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Interferometric studies of 3371 Å N2 laser
Volume 66A, number 1
PHYSICS LETTERS
INTERFEROMETRIC
STUDIES
OF 3371
AN2
17 April 1978
LASER
Jong Jean KIM Department of Physics, Korea Advanced Institute of Science, Chongyangni, Seoul, Korea Received 21 December 1977 Revised manuscript received 3 Ma~rch1978
Experimental fringe visibility curve of a 3371 A N2 laser is presented. A theoretical fit using 19 stronger spectral components is generally in reasonable agreement with experiment but seems to require correlations and fluctuations in the N2 laser theory.
Applications of N2 pulsed lasers have been rapidly expanding in many areas such as dye laser pumping [1], superradiant pulse generation [2] and subnanosecond transient interferometry [3] Phenomenological understanding of N2 pulsed laser systems is so much advanced [4,5] that new variations in the design of simple, reliable high-power N2 lasers are continually introduced [4—7]. N2 pulsed lasers in general are not suitable for direct use in the fields of non linear optics where a high degree of laser coherence is needed. Coherent N2 lasers are successfully investigated to demonstrate the diffraction-limited laser beam of the pulsed N2 laser employing an unstable resonance cavity [8] and the single frequency emission (4278 A) from the N2 laser plifier coupled with a selective resonator-type, narrowband laser oscillator [9] A TEA N2 laser is reported to show a fringe visibility characterized by a doublet beating at least up to an optical path difference of 15 cm [3]. Coherence studies are important to specify the laser characteristics and to understand the underlying physical processes involved in laser action. In this letter we wish to report on our experimental investigation of the fringe visibility curve of the most widely used N2 laser operating at ~-‘4OTorr, ‘—lOO kW peak power and ‘—10 ns pulse width. Fig. 1 shows our experimental apparatus employing the Michelson interferometer to measure the fringe visibiity curve [10] of the N2 laser. Interference fringes
R
.
~-
LASER
BEAM
A
M C
.
_________________________
BS FS
.
Fig. 1. Schematic diagram of the experiment: A: an aperture stop of 0.5 cm diameter, M1: fixed mirror, M2: mirror on micrometer translation stage, BS: beam splitter, FS: fluorescent screen with hole in center, C: camera, typical mterference pattern is shown on photograph.
formed by single-shot laser pulses at variable optical path difference, X (mm), are recorded by a 35 mm camera used with all the lenses removed. The fringes recorded on the film are density scanned by use of a digital microphotodensitometer to measure 19
Volume 66A, number 1
PHYSICS LETTERS
1minC~’)representing iiof Imax(X) and lumination at maxima and minima, from which experimental values of the fringe visibility, V(X) are deter-
relative values
mined, The blackening characteristics of the film were determined by the densitometer readings of the film blackened by the direct N2 laser beam at five different total intensities obtained from single-shot to multiple five-shot exposures, with each shot fired under the same operating conditions and reduced in intensity to avoid overexposure, Michelson’s fringe visibility V defined as V = (~max ~min)/(~max + ~min) gives a quantitative measure of the fringe contrast and can be formulated in terms of the spectral parameters of the interfering light beams [101 The average intensity at a point of the fringe corresponding to a time delay r (or equivalently a path difference X, given by X = cr) between the two interfering beams is given by .
112(i) = (1E1(t) + E2(t h1
+
r)I )
*
~‘2
+
2(E 1 (t)E.,(t
+
=11+12+2
i J
r)~
lWTdw
When the spectral distribution of the light beam,1(w), is a set of discrete lines around the central frequency w0 with all the same line width F, 1(r) in the above equation or equivalently 1(X) becomes [10] 1(X) =10 +Ccos 0—S sin 0, where ~ = ~KlI(Ki),I(Ki) being the relative intensity of the ith component line, C = exp(—FX/2)
1(K1) cos(K1
—
K0)X,
K1
S
=
ex I~FXI2~ EI1K.~sin~K K ~X —
K-
0
‘~
~‘
“
0’
‘
w0r = K0X and K 2ir/X. DerivingI~~~(X) and 1(X) as given above and substituting the results into the definition of V(X), we obtain [10] 2 + S2)1/2/1 V(X) = (C 0 = exp(—ITX/2) 2 + (~J~ sin(K 2] 1/2 X [(~I1cos(K1 K0)X) 1 K0)X) =
Imin(X) from
~
20
—
tions in optics, a broad background spectral distribution from 3000 A to 4000 A [13] and the spatial coherence associated with the 0.5 cm beam size are possible causes to reduce the absolute fringe visibility. The broad spectrum from 3000 A to 4000 A would behave simply as a uniform background illumination on top of the fringes only if X> 1.2 X i0~ mm. A 3371 A filter and a beam expander would be desirable to cut the noise illumination and to improve the spatial coherence, and improve the fringe quality. However if the N laser has subpicosecond fluctuations in amplitudes and phases, further intrinsic reductions of the fringe visibility would result from a significant increase of the uniform background intensity [141. Apart from the overall reduction of the observed values of V(X), the agreement between experiment and theory is very good, granting the simplified assumptions implicit in the theory no correlations between component lines, constant intensities of component lines, etc. ‘.
—.
1(w)e
In fig. 2 the experimental curve is compared with the theoretical one computed according to the above equation for V(X) using the values of A 1 as given in table 1 [11]. All the measured values of V(X), including V(X = 0), had to be multiplied by a factor of 2.5 to fit the theoretical visibility curve, and the experimental curve in fig. 2 represents the multiplied one, however, the fringes continue to be visible for X over X = 82 mm. The overall reduction in the measured values of the fringe visibility probably has several reasons. Apart from small corrections for the instrumental imperfec-
.
=
r
17 April 1978
—
.
Table 1 Values of X1 used to compute the theoretical curve in fig. 2. The numbers in parentheses represent relative intensities; all the component lines are assumed to have the same line width of 0.003 A a) 3370.6188 (0.3), 3370.7533 3370.9190 (1.0), (0.5), 3371.0770 (0.1),
3370.6587 3370.7981 3370.9848 3371.1140
3371.1385 (1.0),
3371.2665 (0.1), 3371.3920 (0.3),
3371.3658 3371.4289 (0.3), (1.0).
(0.5), (1.0), (1.0), (0.3),
3370.7128 3370.8147 3371.0369 3371.1232
(0.8), (1.0), (0.8), (0.3),
3371.3070 (0.1), 3371.4215 (1.0),
a) Based on the estimation of ref. [11] but Ross et al. [121 obtained ‘—13 mA. This should not cause any big change in the present theoretical visibility curve. The referee reminded the author of this deviation.
Volume 66A, number 1
PHYSICS LETTERS
17 April 1978
>-
5
00
2.54
5.08
762 PATH
10.16
12.70
DIFFERENCE (X
,
15.24
7.78
2Q32
mm)
0-
>
2032
22.86
25.40
27.94 30.48 33.02 3556 PATH DIFFERENCE (X,mm)
Fig. 2. Fringe visibility curves of N
38.10
2 pulsed laser, experimental (0) and theoretical fit
In the present simplified picture of an N2 laser the theoretical visibility curve would not depend so much on the exact values of F (or equivalently &~)and I, as on the values of A1, because each of the I~gives contributions in terms of I~/~I~ and the term exp(—rX/2) remains almost constant for X with FX ~ I during the rapid oscillations of the sinusoidal functions of the A1 between +1 and —1. With A0 = 3371 A and &~= 3 mA the condition FX~ 1 is satisfied forX<4lOmm, well over the range covered in the present work. The larger discrepancy between experiment and theory in the very beginning is rather surprising because rX ~ 1 is better satisfied in the beginning. We speculate that this may imply that the strong prepulse of’-—picosecond duration [15] does really exist in the N2 pulsed laser and subsequent redistributions of the spectral density do occur among component lines. Further studies in both experiment and theory are in progress to include correlations, fluctuations and spatial coherence [16]. We would like to thank Prof. D.T. Phillips (Santa Barbara) for the initial suggestion of the problem, Professors D.M. Kim and F.K. Tittel (Rice University) for helpful comments and generous support of the experimental work, and Professor Chul Hui Park for computer programs. We also wish to acknowledge kind ad-
40.64
(—).
vice and valuable comments from the editor and the referee on the original manuscript. References [1] G. Marowsky, Opt. Acta 23 (1976) 855. [2] A. Andreoni, P. Benetti and C.A. Sacchi, Appl. Phys. 7 (1975) 61. [3] H. Schmidt, H. Salzmann and H. Strohwald, Appl. Opt. 14 (1975) 2250. [41 A.J. Schwab and F.W. Hollinger, IEEE J. Quantum Electron. QE-l2 (1976) 183. [5] W.A. Fitzsimmons, L.W. Anderson, C.E. Riedhauser and J.M. Vrtilek, IEEE J. Quantum Electron. QE-12 (1976) 624. [6] R. Polloni, Opt. Quantum Electron. 8 (1976) 565. [7] E.E. Bergmann, Rev. Sci. Instr. 48 (1977) 9. [8] G.C. Thomas and G. Chakrapani, Appl. Phys. Lett. 30 (1977) 633. [91 V.E. Brazovskü, V.N. Lisitsyn and A.M. Razhev, Soy. J. Quantum Electron. 7 (1977) 251. [101 A.A. Michelson, Studies in optics (Univ. of Chicago Press, 1927) ch. IV. [11] J.H. Parks, D.R. Rao and A. Javan, Appl. Phys. Lett. 13 (1968) 142. [12] [13] [14] [15]
Ross et al., Beitr. Plasmaphys. 16 (1976) 111. H.G. Heard, Nature 200 (1963) 667. D.M. Kim, P.L. Shah and T.A. Rabson, Phys. Lett. 35A (1971) 260. A.W. Ali, A.C. Kolb and A.D. Anderson, Appl. Opt. 6 (1967) 2115. [161 D.M. Kim, J.J. Kim and F.K. Tittel, to be published.
21
PHYSICS LETTERS
INTERFEROMETRIC
STUDIES
OF 3371
AN2
17 April 1978
LASER
Jong Jean KIM Department of Physics, Korea Advanced Institute of Science, Chongyangni, Seoul, Korea Received 21 December 1977 Revised manuscript received 3 Ma~rch1978
Experimental fringe visibility curve of a 3371 A N2 laser is presented. A theoretical fit using 19 stronger spectral components is generally in reasonable agreement with experiment but seems to require correlations and fluctuations in the N2 laser theory.
Applications of N2 pulsed lasers have been rapidly expanding in many areas such as dye laser pumping [1], superradiant pulse generation [2] and subnanosecond transient interferometry [3] Phenomenological understanding of N2 pulsed laser systems is so much advanced [4,5] that new variations in the design of simple, reliable high-power N2 lasers are continually introduced [4—7]. N2 pulsed lasers in general are not suitable for direct use in the fields of non linear optics where a high degree of laser coherence is needed. Coherent N2 lasers are successfully investigated to demonstrate the diffraction-limited laser beam of the pulsed N2 laser employing an unstable resonance cavity [8] and the single frequency emission (4278 A) from the N2 laser plifier coupled with a selective resonator-type, narrowband laser oscillator [9] A TEA N2 laser is reported to show a fringe visibility characterized by a doublet beating at least up to an optical path difference of 15 cm [3]. Coherence studies are important to specify the laser characteristics and to understand the underlying physical processes involved in laser action. In this letter we wish to report on our experimental investigation of the fringe visibility curve of the most widely used N2 laser operating at ~-‘4OTorr, ‘—lOO kW peak power and ‘—10 ns pulse width. Fig. 1 shows our experimental apparatus employing the Michelson interferometer to measure the fringe visibiity curve [10] of the N2 laser. Interference fringes
R
.
~-
LASER
BEAM
A
M C
.
_________________________
BS FS
.
Fig. 1. Schematic diagram of the experiment: A: an aperture stop of 0.5 cm diameter, M1: fixed mirror, M2: mirror on micrometer translation stage, BS: beam splitter, FS: fluorescent screen with hole in center, C: camera, typical mterference pattern is shown on photograph.
formed by single-shot laser pulses at variable optical path difference, X (mm), are recorded by a 35 mm camera used with all the lenses removed. The fringes recorded on the film are density scanned by use of a digital microphotodensitometer to measure 19
Volume 66A, number 1
PHYSICS LETTERS
1minC~’)representing iiof Imax(X) and lumination at maxima and minima, from which experimental values of the fringe visibility, V(X) are deter-
relative values
mined, The blackening characteristics of the film were determined by the densitometer readings of the film blackened by the direct N2 laser beam at five different total intensities obtained from single-shot to multiple five-shot exposures, with each shot fired under the same operating conditions and reduced in intensity to avoid overexposure, Michelson’s fringe visibility V defined as V = (~max ~min)/(~max + ~min) gives a quantitative measure of the fringe contrast and can be formulated in terms of the spectral parameters of the interfering light beams [101 The average intensity at a point of the fringe corresponding to a time delay r (or equivalently a path difference X, given by X = cr) between the two interfering beams is given by .
112(i) = (1E1(t) + E2(t h1
+
r)I )
*
~‘2
+
2(E 1 (t)E.,(t
+
=11+12+2
i J
r)~
lWTdw
When the spectral distribution of the light beam,1(w), is a set of discrete lines around the central frequency w0 with all the same line width F, 1(r) in the above equation or equivalently 1(X) becomes [10] 1(X) =10 +Ccos 0—S sin 0, where ~ = ~KlI(Ki),I(Ki) being the relative intensity of the ith component line, C = exp(—FX/2)
1(K1) cos(K1
—
K0)X,
K1
S
=
ex I~FXI2~ EI1K.~sin~K K ~X —
K-
0
‘~
~‘
“
0’
‘
w0r = K0X and K 2ir/X. DerivingI~~~(X) and 1(X) as given above and substituting the results into the definition of V(X), we obtain [10] 2 + S2)1/2/1 V(X) = (C 0 = exp(—ITX/2) 2 + (~J~ sin(K 2] 1/2 X [(~I1cos(K1 K0)X) 1 K0)X) =
Imin(X) from
~
20
—
tions in optics, a broad background spectral distribution from 3000 A to 4000 A [13] and the spatial coherence associated with the 0.5 cm beam size are possible causes to reduce the absolute fringe visibility. The broad spectrum from 3000 A to 4000 A would behave simply as a uniform background illumination on top of the fringes only if X> 1.2 X i0~ mm. A 3371 A filter and a beam expander would be desirable to cut the noise illumination and to improve the spatial coherence, and improve the fringe quality. However if the N laser has subpicosecond fluctuations in amplitudes and phases, further intrinsic reductions of the fringe visibility would result from a significant increase of the uniform background intensity [141. Apart from the overall reduction of the observed values of V(X), the agreement between experiment and theory is very good, granting the simplified assumptions implicit in the theory no correlations between component lines, constant intensities of component lines, etc. ‘.
—.
1(w)e
In fig. 2 the experimental curve is compared with the theoretical one computed according to the above equation for V(X) using the values of A 1 as given in table 1 [11]. All the measured values of V(X), including V(X = 0), had to be multiplied by a factor of 2.5 to fit the theoretical visibility curve, and the experimental curve in fig. 2 represents the multiplied one, however, the fringes continue to be visible for X over X = 82 mm. The overall reduction in the measured values of the fringe visibility probably has several reasons. Apart from small corrections for the instrumental imperfec-
.
=
r
17 April 1978
—
.
Table 1 Values of X1 used to compute the theoretical curve in fig. 2. The numbers in parentheses represent relative intensities; all the component lines are assumed to have the same line width of 0.003 A a) 3370.6188 (0.3), 3370.7533 3370.9190 (1.0), (0.5), 3371.0770 (0.1),
3370.6587 3370.7981 3370.9848 3371.1140
3371.1385 (1.0),
3371.2665 (0.1), 3371.3920 (0.3),
3371.3658 3371.4289 (0.3), (1.0).
(0.5), (1.0), (1.0), (0.3),
3370.7128 3370.8147 3371.0369 3371.1232
(0.8), (1.0), (0.8), (0.3),
3371.3070 (0.1), 3371.4215 (1.0),
a) Based on the estimation of ref. [11] but Ross et al. [121 obtained ‘—13 mA. This should not cause any big change in the present theoretical visibility curve. The referee reminded the author of this deviation.
Volume 66A, number 1
PHYSICS LETTERS
17 April 1978
>-
5
00
2.54
5.08
762 PATH
10.16
12.70
DIFFERENCE (X
,
15.24
7.78
2Q32
mm)
0-
>
2032
22.86
25.40
27.94 30.48 33.02 3556 PATH DIFFERENCE (X,mm)
Fig. 2. Fringe visibility curves of N
38.10
2 pulsed laser, experimental (0) and theoretical fit
In the present simplified picture of an N2 laser the theoretical visibility curve would not depend so much on the exact values of F (or equivalently &~)and I, as on the values of A1, because each of the I~gives contributions in terms of I~/~I~ and the term exp(—rX/2) remains almost constant for X with FX ~ I during the rapid oscillations of the sinusoidal functions of the A1 between +1 and —1. With A0 = 3371 A and &~= 3 mA the condition FX~ 1 is satisfied forX<4lOmm, well over the range covered in the present work. The larger discrepancy between experiment and theory in the very beginning is rather surprising because rX ~ 1 is better satisfied in the beginning. We speculate that this may imply that the strong prepulse of’-—picosecond duration [15] does really exist in the N2 pulsed laser and subsequent redistributions of the spectral density do occur among component lines. Further studies in both experiment and theory are in progress to include correlations, fluctuations and spatial coherence [16]. We would like to thank Prof. D.T. Phillips (Santa Barbara) for the initial suggestion of the problem, Professors D.M. Kim and F.K. Tittel (Rice University) for helpful comments and generous support of the experimental work, and Professor Chul Hui Park for computer programs. We also wish to acknowledge kind ad-
40.64
(—).
vice and valuable comments from the editor and the referee on the original manuscript. References [1] G. Marowsky, Opt. Acta 23 (1976) 855. [2] A. Andreoni, P. Benetti and C.A. Sacchi, Appl. Phys. 7 (1975) 61. [3] H. Schmidt, H. Salzmann and H. Strohwald, Appl. Opt. 14 (1975) 2250. [41 A.J. Schwab and F.W. Hollinger, IEEE J. Quantum Electron. QE-l2 (1976) 183. [5] W.A. Fitzsimmons, L.W. Anderson, C.E. Riedhauser and J.M. Vrtilek, IEEE J. Quantum Electron. QE-12 (1976) 624. [6] R. Polloni, Opt. Quantum Electron. 8 (1976) 565. [7] E.E. Bergmann, Rev. Sci. Instr. 48 (1977) 9. [8] G.C. Thomas and G. Chakrapani, Appl. Phys. Lett. 30 (1977) 633. [91 V.E. Brazovskü, V.N. Lisitsyn and A.M. Razhev, Soy. J. Quantum Electron. 7 (1977) 251. [101 A.A. Michelson, Studies in optics (Univ. of Chicago Press, 1927) ch. IV. [11] J.H. Parks, D.R. Rao and A. Javan, Appl. Phys. Lett. 13 (1968) 142. [12] [13] [14] [15]
Ross et al., Beitr. Plasmaphys. 16 (1976) 111. H.G. Heard, Nature 200 (1963) 667. D.M. Kim, P.L. Shah and T.A. Rabson, Phys. Lett. 35A (1971) 260. A.W. Ali, A.C. Kolb and A.D. Anderson, Appl. Opt. 6 (1967) 2115. [161 D.M. Kim, J.J. Kim and F.K. Tittel, to be published.
21