scattering. When the observation point moves away from the incident angle, the incoherent scattering increases and then fluctuates due to the random phase situation. The fluctuations are characteristic of random scattering, since the bistatic scattering cross section per unit volume will fluctuate from sample to sample. When we increase the number of particles in the simulations, the multiple scattering simulations show increased scattering effects at the incident angle, which is caused by higher-order scattering.In Figure 7, the phase function of independent scattering, sticky particles, and nonsticky cylinders is compared. The sticky cylinders show an angular distribution pattern similar to that of the nonsticky cylinders, but a stronger amplitude than both independent scattering and nonsticky cylinders. The stronger scattering effect of the sticky cylinders is expected because the cylinders adhere to each other to form larger aggregates.
ACKNOWLEDGMENTThis work is supported by NASA contract NAG5-9835 from the NASA Goddard Space Flight Center and by the City University of Hong Kong Research Grant 9380034. , where characterisation of both microstrip and ridge waveguides was described and used to model a microstrip-to-ridge waveguide discontinuity and ridge waveguide step junctions. On the other hand, the finite-difference time-domain (FDTD) method has been demonstrated to be a feasible and powerful tool for the analysis of microwave problems where arbitrary geometries are involved [4]. Nevertheless, a commonly known disadvantage is that it requires large amounts of computer resources, and this fact has limited its use as a design tool. So, it is not difficult to find FDTD-based analysis of waveguide transitions [5, 6], but the use of FDTD for design purposes is still not generalised [7]. The present work explores the design of microstrip-towaveguide transitions using a compact full-wave 2D approach of the FDTD method in combination with the stepped transmission line transformer theory. Specifically a full-wave 2D-FDTD scheme [8] is firstly applied for obtaining the design curves for the shielded microstrip. This technique is then extended to the calculation of the frequency and geometry-dependent parameters for the doubleridged waveguide that will be used in the transition. Finally, a full non-uniform 3D-FDTD analysis is performed over the whole design in order to validate the design process.The structure that we have selected to test the procedure is shown in Figure 1. It is built in a mixed technology consisting of a shielded microstrip zone with upper and lower ridged metallisations that are gradually matched to a standard waveguide. The more common parameters are described in the figure's upper inset, while a frontal sight of an example of a transition profile is also displayed in the same figure. Similar geometries have been successfully used in the design of radiating elements for radar applications [9]. Because of the lower dispersive behaviour of both shielded microstrip and ridged waveguide as compared...