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Simulation of the Electromagnetic Fields and its Properties

With Free-space and Dielectrics Using the FDTD Method

Mark E. Eckman

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FDTD Method For Simulation of an EM Pulse

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• They are equations of a plane wave with the electric field (E) oriented in the x-direction, and the magnetic field (H) oriented in the y-direction.

• The wave itself travels in the z-direction

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Central Difference Approximations for Temporal and Spatial Derivatives

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EM Pulse Plots (Breakdown After 100 Time Steps)

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Modifying the Pulse Shape

Step Size Ratio Changed To 1 Removed Square on Exponent

exp(((t-t0)/)2) exp(-0.5((t-t0)/))

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EM Propagation in a Lossy Dielectric Slab

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FDTD Method for EM Propagation in a Lossy Dielectric

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Dielectric and Conductivity Limits

Setting the dielectric constant to a very large value, while setting the conductivity

to a very small value- or vice versa

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Absorbing Boundary Conditions

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• Removing these boundary conditions entirely:

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Conclusions

• The FDTD is a hands on method to visualize the interactions of electromagnetic waves and materials.