Metamaterials n=μrεr\rightarrow n = - \sqrt{μ_r ε_r}

The optical properties of a medium are governed by the relative permitivity (εr)(ε_r) and relative permeability (μr)μ_r). The refractive index is defined as μrεr=n\sqrt{μ_rε_r} = n. For ordinary material εr>0ε_r > 0 and μr>0μ_r > 0 and the positive sign is taken for the square root.

In 1964, a Russian scientist V. Veselago postulated the existence of material with εr<0ε_r < 0 and μr<0μ_r < 0. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied.

For such materials n=μrεrn = - \sqrt{μ_r ε_r} . As light enters a medium of such refractive index, the phases travel away from the direction of propagation.

(i) According to the description above show that if rays of light enter such a medium from air (refractive index =1) at an angle θθ in 2nd2nd quadrant, then the refracted beam is in the 3rd3rd quadrant.

(ii) Prove that Snell’s law holds for such a medium.

(i)(i) Suppose the postulate is true, then two parallel rays would proceed as shown in Figure. Assuming EDED shows a wave front then all points on this must have the same phase. All points with the same optical path length must have the same phase.

Thus εrμrAE=BCεrμrCD- \sqrt{ε_rμ_r} AE = BC -\sqrt{ε_rμ_r}CD or BC=εrμr(CDAE) BC = \sqrt{ε_rμ_r}(CD - AE)

BC>0,CD>AE\rightarrow BC > 0, CD > AE

As showing that the postulate is reasonable. If however, the light proceeded in the sense it does for ordinary material (viz. in the fourth quadrant, Fig. 2)

Then εrμrAE=BCεrμrCD- \sqrt{ε_rμ_r} AE = BC -\sqrt{ε_rμ_r}CD or BC=εrμr(CDAE) BC = \sqrt{ε_rμ_r}(CD - AE)

As AE>CD,BC<OAE > CD, BC < O, showing that this is not possible. Hence the postulate is correct.

(ii)(ii) Prove yourself. ¨\ddot \smile

Note by Nishant Rai
4 years, 4 months ago

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Try these - Easy if you know about Metamaterials!

Easy if you know about Meta-materials -2!

Nishant Rai - 4 years, 4 months ago

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a comprehension based on this was asked in JEEJEE

Tanishq Varshney - 4 years, 4 months ago

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