Photonic Hall effect for a 1D-dimensional graphene-based photonic crystal with two defects

Highlights

• We proved the existence of two defect modes with different properties.

• We demonstrate that left and right handed defect modes exhibit a step-like transmission map.

• We show that the middle layers between two defects affect the lower-edge defect modes.

Abstract

The presence of two defect layers in a one-dimensional photonic crystal which could be described numerically by the transfer matrix model becomes important when two defects modes might be controlled by the number of the middle layers. In this work, we compute the transmission spectra of a 1D photonic crystal with two graphene-based defect layers in the presence of an applied constant magnetic field. It is observed that an additional defect mode shows up at the lower edge of the photonic bandgap of the optical structure which could to be tuned by the Fermi energy, the intensity of the magnetic field and also the number of the layers between the defects. In addition, we investigated the effect of decreasing the number of middle layers on the transmission spectra of the photonic device.

Introduction

Graphene is a flat monolayer of graphite with carbon atoms arranged in a honeycomb lattice. This 2D material was experimentally isolated for the first time in 2004, which could be employed in many electronic, optoelectronic and photonic applications [1], [2], [3], [4], [5]. However, already Wallace had investigated graphene theoretically, in 1947 [6]. Since 2005, graphene has attracted considerable interest due to its unique electronic properties including, Klein paradox, the high mobility at room the temperature and unconventional Quantum Hall Effect (QHE) [7], [8], [9]. Graphene also has shown outstanding optical properties in the presence of a strong constant magnetic field applied normally to its surface at low temperatures. In this situation, one can observe well-defined Landau energy levels due to the presence of a strong applied magnetic field which could lead to the observation of quantum Hall plateaus [10], [11], [12]. In addition, graphene is an ideal candidate in many fundamental research and applications in optics due to its unusual linear dispersion [12].

In optics, one of the most important features of graphene is its optical conductivity that is tuned by changing the Fermi energy and the intensity of the applied magnetic field [13]. This property provides a proper tool for graphene to be used in 1D photonic crystals (PCs) as an embedded material [14], [15], [16]. PCs are periodical structures with different refractive indices which could be designed in one, two and three dimensions [17], [18]. Upon periodicity-breaking, PCs show defect modes in the corresponding forbidden zone of frequencies controlled by extrinsic factors such as electric and magnetic fields and materials used for creating defects in their structure [19], [20], [21], [22], [23]. Moreover, one can consider an additional defect layer in this optical structure in order to enhance their photonic properties. In this regard, the study of a 1D photonic crystal with two defect layers covered by graphene in the QHE situation is worth attention.

The aim of the present work is to investigate the emergence of the defect modes in a 1D graphene-based photonic structure with two defect layers in the QHE regime. In terms of photonic crystals, embedded materials which can determine the main properties of these optical structures are very important. One of the most promising materials for embedding into photonic crystals has been proved to be graphene. It has simultaneously the properties of both metals and semiconductors so that graphene is also referred as to gapless semiconductor. Graphene also revealed peculiar properties such unconventional and room temperature Quantum Hall effect. Therefore, it is clear that transmission of light into graphene-based PCs under QHE regime for graphene might be of most interest.

This research includes several sections: In Section 2, we express the optical conductivity of graphene sheets by using of transfer matrix method for the propagation of light among layered structures with a defect layer that is surrounded by graphene sheets. We then, in Section 3, report the results of our numerical calculations. Finally, the conclusions are presented in Section 4.