Temporal Coupled-mode Theory Research Articles

Design of hollow metasurfaces for absorption sensors and surface enhanced infrared absorption

Absorption sensors detect variations in the imaginary part of refractive index with selectivity in sensing since analytes can be distinguished according to their characteristic absorption bands. In this study we combine the theoretical analysis based on temporal coupled mode theory and numerical calculations in order to derive design principles of optimal metasurfaces aimed for absorption sensing and surface enhanced infrared absorption (SEIRA). We consider hollow metal–insulator-metal metasurfaces with an empty space between two metallic layers. This space acts as a channel for the infiltration of fluid analytes in the region with the maximal electric field enhancement, which provides high sensitivity. We demonstrate that optimal metasurfaces operate in overcoupled regime where radiative decay rate of the resonant mode is larger than non-radiative decay rate. The operation in this regime is adjusted by choosing appropriate channel thickness (the vertical distance between two metallic layers), which should be around three times larger than the channel thickness at the critical coupling point, associated with equal decay rates and zero reflectance. Metasurface period should be as large as possible, whereas the operating frequency should be equal to the resonant frequency of metasurfaces. The same conclusions hold for hollow metasurfaces aimed for SEIRA, while in addition, their resonant frequency should match the vibrational frequency of an analyte under investigation. The absorption sensitivity (reflectance change divided by the change in the imaginary part of refractive index) of an optimal metasurface is larger than , which provides detection of the imaginary part of refractive index below .

Tunable narrow transparency windows induced by the coupled quasi-guided modes in borophene plasmonic nanostructure

A grating-assisted triple-layer continuous borophene sheets structure is presented to investigate the phase-coupled plasmon-induced transparency (PIT) effect at the near-infrared communication band. In the proposed structure, the diffraction grating is utilized to couple the normal incident waves, which excites the quasi-guided mode in triple-layer continuous borophene sheets. Compared to the patterned structure, the requirement of complicated processing techniques and extra doping configurations for tuning carrier density can be avoided by using the continuous borophene sheet. Additionally, the narrower transparency windows are shown in the spectral responses via the phase coupling between two detuned quasi-guided modes with high quality factors. The transparency windows can be efficiently tuned by adjusting the carrier densities in borophene sheets or the separation distances between the borophene sheets. The analytical results based on temporal coupled mode theory and transfer matrix method are consistent with the numerical simulations via finite-difference time-domain calculations. The proposed scheme provides the promising design of a tunable PIT component that is compatible with optical communication technology.

Manipulating strong coupling between exciton and quasibound states in the continuum resonance

Strong coupling exhibits unique ability to preserve quantum sates between light and matter, which is essential for the development of quantum information technology. To explore the physical mechanism behind this phenomenon, we employ the tight-binding method for expanding the temporal coupled-mode theory, with the absorption spectrum formula of coupled system directly obtained in an analytical way. It reveals all the physical meaning of parameters defined in our theory, and shows how to tailor lineshapes of the coupled systems. Here, we set an example to manipulate the strong coupling in a hybrid structure composed of excitons in monolayer WS$_2$ and quasi-bound states in the continuum supported by the TiO$_2$ nanodisk metasurfaces. The simulated results show that a clear spectral splitting appeared in the absorption curve, which can be controlled by adjusting the asymmetric parameter of the nanodisk metasurfaces and well fitted through our theoretical predictions. Our work not only gives a more comprehensive understanding of such coupled systems, but also offers a promising strategy in controlling the strong light-matter coupling to meet diversified application requests.

Realizing quasi-monochromatic switchable thermal emission from electro-optically induced topological phase transitions.

Explorations into the photonic analogs of topological materials have garnered significant research interest due to their application potential. Particularly in planar systems, the prospects of engendering extinguishable topological states can have wide-ranging implications. With an objective of employing these concepts for thermal emission engineering, here, we design and numerically investigate a quasi-monochromatic highly directional mid-infrared source elicited from inversion symmetry-protected topological interface states. Notably, by relying on the architecture of electro-optic effect-induced topological phase transitions, we introduce the possibility of ultrafast switching of thermal radiation. These reversible phase transitions, being free from carrier transport are inherently fast and evoke thermal emission modulation with a modulation depth upto 0.99. Specifically, our platform exhibits a near-perfect extinguishable spectral emission peak at 4~mum with a quality factor of over 18500, displaying negligible parasitic emissions. Furthermore, the optimized interface state manifests itself for only one of the polarization modes, resulting in polarized emission under resonance conditions. To establish a methodical approach to parameter optimization, we also model our platform as a leaky mode resonator using the framework of temporal coupled-mode theory. We believe, our findings can provide a way forward in establishing complete control over the optical characteristics of the infrared thermal emitters.

Polarization-independent near-infrared superabsorption in transition metal dichalcogenide Huygens metasurfaces by degenerate critical coupling

Strong near-infrared absorption of light in semiconducting transition metal dichalcogenides (TMDs) is essential for improving the photocarrier extraction efficiency in optoelectronic devices. Here, we numerically demonstrate that an original TMD Huygens metasurface is specifically designed to overcome the 50% absorptance limit of a subwavelength thin film. The unique metasurface comprising a TMD nanodisk array shows evidence of characteristic Mie resonances including electric and magnetic dipoles. By carefully optimizing the aspect ratio of nanodisks, the extraordinary spectral overlapping of orthogonal electric and magnetic dipole resonances is successfully realized and, thus, enables the super-high absorptance up to 87% in a subwavelength-thin ($\ensuremath{\approx}0.19{\ensuremath{\lambda}}_{0}$) semiconductor structure by degenerate critical coupling at the wavelength of ${\ensuremath{\lambda}}_{0}=903\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. All numerical results are confirmed by the temporal coupled-mode theory and again via the multipole decomposition method. Importantly, the near-unity absorptance in this TMD Huygens metasurface by degenerate critical coupling not only is tailored throughout the entire near-infrared region but also is both polarization independent and angle insensitive. The absorptance maintaining >80% is observed with the incident angle up to \ifmmode\pm\else\textpm\fi{}10 \ifmmode^\circ\else\textdegree\fi{} at least. Our findings are not only of fundamental interest but could also offer a platform for TMD-based high-speed photodetecting, energy harvesting, and thermal emission.

Tunable plasmonically induced transparency with giant group delay in gain-assisted graphene metamaterials.

We propose a graphene metamaterial consisting of several layers of longitudinally separated graphene nanoribbon array embedded into gain-assisted medium, demonstrating electromagnetically induced transparency-like spectra. Combined with finite-difference time-domain simulations, the transfer matrix method and temporal coupled-mode theory are adopted to quantitatively describe its transmission characteristics. These transmission characteristics can be tuned by altering the gain level in medium layer and the Fermi energy level in graphene. Additionally, it is the incorporation between gain medium and graphene nanoribbons with optimized geometrical parameters and Fermi energy level that the destructive interference between high order graphene plasmonic modes can be obtained, suggesting drastic phase transition with giant group delay and ultra-high group index up to 180 ps and 104, respectively. Our results can achieve efficient slow light effects for better optical buffers and other nonlinear applications.

Au nanorods-TiO2 photonic crystal plasmonic-photonic hybrid sensor for label-free detection and identification of DNA molecules with single nucleotide polymorphisms

Highly sensitive optical sensors for label-free detection of DNA must have high usability and wide applicability for achieving advances in the medical and biological science fields. However, current sensors do not simultaneously satisfy these criteria. Here, we developed a simple, cost-effective, and sensitive plasmonic–photonic hybrid sensor using gold nanorods as nanoantennae and a photonic crystal slab (PCS) as a microcavity. In this report, we performed simple microscopic detection and identification of DNA molecules with Alzheimer’s disease-associated single nucleotide polymorphisms, which is an important indicator for early diagnosis. The PCS was fabricated using nanoimprint lithography; the gold nanorods were controllably coupled with the PCS. The device sensitivity was experimentally assessed by controlling the plasmonic–photonic coupling resonance, which was enabled by tuning the PCS-coupled AuNR amounts. The sensitivity was also investigated by theoretical modeling of the hybrid sensor, based on the temporal coupled mode theory (TCMT). The TCMT-based theoretical model well explained the experimental results. In a demonstration of ultrasensitive detection of DNA, the identification of single nucleotide mismatched DNA molecules (~1 pM) and detection of several DNA molecules (~1000), with a limit of detection of 5.9 aM, were successfully achieved. This sensor may thus have wide applications for DNA analysis.

Enhancing light absorption of graphene with dual quasi bound states in the continuum resonances

Graphene is promising for next-generation optoelectronic devices owing to its unique optical and electronic properties whereas relatively weak light-matter interaction limits its performance. In this work, light can be absorbed totally by graphene with the aid of single layer all dielectric metasurface in the near infrared region. The metasurface is composed of periodically arranged amorphous Silicon nanocuboids quadrumer suspended in air which supports resonances governed by symmetry protected bound states in the continuum. Symmetry perturbation is introduced to the metasurface to induce quasi bound states in the continuum resonances by elements pair movement method in x or/and y direction. Light absorption performance of the hybrid structure can be enhanced to 50% at single-mode critical coupling state and 100% at dual-mode degenerate critical coupling state. Temporal coupled mode theory is used to analyze physical mechanism of max absorption Amax for both single mode and dual mode condition in two-port system as an analog of transparent hybrid structure. Furthermore, absorption performance can be tuned by varying the elevation between graphene and metasurface. Effects of metasurface's geometric parameters including scaling factor and thickness on absorption characteristics are also explored. Our results may provide a new route for enhancing light absorption of graphene or other 2D materials which may facilitate to design advanced modulators and photodetectors.

The design and simulation of a multifunctional logic device based on plasmon-induced transparency using two semicircular resonators

A novel optical logic device based on plasmon-induced transparency (PIT) effect is designed. It is composed of two semicircular resonators coupled with the metal–insulator–metal (MIM) waveguide. By monitoring the different wavelengths, six logic operations (AND, OR, NAND, NOR, XOR, and XNOR) can be achieved simultaneously in the proposed structure. The performance of the device is analyzed by temporal coupled-mode theory and finite-difference time-domain (FDTD) method. Moreover, the influence of structure parameters on device performance such as the radius of semicircular resonator, the coupling distance between two semicircular resonators, and the coupling distance between waveguide and semicircular resonator are discussed in detail. The proposed device that can implement six logic operations greatly improves the integration of photonic integrated circuits (PIC), and it has the potential to provide new idea for designing of optical logic device on-chip.

Lineshape study of optical force spectra on resonant structures.

Understanding the frequency spectrum of the optical force is important for controlling and manipulating micro- and nano-scale objects using light. Spectral resonances of these objects can significantly influence the optical force spectrum. In this paper, we develop a theoretical formalism based on the temporal coupled-mode theory that analytically describes the lineshapes of force spectra and their dependencies on resonant scatterers for arbitrary incident wavefronts. We obtain closed-form formulae and discuss the conditions for achieving symmetric as well as asymmetric lineshapes, pertaining, respectively, to a Lorentzian and Fano resonance. The relevance of formalism as a design tool is exemplified for a conceptual scheme of the size-sorting mechanism of small particles, which plays a role in biomedical diagnosis.

Dynamic routing through saturable absorption in graphene photonic resonators: Impact of carrier diffusion and finite relaxation time

We assess the continuous wave and dynamic routing performance of a compact silicon-on-insulator disk resonator overlaid with a graphene monolayer at telecommunication wavelengths. Switching action is enabled by saturable absorption in graphene, controlled by a pump wave of only a few milliwatts. Graphene saturable absorption is modeled through a carrier rate equation that incorporates both the finite relaxation time and diffusion of photo-generated carriers, providing a realistic account of carrier dynamics. The overall nonlinear response of the resonator is evaluated with a rigorous mathematical framework based on perturbation theory and temporal coupled-mode theory. We thoroughly investigate the effects of carrier diffusion and finite relaxation time, both separately and together. We also take into account nonlinear refraction via a Kerr effect term and quantify its impact on the overall response. In order to suppress the Kerr effect, we replace silicon with silicon-rich nitride, allowing for the individual contributions of the resonator core and graphene (of opposite sign) to exactly compensate each other. Our results contribute to the understanding of carrier dynamics and their impact on the performance of practical graphene-based switching components.

High-Q localized surface plasmon resonance based on bound states in the continuum for enhanced refractive index sensing.

Nanophotonics based on localized surface plasmon resonance (LSPR) has emerged as a vibrant arena for research into enhanced light-matter interactions with potential applications in imaging, sensing, and computing. However, the low quality (Q) factor of LSPR is a significant barrier to comprehensive device applications. Here, we demonstrate that coupling the LSPR of a gold nanowire array with the optical bound states in the continuum (BIC) of a dielectric double-layer grating can significantly increase the Q factor of LSPR. We realize two hybrid modes with Q factors of up to 111 at 558 nm and 83 at 582 nm, which are about 14 and 10 times larger than those of an uncoupled gold nanowire array. Based on temporal coupled-mode theory, we further show that the resonance frequencies and Q factors of the hybrid modes can be modulated and optimized by varying relevant structural parameters. This coupled system provides a new platform for improving the figures of merit (FoMs) of LSPR-based refractive index sensors, and the concept of LSPR-BIC coupling can be extended to other similar nanosystems.

A physical interpretation of coupling chiral metaatoms.

The physical origins of chiroptical responses from artificial optically active media are significant for developing high-performance circular dichroism (CD) spectroscopic techniques. Here, we present a biorthogonal approach based on temporal coupled-mode theory to unravel the underlying physics of chiral metasurfaces. Equipped with physically meaningful parameters, this approach inherits the intrinsic properties of open optical cavities, including time-reversal symmetry and non-Hermitian Hamiltonians, which are found to be in excellent agreement with numerical results. Remarkably, it identifies that the intrinsic chirality of coupled chiral nanocavities arises from (i) the asymmetric coupling between interlayer cross-polarized resonant modes and (ii) a coherent interference between doubly degenerate states. Based on this formalism, a critical coupling condition capable of achieving zero transmission for circularly polarized light is proposed.

Topological cascaded coupled cavities system: Neo-analysis of temporal coupled-mode theory

<p indent="0mm">In recent years, it has been discovered that topological photonics can ensure the robust optical behaviors of multiple optical devices, which eases the impact of defects and other perturbations on the device performance. Therefore, the combination of topological photonics and filter design is on demand. Recently, the transmission efficiency equation in a four-terminal cascaded coupled cavities system was derived based on the temporal coupled-mode theory. And general high-order nonreciprocals add/drop filter structure was designed. The simulation results are in good agreement with the theoretical prediction.

Bandwidth-tunable near-infrared perfect absorption of graphene in a compound grating waveguide structure supporting quasi-bound states in the continuum

Recently, based on the selective excitation of the guided mode, researchers realized quasi-bound states in the continuum (quasi-BICs) in all-dielectric compound grating waveguide structures. In this paper, we introduce a graphene layer into an all-dielectric compound grating waveguide layer supporting quasi-BIC to achieve near-infrared perfect absorption of graphene. The underlying physical mechanism of perfect absorption can be clearly explained by the critical coupling theory derived from temporal coupled-mode theory in a single-mode, one-port system. By changing the Fermi level and the layer number of the graphene, the absorption rate of the system can be flexibly tuned. In addition, by changing the geometric parameter of the compound grating waveguide structure, the radiation coupling rate of the quasi-BIC can also be flexibly tuned. Therefore, the critical coupling condition can be maintained in a broad range of the Fermi level and the layer number of the graphene. The full width at half maximum of the near-infrared perfect absorption peak can be flexibly tuned from 5.7 to 187.1 nm. This bandwidth-tunable perfect absorber would possess potential applications in the design of 2D material-based optical sensors, electrical switchers, and solar thermophotovoltaic devices.

Nonreciprocal dynamically tunable power dividers by three (1x3) based on graphene for terahertz region

This paper presents two new types of dynamically tunable THz nonreciprocal power dividers based on graphene. These components fulfill division of the input power between three output ports. Besides, they possess isolation properties, i.e., a source connected to the input port is protected against unwanted reflections from the output ports. The components consist of a disk-shaped graphene resonator and six graphene waveguides connected to it. The graphene elements are deposited on a dielectric substrate. The resonator is subject to an external electric and DC magnetic field. The dipole mode resonance in the magnetized resonator is excited by surface plasmon–polariton waves propagating in the graphene waveguides. Numerical simulations and the analytical temporal coupled-mode theory are used in the analysis. The division level of the input power between the three output ports of dividers is about −8 dB and the isolation of the source in relation to the output ports is higher than −15 dB with the central frequency 7.45 THz and the bandwidth 3%. DC magnetic field is 0.29 T and Fermi energy is 0.15 eV. The central frequency of the dividers can be dynamically adjusted by an external electric field.

Two tractable models of dynamic light scattering and their application to Fano resonances

Abstract We introduce two tractable analytical models to describe dynamic effects at resonant light scattering by subwavelength particles. One of them is based on a generalization of the temporal coupled-mode theory, and the other employs the normal mode approach. We show that sharp variations in the envelope of the incident pulse may initiate unusual, counterintuitive dynamics of the scattering associated with interference of modes with fast and slow relaxation. To exhibit the power of the models, we apply them to explain the dynamic light scattering of a square-envelope pulse by an infinite circular cylinder made of GaP, when the pulse carrier frequency lies in the vicinity of the destructive interference at the Fano resonances. We observe and explain intensive sharp spikes in scattering cross-sections just behind the leading and trailing edges of the incident pulse. The latter occurs when the incident pulse is over and is explained by the electromagnetic energy released in the particle at the previous scattering stages. The accuracy of the models is checked against their comparison with results of the direct numerical integration of the complete set of Maxwell’s equations and occurs very high. The models’ advantages and disadvantages are revealed, and the ways to apply them to other types of dynamic resonant scattering are discussed.

Critically coupled Fabry\u2013Perot cavity with high signal contrast for refractive index sensing

Perfect absorption at a resonance wavelength and extremely low absorption at the wavelength range of off-resonance in a one-port optical cavity is required for refractive index (RI) sensing with high signal contrast. Here, we propose and analyze an absorption-enhanced Fabry–Perot (MAFP) cavity based on a critical coupling condition in a near-infrared wavelength range. For a one-port cavity, a thick bottom Au is used as a mirror and an absorber. To achieve the critical coupling condition, a top dielectric metasurface is employed and tailored to balance the radiation coupling and the absorption coupling rates, and the one-port cavity is theoretically analyzed using temporal coupled-mode theory. We investigate two types of MAFP structures for gas and liquid. The gas MAFP cavity shows a sensitivity of ~ 1388 nm/RIU and a full-width at half-maximum of less than 0.7 nm. This MAFP cavity resolves the RI change of 5 × 10−4 with a reflectance signal margin of 50% and achieves a signal contrast of ~ 100%. The liquid MAFP cavity shows a sensitivity of ~ 996 nm/RIU when RI of liquid changes from 1.30 to 1.38. With tailoring the period of the metasurface maintaining its thickness, a signal contrast of ~ 100% is achieved for each specific RI range.

High-order nonreciprocal add-drop filter

Topological photonics have led to robust optical behavior of optical devices, which has alleviated the influence of manufacturing defects and perturbations on the device performance. Meanwhile, temporal coupled-mode theory (t-CMT) has been developed and applied widely. However, the t-CMT of cascaded coupled cavities (CCC) system and its corresponding high-order filter has yet to be established. Here, the t-CMT of CCC system is established based on the existing t-CMT. By combining the CCC with topological waveguides, a versatile design scheme of high-order nonreciprocal add-drop filter (HONAF) is proposed. The relationship between the coupling effect of cavities and transmission and the filtering performance of HONAF is analyzed quantitatively. Then, a method to improve the transmission efficiency and quality factor of the filter is given. The proposed HONAF is based on the combination of gyromagnetic photonic crystals and decagonal Penrose-type photonic quasicrystals. The transmission and filtering performance of the HONAF are numerically analyzed, which verifies the consistency between theoretical prediction and numerical simulation. The established t-CMT of CCC system can be widely used in coupled resonator optical waveguides and their related systems. The proposed HONAF with excellent performance can also be applied to wavelength division multiplexing/demultiplexing systems.

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.