Dear Punyatoya,

Reflection, Interference, Diffraction and Diffusion ...

https://onlinelibrary.wiley.com › doi - Traduire cette page1 juil. 2012 - Summary This chapter studies the laws of reflection and transmission of electromagnetic waves at the interface of two mediums. The wave may ...

Usually a flat lens diverges em waves, incident from a point source/source at infinity such that the rays are parallel to each other. You can simply use Snell's law here, at the two interfaces (air to lens and lens to air), you will see that the a normal lens(positive refractive index) will diverge the incident rays, whereas a flat lens with negative index of refraction will converge the rays. The converging effect causes the em waves from antenna falling into the lens to focus and hence increase the gain.

Nitin Kumar : A flat lens with a negative refractive index will have a plane wave pattern in it that goes backwards to meet the incident wave at the boundary. The angle of refraction will be negative. There will be no focussing effect.

Look at some of the simulations of negative index materials that are available on the web, or in metamaterial textbooks.

Agreed Malcolm White what you said is correct for negative index material, but as I said there will be two interfaces here, air to lens and then lens to air. when em waves comes out of the lens instead of diverging they will converge. This is a screenshot from a book by Nader Engheta and Richard Ziollowski.

Although I would like to correct myself about the source of em waves, It should not be at infinity or the beam shouldn't be collimated but must be at some oblique angle.

Nitin Kumar : The diagram you showed does not show any convergence. If the source is a point source in a negative index material and diverges towards the plane boundary, (but with the wave fronts going backwards to the source) then the wave in air will converge to a focus in air (with the wave fronts in air travelling forwards to the focus in air!)

Yes Malcolm White it only shows the air-lens interface but you can extend this to lens-air boundary and observe the effect. This is what i believe, that if there are two rays coming from a point source then they will converge inside the lens and if the lens has significant thickness in terms of wavelength then this point of convergence can again be treated as a secondary source but inside the lens. From this source as you also explained above, the rays will diverge and at the interface following snell's law and keeping in mind the index of refraction the two rays should converge in air.