Using Huygens Multipole Arrays to Realize Unidirectional Needle-Like Radiation

For nearly a century, the concept of needle radiation has captured the attention of the electromagnetics communities in both physics and engineering, with various types of contributions reoccurring every decade. With the near-term needs for highly directive, electrically small radiators and scatterers for a variety of communications and sensor applications, superdirectivity has again become a topic of interest. While it is well known that superdirective solutions exist and suffer ill-posedness issues in principle, a detailed needle solution has not been reported previously. We demonstrate explicitly, for the first time, how needle radiation can be obtained theoretically from currents driven on an arbitrary spherical surface, and we explain why such a result can only be attained in practice with electrically large spheres. On the other hand, we also demonstrate, more practically, how broadside radiating Huygens source multipoles can be combined into an end-fire array configuration to achieve needle-like radiation performance without suffering the traditional problems that have previously plagued superdirectivity.

Popular Summary

The notion of superdirectivity—the possibility of radiating tightly confined fields into a certain direction—has intrigued physicists and engineers for nearly a century. Despite a significant body of research on the topic, the general consensus has been that sensitivity to imperfections and other practical issues render superdirectivity unattainable for real-world applications. However, recent reports of structures realizing anomalous scattering features produced by their geometrical and material properties signify rekindled interest in highly directive systems. Here, we derive an actual current distribution that can produce superdirective, needle-like electromagnetic radiation, and we use it to recover and explain several challenges associated with superdirectivity. By focusing on currents on a spherical surface, we provide insights as to why our theoretical result is not entirely feasible in practice.

We also introduce a metamaterial-inspired paradigm of superdirectivity enabled by an array of broadside-radiating Huygens (unidirectional) electric and magnetic multipole radiators. We use simulations of the array to authenticate the generation of superdirective-like radiation. This credible concept—which evolved from many recent successful realizations of highly subwavelength metamaterial-inspired radio-frequency and millimeter-wave Huygens dipole antennas, and related metamaterial, plasmonic, and all-dielectric-based terahertz and optical Huygens nanoantenna systems—represents a promising route toward practical superdirective radiation.

We expect that our technique, if implemented experimentally, will have an impact on fields as far ranging as microwave, millimeter-wave and optical remote sensing, imaging, communications, wireless power transfer, and directed energy systems.

Figure 1

Directivity pattern (dB) of the Huygens current needle radiation limited to $N$ modes.

Figure 2

Comparison of the maximum directivity of the needle radiation for the Huygens current and the electric-only current cases limited to $N$ modes.

Figure 3

Comparison of the ratio of the maximum directivity of the needle radiation for the Huygens current and the electric-only current cases, limited to $N$ modes, to the Harrington limit (2).

Figure 4

FWHM values of the directivity pattern of the Huygens current needle radiation limited to $N$ modes.

Figure 5

Needle radiation expansion coefficients for various electrical sizes of the sphere, $ka$, as functions of the number of azimuthally symmetric modes, $N$.

Figure 6

Assemblage of the broadside radiating multipoles.

Figure 7

End-fire array of the assembled broadside radiating multipoles.

Figure 8

Directivity pattern (dB) attained with $N$ Huygens multipoles arranged compactly along the $z$ axis.

Figure 9

Polar plot of the directivity produced by 1000 Huygens multipoles arranged compactly along the $z$ axis.

Figure 10

Maximum directivity (dB) attained with $N$ Huygens multipoles arranged compactly along the $z$ axis.

Figure 11

FWHM values of the power patterns generated by $N$ Huygens multipoles arranged compactly along the $z$ axis.

Figure 12

Comparison of the directivity patterns (dB) of the needle and the multipole antennas.

Figure 13

Needle radiation expansion coefficients for various electrical sizes of the sphere, $ka$, as functions of the number of azimuthally symmetric modes, $N$.

Figure 14

Dielectric resonator stack approach to realize the Huygens multipole array.

Figure 15

Two-dimensional version of a coated nanoparticle realization of the multipole effects.

Figure 16

NewFasant predicted 3D directivity pattern for the Huygens dipole ($N=0$) antenna.

Figure 17

NewFasant predicted 3D directivity pattern for the Huygens $N=2$ multipole antenna.

Figure 18

NewFasant predicted 3D directivity pattern for the Huygens multipole end-fire array, which combines the first six multipoles: $N=0$ to $N=5$.

Figure 19

Comparison of the analytically and numerically calculated directivities for the Huygens multipole end-fire array, including the dipole through the $N=5$ multipoles.