There are several ways that metamaterials are helping to achieve size reduction.  One way is simply loading the antenna with high refractive index.  The best way to do this is to introduce permittivity and permeability at the same time so that impedance stays that of air, but the wave slows down thus reducing the wavelength and the size antenna it takes to resonate at that wavelength.  A second way is making antennas very flat using a high-impedance ground plane.  Typically, a dipole would need to be a quarter wavelength above an ordinary ground plane to ensure the reflected wave is in phase.  There is no phase change on reflection from a high-impedance ground plane so the antenna can be placed very close.  Another way is reducing mutual coupling between antenna elements.  This may not reduce the antenna elements themselves, but arrays can be made more compact so size is reduced at the system level.

I am sure a simple literature search will turn up many more things for you.  The main problem with metamaterials is loss.  You must consider loss.

Thank You Sir very very much for such a elaborate explaination@@

Actually i am a beginner started to work on Metamaterial using SIW Technology. Can you kindly recommend me some good weblink/tutorial focusing on basic concept of metamaterial, Left handed materials their working principle and advantages etc.

Thanks a Lot

Regard

Nitin

Take a look at the following course website:

http://emlab.utep.edu/ee5390em21.htm

This has links to lectures recorded on YouTube about many advanced topics in electromagnetics.  It also has the notes in PDF form, and other resources.  For metamaterials, work through Lectures 1-3, 7, 8, 10, 12-15, although working through all the lectures is best.  Since doing the recordings, I have made a good number of revisions and improvements to the notes so you may see some differences.

Sir Thank You so much@@. I t has quite useful information. Thanks . I am  working on design of miniaturized BPF using Folded SIW & concept of Metamaterial.

Thanks and Regards

Nitin