Enhancement of Phase-Shifting Nonreciprocity in Metamate-rial Lines Loaded with Comb-Shaped Stubs Supporting Slow Wave Propagation of Edge Guided Modes

Abstract

Nonreciprocal metamaterials have been investigated to discover new electromagnetic phenomena and to invent state-of-THe-art functional circuits and antennas [1], [2]. By using nonreciprocal metamaterials, we can have unidirectional wavenumber vectors along the wave-guiding structures regardless of the propagation directions. Transmission-line resonators based on such noneciprocal metamaterials show unique characteristics in that the resonance frequency is independent of the resonators’ size and that the field profiles have uniform magnitude and linearly-varying phase distribution, referred to as pseudo-traveling-wave resonators [3]. In addition, phase gradient of the fields along the resonators can be arbitrarily varied by changing the nonreciprocity of the lines under the resonant condition, which is implemented to highly-efficient beam scanning leaky wave antennas [4], and to polarization-switchable circularly polarized antennas. However, most of phase-shifting nonreciprocal metamaterials have resulted in relatively small magnitude of nonreciprocity even with considerably large applied dc magnetic field with the help of strong permanent magnets or huge size of electromagnets, which limit the availability and applications to beam steering antennas for practical use. In order to make the steering beam angle wider for antenna applications or to reduce the magnitude of the dc magnetic field, enhanced nonreciprocity is essential. Recently, the phase-shifting nonreciprocity for the normally magnetized ferrite-based metamaterials was analytically formulated showing that this phenomenon is described by a product of two factors; the one corresponds to off-diagonal component in Polder permeability tensor determining gyro-magnetic characteristics. Another factor is the geometrical asymmetry which is realized by periodically and asymmetrically inserting stubs into the normally magnetized ferrite rod-embedded microstrip lines at the center [5], [6]. So far, shunt stubs periodically inserted in previous metamaterials were constructed on the non-magnetic dielectric substrates to avoid the influence of dc magnetic field on the stub performance. However, capacitive stubs constructed on the dielectric substrate suffer from the coupling between adjacent stubs and cause degradation of enhanced phase-shifting nonreciprocity. In this paper, we propose a new enhancement technique for the phase-shifting nonreciprocity in metamaterial lines loaded with comb-shaped periodic open stubs constructed on the normally magnetized ferrite substrate at one side of strip edges, as shown in Fig 1. In the configuration, the edge guided mode [7] is excited that caused zigzag propagation along each stub. This mechanism corresponds to longer distance for one propagation direction. This situation is realized by reducing the coupling between adjacent stubs. At the other side of strip edges, inductive stubs are periodically inserted to realize negative effective permittivity and to reduce the propagation distance in the opposite direction of propagation. Combination of capacitive and inductive stub insertion results in enhanced nonreciprocity. Polycrystalline Yttrium Iron Garnet was employed as the ferrite material. The configuration parameters for the prototype circuit are as follows; thicknesses of the ferrite and dielectric substrates are both 0.8 mm, dielectric constants of ferrite and dielectric substrates are 15 and 2.6, respectively. The width of the center strip is 2 mm. The length and width of capacitive stubs are 2 mm and 0.8 mm, respectively. The unit cell length is 1.9 mm. In Fig. 2, the simulated and measured phase shifting nonreciprocity Δβ are extracted from the S-parameters for five unit cells and plotted as a function of the operating frequency and externally applied dc magnetic fields. It is found from Fig. 2 that experimental results agree well with numerical simulation results. It is noted that the beam sweep of ±15 degrees in the present configuration corresponds to the nonreciprocity for the external dc magnetic field of ±26 mT only which is about a quarter compared to the typical value of 100 mT required for previous nonreciprocal metamaterials. Thus, reduction of the applied dc magnetic field required for the nonreciprocity will open up realization of tunable nonreciprocity of metamaterials and beam steering antennas for practical use.