Third-Order Nonlinear Optical Susceptibilities of Colloidal Crystals

C. Z. Fan1 , J. P. Huang1 and K. W. Yu2

1.Department of Physics, Fudan University, Shanghai 200433, China2. Department of Physics, The Chinese University of Hong Kong, Hong Kong

On the basis of the Ewald-Kornfeld formulation, we studied the effective third-order nonlinear optical susceptibilities for nondegenerate four-wave mixing and third-harmonic generation in colloidal crystals, which are made of graded metallodielectric nanoparticles suspended in a host fluid. Theoretical results show that both an enhancement and a red shift of the optical nonlinearity in such colloidal crystals appear due to the effects of local fields and lattice structure. Furthermore, the presence of the dielectric gradation is helpful to achieve large enhancement of nonlinearity at low frequencies.

a( )r

r

2 2

d

References:[1] C. Z. Fan, J. P. Huang and K. W. Yu, J. Phys. Chem. C 113, 18504 (2009). [2] C. Z. Fan and J. P. Huang, Appl. Phys. Lett. 89, 141906 (2006). [3] J. P. Huang and K. W. Yu, Phys. Rep. 431, 87 (2006). [4] J. P. Huang, Y. C. Jian, C. Z. Fan, and K. W. Yu, J. Phys. Chem. C 112, 621 (2008).

Graded particle

Drude model:

Theoretical results:

Electric displacement relation:

Effective medium theory:

Graded parameter: Cω

In summary, we have theoretically investigated the third-order nonlinear optical susceptibilities for NDFWM and THG in colloidal crystals which are made of graded metallodielectric nanoparticles. On the basis of the Ewald-Kornfeld formulation, numerical results show that such materials can have both an enhancement and a red shift of optical nonlinearity due to the gradation in the metallic core and the lattice effect arising from period structures.

Ewald-Kornfeld