Spectroscopic and Laser Properties of Europium αNaphthoyltrifluoroacetonate inSolutionE. P. Riedel and R. G. Charles Citation: The Journal of Chemical Physics 45, 1908 (1966); doi: 10.1063/1.1727870 View online: http://dx.doi.org/10.1063/1.1727870 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/45/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Structural and optical properties of europium doped zirconia single crystals fibers grown by laser floatingzone J. Appl. Phys. 109, 013516 (2011); 10.1063/1.3527914 Correlation between the spectroscopic and structural properties with the occupation of Eu 3 + sites inpowdered Eu 3 + -doped Li Ta O 3 prepared by the Pechini method J. Appl. Phys. 106, 063509 (2009); 10.1063/1.3204967 Luminescence and spectroscopic behavior of Eu 3 + -doped Y 2 O 3 and Lu 2 O 3 epitaxial films grown bypulsed-laser deposition J. Appl. Phys. 97, 023513 (2005); 10.1063/1.1830087 Spectroscopic properties of Er 3+ and Eu 3+ doped acentric LaBO 3 and GdBO 3 J. Appl. Phys. 93, 8987 (2003); 10.1063/1.1536724 Photoluminescence properties of Eu 3+ -doped ZnS nanocrystals prepared in a water/methanol solution Appl. Phys. Lett. 80, 3605 (2002); 10.1063/1.1478152

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1908 SMITH, McKENNA, AND MOLLER

. the band at 124.5 cm- l to the (0-1) transition, the resulting F and s values would differ by an unreason­able amount from those obtained in the microwave studies. Also the (1-2) transition is not predicted at 104.5 cm- l . [The fact that this model almost predicts the lower (0-1) transition seems to be due to the fact thatfOi compensates for -h in Formula 13 of Ref. 14.J

If we include all the interaction terms between the two tops, as in Ref. 14, there are two possible assign­men ts: (i) both bands correspond to (0-1) transitions, (ii) the band at 124.5 cm-l is a (0-1) transition and the band at 104.5 cm- l is a (1-2) transition. The case (ii) is improbable because we would expect three (1-2) transitions of approximately equal intensity. There­fore we feel that both bands are (0-1) transitions. Ac­

. cording to the selection rules in Ref. 14 it is possible

that due to tunneling both (0-1) transItIOns can be observed. The splitting of 20 cm-l for the first excited state gives a value of V12 = -28 cm-l which is 10% of the barrier height V. Dreizler and Dendl17 gave a value of V12 corresponding to 7% of V for (CHshSO with a potential barrier of V = 1070 cm-l . In view of this, 10% is still a reasonable value for a low-barrier molecule like acetone.

ACKNOWLEDGMENT

We would like to thank Dr. T. Richter of the Picatinny Arsenal, Dover, N. J., for his continued interest in our work and advice on the purification of the compounds.

17 H. Dreizler and G. DendI, Z. Naturforsch. 20a, 1431, (1965).

THE JOURKAL OF CHEMICAL PHYSICS VOLUME 45, NUMBER 6 15 SEPTEMBER 1966

Spectroscopic and Laser Properties of Europium a-N aphthoyltrifiuoroacetonate in Solution *

E. P. RIEDEL AND R. G. CHARLES

Westinghouse Research Laboratories, Pittsburgh, Pennsylvania

(Received 8 April 1966)

Ultraviolet radiation absorbed by the organic ligands surrounding the europium ion in europium a-naph­thoyltrifluoroacetonate Eu(a-NTF)4- is efficiently converted via intramolecular energy transfer to fluores­cence characteristic of Eu3+. The quantum efficiency for this process is shown to be a constant from 2600 to 3900 A in acetonitrile solution. Laser operation has been observed at temperatures up to -lODC. The effect of the relatively high scattering losses on both the threshold and the radiance of the laser are discussed.

INTRODUCTION

DURING the past few years a considerable amount of information has been obtained on the chemical,

spectroscopic, and laser characteristics of rare-earth chelates.I- lo Much of this work stems from the early

* This work was partially supported by Project Defender under joint sponsorship of ARPA, ONR, and DOD under Contract No. Nonr 5033(00).

1 R. C. Ohlmann, E. P. Riedel, R. G. Charles, and J. M. Feld­man, in Quantum Electronics, P. Grivet and N. Bloembergen., Eds. (Columbia University Press, New York, 1964), Vol. 3, p. 779.

2 R. E. Whan and G. E. Crosby, J. Mol. Spectry. 8, 315 (1962). 3 R. G. Charles and A. Perrotto, J. Inorg. Nucl. Chem. 26, 373

(1964) . 4 R. C. Ohlmann and R. G. Charles, J. Chem. Phys. 40, 3131

(1964) . 6 R. G. Charles and R. C. Ohlmann, J. Inorg. Nucl. Chem. 27,

119 (1965). 6 R. G. Charles, J. Inorg. Nucl. Chem. 26, 2195 (1964). 7 R. G. Charles, J. Inorg. Nucl. Chem. 26, 2298 (1964). 8 R. G. Charles and R. C. Ohlmann, J. Inorg. Nucl. Chem. 27,

255 (1965). 9 F. Halverson, J. S. Brinen, and J. R. Leto, J. Chem. Phys.40,

2790 (1965); 41,157 (1964). 10 M. L. Bhaumik, J. Chem. Phys. 40, 3711 (1964).

demonstration by Weissmannll of intramolecular energy transfer in these materials and their more recently demonstrated suitability for use as the active material in liquid lasers.12- 16 The interesting spectroscopic and laser propertiesl3 ,17 of the europium tetrakis (benzoytri­fiuoroacetonate) anion Eu (BTF)4-, la, have led us to investigate the consequences of altering the structure of the anion while maintaining the basic tetrakis form. One of the compounds we have considered in this study is the piperidinium salt of europium tetrakis (a­naphthoyltrifluoroacetonate), PEu (a-NTF)4, lb. This paper describes some of the spectroscopic, chemical, and

11 S. 1. Weissman, J. Chem. Phys. 10,214 (1942). 12 A. Lempicki and H. Samelson, Phys. Letters 4, 133 (1963). 13 H. Samelson, A. Lempicki, C. Brecher, and V. Brophy, App!.

Phys. Letters 5, 173 (1964). 14 A. Lempicki, H. Samelson, and C. Brecher, J. Chem. Phys.

41,1214 (1964). 16 E. J. Schimitschek, J. A. Trias, and R. B. Nehrich, Jr., J.

App!. Phys. 36, 867 (1965). 16 E. P. Riedel and R. G. Charles, J. App!. Phys. 36, 3954

(1965) . 17 C. Brecher, H. Samelson, and A. Lempicki, J. Chem. Phys. 42,

1081 (1965).

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PROPERTIES OF EUROPIUM a-NAPHTHOYLTRIFLUOROACETONATE 1909

laser properties of this material dissolved in aceto­nitrile:

Ia: R' 0 Ib: R' 8 ~ /;

Ie: R' o s

CF3 \ C-o

1/ HC

\ c=o /

R

EXPERIMENTAL

Materials

Eu

The previously unreported iJ-diketone, a-napthoyltri­fluoroacetone, was synthesized by the condensation of ethyltrifluoroacetone with methyl-a-naphthyl ketone in the presence of sodium methoxide. The procedure was similar to that of Reid and Calvin.Is The compound was conveniently isolated as the crystalline piperi­dinium salt, formed from the crude iJ-diketone and a small excess of piperidine in ethanol. Over-all yield was 59%. Calculated analysis for (CsH12N)+­(C14HsF 30 2)- was C, 65.0%; H, 5.7%; N, 4.0%. Analysis was found to be C, 65.0%; H, 5.8%; N, 3.9%.

The europium chelate PEu (a-NTF)4 was prepared as follows. The piperidinium salt above (6.32 g, 0.018 moles) was dissolved in 60 m195% ethanol by warming. EuCla (0.004 moles) dissolved in 20 ml water was added to the warm solution. The chelate separated as a semisolid which crystallized on standing at room temperature. The solid was washed with 1: 4 (vol/vol) ethanol-water and air dried at room temperature. Yield was 96%, based on the EuCh. Calculated analy­sis for (CsHI2N)+[(C14HgF302)4Eu]- was C, 56.4%; H, 3.4%; N, 1.1 %. Analysis was found to be C, 56.3%; H, 3.5% N, 1.5%.

Solutions in acetonitrile were prepared from Fisher reagent-grade solvent.

Spectroscopy

Absorption spectra of solutions of PEu (a-NTF)4 in acetonitrile were obtained on a Cary Model 14 spectro­photometer. The wavelength range below 3850 A where the absorption cross section is high was obtained

18 J. C. Reid and M. Calvin, J. Am. Chern. Soc. 72, 2948 (1950).

Filler Tube Laser Liquid

Quartz Capillary Tube

Mirror

FIG. 1. Schematic drawing of liquid laser cell (not to scale).

using a concentration of 2.5XlO-3M and 0.05-mm quartz cells (l-cm cells with quartz inserts). For wavelengths longer than 3850 A, a concentration of O.OlM was used and 1.0-mm quartz cells.

Fluorescence spectra were obtained with a !-m Jarrell-Ash spectrometer with a dispersion of 32 A/mm. A photomultiplier with an S-20 characteristic response was used to detect the signal. A Corning CS3-69 filter was placed between the sample and the entrance slit in order to remove scattered lamp light below 510 mM. The fluorescence spectra are presented corrected for system sensitivity as a function of wavelength. The samples were contained in quartz cells. By passing the light from an Osram (XBO-900) xenon-arc lamp through a second !-m Jarrell-Ash spectrometer, the samples were illuminated in a band between 380 and 350 mM. A Corning CS7 -37 filter was placed between the exit plane and the sample in order to eliminate scattered light above 390 mM.

The excitation spectrum was obtained by scanning with the spectrometer used in illumination of the sample and setting the other spectrometer at the desired wavelength of the fluorescence spectrum to be monitored. The spectrum is presented reduced to constant quanta per unit wavelength interval of the exciting beam. This was achieved by detecting with a photomultiplier the fluorescence of a rhodamine-B quantum counterI9 which was excited by a portion of the beam used to excite the sample. This signal was then ratioed with the signal from the sample fluores­cence.

Laser Apparatus

The laser cell used in these experiments is somewhat different than those used by other investigators.2o

The cell shown in Fig. 1 is a O.l-cm-i.d. quartz capillary tube with an active pump length of 6.7 cm and a mirror spacing of 9.3 cm. The ends of the tube were first polished flat to loA and parallel to better than 10 sec of arc. Quartz disks flat to loA and parallel to about 2 sec of arc were wrung on to the ends of the tube. Each disk was then attached to the tube with epoxy cement. Multilayer films having approximately

19 w. H. Melhuish, J. Opt. Soc. Am. 52, 1256 (1962). 20 A. Lempicki and H. Samelson, Proc. Symp. Opt. Masers,

Polytechnic Press, Polytechnic Institute, Brooklyn, N.Y., Micro­wave Res. Inst. Symp. Ser. 13, 347 (1963).

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1910 E. P. RIEDEL AND R. G. CHARLES

Filler Tube

CS 7-59 Filter

Flash Lamp

Mirror --+----hft-~ Aluminum Foil

Quartz Cell

FIG. 2. Schematic drawing of end view of laser assembly (not to scale).

99% reflectivity at 6120 A were deposited on the ou.t­side surface of each disk and are, therefore, not III

contact with the liquid material within the capillary. Three EG & G linear flash lamps (FX-42) are con­nected in series and placed at 120-deg intervals around the cell as shown in Fig. 2 with Corning CS7 -59 filters inserted between the lamps and the cell. A heavy aluminum foil is then wrapped around the outside of the three lamps. The cell assembly is held in an in­sulated chamber so that the temperature may be both stabilized and controlled by a flow of precooled and dry nitrogen.

The intensity of the light output from the end of the laser capillary and from the pump light from th~ flash lamps were presented simultaneously, as a functlOn of time on an oscilloscope screen. The traces were re­cord~d photographically on Polaroid 3000 speed fil~.

The light output-time recording, the spectral width, the wavelength, and the beam divergence of the la.ser emission may all be obtained simultaneously dunng one optical pumping cycle. The first three of these are obtained by passing the light from one end of th: ?ell through a i-m Jarrell-Ash spectrometer and Splittlllg the output, part going to a photomultiplier. and pa~t being recorded on film. The spectrometer IS used III

second order where its dispersion is 16 A/mm. The entrance slit is a Hilger-Watts Model F1497 in­dividually adjustable slit. The exit slit is also a Hilger~ Watts F1497 slit but modified so that it can open to 5 mm. A partially transparent mirror placed two inc?es beyond the exit plane splits the beam-one part gOlllg to a photomultiplier and the remainder to a lens. The lens magnified the spectrum at the exit plane ap­proximately 10 times. The magnified image is recorded on Polaroid 3000 speed film. A Wratten No. 24 red filter is placed in front of the film while a CS2-63 is placed in front of the photomultipli~r in order t~ rem?ve scattered flash lamp light. CalibratlOn of the dlspoerslOn of the system at the film plane which is 1.63 A/mm was accomplished by setting the entrance slit at 1O,u and the exit slit at 4 mm and allowing two neon referen~e lines to expose the film at 6096.16 and 6143.06 A. The source used was a neon-fill hollow cathode lamp.

The laser emission which falls between these two lines21

is then used to expose the film a second time. The resolution of this spectrograph at this entrance-slit setting was found to be 0.2 A by measuring with the aid of a traveling microscope the width of a line on the film obtained by using the 6328 A emission of an He-Ne gas laser as a narrow line source. .

The directionalitv of the laser output was studied during the same fla~h-tube pulse by photographing the far field pattern of the light output from the other end of the laser cell. A red Wratten No. 24 filter and appropriate neutral density filters. were placed ~n front of the Polaroid 3000 speed film III order to obtalll proper exposures free of flash lamp light.

RESULTS AND DISCUSSION

Structural Considerations

The considerable activity in the field of liquid lasers has resulted in the demonstration of laser action with a number of europium chelates. All such lasing species are tetrakis chelates derived from J3-diketones. (Al­though early liquid laser work was carried out with materials thought to be the tris chelates, current evidence indicates that these also were actually the tetrakis forms.) Laser action in solution has not, so far, been obtained with chelates derived from other classes of organic chelating agents nor has it been obtained with rare earths other than europium.

Of the europium J3-diketone chelates which have been investigated, particular interest attaches to those co~­taining a trifluoromethyl group as part of the org~mc structure (the anion of Formula I, above), Slllce solutions containing these compounds show laser action at relatively high temperatures.13.15.16 Most effort has been devoted to solutions containing the europium chelate anion of la, derived from benzoyltri­fluoroacetone. In some instances solutions containing this anion lase near room temperature.13.15.16 The compound Ic in which the 2-thienyl group is sub-

, I' 22 stituted for phenyl in la, also shows aser actlOn, although apparently not at as high tem~eratu:es as I~. Further studies of the compounds I, III which R IS varied would be expected to provide additional evidedce on the structural parameters which influence laser action. We report here data obtained with the compound Ib, in which the a-naphthyl group is sub­stituted for phenyl.

Substitution at R in I can alter the chelate anion in several different ways which could influence laser

'action. (1) The nature of R can affect the ultraviolet absorption spectra of solutions containing I, and hence can alter the wavelength range over which effective

21 American Institute of Physics Handbook, D. E. Gray et al., Eds. (McGraw-Hill Book Co., Inc., New York, 1963), 2nd ed., pp.7-52. " Ch

22 E. J. Schimitschek, R. B. Nehnch, and J. A. Tnas, J. em. Phys. 42, 788 (1965).

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PROPERTIES OF EUROPIUM a-NAPHTHOYLTRIFLUOROACETONATE 1911

optical pumping takes place. (2) R, through resonance and inductive interaction with the chelate rings, can influence the electron distribution within these rings and can alter the energy of the lowest organic triplet level relative to the energy of the europium 5Do reso­nance level. (3) Bulky groups at R could presumably, through steric hindrance, alter the symmetry of the eight bonded oxygen atoms about the Eu3+ and in­fluence the probability of the 5Do--t7F2 transition which gives rise to laser action.

Spectroscopy

When an acetonitrile solution of PEu (a-NTF)4 is illuminated with near-ultraviolet light, characteristic EuH ion fluorescence23 is observed as shown in Fig. 3. As may be seen from Curve A, the 5Do--t7F2 group is by far the most intense, accounting for approximately 90% of the total emission. The main line is centered

50 -7F \ \ \ 7F ,

80 o 4 0

Z' .v;

~ :560 Q> u

~ ~ «J 0 :::l

u::

~ 20 Q;

'"

710 690 670 650 630 610 590 570

Wavelength (m~1

FIG. 3. Room-temperature fluorescence spectra of O.01M PEu (a-NTF)4 in acetonitrile. Gain for Curve B is 19.2 times that for Curve A. Resolution,S A..

at 6118 A with a width at half-height of 28 A. Curve B was obtained by increasing the amplifier gain by a factor of 19.2. This shows in more detail the remaining groups which are barely apparent in Curve A. Analysis of the 5 Do--t7 F 0 emission has been shown to be of value in determining the number of different europium­containing species contributing to the observed fluores­cencep·16 The 5Do--t7Fo emission is shown in greater detail in Fig. 4. The appearance of only one line in this region is consistent with the assumption that only one europium species is responsible for the observed fluorescence spectrum.

The ultraviolet absorption spectrum of Eu (a-NTF)4-in acetonitrile is shown in Fig. S. The very large values of the molar extinction coefficient are characteristic of 7r-,r* absorption bands associated with the organic ligands of the molecule. As has previously been pointed out,! such intense absorption bands prevent effective pumping (at the concentrations required for laser operation) along the axis of a laser cell, even when the

23 G. H. Dieke and H. M. Crosswhite, AppJ. Opt. 2, 675 (1963).

~

.v;

~ :§ 60 Q> U C Q> U ~

~ 40 ~ :::l u:: Q> > ~ 20 Q;

'"

5800 5795 5790 5785 5780

Wavelength (AI

FIG. 4. Room-temperature 5DO->7FO fluorescence of O.01M PEu(a-NTF)4 in acetonitrile.

cell is as small as I-mm i.d. For this reason, the long­wavelength tail of the absorption band is the most effective pumping region for laser purposes. For ex­ample, at a concentration of 0.002M, the penetration depth defined as the reciprocal of the absorption coefficient for pump radiation is equal to the radius of the laser material at a wavelength of 379 mJL. This wavelength excites the cross section of the laser ma­terial in a O.I-cm-bore-diameter cell efficiently and fairly uniformly. At a cOllcentration of O.OIM, the wavelength for a penetration depth of 0.05 cm is shifted to 390 mJL. Wavelengths within this general range will, however, only be effective for laser pumping if the fluorescence quantum efficiency is high for ex­citation at wavelengths within this range.

A change in the quantum efficiency as a function of excitation wavelength may be ascertained by comparing

10 ·19 L....c-,-'--'-,-L-~L....l.-=--'-=-"'-:-'::-'--:':"-'-:=-'-::::-'--=--' m ~ • ~ ~ m _ ~ ~ ~ m Wavelength t mlJ)

FIG. 5. Room-temperature absorption spectrum of PEu(a-NTF). in acetonitrile.

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1912 E. P. RIEDEL AND R. G. CHARLES

§": H U]

i~J 80 t~~ ..,f. i--i ~1

" :,;.~ 60 ~

0 w

'" ~ 0 ::0 H 4() Ii;

t 20 0

r=l J\

t:: H E-< ;"i '"' ~

the absorption spectrum with the excitation spectrum. The excitation spectrum of a solution containing Eu (a-NTF)4- is shown in Fig. 6. For wavelengths longer than 3900 .:t, absorption of the exciting light by the sample decreases very rapidly. However, for shorter wavelengths essentially all of the exciting light is absorbed. The nearly horizontal line below 3900 A indicates therefore a quantum efficiency which is a constant within about ± 10% between 3900 and 2600 A. At room temperature, the quantum efficiency of a O.OIM solution in acetonitrile excited b,' 3150 A radi­ation is 0.S2±0.IS. This was obtained by comparing the fluorescence intensity of this solution with a solution of piperidinium europiunybenzoyltrifluoro­acetonate PEu (BTF)4 in acetonitrile, the quantum efficiencv of which has been measured and found to be O.75±O.IS.16 The decay time of the fluorescence of a O.OIM solution of PEu (a-NTF)4 in acetonitrile at 24°C is 408 J..Lsec. As the temperature is lowered, both the decay time and the quantum efficiency of PEu (a-NTF)4 increase reaching 0.95 (+0.05, -0.15) and 735 J..Lsec, respectively, at - 30°e.

Laser Characteristics

\\le have been able to obtain laser operation at various concentrations of Eu (a-NTF )4- in acetonitrile at temperatures up to -lO°C, As the temperature of the solution is increasecl above - 30°C, the flash-lamp energy required to obtain laser oscillations steadily increases. At -10°C this energy is near the maximum allowable energy for our excitation system and there­fore this is the highest temperature at which we have observed laser operation with this material. The rise in threshold requirements as the temperature is increased is due, at least in part, to the drop in quantum ef­ficiency with rise in temperature. This drop in quantum efficiency is somewhat more severe than it is for Eu (BTF)4- in acetonitrile where we and others have been able to obtain laser operation near room temper­ature,l3·15.16 In order, therefore, to ensure consistent

FIG. 6. Room-temperature excitation spectrum of 5 DO-->7 F2 fluorescence of a O.lJI solution of PEu (a-NTF)4 in aceto­nitrile.

results in laser experiments with Eu(a-~TF)4- we have conducted all experiments discussed in this paper at - 20°C.

A photomultiplier recording of the laser emission at approximately 1.2 times threshold-input energy to the flash lamps is shown in Fig. 7. For approximately the first 360 J..Lsec only a small photomultiplier signal due to spontaneous emission is observed. Intermittent laser emission then occurs for the next 270 J..Lsec followed by the decay of spontaneous emission.

Figures 8(a), and 8(b), and a photograph of the magnified image of the spectrum at the exit plane of the spectrometer were all taken simultaneously (see Ex­perimental section) at approximately 2.3 times thresh­old. In Fig. 8 (a), the laser spikes are again clearly evident. Laser threshold is reached sooner in Fig. 8(a) than in Fig. 7 as one would expect on the basis of the greater pumping rate. The cause of the somewhat more erratic character of the spiking, i.e., the sepa­ration of about 140 J..Lsec between the first two groups of spikes is not clear. One possible explanation for this laser suppression is scattering losses24 due to the effects of nonuniform heating of the liquid. This is a reasonable

FIG. 7. Top, photomultiplier recording of light output from O.OUf PEu (a-NTF)4 in acetonitrile. Bottom, recording of flash­lamp light. 62SJ input (1.2 times threshold). Scale, 200 /Lsec per division from left to right.

24 E. P. Reidel, Appl. Phys. Letters 5, 162 (1964).

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PRO PER TIE S 0 FEU R 0 PI U:\1 a - N ,\ P H THO Y L T R I FLU 0 R 0 ACE TON ATE 1913

explanation, in view of the fact that these losses are shown in a following section of this paper to be quite large even near threshold pumping conditions. In addition, it has been shown24 that the scattering effects increase rapidly as the pumping energy is increased.

Both the wavelength and spectral width of the laser emission during this flash-tube pulse were obtained by photographing the magnified image of the spectrum at the exit plane of the spectrometer. From the position of the laser line relative to the neon lines (see Ex­perimental section) the laser output wavelength was found to be 6118.2 A. From a measurement of the width of the laser line and a knowledge of the dispersion at the film plane (1.63 A/mm) the laser emission was found to take place over a wavelength band O.3±O.1 A wide. Since the spontaneous linewidth at - 20°C is 23 A, considerable spectral narrowing is evident during laser operation. The O.3-A band width is much larger than the spacing between individual modes of a plane parallel resonator25 with the dimensions used in this experiment. Therefore laser oscillations are evident ally taking place in more than one mode during one pumping cycle.

(a)

(b)

FIG. 8. (a) Top, photomultiplier recording of light output from 0.01211 PEu(a-NTF)4 in acetonitrile. Bottom, recording of flash-lamp light. 1160J input (2.3 times threshold). Scale, 200 Itsec per division from left to right. (b) Laser-beam pattern at a distance of 250 cm from one end of laser Cell.

25 G. D. Boyd and J. P. Gordon, Bell System Tech. ]. 25, 489 (1961).

E .'3

500

~ 300-u:: o

0>-f 200

1 - I At this concentration, laser operation was not observed V UP to the maximum input energy (1800J)

[

8 10 Concentration, em-3

FIG. 9. Energy required to reach threshold vs concentration of PEu (a-NTF)4.

Figure 8 (b) shows the pattern of the unaltered laser beam at a distance of 250 em from one mirror. When this exposure is repeated just below the flash-lamp energy needed for laser threshold, no pattern appears, i.e., the film remains completely dark. The diameter of the pattern in Fig. 8 (b) is approximately 2.4 cm. The laser-beam divergence is therefore about 0.01 rad. The pattern size associated with laser operation in the longitudinal mode TE1VIoo such as described by Fox and Li26 would, at this distance, be approximately 0.4 cm in diameter. Therefore since the film in Fig. (8b) is not overexposed, most of the recorded emission, i.e., that outside a central circle about 0.4 cm in diameter, cannot be associated directly with the output from resonant modes. The spiking character of the output radiation shown in Figs. 7 and 8(a) and its narrow spectral width are however consistent with the ex­istence of resonant modes. It seems reasonable to sup­pose that the pattern shown in Fig. 8 (b) represents a composite of the pattern from more than one resonant mode together with the pattern produced by radiation scattered out of these modes. Scattered rays will, of course, be amplified by stimulated emission while traveling back and forth in the liquid. They will also be repeatedly rescattered and finally lost from the resonator by partial transmission at the mirrors ar d by "walkoff."

In order for the output pattern, shown in Fig. 8(b), to consist mostly of scattered radiation, the scattering loss per pass for a resonant mode must be appreciable. An estimate of the scattering losses at threshold can be obtained by using the experimentally determined minimum concentration of ions needed to obtain laser operation. Figure 9 is a graph of the stored electrical energy required to reach threshold vs concentration of FEu (a-NTF)4. The minimum concentration needed

26 A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).

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1914 E. P. RIEDEL AND R. G. CHARLES

to reach threshold is approximately 0.0017 M. This corresponds to a concentration of 1.0X 1018/cm". Because not every ion is inverted, this number is strictly an upper limit to the minimum population inversion ~2V required for threshold. We may use it however to estimate the scattering losses at threshold. At threshold a wave traveling back and forth between mirrors with reflection coefficients rl and r2 and sepa­rated by a distance L must be amplified just enough in the medium to overcome all losses, i.e.,

where a and S are the absorption coefficient and the scattering coefficient of the material, respectively, at the wave frequency, and dl and d2 are the diffraction losses per bounce at Mirrors 1 and 2, respectively. Using this relation, taking account of the degeneracies gi of Levels i, the index of refraction f..L of the laser material, and assuming a Lorentzian line shape, the population inversion requirement at threshold27 may be written as

~N=N2- (g2/gliVl)

= 27r2Cf..L2T~A 12LS -In[rlr2 (l-dl ) (1-d2 ) ] I /A4L, (2)

where lY i is the number of atoms per unit volume in Level i, T is the lifetime of the upper level 2 due to spontaneous emission of radiation by a transition between Levels 2 and 1, A is the wavelength in vacuum at the peak of the Lorentzian spontaneous emission line with a full width at half-height of ~A, and c is the speed of light.

Using the dimensions of the optical cavity and the results of Fox and Li,26 the values of the diffraction losses d1 and d2 for the TEMoo mode may be shown to be 0.018. Spectroscopic and other data yield the following values for the other parameters: f..L = 1.346, T=7.4XI0-4 sec, ~A=2.3XlO-7 cm, A=6.12XlO-5

em, rl =r2=0.99 and L=6.7 cm. Using these values and the minimum concentration of 1.0X 1018 cm-3 for ~N in Eq. (2) yields a scattering loss per pass of 20%. We see therefore that an appreciable scattering loss exists at threshold. If the scattering losses are set equal to zero and the other parameters unchanged in Eq. (1), the required population inversion ~N would be only 1.1 X 1017 cm-3• Thus, a scattering loss of 20% per pass, in this case, raises the required population inversion at threshold by a factor of 9. In addition to raising the threshold for laser oscillations to take place in resonant cavity modes, scattering losses from these modes serve to increase the radiation density in off-axis rays. Since these rays are also amplified in the medium and may traverse the medium a number of

27 A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).

times before walkoff occurs, they can contribute a major portion to the total output beam energy. Since these rays are inclined to the axis of the resonator, they serve to increase the beam-divergence angle of the laser output above that expected for diffraction limited operation in longitudinal resonant modes. This is an important deleterious effect if high radiance is desired in the emitted laser beam since the radiance of a laser is proportional to the inverse of the square of the out­put-beam divergence angle. In addition to this effect, the loss of energy from the laser when walkoff of off­axis rays occurs may be an important factor in lowering the energy of the output beam of the laser.

There appears to be no satisfactory way to avoid these losses in optically pumped liquid lasers employing organic solvents. This is because all organic solvents for which data are available in the range where their viscosity is low have the comparatively large value of the change in refractive index with temperature dn/dT near -4XlO-4;oC. It has been suggested28 •29

that heavy water be used as a solvent for liquid lasers in order to minimize the scattering effects associated with dn/dT. This is because dn/dT for heavy water is zero at approximately 6°C,30 while its freezing point is below this at 3.8°C. It should be noted that the euro­pium tetrakis (i1-diketone) chelates which have been shown to lase in organic solvents are insufficiently soluble for use in water. There is no known reason, however, why suitable water-soluble systems should not be devised. The principal difficulty is that the fundamfntal knowledge relating laser activity to chemical structure is still not sufficiently developed to predict which of the many possible systems in D20 are likely to give laser action. In recent work from this laboratory29.31 we have investigated two different rare­earth systems, each of which has two of the necessary qualifications for laser action in D20, i.e., suitable ultraviolet absorption characteristics and high quantum efficiency for conversion of absorbed energy to rare­earth ion fluorescence. The fact that neither system shows laser action, however, illustrates the importance of other parameters, in addition to ultraviolet ab­sorption and fluorescence efficiency, in determining liquid laser action, and emphasizes the need for further studies in these areas.

ACKNOWLEDGMENTS

The authors thank Miss P. Haverlack for her con­siderable aid in the preparation of materials and Mr. R. K. Williams for his expert help in performing the laser experiments.

28 E. P. Riedel, paper presented at the National Aerospace Electronics Conference, Dayton, Ohio, May 1963.

29 R. G. Charles, E. P. Riedel, and P. G. Haverlack, J. Chern. Phys. 44, 1356 (1966).

30 D. B. Luten, Jr., Phys. Rev. 45, 161 (1934). 31 R. G. Charles and E. P. Riedel, J. Inorg. Nuc1. Chern. 28,

527 (1966).

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