Temporal Coupled-mode Theory Research Articles

Quality factor of plasmonic monopartite and bipartite surface lattice resonances

Surface lattice resonance (SLR) is the collective excitation of nanoparticle resonances arising from the hybridization between localized surface plasmons (LSPs) and propagating Rayleigh anomalies (RAs). When comparing with the corresponding LSPs, SLRs exhibit a much higher quality factor. In fact, as the quality factor depends on the constituting resonances and their hybridization, how one can parametrize it in an analytic form is an important issue. We have studied the SLRs arising from two-dimensional Au monopartite nanoparticle arrays by angle- and polarization-resolved reflectivity spectroscopy, temporal coupled mode theory (CMT), and finite-difference time-domain simulation. The scattering matrix of the SLRs is formulated, revealing the importance of the spectral detuning and the interaction strengths between the LSP and the RAs in governing the quality factor. We then extend the CMT approach to study bipartite arrays where a nanoparticle dimer is employed and find the coupling between two LSPs plays a major role in further boosting the quality factor. Specifically, the coupling takes part in controlling the detuning factor as well as determining whether the coupled bright or dark mode is hybridized with the RAs. The dark mode hybridization can strongly enhance the quality factor, which is otherwise not possible in the monopartite counterparts.

Actively Controlled Frequency-Agile Fano-Resonant Metasurface for Broadband and Unity Modulation

The active control to the local resonant mode of metasurface is a promising route for improving the operation bandwidth limitation of metasurface. Here, we propose and experimentally demonstrated the active tunabilities in a frequency-agile Fano-resonant metasurface. The metasurface with a pair of asymmetric split ring resonators is integrated with double varactor diodes for active control of the sharp Fano resonance. It is found that the sharp Fano-type spectrum appears due to the near-field interferences between the collective electric and magnetic dipole modes. The physical insight is revealed through local field analysis, multipole decomposition and temporal coupled-mode theory. It is also found that the metasurface can be employed as a broadband and unity modulator. Hopefully, our results could inspire sophisticated electrically controlled photonic devices with novel functions.

Independently tunable Fano resonances based on MDM configuration using a ring resonator with nanodots

A novel designed Fano system using metal-dielectric-metal (MDM) configuration is proposed and numerically evaluated via finite element method (FEM). At the same time, the formation mechanism of Fano resonance is explored based on numerical simulations. Moreover, the standing wave theory and the temporal coupled-mode theory (CMT) are utilized to investigate the resonant phenomenon. The system is constructed by the tooth cavity connected into straight waveguide and a circular ring resonator with nanodots (CRRN). The simulation results indicate that the CRRN supports the two kinds of resonant modes: TM2 and like-TM2 mode, whose distribution of field patterns (the resonant point related to like-TM2 mode) can be flexibly controlled by the position of nanodot (the number and thickness of the nanodots). With regard to the excited dual Fano resonances, their emergence or disappearance can be tuned by nanodot position, and the independent tunability of FR2 can be realized by adjusting nanodot’s number and thickness. In addition, the Fano system with a sensing performance of 942 nm RIU−1 has been demonstrated, which can be great promising for detecting glucose concentration. In summary, the proposed Fano structure may provide a feasible scheme to flexibly manipulate the dual Fano resonances and detect glucose concentration.

Graphene perfect absorber design based on an approach of mimicking a one-port system in an asymmetric single resonator.

We proposed a novel perfect absorber with an asymmetric single resonator supporting two degenerate resonant modes, whose operation concept is mimicking a one-port system by making only one of the modes experience loss while using the other for an internal 100% reflector in conjunction with the background scattering. We confirmed the operation principle and the design requirement from a theoretical study using the temporal coupled-mode theory. We also designed an example device based on the guided-mode resonances (GMRs) in a slab-waveguide grating and numerically demonstrated a high absorption of ∼ 99.95% in monolayer graphene with greatly enhanced fabrication error tolerance in comparison to the previously proposed scheme. Our proposed scheme will find various useful applications due to the intuitive design process and relatively easier fabrication, which is attributed to the one-port mimicking operation concept with a single GMR-based broadband flat-top reflector.

Simultaneous detection of complex refractive index and temperature using a compact side-coupled photonic crystal nanobeam cavity

In this paper, we theoretically propose a compact photonic crystal nanobeam cavity (PCNC) side coupled with a waveguide for sensing complex refractive index (CRI) and temperature ( T ). Two Fano resonances are achieved by coupling two discrete states (zeroth-order mode and first-order mode) in a PCNC and the continuous state in the waveguide with a partial transmitting element. The transmission expression is derived based on the temporal coupled-mode theory. By measuring the wavelength shifts and shape changes of two Fano resonances in the transmission spectrum, not only the real part of the refractive index (RRI) and the imaginary part of the refractive index (IRI) can be sensed simultaneously, but also the effect of T on CRI is considered. The sensitivities of RRI for zeroth-order mode and first-order mode are 152.7 nm/refractive index unit (RIU) and 183.7 nm/RIU, respectively. The sensitivities of IRI are − 461 / R I U and − 198 / R I U for zeroth-order mode and first-order mode, respectively. The T sensitivities for zeroth-order mode and first-order mode are 58.6 pm/K and 55.6 pm/K, respectively. The fringe visibility values of both modes are more than 0.5. The relationship between structural parameters and coupling effect is studied and the effect of T on detection accuracy is discussed. To the best of our knowledge, this is the first geometry to simultaneously sense CRI and T . Moreover, the total footprint of the device is only 11 × 1.45 × 0.22 ( l e n g t h × w i d t h × h e i g h t ) µ m 3 , which will contribute to the large-scale integrated sensor array on chip.

Polarization conversion in anisotropic dielectric metasurfaces originating from bound states in the continuum.

We use the semianalytical Cartesian multipole method to investigate the light transmission and reflection spectra of anisotropic dielectric metasurfaces, and extend the multipole decompositions method to account for cross-polarization conversion effects. We observe sharp high-Q resonances arising from a distortion of symmetry-protected bound states in the continuum in asymmetric dielectric metasurfaces, i.e., quasibound states in the continuum. In addition, by further introducing in-plane symmetric breaking perturbation, the polarization conversions of linearly polarized light can be achieved through quasibound states in the continuum. With the aid of temporal coupled-mode theory, we can obtain the limit of cross-conversion under single high-Q resonance, i.e., 0.25. Our work will help to design dielectric metasurfaces to control the polarization states of light.

Unified treatment of scattering, absorption, and luminescence spectra from a plasmon–exciton hybrid by temporal coupled-mode theory

Plasmonic nanostructures are capable of tailoring the emission of a nearby emitter by increasing (or reducing) the brightness, shortening (or prolonging) the lifetime, and shaping the spectrum. Experimental characterization of such coupled plasmon-exciton (plexciton) systems usually relies on the acquisition and comparison of scattering, absorption, or luminescence spectra. However, theoretical accounts of these optical spectra, which are key to distinguishing between the coupling regimes and to standardizing the coupling criteria, often scatters in different frameworks, varying from classical to quantum-mechanical. Therefore, developing a unified and simple formalism that can simultaneously compare all these spectral signatures in different coupling regimes is nontrivial. Here, we use a temporal coupled-mode formalism to reproduce the scattering, absorption, and luminescence spectra of a plexciton system and find that its luminescence reaches a maximum at a critical coupling point, featuring a light-emitting plexciton with intense brightness and ultrafast lifetime. This simple approach provides a unified and phenomenological treatment of these spectra by simply including or excluding an external driving term. It therefore allows for a direct comparison of different spectroscopic signatures from the plexciton system and provides an easy-to-use guidance for the design of broadband light-emitting devices.

Violating Kirchhoff’s Law of Thermal Radiation in Semitransparent Structures

Kirchhoff’s law of thermal radiation imposes a constraint on photon-based energy harvesting processes since part of the incident energy flux is inevitably emitted back to the source. By breaking the reciprocity of the system, it is possible to overcome this restriction and improve the efficiency of energy harvesting. Here, we design and analyze a semitransparent emitter that fully absorbs normally incident energy from a given direction with zero backward and unity forward emissivity. The nearly ideal performance with wavelength-scale thickness is achieved due to the magneto-optical effect and the guided-mode resonance engineered in the emitter structure. We derive the general requirements for the nonreciprocal emitter using the temporal coupled mode theory and the symmetry considerations. Finally, we provide a realistic emitter design based on a photonic crystal slab consisting of a magnetic Weyl semimetal and silicon.

PT Symmetry Induced Rings of Lasing Threshold Modes Embedded with Discrete Bound States in the ContinuumSupported by the National Natural Science Foundation of China (Grant Nos. 12074049, 11727811, and 12047564), the Hong Kong Research Grants Council (Grant Nos. AoE/P-02/12, 16303119, and N HKUST608/17), and the Fundamental Research Funds for the Central Universities (Grant Nos. 2020CDJQY-Z006 and 2020CDJQY-Z003).

It is well known that spatial symmetry in a photonic crystal (PhC) slab is capable of creating bound states in the continuum (BICs), which can be characterized by topological charges of polarization vortices. Here, we show that when a PT-symmetric perturbation is introduced into the PhC slab, a new type of BICs (pt-BICs) will arise from each ordinary BIC together with the creation of rings of lasing threshold modes with pt-BICs embedded in these rings. Different from ordinary BICs, the Q-factor divergence rate of a pt-BIC is reduced and anisotropic in momentum space. Also, pt-BICs can even appear at off-high symmetry lines of the Brillouin zone. The pt-BICs also carry topological charges and can be created or annihilated with the total charge conserved. A unified picture on pt-BICs and the associated lasing threshold modes is given based on the temporal coupled mode theory. Our findings reveal the new physics arising from the interplay between PT symmetry and BIC in PhC slabs.

In-plane excitation of a topological nanophotonic corner state at telecom wavelengths in a cross-coupled cavity

In silicon photonics, the cavity mode is a fundamental mechanism to design integrated passive devices for on-chip optical information processing. Recently, the corner state in a second-order topological photonic crystal (PC) rendered a global method to achieve an intrinsic cavity mode. It is crucial to explore such a topological corner state in silicon photonic integrated circuits (PICs) under in-plane excitation. Here, we study both theoretically and experimentally the topological nanophotonic corner state in a silicon-on-insulator PC cavity at a telecommunications wavelength. In theory, the expectation values of a mirror-flip operation for the Bloch modes of a PC slab are used to characterize the topological phase. Derived from topologically distinct bulk polarizations of two types of dielectric-vein PCs, the corner state is induced in a 90-deg-bend interface, localizing at the corner point of real space and the Brillouin zone boundary of reciprocal space. To implement in-plane excitation in an experiment, we fabricate a cross-coupled PC cavity based on the bend interface and directly image the corner state near 1383 nm using a far-field microscope. Finally, by means of the temporal coupled-mode theory, the intrinsic Q factor of a cross-coupled cavity (about 8000) is retrieved from the measured transmission spectra. This work gives deterministic guidance and potential applications for cavity-mode-based passive devices in silicon PICs, such as optical filters, routers, and multiplexers.

Excitation of a bound state in the continuum via spontaneous symmetry breaking

Bound states in the continuum (BICs) are non-radiating solutions of the wave equation with a spectrum embedded in the continuum of propagating waves of the surrounding space. The complete decoupling of BICs from the radiation continuum makes their excitation impossible from the far-field. Here, we develop a general theory of parametric excitation of BICs in nonlinear systems with Kerr-type nonlinearity via spontaneous symmetry breaking, which results in a coupling of a BIC and a bright mode of the system. Using the temporal coupled-mode theory and perturbation analysis, we found the threshold intensity for excitation of a BIC and study the possible stable and unstable solutions depending on the pump intensity and frequency detuning between the pump and BIC. We revealed that at some parameters of the pump beam, there are no stable solutions and the BIC can be used for frequency comb generation. Our findings can be very promising for use in nonlinear photonic devices and all-optical networks.

Coupled-Mode Theory for Graphene-Based Metasurfaces

In this article, a temporal coupled-mode theory (CMT) formalism is proposed to design graphene-based metasurface (MTS) structures. Such structures may be nonuniform and synthesized by numerous graphene resonators. To obtain a desired functionality, such MTSs may be designed, by performing multiple parametric analyses of the structure's geometric parameters. An accurate calculation of their response may be attained by a full-wave vectorial finite-element method (VFEM), by modeling graphene as a surface boundary condition; however, it requires high computational resources, especially for larger configurations. CMT offers an appealing time- and memory-efficient alternative, by solving a sparse system of equations, of particularly small size, fed by the results of simpler and smaller simulations, with the ability to take into account graphene dispersion. CMT may be used to design more complex MTS structures, by providing approximate and preliminary results, which shall be used as a starting point for the final FEM fine-tuning.

Enhanced directional quantum emission by tunable topological doubly resonant cavities.

How to utilize topological microcavities to control quantum emission is one of the ongoing research topics in the optical community. In this work, we investigate the emission of quantum emitters in a doubly-resonant topological Tamm microcavity, which can simultaneously achieve dual resonances at two arbitrary wavelengths according to the needs of practical application. To achieve the enhancement of quantum emission in such cavities, we have exploited the tunable doubly-resonant modes, in which one of resonant modes corresponds to the pump laser wavelength and the other one is located at the emission wavelength of quantum emitters. Both theoretical and experimental results demonstrate that the pump excitation and emission efficiencies of quantum emitters are greatly enhanced. The main physical mechanism can be explained by the doubly-resonant cavity temporal coupled-mode theory. Furthermore, we observe the faster emission rate and the higher efficiency of unidirectional quantum emission, which have promising applications in optical detection, sensing, filtering, and light-emitting devices.

Ultrawideband bandstop filter based on Fano resonance and rectangular resonators.

In this study, the effect of length of the stub on the formation of the Fano resonance in structures which possess a metal-insulator-metal (MIM) waveguide coupled to rectangular cavities by the stub is investigated theoretically and numerically. The resulting Fano resonance is used to design an ultrawideband bandstop filter that can filter all wavelengths between two telecommunication windows of $\lambda = 850\;{\rm nm}$ and $\lambda = 1310\;{\rm nm}$. The structure is based on two rectangular cavities coupled to the MIM waveguide by stubs that are located at an adjusted distance from each other; the interference superposition of reflected and transmitted waves from each other will make this filtering phenomenon. The center wavelength of the bandstop of the structure is highly adjustable by changing the dimensions of the structure. The theoretical and the numerical results are, respectively, based on the transmission line model and the finite-difference time-domain method. The theoretical results comply well with the numerical ones. To analyze the Fano resonance, temporal coupled mode theory is also exploited. The proposed structure has significant applications in highly integrated optical circuits.

Semi-analytical approach for refractive index sensors based on reflective metasurfaces

We present a semi-analytical approach for the analysis and design of refractive index sensors based on metal–insulator–metal (MIM) metasurfaces. While numerical methods require extensive calculations for all values of geometrical parameters, the semi-analytical approach provides straightforward guidelines for a design of optimal metasurfaces with maximized sensitivity. Semi-analytical formulas for refractive index sensitivities are derived from equations of the temporal coupled mode theory and standing-wave resonance model. They require three numerically calculated parameters (resonant frequency and radiative and non-radiative decay rates of the resonant mode), obtained by the fitting of reflectance spectra. Generality of the presented approach allows us to consider the operation of metasurface sensors in three different interrogation methods: spectral (frequency), intensity (reflectance), and phase. Validity of the proposed approach is confirmed by a good agreement with numerical results. Starting from semi-analytical formulas, we derive working frequencies of metasurface based sensors, prove that the critical coupling with equal decay rates of the resonant mode is the optimal working regime, and demonstrate that optimal MIM metasurfaces should have periods as large as possible with the thickness of MIM cavities determined by the critical coupling condition.

Triple-wavelength filter based on the nanoplasmonic metal-insulator-metal waveguides

In this paper, we present a proposal for compact photonic wavelength filtering and 3-dB wavelength splitting device based on a nanoplasmonic metal-insulator-metal structure. The operating performance of the device has been accurately simulated using the temporal coupled-mode theory. We use a numerical simulation method of eigenmode expansion propagation in the overall design process. We show that the transmission efficiency of the drop filter can be significantly enhanced by applying specific optimization of nanotube waveguide. The proposed structure has potential applications in highly efficient, ultra-compact integrated circuits as well as in optical communication systems at the nanoscale size.

A Tunable Slow Light Device with Multiple Channels Based on Plasmon-Induced Transparency

Slow light devices with buffering capability play a critical role in all-optical signal processing. In this paper, multiple slow light phenomena are implemented based on plasmon-induced transparency (PIT) in our device. The device mainly consists of dual tooth cavities coupled with stub resonators, respectively. Temporal coupled-mode theory model illustrates that the triple PIT phenomena can be achieved based on different formation mechanisms. The simulation results calculated by the finite-difference time-domain method reveal that significant slow light response occurs at two wavelength regions. In addition, the parameters of structure have an important influence on PIT response and slow light characteristics. Moreover, the separate manipulation of wavelength, transmission and group index at transparency peak can be achieved in different slow light channels by adjusting the structural parameters. This plasmonic device is of great significance for the design of optical networks on chips.

Multiple-Mode Bowtie Cavities for Refractive Index and Glucose Sensors Working in Visible and Near-infrared Wavelength Ranges

A multiple-mode metal-insulator-metal plasmonic sensor with four coupled bowtie resonators containing two pairs of silver baffles is numerically investigated using the finite element method and verified by the temporal coupled mode theory. The proposed structure can function as a plasmonic refractive index and glucose sensors working in visible and near-infrared wavelength ranges. Simulation results show that introducing the silver baffles in bowtie cavities can modify the plasmon resonance modes and give a tunable way to enhance the sensitivity and figure of merit. The highest sensitivity (S) can reach S = 1500.00, 1400.00, and 1100.00 nm/RIU and the high figure of merit (FOM) of 50.00, 46.67, and 36.67 RIU−1 from mode 1 to mode 3. The sensitivity obtained from three modes with operating wavelengths in visible and near-infrared simultaneously exceeds 1100.00 nm/RIU along with remarkably high FOM, which are not attainable from other reported literature. The proposed structure can realize multi-mode and shows impressive practical prospects that can be applied for integrated optics circuits (IOCs) and other nanophotonics devices.

Generalization of the Circular Dichroism from Metallic Arrays That Support Bloch-Like Surface Plasmon Polaritons

The broken mirror symmetry in subwavelength photonic systems has manifested many interesting chiroptical effects, such as optical rotation and circular dichroism. When such systems are placed periodically in a lattice form, in addition to intrinsic chirality, extrinsic chirality also takes part, and the overall effect depends not only on the basis and lattice but also the excitation configuration. Here, we study planar chiral nanohole arrays in square lattice that support Bloch-like surface plasmon polaritons (SPPs) and clarify how the system geometry and the excitation contribute to circular dichroism. By using temporal coupled mode theory, the dissymmetry factor and the scattering matrix of the arrays are analytically formulated. Remarkably, we find the dissymmetry factor depends only on the coupling polarization angle and the in-coupling phase difference between the p- and s-polarizations. Furthermore, the upper limit of the dissymmetry factor at \ifmmode\pm\else\textpm\fi{}2 can be reached simply by orienting the lattice of the arrays for properly exciting the Bloch-like SPPs and at the same time making the basis mimic two orthogonal and relatively displaced dipoles, demonstrating the interplay between extrinsic and intrinsic chirality. The models have been verified by numerical simulations and experiments, yielding dissymmetry factors of 1.82 and 1.55, respectively, from the proposed dual slot system.

Spin-VCSELs with Local Optical Anisotropies: Toward Terahertz Polarization Modulation

Putting a different spin on photonics: Spin-injected vertical-cavity surface-emitting lasers (Spin-VCSELs) with strong anisotropies are important in particular for ultrafast and terahertz applications, but the field is being held back in part because of lack of sufficiently predictive physical models. This study uses temporal coupled-mode theory with the transfer-matrix formalism to make progress by extending the spin-flip model. Additionally, the authors propose a spin-VCSEL with an anisotropic intracavity grating. This approach points to engineering solutions for ultrafast optical communication and compact terahertz sources.