3.6 Beam Splitting and Beam Steering
71
3.6 Beam Splitting and Beam Steering
Based on the zero-phase change property of a zero-index medium, two more useful applications can be beam splitting and beam steering [154–162]. Beam splitting
means dividing an incident beam into multiple parts, while beam steering means controlling the orientation of a beam and hence the direction propagation of power. The
zero-phase change and the normal emergence properties of a zero-index metamaterial facilitate both applications [163, 164]. We know that each face (or boundary)
of a zero-index slab acts as an independent source. Light entering through one face
emerges from all the remaining faces. Hence, by controlling the number of faces of
a ZIM slab, the number of emergent beams can be controlled, and by controlling the
area of the faces, the power of the beam can be controlled. If all output faces are of
equal area, multiple beams of equal power emerge from the ZIM slab. In other words,
the power of the input beam gets distributed equally among all the output beam. We
utilized this idea to create ZIM-based beam splitters, whose design schematics and
numerical results are shown in Fig. 3.13. We simulated two types of beam splitters—
a one-to-two splitter and a one-to-three splitter. The former splits the input beam into
two equal parts while the latter divides it into three equal parts.
Figure 3.13a shows the schematic of one-to-two splitter. Light propagating in a
silicon waveguide is fed into a zero-index right-angled isosceles prism from the
hypotenuse side and emerged from the two equal sides. The output radiation is
collected and measured at port 2 and port 3. Figure 3.13b shows the schematic of the
one-to-three splitter, in which light was fed from port 1, propagated toward the ZIM
cube, and emerged from the remaining three sides as shown. The emerged beams
were collected and measured at the three output ports, i.e., port 2, port 3, and port 4.
The output power at the output ports has been mentioned in Table 3.1 for both the
types of beam splitter. In both the designs, the output beams have equal distribution
of power, which is favorable for on-chip employment in photonic integration. In the
case of the one-to-three splitter, the power at port 3 is minutely greater than that at
port 2 and port 4 because of a minute bending loss for the latter two ports.
Next, we demonstrate the phenomenon of beam steering based on the same two
properties of zero phase change and normal emergence. By employing a zero-index
medium, there can be two routes of achieving the beam-steering capability. One
is by using a zero-index prism and manipulating its geometry, and the other is by
using a zero-index slab and varying its permittivity. Both the schemes have been
shown in Fig.3.14. The first method involves the use of a zero-index right-angled
prism, whose base angle A is varied from 0
o to 45
o . The variation of A results in
the change in the slope of the hypotenuse, which further results in the change in
the orientation of the normally emerging beam. The input, in this case, is fed from
the bottom boundary of the ZIM prism. The second method involves a slab, whose
refractive index changes from 0.001 to 1.0. The variation of the refractive index
changes the angle of refraction of the emergent beam. The input, in the second case,
is fed from the left-hand side boundary of the ZIM. In both the designs, the regions
above and below the ZIM are air, and the upper air regions have been backed by
71
3.6 Beam Splitting and Beam Steering
Based on the zero-phase change property of a zero-index medium, two more useful applications can be beam splitting and beam steering [154–162]. Beam splitting
means dividing an incident beam into multiple parts, while beam steering means controlling the orientation of a beam and hence the direction propagation of power. The
zero-phase change and the normal emergence properties of a zero-index metamaterial facilitate both applications [163, 164]. We know that each face (or boundary)
of a zero-index slab acts as an independent source. Light entering through one face
emerges from all the remaining faces. Hence, by controlling the number of faces of
a ZIM slab, the number of emergent beams can be controlled, and by controlling the
area of the faces, the power of the beam can be controlled. If all output faces are of
equal area, multiple beams of equal power emerge from the ZIM slab. In other words,
the power of the input beam gets distributed equally among all the output beam. We
utilized this idea to create ZIM-based beam splitters, whose design schematics and
numerical results are shown in Fig. 3.13. We simulated two types of beam splitters—
a one-to-two splitter and a one-to-three splitter. The former splits the input beam into
two equal parts while the latter divides it into three equal parts.
Figure 3.13a shows the schematic of one-to-two splitter. Light propagating in a
silicon waveguide is fed into a zero-index right-angled isosceles prism from the
hypotenuse side and emerged from the two equal sides. The output radiation is
collected and measured at port 2 and port 3. Figure 3.13b shows the schematic of the
one-to-three splitter, in which light was fed from port 1, propagated toward the ZIM
cube, and emerged from the remaining three sides as shown. The emerged beams
were collected and measured at the three output ports, i.e., port 2, port 3, and port 4.
The output power at the output ports has been mentioned in Table 3.1 for both the
types of beam splitter. In both the designs, the output beams have equal distribution
of power, which is favorable for on-chip employment in photonic integration. In the
case of the one-to-three splitter, the power at port 3 is minutely greater than that at
port 2 and port 4 because of a minute bending loss for the latter two ports.
Next, we demonstrate the phenomenon of beam steering based on the same two
properties of zero phase change and normal emergence. By employing a zero-index
medium, there can be two routes of achieving the beam-steering capability. One
is by using a zero-index prism and manipulating its geometry, and the other is by
using a zero-index slab and varying its permittivity. Both the schemes have been
shown in Fig.3.14. The first method involves the use of a zero-index right-angled
prism, whose base angle A is varied from 0
o to 45
o . The variation of A results in
the change in the slope of the hypotenuse, which further results in the change in
the orientation of the normally emerging beam. The input, in this case, is fed from
the bottom boundary of the ZIM prism. The second method involves a slab, whose
refractive index changes from 0.001 to 1.0. The variation of the refractive index
changes the angle of refraction of the emergent beam. The input, in the second case,
is fed from the left-hand side boundary of the ZIM. In both the designs, the regions
above and below the ZIM are air, and the upper air regions have been backed by