Negative permeability of split ring resonators(SRR)

[Sana5643]

Negative permeability of split ring resonators(SRR) is obtained between the resonant frequency and the Plasma frequency of the SRRs, then what is the meaning 'eigenfrequency' of split ring resonator(SRR).
Is eigenfrequncy is that 'frequency' at what negative permeability occur ??

 

[|squeezed>]

I 'm not sure i fully understand your question but the eigenfrequency of a SRR depends on the polarization of the field: you can excite the LC resonance at the gap, or the SPP resonance at the SRR's branches (or even both). Each one of these is an eigenfrequency of the SRR. [I am referring to the case of normal incidence; the situation becomes complicated for oblique incidence.]

 

[Sana5643]

im asking about eigenfrequency of SRR when it is embedded in dielectric whose permitivitty is non linear.Also permeability is nonlinear. both permitivitty and permeability are incident field intensity dependent.

 

[Born2bwire]

I doesn't matter. When they are talking about eigenfrequencies, they mean the frequencies of the modes, resonant modes, of the structure. It may not necessarily accord to the frequencies where the permeability and/or permittivity are negative. Of course it shouldn't since the resonance means a change in sign in the real/imaginary part and a peak in the imaginary/real part of the parameter (this can be verified via the Kramers-Kronig relation). So at the resonance the permittivity or permeability is generally ill-defined (in an ideal resonance, in reality it's just going to be very small) since it is changing sign. We do not want to operate at the resonance mostly because it corresponds to a peak in the loss (imaginary part). What you generally do is design the SRR so that the resonance is a bit off from the operating frequency so that you can not only be in the small area where the parameter is negative but also try to compromise on the amount of loss.

EDIT: Normally though we do not consider the surrounding dielectric (if there is one) to be nonlinear. As pipe-squeezed-angle_bracket explained, the resonances of the SRR are dependent upon the incident field. If we permeate a volume or surface with our SRR and consider the bulk behavior of this volume/surface so that it has an effective permeability/permittivity then we find that it is non-linear (for the reasons why the physics of the SRR are dependent upon the incident wave).