Multimode Interference Coupled Mode Theory Research Articles

Multiple Fano resonances by MIM waveguide coupling whispering gallery mode resonator and application in Refractive index sensing

In this study, a baffled metal–insulator–metal (MIM) waveguide coupled with a whispering gallery mode resonator (WGMR) is proposed. This structure could excite quadruple Fano resonances. The asymmetric Fano resonance transmittance spectrum and the electric field at the resonance peak were numerically simulated using the finite difference time domain method. The obtained data were fitted using the multimode interference coupled mode theory. The number of Fano resonance peaks was tuned by the outer radius of the WGMR. With other geometric parameters unchanged, the number of Fano resonance peaks increased with increasing outer radius of the WGMR. Thus, it achieved multiple Fano resonances by adjusting solely the radius of the WGMR. When the ring width was fixed, the structure could excite multiple Fano resonances within a certain outer radius range. This structure was used for refractive index sensing and its sensitivity and figure of merit (FOM) were 3004 nm/RIU and 3.14 × 104 in a gas environment, respectively. Therefore, the proposed structure can excite multiple Fano resonances and achieve high sensitivity and FOM, providing a theoretical basis for micro and nano applications.

Refractive index sensor based on a D-shaped resonator and a stub resonator and its slow light characteristics

In this paper, a metal–insulator–metal waveguide structure is proposed based on a D-shaped resonator and a stub resonator, and it can generate multiple Fano resonances. The magnetic field (Z-direction) distribution and transmission spectrum of the structure are analyzed by the finite element method (FEM). The theory results are performed with the multimode interference coupled mode theory (MICMT), and they show high agreement with the simulation outcomes. The calculations also discuss the effect of structural parameters on the transmission spectrum. Moreover, the structure’s sensing characteristics are analyzed in detail, achieving a maximum sensitivity and FOM* of 1300 nm/RIU and 181.44, respectively. In addition, the slow light properties of the structure are also investigated, whose group delay and group index can reach 0.24 ps and 48.93, respectively. The group delay time is dynamically regulated by controlling the number of D-shaped resonators to achieve the effect of a delay line. It can provide some reference value for multifunctional on-chip optical integrated devices based on MIM waveguide structure.

A dual-purpose sensor with a sawtooth U-shaped cavity and a rectangle-shaped cavity in a MIM waveguide structure

To improve the performance of subwavelength refractive index and temperature sensors, this paper proposes a subwavelength metal-insulator-metal (MIM) waveguide structure consisting of a sawtooth U-shaped cavity and a rectangular cavity based on surface plasmon polaritons. The transmission spectrum of the system is simulated using the finite element method (FEM) and verified with multi-mode interference coupled-mode theory (MICMT). The results demonstrate excellent sensing characteristics for the system, with a refractive index sensitivity of 1300 nm RIU−1, a figure of merit (FOM*) of 191.262, and a temperature sensitivity of 0.525 nm/°C. This indicates that the nano-plasma system is highly significant in refractive index and temperature sensing.

Independently tunable refractive index sensor based on metal-insulator-metal waveguide with key-shaped resonator and application in human blood plasma detection

In this paper, a metal-insulator-metal waveguide structure based on a key-shaped resonator is proposed. Firstly, the structure is simulated using the finite difference in time domain (FDTD) method, revealing the generation of three resonant peaks. And the theoretical results are then analyzed using multimode interference coupled mode theory (MICMT), demonstrating a high level of agreement with the simulation results. Then the parameters of the structure are adjusted, so that the resonant peaks can be tuned independently. Notably, the structure exhibits a maximum sensitivity of 1520 nm RIU−1 with a figure of merit (FOM*) of 195.89, highlighting its exceptional sensing capabilities. Additionally, an analysis of the asymmetric structure reveals the emergence of a new Fano resonance. Due to its outstanding sensing performance, the structure holds potential for applications blood plasma concentration testing. Feasibility is assessed in terms of blood plasma concentration detection, achiveing a maximum sensitivity of 3.07 nm l g−1. As a result, this structure offers promising opportunities in the field of on-chip optical integration and the biomedical field, among others.

Dynamic control of Fano-like interference in the graphene periodic structure

We propose and investigate a graphene periodic subsurface structure consisting of a coplanar pair of graphene ring resonators and a graphene ribbon. The Fano-like interference can be actively regulated by the applied magnetic field, incident angle and Fermi energy. Since the excited charges of graphene monolayer have cyclotron properties in the external magnetic field, the transmittance and line-shape can be effectively controlled. At a certain frequency, different magnetic fields have different effects on the conductivity tensor of graphene, which affects the metallic properties of graphene, leading to changes in the transmittance. The Fano-like line-shape can be regulated by adjusting the incident angle to delay the phase between adjacent graphene sheets. In addition, the resonance frequency can be electrically regulated through Fermi energy. Finite element method is introduced to analyze the graphene periodic structure and the results are demonstrated by multimode interference coupled mode theory. The Faraday rotation angle exceeding 85° are observed in a small magnetic flux density B of about 0.5 T. Moreover, a plasma-optic switching with high ON/OFF ratio and large modulation depth (MD) is designed, whose ON/OFF ratio (η) and MD are 19.921 dB and 98.982%, respectively. Notably, combining the influence of magnetic flux density on transmittance and the modulation of resonance frequency by Fermi energy, optical switching can be implemented at any frequency within the frequency range studied. These results provide methods for active regulation of electromagnetic waves in the terahertz field and have potential applications in optical switching and integrated photonic circuit.

Surface Plasmon Polaritons Filter with Transmission Optimized Based on the Multimode Interference Coupled Mode Theory

Surface Plasmon Polaritons Filter with Transmission Optimized Based on the Multimode Interference Coupled Mode Theory

Metal–insulator–metal waveguide structure coupled with T-type and ring resonators for independent and tunable multiple Fano resonance and refractive index sensing

This study proposes a metal–insulator–metal (MIM) waveguide structure coupled with symmetric T-type resonators for exciting double Fano resonances. Furthermore, the proposed structure can generate an additional independent Fano resonance mode when one of the T-type resonators is replaced with a ring resonator. We employed the finite difference time domain method to simulate the transmission spectrum of the structure and the electric field distribution at resonant wavelengths. The formation mechanism of the Fano resonance is explained using the standing wave theory and multimode interference coupled mode theory. After studying the sensing characteristics of the designed structure, we achieved a maximum sensitivity of 1012 nm/RIU and a figure of merit of 5.57 × 104, which is higher than that of most of the structures reported recently. The proposed structure has broad application prospects in the field of nano sensing.

A compact four-peak MIM filter based on asymmetric distribution of resonators

We theoretically propose and numerically analyze a compact Metal-Insulator-Metal(MIM) filter based on an asymmetric structure which can produce four peaks in the spectrum. The filter can generate four transmission peaks while the maximum transmission coefficient of each peak is above 90%, and each transmission peak can be individually tuned by changing the coupling angle between the resonators and the waveguide. The structure consists of a pair of asymmetric cavities above and below the waveguide. By adjusting the coupling angle between the cavities and waveguide, each cavity can filter out light of a specific wavelength. The transmittance of the lowest transmission peak could be 3% and each transmission peak has a narrow frequency width. The quality factor (Q) of the resonances are 29.5, 42.9, 17.3 and 77.1, respectively. The sensitivities are 500nm/RIU, 588 nm/RIU, 659 nm/RIU and 827 nm/RIU. The FOMs are 26.3, 39.2, 15.3, 75.2. Multimode interference coupled-mode theory (MICMT) is used for numerical calculation and theoretical analysis. The structure is compact and easy to be fabricated and has potential applications in nano-optical communication.

Independently tunable dual resonant dip refractive index sensor based on metal–insulator–metal waveguide with Q-shaped resonant cavity

A plasmonic resonator system consisting of a metal–insulator–metal waveguide and a Q-shaped resonant cavity is proposed in this paper. The transmission properties of surface plasmon polaritons in this structure are investigated by using the finite difference in time domain (FDTD) method, and the simulation results contain two resonant dips. The physical mechanism is studied by the multimode interference coupled mode theory (MICMT), and the theoretical results are in highly consistent with the simulation results. Furthermore, the parameters of the Q-shaped cavity can be controlled to adjust the two dips, respectively. The refractive index sensor proposed in this paper, with a sensitivity of 1578 nm/RIU and figure of merit (FOM) of 175, performs better than most of the similar structures. Therefore, the results of the study are instructive for the design and application of high sensitivity nanoscale refractive index sensors.

Dynamically tunable refractive index sensor based on Fano resonance with metal-insulator-metal-graphene nanotube hybrid structure

In practical applications, the performances of conventional metal-insulator-metal (MIM) waveguide structured optical devices cured during fabrication are not dynamically tunable. In order to address the problem that such devices are not dynamically tunable, based on the excellent optoelectronic properties of graphene materials, graphene nanotubes are induced into the metal-insulator-metal waveguide coupled circular resonant cavity structure, thus designing a dynamically tunable MIM-graphene nanotube hybrid structure refractive index sensor in this work. The finite element method (FEM) is used to numerically study the transmission characteristics, electric field distribution and magnetic field distribution of the system, and the theoretical analysis is performed by multimode interference coupled mode theory (MICMT) to verify its correctness. The results show that after adding graphene nanotube to the MIM waveguide coupled ring resonant cavity structure, a Fano resonance peak appears in this system, which originates from the coherent coupling between the TM<sub>10</sub> cavity resonance mode and the graphene plasmonic electrical resonance mode. The sensor can dynamically tune the resonance wavelength and linewidth of Fano resonance in a wide wavelength range by changing the chemical potential of graphene, thus realizing the performance tuning of the refractive index sensor. Hence, the problem that the conventional plasma refractive index sensor is not dynamically tunable issolved. In addition, the influence of the geometrical parameters of the structure on the sensing performance of this system is also studied in detail. The sensor sensitivity increases up to 1250 nm/RIU and the quality factor rises up to 42.4 RIU<sup>–1</sup> at the optimal structural parameters. Compared with the traditional metal-insulator-metal waveguide structure design, this device has many merits such as wide operating band range, easy processing and dynamic tunability, which is a guideline for designing the dynamically tunable high performance nano-photonic integrated devices.

Transmission Optimization and Mode Increasing Effect of Filters Based on Lorentz-Type Multimode Interference Coupled Mode Theory

Transmission Optimization and Mode Increasing Effect of Filters Based on Lorentz-Type Multimode Interference Coupled Mode Theory

Multiple Fano resonances based on clockwork spring-shaped resonator for refractive index sensing

A surface plasmon polarized structure consisting of two metal-insulator-metal (MIM) waveguide coupled with clockwork spring-shaped resonators are constructed in this paper, and its geometric parameters are controlled within a few hundred nanometers. The finite element method (FEM) and multimode interference coupled mode theory (MICMT) are used to simulate and theoretically calculate the optical response of the designed structure. By modifying the structural parameters of the system, the influence on the asymmetry of the Fano resonance line is studied. The changes of the transmission spectra at different refractive indexes are also investigated. Based on this asymmetric resonant line, the sensitivity and FOM* (figure of merit) value of the cavity with different parameters are measured. The sensitivity and FOM* under the best parameters are 1200 nm RIU−1 and 191.6, respectively. The surface plasmon structure proposed and the results in this paper are promising for applications in the field of high-performance sensing and micro-nano optical devices.

Refractive index sensing based on multiple Fano resonances in a plasmonic defective ring-cavity system

A type of coupled plasmonic resonant system using a metal–insulator -metal (MIM) waveguide is proposed and investigated for generating multiple Fano resonances in this paper. The multi-mode interference coupled-mode theory (MICMT) is mainly employed to analyze the system theoretically, and these results agree well with the results numerically obtained with the finite-difference time-domain (FDTD) method. In this proposed system, multiple asymmetrical Fano-resonant peaks are achieved in the spectra by employing two waveguides separated by a metallic baffle and coupled with a defective ring cavity at one side of the MIM waveguide. According to standing wave theory, we can easily manipulate these Fano peaks by adjusting the main parameters of the defective ring cavity, such as the radius and the notch range. As a result, the structures with three and nine ultra-sharp Fano resonances are obtained and discussed, and the sensitivities and figures of merit (FOMs) are also represented. Furthermore, the phase shifts and the group delays that are induced by the mode interactions are investigated. The designed structures show great potential for the high integrated optical circuits of chip-scale optical sensors, slow light devices or splitters.

Tunable Fano resonance in plasmonic MIM waveguide with P-shaped resonator for refractive index sensing

Based on the transmission characteristic of surface plasmon polaritons (SPPs), a compact plasmonic system based on a sub-wavelength metal-insulator-metal (MIM) waveguide coupled with P-shaped cavity is proposed. The results show that double Fano resonance peaks are generated in the transmission spectra, which has been studied by the finite-element method (FEM). The transmission spectrum of the system is theoretically verified by the multimode interference coupled mode theory (MICMT) perfectly. In addition, the simulation results show that the position of the resonance peaks can be adjusted by changing the structural parameters. The sensing characteristics of the resonant cavity are also studied, and the refractive index sensitivity and the figure of merit (FOM) are 2100 nm /RIU and 189.97. The results effectively improve the sensitivity and FOM of nano-scale plasmonic sensors and provide significant guidance for the application of tunable multiple Fano resonance in refractive index sensors, biosensors, optical switches and other plasmonic devices.

A Plasmonic Refractive-Index Sensor Based Multiple Fano Resonance Multiplexing in Slot-Cavity Resonant System

In this paper, a sub-wavelength metal-insulator-metal (MIM) waveguide structure is proposed by using a cross-shape rectangular cavity, of which wings are coupled with two rectangular cavities. Firstly, a cross-shape rectangular cavity is placed between the input and output MIM waveguides. According to the mutual interference between bright and dark modes, three Fano resonant peaks are generated. Secondly, by adding a rectangular cavity on the left wing of the cross shaped one, five asymmetric Fano resonance peaks are obtained. Thirdly, six asymmetric Fano resonance peaks are achieved after adding another cavity on the right wing. Finally, the finite-difference-time-domain (FDTD) method and multimode interference coupled-mode theory (MICMT) are used to simulate and analyze the coupled plasmonic resonant system, respectively. The highest sensitivity of 1 000nm/RIU is achieved.

Multi-Fano resonances in MIM waveguides coupled with split annular cavity connected with rectangular resonator and application for multichannel refractive index sensor

A plasmonic structure, constituted by metal insulator metal waveguides and split annular cavity connected with rectangular resonator (SACRR), is proposed and investigated. Numerical simulation by the finite element method (FEM) has been done to investigate the transmittance properties of the proposed structure and four Fano resonances arise in the results. To analyze and verify the simulation results, multimode interference coupled mode theory is engaged, theoretically. In addition, the structural parameters are analyzed and discussed to design and control the proposed structure, which shows sufficient flexibility. Due to multi-Fano resonances providing multiple monitoring points and the extremely sharp asymmetry of Fano resonance, the structure can service as a high-performance multichannel refractive index nanosensor with a sensitivity of 1000 nm/RIU and maximum figure of merit of 1.358 × 105. The designed structure can surely meet extensive applications for nanoscale devices and integrated optical devices.

High Sensitivity Plasmonic Sensor Based on Fano Resonance with Inverted U-Shaped Resonator.

Herein, we propose a tunable plasmonic sensor with Fano resonators in an inverted U-shaped resonator. By manipulating the sharp asymmetric Fano resonance peaks, a high-sensitivity refractive index sensor can be realized. Using the multimode interference coupled-mode theory and the finite element method, we numerically simulate the influences of geometrical parameters on the plasmonic sensor. Optimizing the structure parameters, we can achieve a high plasmonic sensor with the maximum sensitivity for 840 nm/RIUand figure of merit for 3.9 × 105. The research results provide a reliable theoretical basis for designing high sensitivity to the next generation plasmonic nanosensor.

Sensor based on multiple Fano resonances in MIM waveguide resonator system with silver nanorod-defect

The triple Fano resonance via a plasmonic waveguide system which is composed of an isosceles-triangular resonator coupled with a nanorod-defect is presented. The Fano resonance originates from the narrow discrete resonances and the broad continuous state of the isosceles-triangular resonator and the nanorod-defect, respectively. Multimode interference coupled-mode theory (MICMT) and finite difference-time domain method (FDTD) are proposed to explain the triple Fano resonance. Results show that the Fano line shapes can be independently tuned by the geometrical parameters, such as the radius of nanorod-defect, the height or the base length of the isosceles-triangle resonator. The transmittance of the system can sharply decrease from peak to dip with wavelength shifts of only 8 nm for FR2. The sensitivity and FOM* (figure of merit) of the FR2 can be up to 1250nm/RIU and 88.68, respectively. In comparison to other similar sensors, the proposed plasmonic structure has relatively comparable sensitivity and FOM*, which may have application in slow light device, nanoscale filter, refractive index sensor and other related plasmonic devices.

Tunable sharp resonances based on multimode interference in a MIM-ring coupling plasmonic resonator system

An asymmetric plasmonic resonator system is composed of two metal-insulator-metal (MIM) waveguides and a ring resonator is proposed. And tunable sharp resonance based on multimode interference in MIM-ring coupling plasmonic resonator system is theoretically and numerically studied. The Fano resonance of the two different physical mechanisms in this paper is explained by using the multimode interference coupled mode theory (MICMT). Results obtained by the theory of MICMT are very well consistent with those from the finite element method (FEM) simulation. For an independent MIM-ring coupling plasmonic resonator system, its Fano resonance is formed by different resonance modes of the same ring resonator interfering with each other. Moreover, the theory of ring resonator explains the red shift which is attributable to the increase of the inner ring radius. For the rectangular and ring hybrid coupling plasmonic resonator system, the electromagnetic waves in the ring resonator and the rectangular resonator interfere with each other, which leads to the Fano resonance. We also studied the sensitivity (S) and figure of merit (FOM) of the rectangular and ring hybrid resonator system as a refractive index sensor up to 1350 nm /RIU and 1543, respectively, which has a certain reference value for the bio-chemical sensors, filters and modulator for large-scale photonic integration.

High figure of merit refractive index nanosensor based on Fano resonances in waveguide

Fano resonances based on circle-with-inner-core and stub structure are investigated using data derived from the finite element method and theoretically explained by the multimode interference coupled mode theory and the electric distribution in the system. The parameters of specific structure are modified to investigate the influence of different parts for this metal–insulator–metal system. Due to the high sensitivity to filled dielectric materials, the proposed structure can be applied as a refractive index sensor, whose performances are also explored. High sensitivity is gained as high as 1183.3 nm / RIU. And the figure of merit, a key parameter to describe the sensing characteristic, is achieved as 5.1115 × 104, which is better than most similar structures. Our work is significant for the sensitive refractive index nanosensor.