Dispersion of Polaritons in Biaxial Slabs

In this chapter, organized in a tutorial style, we present a detailed derivation of the dispersion relation of electromagnetic modes in a biaxial slab. We show that our general dispersion relation successfully reduces to several known limiting cases of interest, such as uniaxial and isotropic slabs or semi-infinite crystals, among others. We manage to reduce the general dispersion relation to simple analytical expressions for short wavelength of the modes and small slab thicknesses, which are of great interest for the study of anisotropic polaritons in van der Waals (vdW) slabs. To demonstrate the validity of our analytical approximations, we compare them to full-wave simulations, finding an excellent agreement. Most of the results reported in this chapter were developed in collaboration with Kirill Voronin (Moscow Institute of Physics and Technology, Russia), and published in “Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals”, by Gonzalo Álvarez-Pérez, Kirill V. Voronin et al., in Physical Review B 100, 235408 (2019).