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\subsubsection*{Introduction On Organic Nonlinear Optical Materials}


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{\bf Yong Song}
\end{center}

Department of Physics, University of Cincinnati,Cincinnati,OH,45220


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{\bf Abstract}

Organic materials are important materials for the fast processing of 
information and for optical storage applications. This paper tries to have a 
quick look at their properties and some effects. 


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{\bf 1. Introduction}

Recent developments in the field of nonlinear optics(NLO) has pushing 
organic second-order nonlinear optical materials into practical 
applications. Nonlinear optical materials are the materials in which light 
waves can interact with each other[1]. This paper presents an brief 
introduction on the organ nonlinear optical materials. 


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{\bf 2.Molecular Polarizabilities}


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The following equation describe the normal nonlinear optical effects:


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{\it P}$_{i}$={\it P}$_{0,i }$+ $\varepsilon _{0}$($\chi 
^{(1)}_{ij}${\it E}$_{j}$+ $\chi ^{(2)}_{ijk}$ {\it E}$_{j}$ {\it 
E}$_{k}$ + $\chi ^{(3)}_{ijkl}$ {\it E}$_{j}$ {\it E}$_{k}$ {\it 
E}$_{l}$ + … 


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{\it P}$_{0}$ is the spontaneous polarization and $\chi ^{(n)}$ is the 
{\it n}th order susceptibility tensor. $\varepsilon _{0 }$Is the vacuum 
permittivity. {\it E} is the applied electric field. 


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In organic materials the optical properties are determined by the molecular 
polarizabilities. The following equation expressing the molecular dipole 
moment p as:


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{\it p}$_{i}$ = $\mu _{g,i }$+ $\varepsilon _{0}$ ($\alpha _{ij }${\it 
E}$_{j }$+ $\beta _{ijk }${\it E}$_{j }${\it E}$_{k}$+ $\gamma _{ijkl 
}${\it E}$_{j }${\it E}$_{k }${\it E}$_{l}$… 


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\noindent
where $\mu _{g,i}$ is the ground state dipole moment, $\alpha _{ij}$ is 
the linear polarizability, $\beta _{ijk }$ is the second-order 
polarizability or first-order hyperpolarizability, $\gamma _{ijkl}$ is the 
third-order polarizability or second-order hyperpolarizability. The electric 
field is the one at the location of the molecule. 


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Fig1 shows the different of optical effects between first and second order 
nonlinear optical materials[1]. 

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Fig1 First and Second Order nonlinear optical effects


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Pure first order nonlinear optical effects are in the left and the pure 
second order effects are in the right hand side. The middle column shows the 
effects related to both types of nonlinearity:the photorefractive effect and 
the cascaded optical Kerr effect. 


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The tensors $\chi ^{(2)}_{ijk}$ and $\beta _{ijk}$ describe the 
second-order nonlinear optical and electro-optic effects. They are third 
rank tensors, in the electric dipole approximation, contain nonvanishing 
elements only for noncentrosymmetric molecular and crystalline structures, 
respectively. Third order nonlinear optical effects are described by the 
tensors $\chi ^{(3)}_{ijkl}$ and $\gamma _{ijkl}$. No symmetry 
requirements are imposted on these effects to occur[2].


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\subsection*{3 Organic Nonlinear Optical Effects}


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{\bf 3.1 Bonding Properties of Atoms In The Molecule}


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We assume that the molecules function independently of each other and only 
their net orientations within the crystal lattice are important to the 
contribution of model.


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The bonding with the carbon atom and other elements has two types: $\sigma $ 
bond and $\pi $ bond. $\sigma $ bond is confined along the inter-nuclear 
axis of the carbon -carbon bond. And $\pi $ bonds are regions of delocalized 
electronic charge distribution above and below the inter-atomic axis(Fig2) 
[3] 

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Fig2 Electronic bonding in (a) H$_{2}$ ($\sigma $ bond) and (b) C$_{2}$ 
($\pi $ bond)


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{\bf 3.2 Why Organic Can Has NLO Properties}


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The polarizability of organic materials is generally the contribution from 
the lattice components(atoms,molecules) because of the weak intermolecular 
bonding(Van der Waals, dipole-dipole interactions, hydrogen bonds). 
Nonlinear optical effects of molecular crystals depend on the polarizability 
of the electrons in the $\pi $ bonding orbitals.


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The optical nonlinearity can be increased if you add conjugated 
bonds(increasing L--The length of the conjugated system) or substitute 
donors(can donate electrons into the $\pi $ electron system) and 
acceptors(can accept electrons into the $\pi $ electron system)(Fig3). The 
addition of the functionality at the ends of the $\pi $ system can enhance 
the asymmetric electronic distribution. [4]

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Fig 3 organic materials for nonlinear optical effects of second-order. 
D-Donor A-Acceptor . substituted molecules with $\pi $ electron ring 
systems. (i) one ring systems (ii) two ring systems


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Studies show that conjugated organic molecules with large delocalized $\pi $ 
electron systems have very large nonlinear optical effects. The attachment 
of functional groups with electron-accepting and donating character at 
opposite ends of the conjugation bridge leads to an essentially 
one-dimensional charge transfer, enhancing especially the second order 
non-linearity[1].

A further simplified model (the Equivalent Internal Field, EIF model) of a 
free electron gas corresponding to the delocalized $\pi $ electron density 
of a conjugated approximation $\beta \sim$ L$^{3}$,which shows the strong 
nonlinear dependence of the hyperpolarizability on the lenth of the 
conjugated $\pi $ system. 


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{\bf 3.3 Organic Nonlinear Optical and Electro-Optic Effects}


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The Fig 4 is the schematic representation of important nonlinear optical and 
electro-optic effects[1]. Let us discuss the first five effects briefly.

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Fig4 Important nonlinear optical and electro-optic effects


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{\bf 3.3.1 Sum Frequency Generation }

Sum frequency generation is the mixing of two incident light waves of 
frequencies $\omega _{1}$ and $\omega _{2}$ creating a wave of $\omega 
_{3}$=$\omega _{1}$+$\omega _{2}$. 


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{\bf 3.3.2 Second-Hrmonic Generation(SHG)}

Second-harmonic generation(SHG) or optical frequency doubling is just a 
special case of sum frequency generation. Only one light wave of frequency 
$\omega $ is incident, generating a wave of twice the frequency. 


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Sum frequency and second-harmonic generation are standard techniques to 
create a new coherent output from existing laser systems and especially to 
access the short wavelength range towards the ultraviolet region. 


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{\bf 3.3.3 Difference Frequency Generation}


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Difference frequency generation(DFG) is treated as the interaction of two 
input beams of frequencies $\omega _{3}$ and $\omega _{1}$ resulting in 
an optical field with the frequency $\omega _{2}$=$\omega _{3}$-$\omega 
_{1}$.


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Because of the Conservation of Energy and Momentum, all the nonlinear 
processes discussed have in common that they conserve energy, which was 
already implicitly assumed: $\omega _{3}$=$\omega _{1}$+$\omega _{2}$


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{\bf 3.3.4 Optic Parametric Oscillation/Generation}


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Optic parametric generation is a special case of difference frequency 
generation, where only the pump beam is incident on the nonlinear material 
generating two beams at the frequencies $\omega _{1}$ and $\omega _{2}$. 



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In order to enhance the efficiency of either process, the nonlinear medium 
can be placed inside a cavity with highly reflecting mirrors for the 
frequencies $\omega _{1}$ and/or $\omega _{2}$.


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{\bf 4. Conclusion:}


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The organic materials exhibit extremely large nonlinear optical and 
electro-optic effects. The electronic nonlinearities are essentially based 
on the molecular units. Due to the important advantages of the organic 
materials, they will be widely used in the field of organic chemistry, 
materials science, physics and electrical engineering. 


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{\bf References:}


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[1] P. Güter(Ed.), Nonlinear Optical Effects and Materials (Springer 2000)

[2] J.F. Nye, Physical Properties of Crystals (Clarenndon, Oxford, 1967)

[3] L.L.Hench and J.K.West, Principles of Electronic Ceramics (John Wiley \& 
Sons, 

1989)

[4] Organic Nonlinear Optical materials Ch.Bosshard, K.Sutter, et al. 
(Gordon and Breach Publishers,1995)



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