  Klein's paradox refers to the transmission of a relativistic particle through
a high potential barrier. Although it has a simple resolution in terms of
particle-to-antiparticle tunneling (Klein tunneling), debates on its physical
meaning seem lasting partially due to the lack of direct experimental
verification. In this article, we point out that honeycomb-type photonic
crystals (PhCs) provide an ideal platform to investigate the nature of Klein
tunneling, where the effective Dirac mass can be tuned in a relatively easy way
from a positive value (trivial PhC) to a negative value (topological PhC) via a
zero-mass case (PhC graphene). Especially, we show that analysis of the
transmission between domains with opposite Dirac masses -- a case hardly be
treated within the scheme available so far -- sheds new light on the
understanding of the Klein tunneling.
