Dispersion Engineering of Nonreciprocal Composite Right/Left Handed Metamaterials Using Ferrite Materials in Microwave Region

Abstract

Metamaterials are artificial electromagnetic structures which are composed of smaller elements compared to the wavelength, referred to as unit cell, where macroscopic constitutive relation such as effective permittivity and permeability have been designed and controlled in order to manipulate electromagnetic wave propagation for various applications. Specifically, nonreciprocal metamaterials have been investigated to discover new electromagnetic phenomena and to invent state-of-the-art functional circuits and antennas. Nonreciprocity manifests itself as a result of a combination of two factors; the one is broken time reversal symmetry and another is broken space inversion symmetry. The former factor is realized by using gyrotropic materials such as ferrite in microwave region or magneto-optic media in optical region. For example, a microstrip line constructed on a normally magnetized ferrite substrate supports an edge guided mode [1] showing the field displacement effect in which the fields are asymmetrically concentrated at one of strip edges. The field concentration side can be switched by changing the directions of wave propagation or the externally applied dc magnetic field. In such cases, when stubs are asymmetrically inserted at the strip edges to provide geometrical asymmetry to the wave-guiding structure for broken space inverse symmetry, the propagating wave regards the line as different structures for two anti-parallel propagation directions, which results in nonreciprocal transmission. In the earlier work on nonreciprocal metamaterials, nonreciprocity appearing in the magnitude of transmission coefficients was studied for applications to isolators and circulators [2]. More recently, nonreciprocity appearing in the phase of transmission coefficients was focused on, from the metamaterial point of view [3], [4]. By using the phase-shifting nonreciprocal metamaterials, we can have fascinating situations where forward wave mode is dominant with positive refractive index in one propagation direction and backward wave mode is dominant with negative refractive index in the opposite direction at the same frequency. In the special cases, we can have field profiles with unidirectional wavenumber vectors along the wave-guiding structures regardless of the transmitted power directions. Such nonreciprocal metamaterials were implemented to transmission-line resonators providing 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 [5]. The phase gradient of the fields along the resonators can be arbitrarily varied by changing the nonreciprocity of the lines under the resonant condition. This tunable phase gradient along the resonant structures was implemented to highly-efficient beam scanning leaky wave antennas [6], and to polarization switchable circularly polarized antennas [7], [8]. Nonreciprocal metamaterials can provide potential solutions to improvement of performance in microwave circuits and antennas. For beam steering antennas based on nonreciprocal metamaterials, the beam angle is determined by magnitude of the nonreciprocity in the metamaterial lines. For circularly polarized antennas based on the nonreciprocal metamaterial rings, the phase shift for one circulation corresponds to 360 degrees. Therefore, the enhancement of nonreciprocal phase gradient along the metamaterial line leads to wider beam swing in the leaky wave antennas and miniaturization of the circularly polarized antennas. Recently, it was demonstrated that an appropriate combination of curvatures of lines and asymmetric insertion of stubs enhances the geometrical asymmetry of the line, resulting in the enhancement of the nonreciprocity [9]. Not only magnitude but also dispersion of phase-shifting nonreciprocity in metamaterials have been designed and controlled for improvement of microwave circuits and antennas. For example, beam scanning leaky wave antennas generally suffer from beam squint problem where the beam direction varies with the operational frequency. For the nonreciprocal metamaterial based beam scanning antennas, the beam squint originates from the frequency dependence of phase-shifting nonreciprocity. To eliminate the beam squint, metamaterials with dispersion-less nonreciprocity was proposed and demonstrated to show the phase-shifting nonreciprocity proportional to the operational frequency [10].