China 
Africa 
Explore chapters and articles related to this topic
High-Resolution Nonparametric Spectral Analysis: Theory and Applications
Published in Yingbo Hua, Alex B. Gershman, Qi Cheng, High-Resolution and Robust Signal Processing, 2017
Erik G. Larsson, Jian Li, Petre Stoica
in lieu of (4.4.8). Obviously, the constraint in (4.11.2) is equivalent to requiring that the filter transfer function has a value of unity at both ω and –ω. This is a natural constraint in view of the fact that real-valued signals have symmetric spectra.
Emergence of a new symmetry class for Bogoliubov–de Gennes (BdG) Hamiltonians: expanding 10-fold symmetry classes
Published in Phase Transitions, 2020
The product of time-reversal operator () and particle-hole operator () leads to a third kind of symmetry called chiral symmetry() or sub-lattice symmetry. The symmetry operator is given byIt is a unitary symmetry transformation which anticommutes with the Hamiltonian with ,Chiral symmetry results in the symmetric spectrum. From Table 1, one can observe the presence of either TR or PH results in the absence of chiral symmetry. Also, the absence of both TR and PH symmetries results in either presence or absence of chiral symmetry [16]. Based on the behaviour of Hamiltonian with the TR, PH and chiral symmetries, it is classified into 10 symmetry classes [29]. Table 1 shows the 10 symmetry classes of non-interacting Hamiltonian. One can identify for given spatial dimension d of a system and given set of symmetries which symmetry class it belongs to and its topological properties. and are the topological invariant numbers which take integer values ( and ), and represent the topological distinct phases within a given symmetry class.
Comparative study of coupling to symmetric and antisymmetric cladding modes in long-period fiber gratings
Published in Journal of Modern Optics, 2019
Felipe Delgado, Alexandre Bessa
In order to identify the cladding modes of resonant wavelengths observed in Figure 2, we have simulated the phase-matching curves for the produced arc-induced LPFGs. In our simulations, we have used the modified phase matching condition, which allow us to identify the resonance wavelengths with an error lower than 0.1% (12, 19): where and are the propagation constants of the core and the jth cladding modes, respectively. Λ is the period of the grating, and are the self-coupling coefficients of the core and the jth cladding modes, respectively. Finally, is the coefficient of the first Fourier component of the grating and N is the diffraction order. It is important to mention that for the anti symmetric energy coupling analysis, (LP1j; j ≥ 1) modes must be considered. Therefore, the propagation constants and self-coupling coefficients of these cladding modes must be considered in (2). We have considered the refractive index of the optical fiber as stated in Corning SMF-28 specifications, refractive index difference of Δn = 0.0036 and core and cladding diameter of 8.2 and 125 µm, respectively. Furthermore, we have considered an increase in the cladding refractive index induced by the electric arc discharges to optimize the results (19). The phase-matching curves in Figure 3 illustrate the dependence between the grating period and the resonant wavelengths of the different cladding modes and the black dots correspond to the experimental data from the produced LPFGs with Λ = 470 µm. Therefore, the phase-matching curves in Figure 3(a) confirm that the symmetric transmission spectrum observed in Figure 2 contains the attenuation dips corresponding to the LP02-LP05 modes. Whereas the phase-matching curves in Figure 3(b) identify the four attenuation dips observed in the anti symmetric spectrum in Figure 2, correspond to the energy coupling of the fundamental core mode LP01 to the LP11, LP12, LP13 and LP14 modes.