5 Simulation of Active and Nonlinear Photonic Nano-Materials 83 8D 0 0 D= 0 Ot Kz z 0 8E 0 Ot 0 Oy. (5.12) 0 B 07 ·B= 0 8t 0 0」 0 Ky Fig.5.7.The faces (1),edges (2)and corners(3)a PML has to be separated into. An exemplary assembly of regions for the simulation is shown in Fig.5.7. The inner core is surrounded by three types of PML layers which are finally terminated on the surface of the cube.As only that part of a wave travelling in the direction away from the center of the simulation should be absorbed,the fields components which are perpendicular to the faces of the cube should be effected.The PML has got a finite thickness,therefore edges and corners have to have more than one absorption coefficient to be present.On the faces of the cube,the waves should only be absorbed in the perpendicular direction,along the edges in both transverse directions.And in the corners the waves are to be absorbed in all directions.The conductivities and absorption coefficients oi and Ki have to be set accordingly. Discretisation of 5.11 and 5.12 is straightforward with respect to the dis- cretisation rule(5.3).The results for the x component of the electric field and the displacement field update are shown in 5.13 and 5.14.Other components and field updates are of the same form and can easily be derived.5 Simulation of Active and Nonlinear Photonic Nano-Materials 83   κx 0 κy 0 κz   · ∂ D ∂t +   σx 0 σy 0 σz   · D = r      κz 0 κx 0 κy   · ∂ E ∂t +   σz 0 σx 0 σy   · E      κx 0 κy 0 κz   · ∂ B ∂t +   σx 0 σy 0 σz   · B = µr      κz 0 κx 0 κy   · ∂ H ∂t +   σz 0 σx 0 σy   · H    (5.12) 1 2 3 Fig. 5.7. The faces (1), edges (2) and corners (3) a PML has to be separated into. An exemplary assembly of regions for the simulation is shown in Fig. 5.7. The inner core is surrounded by three types of PML layers which are finally terminated on the surface of the cube. As only that part of a wave travelling in the direction away from the center of the simulation should be absorbed, the fields components which are perpendicular to the faces of the cube should be effected. The PML has got a finite thickness, therefore edges and corners have to have more than one absorption coefficient to be present. On the faces of the cube, the waves should only be absorbed in the perpendicular direction, along the edges in both transverse directions. And in the corners the waves are to be absorbed in all directions. The conductivities and absorption coefficients σi and κi have to be set accordingly. Discretisation of 5.11 and 5.12 is straightforward with respect to the dis￾cretisation rule (5.3). The results for the x component of the electric field and the displacement field update are shown in 5.13 and 5.14. Other components and field updates are of the same form and can easily be derived