Fractal Arrays

Having determined the fundamental properties of higher order FDTD algorithms, a set of more complicated problems will be studied in this section. These include the analysis of microstrip, cavity-backed or dielectric resonator antennas with different polarizations, fractal arrays, and metamaterial-loaded structures. 

Sampling in surface-enhanced Raman and infrared spectroscopy is intimately linked to the optical enhancement induced by arrays and fractals of hot metal particles, primarily of silver and gold. The key to both techniques is preparation of the metal particles either in a suspension or as architectures on the surface of substrates. We will therefore detail the preparation and self-assembly methods used to obtain films, sols, and arrayed architectures coupled with the methods of adsorbing the species of interest on them to obtain optimal enhancement of the Raman and infrared signatures. Surface-enhanced Raman spectroscopy (SERS) has been more widely used and studied because of the relative ease of the sampling process and the ready availability of lasers in the visible range of the optical spectrum. Surface-enhanced infrared spectroscopy (SEIRA) using attenuated total reflection coupled to Fourier transform infrared spectroscopy, on the other hand, is an attractive alternative to SERS but has yet to be widely applied in analytical chemistry. 

Determine the fractal dimension of a Sierpinski carpet (see Fig. 1.28), constructed by dividing solid squares into 3x3 arrays and removing their centers. 

In our studies, we consider several types of aggregated structures such as bispheres, linear chains, plane arrays on a plane rectangular lattice, compact and porous body-centered clusters embedded on the cubic lattice (bcc clusters, the porosity was simulated by random elimination of monomers), and random fractal aggregates (RF clusters). To generate RE clusters, a three-dimensional lattice model with Brownian or linear trajectories of both single particles and intermediate clusters was employed for computer simulations of aggregation process. At the initial time moment, = 50,000 particles are generated at... 

The crystal is a fractal structure and the organization of the primitive unit cells can often be seen in the shape of the macroscopic crystal. A classic example of the fractal repetition of the unit cell is the crystalline structure of a snowflake. The unit cells have the ability to build into a variety of complex shapes, yet each unit cell retains its perfect structure. The primary unit cell structure in the case of a snowflake is hexagonal and undergoes dendritic growth to produce an array of different macro crystals (Figure 2.4). The final shape of the snow crystal will depend on the conditions used in the growth process (temperature, humidity, etc), which leads to a wide variety of observed morphologies. 

Fig. 3 LHS Euclidean macropore array in p-type silicon (Kim et al. 2009) RHS Fractal-like oxide replica of tire pore volume in n-type silicon (Tondare et al. 2008)...

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