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Background Theory

EMWave2D is based on solving the Maxwell’s equations by the finite difference time domain (FDTD) method. The Maxwell's equations for a homogenous, isotropic and non-conductive medium and with no free charges and no free currents are


  
Equations (1)

For two dimensional problem, where the electric and magnetic fields are independent of z coordinate and for transverse magnetic (TM), the above equations reduce to

 
Equations (2)



Figure 1.

Using a staggered arrangement of electric and magnetic fields as in Figure 1, Equations (2) are discretized to

  Equations (3)

Note that the magnetic fields are computed at t=n+1/2 which depend on the the electric fields t=n, and similarly the electric fields are computed at t=n+1 which depend on the the magnetic fields t=n+1/2. By using an initial input fields, one can then use Equations (3) to simulate the propagation of wave. 



References

[1] Yee, K.S.,”Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propagation, Vol. 14, 1966, pp. 302-307.


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