By Esteban Moreno Soriano
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Additional info for MMP MODELING AND OPTIMIZATION OF PHOTONIC CRYSTALS, OPTICAL DEVICES, AND NANOSTRUCTURES
In order to understand the relationship between the degeneracies at the Γ Fig. 4 Resonances of the energy density at an arbitrary point in the cell as a function of the normalized frequency (the point of the 1st BZ considered here is Γ). The denominations “asymmetric”, “odd” and “even” are related to the type and position of the excitation and are explained in the text and in the inset. 67214 Residual (arb. units) Energy density (arb. 67216 ωa / 2πc Fig. 5 Behavior of the energy density and residual cost functions close to the resonance peak B2 (4) shown in Fig.
Without describing in full detail the AMS algorithm, now an appropriate way to incorporate the previous three ideas and rules is presented. 2 shows how, given an interface curve Γij , the locations of the multipole expansions for domain Di are defined. First, an auxiliary curve γi outside Di (see rule 4) and running “parallel” to Γij is constructed and then, starting from one end of γi , multipolar sources are laid along it. Two consecutive multipoles (k, k+1) may be neither too close (see rule 3) nor too far (see rule 2) from each other.
7. 1. The modes associated with plasmons of n L = 2, 4, 8, 10, 14, . . are degenerated at the Γ point and those with nL = 3k, (k ∈ N) are non-degenerated, as expected from the symmetry considerations explained in 48 Computation of eigenvalue problems y (nm) 1000 500 0 0 500 1000 1500 x (nm) Fig. 8 Distribution of multipole expansions. The ◦’s are the locations of the multipole expansions modeling the fields inside of the triangle. The ×’s are the locations of the multipole expansions simulating the field inside the cell around the triangle.
MMP MODELING AND OPTIMIZATION OF PHOTONIC CRYSTALS, OPTICAL DEVICES, AND NANOSTRUCTURES by Esteban Moreno Soriano