Proposal for a graphene nanoribbon assisted mid-infrared band-stop/band-pass filter based on Bragg gratings

Highlights

• Integrating the Bragg grating with a graphene nanoribbon (GNR) result to nanometer scale sizes.

• A tunable plasmonic band-stop/band-pass filter is realized using perfect and defected Bragg gratings, respectively.

• The Transmission spectrum of the proposed structure can be flexibility tuned through external potential adjustments.

Abstract

Application of Bragg gratings for mid-infrared requires a $\mu$m-scale area, while novel on-chip integrated circuits require nm-scale devices. Integrating the Bragg grating with a graphene nanoribbon (GNR), it is possible to scale down the Bragg grating overall footprint to nm-scale sizes and still benefit from their special abilities in light confinement to control mid-infrared transmissions. A band-stop and a narrow band-pass filter are realized using perfect and defected Bragg gratings, respectively. The experimentally feasible values such as doping level and electron relaxation time are implemented for this study to avoid the limiting factor of device performance. The findings of this report quantitatively demonstrate high performance of this plasmonic based GNR assisted device.

Introduction

Over the last two decades, collective surface charge density oscillations on conducting surfaces known as surface plasmons have been widely implemented for various applications such as sensing purposes [1], [2], [3]. These surface plasmons could resonate and propagate at the interface of conductor with an insulating material, when a propagating electromagnetic (EM) field is incident upon interface. This dynamic response of electron motion that occurs as resonances and propagations are widely used in plasmonic science to focus or steer the EM wave, which is usually accompanied with several orders of magnitude enhancement in the electric field intensity [4].

Nevertheless, conventional metallic materials and even noble metals that could possess a negative sign in their dielectric constant often at visible interval-extremely suffer from large Ohmic loss that could result in short surface plasmon propagation [5]. The case becomes worst when a low frequency plasmonic application is required where the sign of metals become positive and they can no more confine surface waves to their interface [6].

Recently, 2D materials and specially one-atom-thick graphene have shown a promising future for plasmonic applications that are required in the terahertz to mid-infrared part of the EM spectrum [7], [8]. Graphene plasmons show large field confinement capabilities, have long propagation distance due to low losses, and exhibit unique external tunability properties [9], [10]. The main reason for these extraordinary properties of graphene can be described by the linear dispersion relation of conduction and valence band of electronic states of graphene. This linear dispersion relation, which results in strong optical response variation in graphene is powerfully depending on the Fermi energy (${\mathit{E}}_f$) of graphene or equivalently, its doping level [11]. Surface plasmon resonance based plasmonic devices have appeared as promising tools in realizing miniature on-chip devices. Optical response dependency of graphene to its Fermi energy has marked its application as a very attractive tool to be used for devices like modulators [7], photodetectors [12], and frequency selective filters [13], [14].

Most of these fascinating applications of graphene mainly depend on the finite size geometry of graphene by which its zero band gap could break up [15]. Previously, refractive index based methods in graphene nanoribbon (GNR) type [16], [17] and graphene disks [18] have been shown to be useful for different sensing or switching purposes. One of the graphene assisted devices is able to detect minute amounts of gaseous quantities down to levels of 50 zeptomol/$\mathrm{\mu }$m² [17]. In [19] and [20], the authors have presented a periodic silicon grating coated with a graphene layer to propose a band-stop filter. By introducing a defect in the bulk silicon grating, a narrow band-pass filter appears within the band-stopped region. Moreover, it is shown in [21] that plasmonically induced transparency (PIT) can be achieved if two graphene layers are used with the condition that the upper layer is sinusoidally curved and the beneath layer is planar. Furthermore, it is possible to cover the surface of a GNR layer with a sinusoidally curved dielectric surface and form a perfect absorption device [22].

The common feature of these works is the application of field localizing properties of graphene material as accompanying medium for surface plasmon propagation. To effectively couple the external EM radiations to localized plasmon excitations, nanoribbon shape of graphene has proven to be useful [13]. Mid-infrared (MIR) EM waves with the wavelength of 3–$30\mathrm{\mu }\mathrm{m}$, having wide applications in the diverse field such as communications, spectroscopy, biomedicine, among the others, are the subject of research, nowadays [23]. Proposed device of the present paper benefits from the subwavelength confinement of the MIR-EM waves using GNRs, as a filter. In the MIR region, the wave vector of the plasmonic waves is larger than that of the incident light, which results in strong confinement of the wave. GNRs can confine the incident light in their edges and overcome the mismatch of the mentioned wave vector difference.

Bragg gratings, which are special kind of one dimensional photonic crystals, have already been intensively investigated [24]. Although the application of Bragg gratings for mid-infrared requires a $\mathrm{\mu }$m-scale area, novel on-chip integrated circuits require nm-scale devices. Assisting the Bragg grating with a GNR allows scaling down the Bragg grating to nanometric sizes on a subwavelength array of high and low dielectric materials and benefits from its unique ability in light confinement to control transmission spectrum, at room temperatures. In [25], a closely spaced pair of parallel graphene sheets that are separated by a uniform dielectric grating where studied which showed an extremely broadband band-stop filtering for the proposed device in the mid-infrared region. Also, a silicon-graded grating structure covered with single-layer graphene was studied in [26] that works in the 10–40 THz interval and was able to act as broadband spectrometer and optical switch. Moreover, in [27], [28] the authors have shown that a stop-band will form around the Bragg wavelengths of a plasmonic Bragg reflector (PBR) when a GNR covered silicon grating is used. They have publicized that by means of hosting a defect within the PBR, a resonance mode will emerge within the stop-band that could be used for various applications.

Graphene-based Bragg grating (GBG) is a subject of interest in recent researches [29], [30], [31], [32]. In [32], for instance, a GBG is used on the microfiber, which can be used in optical fiber communications, tunable filters, sensors, and lasers. However, in this work, the frequency selection capability of Bragg grating is assisted with a GNR plasmonic device to create a highly spectral selective optical filter. Theoretically, the GNR helps the Bragg grating filter to better confine the graphene plasmons with the desired wavelength and thus a finer selectivity could be achieved, which make it feasible to fabricate the device with the smaller footprint. Previous researches usually design the GBG in such way that the grating was introduced inside the silicon substrate [29], [30]. This may facilitate the fabrication process of the substrate, but the deposition of the GNRs cannot be easily implemented in such structures, while most of the structures used suspended GNRs which is difficult to actually be realized. In the proposed GBG device, the GNRs are embedded on the substrate, and the grating is considered to be placed on the top of the GNRs, which makes it feasible to be implemented from the fabrication point of view. The fabrication process may be alike that of the Ref. [33].