Nonlinear optical response of symmetric donor acceptor structures

3switching can take place with femtosecond speed, many orders of magnitude faster than electronic 
processes. Moreover, working at optical frequencies, provides a tremendous gain in bandwidth of 
information processing and optical processing functions are in general free from interference from 
electric or magnetic sources.  
Apart from the field of photonics and related technologies such computing, telecommunications, 
environmental control, medical diagnostics and therapy, there are other potentially interesting and 
important applications of nonlinear optics. Among these are the use of intensity dependent 
transmission properties of materials that might serve to perform useful functions as eye or 
optoelectronic sensor protection from unwanted or stray sources of laser radiation. 
Turning to the substrates exploitable for NLO applications, we can say that, basically, all 
materials exhibit NLO phenomena. This includes all forms of matter, thus gases, liquids and solids. 
The important NLO materials from the device point of view are generally in solid form and must 
meet a wide variety of materials requirement: for instance, they require extraordinary stability with 
respect to ambient conditions and high-intensity light sources. The materials useful in the field 
under investigation can be classified in two types. 
The first one, molecular materials, consists of chemically bonded molecular units that 
interact in the bulk through weak van der Waals interactions. Many organic crystals and polymers 
typify this class of materials. For these materials the optical nonlinearity is primarily derived from 
the molecular structure and the bulk response can be readily related to the response of the 
constituent molecules. The primary step in optimising optical nonlinearities in this class of materials 
is at molecular structure level, which then requires a detailed understanding of the relationship 
between molecular structure and the polarisation which can be induced in a molecule. 
The second major class is bulk materials. Nonlinearities in this materials are thought of as 
arising from electrons not associated with individual ions, such as those in metals and 
semiconductors. The optical nonlinearity in this class is determined by the electronic characteristics 
of the bulk medium and thus requires a different theoretical framework to account for the origin of 
NLO effects. Examples of materials in this category are quantum well structures derived from III-V 
or II-VI semiconductors such as GaAs or CdSe, respectively, and inorganic crystals such as 
potassium dihydrogen phosphate (KTP). 
Compared to the more traditional inorganic nonlinear optical materials, the history of organic NLO 
materials is rather new. Organic and other molecular materials are increasingly being recognised as 
materials of the future because their molecular nature combined with the versatility of synthetic 
chemistry can be used to alter and optimise molecular structures to maximise nonlinear responses 
and other properties. A lot of organic materials, especially high performance polymers, have high 
mechanical strength as well as excellent environmental and thermal stability. Moreover, because of 
4their unique chemical structures (
 bonding), organic molecular materials exhibit the largest 
nonresonant (non absorptive) optical nonlinearities. For inorganic semiconductor systems, 
important NLO effects are resonant (absorptive). Thus, heat dissipation tends to limit the life cycle 
of devices derived from these materials. For a lot of device applications the NLO response time is 
an important consideration. A non resonant electronic optical nonlinearity, by his nature, would 
have the fastest response time, limited only by the width of the driving laser pulse. In contrast, 
resonant optical nonlinearities have response times limited by the lifetime of excitation. Other 
drawbacks associated with optical resonant nonlinearities are beam depletion due to absorption, 
thermal damage and thermally induced nonlinearities associated with refractive index changes, 
which often can dominate the intrinsic electronic optical nonlinearity. 
To summarise, Figure (I-1) shows schematically the path from NLO materials to the applied 
technologies. 
 
Figure I-1: An overview: from NLO materials to applied technologies. 
 
Nonlinear optical phenomenon
Light + Nonlinear material
Nonlinear optical device
Applied technology
NonLinear Material
Organic, Inorganic
Semiconductor, Glass
Form
Bulk, Fiber
Waveguides
Light wavelength conversion
Field effect on Refractive index
Field effect on Absorption coefficient
Optical switch, Optical memory, light source
Optical logic, Optical amplifier 
Ultra high speed, long distance, high density 
 optical communication 
All optical communication involving no 
 electrical signals 
Ultra high speed, high density optical signal 
 and information processing
5I.2 Overview of this work 
 
This research work deals with the field of molecular materials for nonlinear optics. We aim to focus 
our study on the properties of single organic molecules, taking into account that they can be directly 
connected to the properties of the whole molecular material. The microscopic requirement, for 
obtaining large and fast NLO responses is that molecules must posses easily polarisable electronic 
charge as delocalized 
 electrons. To date, however, the NLO parameters exhibited by 
-conjugated 
molecular systems fall short of the values required for technological applications by one or two 
orders of magnitude. A possible solution, reported in the literature, is to exploit the high 
polarisabilities of molecules in an electronic excited state. The main difficulty with this idea is that 
a two-step process is required: in the first step the molecules have to be pumped to an excited state 
and in the second one the NLO response is induced. Optical processes in molecular radical ions 
with unpaired electrons bear some analogies to those of neutral excited molecules: radical ion 
spectra are in fact characterised by transitions involving half-occupied molecular orbitals (HOMO 
for radical cations and LUMO for radical anions). These transitions have low energies and, usually, 
high oscillator strengths. Similar transitions can also be observed in transient absorption spectra of 
electronic excited molecules, that is spectra of molecules that have been initially brought to an 
electronic excited state. Adopting a single configuration description of electronic states, these 
transitions correspond to the transfer of 
 electrons from the next-to-HOMO (HOMO-1) to the 
HOMO in a radical cation, or from the LUMO to the next-to-LUMO (LUMO+1) in a radical anion. 
It is then interesting to perform a study of the NLO properties of molecular radical ions, in 
particular if one considers that some of them are chemically and photochemically stable, which 
makes their study easier than that of neutral exited molecules. 
It is well known that tetrathiafulvalene (TTF) produces stable radical cations. Moreover, 
solid background knowledge exists about this molecule based on experimental measurements, such 
as UV-Vis-NIR, IR and Raman spectra and analyses of these data based on quantum mechanical 
models [2, 3, 4]. 
 Another interesting aspect of these radicals is that they can form stable aggregates of various 
dimensions where the properties of the single radical, previously described, can be associated with 
those typical of molecular clusters. For example, in a linear cluster we can think that the mobility of 
the charges is high because it can be transferred among all the molecules of the system: this 
translates into a high oscillator strength and then in potentially high hyperpolarizabilities. Even in 
the smallest of these clusters, that is in a 
 radical dimer, a new, strong CT transition appears at 
energies lower that those of the intramolecular 
-
* transitions of the open-shell radicals and with a 
6very high oscillator strength. The latter feature is related to the fact that the CT transition amounts 
to the transfer of a full electronic charge over intermolecular distances. 
 
The first purpose of our research work is to characterise both theoretically and experimentally the 
smallest radical cluster of TTF, thus a dimer. The chemical formula of TTF and the 
-dimer 
structure are reported in Figure (I-2) and (I-3), respectively. 
Anyway, a TTF radical dimer is in practise a unique system for its characteristics and it is not easy 
to modify its structure in order to improve its properties. More flexible molecules, from this point of 
view, are typically conjugated polymers and donor-acceptor systems where an intramolecular or 
intermolecular charge transfer (CT) process can be optically activated. These molecules are very 
interesting in particular for their properties as two-photon absorbers. Two photon absorption (TPA) 
is a third order nonlinear process that was theoretically predicted by Goppert-Mayer in 1931 [5] and 
experimentally observed in the 1960s [6, 7, 8, 9]. Pioneering work by Rentzepis in data storage [10] 
and by Webb [11] in microscopy provided early demonstrations of potential applications for TPA 
processes. 
Molecules with a large TPA cross section are nowadays in great demand for a variety of 
applications, including two-photon excited fluorescence microscopy [11, 12], optical limiting [13, 
14, 15], three dimensional optical data storage and up-conversion lasing. The last process, for 
instance, is used to increase the frequency of lasers as shown in Figure (I-4): the simultaneous 
absorption of two identical photons populates an excited state ( 2 ) which afterwards relaxes to a 
lower one ( 3 ). The radiation emitted in the subsequent fluorescence process is exploited to obtain 
a laser frequency larger (short wavelength) than the input one.  
The applications just cited use two key features of TPA, namely, the ability to create excited states 
with photons of half the nominal excitation energy, which can provide improved penetration in 
S
S
S
S
Figure I-2: TTF monomer structure 
Figure I-3: (TTF
	+
)
2
dimer structure 
 
7absorbing or scattering media, and the dependence on I
2
of the process, which allows excitation of 
chromophores with a high degree of spatial selectivity in three dimensions through the use of a 
tightly focused beam. The critical parameter to make a molecule exploitable as two photon absorber 
is its cross section: in the last ten years a lot of effort has been spent in developing guidelines to 
design molecules with the characteristics required for practical applications.  
 
Figure I-4: diagrammatic representation of the up-conversion lasing process. 
 
Within the donor-acceptor compounds, some strategies are commonly followed to optimize their 
characteristics [16, 17, 18, 19]: for example, modifying the donor (D) and acceptor (A) strength, 
modifying the nature of the 
-bridge (in particular increasing its length) or, finally, increasing the 
number of D
A branches in the molecule. 
 We then aim to investigate structures where a charge transfer process is effective, focusing 
our effort on the TPA. From a theoretical point of view, the previously reported systems have been 
investigated both by quantum-chemistry approaches and making use of models: we treat these 
structures with very simple quantum mechanical models where the structural characteristics of the 
molecules are drastically simplified and the electronic features are included in a few basic 
interaction parameters. With this deliberately oversimplified model we cannot aim at obtaining 
quantitative estimates of the TPA coefficients. The goal is rather to investigate trends in the 
structure-property relationships that do not depend on the detailed chemical and structural 
properties of the system. 
 It is worth noticing that also vibrations can play an important role in determining NLO 
properties: for instance, Painelli and coworkers working with analytical models on Donor-Acceptor 
molecules (D-A), found a quite strong contribution to dynamic TPA absorption due to electron-
vibration coupling [20]. Moreover the same subject has been investigated by Agren and his group 
with a quantum mechanical approach, yielding a weak or strong contribution depending on the 
1
2
3
8features (in particular the dimensionality) of the system [21, 22]. On the basis of this background 
we decided to include in the models the electron phonon (e-p) coupling as well.