Anticrossing Region Research Articles

Plasmonic Coupled Modes in a Metal-Dielectric Periodic Nanostructure.

In this study we investigate the optical properties of a 2D-gap surface plasmon metasurface composed of gold nanoblocks (nanoantennas) arranged in a metal-dielectric configuration. This novel structure demonstrates the capability of generating simultaneous multi-plasmonic resonances and offers tunability within the near-infrared domain. Through finite difference time domain (FDTD) simulations, we analyze the metasurface's reflectance spectra for various lattice periods and identify two distinct dips with near-zero reflectance, indicative of resonant modes. Notably, the broader dip at 1150 nm exhibits consistent behavior across all lattice periodicities, attributed to a Fano-type hybridization mechanism originating from the overlap between localized surface plasmons (LSPs) of metallic nanoblocks and surface plasmon polaritons (SPPs) of the underlying metal layer. Additionally, we investigate the influence of dielectric gap thickness on the gap surface plasmon resonance and observe a blue shift for smaller gaps and a spectral red shift for gaps larger than 100 nm. The dispersion analysis of resonance wavelengths reveals an anticrossing region, indicating the hybridization of localized and propagating modes at wavelengths around 1080 nm with similar periodicities. The simplicity and tunability of our metasurface design hold promise for compact optical platforms based on reflection mode operation. Potential applications include multi-channel biosensors, second-harmonic generation, and multi-wavelength surface-enhanced spectroscopy.

Terahertz hybrid optical-plasmonic modes: tunable resonant frequency, narrow linewidth, and strong local field enhancement.

Hybrid optical-plasmonic modes have the characteristics of low loss and small mode volume, which will result in the strong localization and enhancement of electromagnetic field. Such advantages of hybrid optical-plasmonic mode are important for the enhancement of light-matter interactions. Here, terahertz (THz) hybrid modes of Fabry-Perot resonances (FPRs) and spoof surface plasmon polaritons (SSPPs) in the modified Otto scheme are investigated both in theoretical and experimental aspects. The device structure is composed of a metal grating silicon waveguide (MGSW) and a metal slit grating (MSG). The two components are vertically stacked with a variable air gap between them. The THz hybrid modes are originated from the far-field coupling of the FPRs and the SSPP supported by the air gap and the MSG, respectively. By changing the thickness of the air gap, the resonant frequency of the FPR-SSPP modes can be tuned in a frequency range of about 0.1 THz. An anti-crossing behavior between two reflection dips corresponding to the guided-mode resonance in the MGSW and the FPR-SSPP mode is observed, which leads to the narrowing of the reflection dips in the anti-crossing region. Numerical simulations show that at the resonant frequencies of FPR-SSPP mode, there is a huge volume-averaged electromagnetic energy enhancement of about 1600 times in the grooves of the MSG, which is around 8.7 times larger than that induced by the SSPP directly launched by free-space electromagnetic field. The hybrid FPR-SSPP modes can be used to construct THz sensors and detectors with high sensitivity.

Mode transformation properties in the integrated bimodal resonance structure

The bimodal resonance phenomena in photonic structure have received particular attention due to their intriguing optical properties and numerous potential applications. In this work, we investigated the mode transformation behaviors of the guided modes in an integrated bimodal resonance structure consisting of a single groove on the surface of an abruptly ended slab waveguide. Numerical simulations demonstrated that the strong mode transformation can occur in the anticrossing region of resonance at the oblique incidence of a transverse electric (TE)-polarized guided mode on the groove. According to the multiple-beam interference model, a theoretical formula was developed to study the resonance and mode transformation behaviors of the guided modes. The results showed that the different anticrossing behaviors of structure are resulting from the constructive and destructive interference of bimodal resonance. The resonance and mode transformation properties of structure can be controlled by adjusting the geometrical parameters of groove. The mode manipulation with high efficiency in the slab waveguide will have many applications in lab-on-a-chip devices, switching and on-chip spectroscopy.

Photoluminescence at the ground-state level anticrossing of the nitrogen-vacancy center in diamond: A comprehensive study

The nitrogen-vacancy center (NV center) in diamond at magnetic fields corresponding to the ground state level anticrossing (GSLAC) region gives rise to rich photoluminescence (PL) signals due to the vanishing energy gap between the electron spin states, which enables to have an effect on the NV center's luminescence for a broad variety of environmental couplings. In this article we report on the GSLAC photoluminescence signature of NV ensembles in different spin environments at various external fields. We investigate the effects of transverse electric and magnetic fields, P1 centers, NV centers, and the $^{13}$C nuclear spins, each of which gives rise to a unique PL signature at the GSLAC. The comprehensive analysis of the couplings and related optical signal at the GSLAC provides a solid ground for advancing various microwave-free applications at the GSLAC, including but not limited to magnetometry, spectroscopy, dynamic nuclear polarization (DNP), and nuclear magnetic resonance (NMR) detection. We demonstrate that not only the most abundant $^{14}$NV center but the $^{15}$NV can also be utilized in such applications and that nuclear spins coupled to P1 centers can be polarized directly by the NV center at the GSLAC, through a giant effective nuclear $g$-factor arising from the NV center-P1 center-nuclear spin coupling. We report on new alternative for measuring defect concentration in the vicinity of NV centers and on the optical signatures of interacting, mutually aligned NV centers.

Dynamic N14 nuclear spin polarization in nitrogen-vacancy centers in diamond

We studied the dynamic nuclear spin polarization of nitrogen in negatively charged nitrogen-vacancy (NV) centers in diamond both experimentally and theoretically over a wide range of magnetic fields from 0 to 1100 G covering both the excited-state level anti-crossing and the ground-state level anti-crossing magnetic field regions. Special attention was paid to the less studied ground-state level anti-crossing region. The nuclear spin polarization was inferred from measurements of the optically detected magnetic resonance signal. These measurements show that a very large (up to $96 \pm 2\%$) nuclear spin polarization of nitrogen can be achieved over a very broad range of magnetic field starting from around 400 G up to magnetic field values substantially exceeding the ground-state level anti-crossing at 1024 G. We measured the influence of angular deviations of the magnetic field from the NV axis on the nuclear spin polarization efficiency and found that, in the vicinity of the ground-state level anti-crossing, the nuclear spin polarization is more sensitive to this angle than in the vicinity of the excited-state level anti-crossing. Indeed, an angle as small as a tenth of a degree of arc can destroy almost completely the spin polarization of a nitrogen nucleus. In addition, we investigated theoretically the influence of strain and optical excitation power on the nuclear spin polarization.

Publisher Correction: Real-space observation of vibrational strong coupling between propagating phonon polaritons and organic molecules

Phonon polaritons (PPs) in van der Waals (vdW) materials can strongly enhance light-matter interactions at mid-infrared frequencies, owing to their extreme infrared field confinement and long lifetimes. PPs thus bear potential for achieving vibrational strong coupling (VSC) with molecules. Although the onset of VSC has recently been observed spectroscopically with PP nanoresonators, no experiments so far have resolved VSC in real space and with propagating modes in unstructured layers. Here, we demonstrate by real-space nanoimaging that VSC can be achieved between propagating PPs in thin vdW crystals (specifically h-BN) and molecular vibrations in adjacent thin molecular layers. To that end, we performed near-field polariton interferometry, showing that VSC leads to the formation of a propagating hybrid mode with a pronounced anti-crossing region in its dispersion, in which propagation with negative group velocity is found. Numerical calculations predict VSC for nanometer-thin molecular layers and PPs in few-layer vdW materials, which could make propagating PPs a promising platform for ultra-sensitive on-chip spectroscopy and strong coupling experiments.

Real-space observation of vibrational strong coupling between propagating phonon polaritons and organic molecules

Phonon polaritons in van der Waals materials can strongly enhance light–matter interactions at mid-infrared frequencies, owing to their extreme field confinement and long lifetimes1–7. Phonon polaritons thus bear potential for vibrational strong coupling with molecules. Although the onset of vibrational strong coupling was observed spectroscopically with phonon-polariton nanoresonators8, no experiments have resolved vibrational strong coupling in real space and with propagating modes. Here we demonstrate by nanoimaging that vibrational strong coupling can be achieved between propagating phonon polaritons in thin van der Waals crystals (hexagonal boron nitride) and molecular vibrations in adjacent thin molecular layers. We performed near-field polariton interferometry, showing that vibrational strong coupling leads to the formation of a propagating hybrid mode with a pronounced anti-crossing region in its dispersion, in which propagation with negative group velocity is found. Numerical calculations predict vibrational strong coupling for nanometre-thin molecular layers and phonon polaritons in few-layer van der Waals materials, which could make propagating phonon polaritons a promising platform for ultrasensitive on-chip spectroscopy and strong-coupling experiments. Real-space mid-infrared nanoimaging reveals vibrational strong coupling between molecules and propagating phonon polaritons in unstructured, thin hexagonal boron nitride layers, which could provide a platform for testing strong coupling and local control of chemical properties.

Tunable spin and orbital polarization in SrTiO3-based heterostructures

We formulate the effective Hamiltonian of Rashba spin–orbit coupling (RSOC) in (LAO/STO) heterostructures. We derive analytical expressions of properties, e.g. Rashba parameter, effective mass, band edge energy and orbital occupancy, as functions of material and tunable heterostructure parameters. While linear RSOC is dominant around the Γ-point, cubic RSOC becomes significant at the higher-energy anti-crossing region. We find that linear RSOC stems from the structural inversion asymmetry (SIA), while the cubic term is induced by both SIA and bulk asymmetry. Furthermore, the SOC strength shows a striking dependence on the tunable heterostructure parameters such as STO thickness and the interfacial electric field which is ascribed to the quantum confinement effect near the LAO/STO interface. The calculated values of the linear and cubic RSOC are in agreement with previous experimental results.

Role of electron back action on photons in hybridizing double-layer graphene plasmons with localized photons

In this paper, we deal with the electromagnetic coupling between an incident surface-plasmon-polariton wave and relativistic electrons in two graphene layers. Our previous investigation was limited to single-layer graphene (Iurov et al 2017 Phys. Rev. B 96 081408). However, the present work, is both an expanded and extended version of this previous Phys. Rev. B paper after having included very detailed theoretical formalisms and extensive comparisons of results from either one or two graphene layers embedded in a dielectric medium. The additional retarded Coulomb interaction between two graphene layers will compete with the coupling between the single graphene layer and the surface of a conductor. Consequently, some distinctive features, such as triply-hybridized absorption peaks and a new acoustic-like graphene plasmon mode within the anticrossing region, have been found for the double-layer graphene system. Physically, our theory is self-consistent, in comparison with a commonly adopted perturbative theory, for studying hybrid light-plasmon modes and the electron back action on photons. Instead of usual radiation or grating-deflection field coupling, a surface-plasmon-polariton localized field coupling is introduced with completely different dispersion relations for radiative (small wave numbers) and evanescent (large wave numbers) field modes. Technically, the exactly calculated effective scattering matrix for this theory can be employed to construct an effective-medium theory in order to improve the accuracy of the well-known finite-difference time-domain method for solving Maxwell’s equations numerically. Practically, the predicted triply-hybridized absorption peaks can excite polaritons only, giving rise to a possible polariton-condensation based laser.

Robust magnon-photon coupling in a planar-geometry hybrid of inverted split-ring resonator and YIG film

We experimentally demonstrate strongly enhanced coupling between excited magnons in an Yttrium Iron Garnet (YIG) film and microwave photons in an inverted pattern of split-ring resonator (noted as ISRR). The anti-crossing effects of the ISRR’s photon mode and the YIG’s magnon modes were found from |S21|-versus-frequency measurements for different strengths and directions of externally applied magnetic fields. The spin-number-normalized coupling strength (i.e. single spin-photon coupling) {g}_{{rm{eff}}}/2pi sqrt{N} was determined to 0.194 Hz ({g}_{{rm{eff}}}/2pi = 90 MHz) at 3.7 GHz frequency. Furthermore, we found that additional fine features in the anti-crossing region originate from the excitation of different spin-wave modes (such as the magnetostatic surface and the backward-volume magnetostatic spin-waves) rather than the Kittel-type mode. These spin-wave modes, as coupled with the ISRR mode, modify the anti-crossing effect as well as their coupling strength. An equivalent circuit model very accurately reproduced the observed anti-crossing effect and its coupling strength variation with the magnetic field direction in the planar-geometry ISRR/YIG hybrid system. This work paves the way for the design of new types of high-gain magnon-photon coupling systems in planar geometry.

Manifestation of the anticrossing of energy levels in EPR spectra of spin clusters

The EPR spectra of a system of two coupled spins with strongly anisotropic g factors have been calculated. It has been shown that the spectra can exhibit an additional absorption line in the vicinity of the energy level anticrossing. The emergence of this line is caused by strengthening of the off-resonance absorption in the anticrossing region.

Asymmetric long-range hybrid-plasmonic modes in asymmetric nanometer-scale structures

The structural symmetry required for long-range surface-plasmon-polariton modes to take place is examined and mapped to asymmetric plasmonic structures. This study leads to a design methodology that facilitates the realization through systematic design of long-range modes in any asymmetric hybrid plasmonic waveguide (AHPW). Examining the modal behavior of an AHPW reveals that field symmetry on either side of the metal is the only necessary condition for plasmonic structures to support long-range propagation. We report that this field symmetry condition can be satisfied irrespective of asymmetry in a waveguide structure, material, or even field profile. The structure is analyzed using the coupled mode theory, transfer matrix method, and finite-difference time-domain method. The AHPW supports high-loss antisymmetric and long-range symmetric supermodes. Dispersion of these supermodes with respect to waveguide dimensions display similar anticrossing characteristics to those obtained in two coupled harmonic oscillators, where the propagation losses display peaks and troughs in the vicinity of the anticrossing region. To place the work in perspective, an AHPW with a width of 200 nm was found to support a long-range supermode with a subwavelength mode area of 0.23  μm2 and propagation loss of 0.025  dB·μm−1 at the wavelength of 1550 nm, providing a radically improved attenuation confinement trade-off compared with other common types of plasmonic waveguides.

Tunable coupled states of a pair of Tamm plasmon polaritons and a microcavity mode

The coupled states of a pair of Tamm plasmon polaritons and a microcavity mode are studied through the transfer matrix method in a metal–Bragg reflectors–cavity–Bragg reflectors–metal configuration. The properties of coupled states can be adjusted through the cavity thickness, but there is one coupled state for which the frequency remains the same as for the uncoupled Tamm plasmon polariton and independent of the cavity thickness. When the frequency of the uncoupled cavity mode is equal to that of the bare Tamm plasmon polariton, an anticrossing behavior with the most intense coupling occurs. There are three coupled modes with antisymmetry coupling and symmetry coupling in the anticrossing region. As cavity thickness increases, two coupled modes are degenerated into one state with frequency equal to that of the bare Tamm plasmon polariton. The third lower coupled mode and the uncoupled cavity mode are merged into one frequency by steps, but a huge amplification of field occurs in the cavity with the coupled mode. An analytical description is in good agreement with the numerical results.

Magnetic control of a meta-molecule

Metamaterials offer the prospect of new science and applications. They have been designed by shaping or changing the material of the individual meta-molecules to achieve properties not naturally attainable. Composite meta-molecules incorporating a magnetic component offer new opportunities. In this work we report on the interaction between a non-magnetic split ring resonator (SRR) and a thin film of yttrium iron garnet (YIG). Strong hybridized resonances are observed. While the SRR is characterized by a magnetic and electric resonance, in practice, it is found that the YIG couples strongly to this symmetric (electric) mode of the SRR. It is also demonstrated that the anti-crossing region provides fertile ground for the creation of elementary excitations such as backward volume magnetostatic waves.

Organic-based microcavities with vibronic progressions: Photoluminescence

We theoretically study the photoluminescence properties of organic-based microcavities with vibronic progressions. We analyze the relaxation from the exciton reservoirs to the polariton anticrossing region; the presence of vibronic levels qualitatively enriches the physics of the system with the appearance of new decay channels. The relaxation dynamics is studied with a master equation and the cavity photoluminescence is obtained from the polariton stationary population. We show that the exciton radiative recombination in which a molecule ends up in a vibrationally excited level of the electronic ground state can lead to qualitatively new features in the cavity luminescence spectrum.

Field induced crossover in antiferromagnetic spin-frustrated clusters: Influence of static and dynamic structural deformations

We propose a theoretical study of the magnetic behavior of spin frustrated trinuclear clusters in the region of the field induced crossover of the levels which are crucial for the description of the static magnetization and dynamic behavior in a sweeping field. The emphasis is made on a competitive role of the antisymmetric (AS) exchange and static structural distortions of the metal center network as well as on the consequences of the dynamic pseudo Jahn–Teller (JT) instability that is closely related to spin frustration. The structural conformations are shown to be controlled by the magnetic field in the anticrossing region (magnetoelastic coupling). We employ the three-spin model for the cluster anion present in K 6 [ V 15 IV As 6 O 42 ( H 2 O ) ] · 8 H 2 O (V 15 cluster) and analyze the role of different components of AS exchange in the shape of the magnetic susceptibility vs field. Both types of deformations (static and dynamic) are shown to be competitive to the AS exchange and tend to reduce the magnetic anisotropy caused by the AS exchange.

Novel mechanism for rapid spin flip with increasing in-plane wave vector in slightly asymmetric modulation-doped quantum wells

We calculate the electric-field-induced spin splittings in wide slightly asymmetric modulation-doped quantum wells. When spin subbands are anticrossing we demonstrate two-step spin flips as the in-plane wave vector along the [11] direction is increased by 0.002 nm-1. At the beginning of this interval the y-component flips, at the end the x-component. Simultaneously the energy separation stays roughly constant below 1 μeV and the wave functions are interchanged. A bias change of about 1 meV is sufficient to move the Fermi level from below to above the anticrossing region.

Rapid spin flip in a spin subband at an anticrossing region in a slightly asymmetric modulation-doped quantum well

The spin splitting due to structure and bulk inversion asymmetry is calculated for electron subbands in wide slightly asymmetric InGaSb quantum wells. At anticrossings, rapid spin flips in two steps are found as the in-plane wave vector along the [1 1] direction is increased by 0.002 nm −1. First the y-component and then the x-component is flipped. A change of bias of about 1 meV across the quantum well is sufficient move the Fermi level across the anticrossing region.

Electric-field-induced strong mixing betweene1−hh1ande1−hh2excitons in asymmetric double quantum wells

We analyze the electric-field-dependent strong mixing of the two near band-edge ground-state excitons in asymmetric double quantum wells (ADQWs). This excitonic mixing is mainly attributed to the Coulomb interactions between subbands and the valence-subband nonparabolicity. The effect of mixing on the energy levels and oscillator strengths is obtained by a comparison of results including and excluding the Coulomb interaction between different subband pairs which appears in the off-diagonal matrix elements of the Hamiltonian in the calculation of exciton states. We find that a substantial portion of the oscillator strength of the $e1\text{\ensuremath{-}}hh1$ ground-state exciton is due to the $e1\text{\ensuremath{-}}hh2$ subband pair in a bias range of the anticrossing region between pairs of valence subbands. Results also show that excluding the excitonic mixing effect results in significant error in both the energies and the oscillator strengths of the excitons in an ADQW with a thick barrier $(3\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$. Even in an ADQW with a fairly thin barrier $(1.2\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$, the error in the oscillator strengths can be substantial, although the errors in the computed energies may be tolerable. Detailed analysis of ${k}_{\ensuremath{\Vert}}$-dependent Coulomb matrix elements and exciton expansion coefficients reveals that neglecting the off-diagonal elements in the exciton Hamiltonian diminishes the contribution of the ${k}_{\ensuremath{\Vert}}$-dependent subband envelopes around the anticrossing in ${k}_{\ensuremath{\Vert}}$ space to the corresponding excitons. Further, it is demonstrated that the application of almost-degenerate perturbation theory to the uncoupled excitons with the intention of accounting for this mixing effect is to be approached with caution.

Broadening factors ofE1(LO)phonon-plasmon coupled modes of hexagonal InN investigated by infrared reflectance measurements

The LO phonon-plasmon coupling of InN for the ${E}_{1}(\mathrm{LO})$ mode has been found; however, the decoupling for the ${A}_{1}(\mathrm{LO})$ mode has been reported in many issues. Several reports have discussed the electron- and phonon-scattering mechanisms, while there is no detailed investigation on the broadening factors of mode energies even for ${E}_{1}(\mathrm{LO})$ phonon-plasmon coupled scheme. In this issue, the studied InN layers grown by the molecular-beam epitaxy method have residual electron density obtained by Hall measurements in a range from $8\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The electron density measured by infrared reflectance measurements is almost constant with a temperature variation from $5\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The dependence of the observed broadening factors of the ${E}_{1}(\mathrm{LO})$ phonon-plasmon coupled modes on the electron density is found to show the characteristic properties of the level anticrossing, in particular, for the increase of these broadening factors around the level anticrossing region with the temperature increase from $5\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Compared to the recent report on the $\mathrm{LO}$ phonon-plasmon coupled modes for ${A}_{1}(\mathrm{LO})$, smaller broadening for ${E}_{1}(\mathrm{LO})$ is observed here.