Gáti, László

Pintér, Ferenc

Vize, László

English

Vize László

Pintér Ferenc

Gáti László

University of Szeged

ON FIRST ORDER COHERENCE OF RADIATION OF A DYE-LASER By L. VIZE, F. P I N T É R and L. GÁTI Institute of Experimental Physics, Attila József University, Szeged (Received May 23, 1972) The first order (space) coherence of the radiation of a pulse dye-laser with rhodamine 6 G solved in ethanol as active material has been determined as a function of the total energy of the pulse, of concentration of the dye, and of the energy of the lines (bands) of the spectrum of the laser pulse. It has been found that the minima of the degrees of coherence decrease with increasing total energy of the pulse, whereas the degrees of coherence pertaining to constant band energies monotonously increase with increasing concentration. The degrees of coherence as a function of the energy of the lines (bands) first steeply increase, then slowly decrease. Introduction For characterizing the coherence of the electromagnetic radiation field (EMRF), correlation functions of different order [1—4] are used. If the E M R F is comparatively strong, of not too high frequency (see [1] p. 2533), quasimonochromatic, stationary and ergodic, the degree of coherence of the field, of first order according to GLAUBERS definition, can be determined from the intensity distribution of the interference pattern obtained with an interferometer of YouNG-type (T), with the formula [ 5 - 6 ] | V = 7 ™ * - / m i n / ( 1 ) ( 6 ) + / ( 2 ) ( 0 m 1 / 1 2 W l / m a x + / m i „ 2 j / 7 w ( 0 . / 7 ^ ( 0 ' K ) where (/max—/mi„)/(/max + /mi„) is the visibility of the interference fringes; / ( 1 ) ( 0 and / ( 2 ) ( ® are the light intensities which could be measured in the point Q of the screen on which the interference pattern is formed, if only one of the pinholes (1) and (2), respectively, were open. If the delay between the beams arriving to Q from (1) and (2) is small compared to the time of coherence of the light, then Eq (1) gives information about the spatial coherence of the EMRF. (In the following the notation . |y12(T)j = y is used.) Experimental arrangement and method of measurement As the spectrum of the EMRF produced by the dye-laser (DL) under investiga-tion consists of several hundreds of "Fabry—Perot lines", in building up our arrange-ment we first had to determine the sequence of the interferometer Y and of the 108 L. VIZE, F. PINTÉR AND L. GÁTI spectrograph S of Steinheil-type. If tnis sequence is DL, Y, S and the straight line determined by the two pinholes (1), (2) of Y is parallel to the entrance slit of S, then the narrow band cut out by the slit from the fringes perpendicular to the slit will be resolved by S according to wavelength. Such a system of fringes, a "coherence spectrum", is shown in Fig. 1. As our dye-laser gives short pulses and so its power fis comparatively high, therefore 5 may change the struc-ture of the field (polarization, spectrum) both by linear and nonlinear effects; therefore the sequence DL, S, Y is not suitable. Y itself may also cause changes in the structure of the EMRF, e.g. by reflecting part of the radiation from its sur-face back to the resonator; therefore Y must be made with a diffusely reflecting or black surface. On the edges of the pinholes of Y, not only diffraction but e.g. also Brillouin-Fig. 1 -scattering may occur, changing hereby the visibility of the fringes. Because of the circumstances mentioned above, the power density produced by DL and controlled by adjusting the pumping was chosen to be about 103 W/cm2. The energy was measured by the microcalorimeter described in [7] or by the photodetector BPY 10 calibrated with the microcalorimeter, and the time with a cathode ray oscilloscope type EMG 1546. In the case of power densities of this order of magnitude relevant disturbing effects cannot occur. The sequence DL, Y, S has the further experimental advantage that the inter-ference pattern of all "Fabry—Perot lines" of a single pulse can be obtained with the same Y. A diagram of our arrangement is shown in Fig. 2. The cylindrical glass cell C containing the active dye solution was 10 cm long and of 0,8 cm inner diameter. Lj and L2 were Xe flash lamps type IFP-800, receiving the power supply from a condensor of 10 nF capacity loaded to 4—6 kV. The resonator consisted of the ON FIRST ORDER COHERENCE OF RADIATION OF A DYE-LASER 1 0 9 mirrors M1 of 500 cm curvature radius, and of the plane mirror M2, with reflection coefficients of 70% and 99%, respectively. The pinholes of the interferometer Y, reflected by the glass plate G were photographed by the camera CA to give blacken-ings, from which the light intensities / ( 1 ) ( 0 and I(2)(Q), respectively, could be de-termined. Y consisted of a thin aluminium plate with two pinholes of 0.002 cm diameter, the distance between their cen-tres being O.'Ol cm. The lengths 4 , /2, /3 were 40 cm, 100 cm, 15 cm, respectively; 4 and /3 were chosen on the basis of trial measurements. According to these the visi-bility of the fringes did not show significant changes, and increased only slightly with 4 gradually decreasing down to 1 cm. As the intensity of the light of the flash lamps passing through M2 had to be de-creased, /2 was'chosen to 100 cm. An ORWO (Wolfen) film of 27 DIN sensitivity was used as detector and its blackening determined with a Zeiss pho-tometer. To permit to conclude from the blackening to the intensity and the energy, the film was calibrated. The calibration was made with a lamp giving a flash commensurable with the halfwidth in time of the laser pulse. The energy measurements were checked by determining the energy of the same laser pulse — Em and both with a microcalorimeter and E f -EmCin arbitrary Fig. 3  icr cal ri eter a a pho- • tographically, respectively, for flashes of different energies. Supposing the correctness of both methods of measurement, Ef and Em should be proportional. As it is to see from Fig. 3, this desired proportionality subsists with a mean absolute deviation of about +10 units. The degree of coherence can be determined from y calculated from Eq. (1) if the conditions of validity are fulfilled, i.e. if the field under investigation is quasi-monochromatic, stationary and ergodic. This last condition is essentially fulfilled, as the E M R F described by quantum electrodynamics is pseudoergodic; according to our estimation, our field is essentially stationary from the point of view of co-. herence. For this estimation the shape of the pulse was photographed and found that it does not con-tain spikes. In the time interval most important for photography, in which the radiation is the most intensive, the changes in number of photons seem to be small enough, and so the field of the DL can be considered as approximately stationary from-the point of view of the number of photons in this time interval. With regard to the definition of y (see [6]), this also means that the correlation function is approximatively stationary from the point of view of coherence. For calculating y on the basis of Eq. (1), our field must be monochromatic. As the condition of monochromaticity consists in the mean half width Av of the beam being much less than its mean frequency v (see [6] p. 502) and the spectrum of the DL consisting of separate lines, a series of degrees of coherence according 1 1 0 L. VIZE, F. PINTÉR AND L. GÁTI 1 ? » M O N N ' Ö O O ^ C O \ 0 v© V© VD sO V© t— ^O 6-10 U] r" . T j - M — — - M O h V Ű ' Í O l N 1 ?» OIS tq • o ^ O - n ' t ^ - n S ?s m ^ r - V O ^ M O O N T f O V ^ - M O O © rj- kJ 1 O Cí ON — n n i O ^ « ^ - O O O N í N -| n ^ W O N V Ű O ^ M O h - ' t N — O J r n n i n r ^ O <s f > © 04 c o O (N —1 t-- r o s P» ^ ű i n i O T f n n r K N n n n i r i ' O O M0 s T l - m — 1 N r i IT) o C\ h) M J i h n i / I O V ^ ' t n — i n n n - "^t — r ^ 8-10 U) 00 t"- © C» — 00 . s X r t- r f OO — — ^ " O n O ' A l i r i l ^ ^ T l ' n i r i ^ ' t n 7-10 s ?•» lOOO — o SO tu i n n v ű h - c i O M x i a M N O N ' n ' n ^ M y ű 1 ?•» o <n W - ^ • O O O O - - ^ ' • s P» — 0 \ N Tj- 00 00 — 00 t OG vo C \ CO VC •«t — r - r - «O i </í s o t i fe 5 ^ . s 2? ON FIRST ORDER COHERENCE OF RADIATION OF A DYE-LASER 111 § ?» f n ^ O O O M O C O N V O \C I— ^O ^o \o \o n 1 1 o ^ m « — m - ^ t m f S m — s u-ï <N ro VO' © - lô fe) n " n 0 \ 0 \ 0 - I r t f O ' t ?» O h - ^ i o ^ O i r i ' t m ' i r i f ^ m f N n «n . (S «o o en o O O N O ^ r - ' O ' ^ ^ O s O N W O O i n O . — ( N r - r-- r - o o o r i M M n m ^ h s M h - r - M X — T j - i n 'OVOrNr^ r ^ V O ^ ' t T t - n m i S M M i S r S r -in o IT> (N CN o ON CN i — l O O N f ^ O O ' ^ ^ ' - i v Û ' A ^ ^ _ ^ _ _ ^ s r-. t - r < ^ f l n M ^ . (N 2-10 tq VOOO^T fVOOOfSh-^O \ n n h O O ^ N N n s I ^t Tt r̂ - rn ^ r i fN 'sû.f^i ^ ON G\ ON V O ' O ^ i O ^ O ^ ' O f S f O r i n f s J f n M o <N MO tq TtTj-V^VOr-ON'— (N N (N M iS M (S . 1 Î M OO t^ W Tt 0\ o " T l ^ ' î J ' W r i H M ' r - ! <N m m o fN 9-10 - n h Q O O - M M N s «ft ?» 00 1 ' © 00 h) ^ " î ^ o o o c — O ^ r - c o O h — — M f l ^ ^ ' i s ?» 000-3*mv£> — — oo n v i ir) Xf "D "O in ir, <n TNJ 1 1 o r-* I» ^ . O ^ r - h - f N f N ^ - H f N 1 p. ^ • O s o o h - f S i n ^ ^ m o o ^ T j - m h - i t tri o m o VO. b) 1 ?» T t - ^ t i N m i N c N c S c N in 00 <N TI-CS 5-10 h) H T f O0 0 \ 0 0 - " H s OO-H — COTj-OOfNl^ ' i I ^ l ^ r t IO l o m 4-10-iq \ D M O O O \ S O O O vi F-- C\ - - iN^J* 1 1 s o n ' e . s h) S § . s £ v a s_ s 00 G i i N s? w o o s c • s 1 1 2 L. VIZE, F. PINTÉR AND L. GÁTI to frequency v can be associated with each pulse. The dispersion of the spectro-graph used was 12 A/mm in the spectral range employed. The width of the spectrum photographed from the laser pulse was about 20 A. The photometer used enabled us to divide this interval of 20 A into about 20 parts, the halfwidth of each band being less than 1 A, which also complies with the requirement of monochromaticity. Thus a series of the mean degree of coherence of a few "Fabry—Perot lines" of this narrow wavelength interval, ordered according to wavelength, could be coordinated to each pulse. . Results of measurements Using the arrangement • and method described, we determined the coherence spectra of the E M R F produced by our dye-laser in the axis of the laser beams. As active dye, different concentrations of rhodamine 6 G solved in ethanol were used, with 6% acetic acid added. Table I contains the coherence spectrum. The degrees of coherence pertaining to the same concentration expressed in per cents are arranged according to increasing wavelengths. With increasing concentration the mean wavelength of generation is shifted towards greater wavelengths [8]. This slight change is not shown in our table. With each degree of coherence also the energy of its band is given. In Table II the sequences of the degrees of coherence are arranged according to the energy of the band. The three lowest lines of Table II give the total energy E measured with the photodetector, the degree of coherence y100 pertaining to 100 units of band energy and ymjn, the minimum of the degree of coherence for the given concentration. Fig. 4 ON FIRST ORDER COHERENCE OF RADIATION OF A DYE-LASER 1 1 3 Arranging the degrees of coherence for the same concentration according to the band energies, the curves shown in Fig. 4 are obtained. y100 as a function of concentration is plotted in Fig. 5, wheieas in Fig. 6 y,nin as a function of the total energy of the pulse is shown. According to our measurements, the dependence of y on the band energy E for a given concentration is described by. a function steeply increasing in the range of small energies, then monotonously decreasing after a not too sharp maximum, The degrees of coherence of the decreasing sections pertaining to constant band Fig. 5 E(inarbitrary units) Fig. 6 1 1 4 L. VIZE, F. PINTÉR AND L. GÁTI energies show a monotonous increase as a function of concentration in the given concentration range. The minima of the degree of coherence of the same decreasing range decrease monotonously when plotted as a function of the total energy of the laser beam. * * * The authors are indebted to sincere thanks to Prof. I . KETSKEMÉTY, Director of the Institute of Experimental Physics, for valuable discussion and suggestions during the measurements. References [1] Glauber, R. J.: Phys. Rev. 130, 2529 (1963). [2] Glauber, R. J.: Phys. Rev. 131, 2766 (1963). [3] Wolf, E.: Nuovo Cimento 12, 884 (1954). [4] Wolf, E.: Proceedings of the Symposium on Optical Masers (John Wiley & Sons, Inc., New York, 1963). [5] Mandel, L., E. Wolf: Rev. Mod. Phys. 37. 231 (1965). [6] Born, M., E. Wolf: Principles of Optics (Pergamon Press, 1959, p. 503). [7] Dombi, J., L. Gáti, I. Ketskeméty, I. Szalma and L. Vize: Acta Phys. et Chem. Szeged 16, 3 (1970). [8] Ketskeméty, I., I. Szalma, L. Kozma and B. Rácz: Z. Naturforsch. 25a, 1512 (1970). О КОГЕРЕНТНОСТИ ПЕРВОГО РОДА И З Л У Ч Е Н И Я ЛАЗЕРА Н А К Р А С И Т Е Л Е Л. Визе, Ф. Пинтер и Л. Гати Определена зависимость когерентности (пространственной) первого рода излучения импульсного лазера на красителе родамин 6 Ж в этиловом спирте от энергии лазерного им-пульса, концентрации активного вещества и энергии отдельных линий (полос) в спектре излучения. Получено, что с возрастанием энергии импульса минимальная степень когерент-ности уменьшается, а с увеличением концентрации при неизменных энергиях полос возрас-тает. С ростом энергии полос степень когерентности сначала быстро увеличивается, а затем медленно уменьшается. 

On first order coherence of radiation of a dye-laser

ON FIRST ORDER COHERENCE OF THE RADIATION OF A DYE-LASER By L. VIZE, F. PINTÉR and L. GÁTI Institute of Experimental Physics, Attila József University, Szeged • The first order (space) coherence of a pulse dye-laser with rhodamine 6G solved in ethanol as active material has been determined as a function of the energy of the lines (bands) of the spectrum of the laser pulse. The degrees of coherence first steeply increase, then slowly decrease. Examining the coherence spectrum of a pulse dye-laser, it has been found that the half-width of the individual lines are 10"2 Á or smaller, while the degree of space coherence is nearly zero. For characterizing the coherence of the electromagnetic radiation field (EMRF), correlation functions of different order [1—4] are used. If the EMRF is comparatively strong and of not too high frequency, the degree of coherence of. the field, of first order according to GLAUBERS definition, can be determined from the intensity distribu-tion of the interference pattern obtained with an interferometer of YouNG-type (Y), with the formula [5—6] , - , _ / m a x ~ / m i n / ( 1 ) ( 0 + / ( 2 ) ( 6 ) ' ' /max + / m i „ ' where (/max-/mi„)/(/max+/n,in) is the visibility of the interference fringes; (Q) and / (2 ) (Q) are the light intensities which could be measured in the point Q of the screen on which the interference pattern is formed, if only one of the pinholes (1) and (2), respectively, were open. Experimental arrangement and method of measurement As the spectrum of the EMRF produced by the dye-laser (DL) under investi-gation consists of several hundreds of lines, in building up our arrangement we first had to determine the sequence of the Young-interferometer (Y) and of the spectro-graph (S) of Steinheil -type. If this sequence is DL, Y, S and the straight line deter-mined by the two pinholes of the Young-interferometer is parallel to the entrance slit of the spectrograph, then the narrow band cut out by the slit from the fringes per-pendicular to the slit will be resolved by S according to wavelength. Such a system of fringes, a "coherence spectrum", is shown in Fig. 1. A diagram of our arrangement is shown in Fig. 2. The cylindrical glass cell C containing the active dye solution was 10 cm long and of 0.8 cm inner diameter. L1 and Lo were Xe flash lamps type IFP—800, receiving the power supply from a 4 1 8 L. VIZE, F. PINTÉR A N D L. GÁTI 1 t r | I . ¿ 7 ^ wfc m condensor of 10 n ? capacity loaded to 4—6 kV. The resonator consisted of the mir-rors Mx of 500 cm curvature radius, and of the plane mirror M2, with reflection coefficients of 70% and 99%, respectively. The pinholes of the interferometer Y, reflected by the glass plate G were photographed by the camera CA to give blacken-ings, from which the light intensities 7(1) (Q) and 7(2) (Q), respectively, could be determined. Y consisted of a thin aluminium plate with two pinholes of 0.002 cm diameter, the distance between their centres being 0.01 cm. The lengths l l t /2, la were 40 cm, 100 cm, 15 cm, respectively; /2 and l3 were chosen on the basis of trial measurements. According to these, the visibility of the fringes did not show significant changes and increased only slightly with /2 gradually decreasing down to 1 cm. As the intensity of the light of the flash lamps passing through M2 had to be decreased, /2 was chosen to 100 cm. An OR WO (Wolfen) film of 27 DIN sensitivity was used as detector and its blackening determined with a Zeiss photometer. To permit to conclude from the blackening to the intensity and the energy, the film was calibrated. The calibration was made with a lamp giving a flash commensurable with the half-width in time of the laser pulse. For calculating y on the basis of Eq. (1), our field must be quasimonochromatic. As the condition of quasimonochromaticity consists in the mean half-width A v of the beam being much less than its mean frequency v and the spectrum of the DL consist-ing of separate lines, a series of degrees of coherence according to frequency v can be associated with each pulse. The dispersion of the spectrograph used was 12 A/mm and 2 A/mm, respectively, in the spectral range employed. The width of the spectrum photographed from the laser pulse was about 20 A. The photometer used enabled us to divide this interval of 20 A into about 20 or 1000 parts, respectively, the halfwidth of each band being less than 1 A or 0.02 A, respectively. Thus a series of the degree of coherence, ordered according to wavelength, could be coordinated to each pulse. Fig. 1 t: t , Fig. 2 FIRST ORDER COHERENCE O F DYE-LASER RADIATION 4 1 9 Results of measurements Using the arrangement and method described, we determined the coherence spectra of the EMRF produced by our dye-laser.in the axis of the laser beams. As active dye, different concentrations of rhodamine 6 G solved in ethanol were used, with 6% acetic acid added. Fig. 4 4 2 0 L. VIZE, F. PINTÉR A N D L. GÁTI Arranging the degrees of coherence for the same concentration according to the band energies, the curves shown in Fig. 3 are obtained. According to our measure-ments, the dependence of y on the band energy £ for a given concentration is described by a function steeply increasing in the range of small energies, then monotonously decrasing after a not too sharp maximum. 70 U Tnin. (7.) 10 T -| i s 0 3 6 70 E fin arbitrary units) Fig. 5 y100 as a function of concentration is plotted in Fig. 4, where y100 is the degree of coherence pertaining to 100 units of band energy. The degrees of coherence of the decreasing sections pertaining to constant band energies show a monotonous increase as a function of concentration in the given concentration range. In Fig. 5 ymin as a function of the total energy of the pulse is shown, here ymin is the minimum of the degree of coherence for the given concentration. The minima of the degree of coherence of the same decreasing range decrease monotonously when plotted as a function of the total energy of the laser beam. Fig. 6 shows the coherence spec-trum of a dye-laser, measured with a spectrograph of 2 A/mm dispersion. The halfwidths of lines are about 10~2 A, the degree of coherence is nearly zero at intensive lines, thus the low degree of coherence can not be attri-buted to the line-width. Further measurements in this Fig. 6 fields are in course. FIRST ORDER COHERENCE OF DYE-LASER RADIATION 4 2 1 References [1] Glauber, R. J.: Phys. Rev. 130, 2529 (1963). [2] Glauber, R. J.: Phys. Rev. 131, 2766 (1963). [3] Wolf, E.: Nuovo Cimento 12, 884 (1954). [4] Wolf, E.: Proceedings of the Symposium on Optical Masers (John Wiley & Sons, Inc., New York, 1963). [5] Mandel, L„ E. Wolf: Rev. Mod. Phys. 37, 231 (1965). [6] Born, M„ E. Wolf: Principles of Optics (Pergamon Press, 1959, p. 503). О КОГЕРЕНТНОСТИ. ПЕРВОГО РОДА ИЗЛУЧЕНИЯ ЛАЗЕРА НА КРАСИТЕЛЕ Л. Визе, Ф. Линтер и Л. Гати Определена зависимость когерентности (пространственной) первого рода излучения импульсного лазера на красителе родамин 6Ж в этиловом спирте от энергии отдельных ли-ний (полос) в спектре излучения. С ростом энергии полос, степень когерентности сначала быстро увеличивается, а затем медленно уменьшается. Из спектра когерентности получилась, что полуширина отдельных линий порядка 10~2А или меньше, в то же время степень прост-ранственной когерентности приблизительно равна нулю. 

On first order coherence of the radiation of a dye-laser

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On first order coherence of radiation of a dye-laser

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