Propagation of Gaussian beams in free space
2D quadridirectional mode expansion simulations of configurations with the following specification: A homogeneous medium with refractive index n = 1.0, covered by a computational window of width w = 15.1 µm. All calculations are meant for a vacuum wavelength of 1.0 µm and for TE polarization, i.e. Ey is the single nonvanishing component of the electrical field. The field is discretized by 150 Fourier components along both coordinate axes.
 

QUEP simulations
The figures in the table below lead to illustrations of the stationary electric field that is generated by inserting single Gaussian beams, or superpositions of these, respectively.

Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t)
(0) (1) (2) (3) (4) (5) (6) (7) (8) (9)

In simulations (0) - (3), beams of a width of 4µm are launched at a tilt angle of 10o from the left edge (0), the bottom edge (1), and simultaneously from the top and from the right edges (2) or from all four edges (3) into the interiour of the computational window, in each case with an initial offset of 2µm with respect to the center of the window.

For configurations (4) - (6), the tilt angle of the now initially centered beams is increased to 45o such that the rays leave the computational window on the upper or lower horizontal edge, while they are excited on the right (4) or left and right edge (5), (6) of the computational domain.

Simulations (7) and (8) show the spreading of centered, upwards traveling narrower beams with initial widths 1µm (7) and 0.2µm (8). The animation (9) illustrates corner effects: Here a beam of width 4µm is excited on the top edge with a larger tilt angle of 30o and an offset of 1µm, such that it directly hits the lower right corner of the computational window.