We designed and fabricated a centrosymmetric material where one may be able to consider an efficient quadratic nonlinear interaction. We followed a solid phase-supported organic synthesis methodology to covalently bind a large number of highly nonlinear molecules to the surface of polystyrene nanospheres. Such chemically modified optically nonlinear latex spheres, when suspended in water, are seen to perfectly self-organize into a centrosymmetric lattice. Taking advantage of the nonlinear interaction located at the sphere-water interface and the photonic crystal properties of the fabricated material we were able to generate second-harmonic light visible to the naked eye.

Second order nonlinear processes in 3D centrosymmetric materials, as SHG, have been demonstrated in the past using self organized colloidal suspensions of modified polystyrene spheres in water. Taking advantage of the phase matching conditions provided by the photonic crystal and the local braking of the symmetry at the sphere-water interface, the generation of visible SH light is possible.[1]In the present paper we demonstrate that SHG is also possible when modified polystyrene spheres are assembled in a close packing configuration using a method based on the spin coating of a concentrated suspension of polystyrene spheres.[2] In this later case the photonic crystal properties of the material allows us to take advantage of the longer interaction time due to the slow group velocity of the generated light that couples with one of the flat bands that opens at high energy levels. Such small group velocity provides an enhancement mechanism for the nonlinear process. In figure 2 one sees the reflection maximum around 400nm due to one of the first high energy bands for such nonlinear opals. Fig.1. Reflection and SEM picture of a nonlinear opal made of polystyrene spheres modified with a nonlinear organic material.Fig.2 Specular reflection spectrum of the nonlinear opal shown in Fig 1.

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It is widely accepted that quadratic nonlinear processes, such as parametric generation or amplification, require the use of materials with a high degree of ordering. In some occasions, such ordering is found at a nanoscale, and in other cases, the order is at a micron scale. When such ordering is not intrinsic to the material, one may introduce a periodical distribution within the nonlinear material to, for instance, compensate the phase mismatch. In that event, the final material would be, in general, composed of two types of domains, distributed periodically across the entire material, one with a given nonlinear coefficient, and the other with the same coefficient with opposite sign [1]. In principle, one would expect that small deviations from the adequate period, or some dispersion in the size of the domains, would lead to a cancellation of the coherent nonlinear process of three wave mixing. However, very recently, it was observed that with polycrystalline samples fabricated with a random orientation of Zinc Selenide (ZnSe) crystalline domains, when the average size of the domains was close to one coherence length (l c ), difference frequency generation grew linearly with the total length of the sample [2]. Similar observations were reported some years ago from SBN needlelike crystalline domains [3] and with the use of rotationally twinned crystals of ZnSe [4,5]. In all these observations, the efficiency of the process seemed to be strongly linked to an average size of the domain close to the optimal value for quasi-phase matching with periodical inverted domains. Figure 1. SH field amplitude normalized to the amplitude of the incident field as a function of the average thickness of the domains when the Coefficient of Variation is 1% (solid thin line), 10% (solid thick line), and 32% (dashed line).In the present work, we study the process of phase matching to compensate the material dispersion in refractive index in materials where there is no structural ordering. We consider, here, one-dimensional (1-D) structures composed of planar layer domains with a well-defined orientation of the nonlinear susceptibility within the domain. Such domains, however, are randomly ordered and their thickness may vary with a Gaussian distribution around a given average size. In other words, the entire structure exhibits no ordering with respect to the orientation of the dipoles and the domains are allowed to have any possible thickness. Contrary to what one could expect, we observe, as shown in figure 1, that an increase in the amount of disorder is not necessarily detrimental with respect to the efficiency of a second harmonic generation (SHG) process. Moreover, the linear growth of the second harmonic (SH) intensity with respect to the number of domains is seen when the average size of the domains is close to one l c , but also, for any other average thickness of such domains. We are able to establish a clear link between the disorder inherent to the structure and the linear growth of the intensity with respect to the numb...