Oblique-incidence, arbitrary-profile wave injection for electromagnetic simulations

In an electromagnetic code, a wave can be injected in the simulation domain by prescribing an oscillating field profile at the domain boundary. The process is straightforward when the field profile has a known analytical expression (typically, paraxial Gaussian beams). However, if the field profile is known at some other plane, but not at the boundary (typically, nonparaxial beams), some preprocessing is needed to calculate the field profile after propagation back to the boundary. We present a parallel numerical technique for this propagation between an arbitrary tilted plane and a given boundary of the simulation domain, implemented in the Maxwell-Vlasov particle-in-cell code Smilei.

Figure 1

Box model of a simulation where the EM wave is prescribed in a parallel plane at a distance $\delta$ from a boundary.

Figure 2

Box model of a simulation where the EM wave is prescribed in a oblique plane.

Figure 3

Two-dimensional simulation of a tightly focused beam prescribed in a tilted plane. Top panels: Magnetic field $B_z$ at three different times. Bottom panels: Comparison of the obtained (red lines) and requested (dashed black lines) magnetic field profiles, as a function of time (left) at $x=y=0$, and as a function of $y^{\prime }$ (right) at $t=0$.

Figure 4

Same simulations as in Fig. 3, keeping only 16 (top panel) and 4 modes (bottom panel).

Figure 5

Three-dimensional simulation of an oblique-incidence Laguerre-Gauss beam. Left: Three-dimensional rendering of magnetic field isocontours at $B_z=\pm a_0/10$. Top right: spatial profile in the tilted plane at $t=0$. Bottom right: temporal profile at $x^{\prime }=z^{\prime }=0, y^{\prime }=2.12\lambda$. Red and dashed black lines represent obtained and requested profiles, respectively.