Effective Mode Volume Research Articles

Strongly localized nanolaser based on the vertical dipole governed by bound states in the continuum

Ultrasmall mode volumes and strongly localized fields are crucial for the miniaturization and performance enhancement of nanolasers. Here, we demonstrate a nanolaser based on a vertical dipole resonance coupled to its mirror in a periodic array of nanopillars on an Ag mirror, governed by symmetry-protected bound states in the continuum (BICs), which possess extremely small mode volumes and high field enhancement. A nanolaser with a strongly localized field size of only ∼λ/300 (where λ is the resonant wavelength) can be explored by using this vertical dipole. Compared to a vertical dipole nanolaser without a silver mirror, the effective mode volume can be reduced by an order of magnitude, and the threshold can decrease from 5.85 to 0.337 μJ/mm2. Additionally, by controlling further investigated the angle of the incident light, we can also adjust the threshold of the nanolaser. When the incidence angle is adjusted from 9° to 1°, the threshold can be reduced from 1.43 to 0.299 μJ/mm2.

Femtosecond laser direct writing wedge metallic microcavities for terahertz sensing

Metallic resonators allow the manipulation of electromagnetic fields in subwavelength volumes for strong light-matter interaction, underpinning emerging flat-optics devices. Metamaterials designed with optimized effective mode volume (Veff) for stimulating and maximizing the utilization of high-density photons are highly desirable for sensing applications. Here, we demonstrate a bowtie-type terahertz (THz) metallic aperture metamaterial structure with low Veff for enhanced biosensing. The device leverages the inherent characteristic of the femtosecond laser fabrication process enabling wedge cavities down to 3 µm by tailoring the pulse energy, whose sensing performance is superior to trapezoidal ones. Such a substrate-free, microcavity metallic metamaterial sensor with extremely strong interactions achieves an experimentally normalized sensitivity of 0.654 RIU−1, and demonstrates the detection of L-proline down to 0.87 nmol. These findings provide new insights into the design and optimization of efficient THz metamaterials with tightly confined fields for ultrasensitive biomolecular detection.

Generalized Born-Huang expansion under macroscopic quantum electrodynamics framework.

Born-Huang expansion is the cornerstone for studying potential energy surfaces and non-adiabatic couplings (NACs) in molecular systems. However, the traditional approach is insufficient to describe the molecular system, which strongly interacts with quantum light. Inspired by the work by Schäfer et al., we develop the generalized Born-Huang expansion theory within a macroscopic quantum electrodynamics (QED) framework. The theory we present allows us to describe electromagnetic vacuum fluctuations in dielectric media and incorporate the effects of dressed photons (or polaritons) into NACs. With the help of the generalized Born-Huang expansion, we clearly classify electronic nuclear NACs, polaritonic nuclear NACs, and polaritonic electronic NACs. Furthermore, to demonstrate the advantage of the macroscopic QED framework, we estimate polaritonic electronic NACs without any free parameter, such as the effective mode volume, and demonstrate the distance dependence of the polaritonic electronic NACs in a silver planar system. In addition, we take a hydrogen atom in free space as an example and derive spontaneous emission rates from photonic electronic NACs (polaritonic electronic NACs are reduced to photonic electronic NACs). We believe that this work not only provides an avenue for the theoretical exploration of NACs in a nucleus-electron-polariton coupled system but also offers a more comprehensive understanding for molecules coupled with quantum light.

Gain-compensated metal cavity modes and a million-fold improvement of Purcell factors

Using a rigorous mode theory for gain-compensated plasmonic dimers, we demonstrate how quality factors and Purcell factors can be dramatically increased, improving the quality factors from 10 to over 26,000 and the peak Purcell factors from approximately 3000 to over 10 billion. Full three-dimensional calculations are presented for gold dimers in a finite-size gain medium, which allows one to easily surpass fundamental Purcell factor limits of lossy media. Within a regime of linear system response, we show how the Purcell factors are modified by the contributions from the projected local density of states as well as a non-local gain. Further, we show that the effective mode volume and radiative beta factors remain relatively constant, despite the significant enhancement of the Purcell factors.

Simulation of optomechanical interaction of levitated nanoparticle with photonic crystal micro cavity.

We propose and analyze theoretically a promising design of an optical trap for vacuum levitation of nanoparticles based on a one-dimensional (1D) silicon photonic crystal cavity (PhC). The considered cavity has a quadratically modulated width of the silicon wave guiding structure, leading to a calculated cavity quality factor of 8 × 105. An effective mode volume of approximately 0.16 μm3 having the optical field strongly confined outside the silicon structure enables optical confinement on nanoparticle in all three dimensions. The optical forces and particle-cavity optomechanical coupling are comprehensively analyzed for two sizes of silica nanoparticles (100 nm and 150 nm in diameter) and various mode detunings. The value of trapping stiffnesses in the microcavity is predicted to be 5 order of magnitudes higher than that reached for optimized optical tweezers, moreover the linear single photon coupling rate can reach MHz level which is 6 order magnitude larger than previously reported values for common bulk cavities. The theoretical results support optimistic prospects towards a compact chip for optical levitation in vacuum and cooling of translational mechanical degrees of motion for the silica nanoparticle of a diameter of 100 nm.

Effects of Non-Adiabatic Electromagnetic Vacuum Fluctuations on Internal Conversion.

To explore non-adiabatic effects caused by electromagnetic (EM) vacuum fluctuations in molecules, we develop a general theory of internal conversion (IC) in the framework of quantum electrodynamics and propose a new mechanism, "quantum electrodynamic internal conversion" (QED-IC). The theory allows us to compute the rates of the conventional IC and QED-IC processes at the first-principles level. Our simulations manifest that, under experimentally feasible weak light-matter coupling conditions, EM vacuum fluctuations can significantly affect IC rates by an order of magnitude. Moreover, our theory elucidates three key factors in the QED-IC mechanism: the effective mode volume, coupling-weighted normal mode alignment, and molecular rigidity. The theory successfully captures the nucleus-photon interaction in the factor "coupling-weighted normal mode alignment". In addition, we find that molecular rigidity plays a totally different role in conventional IC versus QED-IC rates. Our study provides applicable design principles for exploiting QED effects on IC processes.

On the trade-off between mode volume and quality factor in dielectric nanocavities optimized for Purcell enhancement.

This study explores the effect of geometric limitations on the achievable Purcell factor for single emitters in dielectric structures by employing topology optimization as an inverse design tool to maximize the local density of states. Nanobeams of different lengths with varying fixed central bridge widths are considered to investigate the impact of footprint and geometric length-scale. In single-mode photonic cavities, the Purcell factor is known to be proportional to the ratio of the quality factor Q to the effective mode volume V. Analysis of the optimized nanocavities shows a trade-off between quality factor and mode volume as a function of geometric limitations. Crucially, the design exhibiting the largest Purcell enhancement does not have the highest Q nor the lowest V found in the design pool. On the contrary, it is found that Q consistently drops along with decreasing V as the minimum allowed geometric length-scale decreases while the Purcell factor increases. Finally, the study provides insight into the importance of Q and V for enhancing the Purcell factor under geometric limitations.

Enhanced light-matter interactions in ultrathin transition-metal-dichalcogenide metasurfaces by magnetic and toroidal dipole bound states in the continuum.

Nonradiating states of light have recently received a lot of attention in nanophotonics owing to their ability to confine and enhance the electromagnetic fields at the nanoscale. Such optical states not only offer a promising way to overcome the problem of losses associated with plasmonic materials, but also constitute an efficient platform for interaction of light and matter. Here, we report the radiationless states in compact, ultrathin transition-metal-dichalcogenide metasurfaces, namely bound states in the continuum (BICs). Through applying the multipole analysis to the BIC-based metasurfaces, we demonstrate that the BICs can be classified as magnetic dipole (MD) and electric toroidal dipole (TD) modes, both of which correspond to the Γ-point symmetry-protected BIC. Due to the large field confinement inside the nanoresonators originating from the BICs, the strong coupling is realized between quasi-BICs and the exciton resonance, showing that the Rabi splitting energy can be up to 134 meV and 162 meV for the MD and TD quasi-BIC, respectively. We reveal that reduction of the effective mode volume is highly responsible for the enhancement of coupling strength. Furthermore, it is demonstrated that a large mode volume can lead to increase of the field leakage, which enables our metasurfaces to find applications in, for instance, label-free sensing based on refractometric detection.

Modal properties of dielectric bowtie cavities with deep sub-wavelength confinement.

We present a design for an optical dielectric bowtie cavity which features deep sub-wavelength confinement of light. The cavity is derived via simplification of a complex geometry identified through inverse design by topology optimization, and it successfully retains the extreme properties of the original structure, including an effective mode volume of Veff = 0.083 ± 0.001 (λc/2nSi)3 at its center. Based on this design, we present a modal analysis to show that the Purcell factor can be well described by a single quasinormal mode in a wide bandwidth of interest. Owing to the small mode volume, moreover, the cavity exhibits a remarkable sensitivity to local shape deformations, which we show to be well described by perturbation theory. The intuitive simplification approach to inverse design geometries coupled with the quasinormal mode analysis demonstrated in this work provides a powerful modeling framework for the emerging field of dielectric cavities with deep sub-wavelength confinement.

Label-free DNA biosensing by topological light confinement

Abstract Large-area and transparent all-dielectric metasurfaces sustaining photonic bound states in the continuum (BICs) provide a set of fundamental advantages for ultrasensitive biosensing. BICs bridge the gap of large effective mode volume with large experimental quality factor. Relying on the transduction mechanism of reactive sensing principle, herein, we first numerically study the potential of subwavelength confinement driven by topological decoupling from free space radiation for BIC-based biosensing. Then, we experimentally combine this capability with minimal and low-cost optical setup, applying the devised quasi-BIC resonator for PNA/DNA selective biosensing with real-time monitoring of the binding event. A sensitivity of 20 molecules per micron squared is achieved, i.e. ≃0.01 pg. Further enhancement can easily be envisaged, pointing out the possibility of single-molecule regime. This work aims at a precise and ultrasensitive approach for developing low-cost point-of-care tools suitable for routine disease prescreening analyses in laboratory, also adaptable to industrial production control.

Ultra-confined low-loss surface phonon polaritonic resonances in periodically patterned monolayer hexagonal boron nitride

Surface plasmon polaritons in two-dimensional (2D) materials such as graphene have drawn much attention in the past decades, nevertheless, suffer from ohmic losses. Recently, monolayer hexagonal boron nitride (hBN) has been found the capability to support low-loss surface phonon polaritons (SPhPs). In this work, we theoretically propose the atom-thin metasurface with monolayer-hBN. We reveal that monolayer-hBN disk array can support SPhP resonances with ultra-small effective mode volumes (~10−9 λ03) as well as high quality factors (102-103) in mid-infrared (mid-IR). The corresponding frequency dispersions with geometrical parameters and ambient environment are also discussed in detail. Furthermore, the phenomenon of phonon hybridization is demonstrated based on monolayer-hBN ring array. Finally, the local field enhancement with an enhancement factor ~103 is realized by breaking the symmetry of the ring. This work reveals that monolayer-hBN can play an important role in 2D material polaritonics and atom-thin metasurfaces, and has great potential in mid-IR quantum emission, sensing and spectroscopic applications.

Efficient spontaneous emission by metal-dielectric antennas; antenna Purcell factor explained

The rate of spontaneous emission from an optical emitter can be greatly enhanced using a metallic optical antenna at the penalty of efficiency. In this paper we propose a metal-dielectric antenna that eliminates the tradeoff between spontaneous emission enhancement and radiative efficiency by using nanoscopic dielectric structures at the antenna tips. This tradeoff occurs due to Ohmic loss and is further exacerbated by electron surface collisions. We find that our metal-dielectric antenna can enhance spontaneous emission by a factor 5 × 105 with efficiency = 70%, greatly exceeding the radiative efficiency of a purely metallic antenna with similar enhancement. Moreover, the metal-dielectric antenna design strategy is naturally amenable to short-distance optical communications applications. We go on to discuss the Purcell effect within the context of antenna enhancement. Metallic optical antennas are best analyzed with conventional antenna circuit models, but if the Purcell enhancement were to be employed, we provide the effective mode volume, Veff = (3/4π2)2d2λ(λ/l)5, that would be needed.

Theoretical study on amplifying strong exciton–photon coupling based on surface plasmon in a hybridized perovskite nanowire-metal film-perovskite nanowire structure

We theoretically report a strong light–matter interaction in a sandwich structure composed of hybridized inorganic–organic perovskite nanowires, silica (SiO2) films and a silver (Ag) film. Surface plasmon effectively enhances the strong exciton–photon coupling strength of perovskite nanowires, which depends on reduction of effective mode volume and local field enhancement. By calculation, we find that the thicknesses of SiO2 and Ag films can affect the coupling strength. With the suitable thickness of SiO2 (5 nm) and Ag (30 nm) films, Rabi splitting can reach 319 meV, while without an Ag film Rabi splitting is only 270 meV. Furthermore, Rabi splitting shows a negative correlation with SiO2 film thickness within a limited range. Still, it has a nonlinear relation with Ag film thickness because the imaginary part of the effective index for the hybridized mode shows a nonlinear relation with Ag film thickness. Our structure provides suitable parameters for the experiment and has potential application in nano-lasers.

Dynamically tunable polarization beam splitting with slotted graphene patch arrays in the terahertz regime

Inspired by the reflectarray concept, we propose a polarization beam splitter (PBS) using orthogonally oriented slotted graphene patches configured in a two-layer metasurface, which bidirectionally deflects the incident wave depending on its polarization in the terahertz (THz) regime. Our device employs slotted graphene patch resonators as plasmonic dipoles to provide a nearly 360° phase shift for orthogonal linearly polarized waves, which can be independently controlled for each polarization. The PBS operating frequency is also continuously tunable over a 20% frequency bandwidth, just by equally varying the graphene patches’ Fermi level in the device structure. In light of highly confined electromagnetic fields for slotted graphene patches, they have a very small effective mode volume, enabling us to utilize miniaturized metasurfaces and components. Moreover, due to the pattern simplicity of the slotted graphene patches, they can be used as practical building blocks for other THz metasurfaces with novel functionalities, which can be likely avenues for future telecommunication applications.

Purcell-enhanced photoluminescence of few-layer MoS2 transferred on gold nanostructure arrays with plasmonic resonance at the conduction band edge.

Plasmonic coupling of metallic nanostructures with two-dimensional molybdenum disulfide (MoS2) atomic layers is an important topic because it provides a pathway to manipulate the optoelectronic properties and to overcome the limited optical cross-section of the materials. Plasmonic enhanced light-matter interaction of a MoS2 layer is known to be mainly governed by optical field enhancement and the Purcell effect, while the discrimination of the contribution from each mechanism to the plasmonic enhancement is challenging. Here, we investigate photoluminescence (PL) enhancement from few-layer MoS2 transferred on Au nanostructure arrays with controlled localized surface plasmon resonance (LSPR) spectral positions that were detuned from the excitation wavelengths. Two distinctive regimes in LSPR mode-dependent PL enhancement were revealed showing a maximum enhancement (∼40-fold) with zero detuning and a modest enhancement (∼10-fold) with the red-shift detuned LSPR from the excitation wavelength, which were attributed to LSPR-induced optical field enhancement and the Purcell effect, respectively. By applying the experimental parameters into the Purcell effect formalism, an effective mode volume of ∼0.016λ03 was estimated. Our work provides an insight into how to utilize few-layer MoS2 as a base material for optoelectronics by harnessing Purcell-enhanced optical responsivity.

Quasinormal-mode theory of elastic Purcell factors and Fano resonances of optomechanical beams

We introduce a quasinormal mode theory of mechanical open-cavity modes for optomechanical resonators, and demonstrate the importance of using a generalized (complex) effective mode volume and the phase of the quasinormal mode. We first generalize and fix the normal mode theories of the elastic Purcell factor, and then show a striking example of coupled quasinormal modes yielding a pronounced Fano resonance. Our theory is exemplified and confirmed by full three-dimensional calculations on optomechanical beams, but the general findings apply to a wide range of mechanical cavity modes. This quasinormal mechanical mode formalism, when also coupled with a quasinormal theory of optical cavities, offers a unified framework for describing a wide range of optomechanical structures where dissipation is an inherent part of the resonator modes.

Acoustic diamond resonators with ultrasmall mode volumes

Quantum acoustodynamics (QAD) is a rapidly developing field of research, offering possibilities to realize and study macroscopic quantum-mechanical systems in a new range of frequencies, and implement transducers and new types of memories for hybrid quantum devices. Here we propose a novel design for a versatile diamond QAD cavity operating at GHz frequencies, exhibiting effective mode volumes of about $10^{-4}\lambda^3$. Our phononic crystal waveguide cavity implements a non-resonant analogue of the optical lightning-rod effect to localize the energy of an acoustic mode into a deeply-subwavelength volume. We demonstrate that this confinement can readily enhance the orbit-strain interaction with embedded nitrogen-vacancy (NV) centres towards the high-cooperativity regime, and enable efficient resonant cooling of the acoustic vibrations towards the ground state using a single NV. This architecture can be readily translated towards setup with multiple cavities in one- or two-dimensional phononic crystals, and the underlying non-resonant localization mechanism will pave the way to further enhance optoacoustic coupling in phoxonic crystal cavities.

Bound States in the Continuum in Anisotropic Plasmonic Metasurfaces.

The concept of optical bound states in the continuum (BICs) currently drives the field of dielectric resonant nanophotonics, providing an important physical mechanism for engineering high-quality (high-Q) optical resonances in high-index dielectric nanoparticles and structured dielectric metasurfaces. For structured metallic metasurfaces, realization of BICs remains a challenge associated with strong dissipative losses of plasmonic materials. Here, we suggest and realize experimentally anisotropic plasmonic metasurfaces supporting high-Q resonances governed by quasi-BIC collective resonant modes. Our metasurfaces are composed of arrays of vertically oriented double-pillar meta-molecules covered by a thin layer of gold. We engineer quasi-BIC modes and observe experimentally sharp resonances in mid-IR reflectance spectra. Our work suggests a direct route to boost the resonant field enhancement in plasmonic metasurfaces via combining a small effective mode volume of plasmonic systems with engineered high-Q resonances provided by the BIC physics, with multiple applications to enhance light-matter interaction for nano-optics and quantum photonics.

Photon-level tuning of photonic nanocavities

Energy-efficient optical control of photonic device properties is crucial for diverse photonic signal processing. Here we demonstrate extremely efficient optical tuning of photonic nanocavities, with only photon-level optical energy. With a lithium niobate photonic crystal nanocavity with an optical Q up to 1.41 million and an effective mode volume down to 0.78$(\lambda/n)^3$, we are able to achieve a resonance tuning rate of about 88.4~MHz/photon (0.67~GHz/aJ), which allows us to tune across the whole cavity resonance with only about 2.4 photons on average inside the cavity. Such a photon-level resonance tuning is of great potential for energy-efficient optical switching, wavelength routing, and reconfiguration of photonic devices/circuits that are indispensable for future photonic interconnect.

Low-index-mode photonic crystal nanobeam cavity for refractive index sensing at the 2 μm wavelength band.

We present the design, fabrication, and characterization of a one-dimensional photonic crystal (1D-PhC) low-index-mode nanobeam cavity on the silicon-on-insulator platform for refractive index sensing at the 2μm wavelength band. A Q-factor of 4.35×105 and an effective mode volume of Veff∼1.95(λ/nSi)3 are theoretically achieved. The measured transmission spectrum of the device immersed in NaCl solutions with different mass concentrations demonstrates a sensitivity of 326.1nm/RIU and a Q-factor of ∼1144.