ABSTRACT
Surface or edge states represent an important class of modes in various photonic crystal systems such as in dielectric topological insulators and in photonic crystal fibers. In the later, strong attenuation peaks in the transmission spectrum are attributed to coupling between surface and core-guided modes. Here, we explore a modified implementation of the spatial and spectral interference method to experimentally characterize surface modes in photonic crystal fibers. Using an external reference and a non-uniform Fourier transform windowing, the obtained spectrogram allows clear observation of anti-crossing behavior at wavelengths in which surface and core modes are strongly coupled. We also detect surface modes with different spatial symmetries, and give insight into mode families couple to the fundamental or high-order core modes, as well as the existence of uncoupled surface modes.
ABSTRACT
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.
