During the last few wrs. optical sp~rrmscop~ has gnrwn into a powdbl

tool of research in the field d science and technology. This growth has kd to

the elucidation o f optical and physical pnyxrties o f solids. Furthermore, oprical

spectroscopy is concemcd with the messurcment and interpretation o f optical

spectra arising hnm either emission or absorptron of mdinnt energy by variow

substances. In emissron specrroscop,,, a molecule or aton1 undefgom a transition

from a state o f higher energy to a sute o f lower enrrgy and emits the excess

energy as a photon. In absorprion spcrroscopl~. a trnnsitiun takes place from a

lower level to higher level with trnnsfer of energy fmm thc radiation ficld to an

atom or a molwule.

1.2. Classification o f solids

Solids can he classiticd hmadly into two clnsse?r viz.. crystalline materials

and non-crystalline matcrials or amorphtn~s materials. A pcrfcct cryrrtalline

material is one in which the atoms are amngcd in a pattcm that r w f s

periodically in lhree dimensions to an infinite extent. Any material, which &mi

not meet this criterion of' periodicity. is called non-crystalline or amorphous

solid.

The X-ray diffraction (XRD) technique is normally ured to study the

atomic saucfure o f materials and also to distinguish the crystalline and

amorphous nature of materials. The XRD lipeantm of a crystalline msacrial

exhibits a series of sharp Rmgg peaks, each peak carrcsprmds to a d i f f m t

periodicity in the crystal lattice, which is characlerized by the long-rpngc &. In contrast. the amorphous material sbows broad pits at small scatlcz'iq

angles, which is a prerequisite in the characterization ofamarpbous aWwiP1.

13. Glasses

Glasses are essentially non-crystalline solids obtained by Ereczing

supercooled liquids, which exhibits short range order. According to the A S W

(American Society of Testing Materials) standards. "glass is an inorganic

pmduct of Fusion which has bcvn cmied tcr a rigid condition without

crystallization" [I] . A somewhat quantitative definition of the glassy statc is n

manifestation of the morc general and inclusive mniarphous state of matter,

which exhibits a glass tmnsition 121.

Thc word "glass" is derivrvl fmni an Indo-European nx>t meaning

"shiny", which has also given us the mcrning glen., glow and glaze. 'I'he word

"vitreous" con= from the Latin word for gins.;. No distinction is made hem

between the words glaqsy and vitreous. In vicw of this, the tennr non-cry$telline

solid, amorphous solid and glass an. synonyms.

Glass is one of the most u3eful and vennrile materials, which has also

been the focus point for intensive modcrn research. Archamlogical site# hnve

yielded fragments of glass vcrssels tmccablc to 15(M f3.C indicating very long

history of glmes (31. Recipes for glass comptnritiotla can bc f m d in A ~ y r i a n

c u n e i f m tablets dating to approximately thc sixth cczntury B.C. The content of

glass as revealed by thaw ancient tablets do not diffkr dramatically from certain

chapler 1 httwh1tm

glasses, wh~dr are i n common usage today. Owing the past 3000 ycars, nian has

learned how to make controllwl melts o f glass. Glass technology has p d v d

slowly, with mom progress in the past IOU ycus than that glass making exiaoed

in all the preceding years. This progress began i n the 18@' cenhuy with the

industrial revolution and the establishment o f scientific m a r c h in industry. The

science o f glass is going thmugh a rrvtrlutic~~, paving the way for next

generation o f condensed matter physics 14-71.

1.3. I. Classificarion of glasses

(a) Nalurul glasses

These gtasses are formed when molten leva rraclm the surface o f the

Earth's crust and is cooled rap~dly, c.g. obsidians. pcchsainu, pumice, etr.

Natural glasscs cm also he formed hy the sudden increase in tetnpcratum

following stmng shock waves, e.g, tectitus 181. In some rarc caws. h~crlogical

process can lead lo glass fornlation. The skelettrri af some deep water spc)ngci

(monoharpis) consists ol'a large d of' vitreous SiO? 191.

(b) Arlt/icral glawes

The artificial formation of giauses occurs in very divene clrr~eea o f

materials. Although many substances can be uyed to form glaam, only mmr af

them are of practical value.

(i) Oxide glasses

Among inorganic glasses, oxide ghs~ea are the wt important.

e.g. silicate ( S a d , bornre (B20.1). ph*BphBt~ t P ~ 0 5 ) aid germanate (GeOl)

glasses.

(ii) Halide glawcj

BeF, is a glass-network fonncr. which may be considered as a w#rbned

model of Si@ and its strucnire is based on BeF, tcb.clbednr. These glasses are

the best candidates for high power lasers fur thcnnonuclrar F u P b apphtbm~.

e.g. tluorozirconate, fluoroboratrs, fluomphosphates. AIFI. GaFt, PbF1. ZnCl2

glasses

(iii) Chalcogenide glasses

These glasses are based oa elements from group V1 (S. Se and Tc)

combined with elements fmm grcrup IV (SI and Ge) and group V (P, As. Sb and

Bi), which do not contain oxygen an: interesting for their i n f m d opticaf

transmission and electrical switching properties. Vitreaus Se posmsrs

photoconductive properties and i s uscul in photcxopiers (xen~gmphy), The

Cie-As-Si glasses have opto-acoustic applic~trions and are used as tn~rdulatcrrs and

deflectors for LR rays.

(iv) Metallic ~ l a s s r s

Metallic glasses are the materials of the pmcnt century. 'l'hcy may he

sub-divided into two classes, viz., metal-metalloid alloys and metal-mcd alloy%,

These glasses have extremely low magnetic l o r n , zm) magnetoatriclion, high

mechanical strengfi and hardness, radiation mistance and high chrmkal

c o r n i o n resistance properties. These matttrials are u.ml rrs corcr in moving

magnets, W i n g camidga, amorphws tbeaBs for audio and computer trqse

recording and hi&-fnvrucwy p w e r trmformcrs.

Glasses d i f i a fmm cryslals with lack of long-range sparial ordernfrr

Furthermore. owing to their higb viscosities, glasses an less favourable to the

internal rearrangements displayxi by liquids. Glasses have many advantap

over crystalline materials. They can be cast i n a variety o f fonns and siues, fmm

small fiben to meter stzed pipes. Furthermore, large p i e m of l a m glass~s ure

be made with excellent hamogemity. uniformly distributed conceamtions, low

birefringence and can be finished easily even in larger sizes. The only mqjor

drawback o f glass is its low thermal conductivity, which limits iu applicability

in high average power systems.

1.3.2. General characterisrics of glasses

(i) Glass is tranqmmnt hut non-crystalline, a major paradox in thc

Pllysics of Condend Matter.

(ii) Short range atomic order.

(iii) Structure is isotropic, so the properties nrc uniforn\ in all dirccticnw.

( iv ) Typically g c d electrical and thermal ~nru la tw.

(v) The composition dependent properties are dma~ty, elastic i:onstano,

specific heat, dielednc permittivity, etc. ' h s c propertim &re

smctwe inscnaitive and additive reletions b v c been pmpwed.

(vi) Glass is hard and yet brittle. When it cracks, it shatters at sprd of

sound.

(vii) Soften before melting, sa they can be formed easily by various glmr

Chptrrr I I n ~ r ' o n

(viii) The internal energy of a glass is always gram than that carresponds

to a crystalline p k e of h e smke ccxnpsition.

Non-crystalline materials pusses fandc~mncss trr same d C g r ~ ~ and C B ~

occur in several forms, of which topological, spin. substitutional or vibrational

d i s o k r s are the most important. These types of disorders are illustmted

sche&tically in Fig. 1.1. A brief description of the four types of disorders ir

given below.

((4) Topological disorder

Topological or gco~netric disorder is a fonn d mndomncss in which

there is no translaticma1 periodicity as shown in Fig. I . 1 (a). Nevertheless, them

are 'degrees' of topological disorder. Cemin amarphtxlr metMiala have

considerable shun-range order. tfowcver. dl amorphous cr glassy sal iL an:

distinguished by their lack of pritdicity.

(b) Spin disorder

'This disorder is charactenzed by an undcrlyi~lg perfect crystalline lattice,

but each atom site possesses a spin or rnagndic tnommt which b rrriented

randomly as shown in Fig. 1 .I (b). The meteridr, which are topoliwically

disordered and possess randomly oriented spins arc known as 'spin glwaa'.

Hencc one should.not be wnfused hetween "glasscn" end "spin glasses"'.

(c) Subs~ir~tional disorder

This type of disorder exists in a l lop e.g. Cu-Au. In this, a prfsrt

crystalline lattice is preserved but one type of atom randomly subatituten for

1.1. Typa o l d i l o d t ~ in ~ I I I O ~ ~ ~ O U I rn~t~dab

(a) Topological dlmtdar [b) Spin dlrudcr

the other in the lattice as shown in Fig. 1.1 (c). These mawrials heave gmt

importance in metallurgy and other branches o f materials science.

(dl Vibmrional disorder

The atoms and molecules in a glass are able to undergo lhemal vibrations

around and average fixed position. Therefom. at any finite tcmpmmm, the

random motion o f atoms ahout their equilibrium pusitinns Jcsvoys the pcrf'oct

periodicity, which is shown In Fig. 1.1 (d). The concept of a perfect crystal i s

valid at the absolute zcm temperature (if zen, point motion i s ignored at 0 K).

1.3.3. The glass tmasitioa

When a liquid is coolcd. one of the following two phmonlena nray i ~ x u r ,

Either crystallization may takes place at the tnclting pcmt ('I',) or else the liquid

wil l bccomc 'suprcmled' at ten~punttures k l o w 'r,,,. hrvontinp lnorc viscous

with decreasing tempernturc. and may ul~imately fbrn~ n glws. 'These changes

can be ohscrvcd rcadlly by n~onrtortng the volurnr as n function o f tcmpcraturc

as shown in Fig. 1.2.

The crystallizat~on prcrcss IS manlfeatrd hy an irhrupt cbngc in volume

at T,, whereas glass formation is charactcrizcd by a grdual break in slope. 1Ke

region over which the change o f slope accurv is termed a?j glass transition

temperature (Tb, Thus a glassy material exhibitr this 'glass ~ranaiticm' as a

characteristic bchaviour.

Tamparature ---1+

F& 1.2. VnrlrUw of the rprrllk volume (VJ rs r funrtlon of tcmpemlrra (T)

Chaprer I I-non

1.3.4. Glass prepamtion methds

Various techniques used to pnparr amiwphnus materials arc w f~llows:

1. Thermal evapc>ration

2. Sputtering

3. Glow-discharge dr~omposition

4 Chemical vapour &position

5. Melt quenching

6. Gel desiccation

7. E1ectn)lytic drqwbitiun

8. Cheniical reactlon

9. Rcaction anwph~ration

10. Imd~ation

1 I Shock-wave transfi~rmidtic~n

12 Shear iimcrrphization

Anlong these methtds, melt r~uench~ng atid gcl desiccation tcchniqucs are

widely used in the preparaticrn of glaxm. In the prcrcnt invmitipation, the

glasscv were pr~pamd by the melt quenching tcchnjquu, which i8 more

emphasized in Chapter 2. Different quenching tcchniqucs of glaurcs and their

cooling rafts are given in Table I. I.

Tabk 1.1

Different qreaching tuhniqsn rmd their cooling nta

Tecboiquc Cooling rric (Klr)

Annealing lo'5 .- IQ"'

Air quenching I - 10

Liqu~d qucriclling 1(1? 10'

Chill-hlwk

splat cooling 10'

melt-spinning. extraction 10" 10"

Evaporat~on c lo7

1.ascr glazing 10"' 1 o'] ---------.em -

1.4. Rare Earths

Of all the groups in the periodic tahle of chemical ckmenrs pCrhap~ the

most fascinating arc tbose commonly known as the ram caIth elements or the

lanthanide wries. The lanthanides from a special p u p of elements, ususlly

shown at the bottom of the pcrricwiir tahle. 4f block elements arc also called aa

lanthanides, lanthanm tlr rare earths. The first two names were given

of their stmng resemblance to lanthanum. The name rare cart11 was given to

them hecause they were c~riginally extracted from oxides for which ancient name

was earth and which were considered to be ram. In fact, thc name lanthanides

have k e n derivcd from lanthanum, which is the protcrtypcl of lanthanides,

Lanthanides constttute the lint inncr transition sorics. ICurther mrwe, the gnwp

of elements known as Ianthanidc comprises litken clcmcnts in which a

pmgrcssivu tilling of the Jf shell occurs. Thc p u p starts wilh lsnthanultr

( 2 ~ 5 7 ) and ends with lutdium (% -71). Table 1.2 yivcs the electronic

configuration of lanthilnidc ions along with their ground strtrr.

11e history of the lanthanrtlc5 started in 1788, when captair~ Arrh~qiw

found a black stone near Yct~erby in Sweden [IO], Thc Stone was called Yntie.

Another mineral was found by Klapruth in 1803 and mimed a!! Ccria. Aner few

decades it was found that the minerals Cena and Yttria were mixtures of e

number of new elements and an effort was made to separate thcm. Fmm the

mineral Ceria the light fanthoutidcs, lanthanum, cerium, didymjum, samarium,

europium and gadolinium wcre extracted [ I I]. Didymium was later m a l e d

into paseodymium and neodymium. From the m i m l Yttria the rlrnlcnts

The c k c h n k eoafiguraths of mn earth (RE) bas with rbdr ground

state terms

Trlwlcllt atom {RE$+) Atomic Lanthanidr Symbol Neutral Atom - -

Electronic G m a d number Ekrnent Ekrtroak

(2) configuration term

coafigwrrtlon

Lanthanum

Cerium

Prasctdyrniuni

NrcKiyniiurn

l'nmlcthium

Samarium

Europium

Ciadoliniunl

Terbiunl

Dysprosium

Holmium

La

Cc

Pr

Nd

1'111

Sm

Eu

Cid

'rh

DY

ti0

I X e ] 4P ~ d ' 6s'

[Xe) 4f) 6s'

1 X r ] 4f' 6s'

(Xc] 41' 6s'

(Xc j 4t6 6s'

[Xc] 4 f 6s'

jXc] 4f7br'

IXc] 4r7 5d' 6s'

[Xej 4 f 6s'

[Xe] 4P"hs3

[Xe] 41'' 6s2

[Xe] 4i"

[Xcl4r'

[Xc l4P

(Xcj 41"

I X c ) 4f4

1 Xc) 4 e

[ X c ] 4fh

[Xc] 4fa

I Xc] 4P

[Xe] 4fU

[Xc] 4 P '

68 Erbium Er [Xc] 4 t ' d [Xc] 4r" 4 h n

69 Thulium Tm [Xe] 4t'66s2 [Xc] 4f" 'N,

70 Ytterbium Yb [Xc) 4f46s2 [xc] 4 t S l ~ 7 n

71 Lutcltium Lu (Xe] 4 t 4 5d' 6' [Xe] 4t4' ' su -...--"--~--~ ---.-----* *-m-- Me*--. *. -- -- --"".---"--"-

ClbpdrrI InhodLrrion

terbium, erbium, flterbiutn, holmium, Luliurn, dysprosium and finally lutetium

were isolated [I I]. In lanlhanidc group. Ihr iutls diffu in the number of

electrons in the 4f shell. The ground state elwmbnic configurndon is 4fN a d tbc

first excited configuration is 4f""'kl. The RE ions in solids exist e i k in

divalent or trivalent. Thcir clectrunic configuration is 41H 5s2 Spb or 4f""5s2 spB

respectively. By far the most common vnlenoc state of $re RE ions in solids is

the hvafent. The relative lacation and energy extent of the 4kN and 4 p ' ~ d

configurations fur rhc mpositive ram wth ions is shown in Fig. I .3 and ekcmn

configuration o f t r ip i t ive rare earth ions an presented in Table 1.2. The 4f

electrons arc not the outer most anes. The 4f orbitals ore shielded from the

surrounding by the Lillcd 5s' 5pb orbitah. which cxplarns the Itumic" nature of

thcir spectra 1121. Thus the 4f elcctruns an: only weakly pcrturbcd by the charge

of rhc sum~unding lignnds. Thc spcxtra of Ln cr>mp)unds ruc sharp and rinlilar

to thc spcrtra of atoms. The shicldcd chPrmctcr of thc 4f orbilalls iu allso

responsible for the unique optical propnierr of mrr mrch ions [I 31. By the early.

1960's the Johns Hopkins gmup, under thc direction of Diekc ( 141 had gcncrated

complclr set of energy level assignmmtv f ~ r dl trivalent rare earth ions in

anhydrous trichloridcs. The location of d i f f m t energy lev& and trmitioas of

trivalent lanthanides are shown in F1g.1.4. Pt is useful os a good guide for tho

location of J states of the trivalent ram earlL, rincc the centers of gravity of J

manifolds exhibit very small variations with the hcmt. The ordcr and weperation

o f the levels within a J manifold on the other had, vary comidmbly f hm h t

to kwt. The overall extent of thc crystalline Stark splitting# i a small on the

energy scale of Fig. 1.4.

Fig. 1.4. Diagram of cnwp term8 snd cmhd

due t~ X-ray cxcltntiaa

1.4.1. Colour uf the mre c p ~ k ieas

Main-Smith [ 15 j m d to correlate the colour spqwnce in rsrr earth series

with the 4f electmnic configuratlcall of the tnpusitivc ions. The c h a r a ~ c i c

colours o f the tripositive ions are caused by rhe intemttl m s i t i a n o f h e 4f

electrons, occumng In the. vtsiblc region of the spectrum. Fmm Table 1.3 MI(?

ran observe a striking similarity bctwan the ions having 4fN and 4PmN

configurations. However, the nonmposit~vc ions show wick divergence in

colour compared to the i soe lw~n tc triposii~vc ma. 'Thus, the uolmrs of the

nonmpositive rare earth ions arc: CC" (4t4') orange, sm2' (4P) mldizh brown,

EU?' (4s') straw yellow, ~ ~ " ( 4 f " ' ) g m hmwn, ~ m " (4r") purple w d ~ h ? '

(4tq4) grwn.

Tri~alent litnthurrides have been the nlost extcnrtvely used as wtivatc>r

ions becauss of' the Ibllowinp wasons:

(i) They emit narrow I~ncs, almost tnoncxltnjmatic light and have long

en~ivsion lifctimcc

(ii) They possess nlnny fluorcsciny slirtcs and wavelengths to choose

among the 4f electronic configurations

(iii) Their intracanfigunrtional Cf tranait~uns have small homogtncous

linewidths.

(iv) The local fields in glasses can be treated as small perturbations an the

free-ion energy levels.

(v) Welt developed theoretical models a n available foi accurate energy

level analpis, transition intensities and 10 pdicllundetrsund excited

stare dynamics.

Tabk 13

Cdosr squcnce of tbc h.lpatltivc ram earth ion8

Colourlcr;s Lu (4t4')

Colourlcss Y h (dl4')

<inu.n Tm (4f':)

I'ink E r (dl4')

Orrrngr l io (4fU')

Ycllow n y (4P)

Pale pink 1% (41')

Colourlcss

Chuprer I I n t h r i m

itate earthf arc lb most widely used ions in sdid-state lam f16.17].

The wide applicability and versatility o f nur eurhs arise tiam w e a l amsctivc

speclroscopic properties favwrabk fnr achieving law thrcshald and efficient

laser sction.

(i) The electronic staces o f the p u m l 4 . p cantigumtion provide cmplex

and varied optical energy level stmc~ur:. Thus there an many

possible thm and four- level lasing schemes.

(ii) 'There arc a large number o f excited semi suitable for optical

pumptng.

(~ii) These excited states decay m>n-mdiatively to mm-schlc states having

hlgh radiative quantum cficicmc~cr m d nnmlw 4f-4Fcmi5sion I~nes.

In additlon the e~wrgy levels of KI-," tcnla do not change grrntly with host. i f n

givcn ion is dernonstmted to lase In one host. thew are usually many other host

p m s i b ~ l ~ t ~ t ~ .

1.5. Rare earths in glasses

The incorporation of rare earth elrmmts m glassy matrices has getl~wItd

great deal o f interest a% potential materials for optical devices in Imw technology

118-231. L a m action in glasses has been obtained only rmni trivalent tarc

earths. Rarc earth ions am used a% dopants in glasses mainly for two ma

namely (if their well dcfured and. sharp energy lcvelia m y nerve an stmctural

probes fw the environment of the dopants and (ii) the modifications o f energy

level structures or dK mrtb ions caused by thr glwy environment m y lead

to interesting applications (24). Spscba of RE" iuns in glwm lvcr similrv to

those of RE'* ions in liquids. The spcctn in liquids show a crystal-field splitting

although very broad limn;. This is an indication that RE" ions in a liquid am

surrounded by a near a e i g h h shell of ligan& similar to the cnvimnmonl f w d

in a solid and is same far every dissolved RE" ion (25,261.

The intense activity in the study of the optical pmprnin elf rare earth

clopad glasses is relatad ta the c f i m to develop high power laser &vim, glm

fibers, tunable lasers, optical amplitias, upccmvrrtm. memory devices,

phosphors, sensors, tlat-panel display and uptical filters clc. (27-441. Eapccislly,

optical properties of ~ d " and ~ r " -duped glasscs have bcrn fcwnd miml useful

for stimulated emission devices (45-471.

1.5. I. Importance of trivalent ran eclt~h ions in glasses

The me earth ions In glnsser exh~h~t unrque properties (271, wlrich arc not

atta~nable hy other elements. such au

( I ) tI~gh refraction with wlatively low op!icclt d~upuruiun.

( i ~ ) Very selc~tive abstirptlon of' radiation within thc ntngr: of' visible tw

well as UV and NIK rcgiono.

(iii) Luminescence in various rpcclral rangcs.

(iv) The pogibilrtics of' inducing laser action.

1.5.2. Applicdons of rare earth elcmena in giass techno/@gy

Thc usage of rare earth elements in glass technology has rcvcaled several

scientif~: and technological applications. Some of them are:

(i) Optical glazses; f i l m ad Icnses

C ' p r f f I I d t i m

ti i) Light smsitivc and pbo-mic gkmes

(iii) Colwring and decalwring agents

(iv) Glass polishing agents

(v) P" electides

(vi) X-ray and y-ray absorbing glasses.

(vii) Communication fibers and glass lasen

(viii) Colour television phosphors etc.

1.5.3. Rcquiwmen&s for a laser a& m&m

The requirrmentq ror selecting law active tnadium arc as fc~lluws:

(i) B m d absorption hands for optlcnl pumpinp

(ii) Population inversion nf the emitting level

(iii) High quantum efficiencic~ of light emlsslnn

(IV) High crms-.section of stimulated laser emirsicrn

(v) QUIC~ ncin-rad~ative relaxohon of the tower h e r IeveI

1.6. Transition mechanisms for lanthsnidt ions

1.6 1. Intracon~gurarlonalf-f ~ransitions

Optical absorption and lumincscencc spxtnrsccrpy arc important

techniques in the study of lanthanide systcmr. hfceuw they allow to determine

thc natural frequencies o f a lanthanidc icm, The ab?rpticcn rsprctm of lanthanidc

&qxd single crystals and salts show g r r ~ p s of ~ m ~ w lincs. In rsolutim mi

gfasscs, the lines within a group art h r d a e d lo ijrw absorption hand. Thew

Chapter I I n t m k h

bgnds and lines have to be ascribed aa ekctmnic d t i o h s in$& rhr: 4F shell.

Each band conesponQ to a mnsi~hon between two h"~, fke ion e m ~ ~ y leval~.

These are called ~nwaconfigurational a~ns~tions. In aaadraY way. the 4f4f

transitions arc nat accompanied by a change In configufatirm~ htncQ they src

called as inbaconfigurationol aansibons. The shapnw nnd wavch&~

Independence of the peaks are not compatible with mna~rions to excited

configurations (e.g., 4t* '5di). bcceuse such mmsitions arc murc influracad by

the surrounding ~ons. The 4f4f transitlunu an! Pharp, hccauao the 4f electmna

are very cffrctrvely shleldcd by the fillrd 5s and 5p shells. Three rnwhrvltsma

grven by Bnw rt al. [4HI must be consr&rd for the intnprctation irf thc

observed transltlons: (I) clcrmc dlpnlc d induced rlcctne drpolr mruitionm,

(ii) magnetic drpole trrmasttlc>ns and (111) electnc qucrdrupole tmsit~rurr.

(I) Electrlc dtpok und rntl~lred ttccrrrc drplr rrunur~mns

Electr~c dipole trans~t~c~ns bctwnn slates of 41' fuKi 5d ~~nftguratuns uc

panty allowed. The orcrllatix strcnyths for f-d MnaltrrmJ an: M m much

larger than that of f-f mlnsltrons wrth nlagn~tucle of' 10 '- 10 '. "the selection rub

for electnc dipole aansltrons are AI * 21; Ac a 0; AS 0; lA1-1 % 6; (1211 5 4,

IAJJ = 2.4.6 if J= 0 (or) J'4. An electnc dipole trandiit~on is the cxmcqumca of

thc interaction of the specttaclccrpicdly acllve ion (Ln ion) with the electtic Wld

vector of the electromagnetic radiation thmugh itn ek t t i c dipole. The creation

of an electric dipak supposes a l i m r movement of charge, whid, has 6dd

parity. The ekEtrie dipok op~ator has ~~W&OIV odd t ~ ~ f ~ m n r t i o n OwpMtier

Mder invcnion wid! respect to an inversion otntcr. Inttaconfipuntional electric

ch0pl.p I 1-

dipok tramitions me forbidden by the Lsporoc selection mle. However. the

f o r b i f-f electric dipoh tnmit i~~~ arise iiam pdmixurc of rhc 4t'

configuration with the cxcitcd canfiguration of rhe appazrie parity (e.g. 4Pi5d

(or) 4P15g). Noncmfl~liyrnmetTicB) interactions allow thc mixing of ciactmnic

states of opposite parity. The observed m i t i u n s are much w & u than the

ordinary electric dipole tranrlriuns. Thesr are called as induced electric dipole

lransltions possessing the intcnsitm of the order of 10". Thc intensities of the

induced electric dipole tnrnsirions we described by the Judd-Otdl 149.503

theory.

(ill Magnerir dipole trunrrrrons

Magnetic dipole transit~onv are uruscd by interaction of the apcctmgic

active ion (1.e. lanthan~de 1011) wrtt~ lllr magnetic: lield wmprmrnt at' the lrght

through a magnetic dipole. Ihe intensity uf the mirgnet8c d t p k transitions is

weaker (of the order of 10') han that of ~nrlosctl electric dipole uransrtionr.

Magnet~c dipole transitions arr: parity a l lowd b c t w ~ v i ~ states of lN and subject to

selection NICS AT = AS - 0 rind N - 0, f I (but 0 o 0 forbidden) in Lhe

Russel-Saundcrs Ilmit.

(rii) Elecrrrc quadruple lranstriotu

The electric quahpole trana~tionrr anse from a displacement af charge

that hes a quadnpolar nature. An electric quadrupl>k consists of four psint

charges with overall zcm charge and zem dipole moment. An e l d c

quadntpole bas even parity. Elcctric quwlnrpok: varuitim are much weaker

lhsa the induoca electric dqwk ond che ms$netic Jipok transitions. So fw, no

experimental evidence exisa for the ~ccurmnx of qdn~pok traasitian i n

lanlhanide spectra. Howcvcr, hypetscnritive wansitions am conr~idarod as

pseuda-quadmpole transitiam, hccaw these transitions obay tbt sc1Ection mles

of qudupole tnmsitions. These transitions rve parity d b w d a m n g the StIUeS

of fN with the selection nrlm AS = 0 and Ir\L(, IAJI s 2.

One or two absorption bands of each ran. conh ion will be found ta he

very sensitive to &e host environment d tht: ion concentrations. Since t h e io

some peculiarity in their intensity vnriatians, such absorptian mnsitions arc

known as "hypersensitive transit~o~a". A l l hypcmnsitive vansitions &auld

obey the selection rules AS = 0, 1AL.I s 2 and lAJl s 2 IS1,52). These rrcledtim

rules are thc same as tha~ of a purr quedrup~lc tmnxttionr, but calculaticma have

revealed that phr intensities o f hyperswitive transitions arc larger in rnapitwk.

Thcretbre hypclsngttivc transitiunii h v e hcen called t~ prrwdo-quatkuplc

transitions. According to Jorgcnsen and Judd (53). Ihe hyperscnnitivity afbanda

is due to the inhomc>geneity of the ltgand environment. The pc7lariwhility illso

plays a pan in the hypersensttivc tramitionr. Judd 1491 no l icd that l e

hypersensitive transitions arc associated with the lnrgc valucs o f the d u d

matrix elements IIU'~~. Ffyperacnsitivcnms is descriherl by thc plrmtcra, if

the H ~ H and 11v1i matrix elements for thc hypmmsidvc tranuitians arc small.

The rcb ivc variation of R2 pllrametcr for a 1.n ion i n d i f f m r t mviranments

gives the measurr o f dtgrcc of hypersensitivity exhibited by that ~ ) n .

Karmker 1541 conclude4 that the hpmcmi t i ve tranaltimrp shmv diff'crcncw,

which are the cbamcwistic for the c m d a a h and symmerry sf tbe laathanide

ion. Choppin ct al. [SS] su&~csted that the bond shap and intensity of

hypersensitive transitions could be used as a qualitative indication o f the sire

symmetry.

1.7. Spectral intensities

I . Z I . Inrmsily of absbrptior bond

The intensily o f an absorption band is mcasud by its oscilltrtor stwngth.

The concept of oscillator strength was first intnntucd hy 1-adenbuv (561. The

oscillator strength of a tmsitrc~n is R IIIC~LSU~' of thc ~ w n g t h of a trrmaifit)n and

it i s the ratlo of the actual ~ntensity to thc intensity mdruted hy unc clwmn

oscillating harmonically in thwe dimensionc 157). In ancnhcr way, thc intcn~ity

of an ahsorpt~on hand is rcprcsented by its cmillstrrr strength (f). which is

directly proportional to the arcn undcr the uhsnrption curvc. Tke cxpcrimcntal

oscillator strcngth we,,) can he dctcrn~in~d from thc absorption spectra using the

relation [S8,59)

where the term before the integral 1s rcpreyenlaf by thc alomie constants o f

which m and e are mass and charge of clcclrun, c u (hc vclcxily o f light and N ia

the Avqgadm number. The integral i id f ccrmqxmcls to Qc arm under the

absorption curve. Efv) is the molar absorption ctwflieitnl aml rhe oacillrrtnr

strength (0 is a dimensionless quentity.

From the k-Lambert hw lfre molar a b w p t h oa~fficient at r givea

Ernxgyv(~rn')isey~esscdw

where C is the conccntretion of the trivalent lanthanide ion i n mldl. I is h

light path i n an ahsohiag medium (cm) and b ('1 is thc ahscwptivity or

optical dmsity. Nonnally thc oscillu~or sttcngths for 1.n" ions arc found to he

the order of 10".

1.7.2. Mired electric and ma~nr t ic dtjmk osrillator stnng~hs

I n gcneral ccrtcirn 1.n" intraconiiguri~tionol transltltvns arc netther pure

induccrl clectnc dipc~lc (ED) nor purv niagnetic diycllc (MI)). hut contains both

ED and partial MD con(nhuttons Thc fS1) i ~ n d MI) osc~llator stwng~hx havc to

tw caIculatcYI sepsratcly. Thc cxpcr~nrcntal osclllotcrr atrcngths V,,) arc: to he

cornparcd wrtti ~ h c total oscillattrr strcngth~ o f the i~hsotpticm hands of 6.n" ions

hy thc cxpressron

fc.,. fed + / & (1.3)

T h ~ s means that cxprimtnlel#y mco~ured c)scillalor strengths u ~ ~ l d be

expressed to a gcxd approximotion in tcrms o f ahsr)rptian of light by clcctric and

magnctic dipolc mechanisms. But, the magnellf dipolc transitions arc w a k a d

their intcnsitia are telativcly rndcpcndmr of the sum~unding ianthanik ians.

The magnetic dipolc osci l latc~ amgthr are fmnd 10 be 1% or lw tJuin thanthe

-

electric dipole uscillatar semgths U i ) . Thr cxpmimen~al oscillator strengths am

1.8. Judd-Ofelt theory

In 1962. Judd and Ofclt [49.50] indqmdcntly derived exprwi im fur Lhe

oscillator strength of induced elcvtric dipcde transitions for the wnfiguratio~ur.

Their thcories werc known as Judd-0feI1 theory. since their results were similar

and published simultmcously. 'fit hsic ids8 01' Judd-Ofelt theory is that thc

intensity of tllc forhidden F f el~'~'tric dipole tmnsiti~ns arise f n ~ n thc ~dn~ixurc

o f the 4tN contigumtion with the excited configum~ions s f opyosilc parity

(c.g. 4fN"5d or 41""~~) . According to the Judd-Ofell intc~lsily n~cdel, the

calculated oscillator strength of electric dipole 1'4 transitions of vivalcnt ram

earth ions from initial ~ t a t e ( ~ ~ ) lo a por f i~~ lur tinul state (y'~')ifi equal lo

whcrc h is the planck's constant, n is che index of reliection, v(cmv') L the

wavmumber of the absaptim transition. [!!:f JL is the L m t z Id fieid Y n

correction for the absorption and Accounts for the dipole-dipole cormtion.

ClrqpPrJ

1 1 ~ ~ 1 1 are the doubly-reduced matrix elements of the unir msar cgrcmtcrr of

rankl. which am cansidmd to b@ tk imkpcndent of the hast f26).

5-2, (k - 2,4.6) are the host ckpmdent J-0 intensity parameten obtained f m the

least squares fit. The goodness of the fit is cklcnnind by the rrwt tnean squm

(ms) deviations hetween the and calculated cwcillator strengths hy the

relation

where N is the number of ohscrvcd transitions used in thc fit .

1.8.1. Electric dipole line strengths

Tl~c linc strengths of the electric dipolr. twnrltion i s given hy thc

uxpression

s,, c.2 c f l A (VJ /I liql v : J ' ) ~ (1.7) A m 2 . 4 , h

'The matrix elements I I U ~ I ~ In Eq ( 1.7) can be calculatcd in the LS huts using rl~e

following expression

(fNu S1.J 1111'11 fhl (L' S J')

J J' A' - ( - I )''L'''*' ((21 + I )(lJ1+ L)] I f? ] (Pi u ~ l _ l l l lk/l P( a' S I.') ( I .8) 1- S

The reduced matrix element% on the nght side of F4. (1.8) w m trmhulrtcd by

N~elson and Kostcr [Wj. The matrix elementr as computcct muat he fnuuformed

f i the LS h i s to intmndiatc ctnrpling xhwe hefore being squad and

substituted in Eq. (1.5). The intmcdiatc muplhg d , g a ~ t r t ~ s , ~p\lrh a

expressed in tmns of LS b i r sates, IP aSIJ;. by

1 f N ~ ) = G c(a s L ) 1 f N a SU) (1.9) u S.L

1.82. Magarrir dipdc line strcnflk

Fvllowing the resulrs of Condan aml S h ~ l e y 1611, the magnetic dipole

line strength is given by

The non-zero matrix clcrnentv wtl l he thtwr. of the diagimrai in the quantum

numbers (1. S. and 1 Ihs wlscrion n~lc c ~ t l J 1s A i - 0. * I , whish restricts

considcra~ion of tlic Ibll~>\v~ng thnv cusu

(I) J' J

(U Sl-J]I,+2S/u SI.Jf) gh [J(J+ 1)(2J+ 1)j' ' ( 1 . 1 1 )

(ii) J' = J-I

(uS1.J 11.6 2Sj rrS1.J- I )

The matrix elcments calculated from Eqs. ( 1.1 1 - 1.13) must br fmfatmed into

the interniediate crbupling schenlc bcft)m ccmtputnlic~ crf the magnetic dipole

contribution ~ ~ n t c d by Eq. ( I. lo).

The total oscillator strength (0 of an ahncxption band witb c n q y

v (cm ') is given by

I . dl 3. Radiarivr transttions probabllitics

The Judd-Ofclt intcnslty parameters Ilk an. uwd to mlittletc sevaml

imporiant radiative properttrs such as d ia t i vc transation probehilitios (AR).

rad~ativc life t ima (rR) and branching ratios (aR) fhr ccmin excitcd transition i n

~ n " doped glasrcs. Axe I621 soivcd the pn)blem of c x p m i n g the radiative

process in quantitative terms using the J - 0 theory. In ttcolting thc fluntcw;ence

process, electric (Ad) and magnrtrc (Ad) dipok dus l ivc transition

probabilities are evaluated from the fbllowing expressions

Chapter i Initduction

and And = 64rc4v3

3h (2J + 1) n3snld

The sum of the A d and Ad gives the radiative transition probability (or)

probability for spontaneous emission (AR) for a transition yd -, ~ 3 ' as

AR (N, YY' ) = & + A d (1.17)

The total radiative transition probability of an excited state is given by the sum

of the spontaneous emission rates of all the terminal states

AT(N)= C A~ (vJ~v'J') (I.19) v7'

As an excited state yJ is relaxed to several lower lying states (yy', the

radiative branching ratio (BR) is defined as

The branching ratios can be used to predict the relative intensities of all emission

lines originating from a given excited state [63]. 'The experimental branching

ratios can be found from the relative areas under the emission liner. The

fluorescence branching ratio is a critical parameter for the laser designer,

because it characterises the possibility of attaining stimulated emission for a

specific transition.

The radiative lifetimes (tR) of an excited state ( yJ) can be extracted from

the total radiative transition probability by using the expression

High emission probabilities and more tmnsitions from a level lead to faster

decay and shorter lifetimes. The theoretical radiative lifetime r R ( ~ ) d c u l a t e d

from J-0 intensity parameters (aL), can be compared with the measured

lifetimes r,,(yJ). The discrepancy between the measured and calculated

lifetimes is clearly due to the manifestation of non-radiative processes either by

multiphonon relaxation rate or energy transfer, which is estimated according to

the formula

1 1 WNR = ---- - - ( 1.22) r m , r~

where WNR is the non-radiative relaxation rate (s '), r,,,,, arid r~ an. the measured

and calculated lifetimes respectively. From the measured and caiculated

lifetimes, the quantum efficiency (q) is estimated by the expression

The stimulated emission cross-section U , . ( ~ J , ~ ~ ' ) , which is one of the

most important parameters that influences the potential laser performance, is

determined from the emission spectra by the relation

Chapter 1 l h t i m

where 1, is the wavelength of the emission peek (nm), A h f l is the effective

linewidth of the transition (nm), which is also known as the full width at half

maximum (FWHM) of the emission band.

A11 the above Eqs. (1.1)-(1.24) are used to evaluate various specmscopic

parameters, which are necessary to characterise the materials for the design and

development of lasers and certain other optical devices. For the prediction of an

ideal host material, a schematic correlatio~l diagram describing the ~ s u l t s

concerned with the absorption, emission and fluorescence decay times of the

earth doped materials has been shown in Fig. l .S.

Emission spe~lru F I ~ o m c e n ~ d q

1 Emission wavelengths (I,)

Lifetimes ( ?A Branching ratios (p,,)

Stimulated emission cross-sections (o,)

4

Quantum emciencicil Crl'/o)

a

Absorption spectra

Radiative lifetimes (rR)

Judd-Ofelt intensity

parameters -

Radiative proprtla (A, Ar, PR) 1

Fig. 1.5. The correlation between tbe abnorption and emlnslon properties to

Identify the trivalent rare earth doped ideal laser hart material.

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