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Prof. Ivan Biaggio
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Optimizing the third-order nonlinearity of small molecules

[Image: the DDMEBT molecule]

Two related molecules with large intrinsic third-order susceptibilities. The TDMEE molecule has a planar structure. The DDMEBT molecule contains almost the whole structure of TDMEE as a subunit, but has an additional component that gives it a nonplanar structure. A three-dimensional view of DDMEBT is shown on the right.

Recent research in our group focused on developing a new paradigm for creating third-order nonlinear optical materials based on organic molecules: Instead of large molecules or polymers, which are difficult to use, we focus on small molecules. Instead of diluting their properties in a polymer matrix, we look for a material that consists only of optimized molecules, with no wasted space in between. To develop these new ideas, we needed to avoid the fundamental issue that smaller moleucles must have smaller third-order nonlinearity, and often the nonlinearities drop very fast, faster than the decrease in volume of a molecule. The important fundemantal question was: how is it possible to maintain a relatively high nonlinearity despite the fact that the moleucules become smaller?

Clearly, if our ultimate aim is to create a nonlinear optical material that consists of a dense, single-component assembly of nonlinear optical molecules, then what counts is the nonlinear response of a molecule relative to its size. Our research was guided by two important figures of merit: The specific third-order polarizability, which gives the potential that high density supramolecular assembly of molecules can have large third-order susceptibilities, and the intrinsic third-order polarizability, which tells how close the third-order polarizabiltiy of a molecule is to the quantum limit, and thus is a measure of hte efficiency of the nonlienar optical response of the molecule.

The efficiency of a molecule can be assessed in two ways. First, one can compare its experimentally observed nonlinearity to the maximum possible nonlinearity that one can expect given the size of the conjugated system and the excited state energies. This gives information on the efficiency of a given molecular design. Second, one can compare an experimentally observed nonlinearity to the size of the molecule, because this is an indication of what the nonlinearity will be in the solid state once a dense small-molecule material has been assembled. These two comparisons lead to the concepts of intrinsic and specific third-order polarizabilities.

Intrinsic third-order polarizabilities

The fundamental quantum limit to the nonlinear optical response of a moleucle provides a very simple reference for judging how optimized the design of a specific molecule is, and we have found that it can be a very useful guide for the development of new molecules. It can be used to express the third-order nonlinearity of a molecule by its intrinsic third-order polarizability, a dimensionless number defined as the ratio between what is experimentally observed in the zero-frequency limit and the fundamental limit for a given molecule. This scale-invariant quantity reaches record-high values around 0.025 in some compounds we have investigated.

Specific third-order polarizabilities

For dense supramolecular assemblies, the third-order polarizability of a molecule must not just be large, it must be large compared to the molecular volume, which determines how densely the molecules can be packed together. This point has often been neglected in past studies that concentrated only on the molecular polarizability, but it has been a main focus of our research. A practical figure of merit that reflects this issue is the specific third-order polarizability, which we defined as simply the experimental rotational average of the third-order polarizability of a molecule devided by the amss of the molecule in kg. This quantity is easy and quick to calculate, and it still gives a pretty good idea of how the nonlinear response of a molecule relates to its size. It could have been possible to express this in terms of the number of conjugated electrons, or the actual volume that would be taken up by a molecule, but we felt that expressing it as a nonlinearity per mass had large practical advantages while at the same time making the calculation this figure of merit trivial and accessible to everyone.

Donor acceptor substitution in small molecules

[Image: How third-order polarizabilities change with size in small moleculs]

Donor-acceptor susbstitution in smaller molecules makes the distance between excited states less dependent on size and allows small molecules to achieve the same specific third-order polarizabilities of larger molecules without donor-acceptor substitution.

The addition of special electron-donating or electron-accepting chemical groups basically sets the distance between the excited states of a molecule without significantly affecting its size too much. There is then a range of molecular sizes where ground and excited states stillmaintain a large transition dipole moment while at the same time the energy difference between the states is still determined by the properties of donor and acceptor groups. This makes it possible to change the size of the conjugated system connecting the donor and acceptor groups and have a much reduced effect on the the third-order polarizability of the molecule when compared to molecules that don't have donor-acceptor substitution. Since the third-order nonlinearity grows both with the dipole transition matrix elements and also with shrinking excited state energy, this feature of donor-acceptor molecules means that the third-order nonlinearity will not decrease as much as for other molecules when the size of the molecule is reduced. At the end, this means that the specific third-order polarizability of a small donor-acceptor substituted molecule can be as large as that of much larger molecules. But smaller molecules are much better when it comes to putting them together into a dense solid state piece of plastic!



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