Effect of internal period on the optical dispersion of indefinite-medium materials

The effect of internal period on the optical dispersion of indefinite medium material (IDMM) is analytically studied under the condition of the period much smaller than the operating wavelength, based on a simplified dipole model for the material. Interesting phenomena associated with the internal period, such as upper cutoff for wave vector, additional propagating mode, and parabolic dispersion in a limiting case are demonstrated in detail. However, for the normal wave vector (k) region, where vertical bar k vertical bar similar to k(0) or vertical bar k vertical bar << k(0) (k(0) is the free-space wave number), the hyperbolic dispersion behavior can still be realized by IDMM as long as its internal period is small enough. Our analysis also shows that unlike the homogeneous indefinite medium, there exists no special boundary for IDMM, on which the refraction problem cannot be physically solved. Finally, the dispersion properties obtained from the dipole model are verified by using a real example of layered IDMM.