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Streak camera analysis of light filaments generated in a resonant atomic vapor
Volume 65, number 4
OPTICS COMMUNICATIONS
15 February 1988
STREAK CAMERA ANALYSIS OF LIGHT FILAMENTS GENERATED IN A RESONANT ATOMIC VAPOR Ph. K U P E C E K C.E.A., 1.R.D.I., D.E.S.I.C.P, D~partement de Physico-Chimie, C E ~ de Saclay, 91191 G~f-sur-Yvette, France and Universit~ P. et M. Curie, Paris, France
M. C O M T E , J.-P. M A R I N I E R , J.-P. B A B U E L - P E Y R I S S A C C.E.A., I.R.D.I., D.E.S.I.C.P, D~partement de Physico-Chimie, C.E.N. de Saclay, 91191 Gifsur- Yvette, France
and
C. B A R D I N C1Sl-lng~'nierie D.C.L BP 24, 91190 Gif-sur- Yvette, France
Received 17 November 1987
We present a spatio-temporal streak camera analysis of laser pulses interacting with a resonant degenerate atomic vapor. We interpret the results as due to the combined effects of small-scale defects amplification and self-induced transparency.
1. Introduction
2. Experimental set-up
Self-focusing in dense resonant atomic v a p o r has given rise to m a n y theoretical and e x p e r i m e n t a l works. In particular, in the coherent p r o p a g a t i o n regime, when the relaxation time is long c o m p a r e d to the pulse width, it can be observed for exact tuning on the atomic line [ 1,2]. This effect m a y lead to the decrease o f the b e a m size as a whole when strong diffraction effects occur, or to the breaking into m a n y filaments when diffraction is negligible (small scale self-focusing: SSSF). In the latter case a t t e m p t s have been m a d e to m o d e l i z e the growth o f transverse perturbations [ 3,4]. Built up in the general context o f laser isotope separation, we describe here an e x p e r i m e n t a l study o f s p a t i o - t e m p o r a l b e h a v i o r o f a laser b e a m after interaction with a dense atomic vapor in the small scale coherent self-focusing regime, whose onset is tentatively m o d e l i z e d as the growth o f pre-existing transverse perturbations.
We use for resonant m e d i u m atomic thulium (Tm169) excited on the J = 7 / 2 - - . J = 7/2 f u n d a m e n t a l transition at 5895 A, having a mean dipole m o m e n t o f / t = 0 . 2 5 D. T h u l i u m has only one stable isotope with nuclear spin I = 1/2, the hyperfine structure for the chosen transition being distributed on about 500 MHz. The m e d i u m is o b t a i n e d using v a p o r pressure o f solid thulium heated in a t e m p e r a t u r e controlled oven o f 1 m active length, with less than 0.5 Torr of xenon for w i n d o w protection (collisional relaxation time ~ ~ 300 ns). F o r the working temperature, the D o p p l e r linewidth is about 900 MHz. The pulsed light source consists o f a frequency d o u b l e d single-mode pulsed Y A G : N d 3+ laser amplifying the output o f a Ar + p u m p e d C W stabilized single-mode dye laser. After spatial filtering the tunable pulses have a fairly good gaussian profile o f 0.2 cm 2, and a smooth 12 ns temporal profile with a related 80 M H z bandwidth. Characterization o f the emerging pulses is done with an I M A C O N 500 streak camera and C C D video
306
0 030-4018/88/$03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )
Volume 65, number 4
OPTICS COMMUNICATIONS
cameras, in the imaged output plane o f the active medium. The schematic diagram o f the apparatus is given on fig. 1.
3. E x p e r i m e n t a l
beam. This suggests the following interpretation: the behavior o f the propagating light is the result o f the combined effects of small scale perturbations amplification and self-induced transparency (SIT) in created filaments. One can then argue for SIT as follows: - for low input intensities (for instance one tenth o f the saturation intensity), light can cross the medium without important losses, with m a x i m u m delays and pulse reshaping; - this transparency effect occurs with a well defined threshold value for the entrance intensity which, within the experimental accuracy, corresponds to a n pulse area; - at last, the pulse area in an individual filament which can be evaluated knowing the input peak intensity and using the resonant and off resonant streak camera images is 2n within the experimental uncertainty. Although the situation is different, we also made experiments immediately below the concentration threshold for transverse effects, to observe a genuine self-induced transparency phenomenon. Because of the hyperfine structure (two main components of nearly equal intensity and separated by 470 M H z ) and because of the Zeeman sublevels, the transition is highly degenerate. However, degeneracy does not prevent SIT to occur [5,6]. The streak
results
For an atomic concentration N above 3 × 10 ~2 atoms/cm 3, SSSF occurs. Let us describe the situation for N = 8 X 1012 atoms/cm 3 and an input peak intensity at beam center Io = 200 W / c m 2 (pulse area slightly under 2n). Fig. 2 displays the transverse pattern of the output beam. This pattern is reproducible from shot to shot. Fig. 2a is out o f resonance and fig. 2b is for exact tuning. A streak camera makes a transient analysis o f a diameter of this beam, shown on fig. 2c out of resonance and fig. 2d on resonance. The typical features seen on the temporal display o f the transversally perturbed beam are the general delay of the light travelling through filaments (compared with the non-delayed remaining fluorescence) and the duration o f this filamentary light which is about two times the original pulse length. The question arises if the strongly delayed spatially reshaped light is coherent with the input pulse. A positive answer is obtained by producing an interference pattern between the hot spots light and a delayed part o f the input
II Ii
15 February 1988
II
It
IJ
tl
II
4
J
I~.
x~v I
Fig. 1. Experimental setup. 1: CW Ar ÷ laser; 2: dye laser; 3:532 nm YAG:Nd3÷ pulsed laser; 4: flow dye cell; 5: Thulium oven; 6: streak camera; 7: C.C.D. camera. 307
Volume 65, number 4
OPTICS COMMUNICATIONS
15 February 1988
Fig. 2. Output beam analysis when SSSF occurs. N = 8 X 1012 atoms/cm 3, lo=200 W/cm 2. Beam pattern: (a) out of resonance, (b) on resonance. Streak camera analysis: (c) out of resonance, (d) on resonance.
camera image for N = 2 X 1012 atoms/cm 3 and peak central intensity 1500 W/cm 2, pulse area slightly under 5n, is shown on fig. 3. As predicted by standard SIT theory [7], the light in the central part of the beam, where the intensity is maximum, breaks up rapidly into two pulses whereas on the wings, it can be seen that less intense light propagates much more slowly. Moreover, from the digitized image, one can approximately locate on fig. 3 the transverse position where the local incident pulse area is slightly above n. It is found to correspond nearly to the disappearance of transmitted light, as expected from SIT theory. One also observed the streak camera image of a 2n central area pulse (fig. 4). In the last case, the output pulse has nearly the same duration as the input pulse and undergoes a delay of 14 ns, smaller than the value expected from the simple formula ~ST=½oLLTwhich leads to c~T~50 ns. This observation agrees with the results of ref. [8].
,IOns
4. Numerical simulation -b-
The laser-vapor system can generally be described by the well-known Maxwell-Bloch equations [ 9,10 ]. In the experimental situation last described (i.e., in the absence of SSSF), it is acceptable to use a computer code assuming cylindrical symmetry to solve 308
Fig. 3. Spatio-temporal behavior for a pulse area slightly below 5n. (a) Streak camera analysis, (b) digitized intensity versus radius and time.
Volume 65, number 4
OPTICS COMMUNICATIONS
15 February 1988
ion5
Fig. 4. Spatio-temporal behavior for a pulse area slightly below 2n; streak camera image. them. We used such a code [ 10] to predict the spario-temporal behavior of the laser intensity in the output plane of the vapor. Fig. 5 shows the resulting 3D plot of the intensity versus transverse distance r and time t with corresponding isophotes, computed with the experimental data of fig. 3, the input optical area being slightly below 5n. This computation neglects Zeeman degeneracy and Doppler broadening. An effective atomic density of only 7×101~ atoms/cm 3 is used to take into account the partial covering of the Dopper distribution (900 MHz) by the input Rabi frequency (135 MHz). Fig. 5 displays the same typical double horseshoe pattern as fig. 3, except the following: the two light pulses are shorter in time and more clearly separated than in the experimental image (of about 1.5 times), probably because of the absence of the Zeeman and Doppler effects in the code. Moreover, we checked on the computed results that each of the two light pulses causes a short transient total inversion, thus confirming the idea of 2n pulses formation. The propagation delay of the 2n pulse was found to be 12 ns by a code including Zeeman and Doppler effects, in good agreement with the experimental value. For higher atomic densities, we tentatively describe the SSSF as an amplification of the small intensity defects of the input laser beam. As the cylindrical symmetry assumption is obviously inadequate and a 3°dimensional computation is not practical, we resorted to a perturbative approach: try to determine theoretically which perturbations are
-
b
-
Fig. 5. Computed intensity for a pulse area slightlybelow 5n. (a) Isophotespattern, (b) intensity versus radius and time. amplified faster and at which rate. This is similar to the approach used by Bespalov, Talanov [11] and Suydam [ 12 ] to describe multifilamentation in nonlinear liquids and neodymium glass laser rods. The laser field is taken to be the sum of a plane wave (o and a perturbation ~ with periodic transverse dependence: ~ =A sin(Kx/xf2)
sin(Ky/x/2).
The Maxwell-Bloch equations are developped at first order in ~ , and the resulting perturbation equations are solved numerically. In the input plane, the temporal behavior of the perturbation and of the plane wave are taken to be identical. So we obtain an amplification factor fl of the perturbation energy as a function of K 2 and penetration length z for a 309
Volume 65, number 4
OPTICS COMMUNICATIONS
~z
2O
0
I
I
ROO
I
I
I
-qo0
~, Cr_m-~ ) Fig. 6. Perturbative gain versus transverse wavenumber. N= 8 × 10~2atoms/cm3, Io= 200 W/cm2. given i n p u t optical area. It appears that the natural longitudinal a n d transverse length units for this problem are respectively:
Lg : 47~~.ohC/27cNlt2 o) T ,
rp = (2Lg/4n) 1/2 ,
where T is the laser pulse duration. In the conditions of fig. 2, we get the curve of fig. 6 for z = 7 cm ( 10 Lg). One sees that the perturbation has grown faster for K = K m ~ 2 5 0 cm ~, giving an interfilament spacingof2n/Kx ~ 2 n \ / 2 / K ~ 0.035 cm, when the experimental value is about 0.060 cm. One sees that Km is about 1.6 times 1/x//~g, which is the expected order of magnitude for the 2n pulse as given in ref. [3]. The m a x i m u m of the gain curve gets
310
15 February 1988
higher and sharper with increasing penetration length, but the limits of the perturbative regime are reached, for any practical laser beam, well below the total length of 1 m. The existence of a preferred transverse periodicity allows one to u n d e r s t a n d the genesis of light filaments qualitatively in analogy with the Suyd a m model. In summary, the complicated situation of a dense atomic degenerate m e d i u m interacting with a spatially slightly perturbed resonant laser beam can be satisfactorily understood by separating transverse reshaping and temporal mechanisms, at least for a qualitative interpretation.
References [1] H.M. Gibbs, B. B61ger and L. Baede, Optics Comm. 18 (1976) 199. [2] H.M. Gibbs, B. BNger, F.P. Mattar, M.C. Newstein, G. Forster and P.E. Toschek, Phys. Rev. Lett. 37 (1976). [3] L.A. Bol'shov, V.V. Likhanskii and A.P. Napartovich, Soviet PhysicsJETP 45 (1977) 928. [4] M.J. Ablowitzand Y. Kodama, Phys. Lett. A70 (1979) 83. [5] G.J. Salamo, H.M. Gibbs and G.G. Churchill, Phys. Rev. Lett. 33 (1974). [6] H.M. Gibbs, S.L. McCall and G.J. Salamo, Phys. Rev. A, 12 (1975). [7] S.L. McCall and E.L. Hahn, Phys. Rev. 183 (1969) 457. [8] R.E. Slusher and H.M. Gibbs, Phys Rev. A 5 (1972) 1634. [9] F.P. Manar, Appl. Phys. 17 (1978) 53. [10] Ph. Kupecek, M. Comte, B. Visentin and J.-P. Marinier, Optics Comm. 56 (1985) 1. [ 11 ]g.I. Bespalov and V.I. Talanov, JETP Lett. 3 (1966) 307. [ 12] B.R. Suydam, IEEE J. Q.-E. QE 10 (1974) 837.
OPTICS COMMUNICATIONS
15 February 1988
STREAK CAMERA ANALYSIS OF LIGHT FILAMENTS GENERATED IN A RESONANT ATOMIC VAPOR Ph. K U P E C E K C.E.A., 1.R.D.I., D.E.S.I.C.P, D~partement de Physico-Chimie, C E ~ de Saclay, 91191 G~f-sur-Yvette, France and Universit~ P. et M. Curie, Paris, France
M. C O M T E , J.-P. M A R I N I E R , J.-P. B A B U E L - P E Y R I S S A C C.E.A., I.R.D.I., D.E.S.I.C.P, D~partement de Physico-Chimie, C.E.N. de Saclay, 91191 Gifsur- Yvette, France
and
C. B A R D I N C1Sl-lng~'nierie D.C.L BP 24, 91190 Gif-sur- Yvette, France
Received 17 November 1987
We present a spatio-temporal streak camera analysis of laser pulses interacting with a resonant degenerate atomic vapor. We interpret the results as due to the combined effects of small-scale defects amplification and self-induced transparency.
1. Introduction
2. Experimental set-up
Self-focusing in dense resonant atomic v a p o r has given rise to m a n y theoretical and e x p e r i m e n t a l works. In particular, in the coherent p r o p a g a t i o n regime, when the relaxation time is long c o m p a r e d to the pulse width, it can be observed for exact tuning on the atomic line [ 1,2]. This effect m a y lead to the decrease o f the b e a m size as a whole when strong diffraction effects occur, or to the breaking into m a n y filaments when diffraction is negligible (small scale self-focusing: SSSF). In the latter case a t t e m p t s have been m a d e to m o d e l i z e the growth o f transverse perturbations [ 3,4]. Built up in the general context o f laser isotope separation, we describe here an e x p e r i m e n t a l study o f s p a t i o - t e m p o r a l b e h a v i o r o f a laser b e a m after interaction with a dense atomic vapor in the small scale coherent self-focusing regime, whose onset is tentatively m o d e l i z e d as the growth o f pre-existing transverse perturbations.
We use for resonant m e d i u m atomic thulium (Tm169) excited on the J = 7 / 2 - - . J = 7/2 f u n d a m e n t a l transition at 5895 A, having a mean dipole m o m e n t o f / t = 0 . 2 5 D. T h u l i u m has only one stable isotope with nuclear spin I = 1/2, the hyperfine structure for the chosen transition being distributed on about 500 MHz. The m e d i u m is o b t a i n e d using v a p o r pressure o f solid thulium heated in a t e m p e r a t u r e controlled oven o f 1 m active length, with less than 0.5 Torr of xenon for w i n d o w protection (collisional relaxation time ~ ~ 300 ns). F o r the working temperature, the D o p p l e r linewidth is about 900 MHz. The pulsed light source consists o f a frequency d o u b l e d single-mode pulsed Y A G : N d 3+ laser amplifying the output o f a Ar + p u m p e d C W stabilized single-mode dye laser. After spatial filtering the tunable pulses have a fairly good gaussian profile o f 0.2 cm 2, and a smooth 12 ns temporal profile with a related 80 M H z bandwidth. Characterization o f the emerging pulses is done with an I M A C O N 500 streak camera and C C D video
306
0 030-4018/88/$03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )
Volume 65, number 4
OPTICS COMMUNICATIONS
cameras, in the imaged output plane o f the active medium. The schematic diagram o f the apparatus is given on fig. 1.
3. E x p e r i m e n t a l
beam. This suggests the following interpretation: the behavior o f the propagating light is the result o f the combined effects of small scale perturbations amplification and self-induced transparency (SIT) in created filaments. One can then argue for SIT as follows: - for low input intensities (for instance one tenth o f the saturation intensity), light can cross the medium without important losses, with m a x i m u m delays and pulse reshaping; - this transparency effect occurs with a well defined threshold value for the entrance intensity which, within the experimental accuracy, corresponds to a n pulse area; - at last, the pulse area in an individual filament which can be evaluated knowing the input peak intensity and using the resonant and off resonant streak camera images is 2n within the experimental uncertainty. Although the situation is different, we also made experiments immediately below the concentration threshold for transverse effects, to observe a genuine self-induced transparency phenomenon. Because of the hyperfine structure (two main components of nearly equal intensity and separated by 470 M H z ) and because of the Zeeman sublevels, the transition is highly degenerate. However, degeneracy does not prevent SIT to occur [5,6]. The streak
results
For an atomic concentration N above 3 × 10 ~2 atoms/cm 3, SSSF occurs. Let us describe the situation for N = 8 X 1012 atoms/cm 3 and an input peak intensity at beam center Io = 200 W / c m 2 (pulse area slightly under 2n). Fig. 2 displays the transverse pattern of the output beam. This pattern is reproducible from shot to shot. Fig. 2a is out o f resonance and fig. 2b is for exact tuning. A streak camera makes a transient analysis o f a diameter of this beam, shown on fig. 2c out of resonance and fig. 2d on resonance. The typical features seen on the temporal display o f the transversally perturbed beam are the general delay of the light travelling through filaments (compared with the non-delayed remaining fluorescence) and the duration o f this filamentary light which is about two times the original pulse length. The question arises if the strongly delayed spatially reshaped light is coherent with the input pulse. A positive answer is obtained by producing an interference pattern between the hot spots light and a delayed part o f the input
II Ii
15 February 1988
II
It
IJ
tl
II
4
J
I~.
x~v I
Fig. 1. Experimental setup. 1: CW Ar ÷ laser; 2: dye laser; 3:532 nm YAG:Nd3÷ pulsed laser; 4: flow dye cell; 5: Thulium oven; 6: streak camera; 7: C.C.D. camera. 307
Volume 65, number 4
OPTICS COMMUNICATIONS
15 February 1988
Fig. 2. Output beam analysis when SSSF occurs. N = 8 X 1012 atoms/cm 3, lo=200 W/cm 2. Beam pattern: (a) out of resonance, (b) on resonance. Streak camera analysis: (c) out of resonance, (d) on resonance.
camera image for N = 2 X 1012 atoms/cm 3 and peak central intensity 1500 W/cm 2, pulse area slightly under 5n, is shown on fig. 3. As predicted by standard SIT theory [7], the light in the central part of the beam, where the intensity is maximum, breaks up rapidly into two pulses whereas on the wings, it can be seen that less intense light propagates much more slowly. Moreover, from the digitized image, one can approximately locate on fig. 3 the transverse position where the local incident pulse area is slightly above n. It is found to correspond nearly to the disappearance of transmitted light, as expected from SIT theory. One also observed the streak camera image of a 2n central area pulse (fig. 4). In the last case, the output pulse has nearly the same duration as the input pulse and undergoes a delay of 14 ns, smaller than the value expected from the simple formula ~ST=½oLLTwhich leads to c~T~50 ns. This observation agrees with the results of ref. [8].
,IOns
4. Numerical simulation -b-
The laser-vapor system can generally be described by the well-known Maxwell-Bloch equations [ 9,10 ]. In the experimental situation last described (i.e., in the absence of SSSF), it is acceptable to use a computer code assuming cylindrical symmetry to solve 308
Fig. 3. Spatio-temporal behavior for a pulse area slightly below 5n. (a) Streak camera analysis, (b) digitized intensity versus radius and time.
Volume 65, number 4
OPTICS COMMUNICATIONS
15 February 1988
ion5
Fig. 4. Spatio-temporal behavior for a pulse area slightly below 2n; streak camera image. them. We used such a code [ 10] to predict the spario-temporal behavior of the laser intensity in the output plane of the vapor. Fig. 5 shows the resulting 3D plot of the intensity versus transverse distance r and time t with corresponding isophotes, computed with the experimental data of fig. 3, the input optical area being slightly below 5n. This computation neglects Zeeman degeneracy and Doppler broadening. An effective atomic density of only 7×101~ atoms/cm 3 is used to take into account the partial covering of the Dopper distribution (900 MHz) by the input Rabi frequency (135 MHz). Fig. 5 displays the same typical double horseshoe pattern as fig. 3, except the following: the two light pulses are shorter in time and more clearly separated than in the experimental image (of about 1.5 times), probably because of the absence of the Zeeman and Doppler effects in the code. Moreover, we checked on the computed results that each of the two light pulses causes a short transient total inversion, thus confirming the idea of 2n pulses formation. The propagation delay of the 2n pulse was found to be 12 ns by a code including Zeeman and Doppler effects, in good agreement with the experimental value. For higher atomic densities, we tentatively describe the SSSF as an amplification of the small intensity defects of the input laser beam. As the cylindrical symmetry assumption is obviously inadequate and a 3°dimensional computation is not practical, we resorted to a perturbative approach: try to determine theoretically which perturbations are
-
b
-
Fig. 5. Computed intensity for a pulse area slightlybelow 5n. (a) Isophotespattern, (b) intensity versus radius and time. amplified faster and at which rate. This is similar to the approach used by Bespalov, Talanov [11] and Suydam [ 12 ] to describe multifilamentation in nonlinear liquids and neodymium glass laser rods. The laser field is taken to be the sum of a plane wave (o and a perturbation ~ with periodic transverse dependence: ~ =A sin(Kx/xf2)
sin(Ky/x/2).
The Maxwell-Bloch equations are developped at first order in ~ , and the resulting perturbation equations are solved numerically. In the input plane, the temporal behavior of the perturbation and of the plane wave are taken to be identical. So we obtain an amplification factor fl of the perturbation energy as a function of K 2 and penetration length z for a 309
Volume 65, number 4
OPTICS COMMUNICATIONS
~z
2O
0
I
I
ROO
I
I
I
-qo0
~, Cr_m-~ ) Fig. 6. Perturbative gain versus transverse wavenumber. N= 8 × 10~2atoms/cm3, Io= 200 W/cm2. given i n p u t optical area. It appears that the natural longitudinal a n d transverse length units for this problem are respectively:
Lg : 47~~.ohC/27cNlt2 o) T ,
rp = (2Lg/4n) 1/2 ,
where T is the laser pulse duration. In the conditions of fig. 2, we get the curve of fig. 6 for z = 7 cm ( 10 Lg). One sees that the perturbation has grown faster for K = K m ~ 2 5 0 cm ~, giving an interfilament spacingof2n/Kx ~ 2 n \ / 2 / K ~ 0.035 cm, when the experimental value is about 0.060 cm. One sees that Km is about 1.6 times 1/x//~g, which is the expected order of magnitude for the 2n pulse as given in ref. [3]. The m a x i m u m of the gain curve gets
310
15 February 1988
higher and sharper with increasing penetration length, but the limits of the perturbative regime are reached, for any practical laser beam, well below the total length of 1 m. The existence of a preferred transverse periodicity allows one to u n d e r s t a n d the genesis of light filaments qualitatively in analogy with the Suyd a m model. In summary, the complicated situation of a dense atomic degenerate m e d i u m interacting with a spatially slightly perturbed resonant laser beam can be satisfactorily understood by separating transverse reshaping and temporal mechanisms, at least for a qualitative interpretation.
References [1] H.M. Gibbs, B. B61ger and L. Baede, Optics Comm. 18 (1976) 199. [2] H.M. Gibbs, B. BNger, F.P. Mattar, M.C. Newstein, G. Forster and P.E. Toschek, Phys. Rev. Lett. 37 (1976). [3] L.A. Bol'shov, V.V. Likhanskii and A.P. Napartovich, Soviet PhysicsJETP 45 (1977) 928. [4] M.J. Ablowitzand Y. Kodama, Phys. Lett. A70 (1979) 83. [5] G.J. Salamo, H.M. Gibbs and G.G. Churchill, Phys. Rev. Lett. 33 (1974). [6] H.M. Gibbs, S.L. McCall and G.J. Salamo, Phys. Rev. A, 12 (1975). [7] S.L. McCall and E.L. Hahn, Phys. Rev. 183 (1969) 457. [8] R.E. Slusher and H.M. Gibbs, Phys Rev. A 5 (1972) 1634. [9] F.P. Manar, Appl. Phys. 17 (1978) 53. [10] Ph. Kupecek, M. Comte, B. Visentin and J.-P. Marinier, Optics Comm. 56 (1985) 1. [ 11 ]g.I. Bespalov and V.I. Talanov, JETP Lett. 3 (1966) 307. [ 12] B.R. Suydam, IEEE J. Q.-E. QE 10 (1974) 837.