Strain-induced pseudomagnetic field and Landau levels in photonic   structures
  Magnetic effects at optical frequencies are notoriously weak. This is evidenced by the fact that the magnetic permeability of nearly all materials is unity in the optical frequency range, and that magneto-optical devices (such as Faraday isolators) must be large in order to allow for a sufficiently strong effect. In graphene, however, it has been shown that inhomogeneous strains can induce 'pseudomagnetic fields' that behave very similarly to real fields. Here, we show experimentally and theoretically that, by properly structuring a dielectric lattice, it is possible to induce a pseudomagnetic field at optical frequencies in a photonic lattice, where the propagation dynamics is equivalent to the evolution of an electronic wavepacket in graphene. To our knowledge, this is the first realization of a pseudomagnetic field in optics. The induced field gives rise to multiple photonic Landau levels (singularities in the density of states) separated by band gaps. We show experimentally and numerically that the gaps between these Landau levels give rise to transverse confinement of the optical modes. The use of strain allows for the exploration of magnetic effects in a non-resonant way that would be otherwise inaccessible in optics. Employing inhomogeneous strain to induce pseudomagnetism suggests the possibility that aperiodic photonic crystal structures can achieve greater field-enhancement and slow-light effects than periodic structures via the high density-of-states at Landau levels. Generalizing these concepts to other systems beyond optics, for example with matter waves in optical potentials, offers new intriguing physics that is fundamentally different from that in purely periodic structures. 
Mikael C. Rechtsman, Julia M. Zeuner, Andreas T\"unnermann, Stefan   Nolte, Mordechai Segev and Alexander Szameit
cond-mat.mes-hall physics.optics