Optical and Quantum Electronics 24 (1992) 591-601
Emission spectra and cross-section spectra of neodymium laser glasses
J . F U R T H N E R , A . P E N Z K O F E R
Naturwissenschaftliche Faku/tat II - Physik, Universitat Regensburg, W-8400 Regensburg, Germany
Received 7 August; revised 15 November; accepted 3 December 1991
Amplified spontaneous emission spectra and light amplification spectra of some Nd3 +:glass rods (silicate glass Schott LG680, phosphate glasses Schott LG760 and Hoya LHG5) are measured by pulsed flashlamp excitation. The spontaneous emission distribution, the stimulated emission cross-section spectra and the excited state absorption cross-section spectra are extracted. Excited state absorption prevents laser action around 1320 nm for the 4F3 /2-4l1 3 /2 transition of N d3 + in the investigated glasses.
1 . I n t r o d u c t i o n
N d3 + d o p e d crystals a n d glasses are w i d e l y a p p l i e d solid-state laser m a t e r i a l s [1-6]. F r o m
the 4F3 / 2 u p p e r laser level o f the 4f3 electrons o f the N d3 + i o n s t r a n s i t i o n s o c c u r to a l l levels
o f the 4Iy m a n i f o l d w i t h J = 15/2 ( t r a n s i t i o n w a v e l e n g t h X « 1.8 / m i ) , J = 13/2 (X « 1.32/mi), / = 11/2 (A « 1.06 / m i ) a n d / = 9/2 (X « 0.88 / m i , g r o u n d state). A n energy level d i a g r a m is i n c l u d e d i n F i g . 8 [2]. T h e N d : glass lasers generally operate o n the 4F3 / 2-4I1 1 / 2 t r a n s i t i o n e m i t t i n g a r o u n d 1.06 / m i where they have great i m p o r t a n c e as h i g h p o w e r a n d short pulse solid-state lasers. L a s e r a c t i o n o f N d : g l a s s lasers o n the
4F3 / 2-4I1 3 / 2 t r a n s i t i o n [7-9] (flashlamp p u m p i n g at r o o m temperature) a n d o n the 4F3 / 2-4I9 / 2
t r a n s i t i o n ( r o o m temperature laser p u m p i n g [10] a n d l o w temperature flashlamp p u m p i n g [8, 11, 12]) has been r e p o r t e d .
T h e luminescence l i n e w i d t h s o f the N d : glass laser t r a n s i t i o n s are rather b r o a d ( A v « 100 to 200 c m- 1) due to S t a r k s p l i t t i n g o f the i n v o l v e d levels a n d i n h o m o g e n e o u s b r o a d e n i n g i n the glass m a t r i x [2-6]. L a s e r w a v e l e n g t h t u n i n g across the luminescence l i n e w i d t h is r e a d i l y a c h i e v e d b y i n s e r t i o n o f a t u n i n g element i n the laser o s c i l l a t o r [13-16].
T h e possible laser t r a n s i t i o n s a n d w a v e l e n g t h t u n i n g ranges d e p e n d o n the effective a m p l i f i c a t i o n cross-section d i s t r i b u t i o n o&(X) = &em(X) — oQX{X) where cre m is the stimulated emission cross-section a n d <rex is the excited state a b s o r p t i o n cross-section. F o r the 4F3 / 2-4I1 1 / 2
t r a n s i t i o n cje f f values at the laser frequency were d e t e r m i n e d b y laser t h r e s h o l d measure- ments [17-19]. P e a k s t i m u l a t e d e m i s s i o n cross-sections c re m P for the 4F3 / 2-4I1 1 / 2 [ 2 , 2 0 - 2 3 ] a n d
the 4F3 / 2-4I1 3 / 2 [21] t r a n s i t i o n s were d e t e r m i n e d b y m e a s u r i n g a b s o r p t i o n cross-sections a n d
a p p l y i n g the J u d d - O f e l t m o d e l o f crystal-field i n d u c e d electric d i p o l e t r a n s i t i o n s [2, 20, 24, 25]. T h e r e are few reports o f excited state a b s o r p t i o n measurements i n N d . g l a s s systems [20, 26]. I n [26] excited state a b s o r p t i o n o f the 1.06/mi r a d i a t i o n was extracted f r o m g a i n s a t u r a t i o n measurements (<rex « crem/3), a n d i n [19] the J u d d - O f e l t theory was a p p l i e d to determine the 4F3 / 2-2G9 / 2 o s c i l l a t o r strength f o r the excited state a b s o r p t i o n o f the 1.06 / m i
0306-8919/92 © 1992 Chapman & H a l l 591
Figure 1 E x p e r i m e n t a l a r r a n g e m e n t . L R , laser r o d ; A 1 , A 2 , a p e r t u r e s ; L 1 , L 2 , lenses; F, filters; M , a l u m i n i u m m i r r o r ; M O , m o n o c h r o m a t o r ; P D , P b S d e t e c t o r .
r a d i a t i o n (4F3 / 2-2G9 / 2 o s c i l l a t o r strength is a p p r o x i m a t e l y e q u a l to one tenth o f 4F3 / 2-4I1 1 / 2
o s c i l l a t o r strength).
I n this paper spontaneous e m i s s i o n spectra, s t i m u l a t e d e m i s s i o n cross-section spectra, a n d excited-state a b s o r p t i o n cross-section spectra o f some N d : glasses (silicate glass S c h o t t L G 6 8 0 , p h o s p h a t e glasses Schott L G 7 6 0 a n d H o y a L H G 5 ) are d e t e r m i n e d b y a m p l i f i e d spontaneous e m i s s i o n [4] a n d light a m p l i f i c a t i o n measurements [27]. T h e studies give relative cross-section d i s t r i b u t i o n s . A b s o l u t e cross-section d i s t r i b u t i o n s are o b t a i n e d b y c a l i b r a t i n g the results to reported peak s t i m u l a t e d e m i s s i o n cross-sections c re m P at the w a v e l e n g t h AP a r o u n d 1.06 ^ m . ae x(/lP) is assumed to be zero because c re m P c a l c u l a t i o n s [2, 20-23] a n d ce f f( AP) measurements [17-19] gave s i m i l a r results w i t h i n the e x p e r i m e n t a l uncertainties. D e v i a t i o n s f r o m 0"ex(AP) = 0 s h o u l d s h o w u p i n the d e t e r m i n e d spectra i n regions o f negative cre x. I n this case a v o i d i n g negative cre x values w o u l d a l l o w for the d e t e r m i n a t i o n o f ae x( ^P) . T h e 4F3 / 2-4I1 3 / 2,4F3 / 2-4I1 1 / 2 a n d 4F3 / 2-4I9 / 2 e m i s s i o n transitions are considered.
2. E x p e r i m e n t a l d e t a i l s
T h e e x p e r i m e n t a l arrangement for the a m p l i f i e d spontaneous e m i s s i o n ( A S E ) a n d the light a m p l i f i c a t i o n measurements is s h o w n i n F i g . 1. T h e N d : g l a s s r o d L R a n d t w o linear flash l a m p s ( I L C T e c h n o l o g y m o d e l L - 2 4 2 6 ) are m o u n t e d i n a h i g h l y reflective d o u b l e - e l l i p t i c a l c y l i n d e r ( m a t e r i a l is a l u m i n i u m ) . C o o l i n g water c o n t a i n i n g N a N 02 for u l t r a v i o l e t ( U V ) light filtering is c i r c u l a t e d t h r o u g h the p u m p c a v i t y . T h e p o w e r s u p p l y ( J K Lasers type System 2000) has a c a p a c i t o r b a n k o f C = 500 fiF. T h e flash l a m p pulse w i d t h is a p p r o x i - m a t e l y 650 fis. T h e p u m p source a l l o w s a r e p e t i t i o n rate o f u p to a b o u t 0.2 H z . T h e r o d sizes are 3/8" i n diameter a n d 4" i n length.
I n the A S E measurements the right l i g h t p a t h is closed a n d the l i g h t o u t p u t f r o m the left r o d surface is collected b y lens L I a n d transferred to the m o n o c h r o m a t o r b y lens L 2 . T h e m o n o c h r o m a t o r o u t p u t s i g n a l is detected w i t h a P b S p h o t o c o n d u c t o r ( V a l v o S V 6 1 ) . T h e r e c o r d i n g w a v e l e n g t h is tuned m a n u a l l y f r o m shot to shot. T h e measured signals are corrected for the w a v e l e n g t h dependence o f the detection system. T h e spectral sensitivity was d e t e r m i n e d by r e c o r d i n g the spectral d i s t r i b u t i o n o f a h a l o g e n - t u n g s t e n l a m p o f k n o w n c o l o u r temperature ( O s r a m type H L X 64655, T = 3450 K at 12 V voltage) [28]. F r o m the A S E spectra the spontaneous e m i s s i o n spectra a n d the s t i m u l a t e d e m i s s i o n cross-section spectra are extracted (see S e c t i o n 4 b e l o w ) .
T h e l i g h t a m p l i f i c a t i o n is measured b y feeding b a c k the light emitted at the right side o f the r o d w i t h the a i d o f the m i r r o r M a n d b y detecting the s i g n a l increase caused b y the feedback light. T h e a m p l i f i c a t i o n is measured at a l o w p u m p voltage a n d a h i g h p u m p
T—i — i — i — i — i — i — i — i — i—I—i — i — i — i — i — i — i — i—I—i — i — i — i — i — i — i—i—i — i — i — i — r
pi i i i I i i i i I i I i l i i i i l i I i i l i i i i l i i i i i
900 950 1050 1100 1300 1350 H 0 0
WAVELENGTH X (nm)
Figure 2 N o r m a l i z e d a m p l i f i e d s p o n t a n e o u s e m i s s i o n p o w e r s p e c t r a ( ) a n d n o r m a l i z e d s p o n t a n e o u s e m i s s i o n p o w e r s p e c t r a ( ) f o r s i l i c a t e laser g l a s s S c h o t t L G 6 8 0 . P u m p v o l t a g e U = 8 0 0 V. T h e c u r v e s in t h e left a n d r i g h t f i g u r e are e x p a n d e d v e r t i c a l l y b y 4 x a n d 5 * , r e s p e c t i v e l y .
voltage. F r o m the a m p l i f i c a t i o n factor o f the feedback l i g h t the effective a m p l i f i c a t i o n cross-section d i s t r i b u t i o n <reff(/l) = &cm(X) — aQX{X) is extracted (see S e c t i o n 4 b e l o w ) .
3. E x p e r i m e n t a l r e s u l t s
T h e n o r m a l i z e d A S E spectra /ASEW/^Wmax of the three investigated N d : g l a s s r o d s are s h o w n i n F i g s 2 (LG680), 3 (LG760) a n d 4 ( L H G 5 ) . PASEfmax is the m a x i m u m spectral p o w e r w h i c h occurs f o r the 4F3 / 2-4I1 1 / 2 t r a n s i t i o n . T h e wavelengths lv o f PAsE,max 0e-
^ A S E ( ^ P ) = ^ASE,max) are ^P = 1061 n m f o r LG680 ( F i g . 2), AP = 1054 n m f o r LG760 ( F i g . 3), a n d AP* = 1055 n m f o r L H G 5 ( F i g . 4). T h e 4F3 / 2-4I9 / 2 A S E spectra are Stokes shifted f r o m the 4l 9 / 2 -4F3 / 2 a b s o r p t i o n spectra ( s h o w n i n F i g s 6 t o 8) because o f fluorescence r e a b s o r p t i o n b y the 4I9 / 2 g r o u n d state level p o p u l a t i o n a n d because o f t h e r m a l i z a t i o n o f e x c i t a t i o n w i t h i n the i n h o m o g e n e o u s l y b r o a d e n e d 4F3 / 2 level.
T h e a m p l i f i c a t i o n o f the l i g h t fed b a c k to the laser r o d is s h o w n i n F i g . 5 f o r LG680. T h e
4F3 / 2-4I1 1 / 2 a n d 4F3 / 2-4I1 3 / 2 t r a n s i t i o n s are c o n s i d e r e d . T h e r a t i o p = (i> t ot"^ASE)/^ASE *s
p l o t t e d versus w a v e l e n g t h f o r t w o sets o f p u m p voltages U{ = 1000 V a n d U2 = 2000 V .
Pt o t is the t o t a l s i g n a l c o m p r i s i n g the A S E s i g n a l PA S E a n d the a m p l i f i e d feedback s i g n a l .
S i m i l a r curves are o b t a i n e d f o r LG760 a n d L H G 5 . I n regions o f p(X, U2) > p{K Ux) the feedback l i g h t is a m p l i f i e d i n the r o d (creffW > 0), w h i l e i n regions o f p(X, U2) < p(K Ux) the feedback l i g h t is attenuated (o&{k) < 0).
4. T h e o r e t i c a l r e l a t i o n s
T h e t h e o r e t i c a l relations between a m p l i f i e d s p o n t a n e o u s e m i s s i o n , light a m p l i f i c a t i o n ,
WAVELENGTH X (nm)
Figure 3 N o r m a l i z e d a m p l i f i e d s p o n t a n e o u s e m i s s i o n ( ) a n d n o r m a l i z e d s p o n t a n e o u s e m i s s i o n s p e c t r a ( ) f o r p h o s p h a t e laser g l a s s S c h o t t L G 7 6 0 . P u m p v o l t a g e U = 8 0 0 V. T h e c u r v e s in t h e left a n d r i g h t f i g u r e are e x p a n d e d v e r t i c a l l y b y 1 0 * a n d 5 * , r e s p e c t i v e l y .
* A S E ( A > - ^ sP( A > TZr~FT\ _ / 1 MA r J
spontaneous e m i s s i o n , s t i m u l a t e d e m i s s i o n cross-section, a n d excited-state a b s o r p t i o n cross-section are d e r i v e d i n the f o l l o w i n g .
4 . 1 . Relation between spontaneous emission and amplified spontaneous emission
T h e r e l a t i o n between a m p l i f i e d s p o n t a n e o u s e m i s s i o n p o w e r d i s t r i b u t i o n P A S E W and spontaneous e m i s s i o n p o w e r d i s t r i b u t i o n Psp(X) is g i v e n b y [4, 27, 29]
exp{[<xe mffl - Gex(X)]NJ} ~ 1
I n E q u a t i o n 1 it is assumed that the N d3 + e x c i t a t i o n is constant across the r o d diameter, i.e. Nu(r9 z) = Nu(z) where r is the r a d i a l r o d c o o r d i n a t e a n d z is the a x i a l r o d c o o r d i n a t e . Nu is the upper laser level p o p u l a t i o n n u m b e r density averaged over the r o d length, i.e.
Nu = ^ A Tu( z ) d z / / . Nu depends o n the flashlamp p u m p p o w e r , the 4F3 / 2 spontaneous emission lifetime a n d the a m p l i f i c a t i o n o f the spontaneous emission [27,29]. A n a c c u m u l a t i o n o f p o p u l a t i o n i n the t e r m i n a l laser levels is neglected.
T h e g a i n factor G o f light a m p l i f i c a t i o n is
G(X) = e x p { Km( A ) - aex(X)]NJ} (2) Insertion o f E q u a t i o n 2 i n t o E q u a t i o n 1 a n d r e a r r a n g i n g the terms gives
PVW = PASEW^Z! (3)
Figure 4 N o r m a l i z e d a m p l i f i e d s p o n t a n e o u s e m i s s i o n ( ) a n d n o r m a l i z e d s p o n t a n e o u s e m i s s i o n s p e c t r a ( ) f o r p h o s p h a t e laser g l a s s H o y a L H G 5 . P u m p v o l t a g e U = 7 0 0 V. T h e c u r v e s in t h e left a n d r i g h t f i g u r e are e x p a n d e d b y 1 0 * a n d 5 x , r e s p e c t i v e l y .
F o r w e a k a m p l i f i c a t i o n G 1 ( l o w f l a s h l a m p p u m p v o l t a g e o r s m a l l cre f f) the s p o n t a n e o u s e m i s s i o n Ps p becomes e q u a l to the a m p l i f i e d s p o n t a n e o u s e m i s s i o n PASE-
4.2. Relation between spontaneous emission and stimulated emission cross- section
T h e r e l a t i o n between the s p o n t a n e o u s e m i s s i o n d i s t r i b u t i o n E(X) = Psp(X)/jPsp(X)dl ( i n t e g r a t i o n over a l l 4F3 / 2 -> % transitions) a n d the s t i m u l a t e d e m i s s i o n cross-section d i s t r i b u t i o n <7e m(A) is [4, 20, 30, 31]
ff«nW = o in\ — (4)
where rr a d is the r a d i a t i v e lifetime o f the u p p e r laser level, c0 is the l i g h t v e l o c i t y i n v a c u u m , a n d n(X) is the refractive i n d e x at the e m i s s i o n w a v e l e n g t h . T h e refractive indices at 632.8 n m a n d at the peak l a s i n g w a v e l e n g t h AP a r o u n d 1.06/mi are g i v e n i n the N d : g l a s s d a t a sheets o f S c h o t t [32] a n d H o y a [33]. n(X) is a p p r o x i m a t e l y d e t e r m i n e d b y a p p l y i n g the single o s c i l l a t o r d i s p e r s i o n r e l a t i o n [n2(X) — \]j[n2{X) + 2] = C / ( A0"2 — I '2) where C a n d
are fitting constants [34].
I n o u r studies the s t i m u l a t e d e m i s s i o n cross-sections oem{kv) at the peak l a s i n g w a v e - length i P a r o u n d 1.06/im are t a k e n f r o m d a t a sheets [32, 33] a n d the spectral dependence o f the s t i m u l a t e d e m i s s i o n cross-sections is c a l c u l a t e d b y
^ psp( i y qP)
0.61—I 1 1 1 I =1 0.71 I I 1 1 I I 1 1 1 1 I—
1050 1100 1300 1350 U 0 0
WAVELENGTH X (nm)
Figure 5 N o r m a l i z e d a m p l i f i e d f e e d b a c k l i g h t p o w e r (left o r d i n a t e s ) a n d a m p l i f i c a t i o n f a c t o r G ( r i g h t o r d i n a t e s ) v e r s u s w a v e l e n g t h f o r S c h o t t glass L G 6 8 0 . U = 1 0 0 V ( ), U = 2 0 0 0 V ( ) . T h e ( ) c u r v e s r e p r e s e n t t h e a v e r a g e f e e d b a c k f a c t o r / = Pbi-m/PASE ( ' e f t o r d i n a t e a p p l y ) .
E q u a t i o n 5 is d e r i v e d b y a p p l i c a t i o n o f E q u a t i o n 4 f o r <7e m(A) a n d c re m( AP) w i t h E(X) p r o p o r t i o n a l t o Ps p( A ) .
C a r e has t o be t a k e n f o r the 4F3 /2 -4l 9/2 t r a n s i t i o n since Ps p( A ) is reduced b y luminescence r e a b s o r p t i o n d u e t o ground-state a b s o r p t i o n . E q u a t i o n 5 applies o n l y to the l o n g w a v e - length side where the t h e r m a l p o p u l a t i o n o f the S t a r k split 4I9 / 2 levels becomes s m a l l a n d the luminescence r e a b s o r p t i o n becomes w e a k (see S e c t i o n 5).
4.3. A m p l i f i c a t i o n of feedback A S E light
T h e a m p l i f i c a t i o n factor G = Ph,0utlFh;m o f the feedback A S E l i g h t is g i v e n b y E q u a t i o n 2.
T h e i n p u t feedback l i g h t p o w e r is PB I N = / PAS E where / is the feedback f r a c t i o n . T h e a m p l i f i e d feedback l i g h t p o w e r is Phout = Piot — PASE. These relations give
1 7 w
- 1 = e x p { [ ae m( / l ) - ffcxWR'} (6) K n o w i n g c re m( AP) — c re x( AP) ( = < 7e m( AP) i n o u r case) then aem(X) — <rex(A) m a y be expressed by
In
^emW - tfexOO = K m ( A p ) — 0"e x(/lP)]
1
In 1
1
FASE(^P)
- 1
(7)
T h e d e t e r m i n a t i o n o f aem(X) — <7e x(A) relative to < 7e m( Ap) — c re x( AP) a v o i d s the necessity to determine Nu e x p l i c i t l y .
i I i i i — i—r~ n — i — i — i |_ i i i i — i I i i i i — i — [ - I—m—i—r
0 61 I 1 I I I I 1 I I I I
1
I I I I II
I I I I I I I I I 1 I850 900 950 1050 1100 1300 1350 U 0 0
WAVELENGTH X (nm)
Figure 6 C r o s s - s e c t i o n s o f S c h o t t G l a s s L G 6 8 0 . C u r v e s are c a l i b r a t e d t o oem? = < 7e m( AP) = 2 . 9 * 1 0 "2 0c m2
w i t h XP = 1 0 6 1 n m [ 3 2 ] . c re x( AP) = 0 is a s s u m e d . A b s o r p t i o n s p e c t r u m ffabs(^) is c a l c u l a t e d f r o m t r a n s - m i s s i o n s p e c t r u m i n [ 3 2 ] .
T h e feedback f r a c t i o n f(X) is nearly wavelength-independent. A s s u m i n g a l i n e a r r e l a t i o n between the u p p e r laser level p o p u l a t i o n NU a n d the square o f the f l a s h l a m p p u m p voltage U, the feedback f r a c t i o n/ ( 2 ) m a y be d e t e r m i n e d f r o m E q u a t i o n 6 b y the f o l l o w i n g r e l a t i o n :
A*) = - 1 QXp[-K(X)Uf] (8)
PA S E( i , U{)
where K(X)U2 = [<7e m(T) — oex(A)]NU(U)l = \n[G(l, U)]. K(2) m a y be expressed b y l n [ G 0 l , U2)] - ln[G(l, U,)]
K(1) = V\ - Uf
l n [ Pt o t( A , U2)/PASE(^ U2) - 1] - l n [ Pt o t( A , U^/P^X, Ux) - 1]
F o r s m a l l p u m p voltages f(X) a p p r o a c h e s [Piot(X, U - > 0 ) / PA S E( A , £ / - » ( ) ) ] — 1. W i t h i n the
4F3 / 2-4I1 3 / 2 a n d the 4F3 / 2-4I1 1 / 2 e m i s s i o n b a n d s average f(X) values are used.
T h e analysis described a b o v e is n o t a p p l i c a b l e to the 4F3 / 2-4I9 / 2 t r a n s i t i o n because ground-state light a b s o r p t i o n has n o t been i n c l u d e d . F o r this case E q u a t i o n 2 has to be rewritten to
G{X) = exp{[cre mW - <reK(X)]NJ - <7abs(A)7Vg/}
where <rahs(l) is the 4I9/2-4F3 / 2 ground-state a b s o r p t i o n cross-section a n d JVg is the 4I9 / 2 ground-state level p o p u l a t i o n . N e t g a i n G > 1 requires Nu > Nga&hs(X)l[(Tem(X) — vex(X)]
as i n three-level laser systems [ 4 ] .
WAVELENGTH X (nm)
Figure 7 C r o s s - s e c t i o n s o f S c h o t t Glass L G 7 6 0 . C u r v e s are c a l i b r a t e d t o < re m( ^P) = 4 . 2 x 1 0 2 0c m2
(/lp = 1 0 5 3 . 5 n m [ 3 2 ] ) . c re x( lP) = 0 is a s s u m e d . o -a b s( 2 ) is c a l c u l a t e d f r o m t r a n s m i s s i o n s p e c t r u m in [ 3 2 ] .
5. T h e o r e t i c a l r e s u l t s
A v e r a g e feedback factors / are d e t e r m i n e d f r o m the ( Pt o t — P A S E V ^ A S E curves b y a p p l i c a - t i o n o f E q u a t i o n s 8 a n d 9. T h e y are s h o w n b y the d a s h - d o t t e d lines i n F i g . 5 for L G 6 8 0 . U s i n g the r i g h t ordinates o f F i g . 5 the d a s h e d a n d s o l i d curves present the g a i n curves G = ( Pt o t - PAsE)l(FASEf) for the p u m p voltages o f 1000 V (dashed) a n d 2000 V (solid).
G > 1 represents d o m i n a n t a m p l i f i c a t i o n a n d G < 1 represents d o m i n a n t a t t e n u a t i o n . K n o w i n g G(A, U), the PASEWIPASE^X curves o f F i g s 3 a n d 4 ( s o l i d curves) m a y be transferred to PSP(X)IPSP^MAX curves b y a p p l i c a t i o n o f E q u a t i o n 3. T h e y are s h o w n b y the dashed curves i n F i g s 2, 3 a n d 4. T h e spectral n a r r o w i n g o f the A S E curves c o m p a r e d to the s p o n t a n e o u s e m i s s i o n curves is s m a l l because the g a i n G(XP) is s m a l l for d i s p l a y e d A S E spectra (G(AP, 800 V ) « 1.1 for L G 6 8 0 , G(AP, 800 V ) « 1.25 for L G 7 6 0 , a n d G(AP, 700 V ) « 1.19 for L H G 5 ) . T h e 4F3 / 2-4I1 3 / 2 fluorescence peaks a r o u n d 1 3 3 0 n m are a p p r o x i m a t e l y a factor o f 9.3 smaller t h a n the 4F3 / 2-4I1 1 / 2 fluorescence peaks Ps p > m a x at AP a r o u n d 1055 n m for a l l three investigated N d : g l a s s rods. T h e 4F3 / 2-4I9 / 2 fluorescence peaks o f the phosphate laser rods L G 7 6 0 a n d L H G 5 o c c u r a r o u n d 907 n m a n d are a p p r o x i m a t e l y a factor o f 11 smaller t h a n Ps p ? m a x, while the 4F3 / 2-4I9 / 2 fluorescence peak o f the silicate laser r o d L G 6 8 0 is located at 918 n m a n d its relative height is Ps p( 9 1 8 n m ) / Ps p m a x = 0.21.
T h e stimulated emission cross-sections <7em(A) are derived f r o m E q u a t i o n 5 a n d are dis- p l a y e d by the s o l i d curves i n F i g s 6, 7 a n d 8 for the laser glasses L G 6 8 0 , L G 7 6 0 a n d L H G 5 , respectively. T h e curves are adjusted to the <xe m(AP) values o f the d a t a sheets [32, 33]. F o r the
4F3 / 2-4I9 / 2 t r a n s i t i o n o n l y the long-wavelength part o f the s o l i d curves (X > 930 n m for
L G 6 8 0 , X > 910 n m for L G 7 6 0 a n d L H G 5 ) gives correct cre m values. T h e dotted curves s h o w
Figure 8 C r o s s - s e c t i o n s o f H o y a Glass L H G 5 . C u r v e s are c a l i b r a t e d t o <7e m( ^ p ) = 3 . 9 * 1 0 "2 0c m2
( 2P = 1 0 5 4 n m in [ 3 3 ] ) . oex(X?) = 0 is a s s u m e d . < ra b s( A ) is r e d r a w n f r o m [ 3 5 ] . T h e i n s e r t e d level d i a g r a m is r e d r a w n f r o m [ 2 ] .
the expected wavelength dependence o f oem. T h e y are d r a w n by assuming a m i r r o r symmetry between <rem a n d <rabs [5, 31]. T h e 4F3 /2 -4I9 /2 a b s o r p t i o n spectra are s h o w n b y the short-dashed curves. T h e y are calculated f r o m transmission spectra displayed i n [32] for the Schott glasses L G 6 8 0 a n d L G 7 6 0 a n d f r o m a n o p t i c a l density spectrum o f L H G 5 given i n [35].
T h e (Teff(A) curves are d e r i v e d f r o m E q u a t i o n 7 a n d are d i s p l a y e d b y the d a s h e d curves i n the F i g s 6 to 8. <rex(AP) = 0 is assumed. F o r the 4F3 / 2-4I9 / 2 t r a n s i t i o n s the <reff spectra are n o t s h o w n because o f the g r o u n d state l i g h t a b s o r p t i o n . T h e difference o f <re m(^) — G^{X) gives the excited state a b s o r p t i o n cross-section. F o r the 4F3 / 2-4I i3 / 2 t r a n s i t i o n s a r o u n d
1.32 / m i the crex(A) spectra are s h o w n b y the d a s h - d o t t e d curves.
T h e excited state a b s o r p t i o n cross-sections are r e m a r k a b l y large i n the r e g i o n o f the peak s t i m u l a t e d e m i s s i o n cross-section o f the 4F3 / 2-4I1 3 / 2 t r a n s i t i o n . T h i s f i n d i n g is i n agreement w i t h the o b s e r v a t i o n o f a l o n g - w a v e l e n g t h shift o f laser a c t i o n to the r e g i o n between
1.35 / m i a n d 1 40 / m i [7-9] w h i l e the p e a k o f spontaneous e m i s s i o n is between 1.325 / m i a n d 1.335 / m i . T h e excited state a b s o r p t i o n is due to t r a n s i t i o n s f r o m the 4F3 / 2 level to the 2K1 3 / 2,
4G7 / 2, a n d 4G9 / 2 levels as is seen b y the level d i a g r a m inserted i n F i g . 8. T h e s t r o n g excited
state a b s o r p t i o n a r o u n d 1.32/mi is u n f a v o u r a b l e f o r the a p p l i c a t i o n o f N d : g l a s s lasers o n the 4F3 / 2-4I1 3 / 2 t r a n s i t i o n .
T h e ce f f(A) a n d <7em(/l) curves f o r the 4F3 / 2-4I1 1 / 2 t r a n s i t i o n a r o u n d 1.06 / m i agree w i t h i n the uncertainties. T h e p e a k heights at kv are adjusted to the same v a l u e . Gex(X) values u p to a b o u t 2 0 % o f the <rem(/lp) values c a n n o t be e x c l u d e d because the a s s u m p t i o n c re x( 2P) = 0 is o n l y v a l i d w i t h i n this l i m i t [20,26] a n d the d e v i a t i o n s between cjem a n d <7EFF are o f this order.
T h e ground-state a b s o r p t i o n o c c u r r i n g for the 4F3 / 2-4I9 / 2 t r a n s i t i o n hinders a d e t e r m i n a - t i o n o f cre f f(A) a n d o"ex(/l). T h e cre m(A) d i s t r i b u t i o n s c o u l d be d e t e r m i n e d r o u g h l y f r o m the
4F3 / 2-4I9 / 2 a b s o r p t i o n spectra. L a s e r a c t i o n o n the 4F3 / 2-4I9 / 2 t r a n s m i s s i o n seems to
be possible u n d e r s t r o n g p u m p i n g c o n d i t i o n s as they are necessary for three-level laser systems [4, 5].
6. C o n c l u s i o n s
S t i m u l a t e d e m i s s i o n cross-section, c re m, a n d excited-state a b s o r p t i o n cross-section, ere x, d i s t r i b u t i o n s for n e o d y m i u m d o p e d glasses have been d e t e r m i n e d b y a m p l i f i e d s p o n t a n e o u s emisssion a n d light a m p l i f i c a t i o n measurements o f flashlamp p u m p e d r o d s . T h e o b t a i n e d effective s t i m u l a t e d e m i s s i o n cross-section curves, <jeff = aem — ce x, give a clear i n d i c a t i o n o f the possible l a s i n g regions o f the glass r o d s . T h e described measurement technique m a y also be a p p l i e d to other solid-state laser materials e m p l o y i n g four-level laser transitions.
T h e absolute p e a k s t i m u l a t e d e m i s s i o n cross-sections, c re m( 2P) , were t a k e n f r o m the literature. I f a d d i t i o n a l l y the r a d i a t i v e lifetime, ir a d, o f the u p p e r laser level is d e t e r m i n e d (see E q u a t i o n 4 [31]), e.g. b y fluorescence lifetime, Tf, a n d fluorescence q u a n t u m y i e l d , 0F, measurement ( rr a d = Tf/ 0f) , then absolute o"e m(A) curves are o b t a i n a b l e .
A c k n o w l e d g e m e n t s
T h e a u t h o r s t h a n k the D e u t s c h e F o r s c h u n g s g e m e i n s c h a f t for financial s u p p o r t .
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