Perfectly matched layer absorbing boundary condition for truncating the boundary of the left-handed medium

✍ Scribed by Yan Shi; Yun Li; Chang-Hong Liang

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 429 KB
• Volume: 48
• Category: Article
• ISSN: 0895-2477
• DOI: 10.1002/mop.21260

✦ Synopsis

The terms on the right sides of (5) 1 and (5) 2 are mutually exclusive. Whereas A គ ( x គ , ) and ( x គ , ) are some fields that are not necessarily electromagnetic, the six scalars ␣ Ϯ (), and so on, are uniform in the respective regions and may be considered as constitutive scalars.

A blind application of the boundary conditions (4) 3 and (4) 4 would involve all six constitutive scalars appearing on the right sides of (5) 1 and (5) 2 . Would that be correct?

3. THE ANSWER

Boundary conditions in electromagnetism are not externally imposed, but instead emerge from the fundamental differential equations [5]. Therefore, in order to answer the question posed in the previous section, let us first substitute Eq. ( 5) in Eqs. ( 2) and ( 3). The resulting differential equations are as follows:

The following correct boundary conditions emerge from the application of the standard techniques [3, 4] to Eqs. ( 1), ( 6), and (7): (8)