Realization of type-II double-zero-index photonic crystals

Some photonic crystals (PCs) with Dirac-like conical dispersions exhibit the property of double zero refractive index (that is, both epsilon and mu near zero (EMNZ)), wherein the electromagnetic waves have an infinite effective wavelength and do not experience any spatial phase change. The Dirac-like cones that support EMNZ are previously thought to present only at the center of the Brillouin zone ($\Gamma$ point) with a zero wavevector (we refer to as type-I EMNZ), which is constrained by the proportional relationship between phase refractive index and wavevector ($n=kc/\omega$). Here, we demonstrate the existence of an anomalous type-II EMNZ in PCs, which is associated with the Dirac-like point at off-$\Gamma$ points. By introducing a wave modulation approach, we theoretically elucidate its physical mechanism, and resolve the paradox of type-II EMNZ with non-zero wavevectors. We then fabricate a type-II EMNZ PC operating at the X point, and experimentally demonstrate that both its effective permittivity and permeability are zero at the Dirac-like point. Type-II EMNZ PCs exhibit a range of intriguing phenomena, including angle-selective transmission, wavefront flattening, a 180$^{\circ}$ phase shift upon transmission, and waveguiding with natural zero radiation loss. The extraordinary properties of type-II EMNZ PCs may open new avenues for the development of angle-selective optical filters, directional light sources, phase-controlled optical switches, ultracompact photonic circuits, nanolasers, and on-chip nonlinear enhancement.