RENORMALIZATION EFFECTS OF THE POLARITON DISPERSION

(1)

HAL Id: jpa-00223092

https://hal.archives-ouvertes.fr/jpa-00223092

Submitted on 1 Jan 1983

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

RENORMALIZATION EFFECTS OF THE POLARITON DISPERSION

F. Tomasini, J. Bigot, R. Levy

To cite this version:

F. Tomasini, J. Bigot, R. Levy. RENORMALIZATION EFFECTS OF THE POLARITON DISPER- SION. Journal de Physique Colloques, 1983, 44 (C5), pp.C5-79-C5-82. �10.1051/jphyscol:1983512�.

�jpa-00223092�

(2)

JOURNAL DE PHYSIQUE

Colloque C5, supplement au nO1O, Tome 44, octobre 1983 page C5-79

RENORMALIZATION EFFECTS OF THE POLARITON DISPERSION

F. Tomasini, J . Y . Bigot and R . Levy

Laboratoire de Spectroscopic e t d'optique du Corps SoZide*,Univ. Louis Pasteur, 5, rue de Z 'Universite', 67000 Strasbourg, France

RBsum6 - La d i s p e r s i o n d e s p o l a r i t o n s e s t BtudiBe experimentalement dans l e c h l o r u r e cuivreux l o r s q u e l e c r i s t a l e s t e c l a i r 6 p a r une s o u r c e l a s e r intense.

Des e f f e t s de r e n o r m a l i s a t i o n d u s l ' a b s o r p t i o n de deux photons a p p a r a i s s e n t au v o i s i n a g e de l a resonance b i e x c i t o n i q u e .

A b s t r a c t - The p o l a r i t o n d i s p e r s i o n i s i n v e s t i g a t e d e x p e r i m e n t a l l y i n cuprous c h l o r i d e when t h e c r y s t a l i s e x c i t e d w i t h a high i n t e n s i t y l a s e r source.

Xenormalization e f f e c t s due t o two-photon a b s o r p t i o n occur n e a r t h e b i e x c i t o n resonance.

INTEODUCTION

A s known from n o n l i n e a r o p t i c s , t h e d i e l e c t r i c f u n c t i o n ~ ( q , S1, up, n ) which g i v e s t h e response of a semiconductor a t photon energy (momentum) h n ( g ) when e x c i t e d by a P high i n t e n s i t y l a s e r s o u r c e a t a photon enerT1 ?lap, depends on t h e d e n s i t y np o f p o l a r i t o n s p r e s e n t i n t h e c r y s t a l . For CuC1, t h i s dependence of b o t h t h e r e a l and imaginary p a r t s o f E changes t h e well-known p o l a r i t o n d i s p e r s i o n (Re E ) [ I ] . These m o d i f i c a t i o n s a r e c a l l e d r e n o r m a l i z a t i o n e f f e c t s . They a r e very i m p o r t a n t i n CuCl where, due t o t h e g i a n t - o s c i l l a t o r s t r e n g t h of t h e e x c i t o n - b i e x c i t o n t r a n s i t i o n , a s t r o n g two-photon a b s o r p t i o n c r e a t e s b i e x c i t o n s a t energy EBi [ 2 ] .

Two e f f e c t s a r e p r e s e n t :

F i r s t , when.hap = EBi/2, t h e a b s o r p t i o n of two photons of same energy of t h e l a s e r w i l l modify t h e d i s p e r s i o n curve a t ~ ~ ~s i n c e t h e a b s o r p t i o n ( I m / 2 , E ) i s r e l a t e d t o t h e d i s p e r s i o n (Re E ) by a Kramers-Kronig r e l a t i o n . This e f f e c t i s c a l l e d auto- r e n o r m a l i z a t i o n of t h e l a s e r . It h a s f i r s t been observed by I t o h e t a 1 [ 3 ] . Second, t h e r e i s a p o s s i b i l i t y f o r p o l a r i t o n s w i t h energy :

nn = E . - n w

B 1 P (1)

t o b e a l s o absorbed. The p r e s e n c e o f t h e photons hap of t h e l a s e r beam m a n i f e s t s i t s e l f by an induced gap i n t h e o r i g i n a l d i s p e r s i o n curve a t t h e energy Pin.

The experimental methods we used t o i n v e s t i g a t e both r e n o r m a l i z a t i o n e f f e c t s a r e Hyper-Raman S c a t t e r i n g 141 and non-degenerate Four-Wave F i x i n g [5J .

HYPER-RAMAN SCATTERING (H. R. S . ⁾

I n H.R.S., two photons o f a l a s e r c a l l e d "Pump" (energy nup, p o l a r i t o n momentum _k i n t h e c r y s t a l ) a r e absorbed v i a t h e b i e x c i t o n s t a t e . They recombine spontaneous?y toward p o l a r i t o n branches, energy and momentum b e i n g conserved d u r i n g t h e whole p r o c e s s . I n a forward s c a t t e r i n g c o n f i g u r a t i o n , two H.9. l i n e s R$ and R;, a r e observed. F i g u r e l a shows t h e s h i f t s o f t h e s e two l i n e s with r e s p e c t t o t h e l a s e r

'Associb au C.N.R.S., ~ ~ 2 3 2

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983512

(3)

C5-80 JOURNAL DE PHYSIQUE

photon energy &up. The d e n s i t y o f photons i s n = 4 . l o i 5 photons/cm3. The induced gap e f f e c t can be seen when t h e energy hfi of tRe e m i t t e d H.R. p o l a r i t o n s f u l f i l l s e q . ( 1 ) . The a u t o r e n o r m a l i z a t i o n e f f e c t i s a l s o observed when nuL = EBi/2. I n con- t r a s t , s p e c t r a l p o s i t i o n s of H.R. l i n e s a t very low l a s e r i n t e n s i t y (dashed l i n e s ) show no r e n o r m a l i z a t i o n e f f e c t s .

I n a d d i t i o n t o t h e two e f f e c t s mentioned above, a g l o b a l s h i f t o f t h e H.R. l i n e p o s i t i o n s has a l s o been observed f o r s m a l l a n g u l a r c o n f i g u r a t i o n s ( a = 0 ° , B = 11')

( s e e F i g . I b ) . This e f f e c t , although b e i n g l a s e r i n t e n s i t y dependent, does n o t show any resonance a t EBi/2. I t i s t a k e n i n t o account by assuming t h a t t h e background d i e l e c t r i c c o n s t a n t sb i s i n t e n s i t y dependent through an a d d i t i o n a l term Aa ( n ) .

b p

F i g . 1 - S p e c t r a l p o s i t i o n s of hyper-Raman emission l i n e s a ) = 23O , a = 0" ; b) 6 = 11" , u = 0"

F i g . 2 - Lower branch of t h e p o l a r i t o n d i s p e r - s i o n .

F u l l l i n e : non-renormalized d i s p e r s i o n (np = 0 ) .

Dotted l i n e : renormalized curve ( n ⁼1015 photons/crn 3 ) .

P

(4)

A numerical a n a l y s i s of t h e s p e c t r a l s h i f t s of t h e H.R. l i n e s i n c l u d i n g a t h e o r e - t i c a l model f o r ~ ( q , Q , w , np), allows t o determine t h e p o l a r i t o n d i s p e r s i o n . When u s i n g t h e model of Mdrz e! a 1 161, t h e corresponding d i s p e r s i o n i s p l o t t e d i n f i g u r e 2 ( t h e damping of t h e b i e x c i t o n i s n o t taken i n t o a c c o u n t ) .

H.R.S. i s a spontaneous p r o c e s s i n which t h e phase matching c o n d i t i o n

Ak ⁼2% - ^Q- K = 0 i s f u l f i l l e d 9 and K b e i n g t h e momentum of e m i t t e d H . R . pola- 1 2

r i t o n s . ~ o r F i n g w i t h a second l a s e r s o u r c e , c a l l e d " T e s t " (energy h u t , momentum Lt),

t h e i n t e n s i t y of which i s about one p e r c e n t of t h e i n t e n s i t y of t h e pump beam, we were a b l e t o produce t h e corresponding induced p r o c e s s , which i s F.W.M. g e n e r a t i o n . This p r o c e s s i s t h e lnduced recombination of v i r t u a l b i e x c i t o n s c r e a t e d by t h e a b s o r p t i o n of two photons of t h e Pump l a s e r , i n t o p o l a r i t o n s w i t h wavevector

(energy) &t ( R u t ) . A p a r a m e t r i c emission i s then observed a t energy 2 RwP - *wt. I t s i n t e n s i t y i s maximum when t h e c o n s e r v a t i o n of w a v e v e c t o r s i s achieved. We have s t u d i e d t h e e f f i c i e n c y of F.W.H. a s a f u n c t i o n of phase mismatch, by v a r y i n g t h e t e s t energy hwt a s shown i n f i g u r e 3. The e x c i t a t i o n s p e c t r a o b t a i n e d d i s p l a y maxima a t e n e r g l e s which c o i n c i d e w i t h H . R . emlssion peaks. This can b e w e l l understood by remember~ng t h a t , f o r H.R.S., t h e phase matching c o n d i t i o n i s a u t o m a t i c a l l y f u l - f i l l e d . Thus, and because of i t s high efficiency, F.W.M. allowed us t o s t u d y renor- m a l i z a t i o n e f f e c t s over a wider s c a l e of pump l a s e r i n t e n s i t i e s t h a n with H.R.S.

Fig. 3 - I n t e n s i t y of t h e F.W.?l. emission l i n e obeying X U ( ' ) = 2&wp - nwt, a s a f u n c t i o n of f i w ( l ) . Arrows i n d i c a t e t h e s p e c t r a l p o s i t i o n s o f H.R.S. emission l i n e s $ and 5 of t h e pump beam.

llwp i s f i x e d a t : ( x ) : 3.1858 eV , ( 0 ) : 3.1856 eV , ( A ) : 3.1854 eV ,

(.) : 3.1851 eV r e s p e c t i v e l y .

We have worked w i t h two p o l a r i z a t i o n c o n f i g u r a t i o n s , i . e . t h e pump and t e s t beam having e i t h e r t h e same ( T / / P ) o r c r o s s e d (TIP) p o l a r i z a t i o n s . F i g u r e 4a shows t h e dependence of t h e width of t h e induced gap upon t h e pump i n t e n s i t y f o r

hwp = 3.1845 eV. We n o t i c e t h a t t h i s e f f e c t was observed only f o r t h e c o n f i g u r a t i o n (T//P). T h i s can b e understood by t h e two following remarks : f i r s t , due t o t h e symmetry T I of t h e b i e x c i t o n l e v e l , p a r a m e t r i c and t e s t photons a r e i d e n t i c a l l y p o l a r i z e d ; second, t h e two-photon a b s o r p t i o n from t h e c r y s t a l ground s t a t e t o t h e b i e x c i t o n s t a t e can only b e achieved w i t h two photons having t h e same p o l a r i z a t i o n . So, no i r d u c e d gap i s o b t a i n e d f o r photons of t h e t e s t ( p a r a m e t r i c ) with a p o l a r i z a - t i o n p e r p e n d i c u l a r t o t h a t of t h e pump. I n f i g u r e 4 b ) , t h e dependence of t h e term

) upon t h e d e n s i t y of photons i s g i v e n when t h e energy of t h e pump i s liwp = 3.1807 eV. A s a t u r a t i o n of e f f e c t s shows up i n f l g u r e 4 f o r photon densities g r e a t e r t h a n n = 1016 photons/cm3

P

(5)

JOURNAL DE PHYSIQUE

3,,89b

hwr=3.1845 eV T I P

F i g . 4 - Study of r e n o r m a l i z a t i o n upon t h e d e n s i t y of photons n i n t h e c r y s t a l a ) s p l i t t i n g e f f e c t f o r t h e p a r a l l e l c o n f i g u r a t i o n P

(T//P) b ) s h i f t e f f e c t f o r c r o s s e d p o l a r i z a t i o n ( T I P ) .

( f o r Iplax, np = 1016 photons/cm3).

CONCLUSION

We have used H.R.S. and F.W.F. techniques i n CuCl t o s t u d y r e n o r m a l i z a t i o n e f f e c t s showing up i n t h e d i s p e r s i o n curve of p o l a r i t o n s near h a l f t h e b i e x c i t o n energy.

Three e f f e c t s have been observed : an induced gap a t t h e energy EBi - Tiup, an auto- r e n o r m a l i z a t i o n a t t h e photon energy ~ ~ ~ / 2 , a n d a s l i g h t m o d i f i c a t i o n o f t h e background d i e l e c t r i c c o n s t a n t w i t h t h e l a s e r i n t e n s i t y . Each technique h a s i t s advan- t a g e : H.X.S. is convenient when e x p l o r i n g a wide range of s p e c t r a l e n e r g i e s , w h i l e F.W.M. i s much more adapted when we want t o s t u d y t h e s e e f f e c t s over a l a r g e s c a l e of l a s e r i n t e n s i t i e s .

This work was supported by a c o n t r a c t w i t h t h e "MinistGre des P.T.T." of France - D.G.T. - D i r e c t i o n d e s A f f a i r e s I n d u s t r i e l l e s e t I n t e r n a t i o n a l e s .

1 Honerlage B . , Bivas A. and Vu Duy Phach, Phys. Rev. L e t t . 41 (1978) 49.

2 Hanamura E . , S o l i d S t a t e Comrn. 12 (1973) 951.

3 I t o h T. and Suzuki T . , J . Phys. Soc. Japan 45 (1978) 1939.

~ t o h T . , Suzuki T. and Ueta PI., J . Phys. Soc. Japan 3 (1978) 345.

4 Grun J . B . , Honerlage B. and Levy R., S o l i d S t a t e Comm. 46 ⁽¹⁹⁸³⁾^51.

5 Honerlage B., Levy R. and Grun J . B . , O p t i c s Comm., 43 (1982) 443.

6 nlarz R . , Schmitt-Rink S. and Haug H . , Z. Phys. B g (1980) 9.