52
2 Zero-Index Metamaterials
(a)
1.4
1.5
1.6
1.7
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Wavelength ( μm)
Effective refractive index
(b)
(c)
Fig. 2.25 Design and principle of phase-free propagation
waves of the same frequency traveling in opposite direction superimpose on each
other. The energy distribution of a standing wave is such that particular points in the
medium always remain at rest or vibrate the least, called the nodes, while certain
others experience maximum displacement or vibration, called the antinodes. The
vibration at the nodes can be reduced to zero if the two interfering waves are of
equal amplitude. In a waveguide of zero refractive index, the effective wavelength
must be infinite and the nodes must disappear since separation between them also
becomes infinite. The disappearance of nodes was observed by Reshef et al. during
their experiment and reported in their paper.
To numerically demonstrate the phase-free propagation, we used a similar zeroindex waveguide whose design is shown in Fig. 2.25a. The waveguide has been
designed to operate at 1550 nm (telecom wavelength) [11, 124–127]. A small strip
cut out from a zero-index metamaterial, highlighted by a green rectangle, has been
used as the waveguide here. The radius of air holes is r = 183 nm and the periodicity
of the holes is a = 581 nm. The effective refractive index of the metamaterial, as
a function of wavelength, has been shown in Fig. 2.25b. It can be observed that the
refractive index tends to zero around 1550 nm. It means that to the light of wavelength
1550 nm, the waveguide should offer zero refractive index and facilitate a phase-free
propagation.
To generate a standing wave in the waveguide, two waves of the same freespace wavelength and amplitude were fed into the two ends. As the two antiparallel
waves superimpose, a standing wave (shown in Fig. 2.25c) is generated with nodal
and antinodal regions. It is a known fact that distance between two adjacent nodes
2 Zero-Index Metamaterials
(a)
1.4
1.5
1.6
1.7
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Wavelength ( μm)
Effective refractive index
(b)
(c)
Fig. 2.25 Design and principle of phase-free propagation
waves of the same frequency traveling in opposite direction superimpose on each
other. The energy distribution of a standing wave is such that particular points in the
medium always remain at rest or vibrate the least, called the nodes, while certain
others experience maximum displacement or vibration, called the antinodes. The
vibration at the nodes can be reduced to zero if the two interfering waves are of
equal amplitude. In a waveguide of zero refractive index, the effective wavelength
must be infinite and the nodes must disappear since separation between them also
becomes infinite. The disappearance of nodes was observed by Reshef et al. during
their experiment and reported in their paper.
To numerically demonstrate the phase-free propagation, we used a similar zeroindex waveguide whose design is shown in Fig. 2.25a. The waveguide has been
designed to operate at 1550 nm (telecom wavelength) [11, 124–127]. A small strip
cut out from a zero-index metamaterial, highlighted by a green rectangle, has been
used as the waveguide here. The radius of air holes is r = 183 nm and the periodicity
of the holes is a = 581 nm. The effective refractive index of the metamaterial, as
a function of wavelength, has been shown in Fig. 2.25b. It can be observed that the
refractive index tends to zero around 1550 nm. It means that to the light of wavelength
1550 nm, the waveguide should offer zero refractive index and facilitate a phase-free
propagation.
To generate a standing wave in the waveguide, two waves of the same freespace wavelength and amplitude were fed into the two ends. As the two antiparallel
waves superimpose, a standing wave (shown in Fig. 2.25c) is generated with nodal
and antinodal regions. It is a known fact that distance between two adjacent nodes