Javier Perez-Moreno, Shoresh Shafei, and Mark G. Kuzyk, "Applying universal scaling laws to identify the best molecular design paradigms for second-order nonlinear optics," J. Opt. Soc. Am. B 33, E45-E56 (2016)
We apply scaling and the theory of the fundamental limits of the
second-order molecular susceptibility to identify material classes
with ultralarge nonlinear optical response. Size effects are removed
by normalizing all nonlinearities to get intrinsic values so that the
scaling behavior of a series of molecular homologues can be
determined. Several new figures of merit are proposed that quantify
the desirable properties for molecules that can be designed by adding
a sequence of repeat units, and used in the assessment of the data.
Three molecular classes are found. They are characterized by
subscaling, nominal scaling, or superscaling. Superscaling homologues
most efficiently take advantage of increased size. We apply our
approach to data currently available in the literature to identify the
best superscaling molecular paradigms with the aim of identifying
desirable traits of new materials.
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The listed value of is the one for the molecule
with the least number of repeat units in the class, denoted by
. is the number of effective
electrons of the molecule with the least repeat units.
, , , and
are the linear fitting
parameters ( and ). is the value of the best
intrinsic hyperpolarizability in the class for the molecule
that has repeat units.
is the value of the absolute
first hyperpolarizability for the molecule with
repeat units in the series.
is the predicted value of the
absolute hyperpolarizability at the saturation length, FOM is
the proposed figure of merit [Eq. (11)] and
is the incremental addition
to the absolute first hyperpolarizability per repeat unit
[Eq. (12)].
Table 2.
Relevant Parameters for the Quantum Limits Analysis Applied to the
Two Classes of Organometallic Ruthenium(II) Ammine Complexes
(Class A and Class C)
Compound
(repeat
units)
Predicted
Experimental
A1
2.1
0
2.29
4.6
A2
2.08
1
2.26
3.9
A3
2.1
2
2.46
3.5
A4
2.18
3
2.33
3.2
C1
2.06
0
2.21
4.6
C2
2.05
1
2.34
3.9
C3
2.09
2
2.29
3.5
C4
2.18
3
2.35
3.1
Tables (2)
Table 1.
Scaling Parameters for the First Hyperpolarizability Molecular
Classesa
The listed value of is the one for the molecule
with the least number of repeat units in the class, denoted by
. is the number of effective
electrons of the molecule with the least repeat units.
, , , and
are the linear fitting
parameters ( and ). is the value of the best
intrinsic hyperpolarizability in the class for the molecule
that has repeat units.
is the value of the absolute
first hyperpolarizability for the molecule with
repeat units in the series.
is the predicted value of the
absolute hyperpolarizability at the saturation length, FOM is
the proposed figure of merit [Eq. (11)] and
is the incremental addition
to the absolute first hyperpolarizability per repeat unit
[Eq. (12)].
Table 2.
Relevant Parameters for the Quantum Limits Analysis Applied to the
Two Classes of Organometallic Ruthenium(II) Ammine Complexes
(Class A and Class C)