The new physics of magic-angle twisted bilayer graphene (TBG) motivated extensive studies of flat bands hosted by moiré superlattices in van der Waals structures, inspiring the investigations into their photonic counterparts with potential applications including Bose-Einstein condensation. However, correlation between photonic flat bands and bilayer photonic moire ´ systems remains unexplored, impeding further development of moire ´ photonics. In this work, we formulate a coupled-mode theory for low-angle twisted bilayer honeycomb photonic crystals as a close analogy of TBG, discovering magic-angle photonic flat bands with a non-Anderson-type localization. Moreover, the interlayer separation constitutes a convenient degree of freedom in tuning photonic moire ´ bands without high pressure. A phase diagram is constructed to correlate the twist angle and separation dependencies to the photonic magic angles. Our findings reveal a salient correspondence between fermionic and bosonic moiré systems and pave the avenue toward novel applications through advanced photonic band or state engineering.
It is generally believed that the high energy end of synchrotron emission, generated by the most energetic tail of relativistic electrons in the jets, account for the X-ray emission of high-energy peaked BL Lac objects (HBLs) and the optical emission of intermediate-energy peaked BL Lac objects (IBLs). It is thus expected that both should show similar variability characteristics. One of the important variability parameters is the inter-band time lag which probes the acceleration and cooling of relativistic particles responsible for the emission. The switches between soft and hard lags have been detected in the intra-day X-ray variability of a few HBLs, which is not the case for the intra-day optical variability of IBLs yet. We present the results of our intra-night optical observations for BL Lacertae, aiming at searching for hard lags of its optical variations, performed with the 80 cm telescope in fourteen nights of 2010 September-November. Intra-night changes of ∼ 0.2 mag were detected in most of nights. The intra-night variability amplitude tends to become larger from red to blue wavelength, and the optical spectrum hardens with increasing brightness. The intra-night variations correlate between different wavebands, but we did not find significant time lags, either soft or hard. Nevertheless, on November 2, the B band variations showed a sign of lagging the R band ones by 317±214 s. The claim of this hard lag is strongly limited by the photometric precision and time resolution. Therefore, the switches between soft and hard lags of IBLs in the optical bands needs further demonstration with more higher quality observations.
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