Shooting and Bouncing Rays (SBR)

SBR+ uses a high-frequency (asymptotic) ray-tracing approximation that efficiently computes scattering from electrically large geometries. SBR+ can be thought of as a hybridization of geometrical optics (GO) and physical optics (PO). Many GO rays are launched from a radiation source (e.g., Tx antenna) toward the visible surfaces of the scattering geometry. The launched GO rays are vector-field weighted by the source antenna pattern or current distribution and represent diverging volumetric ray tubes. When a ray hits a surface, the ray "paints" a PO current on the geometry according to the GO boundary condition. These currents are radiated to the analysis observation domain for determination of far-field radiation or antenna coupling. Then, the ray is reflected and traced, possibly to a second bounce. Its vector fields are updated according to GO and the material properties of the reflecting surface. When the reflected ray hits a surface again, it paints a second-bounce current and progresses to third bounce and so on. The process continues until the ray escapes from the scene without hitting another surface or reaches a maximum bounce number. If a penetrable surface is encountered by the ray, then a transmission ray is also generated in addition to the reflection ray.

The SBR methodology is intended to predict scattering from large-scale geometry, such as an antenna installation environment or platform. In general, it is not suitable for detailed simulation of the antennas, themselves, excepting cases where the antenna proper includes electrically large scattering geometry (e.g., reflector antenna). For this reason, HFSS SBR+ simulation requires some electromagnetic description of the source that launches and weights the rays. Conceptually, this source description can come in one of several supported forms when using HFSS SBR+:

• FEBI and/or IE simulation of antenna, resulting in distributed current sources or a far-field pattern excitation
• Idealized antenna source models (e.g., dipoles, monopoles, slots, horns, etc.)
• Imported far-field antenna patterns
• Plane-wave source (RCS application)

The first three are antenna characterizations that can also serve as receivers in an SBR antenna-coupling simulation. In the case a plane-wave source for determining RCS, the rays are launched in parallel from a plane outside the scattering geometry, being given equal initial weight. In this case, the represented volumetric ray tubes are initially neither diverging nor converging.

SBR workflow

The algorithm implemented in HFSS SBR+ is summarized in the following steps:

1. SBR sources may be introduced through Parametric Antennas in the SBR+ Solution Type, Linked Source designs, or an antenna design (with FE-BI or Radiation boundaries) within the same Driven Modal or Driven Terminal solution type. Also, Incident Plane Wave may be used for Radar Cross Section (RCS).
2. Launch many rays from the source toward the scattering geometry. The rest of the steps are the same for each ray.
3. Assign each ray a vector field weight according to the source field distribution.
4. For each launched ray:

1. If the ray escapes from scene without hitting any surface, ignore it.
2. If the ray hits a surface, generate a reflected ray. The reflected ray propagates GO reflected fields modified to account for surface curvature at the hit point and the surface material interface.
3. If the ray hits a penetrable surface, also generate a transmitted ray, heading in the same direction as the incident ray. The transmitted ray propagates GO transmitted fields modified to account for the surface material interface.

5. At the ray hit-point, compute the incident, reflected, and if penetrable transmitted, field based on material properties of the surface. Use these and the PO approximation to determine equivalent surface currents.
6. Radiate the equivalent currents to observation angles/points. If the observation point represents an Rx antenna, compute the coupling of the radiated fields into the receiver according to the Rx gain or current distribution.
7. Continue tracing the reflected and transmitted rays generated in step 3 and repeat from there. The process continues until either the ray escapes from scene or the maximum bounce limit is reached.

Step 6 is implemented with the following equation:

where Es is the scattered electric field at the observation point, S' is the domain of the ray tube at the hit point and projected onto the surface, E and H are the total electric and magnetic fields at the surface when considering the incident, reflected ray and transmitted R is the distance from the source to the observer (R = |r - r'|, which depends on the integration point within S’), r' is the position vector to the equivalent current density in the ray footprint, is the surface normal, r is the position vector to the observer, μ₀ is the free-space magnetic permeability. The equivalent currents mentioned in Step 5 are those obtained by the cross product or dot-product of with E or ̅ H, as indicated in Eq. (1).

The above expression can be used to compute the scattered field contribution in near- or far-field observations. For far-field observation angles, the factor exp(-jkR)/R in Eq. (1) is replaced with a phase factor corresponding to the chosen phase reference point, yielding a result in units of volts instead of volts-per-meter.

For Tx/Rx antenna coupling, Es is converted into the scattered field contribution to an S-parameter (i.e., coupling ratio) by computing received signal, b, at the Rx port using the Rx antenna gain or current distribution. The S-parameter is the ratio of the received signal to the incident signal, a, at the Tx port:

S = b/a.

When an Rx antenna is characterized to SBR in a far-field representation, the received signal b is given by

where g_Rx is the field-scale (complex), far-field, polarized (vector) gain of the Rx antenna. Here, gain differs from antenna directivity by incorporating the effects of mismatch between the Rx antenna and its port and also ohmic losses in the Rx antenna. E is the total electric field at the Rx antenna, and η₀ is the free-space impedance. The obtained quantity, b, is the complex amplitude of the received signal delivered to the port. Since antenna gain has angular dependence and cannot be reduced to single number (or vector) for a given antenna, a subtle point of Eq. (2) in this context is that it is actually a summation over all contributing “ray paths”. Each term in that summation has an associated electric-field contribution (E), and the direction of the incoming ray path to the Rx antenna resolves the angular dependence in the Rx antenna gain to a concrete vector, allowing the dot-product to be evaluated. These contributions comprise the incident-field contribution from the Tx antenna and the scattered-field contributions (see Eq. (1)) from each ray footprint, thus yielding the total-field contribution to the received signal. “Ray paths” as used here should not be confused with SBR GO rays that, for the most part, travel nowhere near a given Rx antenna. Here, “ray path” merely means the vector from the Tx antenna (incident-field) or SBR ray footprint (scattered-field) to the Rx antenna.

For an Rx antenna described by a current distribution, Eq. (2) generalizes to a more accurate one where the incident and scattered electric- and magnetic-fields are multiplied by the amplitude vectors of the Rx antenna current distribution through a vector dot product. That is, the incident or scattered field is computed separately at each current "source" of the Rx antenna and the vector dot products are then coherently summed.

Although the current sources and gain pattern represent the Rx antenna as a radiator, they serve to also characterize the Rx antenna as a receiver according to the reciprocity theorem. For example, reciprocity is the basis for using Eq. (2) to determine the received signal of an Rx antenna characterized by its far-field radiation gain pattern.

Additional capabilities in SBR+

In HFSS SBR+, the baseline SBR solution described above can be improved with ray-based physics additions. Physical Theory of Diffraction (PTD) corrects surface currents near wedges. Uniform Theory of Diffraction (UTD) shoots additional diffracted rays from wedges. Creeping Waves shoots rays propagating along smoothly curved surfaces.