Marc Maymó

Visible second-harmonic light generated from a self-organized centrosymmetric lattice of nanospheres

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.

Light generation at the anomalous dispersion high energy range of a nonlinear opal film

We study experimentally and theoretically light propagation and generation at the high energy range of a close-packed fcc photonic crystal of polystyrene spheres coated with a nonlinear material. We observe an enhancement of the second harmonic generation of light that may be explained on the basis of amplification effects arising from propagation at anomalous group velocities. Theoretical calculations are performed to support this assumption. The vector KKR method we use allows us to determine, from the linear response of the crystal, the behavior of the group velocity in our finite photonic structures when losses introduced by absorption or scattering by defects are taken into account assuming a nonzero imaginary part for the dielectric constant. In such structures, we predict large variations of the group velocity for wavelengths on the order or smaller than the lattice constant of the structure, where an anomalous group velocity behavior is associated with the flat bands of the photonic band structure. We find that a direct relation may be established between the group velocity reduction and the enhancement of a light generation processes such as the second harmonic generation we consider. However, frequencies for which the enhancement is found, in the finite photonic crystals we use, do not necessarily coincide with the frequencies of flat high energy bands.

High band anomalous group velocity dispersion for the enhancement of the nonlinear interaction

Second order nonlinear processes in 3D centrosymmetric materials, as second harmonic generation (SHG), have been demonstrated in the past using self organized colloidal suspensions of modified polystyrene spheres in water. This paper demonstrates 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. The photonic crystal properties of the material allows 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.

Nonlinear light generation at the high energy range of a 3D opal film

Most of the applications based on the special optical properties that photonic crystals (PC) offer to control the interaction between matter and electromagnetic radiation, are based on the periodic structure response at the low energy region of the spectra, where the first order Bragg diffraction takes place. Among those reported applications of PCs some are devoted to the nonlinear (NL) optical processes such as the second harmonic generation (SHG).

Nonlinear Generation of Light in Random Structures

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. 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 (lcc), difference frequency generation grew linearly with the total length of the sample. Similar observations were reported some years ago from SBN needlelike crystalline domains and with the use of rotationally twinned crystals of ZnSe. 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. 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 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 lc, 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 number of domains. It is also possible to obtain such type of nonlinear processes in random media where there is an index contrast between the several nonlinear domains. Recently significant progress has been made in the development in structured nonlinear materials. In the present paper we will review the performance of some of these nonlinear photonic materials that, eventually, could be implemented in a disordered configuration where the proposals of the present work could be experimentally tested

Second order nonlinear processes in photonic crystals

We show that the second-order parametric nonlinear interaction from waves that are counter propagating may be perfectly phase matched in the framework of a photonic crystal. We observe that the large momentum mismatch of such parametric process is compensated because of the interfaces present in the nonlinear photonic crystal considered, which separate a linear from a nonlinear material. The numerical results presented indicate that such nonlinear photonic crystals could be a very good material to consider the observation of backward parametric oscillation without mirror feedback. In the search for a material capable of holding such type of oscillation, we have performed second harmonic generation experiments using several nonlinear colloidal crystals. We compared the efficiency between such different nonlinear crystals obtained by binding different types of organic nonlinear molecules onto the surface of a polystyrene particle.

Phase matched third harmonic generation in 3D photonic crystal

In this paper, we present experimental evidence of phase matched third harmonic generation at 355 nm from a beam at 1064 nm incident on a photonic crystal made of 120 nm in diameter polystyrene spheres ordered in an fee lattice. Numerical calculations show that at the lower angle edge of the Bragg reflected band, the periodical structure induced effective index of refraction at 355 nm matches the index of refraction at 1064 nm.