Twisted bilayer photonic crystal slabs open doors to stoplight

Light is one of the carriers of quantum/optical computation. The speed of information and energy transmission can be controlled by the speed of light propagation in the media. Moreover, stoplight can be used as the memory of information and provide numerous possibilities for quantum/optical computation. We present twisted bilayer photonic crystals (TBPhCs) with ultra-flat photonic bands that exhibit extreme slow light behavior in the C-band of the telecom window. The flat band at the so-called ‘magic twist angle’ (θ = 1.89°) has an ultra-narrow bandwidth of 0.217 THz and vanishing group velocity.

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Twisted bilayer graphene (TBG) has long been heralded as a playground for electron superconductivity due to its unconventional flat electronic band structure and vanishing Fermi velocity. Even though flat photonic bands and slow-light behavior have drawn attention from the optical community, there are limited studies on flat band optics using a twisted bilayer photonic material. 

This work considers two silicon photonic crystal (PhC) layers twisted by an angle θ relative to one another (see Fig. 1a). This produces a moiré pattern with a macroscopic periodicity of distinct AA (mostly aligned) and AB/BA (mostly misaligned) stacking regions that grow in size as the angle decreases (see Fig. 1c). The guided resonances in the two twisted PhC layers couple through an evanescent tunneling pathway which is stronger in the AA site than the AB/BA site (see Fig. 1b,d). The electromagnetic modes are therefore localized around the AA site (see Fig. 2a), and the group velocity decreases. 

Figure 1                Twisted bilayer Photonic Crystals (a) Bilayer photonic crystal (BPhC) consisting of a tunneling layer with low refractive index (PMMA) sandwiched between two twisted dielectric layers (crystalline silicon).  (b) Two layers are separated by PMMA with only a subwavelength distance, suggesting an evanescent coupling between two layers of photonic crystals. (c) moiré pattern for a TBPhC, where the two dielectric layers are rotated by angle θ with respect to each other around the AA-stacked center. In a moiré pattern, lattice structure locally resembles the regular stacking arrangement such as AA, AB, and BA. (d) Evanescent waves from two layers of photonic crystals are mostly coupled in the AA-stacked region.

Figure 2                The quasi-TE modes are mostly localized when θ=1.89°. (b) Band structure obtained from the finite-element calculation (Black dots) and fitted continuum model band structure (blue line) θ=1.89°. At small angles, the Dirac cones from each layer are pushed together and hybridize due to the interlayer tunneling.

We present twisted bilayer photonic crystals (TBPhCs) with ultra-flat photonic bands that exhibit extreme slow light behavior in the C-band of the telecom window. The flat band at the so-called ‘magic twist angle’ (θ = 1.89°) has an ultra-narrow bandwidth of 0.217 THz and vanishing group velocity (see Fig. 2b). At the magic twist angle, the twisted bilayer photonic crystals have near-zero group velocity over the entire Bouillon zone and provide access to slow-light effects, light localization, and high quality-factors (varying from 105 to 107) that are far out of the reach of conventional photonic crystals. These materials will therefore greatly enhance access to optical nonlinearities and quantum interactions in photonic devices. The band structure can easily be engineered by adjusting the device geometry, giving significant freedom in the design of devices. The fabrication of such devices is immediately feasible because our twisted bilayer photonic crystals are designed for standard wafer processes.

The Harvard University team acknowledges support from DARPA under contract URFAO: GR510802. The finite-element simulations in this paper were run on the FASRC Cannon cluster supported by the FAS Division of Science Research Computing Group at Harvard University.

Haoning Tang

Postdoc, Harvard University