ARCH Ls 87

91 Pages·2014·2.32 MB·English

VIBRATIONAL CONTRIBUTIONS
TO THE SECOND HYPERPOLARIZABTLITY OF CF,*
BY
ZHENGFANG LU
A TTlESIS
SUBMITTED TO THE FACULTY OF
GRADUATE STUDIES IN PARTIAL FULFILMENT
OF TIIE REQUIREMENTS FOR TIIE DEGREE
OF MASTER OF SCIENCE IN
PHYS IC S
"
Ì'{ARCH Ls 87 ffi
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rsBN
0_315.-37464*0
THE UNIVERSITY OF MANITORA
LIBR.ARIES
VIBRATIONAL CONTRIBUTIONS TO THE SECOND
HYPERPOLARIZABILITY OF CF4
BY
ZHENGFANG LU
A thesis subnritted to the Faculty of Graduate Studies of
the Ultiversity of Manitoba in partial fulfillment of the requirenrerrts
of the degree of
MASTER OF SCIENCE
o
1987
Permissio¡r has been granted to the LIBRARY OF THE UNIVER-
SITY OF MANITOBA to lend or sell copies of this thesis, to
the NATIONAL LIBRARY OF CANADA to microfilnr this
thesis a¡rd to lend or sell copies of the film, and UNIVERSITY
MICROFILMS to publish an abstract of this thesis.
The author reserves other publication rights, and neither the
thesis nor extensive extracts from it may be printed or other-
wise reproduced without the author's writteu permission.
I
ACKNOI^TLED GEME NT
I am grateful Eo ny supervisor, Dr. D.P. ShelEon for
his paÈience, êûcouragement, and very friendly guidance
throughouË the whole period of thís study. The frlendship
has made the cold day in Winnipeg become enjoyable.
I1
ABSTRACT
The frequency ctependence of Ehe second
hyperpolarizabilj-ty ( Y ) of CFq has been measurerl in the
visible (488 nm < < 660 nn) by means of. gas-Phase
À
electric-fie1d-induced second harmonlc generaEion (ESHG).
The results of Ehese experimenÈs are compared with Èhe
results of other nonlinear opEics experiments which have
measured y by third harmonfc generaE"lon (THG), ESHG and the
dc Kerr effect. In order t.o obtain information about the
vibraÈional contributions to the second hyperpolati-zabillty
from Ehis comparison, exPressions for Ehe vibraEional
conErlbutlons to YCF,+ have beerr derived and numerically
evaluated for each of these opEical Processes. It 1s
cofrcluded that vibrational contributions Eo YCF,* are
negligible for THG, but significant for both the dc Kerr
effect and ESHG.
CONTENTS
Acknowl edgement
]-
Abstract 1I
Chapter 1 Introduction: Ilistory and PresenE Interest
1
Chapter 2 Theory
4
2.I Quantum Mechanical Expression For The
Second Hyperpol atizabili ty
4
2.2 Expression For Yfff C For CF q I
2.3 Expression For YtSffC For t2
CF,*
2.4 Expression For Yil"r, For
CF L7
u
Ch ap E er 3 Expe r iment 26
3.1 Experimental System For dc ESHG 26
3.2 Sample Preparation And Effecc
0f Irnpuricies
29
3.3 Signal Curve And Data Analysis 31
ChapEer 4 Experiment Results 38
4 I Local Field Correction Factor 38
2 DLspersion 0f The Second Hyperpolarlzability
4
0f CF,* From ESHG Experiment 42
Chapter 5 Discussiont Ylnc, Yürra And Yilu* For CFu.....48
5.1 Ylnc And Ytsnc For CF 48
u
5. f. I previ ous Result s Of Yar u In THG, ESHG And
The Kerr Effect 48
5.1 2 Ylnc And Ytsuc For CF,*.. ...5f
5 1 3 Hyper-Raman ß 54
5.2 Y{"rr For CF4.... ...56
5.2.I The Nature 0f The Vibrat ions For CF q . . . . .56
5.2.2 Y{"rt Signí ficant But Not Large 58
Chapter 6 Conclusion 70
References 72
Appendix Programs For The CalculaEions In The Thesis ...76
Index 0f Figures
Figur e 2.L Diagrams For The Five Essential Types
0f Terms Which Contribute To Yv
24
Figure 3.1 Experimental System
34
Figure 3.2 Signal Curve And Least Squares Fitting
P o lyn omi a1
36
Figure 4.1 The Measured Values of YaUu By ESHG
44
Figure 5.1 Yaa I'leasured By Several Nonlinear
u
0ptical Processes
6l
Flgur e 5.2 The Normal Vibrations 0f CF
q
....'63
Index 0f Tables
Table 4.1 Local Field Correction Factor
46
Tabl e 4.2 Experimencal Results For tat
u
47
Table 5.1 YCp u Measured By Several Nonlinear
0ptlcal Processes
50
Table 5.2 Matrix Elements
65
I
CHAPTER
1
INTRODUCTION: HISTORY AND PRESENT INTEREST
The world we are living in is a "nonlinear" colorful
wor1d. Studies of nonlinear phenorDena have a long history.
Even in optlcs, Ehe Faraday effect hras discovered in 1845
and t.he Kerr effecc in f875. "Nonlinear optics" 1s usually
used t.o ref er Eo those phenomena involving light \¡Iaves
t
which must be descríbed in Eerms"containlng other Èhan Ehe
first power of the electric and magnetic field strengt.hs.
In physics, many importanE phenomena depend on the elecErlc
dipo 1e monents induced in atoms or molecules by externally
applled electric flelds. 0n the oEher hand, many nonllnear
optical processes can provide much information related Èo
Ehe polarlzability and hyperpolarízability. However, since
nonlinear opÈical phenomena are really observable only if
the electric field is large enough for the nonlinearity of
Ë.he polarizat. lon to appear, nonlinear opËics became a
subjecE of greaE common interest only after Ehe laser was
invenLed.t The remarkable first observation of a nonlinear
optical effect was made by Franken, IIill, Peters and
Weinrelch in 1961 when t.hey observed opt. lcal second-harmonic
2
generaEion (sIlG) using a ruby laser. Since then many
ímportant nonlinear optical processes including
third-harmonic generation (THG), the dc Kerr effecc and
four-\dave mixlng (Ft{M) have been widely observed in solids,
liquids and gases*'2 At Ehe same EÍme a number of
s emi -c 1a s s ical theo re t i cal treat.ments of high order
polarízabili ties including those by Bloembergen eE af in
1962 and Ward in 1965 aPPeared 1,3,t+
Here, what \¡¡e are concerned about is Ehe víbratlonal
contribution to the second hyp'erpol arízability of a certain
molecule. The Èhird-order nonlinear susceptibility Xtt',
which mediates a wide range of nonlinear-opEical processes'
is Ehe macroscopic expression of the microscopic second
hyperpolarizabiltty Eensor Yl:'* Perturbation Eheory gives a
single expression for Y , and Ehe hyperpol arízabilities
corresponding to each of the various nonlinear optical
processes are just special cases of Chis general expressions'+
The underlying unlty of Lhe fundamenCal theoretical
description is obscured in Practice because Y for each
nonlinear optical process has a characterisEically díff erent
balance of conErtbuEions from the electronic, vibrational
and rotatlonal degrees of freedom of each molecr, 1å1 0
Recently there has been much theoreEical inEeresc and