Volume 1 4 , N u m b e r 4 D e c e m b e r 2 0 0 4
Contents
P a g e
1. D a o V o n g D u e a n d N g u y e n N g o c T h u a n - A lgorithm for G eneralised D eutsch - Like Problem in 1 93 - 196 Q u an tu m C o m p u ta tio n
2. N g u y e n M a n h C u o n g a n d N g u y e n A i V i e t - T h e B inding E nergy o f E x cito n in S em iconductor 1 9 7 - 201 C arbon N a n o tu b e s
3. N g u y e n A n h K y a n d N g u y e n T h i H o n g V a n - H opf S tru c tu re an d R ep re se n ta tio n s of th e T w o 2 0 2 - 2 0 8 P a ra m e tric Q u a n tu m S u p e ra lg e b ra U Piq [ g / ( 2 / l ) ]
4. N g u y e n V a n D o a n d P h a m D u e K h u e - N eu tro n Y ields from T h ick T a T a rg e t B om barded by 2 09 - 2 14 65 M eV E le c tro n B eam
5. N g u y e n T h e B i n h - H y p er-R ay leig h S c a tte rin g in Solution of O rganic M olecules 215 - 2 2 0 6. H o a n g D a c L u c , T V in h V a n G i a p , a n d D a n g D u e N h a n - M odeling of G ro u n d w a te r Flow by 221 - 2 2 6
Black Box M odels a n d E n v iro n m e n ta l Isotopes
7. G . M o h a n t y a n d p . K . S a h o o N o n -E x isten ce of P lan e S y m m etric S trin g C osm ological M odel in 2 2 7 - 2 3 0 B im etric T h e o ry
8. N g u y e n C h i n h C u o n g - S q u a rk D ecays in to H° in th e M SSM w ith C om plex P a ra m e te rs 2 31 - 2 3 7
9. D o V a n N a m - P h a s e R e la x a tio n T im e in 2 D -Q u an tu m D ot 2 3 8 - 2 4 3
10. V u V a n H u n g , N g u y e n Q u a n g H o c , a n d D i n h Q u a n g V in h - Debye - W aller F a c to r in Solid 2 4 4 - 2 5 0 3He an d ‘‘ H e A n h a rm o n ic C ry sta ls
11. N g u y e n V a n D o a n d P h a m D u e K h u e - Isom eric C ross-Section R a tio in th e 45Sc(7,n ) Sc<Um’3 25 1 - 2 5 6 R eaction In d u ced by 65 M eV B re m s stra h lu n g
Communications in Physics, Vol. 14, No. 4 (2004), pp. 215-220
H Y PE R -R A Y LE IG H s c a t t e r i n g i n s o l u t i o n
OF ORGANIC MOLECULES
N G U Y E N T H E BINH
Faculty of Physics, Hanoi National University
s t r a c t . Nonlinear optical (NLO) organic materials with electronic and optical properties of semiconductors are especially attractive for applications in opto-electronic devices Many efforts have been made to develop new organic materials with large hyperpolanzabilities 0. However, there has been a complicate problem in experimental determination of the microscopic second order NLO polarizability p of a molecule (or the first -order optical hyperpolarizability Ị3). Recently, the hyper-Rayleigh scattering (HRS) has been used as a new technique with many advantages to determine the first -order optical kyperpolarizability 0 in solution. Since the efficiency of Hyper-Rayleigh scattering is small, high-power laser pulses are required . We studied to use a femtosecond laser system nnth, high peak power at 860nm wavelength as a pump source for HRS. An experimental setup was performed to measure the first -order optical hyperpolarizability p of para-niroanaline (pNA) in methanol.
Our results and discussions are reported in this paper.
I. I N T R O D U C T I O N
O v e r t h e l a s t d e c a d e , m a n y r e s e a r c h e s t o d e v e l o p c h r o m o p h o r e s w i t h h i g h m i c r o s c o p i c s e c o n d - o r d e r N L O p o l a r i z a b i l i t i e s 0 h a v e b e e n r e p o r t e d [1,2], I n a d d i t i o n , s o m e m e t h o d s t o m o d u l a t e o r e n h a n c e t h e P- v a l u e b y p h o t o e x c i t a t i o n w e r e p r o p o s e d [3,4], F o r exam ple, th e NLO response of para-nitroaniline (pNA) changes w ith photoexcitation and t h e ,5 -v a lu e w a s e n h a n c e d b y 11 t o 32 t i m e s a t t h e e x c i t e d s t a t e [5], N o n l i n e a r o r g a n i c m aterials are exp ected to take an im portant role in the future opto-electronic devices for telecom m unication, optical sw itching and signal processing [6,7].
I n o r d e r t o e v a l u a t e t h e f i rs t h y p e r p o l a r i z a b i l i t i e s /? o f N L O m a t e r i a l s s e v e r a l t e c h n i q u e s w e r e p r o p o s e d . T h e r e h a s b e e n a c o m p l i c a t e p r o b l e m in t h e (3- v a l u e m e a s u r e m e n t s
due to the symmetry requirements for observation of a macroscopic second-order NLO sus
ceptibility. Second harmonic generation - the typical technique to measure the /?-value - is forbidden in solu tion s and liquids. In m ost cases, they have to create a noncentrosymm e- try to m olecular structure. Typically, electric-field-induced second harmonic generation (E FISH G ) technique was proposed. T he sym m etry of the solution is broken by the appli
cation of an electric field to orient the dipoles in NLO molecules. Following the EFISHG technique, they have to measure the dipole moment /i, the third -order hyperpolarizabil- ity 7 to extract the first hyperpolarizabilities p from the value (7 + /X/3/5kT) measured in EFISH G [8]. A lth ou gh second harmonic generation in isotropic m edia is forbidden for reason of symmetry, incoherent second harmonic light scattering (Hyper-Rayleigh Scatter
ing -HRS) in isotropic media has been observed and became a new suitable technique to
2 1 6
NGUYEN T H E BINH
d e t e r m i n e t h e h y p e r p o l a r i z a b i l t i e s o f N L O m o le c u l e s . In t h e H R S t e c h n i q u e , t h e s a m p l e (e.g . c h r o m o p h o r e s o l u t i o n ) is i r r a d i a t e d b y a la s e r b e a m o f f u n d a m e n t a l f r e q u e n c y u a n d t h e s c a t t e r e d p h o t o n a t 2u w e r e d e t e c t e d . H R S c o u l d b e c o n s i d e r e d a s a n i n c o h e r e n t s c a t t e r e d s e c o n d h a r m o n i c g e n e r a t i o n in i s o t r o p i c m e d i a . T h e H R S t e c h n i q u e h a s t h e a d v a n t a g e o v e r t h e E F I S H G o n e . I n H R S t e c h n i q u e , n o e l e c t r i c field is n e e d e d a n d t h e f ir s t h y p e r p o l a r i z a b i l t i e s c a n b e i n d e p e n d e n t l y d e t e r m i n e d w i t h o u t t h e d i p o l e m o m e n t ụ.
a n d t h e t h i r d - o r d e r h y p e r p o l a r i z a b i l i t y 7.
S i n c e t h e ef f ic i e n c y o f H y p e r - R a y l e i g h s c a t t e r i n g is s m a l l , h i g h - e n e r g y la s e r p u ls e s a r e r e q u i r e d . T y p i c a l l y , a Q - s w i t c h e d N d : Y A G l a s e r o f 6- 8n s p u l s e d u r a t i o n a n d h ig h p o w e r a t 1 0 6 4 n m w a v e l e n g t h w a s u s e d [8,11,12] t o o b s e r v e H R S in s o l u t i o n . H o w e v e r , m a n y d i p o l a r m o l e c u l e s w i t h l a r g e /3 -values h a v e a n e l e c t r o n i c c h a r g e - t r a n s f e r r e s o n a n c e a r o u n d 5 3 2 n m . T h u s , t h e r a d i a t i o n a t 1 0 6 4 n m m a y g iv e ris e t o tw o - p h o t o n a b s o r p t i o n a n d r e s u l t s i n t w o - p h o t o n a b s o r p t i o n i n d u c e d flu o re s c e n c e ( T P F ) , w h i c h w o u l d b e i n c l u d e d in H R S s i g n a l a n d i n f l a t e t h e /3 -v alu e [9], B y u s i n g a n u l t r s f a s t la s e r s y s t e m [10] t h e t w o - p h o t o n a b s o r p t i o n i n d u c e d f l u o r e s c e n c e ( T P F ) c a n b e s u b t r a c t e d o r s u p p r e s s e d . I n t h i s e x p e r i m e n t , w e s t u d i e d t o u s e a f e m t o s e c o n d - la s e r s y s t e m w h i c h c o n s i s t o f a T i : S a p p h i r e la s e r ( T s u n a m i , S p e c t r a - P h y s i c s ) a n d a R e g e n e r a t i v e A m p l i f i e r ( S p i t f i r e , S p e c t r a - P h y s i c s ) w i t h r e p e t i t i o n r a t e o f 1 K H z t o p u m p H R S a n d m e a s u r e d t h e firs t - o r d e r o p t i c a l h y p e r p o l a r i z - a b i l i t y Ị3 o f p a r a - n i r o a n a l i n e ( p N A ) in m e t h a n o l . T h i s e x p e r i m e n t a l a r r a n g e m e n t c a n b e also used to stu d y HRS of other NLO organic materials in solution.
II. T H E O R E T IC A L B A S IC S
T h e i n d u c e d d i p o l e m o m e n t fo r a s in g l e m o l e c u l e i n t h e p r e s e n c e o f a n e l e c t r i c field E c a n b e e x p r e s s e d a s f o llo w s [8]:
Mi Ct'ij EJ-|- Ek -f~ hjkiEjEkEi + ... (1)
w h e r e Hi is t h e c o m p o n e n t o f t h e i n d u c e d d i p o l e m o m e n t a l o n g t h e m o l e c u l e -fix ed i a x is , Ctij is t h e i j c o m p o n e n t o f t h e ( s e c o n d - r a n k , firs t o r d e r ) p o l a r i z a b i l i t v t e n s o r Q, Pijk is i j k c o m p o n e n t o f t h e m i c r o s c o p i c ( t h i r d - r a n k , s e c o n d - o r d e r ) firs t h v p e r p o l a r i z a b i l i t y t e n s o r 0 , 7ijki is t h e i j k l c o m p o n e n t o f t h e m i c r o s c o p i c ( f o u r t h - r a n k , t h i r d - o r d e r ) s e c o n d h y p e r p o l a r i z a b i l i t y t e n s o r 7 , a n d E j is t h e e l e c t r i c field c o m p o n e n t o f f r e q u e n c y UJ a l o n g t h e j a x i s .
I n t h e c a s e o f s e c o n d - o r d e r l i g h t s c a t t e r i n g , t h e i n d u c e d d i p o l e m o m e n t f o r a s in g l e
molecule is then:
f i t = O L i j E j + 0 lj k E j E h (2)
a n d t h e F o u r i e r a m p l i t u d e o f t h e i n d u c e d d i p o l e m o m e n t p e r u n i t v o l u m e a t 2uj is g i v e n by:
P i ( 2 u j ) = B l k i { - 2 u j , u j , u j ) . E k { u j ) E i ( L j ) (3)
where B,ki is the ikl component of the macroscopic second -order susceptibility. In the isotropic media, only the average value of Bm is zero due to orientation fluctuation.
Correlation between the values of Biki for two different volumes 1 and 2 is assumed to
HYPER-RAYLEIG H s c a t t e r i n g i n s o l u t i o n o f o r g a n i c 21 7
exsist only over distances small compared to the wavelength. The intensity of the second- harmonic scattering light is proportional to (Biki iB JTnn 2)avdv. Since the scattering centers are randomly oriented molecules, the intensity of the second-harmonic scattering light then become proportional to the number density N and to {BuvwB xyz)avdv. Averaging the products of direction cosines over all directions performs the transformation to molecular axes UVVJ for isotropic media. Considering NLO molecules as asymmetric conjugated 7r- electron systems, we could calculate and find the expression for HRS intensity as follows
[8]: “
h ^ = g 0 2I * = 9 Ỵ ^ N s0 2s I 2u (4)
where Ỉ2u, is the HRS intensity at 2cj, / w is the incident laser intensity at U), N5 is the
n u m b e r d e n s i t y o f s p e c ie s s w i t h s e c o n d - o r d e r N L O p o l a r i z a b i l i t y P s = 0 Z Z Z S , s d e p e n d s
on the scattering geometry and contains the averages of the products of the direction cosines and the local field corrections at optical frequencies.
The HRS intensity for a two -component solute-solvent system at low chromophore concentrations is then:
/2* - G{Naf i + Nc0 l ) l l = G B 2l l (5)
which can be expressed as:
% = G {N s01 + N c0 ị ) — G B 2 (6)
U)
where subscripts s and c stand for solvent and chromophore, respectively, N refers to the number density; G is a constant including g and instrumental factors [12].
For low chromophore concentrations, the number density N s of the solvent molecules can be considered as constant. Eq. (6) indicates a linear dependence for Ỉ2uj i t plotted against N c. The process of measuring pc is follows: first, the HRS intensity I2UJ is mea
sured as a function of incident laser intensity at different number densities of the solute
( c h r o m o p h o r e ) t o o b t a i n a l i n e a r d e p e n d e n c e o f G B 2 o n N c. T h e n , f r o m t h e i n t e r c e p t
and the slope, the /3c-value of chromophore can be determined with the known values of
N s a n d p .s . This m e t h o d is r e f e r r e d t o a s t h e i n t e r n a l s t a n d a r d m e t h o d b e c a u s e /3c is
determined by using ị33 as an internal reference.
III. E X P E R I M E N T A L S E T U P
In our experiments, we used a femtosecond- laser system which consist of a mode locked Ti: Sapphire laser (Tsunami, Spectra-Physics) and a Regenerative Amplifier (Spit
fire, Spectra- Physics). The laser system was set to give laser pulses with pulse duration of lOOfs, repetition rate of I KHz and pulse energy of over lm j at 860nm wavelength.
A layout of our experiment was shown in Fig. 1.
The output beam passed through the polarizer Pi and became completely linear polarized
The rotation of the half-wave plate HW and the polarizer p 2 can modulate the intensity and the polarization state of the fundamental laser beam. A plano-convex lens
2 1 8
NGUYEN THE BINH
with focal length f =100mm (L) was used to focus the fundamental laser beam into the center of a long cylindrical cell which was filled with pNA solution. The long cell design ensures low laser intensity on the cell windows and eliminates second harmonic generation in the entrance and exit window glass. Before focusing, a high-pass filter RG filtered the fundamental light and a small fraction of the fundamental beam was split by a splitter BS and directed into a fast photodiode FPD.
F i g . 1. E x p e r im e n ta l se tu p o f H R S system
Para-nitro-aniline was dissolved in methanol at different concentrations. The solu
tion was filtered through a 0.1 membrane before use. Our experiments were carried out at room temperature. The second-order scattered light at 430nm was collected by a condenser system . This system consists of a concave mirror CM, an aspherical lens ASL, an infrared cut filter IRF, a plano-convex lens PCL and an interference filter INT at 430nm. To detect the secon-order scattered light we used a photomultiplier tube PMT (Hamamatsu R-928). The detected signal was accumulated and stored in a digital real
time oscilloscope (Tektronix TDS-360, 2 channels, 200 MHz) and analysed by a personal computer. This experiments was carried out at the ESCA Laser Lab., Uppsala University, Sweden.
I V . R E S U L T S A N D D I S C U S S I O N S
The pulse signals from fast-photodiode FPD and from PMT were obtained with the sync output of the laser head. The high repetition rate (lKHz- quasi-continuous) and the perfect stability of the femtosecond laser system facilitated our observations. We could retrieve the relative values for the intensities of the fundamental and Hyper Rayleigh scattered light pulses from digital oscilloscope data. The absorption measurement of pNA in methanol showed a high peak at 370nm. We selected the fundamental wavelength at 860nm, so that the second-harmonic scattered light (at 430nm) was out of the pNA absorption band. T his ensures a high efficency for weak HRS signals and eliminates the fluoresence induced by two-photon absorption.
According to equation (5), the HRS intensity Ỉ2uj is proportional to the square of
HYPER-RAYLEIGH SCATTERING IN SOLUTION OF ORGANIC 21 9
t h e f u n d a m e n t a l i n t e n s i t y /5. T o v e r if y t h i s q u a d r a t i c d e p e n d e n c e , w e p l o t t e d t h e H R S i n t e n s i t y Ỉ2uj a g a i n s t t h e q u a d r a t i c f u n d a m e n t a l o n e 75 for p N A s o l u t i o n s a t 4 d if f e r e n t n u m b e r d e n s i t i e s N c ( m o l e c u l e s / m 3). T h e g r a p h s w e r e s h o w n in F i g . 2.
0 20 ô0 6D 00 100 120
Q u a d r a t i c f u n d a m e n t a l i n t e n s i t y ( a . u )
F i g . 2. T h e d e p e n d e n c e of th e H R S in tensity Ĩ2u on th e q u a d r a t i c f u n d a m e n ta l inte n
s ity (Iw)2 a t different n u m b e r densities N c of pNA. a / N c = 9 6 . 1024 m - 3 ; b / N c= 4 8 .1 0 24 m , c / N c= 24.1024 m “ 3 . ; d / N c= 1 2 . 1 0 24 m “ 3
A c c o r d i n g t o t h e E q . (6 ), t h e l i n e a r d e p e n d e n c e o f G B 2 o n t h e n u m b e r d e n s i t y N c o f c h r o m o p h o r e c a n b e o b t a i n e d b y p l o t t i n g t h e f r a c t i o n Ĩ ^ Ị ĩ t a g a i n s t N c. W e p l o t t e d t h e d e p e n d e n c e o f G B 2 o n d i f f e r e n t d e n s i t i e s N c a s s h o w n i n F i g . 3. T h e n , f r o m t h e i n t e r c e p t a n d t h e s l o p e , t h e /3c- v a l u e o f p N A c a n b e r e t r i e v e d . W i t h t h e k n o w n v a l u e s o f N s — 1 . 4 8 7 5 . 1 0 28 m - 3 a n d /3S — 0 . 6 9 . 1 0 -3 0 e s u for m e t h a n o l [13] w e c a l c u l a t e d t h e fist h y p e r p o l a r i z a b i l i t y o f p N A t o b e (3C — 31 -1 0 —30 esu.
Number density o f pNA (x lO : j m ! )
F i g . 3. T h e lin e ar d e p e n d e n c e of GB^ on different densities N c of p a r a -n i t ro a n i l i n e in m e t h a n o l
220 NGUYEN TH E BINH
V . C O N C L U S IO N
The first hyperpolariability 0 of para-nitroaniline in methanol was determined by our HRS m easurem ent system . T his value is in good agreement with th e range of reported v a l u e s f r o m 2 3 . 1 0 30 e s u [8] t o 3 4 . 1 0 — 30 e s u [14,15]. O u r e x p e r i m e n t a l a r r a n g e m e n t w a s s u i t a b l e fo r H R S m e a s u r e m e n t . T h e f e m t o s e c o n d la s e r s y s t e m w i t h h i g h r e p e t i t i o n r a t e ( l K h z ) IS q u a s i - c o n t i n u o u s a n d s t a b l e so t h a t w e c a n c o n t r o l , m o d u l a t e a n d d e t e c t H R S signal w ith facilities. The high peak power of femtosecond laser pulses w ith low energy g i v e s h i g h e ff ic i e n c y for H R S effec t b u t d o e s n o t c a u s e t h e r m a l e ffec ts . T h e b e a m d i a m e t e r o f t h e T i : S a p p h i r e f e m t o s e c o n d - l a s e r s y s t e m is a b o u t 2m m ( a g a i n s t 10m m for nano-second-laser system ) that enables to reduce the solution volum e of precious new candidate NLO m olecules when using a shorter focal length lens and a shorter cell for a tighter focus. T his result is the first step to develop the tim e-resolved technique with t h e f e m t o s e c o n d l a s e r s y s t e m t o d i s c r i m i n a t e b e t w e e n H R S l i g h t a n d f l u o r e s c e n t e m i s s i o n i n d u c e d b y m u l t i p h o t o n a b s o r p t i o n . T h e firs t h y p e r p o l a r i z a b i l i t y (3 o f a f l u o r e s c e n t m o l e c u l e , w h i c h is o f t e n o v e r e s t i m a t e d w h e n u s i n g a n a n o - s e c o n d l a s e r , w ill b e c o r r e c t e d by this technique.
A C K N O W L E D G E M E N T S
T h e a u th o r w is h to th a n k to th e fin a n c ia l su p p o rt from T he N a tu r a l R e sea rch P r o g r a m o f V N U ( P r o j e c t Q G - 0 4 - 0 4 )
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R eceived 12 Ju ly 200Ị
Đ Ạ I HỌC Q U Ố C G IA H À NỘI T R U Ồ N G Đ Ạ I H ỌC K H O A HỌC T ự N H I Ẽ N
NGUYỄN HUY BÌNH