  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.
