2.7 Decoupling of the Electric and Magnetic Fields in Zero-Index Medium
53
(a) 1400 nm
(b) 1475 nm
(c) 1550 nm
(d) 1625 nm
(e) 1700 nm
Fig. 2.26 Formation of standing waves of different wavelengths. The distance between the nodes
increased as zero-index wavelength is approached
is equal to half of the wavelength inside the medium, which itself depends on the
effective refractive index of the medium. Conclusively, the lesser the refractive index
of the medium, the longer the effective wavelength and more distant the nodes are.
To recreate the experimental results numerically, here we have used a rectangular
waveguide whose refractive index varies w.r.t. wavelength in the same manner, as
it is shown in Fig. 2.25b. On launching the waves of five different free-space wavelengths into the two ends of the waveguide, five types of standing wave patterns,
shown in Fig. 2.26a–e, have been obtained. The wavelength has been varied from
1400 to 1700 nm, and correspondingly the refractive index transits from positive to
negative values through a zero value at 1550 nm. In Fig. 2.26, the black regions in the
waveguide are the nodes, and the white regions are the antinodes. It can be observed
that as the refractive index decreases, the separation between the nodes increases.
The nodes of 1475 nm wave are more distant than the nodes of 1400 nm. The most
interesting one is the case of 1550 nm (Fig. 2.26c), where no nodes are present in the
waveguide since the effective refractive index has reduced to almost zero, and the
effective wavelength has become very large. It is necessary to scrutinize the color bar
in this case, because one may misinterpret the dark ends of the waveguide as nodes.
Please note that the minimum of the color bar of 1550 nm is 0.9634, unlike other
cases. It means that the magnitude of the field is 0.9643 at the two ends of the waveguide, which is a slight reduction than the maximum value “1” at the center, but not a
53
(a) 1400 nm
(b) 1475 nm
(c) 1550 nm
(d) 1625 nm
(e) 1700 nm
Fig. 2.26 Formation of standing waves of different wavelengths. The distance between the nodes
increased as zero-index wavelength is approached
is equal to half of the wavelength inside the medium, which itself depends on the
effective refractive index of the medium. Conclusively, the lesser the refractive index
of the medium, the longer the effective wavelength and more distant the nodes are.
To recreate the experimental results numerically, here we have used a rectangular
waveguide whose refractive index varies w.r.t. wavelength in the same manner, as
it is shown in Fig. 2.25b. On launching the waves of five different free-space wavelengths into the two ends of the waveguide, five types of standing wave patterns,
shown in Fig. 2.26a–e, have been obtained. The wavelength has been varied from
1400 to 1700 nm, and correspondingly the refractive index transits from positive to
negative values through a zero value at 1550 nm. In Fig. 2.26, the black regions in the
waveguide are the nodes, and the white regions are the antinodes. It can be observed
that as the refractive index decreases, the separation between the nodes increases.
The nodes of 1475 nm wave are more distant than the nodes of 1400 nm. The most
interesting one is the case of 1550 nm (Fig. 2.26c), where no nodes are present in the
waveguide since the effective refractive index has reduced to almost zero, and the
effective wavelength has become very large. It is necessary to scrutinize the color bar
in this case, because one may misinterpret the dark ends of the waveguide as nodes.
Please note that the minimum of the color bar of 1550 nm is 0.9634, unlike other
cases. It means that the magnitude of the field is 0.9643 at the two ends of the waveguide, which is a slight reduction than the maximum value “1” at the center, but not a