Читать книгу Electromagnetic Simulation Using the FDTD Method with Python - Dennis M. Sullivan - Страница 17

In order to simulate a medium with a dielectric constant other than 1, which corresponds to free space, we have to add the relative dielectric constant ε_r to Maxwell’s equations:

(1.13a)

(1.13b)

We will stay with our one‐dimensional example,

(1.14a)

(1.14b)

then go to the finite‐difference approximations and make the change of variables in Eq. (1.5):

(1.15a)

(1.15b)

From this we can get the computer equations

(1.16a)

(1.16b)

Figure 1.4 Simulation of a pulse striking dielectric material with a dielectric constant of 4. The source originates at cell number 5.

where

(1.17)

over those values of k that specify the dielectric material.

The program fd1d_1_3.py simulates the interaction of a pulse traveling in free space until it strikes a dielectric medium. The medium is specified by the parameter cb in Eq. (1.17). Figure 1.4 shows the result of a simulation with a dielectric medium having a relative dielectric constant of 4. Note that one portion of the pulse propagates into the medium and the other is reflected, in keeping with basic EM theory (6).