture and pump conditions assumed in our calculations the .N-th pulse crosses the active medium during the falling part of α(ί), when the medium is already saturated. In this case we have EH/ EN_1 ~ 1. However, the quantity Ks§m = EN,m/EN.m. 1 (m = l,2, ) may be considerably greater if the (N — m - l)-th pulse crosses the active medium under linear amplification conditions, whereas the (N-w)-th pulse already causes saturation. Since the dependences £„(£) are periodic in the period 5TL (as shown in Ref. 5), it follows that KNtm is also periodic. Figure 2 shows the dependences of the maximum values of En_m obtained for

FIG. 2. Dependences of the energy of the selected pulse £*_„,

Apollonovef al.

527

TABLE Π. CO,: Ν,: He

m-'

Front duration,

Λ cm

£ i n j

, l o - " \ T, nsec

100

25,6

0.92

16

150

16.7:33.4:50

3,16

2,5

150

21.2

2,12

16

250

100

31.2

1,47

5

50

20:40:40

3,75

2,5

150

59

3,13

5

300

100

21,4

2,08

16

350

150

135

4,08

16

350

100

40.9

2.97

5

350

150

255

5.69

16

350

100

78,6

3-96

16

200

150

4,7

8.15

5

300

25:25:50

30:30:40

36:24:40

4.12

4.38

4.5

2,0

2,0

1.5

a fixed contrast in the range KNtm> 20 but different values of T, on KN>m when Z= 100 or 150 cm. It is clear from this figure that EK_m decreases on increase inKNwm, whereas for fixed KNt