Flat bands of optical dielectric beats

When we combine two periodic dielectric functions of slightly different spatial frequencies, we have spatial dielectric beats, which are periodic supercells in the longer spatial scale. This paper investigates these dielectric beats by solving the one-dimensional Maxwell's equation using a slowly varying envelope approximation. We show that the Maxwell's equation reduces to a three-term recurrence relation, leading to a tridiagonal eigenvalue problem with a dense number of eigenmodes with ultrasmall dispersions. These eigenmodes have vanishing group velocities and exist despite an optical structure with a low refractive index contrast. Optical dielectric beats have enormous potential for use in nonlinear optical and slow light applications.