**1. Introduction**

Terahertz (THz) electromagnetic waves ranging from 0.1 THz to 10 THz have been investigated in numerous applications including imaging, spectroscopy, environmental surveillance, remote sensing, high-resolution radars and high-speed communications [1–4]. With the advancement in THz sources and detectors, these investigations have gained grea<sup>t</sup> interest from researchers. Polarization manipulators, in their applications to rotate or convert polarization states of electromagnetic waves, have been comprehensively explored for stealth, cloaking and in diode-like applications [5–8]. Circular polarization is a preferred choice for THz wireless communication due to its lower sensitivity towards multipath fading and polarization mismatch with receiver mobility.

Dual-band circular polarized waves are required in any satellite communication for the uplink (U/L) and downlink (D/L) operational bands. The handedness for U/L and D/L operations needs to be opposite to offer adequate polarization diversity. A generic solution for this is to use a linearly polarized antenna in cascade with orthomode transducer (OMT) as a feeder to a transmit-array or reflector. This solution is quite complicated, bulky and expensive. Another solution is to use phased array dual-band patch antennas. Both of these solutions are not feasible at THz frequencies. There is another possibility to obtain dual-band dual polarizations, i.e., using a linearly polarized wave generated by a linearly polarized antenna in cascade with dual-band linear polarization to circular polarization (LP-to-CP) converters. This solution is advantageous in terms of size and complexity. In addition, dual-band operation for LP-to-CP can be used to merge multiple systems for cost and volume reduction.

In the past, birefringent structures have been used to convert one state or type of polarization into another, including waveplates [9–11], liquid crystals [12–14], and wood and paper [15,16]. However, these solutions are bulky and complicated to integrate with existing THz systems. Metamaterials, chiral metamaterials and quasi-periodic planar arrays of sub-wavelength elements have attracted many researchers because of their distinguished properties, such as asymmetric transmission and polarization conversion with tenability and flexibility [17–19]. Metasurfaces, as the 2D equivalent of metamaterials, have been explored for the possibility of polarization manipulation, including linear to circular polarization conversion [20–22]. Particularly, they have been explored for single band linear to circular polarization conversion capability [20,23–27]. Wideband linear to circular polarization conversion operation has been explored using reflection and transmission modes [23–27]. Controlling electromagnetic fields, termed 'wave engineering', has been explored using metasurfaces [28–32]. Hadad et al. [28] proposed transverse temporal gradient-based metasurfaces for efficient transmission that is otherwise difficult using thin layered metasurfaces. Taravati et al. [29] proposed an advanced wave engineering technique based on unidirectional frequency generation and spatial decomposition in space–time-modulated slabs. Taravati et al. [30] realized an extraordinary beam splitter with one-way beam splitting-amplification. The proposed technique offers high isolation, transmission gain and zero beam tilting. Shi et al. [31] proposed a nonreciprocal metasurface that can achieve optical circulation and isolation. Wang et al. [32] proposed a technique for nonreciprocal wavefront engineering using time-modulated gradient metasurfaces. The essential building block of these surfaces is a subwavelength unit-cell whose reflection coefficient oscillates at low frequency. Such devices have been demonstrated theoretically [28–31] or experimentally [32] in an excellent manner for a wide range of applications, including cloaking, camouflage, amplifiers, isolators, duplexer antenna systems and mixers. However, there has been a lack of devices with incident normal polarization with transmitted circularly polarized waves using metasurfaces. Such devices are required in systems where transmitted waves and incident waves need to be aligned. These systems are predominantly used in THz wireless communication systems, including satellite communication. Such devices fabricated on flexible substrates can be integrated with linearly polarized wide-band THz antennas to have a dual wide-band outgoing transmitted wave with opposite handedness.

For dual-band LP-to-CP operation, there can be two possibilities: one is to use a wideband LP-to-CP converter so as to cover both required frequency bands. This is usually very difficult as it will practically increase the operational bandwidth for LP-to-CP operation. In the literature, a fractional bandwidth greater than 40% using transmissive metasurfaces has not been quoted so far. Moreover, no work has been reported to claim dual polarization in the same frequency band so as to cover applications requiring polarization diversity. The other possibility is to design a dual-band LP-to-CP converter that works over two different frequency bands with outgoing circular polarizations having opposite handedness in two bands.

Dual-band polarization manipulators including cross polarization converters [33,34] and LP-to-CP [35–39] converters have been proposed in the past. Liu [34] et al. and Xiaojun Huang et al. [35] reported metasurfaces based dual-band polarization converters for outgoing cross polarization. Recently reported dual band LP-to-CP polarization converters in microwave and THz bands are either complex or based on reflection type frequency selective surfaces [36–40]. Moreover, the operating bandwidths for the two bands are not wide. For example, Qingyun et al. [36] reported dual-band transmission type LP-to-CP converter based on frequency selective surfaces. Qingyun et al. [36] used four metallic layers to obtain 31.6% and 13.8% fractional bandwidths in C and Ku bands, respectively. The proposed structure's first and fourth metal layers consist of a split ring resonator bisected by a metallic strip; second and third metallic layers consist of a rectangular patch surrounded by a rectangular ring. Parinaz et al. [37] presented the design of dual-band LP-to-CP using transmissive metasurfaces whose unit cell is composed of three metallic layers. The first and third layers consist of a metallic patch enclosed in a split ring resonator, whereas the second layer consists of a circle-eliminated square patch with a central rectangular metallic strip. In other research, 3 dB fractional bandwidths of about 5% and 8% for dual-bands in the Ka band have been achieved [37]. Wang et al. [38] presented a dual-band LP-to-CP converter using Jerusalem cross and "I" dipole patterned frequency selective surfaces. Dual-band operation has been achieved for 29% and 12% fractional bandwidths. Youn et al. [39] reported a multilayered radial-shaped resonator-based dual-band LP-to-CP in the Ka band and achieved 14.4% and 4% fractional bandwidths. The only work reported of a THz dual-band LP-to-CP [40] discusses a reflection-based double-layered structure with the bottom layer used as gold reflectors. Such devices achieve a wide band of operation but tend to block and interfere with feeding elements such as linearly polarized arrays. The transmission-based dual-wide-band LP-to-CP converter based on a simple configuration is still a challenging problem.

In this paper, a novel dual-wide-band dual polarized LP-to-CP THz converter consisting of bi-layered transmissive metasurfaces has been presented. The proposed structure is novel, as it achieves dual-band widest transmission-based LP-to-CP operation with fractional bandwidths of 34% and 29% for the two bands in THz. Also, the structure consists of bi-layered metasurfaces. Dual-band operation is realized due to the excitation of two Eigenmodes generating phase delays. The position of frequency bands can be tuned by tuning the dimensions of square patches.

This paper is organized as follows: Section 2 of this paper describes the design of the proposed dual-wide-band LP-to-CP converter. Section 3 is about simulation and analysis of the dual-band LP-to-CP converter, and the principle of operation is described in Section 4. Physical mechanisms and equivalent circuit analyses are explained in Section 5. The impact of di fferent structural parameters on the performance of the dual-band LP-to-CP converter is discussed in Section 6. The conclusion is presented in Section 7.
