Creeping Waves

Traditional SBR is limited by its reliance on straight-line geometrical optics (GO) ray tracing for the electromagnetic interaction with the scattering geometry. The Creeping Wave (CW) option is an additive physics enhancement to SBR (and part of HFSS SBR+) that addresses this limitation. The CW scattering mechanism complements both the field-transport and the current radiation aspects of SBR.

In a similar way as SBR rays, CW rays paint currents on the scattering geometry that are then radiated to field observers and receiving antennas. The main difference is that creeping rays are traced on the scattering surface in geodesic paths rather than through space in straight-line paths. As with SBR’s GO rays, the CW rays are never used to directly transport energy to field observers, and they comply with Fermat’s principle of least time.

The currents painted by SBR on the CAD geometry via the physical optics (PO) approximation are abruptly truncated at the so-called shadow boundary, the mathematical border between directly illuminated and shadowed surface regions. This non-physical truncation of the surface current leads both to a false diffraction effect (which is particularly a problem in Radar Cross Section (RCS) predictions) and to missing progressive surface diffraction beyond the shadow boundary (which is particularly a problem in cosite antenna coupling predictions). The introduction of CW rays provides a current-based correction to the SBR-PO currents that addresses both problems by painting currents beyond the shadow boundary, smoothly blending SBR and CW currents across the shadow boundary.

Creeping wave propagation follows a minimum path distance rule (i.e., Fermat’s least-time principle), resulting in a geodesic path on a curved surface. Creeping waves decay quickly in the shadow region as they propagate since they progressively shed energy to space along their direction of travel. Even if creeping rays can indefinitely propagate on an uninterrupted smooth surface, such as a sphere, the currents they paint on a surface are important only up to a certain travel distance. Ray Decay Threshold [dB] controls how far the creeping rays are allowed to propagate by terminating each ray once its power density decays below a threshold, defined as dB down from its power density at the shadow boundary.

The SBR+ Creeping Wave implementation is entirely consistent with its baseline SBR solution as a coherently additive correction component to the scattered field. That is, both can concurrently contribute to the scattered field, and in a manner that improves accuracy over the baseline SBR solution alone. In areas of the lit region where SBR first-bounce rays and CW rays would both paint currents, care is taken in the implementation to prevent double-counting of scattering mechanisms.

For RCS simulations, the shadow boundary is identified via SBR first-bounce rays from plane wave incidence. The CW rays are then launched into the shadow region from many points along the shadow boundary, initially advancing in the same the direction of the incident plane wave. CW currents are painted as the CW rays advance along geodesic paths that adhere to the curved surface. The formulation for first-bounce SBR currents is also modified so that surface currents across the shadow boundary transition smoothly between the lit and shadow regions. This has the important benefit of eliminating a spurious diffraction from the shadow boundary that arises in the SBR-only solution due to abrupt truncation of PO currents there.

For simulations involving transmitting antennas, CW analysis can only be performed from either 1) a near-field link to an HFSS source such as a FEBI or IE region, or 2) one of the current source based parametric antennas, which are available in the SBR+ solution type. In either case, the antenna must also have an infinite PEC ground plane, and part of the antenna must be located close (distance less than λ/2) to the nearest PEC or PEC-like surface.

The latter requirement is why only near-field sources are supported. With transmitting antennas, creeping waves launch from the closest point on the surface below each current source.

The creeping wave in SBR+ is limited to specific conditions:

The implementation does not require that the scattering geometry to be globally convex, such as a sphere or ellipsoid. However, the creeping-wave rays will terminate upon encountering local regions of surface concavity or saddle-shaped curvature (convex along one principal direction, concave along the other). This a requirement of the implemented CW formulation, but it can also be understood in terms of the of the minimum-path-distance rule. Where the surface becomes concave, the shortest path between the surface crests bounding the concavity no longer resides on the surface but, instead, is a straight line through space. When a local concavity is small and should be ignored, a relaxed value of Irregular Surface Tolerance allows CW rays to propagate over it.

Irregular Surface Tolerance is a single control for a collection of tolerances that determine creeping rays’ sensitivities to local surface irregularities that theoretically should block their further propagation. Moving the slider toward Relaxed allows creeping rays to propagate through small surface irregularities that may arise through defects in the input geometry or due to limitations of curvature extraction accuracy. However, setting this tolerance too relaxed may allow creeping waves to pass through concave surfaces, saddle surfaces, or wedges, which are not supported by creeping wave physics. Therefore, users are strongly encouraged to perform a creeping-wave visual ray trace (VRT) to determine an acceptable setting for this tolerance, which will differ from model to model. The intention is that creeping rays only propagate over the convex portions of surfaces, and some user judgment is required in correctly setting the Irregular Surface Tolerance for each situation.

When a CW ray is shot, each CW ray stops propagating when it triggers a termination condition. The CW ray termination type for VRT with Creeping Wave may be found as render and filter parameters appearing in Properties of the parent Visual Ray Trace CW folder. Use the Render tab to set the color for each termination type. The configurable filters help in identifying issues for a specific termination type. Termination types include:

Related Topics:

Technical Notes: HFSS SBR+ Technical Overview

HFSS with SBR+

Design Flow for SBR Solution Type