  Due to the advantage of tunability via size, shape, doping and relatively low
level of loss and high extent of spatial confinement, graphene quantum dots
(GQDs) are emerging as an effective way to control light by molecular
engineering. The collective excitation in GQDs shows both high energy plasmon
frequency along with frequencies in the terahertz (THz) region making these
systems powerful materials for photonic technologies. Here, we report a
systematic study of the linear and nonlinear optical properties of large
varieties of GQDs (400 systems) in size and topology utilizing the strengths of
both semiempirical and first-principles methods. Our detailed study shows how
the spectral shift and trends in the optical nonlinearity of GQDs depends on
their structure, size and shape. Among the circular, triangular, stripe, and
random shaped GQDs, we find that GQDs with inequivalent sublattice atoms always
possess lower HOMO-LUMO gap, broadband absorption and high nonlinear optical
coefficients. Also, we find that for majority of the GQDs with interesting
linear and nonlinear optical properties have zigzag edges, although reverse is
not always true. We strongly believe that our findings can act as guidelines to
design GQDs in optical parametric oscillators, higher harmonic generators and
optical modulators.
