Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals W. Walasik a , M. Jarema a , G. Pawlik a , R. Orlik a , A.C. Mitus a , F. Kajzar b a Institute of Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, Poland b Laboratoire POMA CNRS, Universite d’Angers, Angers, France ABSTRACT Khoo et al. 1, 2 have shown that nanosphere dispersed nematic liquid crystal (NDLC) constitutes a new type of metamaterial with index of refraction tunable from negative to positive values. Recently 3 we have combined this approach with Monte Carlo simulations of inhomogeneous molecular order in planar NLC cells. Lebwohl - Lasher effective hamiltonian with Rapini - Papoular term for anchoring forces was used. Electric field and amplitude of anchoring forces are control parameters which determine the profiles of order parameter. In this paper we study, using the same approach, local spatial distribution of refractive index in NDLC planar cell. We show that NDLC material consists of layers with negative–zero–positive index of refraction. The spatial organization of those layers strongly depends on incident light wavelength. The role of spatially modulated external electric field for tuning of refractive index of NDLC is briefly discussed. Keywords: negative index of refraction, metamaterials, nematic liquid crystals, Monte Carlo 1. INTRODUCTION The concept behind modern science of materials with negative refractive index was formulated by Veselago 40 years ago. 4 Since ten years metamaterials have been in center of interest because of their potential unusual optic and photonic applications. In this context, tunability of negative-zero-positive refractive index metamaterials is particularly desirable. Recently, this topic was addressed in a seminal paper of Khoo and co-workers. 1 It generalizes the approach of Wheeler at al. 5 by using nematic liquid crystal (NLC) as a medium in which the coated nanospheres are dispersed. The nanosphere–dispersed liquid crystal (NDLQ) model system displays negative real part of diffraction index at infrared frequencies. In paper 1 only uniform NLC order was studied. Successive applications of this approach were published in Refs. 6, 7 Inhomogeneous order in NLC host may be a direct cause of a non–uniform spatial distribution of negative refractive index, giving rise to tunable structure of inhomogeneous metamaterials. The simplest way to induce an inhomogeneous order in a planar NLC cell with anchoring forces is to apply either constant or modulated electric (magnetic) field. Monte Carlo simulations enable a detailed ”microscopic” study of inhomogeneous order in NLC systems. In particular, spatial distribution of refractive index can be calculated. The nature of orientational NLC order depends on amplitudes of two control parameters: anchoring force α and applied electric field E. The chess– board NLC order was studied in paper. 8 The phase diagram in α − E variables calculated in 9 displays a new line of transitions caused by anchoring forces. Further extensions of the method, in particular an application to twisted NLC displays, were presented in papers. 3, 10, 11 Recently, 3 we have combined Monte Carlo simulations with the approach of Khoo 1 to calculate the phase diagram in α − E variables of averaged permittivity. We have shown that the amplitude of anchoring forces constitutes a new control parameter for tuning of negative–positive values of refraction index in NDLC. The aim of this letter is to analyze the spatial inhomogeneity of refractive index in NDLC metamaterial for chosen values of incident light wavelength λ, anchoring force α and external electric field E. Further author information: (Send correspondence to antoni.mitus@pwr.wroc.pl) Invited Paper Organic Photonic Materials and Devices XI, edited by Robert L. Nelson, François Kajzar, Toshikuni Kaino Proc. of SPIE Vol. 7213, 72130A · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.809718 Proc. of SPIE Vol. 7213 72130A-1