Double excitation of Nd3+ pairs in LaF3 by two step and double quantum processes

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Double excitation of Nd3+ pairs in LaF3 by two step and double quantum processes

R. Buisson, J.Q. Liu, J.C. Vial

To cite this version:

R. Buisson, J.Q. Liu, J.C. Vial. Double excitation of Nd3+ pairs in LaF3 by two step and double quan- tum processes. Journal de Physique, 1984, 45 (9), pp.1533-1541. �10.1051/jphys:019840045090153300�.

�jpa-00209893�

Double excitation of Nd3+ _pairs ⁱⁿ _{LaF3 by} two step and double quantum processes (+)

R. Buisson, ^J. Q. Liu and J. C. Vial

Laboratoire de Spectrométrie Physique (*), Université Scientifique ^{et Médicale de Grenoble,}

B.P. 68, ^{38402 Saint Martin d’Hères} Cedex, ^France

(Reçu ^le 10 octobre 1983, revise le 23 mars 1984, accepté ^{le 26 avril} 1984)

Résumé.

Grâce au déplacement des niveaux d’énergie qu’un ^{ion Nd3+ induit sur un autre ion} Nd3+ occupant

un site voisin, l’excitation sélective d’une catégorie ^de paires ^{d’ions est} possible, ^dans des échantillons faiblement concentrés, ^{à l’aide} d’un laser spectralement ^fin. L’observation d’une fluorescence anti-Stokes montre qu’une paire peut ^{absorber deux} photons. On prouve par des expériences ^sous champ magnétique que, lorsqu’un ^seul

laser est utilisé, ^cette double excitation de paires moyennement couplées ^est essentiellement produite par ^un processus à deux quanta ^{au cours} duquel ^deux photons ^{sont absorbés} simultanément. Par contre, ^les paires ^forte-

ment couplées ^ne peuvent ^être doublement excitées que par l’emploi de deux lasers de fréquences différentes.

La différence entre ces fréquences ^{fournit un ordre de} grandeur ^du couplage ^{entre les deux ions.}

Abstract.

Using the energy level shift induced by ^{a Nd3+ ion on a} neighbour ion, the selective excitation of a

class of (Nd, Nd) pairs ^is possible ⁱⁿ weakly doped samples ^{with a} spectrally ^narrow laser. The observation of an

anti-Stokes fluorescence shows that a pair ^{can absorb two} photons. ^From experiments ^{with a} magnetic field,

it is shown that using ^a single laser, the double excitation of moderatly coupled pairs ^is essentially ^induced by ^a double quantum process by ^{which two} photons ^are simultaneously ^{absorbed. The} strongly coupled pairs, ^{on the} contrary, ^can only ^be doubly ^excited by ^{two lasers of different} frequencies. ^{Orders of} magnitude ^{of the} coupling strength between the two ions are deduced from the difference between these frequencies.

Classification

Physics ^Abstracts

78.50 - 78.55

1. Introduction.

Materials having ^the property ^to produce, by optical pumping, ^a light ^of wavelength shorter than that of the pumping light ^{can have} interesting applications

as for example ^for luminescent materials used in

display ^{devices or} in ultraviolet lasers. Their study

has been stimulated after the demonstration by

Auzel [1, 2] in 1966 that the conversion could have ^a

good efficiency if energy transfers between different ions were used A good review paper has been written in 1973 by ^Auzel [3]. ^{All the} experiments done in this field involve basic processes which ^are described in this _paper. Of course, the use of lasers as pumping

sources has opened ^new experimental possibilities

and _many interesting results have been obtained Among ^{them, the} work of Rand et al. [4] ^{can be under}

lined because it shows that cooperative fluorescence may be so strong ^that stimulated emission could be

possible.

(+) ^Work partly supported by ^D.R.E.T.

(*) Laboratoire associ6 au C.N.R.S.

As pointed ^out by Dexter in his first works [5],

the basic element in all these effects is the ion pair,

even if three ions clusters have sometimes to be considered However, ^the experimental ^{work on the}

various _processes was done on crystals having ^{a so} large ion concentration that all classes of pairs present in the crystal contributed to the observed signal.

Since the efficiency ^{of the} cooperative processes is

strongly dependent ^oil the distance between the two involved ions, ^{such a} signal ^{is an} average ^over all

possible situations. It is only recently that the direct

study ^of excitation transfer between two ions asso-

ciated in a pair ^has begun [6]. ^{With the} LaF3 : ^{pr3 +} system, ^{transfer rates have} been measured for various classes of pairs ^{as well for} up conversion [7] ^{than for} quenching [8] processes and, using ^{a two} laser spec- troscopy technique, ^a very good ^{estimate of the} coupling strength ^{has been obtained} [9]. ^{All these}

results show the existence of a short _range interaction

generally ignored ^{in rare earth} compounds. ^{In another} Laboratory, monochromatic excitation experiments

on Nd and Pr doped LaCl3 crystals ^{have also shown}

the existence of satellites associated with pairs [10].

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019840045090153300

1534

It must be pointed ^out that these results have been obtained with weakly doped samples ^{in such a} way that pairs ^are isolated from other ions and that their intrinsic behaviour is observed. The fact that their number is then _very low and thus that the

experimental signals ^are weak is balanced by ^the

selective excitation with a narrow laser. For the

experiments concerning the double excitation of the

pairs (as ^those reported here) ^the sensitivity is increased because only doubly ^excited pairs produce ^{a fluo-}

rescence : it is easier to detect a small signal ^{than to}

observe a small change ^{in a} large signal.

This new approach ^{has been} applied ^{to the} LaF3 : ^{Nd3 +} system ^where Nd3 + pairs ^also give

resolved satellites whose selective excitation is _pos- sible with a narrow laser. The results concerning ^the quenching ^{of the} 4F3/2 ^{level are described in a compa-}

nion _paper [11]. Here, ^{the various} possibilities ^to doubly ^{excite a} pair will be illustrated and discussed.

This double excitation, detected via an up-conversion fluorescence, ^{has been obtained as well with a} single

laser as with two lasers of different wavelengths. ^The experimental ^{results are} presented in section 2. In section 3 the two possibilities for the double excita- tion with a single laser, namely the successive absorp-

tion and the simultaneous absorption ^{of two} photons,

are considered The theoretical estimate of the rates of the two processes and the experimental ^results

obtained with an applied magnetic ^{field are in favor}

of the latter _process. The results of the two laser

experiments ^{are used to deduce} qualitative ^infor-

mations on the coupling strength between the two ions of the pairs.

2. Experimental ^results.

The LaF3 samples, produced by ^{OPTOVAC, are} doped ^{with 0.1} % ^and 0.2 % ^{Nd3 +.} The excitation spectra, ^described below, ^{have been obtained with}

one or two nitrogen pumped dye lasers. One of them is a SOPRA dye ^laser equiped ^{with a} telescope ^{as a}

beam expander ^{and with an} intracavity Perot-Fabry

etalon. By changing ^the pressure of the assembly

from 0 to 2 bars, ^the wavelength ^{of the} dye ^{laser can}

be scanned through part ^{of the} spectrum. ^{This laser} works near its threshold in such a way that only ^one

mode of the etalon is lasing. ^{It is followed} by ^an amplifier pumped by ^{the same} nitrogen ^{laser. The}

other is a home made dye laser with a beam expander

made of four prisms. Although ^no Perot-Fabry

etalon is used, ^its spectral ^{width is} nearly ^{the same}

as that of the other laser, namely ^{0.1 cm -1. When}

the two lasers are used, they ^are triggered by ^two pulses ^{whose time interval can} be varied Both lasers have pulses ^{of 5 ns} length. ^{For some} experiments,

a 30 kG superconductive ^{coil is used}

The _energy levels of Nd3 + in LaF3 ^{have been} represented ⁱⁿ figure ^1. They ^{are now} very well known and their energies have been tabulated by

Camall et al. in a complete report ^{on rare earth}

Fig.1.

Energy ^{levels of a Nd3 +} ion. The width of the lines

gives ^an indication of the crystal ^field splittings.

doped LaF3 f 12]. ^{In the} experiments reported ^here,

the laser excites the two lower states of the 4G 5/2

multiplet ^at 17 306 and 17 316 cm -1.

Figure 2A shows the absorption spectrum ^obtained with a THR JOBIN YVON monochromator having

a resolution better than 0.1 cm -1 around the

transitions. Figure 2B shows the excitation spectrum of the IR fluorescence of the "F3,2 level with the laser resolution, ^{i.e. 0.1 cm-1. For these} spectra, ^the

intensity ratios between the satellites and the central lines are not the same due to the non linearity ^{of the}

excitation spectrum resulting ^{from the} strong absorp-

tion of the two central lines. The good proportiona- lity of the satellite intensities for these two spectra

must however be underlined Having ^{a narrow} laser,

Fig. ^2.

^{A :} Absorption spectrum. ^{Well resolved satellites} of the 17 306 cm-’ transition have been numbered 1 to 7.

B : Excitation spectrum ^{of the} 4F 3/2 infra-red fluorescence.

C : Excitation spectrum ^{of the} 4D3/2 ultra-violet fluores-

cence. Lines located near the 17 306 cm-1 transition have been labelled by ^{letters a to} g. All these spectra ^{have been} obtained at 1.2 K with a 0.1 % ^{Nd3 +} doped LaF3 crystal.

it is easier to get ^an excitation spectrum ^{than an}

absorption spectrum ^{with the same} resolution. In all the experiments, ^an excitation spectrum ^{is used as a} guide for selective excitations. Finally ^{it must be said}

that no new line _appears when the temperature ^is raised to 30 K.

Figure 2C shows the excitation spectrum of the U.V.

part (observed through ^{a wide band} filter) ^{of a fluo-}

rescence induced by ^an excitation of the 4G5/2 ^states

in the 578 nm range. From the _presence in the spectrum of this fluorescence of groups of lines attributed ^to

4D3/2 -+ 4I 9/2

4D3/2 -+ 41 11/2 ^and 4D3/2 -+ 41 13/2

transitions, it is concluded that it originates ^{from the}

4D3/2 level. The structure of the excitation spectrum recalls similar results previously observed with

LaF3 : ^{Pr 31} [7] ^and strongly suggests that the fluo-

rescence results from the excitation of the two ions

ofNd3+ -Nd3+ pairs. The rise time of the fluorescence

signal is less than 100 ns and its decay ^{time is} 20 gas for lines near the two central lines and _{1 ps} for the isolated line labelled « a » between the two groups.

Most of the lines of figure ^{2 have a width} slightly larger ^{than 0.1 cm -1 due to} the laser width and the linewidth itself estimated to be slightly smaller than 0.1 cm-1. The relative position of the lines for the two excitation spectra ^of figure ² is better than 0.1 cm-1 owing ^{to a} simultaneous recording ^{of the}

IR and U.V. fluorescence on a X Y recorder having

two Y channels. The non linearity ^{as well as the} non-reproducivity ^{of the X} signal (which ^is produced

either by ^a differential manometer for a pressure

scanning ^or by ^a potentiometer ^{mounted on the} grating axis) ^{are thus} eliminated It must be pointed

out that the laser spectral width is sufficient to resolve c, d, e, f lines (with ^a setting of the laser which opti-

mizes the spectral ^{width to the detriment of the} spectral range, these lines are better resolved) ^which

are however hidden within the central line of the

absorption spectrum.

Experiments ^{with two} lasers have also been done to try ^to understand the absence of up-conversion

fluorescence after the excitation of some satellites.

These experiments ^are analogous ^{to those} previously reported ^on LaF3 : ^{Pr3 + [9]. Laser} L1 being ^tuned

to one satellite of the absorption line, ^laser L2 ^whose pulse ^{arrives at the same} point ^{in the} crystal ^but

with a delay ^{i, is} scanned around the central line while the 4D3/2 ^U.V. fluorescence is monitored. For each value of the L1 wavelength, ^an excitation _spec- trum of L2 ^{is thus} obtained Such a spectrum ^is shown in figure ³ with, ^for comparison, the excitation spectrum obtained without L1 ^{laser. New} lines, ^of

similar intensities, ^are clearly ^visible (laser L1 having

a larger intensity than laser L2, ^{it is not} surprising

that lines due to both lasers are more intense than those due to L2 alone). When the time interval between the L1 ^and L2 ^{pulses is} increased, ^{the inten-} sity ^{of the new} lines decreases exponentially ^{with a}

caracteristic time equal ^{to the} decay ^{time of the}

4 F3/2 ^IR fluorescence.

Fig. ^3.

A : Excitation spectrum ^{of the} up-conversion ^U.V.

fluorescence (the ^{same as that of} Fig. 2C) ^{when a} single ^laser

is used B : Excitation spectrum ^{of the} up-conversion ^U.V.

fluorescence for the second laser (L2) when the first laser

(L1) ^{is tuned to satellite} (4) ^of figure 2A, ^{as shown} by ^the

arrow (L1). ^Laser (L2) ^is delayed by 5 us.

1536

Many excitation spectra analogous ^{to that shown}

in figure ³ have been obtained Also, by tuning ^laser L2 ^{to one of the new} lines observed for a given posi-

tion of L1 ^and by scanning L1, lines of the absorption

spectrum leading ^to the double excitation of the pair

have been found In figure 4, the various excitation spectra ^are summarized : arrows show where L1 ^or L2 ^{is tuned, bars} represent the lines of the excitation spectra. ^{The vertical} straight ^lines correspond ^{to the}

lines of the one laser excitation spectrum. ^{At the} bottom ^are shown the satellites visible in the absorp-

tion spectrum. Neither the line intensities ^nor the linewidths have been shown in figure ^{4 because} only

the existence and the position ^{will be} considered in the discussion. As explained above, ^the precision ^for

the location of the lines is of the order of 0.1 cm-1.

Thus, ^{the new line} R1 ^{observed with} L2 ^when L1 ^is

tuned to R1 ^or R3 ^{seems to} coincide with line 4 of the absorption spectrum but it is not definitively

established However, ^when L1 excites satellite 7, ^the

new line is clearly ^shifted and numbered R’1 ⁱⁿ figure ^4.

The rise time of the new lines is _very short, ^less than 100 ^ns. Their decay time is of the order of _{1 tits} except ^{for the} following conditions : L1 ^{tuned to} R1

and L2 ^to R4, L1 ^{tuned to} R4 ^and L2 ^to R’, ^where

it is 20 _us, i.e. the same value as that of most of the

one laser lines.

The experiments ^{with a} magnetic field have first been done with the two main lines associated with the isolated ions. For B parallel ^{to the C} axis of the

crystal, all sites are equivalent and each line is split

into four components corresponding ^to transitions between two Kramers doublets. Figure ^{5A shows an}

excitation spectrum ^{of the} 4F3/2, ^IR, fluorescence whose lines have the same position, although ^{not the}

same intensity, ^{as the} absorption ^{lines as} explained

above. If _go, 91, 92 are the g factors of respectively

419/2(1), 4G5/2 (1), 4GS/2(2), the transition energies ^are

From the _spec- trum one deduces

In spite ^{of a medium} accuracy of the B values, the go value is in correct agreement ^{with the more} precise

g = 2.40 deduced from the values gx

^{1.356 and}

gz = 3.11 measured by ^EPR by ^{Baker and Rubins} [13], tacking ^{into account the} orientation of the c axis in the xz plane ^at 450 from the z axis. In figure ^{5B is}

shown the excitation spectrum ^{of the} 4D3/2’ ^U.V.,

fluorescence around the 4I9/2(1) ^-+ 4Gs/2(1) ^{and the} 419/2(1) - 4G,/2(2) transitions. The _very great number of lines makes impossible ^to follow their evolution

as a function of the magnetic ^{field. It can however}

be noted that the spectrum ^{with the} magnetic ^field

cannot be explained by ^a splitting ^{of the zero field}

lines identical to that of the main lines. However,

the magnetic field induced splitting ^{of the « a » line}

Fig. ^4.

Position of the new lines in the excitation spectra of one laser when the other is kept fixed Solid lines corres-

pond ^{to lines a to} g observed with a single ^laser (see Fig. 2C).

Arrows show the location of the fixed laser (L1) ^or (L,).

Time interval between (L1) ^and (L2) is 5 ps. New lines are

labelled Ri, R’i ^etc... At the bottom are shown the satellites of the absorption spectrum.

Fig. ^5.

^{A :} 4F3/2 excitation spectrum. B : U.V. excitation spectrum. ^Both spectra ^{are obtained at 1.2 K with a} magnetic

field B

2.68 tesla.

located between the two groups of lines can be studied

as shown by ^the typical spectra ^of figure ^{6. The evo-}

lution of the positions ^{of the} split ^{lines are shown on}

the same figure. Clearly, in addition to the expected

lines at g

go ± _gl ^{new ones} of comparable ^inten- sity ^{are observed} at g - ⁰ and g N go. Spectra analogous ^{to those} given ⁱⁿ figure ^{6 but obtained}

with different B values show that the line intensity

variations are irregular ^{and even non monotonic.}

Fig. ^6.

^{At the} top ^{are shown} spectra ^{observed around the} line a of figure ^{2C for various} magnetic ^{fields. The dotted} line corresponds ^{to the} position ^{of line « a » in zero field}

At the bottom, points ^{show the} observed line positions,

solid lines give ^the expected positions ^{for two successive} single photon processes,,dotted ^and solid lines the expected positions ^{for double} quantum processes.

This can be noted from the three spectra ^of figure ⁶

and also from the full spectrum ^of figure 5B, ^obtained with B

2.68 Tesla, ^{where two} of the seven lines have a much larger intensity than the other ones.

3. Discussion

3 .1 CHARACTERISTIC TIMES OF ONE ION FLUORESCENCES.

-

For the following discussion, ^{it is} important ^to keep in mind the dynamical properties ^{of Nd3 + ions}

whose energy levels ^are shown in figure ^{1. The} 4F3/2

level has a radiative lifetime of 780 _J.1s. The 4 G:5/2

level has an observed lifetime r - 0.1 _J.1s resulting

from a fast multiphonon relaxation. The rate of such

a relaxation can be estimated from the phenomeno- logical ^formula

where A and B are empirical coefficients and L1 the

energy difference between the excited level and the first lower level. From the values of A and B tabulated

by Reisfeld and Jorgensen [14], ^{one finds r - 0.4} uS in relatively good ^{agreement with our} measurements.

Using ^{the same} coefficients, ^the characteristic risetime of the 4F 3/2 population resulting ^{from the cascade of}

relaxations can be estimated as - 1 us. The 4D3/2

state has an observed lifetime of 35 _ps. Since the estimated non radiative lifetime is 46 us, the contri- bution of radiative lifetime is significant ^{For the}

lower levels 4I11/2, 4113/2’ 4115/2 ^no value is known.

Using again ^the empirical coefficients, ^{the non radia-}

tive lifetimes can be estimated respectively ^as 3.5, ¹⁴ and 5 _us.

3.2 UP-CONVERSION PROCESSFS. - It must first be

pointed ^out that, _contrary ^{to what was} observed in the LaF3 : Pr3 + system, ^{no U.V.} fluorescence is induced by ^an excitation at the _very centres of the two studied transitions. An up-conversion ^fluores-

cence was observed in LaF3 : ^{Pr3 +} but, ^{due to the} strong absorption ^{at the centre of the} 3H4 -+ lD2(2)

transition, this fluorescence was present only ^near

the face of the crystal irradiated by the laser beam [7].

The present situation is entirely different. As the ions responsible ^{of the centre of the} absorption ^line

are quasi-isolated, the absence of up-conversion

excited in this spectral region is easy ^to understand since : i) ^{there is no} energy level of Nd3 + ions at E

2 h vo which could be populated by ^{a two} step absorption process and ii) ^{due to} the lifetime of the

4G5/2 ^{pumped level (100 ns), the} lower energy levels from which a possible photon absorption ^could

excite higher ^{levels are not} populated during ^{the laser} pulse ^{of 5 ns.} Since U.V. fluorescence is visible only

when some satellites are excited by ^the laser, ^{it is}

concluded that fluorescence results from a process between two ions associated in pairs, ^{as for} Pr3 + : LaF3 [7].

To discuss the various up-conversion processes, it is convenient to consider the _energy levels of a Nd3 + pair which is the useful entity. Those of the levels which are relevant for this paper have been drawn in figure ^7. They ^are labelled I (x, P > by ^reference

to the states a > and I P > ^{of the two ions} supposed uncoupled ^{Of course, the} coupling between the two ions will lift the degeneracy and shift the various components. ^As Nd3 + is a Kramers ion, ^each crys- talline level is a doublet An a, at > ^{state has there-}

for a 2 x 2

4-fold degeneracy ^while an I a, p >

state has a 2 x 2 x 2

8-fold degeneracy ^{since one}

ion or the other can be in the a ) ^{state. The} splitting

of the pair ^{states induced} by the interaction between the two ions has not been shown. Due to the low site symmetry, ^the degeneracy ^{can be} completely ^lifted.

Since the U.V. fluorescence is identical to that of the 4 D3/2 level of isolated ions, ^{it can} be emitted

only from 4 D3/2, ^{a ) pair} levels. Since the fluores-

cence is observed with ^a decay time of 0.5 - 20 _J.1s,

1538

Fig. ^7.

Energy ^{levels of a Nd3 +} pair. ^The labelling I a, p >

recalls the states a and fl ^{of the} uncoupled ions; ^the splitting

induced by ^the coupling ^{is not} shown. The left part ^shows the double excitation of the pair by ^{a double} quantum process, the right part the double excitation by ^{a two} step process.

I ex > ^is necessarily ^a metastable state i.e., 4I11/2, 4I13/2, 4115/2 ^{or the ground state} 419/2. ^{From the}

lifetimes of these levels estimated above, ^{it is} possible

that _many of these pair ^{states emit the observed}

fluorescence. These emitting pair ^{states can be} popu- lated only ^after absorption ^{of two} photons by ^the pair. ^{For the} experiments ^{with a} single ^{laser the} absorption ^{of these two} photons puts ^the pair ^into the 14 G5/2

4G5/2 ) ^{state although for the two laser}

experiments ^the pair ^{relaxes to} the 4F3/2, 419/2 >

state after the first pulse ^{and is} put ^into the I 4G 5/2’

4F3/2 > ^{state by the second pulse. The double exci-}

tation of the pair ^{with a} single ^{laser can be obtained}

either by the successive absorption ^{of two} photons,

a process which ^{will be} called a « two single quantum process ^» (2 ^x S.Q.) ^or by ^the simultaneous absorp-

tion of two photons, ^{a « double} quantum process »

(D.Q.). This last process does ^not need the. interme- diate level to be exactly resonant, but the transition

probability depends ^on its energy detuning.

3.3 EVIDENCE FOR THE D.Q. NATURE OF THE DOUBLE EXCITATION.

All the complex experimental ^results

described in the present paper will not be explained

in this discussion. Even the apparently ^clearer part of these results, namely ^the evolution under magnetic

field of the U.V. excitation spectrum ^{around the « a »} line, ^{cannot be} interpreted definitively. Nevertheless,

some qualitative conclusions can be drawn. In the next section, the interaction strength will be discussed.

In this section, ^it is shown that the unexpected ^lines observed in the magnetic ^field experiments ^can only

be interpreted ^as resulting ^from D.Q. transitions.

In figure ^{8 are} schematized the energy levels of the

StateS I 419/2’

4Igj2 >, 14 G5/2 , 4jg/2 > ^and 14 G5/2, 4GS/2 ) ^{of a pair in presence of a magnetic field but}

ignoring ^the coupling between the two ions. From this scheme, it is clear that a single ^{laser can} doubly

Fig. ^8.

Splittings ^of pair ^states by ^the magnetic ^{field in} absence of coupling. ^{At zero} energy is the ground ^state 1 41,1" 419/2 ^{), at energy E1 the singly excited state} I 419/2’

4G5/2 ^{), at energy 2 E, the doubly excited state 14 G5/2,}

4G 5/2 ) ^{(see also Fig. 7). The double} excitation of the pair

with a single ^{laser is} possible by ^two successive absorptions

of photons (solid ^{lines on the left} part) ^or by ^double quantum

transitions (solid ^{lines and dotted} lines).

excite the pair only ^with photons ^{such that}

or, using the g values of the isolated ions found above :

In figure 8, ^the associated transitions have been drawn with full lines.

Double quantum transitions are possible ^{with these} photons but also with photons ^{such that :}

The associated transitions have been drawn with broken lines in figure ^8. Clearly, ^{the two former tran-}

sitions correspond ^{to the} unexpected lines of the

experimental spectra, the latter cannot be resolved, being in coincidence with ^one S.Q. line. This analysis

shows thus unambigously ^the D.Q. ^{nature of the tran-}

sitions leading ^{to the double} excitation of this class of pairs.

This simple description ^{must be} completed by introducing ^the coupling between the two ions.

However, ^the precise determination of the manner by

which this coupling ^{lifts the} degeneracy ^{of the} ground

state, ^the singly ^{excited state and} doubly ^{excited state}

of the pair in absence and in _presence of the magnetic

field would need a very detailed spectroscopy ^{of the} pair ^{with two} synchroneous ^narrow lasers, taking

into account the polarization ^effects already ^observed

but not studied A likely ^model, compatible ^{with the}

present experimental results, ^can nevertheless be des- cribed as follow : i) ^the splitting induced in the ground

state and in the doubly ^{excited state} is smaller than the laser width but it is of the order of 0.5 cm’ for the

singly ^{excited state;} ii) ^{for this} state, ^the coupling ^is (sl . s2) ^like, producing ^{the S}

^{0 and S = 1} (S

s, ⁺ s2)

states at zero field Then, ^{the two} lines visible in the

absorption spectrum (satellites ^{1 and} 2) ^{as well as the} single line in the UV excitation spectrum ^are explained,

the nearly coincidence of this latter with satellite 1

being accidental. When a magnetic ^{field is} applied, ^the ground ^{state and the} doubly ^{excited state are} split ^as

shown in figure ^{8 and the} position of the lines varies

as shown in figure 6. The evolution of the levels for the singly ^{excited state is not} simple ^{but it cannot} changes ^the position ^{of the} D.Q. lines which depends only ^on the initial and final states. It can however have

an influence on the intensity ^{of the} D.Q. transitions by changing ^the intermediate level energy detuning. ^That

could be the explanation ^{of the} irregular intensity

variations observed

A confirmation of the D.Q. ^nature of these transi-

tions is given by ^a theoretical calculation of the D.Q.

transition probability. ^{The results,} which will be

published elsewhere, show that for LaF3 : Nd3 + ^the

number of pairs doubly ^excited by D. Q. transitions

always exceeds the number of pairs doubly ^excited by

2 x S.Q. transitions and that these numbers become

comparable (but very small) only ^{if the} pairs ^are strongly coupled ^The greater efficiency ^{of the} D.Q.

processes is mostly ^{due to the weak} value of the homo- geneous width of the pumped ^{level. For the} previously

studied system, LaF3 : ^{Pr 31 [7],} this width ^was large

and the 2 ^x S.Q. processes dominated

The nature of the two groups of one laser lines observed in the U.V. excitation spectra ^{cannot be} found from Zeeman effect measurements. We have

seen that the spectrum ^becomes very complicated

when a magnetic ^{field is} present ^The fact that this spectrum ^{cannot be} explained by ^{a «} simple » ^Zeeman

effect and the orders of magnitude ^{of the 2 x} S.Q. ^and D.Q. transition probabilities calculated for weakly coupled pairs ^are in favor of the D.Q. ^{nature of these}

transitions.

3.4 INTERACTION STRENGTH OF VARIOUS PAIRS. -

The U.V. excitation spectra, ^{with one or two} lasers, and the dynamics of the lines can be used to deduce informations on the interaction between the ions of the various classes of pairs.

3.4.1 The first point is related to the short life- time of the "G,,2 ^pumped level : 100 ns. It is clear that once a pair has been excited into the I 4GS/2’

4G5/2 > ^{state it can} either relax to 14F3/2’ 4F3/2 > ^or

« transfer » to I 4 D3/2’ 4I15/2 > from which U.V. fluo-

rescence will be emitted. Since the relaxation is _very

fast, only pairs having ^a strong coupling ^will produce

U.V. fluorescence. It is the reason why ^{no U.V. fluo-}

rescence is observed when the laser excitation is _very

near the center of the two studied transitions : the

pairs, whose associated satellites are hidden in the line due to isolated ions have a small coupling. ^{It should}

be recalled that, ^{with the} Pr3 + : LaF3 system, ^{the situa-} tion was different because the lifetime of the pumped

level was much longer, - ⁵⁰⁰ us : ^an up-conversion

fluorescence ^was then. observed ^even by excitation at the _very centre of the main line [7].

3.4.2 For the pairs whose double excitation can

be obtained with a single laser and which correspond

in the U.V. excitation spectra ^{to the} groups of lines located near the centres of the two transitions, ^the

transfer rate is larger than the relaxation rate of the

4G,/2 ^{state namely 10’ s-’. As} the transfer is phonon assisted, ^{it is} difficult to deduce the value of the coupling

between the ions of the pair ^because many possibilities

exist for this transfer with emission of phonons ^of

various _energy. One can only deduce it is moderately

strong, ⁱⁿ agreement with the order of magnitude ^of

the shift of the associated satellites and also of the

relatively ^weak quenching ^{of the} 4D3/2 fluorescence

1540

emitted after the transfer. It must however be pointed

out that the two last arguments ^{do not} apply ^{to the}

isolated line «a». Indeed, contradictory arguments

can be given concerning ^the coupling strength ^{of the} corresponding pair. ^The strong shift and the strong

4D3/2 ^{quenching (the} observed lifetime is 1 ps) ^are

indications of ^a strong coupling although ^the possi- bility ^{of a} double excitation with a single ^{laser is an}

indication of a medium coupling. ^Such contradictory

behaviour has already been observed for ^a class of Pr3 + pairs ⁱⁿ LaF3 [9].

3.4.3 Finally, ^{the case of} pairs ^{which can be dou-} bly ^excited only ^{with two lasers must} be considered.

From the experiments summarized in figure 4, lines

R1, R2, R3 ^and R4 ^{form a} group, Rs, R’, R6, Ray

another _group. For the former, the four lines (either

in their original position ^{or in the} slightly modified, primed, one) ^{are visible in the} excitation spectrum ^of the second laser when the first is tuned to R1, R3 ^or R4 position. R1 ^and R4 correspond ^{to an} absorption

line clearly visible while R3 ^{is too near the center of}

the main absorption ^{line to} be observed R2 ^{does not} correspond ^{to an} absorption ^and indeed, ^{when the}

first laser is tuned to R2, ^{no new line is observed when}

the second laser is scanned. Two facts must be pointed

out : i) ^the absorption of the second laser shows four

lines after the first has excited one satellite, ii) ^{at least}

two lines of the absorption spectrum ^{show the same} excitation spectrum for the second laser when they

are excited From that, ^{it can be} deduced that the lines

R1 ^and R4 (and probably R3 ^{if it were} resolved) belong

to the same pair ^{of Nd3 +} ions and their splitting ^results

from the combined effect of the interaction between the two ions and of the perturbation ^{of the} crystal

field that each ion induces at the site of the other. It must be recalled that analogous experiments ^with Pr3 + pairs ⁱⁿ LaF3 ^{have shown, with} only ^one excep-

tion, that after excitation of one absorption ^line by

the first laser, only ^{one line was} present ^{in the excitation} spectrum ^of the second laser [9]. ^{Since the} crystal

field levels of Pr 3’ are singlets, this result was quite

clear. Since for Pr3 + pairs ^the absorption ^{line from}

the ground ^{state and the} absorption ^{line from the}

excited state were near one another and well shifted from the central line, ^{it was concluded that the} large

shift was created by ^the crystal ^field perturbation ^and

the splitting by ^the interaction itself In fact, ^{this dicho-} tomy ^{is more} intellectual than physical. The presence of another R.E. ion in the neighbourhood ^{of a} given impurity ought ^to be considered from the first prin- cipes ^{or at} least within a molecular orbitals model from which energy levels and wavefunctions could be found. This difficulty appears ^more clearly ^{with Nd3 +} pairs ^{than with Pr3 +} pairs ^{because the} degeneracy ^of

the excited states of the pairs ^is higher, ^{4 or 8 instead}

of 2. Taking ^{into account all} aspects of ^{the mutual}

perturbation ^induced by ^{each ion on its} neighbour,

the degeneracy ^{can be} fully removed and it is not sur-

prising ^{that a} given pair ^{has more than one} absorption

line from the ground ^{state. But the total} splitting ^of

3 cm-1 between R1 ^and R4 ^cannot be attributed to one part (the crystal ^field part) ^{or to another} (the

interaction part) of the mutual perturbation. ^{It seems}

however that the experimental ^results bring ^informa-

tions which could be used for ^a theoretical analysis.

For instance, ^{the fact} that ^the absorption ^{lines from}

the ground ^state (R1, R4 ^and probably R3) ^{are very}

near the absorption lines from the excited state

(R’, R4, R3), ^{if not} understood, ^{is an undoubted}

result All which has been said on the group of lines

(R1, R2, R3, R4) applies qualitatively ^{to the} group

(R5, R’5, R6, R7) ^{and to} the group (R., R9, Rlo, R11)’

As a final remark concerning pairs which need two lasers for their double excitation, ^{it can be} pointed

out that the fast decay of the U.V. fluorescence emitted from the 4D3/2 ^{level (less than 1 J.1s) and resulting from}

the quenching ^{of this level is an} additional proof ^that

these pairs ^are strongly coupled

4. Conclusion.

Processes of double excitation of ion pairs ^{with one}

or two lasers have been experimentally ^studied through

the observation of ^an up-conversion fluorescence. The

advantage of the method is that a signal ^is present only when the double excitation has been obtained This increases greatly ^the sensitivity ^{and makes} pos- sible experiments ^{on isolated} pairs ⁱⁿ weakly doped samples. ^{When a} single ^{laser is} used, ^two processes ^can

produce ^{the double} excitation of the pair : ^{either two}

successive absorptions ^{of one} photon ^{or a simulta-}

neous absorption ^{of two} photons by ^a double-quantum

process. Experiments ^{with a} magnetic field have proved that, ^{for a} pair whose associated satellites are well resolved from the central line, the double quantum process dominates, ^a result confirmed by ^a theoretical calculation (not given here) ^{of the 2 x} S.Q. ^and D.Q.

transition probabilities.

An analysis of the results has shown that weakly coupled pairs ^{do not} produce ^an up-conversion ^fluo-

rescence when they ^are doubly excited, ^that pairs strongly coupled ^{can be} doubly ^excited only ^{with two}

lasers of different wavelengths, ^{and that} pairs produc- ing ^an up-conversion fluorescence when excited with

a single ^{laser have an} intermediary coupling, ^{An order}

of magnitude ^{of the} coupling ^{is found for} strongly coupled pairs, ^but precise ^{values cannot} be obtained because only ^{the combined} effect of the coupling ^and

of the perturbed crystal ^{field is observed A} theoretical

analysis ^{should be} necessary ^to find each of them. The results obtained here could form a basis to predict

the behaviour of more concentrated crystals (1) by ^an analysis ^{similar to} that used in the companion paper devoted to the fluorescence quenching.

Acknowledgments.

It is a pleasure for the authors to thank F. Mad6ore for his technical assistance, particularly ^{for the two}

laser experiments.

Note.

(1) ^{A recent} paper ^on up conversion in LaF3:Nd3+ ^has

been published by ^{B. R.} Reddy and P. Venkateswarlu [15].

As only ^{results obtained at} liquid nitrogen ^{and room tem-} peratures ^are discussed, ^{a detailed} comparison ^{with the}

present work ^is meaningless. Indeed, ^it should be interesting

to try ^to selectively ^excite pairs ^{in a dilute} sample ^at liquid

nitrogen temperature, ^{if the} linewidths ^are not too large,

and compare the results with those reported by Reddy ^and

Venkateswarlu.

It can however be pointed ^{out that} writing ^{down rate} equations ^{to find the} up-conversion dynamics supposes, ^as

explained in J. C. Vial’s thesis (unpublished), ^{a diffusion of}

the excitation among the ions. If this is probably ^{the case}

at high temperatures, ^{this can} be wrong ^at low temperatures where consideration of pair dynamics ^becomes fundamental.

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