I suggest putting off looking at their actual structures for now.  Ask yourself what amazing thing you can do given some extraordinary constitutive values.  Given that, then seek the geometry of the metamaterial.  When you do, look for equivalent circuit models of the metamaterials.  I think those papers will have what you are looking for.

I suggest putting off looking at their actual structures for now.  Ask yourself what amazing thing you can do given some extraordinary constitutive values.  Given that, then seek the geometry of the metamaterial.  When you do, look for equivalent circuit models of the metamaterials.  I think those papers will have what you are looking for.

thank you sir ... is there any paper for that ....

first look for the basics that how metamaterial effect is generated. Chapter 1 of Christophe caloz and T Itho book on Metamatrial transmission line, may help you in understanding the basic. One can see the published literatures of these authors for more understanding.

This question raises an important issue. I have not seen any paper that deals with the basics of relating shapes to metamaterial effects. Many researchers have investigated split rings and complementary rings. They are satisfied with the obtained results once they show the required effect of metamaterials. 

@khalil.H.sayidmarie   yes sir . and also many researchers used different shapes to obtain metamaterial effects . they not mentioning how shapes related to that work . 

 thank you Shrikanth Reddy

Please check the reference by Prof. Sorolla, Prof. Martin and Prof. Marques in relation with SRR and CSRR elements. The fundamental parameter is not actually shape, but currents (in the case of SRR) and equivalent magnetic currents (in the case of CSRR). The key question is excitation of these circuits, polarizability and anisotropy/bi-anisotropy. In the case of SRR/CSRR elements, a wide knowledge base founded on equivalent circuit models provide design tools. Hope this can help. All the best.

Basically, metamaterial is an artificial and non homogeneous material. Hence, any theory may not be possible to apply straight way. However, it can be anylized, in a small section.

One of the good paper explains basic theory is "The Nature of Electromagnetic waves in Metamaterials and metamaterial-inspired configurations" by Rui yang and Yongjun Xie can be useful for you  

@Francisco Falcone

  thank you sir . i will go through your references sir .

Sure, hope it helps! Good luck with all your MTM research! All the best,

Francisco

yes dear. and also many researchers used different shapes and geometries to obtain metamaterial medium which can be checked be obtaining the mu and epsilon. also the refractive index must be negative in the band of operation.and there are some papers discuss these shapes and the main differences however there is compact shapes but this depend on your application.

thank you Hussein Srour.... i will check that paper .