Yevgen Grynko

Validity criteria of the discrete dipole approximation.

There are two widely accepted restrictions on the application of the discrete dipole approximation (DDA) in the study of light scattering by particles comparable to the wavelength: (1) when considering dielectric particles, the size of the cells must satisfy the condition kd|m|<0.5, where k is the wavenumber, d is the size of the cells, and m is the complex refractive index of the constituent material and (2) when considering conductive particles, the size of the cells must be small enough to reproduce sufficiently the evolution of the electromagnetic field in the skin layer. We examine both restrictions when the DDA is applied to irregularly shaped particles and show that its restrictions are not as strong as is widely accepted. For instance, when studying irregularly shaped particles averaged over orientations, even at kd|m|=1, the DDA provides highly accurate numerical results. Moreover, we show that the impact of using large constituent cells is similar to that produced by surface roughness; therefore, the replacement of the target particle by an array of large constituent cells has the same effect, qualitatively, as incorporating additional small-scale surface roughness on the particle. Such a modification of the target particle can be desirable in many practical applications of DDA when irregularly shaped particles are considered. When applying DDA to conductive, nonspherical particles, the insufficient description of the electromagnetic field in the skin layer does not lead to a violation of the Maxwell equations, although it has a visible but nonmajor influence on the light-scattering properties of the target.

Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas

Plasmonic nanoantennas provide unprecedented opportunities to concentrate light fields in subwavelength-sized volumes. By placing a nonlinear dielectric nanoparticle in such a hot spot, one can hope to take advantage of both the field enhancement provided by nanoantennas and the large, nonlinear optical susceptibility of dielectric nanoparticles. To test this concept, we combine gold gap nanoantennas with second-order, nonlinear zinc sulfide nanoparticles, and perform second harmonic generation (SHG) spectroscopy on the combined hybrid dielectric/plasmonic nanoantennas as well as on the individual constituents. We find that SHG from the bare gold nanoantennas, even though it should be forbidden due to symmetry reasons, is several orders of magnitude larger than that of the bare zinc sulfide nanoparticles. Even stronger second harmonic signals are generated by the hybrid dielectric/plasmonic nanoantennas. Control experiments with nanoantennas containing linear lanthanum fluoride nanoparticles reveal; however, that the increased SHG efficiency of the hybrid dielectric/plasmonic nanoantennas does not depend on the nonlinear optical susceptibility of the dielectric nanoparticles but is an effect of the modification of the dielectric environment. The combination of a hybrid dielectric/plasmonic nanoantenna, which is only resonant for the incoming pump light field, with a second nanoantenna, which is resonant for the generated second harmonic light, allows for a further increase in the efficiency of SHG. As the second nanoantenna mediates the coupling of the second harmonic light to the far field, this double-resonant approach also provides us with control over the polarization of the generated light.

Light scattering by randomly irregular dielectric particles larger than the wavelength

We present results of simulation of light scattering by randomly irregular particles that have dimensions larger than the wavelength of incident light. We apply the discontinuous Galerkin time domain method and compare the accurate solution with that obtained using an approximate geometric-optics model. A qualitative agreement is observed for scattering angle curves of intensity at the size parameter of X=60, whereas angular dependence of polarization appears to be more sensitive to the wave effects and requires larger sizes for application of geometrical optics.

Light scattering from particulate surfaces in geometrical optics approximation

Measurements of light scattered from particulate surfaces provide information about the composition and structure of the surfaces. An obvious way to characterize the scattering properties is to consider how the brightness and polarization of scattering depend on the wavelength λ of incident light and the geometry of observations. The geometry is often characterized by the phase angle α which is defined as the source-object-detector angle. Instead of α the scattering angle θ = π − α is used also. The plane defined by the light source, scattering object and detector is called the scattering plane. The method of optical remote sensing of particulate surfaces is based on the measurements of the characteristics as functions of λ and α. The problem of theoretical interpretation of this kind of data is not solved at present. Numerical modeling based on the geometric optics (GO) approximation can be efficient for some practical applications. In chapter we give an introduction to the past and current status of the theoretical methods and GO simulation results achieved for media consisting of particles large compared to the wavelength of incident light.

Light scattering by irregular particles much larger than the wavelength with wavelength-scale surface roughness

We simulate light scattering by random irregular particles that have dimensions much larger than the wavelength of incident light at the size parameter of X=200 using the discontinuous Galerkin time domain method. A comparison of the DGTD solution for smoothly faceted particles with that obtained with a geometric optics model shows good agreement for the scattering angle curves of intensity and polarization. If a wavelength-scale surface roughness is introduced, diffuse scattering at rough interface results in smooth and featureless curves for all scattering matrix elements which is consistent with the laboratory measurements of real samples.

Light scattering by random irregular particles of two classes of shape.

We calculate light scattering properties of random irregular particles of two different classes of shape, compact Gaussian random field particles and agglomerated debris particles, at size parameters X=50 and X=32. Surprisingly, very similar angular dependencies of all nonzero scattering matrix elements are obtained for both classes in the case of nonabsorbing material. For highly absorbing particles external scattering becomes dominant, which introduces a difference in the positive polarization due to different morphologies of their surfaces.

Optimal Second-Harmonic Generation in Split-Ring Resonator Arrays

Previous experimental measurements and numerical simulations give evidence of strong electric and magnetic field interaction between split-ring resonators in dense arrays. One can expect that such interactions have an influence on the second harmonic generation. We apply the Discontinuous Galerkin Time Domain method and the hydrodynamic Maxwell-Vlasov model to simulate the linear and nonlinear optical response from SRR arrays. The simulations show that dense placement of the constituent building blocks appears not always optimal and collective effects can lead to a significant suppression of the near fields at the fundamental frequency and, consequently, to the decrease of the SHG intensity. We demonstrate also the great role of the symmetry degree of the array layout which results in the variation of the SHG efficiency in range of two orders of magnitude.

Simulation of Second Harmonic Generation from Photonic Nanostructures Using the Discontinuous Galerkin Time Domain Method

We apply the Discontinuous Galerkin Time Domain (DGTD) method for numerical simulations of the second harmonic generation from various metallic nanostructures. A Maxwell–Vlasov hydrodynamic model is used to describe the nonlinear effects in the motion of the excited free electrons in a metal. The results are compared with the corresponding experimental measurements for split-ring resonators and plasmonic gap antennas.

Radar backscattering from a large-grain cometary coma: numerical simulation

We numerically simulate the circular polarization ratio of the radar signal backscattered from a large-grain cometary coma and compare the simulation results with the radar measurements for seven comets. We apply the discrete dipole approximation method and a model of random irregular particles. Our results confirm water ice composition of the cm-sized chunks detected by the NASA Deep Impact space probe in the vicinity of the nucleus of Comet 103P/Hartley 2. The index of the power-law size distribution in this case can be constrained to the range n ≈ 3.3–4.3. For the other considered comets the circular polarization ratio can be reproduced with variations of the power index between 2 and 5.

Near-field coupling and second-harmonic generation in split-ring resonator arrays

We simulate the linear and nonlinear optical response from split-ring resonator (SRR) arrays to study collective effects between the constituent SRRs that determine spectral properties of the second harmonic generation (SHG). We apply the Discontinuous Galerkin Time Domain (DGTD) method and the hydrodynamic Maxwell-Vlasov model to calculate the SHG emission. Our model is able to qualitatively reproduce and explain the non-monotonic dependence of the spectral SHG transmission measured experimentally for SRR arrays with different lattice constants [1].