Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 241

Figure (5.13) shows the ray diagram of a DNG slab acting as a lens due to the negative refraction [J.3]. It has two foci N and Q. The focal length f₁ of focus N is located inside the DNG slab of thickness d. The focal length f₂ of focus Q is located outside the slab. To avoid mismatch at the interface, the DNG slab has μ_r = ε_r = − 1 and . Figure (5.13) shows the angles of incidence θ_i and refraction θ_r and other geometrical dimensions. Snell's law for the DNG slab is written below:

(5.5.31)

The first focal length f₁ is determined as follows:

(5.5.32)

The incident ray OM and the output ray P₁ Q are parallel, i.e. θ_i = θ_o.

Figure 5.13 Ray diagram of a DNG flat lens.

The second focal length f₂ is computed as follows:

(5.5.33)

For d > f₁, equations (5.5.32c) and (5.5.33c) provide a relation between two focal lengths:

(5.5.34)

Equation (5.5.31) shows a matched DNG slab has θ_i = θ_r. For this case, both focal lengths, and also distance D between the object and image at the second focus are given below:

(5.5.35)