By Ibanescu, Mihai
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Additional resources for Cylindrical Photonic Crystals
For modes other than the TEoe modes, the absence of the node in the electric field near the core-layers interface results in more penetration of the field into the cladding, and also different scaling laws for the R dependence. Turning back to Fig. 2-7, we see that the TM0 1 dissipation loss follows exactly a 1/R dependence (solid blue line), while the loss of HE1 l has some intermediate dependence, with a slope that approaches 1/R for large R. Another reason for the low losses of the TE01 mode is the fact that this mode is confined in the core only by the TE gap.
230 (2r/a). E is plotted for the five All modes are normalized such that the power flowing in the z direction is the same. Also, in order to capture 36 the angular dependence of a mode, we no longer use the eimo complex form of the field. Instead, we use linear combinations of the degenerate m and -m modes to obtain real fields. All modes appear to be very well confined to the hollow core. The energy density in the cladding layers is much smaller than the energy density in the core, which is why the cladding layers appear dark in the Figure.
Because of the small amplitude of Es, at the core-layers interface, it is the derivative of Es, with respect to r that connects the amplitudes Alayersand Acore. If we approximate the radial field oscillations by sinusoidal oscillations, the derivative of E s close to a node is given by the transverse wave vector times the amplitude of Ed. Thus, the amplitudes in the core and in the layers are connected by kT,coreAcore- kT,ltayersAT,Itayers. The transverse wave vector kT,core is inversely proportional to R, because the TE0 , mode always has half an oscillation of E, between the origin and r = R.
Cylindrical Photonic Crystals by Ibanescu, Mihai