# Plasmonic Filter and Demultiplexer Based on Square Ring Resonator
## 1 Introduction  
Surface plasmon polaritons (SPPs) are an electromagnetic field transferred on a metal-dielectric interface and have been widely studied due to their ability to trap energy with high density and break the diffraction limit of light [1]. The metal-insulator-metal (MIM) waveguide, one of the basic plasmonic slot waveguides, not only has the capability of confining light within a considerate SPPs propagating length, but also meets the demands of highly integrated all-optical circuits with easy fabrication [2]. Traditional dielectric-based devices have relatively large dimensions which cannot be reduced when the diffraction limit is reached, and do not meet the requirements of future ultra-compact photonic integrated circuits (PICs) [1]. However, the MIM structure can provide a nanoscale optical path to overcome such a limit, and a device based on the MIM structure can manipulate light on the subwavelength scale, which will greatly reduce the size of the device [1]. As a trade-off, however, its intrinsic loss (ohmic loss) is significant [3]. Besides, compared with dielectric-based PICs, such a plasmonic system is able to work easily at near-infrared and visible wavelengths due to its relatively smaller footprint [3]. Therefore, MIM-based plasmonic devices will play an important role in future PICs. Recently, many kinds of plasmonic devices utilizing the MIM structure have been introduced, such as filter [4; 5; 6], demultiplexer [7; 8; 9], switch [10; 11; 12; 13], and sensor devices [14; 15; 16; 17; 18; 19].  
In the PIC, the ring resonator is not only an essential component to realize various filters with compact footprints, but it also offers multifunctionals such as wavelength selection, buffering, and switching [20]. However, it has been found to be difficult to apply a ring resonator with high efficiency in an MIM system due to the high ohmic loss and short coupling length [6]. Recently, an MIMsquare-ring resonator (SRR) was proposed by [PERSON] [21]. The SRR can be fabricated more easily than a ring resonator and possesses a longer coupling length. Various works based on the SRR have been reported to achieve aperture-coupled structure [22], band-stop filter [23; 24; 25], plasmon-induced transparency (absorption) [26; 27], and SPPs flow control [28]. However, few works focus on dropping the resonant wavelength in the SRR to realize a channel drop filter and demultiplexer, which are indispensable devices in PICs. [PERSON] proposed a side-coupled crossbeam SRR and the resonant wavelength can be downloaded [25], but the efficiency is low.  
Here, we numerically propose a plasmonic MIM band-stop filter with an SRR, as well as introduce a unique side-coupling method to drop the resonant wavelength with considerable efficiency and full width half maximum (FWHM). By introducing the reflector structure, the performance can be appreciably improved. The corresponding phenomenon can be theoretically analyzed by coupled mode theory (CMT). Besides, such a structure also has potential for optical sensing and switching. Finally, we realize a dual demultiplexer based on SRRs at telecommunication wavelengths with great performance. This work provides a simple scheme to integrate a ring resonator into a plasmonic system, which will promote the progress of all-optical ultra-compact networks.