SOME BEHAVIORAL PECULIARITIES OF A ONE-FREQUENCY HELIUM-NEON LASER IN A LONGITUDINAL MAGNETIC FIELD S. S. Kartaleva, T. N. Draishu, and V. T. Ilkova

UDC 621.375.8

A one-frequency helium-neon laser emitting one longitudinal mode of the 632.8 nm line is needed for solving a number of problems. Many methods for suppressing superfluous modes in gas lasers have thus far been developed (see, e.g., [1-5]). The characteristics of a one-frequency helium-neon laser in a magnetic field have been studied in a number of works, [6-9]. In this paper we report on experimentally observed peculiarities in the behavior of a one-frequency helium-neon laser placed in a longitudinal magnetic field. A discharge tube with length s = 0.58 m and diameter d = 1.85 mm was filled with a natural mixture of helium and neon isotopes. The laser resonator was chosen so that lasing occurred only dn the fundamental transverse mode TEM00. The axial magnetic field was generated with a solenoid 0.67 m long. The field nonuniformity along the tube did not exceed 5%. One-frequency lasing was realized by raising the pressure of the active mixture. In this case the homogeneous line broadening increases and because of competition between the longitudinal modes lasing occurs in only one longitudinal mode, in which the gain is highest [3]. In the laser studied the one-frequency lasing regime is realized at a pressure P exceeding 800 Pa and the ratio of the partial pressures of helium and neon PHe/PNe = 15-30. The interferrogram of one-frequency lasing at P = 827 Pa and PHe/PNe = 25 is shown in Fig. la. Two neighboring orders of the interferrometer, the frequency interval between which equals 2,000 MHz, can be seen in it. When a magnetic field is imposed on the active medium of the laser (without changing the pressure) lasing also appears on two neighboring longitudinal modes (see Fig. ib). The frequency interval between the central and neighboring modes, determined from the equality A~ = c/2L, where c is the velocity of light and L is the length of the laser resonator, equals 180 MHz. The intensity of the magnetic field Hcr , with which lasing in neighboring modes starts, depends on the gas pressure. For P = 827 Pa, H c r = 130 Oe. As the magnetic field is intensified the intensity of the neighboring modes increases gradually and then lasing starts in the next longitudinal modes, also separated by a frequency interval Av = c/2L. Figure Ic shows the interferrogram of lasing with H = 185 Oe. One can see that the typical multifrequency lasing is realized. It should be emphasized that this lasing regime was obtained only in the presence of a magnetic field. In our opinion, this transition of one-frequency lasing into multifrequency lasing has not been reported in the literature. When the magnetic field intensity is further increased the multifrequency lasing transforms in a jumplike fashion into two-frequency lasing and the interval between the frequencies increases. Figure id shows an interferrogram of two lasing frequencies with H = 460 Oe. T h e jump is observed when the frequency interval between the orthogonally polarized o+ and ocomponents of the Zeemann splitting equals the Doppler width of the line. The ratio of the intensities at two lasing frequencies strongly depends on the gas pressure. This dependence is shown for H = 440 Oe in Fig. 2a. At pressures above 1270 Pa lasing occurs only at the single frequency ~l. Then, as the pressure is reduced, lasing also starts at the frequency ~2, and its intensity increases. To explain this behavior of the two frequencies additional studies are being performed. The dependence Of Hcr on P is shown in Fig. 2b. One can see that as the pressure is increased the intensity of the magnetic~ field at which a transition occurs from one- to multifrequency lasing increases substantially. Institute of Electronics, Bulgarian Academy of Sciences. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 48, No. 5, pp. 717-722, May, 1988. Original article submitted May 14, 1987. 472

0021-9037/88/4805-0472512.50 9 1988 Plenum Publishing Corporation

Fig. i. Interferrogram of the lasing spectra of a laser with magnetic field intensities of H = 0 (a), 130 (b), 185 (c), and 460 Oe (d). P = 827 Pa.

2Z fO 18 7k /q IZ

Hcr, Oe qgO.

b

J00

/O 8

200" q f

gOD

~0D

frO0 P, Pa 800

~gg

ff~gP, Pa

Fig. 2. The ratio of the intensities at the frequencies ~i and ~2 (a) and the intensity of the magnetic field Hcr (b) as a function of the gas pressure P. H = 440 Oe (a). To explain the muitifrequency of the gain and the magnetooptical

lasing obtained (see Fig. Ib) we made theoretical estimates losses.

Using the dependence, obtained in [i0], of the unsaturated gain for lasing at one frequency on the splitting of the o + and o- components (it is assumed that the generated radiation is linearly polarized), the dependence of the ratio of the unsaturated gains kc~ ~ for neighboring ~c and the central ~0 frequencies (A~ = ~0 - ~c = c/2L) on the Zeemann splitting was determined:

c k~

--e 2

(0"6AvH)

e

(1)

(0"6AVd)-"--~-e (0 6AVdV

where A~d is the Doppler width of the line; 2A H = ~0+ - ~0-; v0+ is the central frequency of the o+ components; and, v0- is the central frequency of the o- component (AH = gp~H, where g is the Lande factor and PB is the Bohr magneton). The results of the calculation of the dependence of the ratio kc~ ~ on the magnetic field intensity H for the conditions of our e~periment (where Av = c/2L = 180 MHz; Av d = 1600 MHz) are shown in Fig. 3a. One can see that as H is increased the ratio of the un-

473

T

. . . . .

,

a,V%

,

,

,

,

,

,

,

109 20DJ00 ~OQ500 bat///~ Oe SO 1DOISUrOD250_Y00350/r Oe

Fig. 3. The ratio of the unsaturated gains at the neighboring and central frequencies kc~ ~ (a) and the amplitude transmission Igl[ for the central (i) and neighboring (2) frequencies (b) as a function of the intensity of the magnetic field. P = 973 Pa (b). saturated gains at the central and neighboring frequencies changes in favor of the latter. Therefore as the magnetic field is intensified the conditions for lasing at the neighboring frequency improve compared with lasing at the central frequency. These estimates must be regarded as being qualitative only, since they were made for the case when the homogeneous broadening is much smaller than the Doppler broadening, which does not occur in our case, since the laser operates at an elevated pressure and the homogeneous linewidth cannot be neglected. The magnetooptical losses at the central and neighboring frequencies were also evaluated theoretically. Using the Jones matrix formalism [7, ii], we shall find the amplitude transmission for two orthogonal polarizations for a resonator with a linear amplitude anisotropy, when the laser is in a longitudinal magnetic field. For a laser with two fused quartz windows, oriented at Brewster's angle, the Jones matrix A l can be written in the coordinate system tied to the principal directions of the polarizers in the form [12] ^

^

^2

~Z : ApolAamAp~

^

^

(2) ^

^

where the Jones matrix of the polarizer Apo I and of the active medium Aam have the form

ol ~

0

r

'

Aam

--sinO(~)

cosO(v)

"

Here 1 and r are the amplitude transmission coefficients of the window along two principal directions; 9(~) is the angle of rotation of the polarization plane in a single passage of the radiation through the active medium. Substituting (3) into (2) and solving the characteristic equation (7) for the eigen values gi,2 of the matrix (2), determining the amplitude transmission for two orthogonal polarizations, we obtain the expression 1 e,,2 ~ -

The a n g l e

of rotation

[( 1 + r2) 2 cos2@ - - 2r 2 • (1 + r a) cos @ •(1 + rZ)z cos 2 @- - 4r2]. of the polarization

O(x)=

474

plane

kol [ V(x', y) 2 2U(O, V)

is

determined

V(x", y) ] 2U(O, y) '

by t h e

(4) expression

[13]

(5)

where x = v--vo

AVd

2 ~rln2; y -- - -7

Avn

]/-i~; x ' _ ~ x - - ~ 2AH1 / - f - ~ ; Avd

x"= x-b

A. 2trl~- ~ ; vo is t h e Av d

central frequency of the unspiit contour; ~ is the homogeneous width of the line; and functions V and U are tabulated in [14].

the

The dependences of ~0 and O c on the intensity of the magnetic field H were determined for the central and neighboring frequencies (Av d = 1600 MHz, kol = 0.i, and the value of was determined from [15]). Using them and the expression (4), the amplitude transmission of the generated linearly polarized radiation was calculated for the central and neighboring frequencies as a function of the magnetic field intensity H. These dependences are shown in Fig. 3b. One can see that as the magnetic field is intensified the amplitude transmission at the central frequency decreases more rapidly than at neighboring frequency. Therefore the magnetooptical losses at the central frequency grow more rapidly as the magnetic field is varied than do the losses at the neighboring frequency. It should be emphasized, however, that the absolute magnitude of the difference in transmission (and therefore, the losses also) at the two neighboring frequencies is small. Theoretical calculations show that as the magnetic field is intensified, as a result of the change in the gain and magnetooptical losses, the conditions for the neighboring frequencies improve compared with the central frequency. This explains the behavior of the lasing at several neighboring frequencies as H is increased. But since the homogeneous linewidth [15] is much larger than the intermode splitting, three-frequency (Fig. Ib) and multifrequency (Fig. ic) lasing should be realized under the conditions of competition between the neighboring axial types of oscillations [16]. We assumed that the time-averaged interferogram of lasing is observed (s ib and c), since the time for one scan of the interferometer equals 0.01 sec, while in order to observe the competition between modes the spectrum must be scanned with a resolution of ~i0 -s sec [i0]. As a check we performed the following experiment. A regulated constant voltage was applied to the piezoelectric ceramic element of the scanning interferometer instead of a n alternating voltage. By varying the scanning voltage of the interferometer scanning could be stopped when maximum transmission was achieved in the contour line corresponding to a definite frequency. Thus by recording the intensity of the generated radiation transmitted by the interferometer we can observe the behavior of the lasing power in a definite mode as a function of time. The time scan of the power with constant transmission of the interferometer, when it is tuned to the maximum transmission at the central frequency (Fig. Ib), is performed with an oscillograph (the time sweep equals 0.05 msec/division) and shows that the power at the central frequency does not drop to zero. To check the time constant of the system we recorded the frequency-modulated one-frequency lasing, when the interferometer is stopped. The modulated signal with a period of 0.05 msec was recorded with a system with small distortions, while the signals with long duration were not distorted. Therefore within the accuracy of our experiment it can be asserted that simultaneous stable lasing occurs at three and more frequencies. It should be emphasized once again that this regime is realized when the homogeneous linewidth Significantly exceeds the frequency interval between the neighboring axial types of oscillations. For example, with a pressure of 1,133 Pa and the ratio PHe/PNe = 26 the homogeneous linewidth estimated based on [15] equals 760 MHz while the intermode splitting equals 180 MHz. In our opinion, the question of the reasons for the existence of this state remains open. The results obtained show that if an axial magnetic field is applied to a one-frequency He-Ne laser with an elevated:pressure of the mixture, then some peculiarities appear in the behavior of the lasing parameters. First, the intensities at the two frequencies vl and v2 (Fig. id) differ and the difference depends on the pressure of the active mixture (Fig. 2a). Second, the intensity of the magnetic field Hcr depends on the pressure (Fig. 2b). Our calculations of the ratio kc~ ~ were made in the limiting case, when the inhomogeneous broadening of the line is much greater than the homogeneous broadening, and in order to explain this dependence the homogeneous broadening must obviously be taken into account. Finally, stable simultaneous generation at neighboring frequencies can be realized when the intermode splitting is much smaller than the homogeneous linewidth. Additional theoretical and experimental studies are required in order to clarify the reasons for these peculiarities. 475

It is our duty to thank A. P. Voitovich, V. V. Lebedev, and B. Stefanov for a discussion of the experimental results and for valuable remarks. We also thank S. Gatev for partici-. pating at the starting stage of the experimental work. LITERATURE CITED i. 2. 3.

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