General strategy of calculations

Fig.6.1 provides a general view of the waveguide handled by TRACEO. The source can be located anywhere inside a range ``box'' (hereafter called rbox), and ray tracing is terminated every time a ray exits the box. Placing the source on any of the rbox ranges prevents any calculations of being performed. For the sake of numerical stability it is strongly recommended (but not required) that both surface and bottom coordinates are defined beyond the ranges of the rbox.

Figure 6.1: General view of TRACEO's waveguide.

Launching angles can be defined clockwise or counter clockwise, as desired, but launching angles too close to 90 $\mbox{$^\circ$}\xspace$ (which are detected by the condition $\left\vert \cos\theta \right\vert < \varepsilon$) are skipped. Additionally, TRACEO uses the convention that rays launched towards the surface have a positive launching angle, while negative launching angles indicate propagation of rays towards the bottom. Depending on the reflection coefficient $R$ any boundary waveguide (including objects) can be one of four different types, namely absorbent ($R = 0$), rigid ($R = 1$), vacuum ($R = -1$) or elastic ($R$ is calculated as described in section 4.1). Rays arriving at an absorbing boundary are no longer traced. Another condition for ray termination is that $\left\vert R \right\vert < \varepsilon$. The array can be horizontal, vertical, rectangular or linear.

The general strategy of calculations can be resumed as follows:

• For every launching angle trace the ray, until it is terminated or exits the rbox.
• At every step of ray integration check if the ray is above the surface, below the bottom or inside an object. For a positive check determine the intersection of the ray with the boundary, reflect the ray, and continue with the integration of ray equations.
• After exiting the rbox calculate the $(p,q)$ parameters and the amplitude of the ray.
• Use ray coordinates and amplitudes to calculate the output requested by the user.