Temporal Coupled-mode Theory Research Articles

Hysteretic optomagnetic bistability based on the plasmon-induced inverse Faraday effect in magnetoplasmonic disk resonators

We investigate the inverse Faraday effect (IFE) by surface plasmon traveling modes in an ultracompact magnetoplasmonic disk resonator side-coupled to a plasmonic waveguide. The magnetic field by the IFE reacts to the traveling modes and leads to a nonlinear shift of the resonance in the disk resonator. Describing those nonlinear phenomena analytically by using the temporal coupled mode theory and the Lorentz reciprocity theorem, we propose a conception of hysteretic optomagnetic bistability that the system has two stable states of optically induced magnetic field to switch on and off, depending upon the history of the incident optical power. The numerical simulations agree well with the analytical prediction. The proposed conception may find potential applications in all-optical magnetic recording and switching with nanometer resolution.

Coupled-mode theory for plasmonic resonators integrated with silicon waveguides towards mid-infrared spectroscopic sensing.

Advances in mid-IR lasers, detectors, and nanofabrication technology have enabled new device architectures to implement on-chip sensing applications. In particular, direct integration of plasmonic resonators with a dielectric waveguide can generate an ultra-compact device architecture for biochemical sensing via surface-enhanced infrared absorption (SEIRA) spectroscopy. A theoretical investigation of such a hybrid architecture is imperative for its optimization. In this work, we investigate the coupling mechanism between a plasmonic resonator array and a waveguide using temporal coupled-mode theory and numerical simulation. The results conclude that the waveguide transmission extinction ratio reaches maxima when the resonator-waveguide coupling rate is maximal. Moreover, after introducing a model analyte in the form of an oscillator coupled with the plasmonics-waveguide system, the transmission curve with analyte absorption can be fitted successfully. We conclude that the extracted sensing signal can be maximized when analyte absorption frequency is the same as the transmission minima, which is different from the plasmonic resonance frequency. This conclusion is in contrast to the dielectric resonator scenario and provides an important guideline for design optimization and sensitivity improvement of future devices.

Surface plasmon induced transparency in coupled microcavities assisted by slits

The coupled waveguide-microcavity structure has a wide range of applications in optical filters and optical modulators. The optical transmission properties of structure are mostly determined by the coupling strength of the modes. In the conventional waveguide-microcavity structure, the mode coupling is finished by the form of evanescent field, which is usually achieved by controlling the geometric spacing between waveguide and microcavity. Surface plasmon polaritons are the excitations of the electromagnetic waves coupled to collective oscillations of free electrons in metal. Since the electromagnetic waves are attenuated sharply in the metal, this requires precise control of the spacing between the waveguide and the metal microcavity, and poses a great challenge for controlling the coupling of modes in the metal waveguide-cavity structure. In this paper, we proposed a scheme of using a metal-dielectric-metal waveguide side coupling metal microcavities to overcome this limit. Based on the resonant characteristics of the Fabry–Pérot mode in the metal microcavity, a slit is introduced to connect the waveguide and microcavities. By adjusting the width and the offset location of slits, the leakage rate and coupling strength of the mode in metal microcavity can be controlled. The finite difference frequency domain (FDFD) method was used to numerically simulate the electromagnetic properties of structure. First, we have studied the transmission behaviors of surface plasmon polaritons in the system consisted by metal waveguide and single microcavity. As other microcavity is introduced to the structure and connected the original microcavity by slit, the electromagnetically induced transparency phenomena based on surface plasmon polaritons are demonstrated in the coupled metal waveguide and double microcavities structure. As the width of slit connected the microcavity is increased, the transmission peak of structure and the full width at half maximum of the transparency window also increase accordingly. The change of the geometric parameters of slit will modulate the resonance characteristics of structure, and the corresponding physical mechanism is explained by the temporal coupled mode theory. In our works, the metal waveguide and microcavities are coupled by the energy leakage of microcavities assisted by slits, which breaks the limit of separation distance between metal waveguide and microcavity, and contributes to the manufacture of devices. The results of the paper will have applications in designing the compact photonic devices based on surface plasmon polaritons.

Theoretical Investigation on Microcavity Coupler for Terahertz Quantum-Well Infrared Photodetectors

Resonant behaviors and absorption enhancement of metallic grating-dielectric-metal (GDM) microcavity are theoretically investigated. The GDM structure is treated as periodic unit cells of two serially-connected metal-dielectric-metal (MDM) and air-dielectric-metal (ADM) waveguide resonators. The resonant modes can be divided into three types: the LC mode, the TEM modes supported by the MDM waveguide resonator, and the TEM-TM hybrid modes supported by the whole GDM structure. The resonant frequencies of LC and TEM modes are independent on a small incident oblique angle. However, for the TEM-TM hybrid modes, each mode splits into two branches with non-zero incident angles. Based on the temporal coupled-mode theory, the intersubband absorption efficiency of multi quantum wells inserted into the GDM microcavity is calculated and discussed qualitatively. We point out that the condition of critical coupling is not the optimal condition for intersubband absorption efficiency when the metallic loss cannot be neglected. An optimization procedure is given for the design of high performance GDM-microcavity-coupled terahertz quantum-well infrared photodetectors.

Phase-induced Fano antiresonance in a planar waveguide with two dielectric ridges

The resonant optical phenomena associated with the physics of Fano resonances have received particular attention due to their numerous potential applications. In this work, the Fano resonance behaviors of a planar waveguide with two dielectric ridges have been theoretically studied. By using the temporal coupled-mode theory, a general formula was obtained for describing the Fano response of a structure, and general conclusions for the determination of the resonance parameters were drawn. A special type of Fano resonance (i.e., Fano antiresonance) was demonstrated by tuning the resonance parameters. Different from the results by using two effective coupling oscillators, two kinds of Fano antiresonance phenomena were found. We showed that the Fano antiresonance effects of a structure can suppress the transmission of the guided mode and contribute to different field localization behaviors in the ridges due to the different interference effects. By obviating the need for a near-field interaction, the Fano antiresonance effects induced by phase coupling pave the way toward dynamic control of the spectral response and field localization behaviors in the integrated optoelectronic system.

Bound states in the continuum in double-hole array perforated in a layer of photonic crystal slab

We theoretically investigate optical bound states in the continuum (BIC) supported by a double-hole array. It verifies BICs around 0° can be observed only in the structure with symmetrical nanohole shape in one lattice. At arbitrary oblique incident angles, BIC with Q-factors exceeding 106 can be found in the double-hole arrays in both types, which are sensitive to the refractive index of the surrounding medium. Results from both finite-difference time-domain method and temporal coupled mode theory accord well, and they are helpful in the design of novel photonic elements based on BICs, such as sensors, and filters.

Polarization-based branch selection of bound states in the continuum in dielectric waveguide modes anti-crossed by a metal grating

We investigate bound states in the continuum (BICs) in a planar dielectric waveguide structure consisting of a gold grating on a dielectric layer with a back layer of metal. In this structure, Friedrich–Wintgen (FW) BICs caused by the destructive interference between the radiations from two waveguide modes appear near the anti-crossing point of the dispersion curves. In this study, it is revealed that the branch at which the BIC appears changes according to the polarization of the modes. Based on a temporal coupled mode theory, it is shown that the BIC branch is determined by the sign of the product of the coupling coefficients between the two waveguide modes and external radiation, which is consistent with FW theory. The signs of the coupling coefficients are estimated by the waveguide-mode decomposition of the numerically obtained electric fields and are confirmed to vary depending on the polarization.

Transparent conductive oxides for the epsilon-near-zero Tamm plasmon polaritons

We demonstrate the possibility of using transparent conducting oxides [aluminum-doped zinc oxide (AZO), gallium-doped zinc oxide (GZO), indium tin oxide (ITO)] to form Tamm plasmon polaritons in the near-infrared spectral range where the permittivity of oxides is near zero. The spectral properties of the structures are investigated in the framework of the temporal coupled-mode theory and confirmed by the transfer matrix method. It is found that in the critical coupling conditions, the maximal $ Q $Q-factor of a Tamm plasmon polariton is achieved when a photonic crystal is conjugated with the AZO film, while at the conjugation with the ITO films, the broadest spectral line is obtained. The sensitivity of the wavelength and spectral width of the Tamm plasmon polariton to changes in the oxide film thickness, bulk concentration of a dopant, and angle of incidence is demonstrated.

Simultaneous sensing of refractive index and temperature based on a three-cavity-coupling photonic crystal sensor.

Healthcare and biosensing have attracted wide attention worldwide, with the development of chip integration technology in recent decades. In terms of compact sensor design with high performance and high accuracy, photonic crystal structures based on Fano resonance offer superior solutions. Here, we design a photonic crystal structure for sensing applications by proposing modeling for a three-cavity-coupling system and derive the transmission expression based on temporal coupled-mode theory (TCMT). The correlations between the structural parameters and the transmission are discussed. Ultimately, the geometry, composed of an air mode cavity, a dielectric mode cavity and a cavity of wide linewidth, is proved to be feasible for simultaneous sensing of refractive index (RI) and temperature (T). For the air mode cavity, the RI and T sensitivities are 523 nm/RIU and 2.5 pm/K, respectively. For the dielectric mode cavity, the RI and T sensitivities are 145 nm/RIU and 60.0 pm/K, respectively. The total footprint of the geometry is only 14 × 2.6 (length × width) µm2. Moreover, the deviation ratios of the proposed sensor are approximately 0.6% and 0.4% for RI and T, respectively. Compared with the researches lately published, the sensor exhibits compact footprint and high accuracy. Therefore, we believe the proposed sensor will contribute to the future compact lab-on-chip detection system design.

A graphene-assisted all-pass filter for a tunable terahertz transmissive modulator with near-perfect absorption

We proposed an all-pass filter based perfect absorber scheme which also can function as a highly efficient transmissive modulator. We theoretically analyzed the proposed scheme using the temporal coupled mode theory and showed that near-perfect absorption could be achieved with practically modest deviation from the critical coupling condition. We also demonstrated the feasibility of the proposed scheme in a grating-based all-pass filter device with a variable loss implemented by two separate graphene layers, achieving an absorption of ~99.8% and a transmission modulation depth of ~70 dB in a terahertz frequency range. We also numerically investigated the tunability of the designed device.

Wave optics light-trapping theory: mathematical justification and ultimate limit on enhancement

This paper addresses a number of important and underlying theoretical and practical questions regarding the recently developed wave optics light-trapping theory for solar cells. We provide a rigorous and complete justification of its mathematical validity, using the second law of thermodynamics as well as fundamental properties of resonant scattering as described by the temporal coupled-mode theory. For maximal absorption, all optical modes supported by a solar cell structure must couple and only couple to the incident channel of sunlight radiation. For the first time to the best of our knowledge, we derive the ultimate limit of light trapping, which depends positively on the number of optical modes and hence on the periodicity of the structure. The ultimate limit is reached when every mode in the structure can couple only to the incident channel. Furthermore, we predict the theoretical optimal operating regimes of nanophotonic solar cells under practical scenarios. Our work reveals significant gaps between state-of-the-art nanophotonic solar cell designs and the ultimate limit, pointing to important future opportunities for nanophotonic light management for efficiency enhancement and cost reduction of solar cells.

Active control of EIT-like response in a symmetry-broken metasurface with orthogonal electric dipolar resonators

The active control of electromagnetic response in metamaterial and mutual coupling between resonant building blocks is of fundamental importance in realizing high-quality metamaterials. In this work, we propose and experimentally demonstrate the tunabilities of symmetry-broken metasurfaces made of orthogonal electric dipolar resonators. The metasurface with vertical and horizontal wires is integrated with a PIN diode for active control. It is found that the electromagnetically induced transparency (EIT)-like spectrum appears due to the destructive or constructive interferences between the two electric dipolar modes when the structural symmetry broken is introduced to the metasurface. Different from previous works on the EIT-like effect, there is only electric dipole response in our metasuface. The microscopic response of the metasurface is numerically calculated to illustrate the mode coupling between the orthogonal electric dipolar resonators. By applying temporal coupled-mode theory, the interaction between the electromagnetic wave and the symmetry-broken metasurface is described, and the characteristic parameters of the resonator system, which determine the electromagnetic response of the metasurface, are acquired.

Anapole: Its birth, life, and death.

Despite the recent extensive study of the nonradiating (anapole) mode in the resonant light scattering by nanoparticles, the key questions, about the dynamics of its excitation at the leading front of the incident pulse and collapse behind the trailing edge, still remain open. We answer the questions, first, by direct numerical integration of the complete set of the Maxwell equations, describing the scattering of a rectangular laser pulse by a dielectric cylinder. The simulation shows that while the excitation and the collapse periods, both have the same characteristic time-scale, the dynamics of these processes are qualitatively different. The relaxation to the steady-state scattering at the leading front is accompanied by high-amplitude oscillatory modulations of the envelope of the basic electromagnetic oscillations, while behind the trailing edge the decay of the envelope is monotonic. Then, we present the general arguments showing that this is the case for the anapole excited in any classical system. Next, we introduce a simple, exactly integrable yet accurate, physically transparent model describing the dynamics of the anapole. The model admits generalization to a broad class of resonant phenomena and may be regarded as a compliment to the commonly used Temporal Coupled-Mode Theory.

Tailoring Fano Resonance for Flat-Top Broadband Reflectors Based on Single Guided-Mode Resonance

We investigated on the interaction between a single guided-mode resonance and Fabry-Perot resonance (FPR) in a high contrast grating (HCG) from a viewpoint of Fano resonance. It has been found that the background reflection due to the FPR in the HCG is useful to implement flat-top broadband reflectors via tailoring the phase polarity of Fano resonance. The novel conceptual approach was elucidated theoretically with the temporal coupled-mode theory (TCMT), which was confirmed by the Si HCG broadband reflector design of 380-nm bandwidth for R > 99.9 from 1400 to 1780 nm (a fractional bandwidth of 24.5%). The TCMT model was in good agreement with the rigorous coupled wave analysis calculation. We believe that our approach provides expanded understanding on Fano resonance in a grating, enabling more intuitive and simpler design of a flat-top broadband reflector with grating structures.

Wideband and Narrowband Circuit Models for Fano-Shape Guided-Mode Resonance

In this paper, we propose two different types of circuit models for Fano-shape guided-mode resonance (GMR) in waveguide gratings. Both the models constitute a resonant tank circuit together with a direct non-resonant channel between the incident and scattered light. One neglects the frequency dependence of the direct non-resonant channel and is only more accurate in the immediate vicinity of the Fano-type resonance. The other accounts for the frequency dependence of the direct non-resonant channel and thus remains accurate within a wider range of frequencies. The former being referred to as the narrow-band model is extremely accurate, insofar as the isolated GMR is of interest within a narrow band spectrum. The latter being referred to as the wide-band model, on the other hand, is of interest when the GMR partly blends with the Fabry–Perot resonance supported by the direct channel between the incident and scattered light. An interesting case of low-frequency GMR is also reported, which can also be well captured by our circuit models. Having derived simple circuits for the physical phenomenon at hand, the concept of energy amplitude in the narrow-band circuit model is also introduced, and thus, the dynamics of the circuit is explained by differential equations that parallels the temporal coupled-mode theory for GMR in waveguide gratings. The proposed models are validated by using the rigorous coupled-wave analysis. These models may be useful in guiding the design of waveguide grating devices that make the use of GMR in various applications.

Fano Metamaterials on Nanopedestals for Plasmon-Enhanced Infrared Spectroscopy

We report a sensing platform for surface-enhanced infrared absorption (SEIRA) spectroscopy, based on Fano metamaterials (FMMs) on dielectric nanopedestals. FMMs consist of two parallel gold (Au) nanorod antennas, with a small horizontal coupler attached to one of the nanorod antenna. When placed on SiO2 dielectric nanopedestals, which exhibit strong field enhancements caused by the interference between subradiant and superradiant plasmonic resonances, they provide the highly enhanced E-field intensities formed near the Au nanoantenna, which can provide more enhanced molecular detection signals. Here, the sensing characteristics of FMMs on nanopedestals structure was confirmed by comparison with FMMs on an unetched SiO2 substrate as a control sample. The control FMMs and the FMMs on nanopedestals were carefully designed to excite Fano resonance near the target 1-octadecanethiol (ODT) fingerprint vibrations. The FMMs were fabricated by using nanoimprint lithography and the nanopedestal structures were formed by isotropic dry-etching. The experimental reflection spectra containing the enhanced absorption signals of the ODT monolayer molecules was analyzed using temporal coupled-mode theory. The FMMs on nanopedestals achieved over 7% of reflection difference signal, which was 1.7 times higher signal than the one from the control FMMs. Based on the FMMs on nanopedestal structures proposed in this study, it may be widely applied to future spectroscopy and sensor applications requiring ultrasensitive detection capability.

Optical Bound States in the Continuum with Nanowire Geometric Superlattices.

Perfect trapping of light in a subwavelength cavity is a key goal in nanophotonics. Perfect trapping has been realized with optical bound states in the continuum (BIC) in waveguide arrays and photonic crystals; yet the formal requirement of infinite periodicity has limited the experimental realization to structures with macroscopic planar dimensions. We characterize BICs in a silicon nanowire (NW) geometric superlattice (GSL) that exhibits one-dimensional periodicity in a compact cylindrical geometry with a subwavelength diameter. We analyze the scattering behavior of NW GSLs by formulating temporal coupled mode theory to include Lorenz-Mie scattering, and we show that GSL-based BICs can trap electromagnetic energy for an infinite lifetime and exist over a broad range of geometric parameters. Using synthesized NW GSLs tens of microns in length and with variable pitch, we demonstrate the progressive spectral shift and disappearance of Fano resonances in experimental single-NW extinction spectra as a manifestation of BIC GSL modes.

Thermally controllable Mie resonances in a water-based metamaterial

Active control of metamaterial properties is of great significance for designing miniaturized and versatile devices in practical engineering applications. Taking advantage of the highly temperature-dependent permittivity of water, we demonstrate a water-based metamaterial comprising water cubes with thermally tunable Mie resonances. The dynamic tunability of the water-based metamaterial was investigated via numerical simulations and experiments. A water cube exhibits both magnetic and electric response in the frequency range of interest. The magnetic response is primarily magnetic dipole resonance, while the electric response is a superposition of electric dipole resonance and a smooth Fabry–Pérot background. Using temporal coupled-mode theory (TCMT), the role of direct scattering is evaluated and the Mie resonance modes are analyzed. As the temperature of water cube varies from 20 °C to 80 °C, the magnetic and electric resonance frequencies exhibit obvious blue shifts of 0.10 and 0.14 GHz, respectively.

Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator Due to Stochastic Surface Roughness Scattering

We make use of a phase-sensitive set-up to study the light transmission through a coupled waveguide-microdisk system. We observe a splitting of the transmission resonance leading to an unbalanced doublet of dips. The experimental data are analyzed by using a phasor diagram that correlates the real and the imaginary parts of the complex transmission. In addition, detailed features are evidenced by a complex inverse representation of the data that maps ideal resonances into straight lines and split resonances into complicated curves. Modeling with finite element method simulations suggests that the splitting and the unbalance is caused by an induced chirality in the propagation of the optical fields in the microdisk due to the interplay between the stochastic roughness and the intermodal dissipative coupling, which yield an asymmetric behavior. An analytical model based on the temporal coupled mode theory shows that both a reactive and a dissipative coupling of the counter-propagating modes by the surface roughness of the ring resonator are required to quantitatively reproduce the experimental observations and the numerical simulations.

Connection of temporal coupled-mode-theory formalisms for a resonant optical system and its time-reversal conjugate

Temporal coupled-mode theory has been widely used to describe the physics of resonant optical systems. In general, an optical system can be constrained by energy conservation, time-reversal symmetry, and reciprocity. Most previous developments of temporal coupled-mode theory made use of all three constraints. In this paper, we consider separately the implication of each of these constraints on the parameters of temporal coupled-mode theory. For this purpose we made extensive use of the connection between a physical system and its time-reversal conjugate. This connection also indicates some of the nontrivial implications of the relation between the resonant properties of a physical system and its time-reversal conjugate. We validate these implications numerically by direct electromagnetic simulations of a guided resonance system. This work should enable the application of temporal coupled-mode theory to a wider range of resonant systems.