We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrief...We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrieffer-Heeger chains.The formation of topological Floquet BICs can be adjusted only by tuning the driving amplitude or frequency,regardless of whether the static system has BICs or not.The interchain bias can only change the localization property of topological Floquet BICs,and a bigger bias can lead to transforming topological Floquet BICs into bound states out of the continuum(BOCs).But it does not change the topological properties of these topological Floquet states.Based on the repulsion effect of edge states,we propose to detect occurrence of topological Floquet BICs and transition point between topological Floquet BICs and BOCs using quantum walk.Our work provided a convenient and realistic approach for the experimental realization and manipulation of BICs in a single-particle quantum system.展开更多
Compared to traditional single-frequency bound states in the continuum(BIC),dual-band BIC of-fers higher degrees of freedom and functionality.Moveover,implementing independent control of dual-band BICs can further enh...Compared to traditional single-frequency bound states in the continuum(BIC),dual-band BIC of-fers higher degrees of freedom and functionality.Moveover,implementing independent control of dual-band BICs can further enhance their advantages and maximize their performance.This study presents a design for a dielectric metasurface that achieves dual-band BICs in the terahertz(THz)range.By adjusting two asym-metry parameters of the structure,independent control of the two symmetry-protected BICs is achieved.Fur-thermore,by varying the shape of the silicon holes,the design's robustness to geometric variations is demon-strated.Finally,the test results show that the figures of merit(FOMs)for both BICs reach 109.This work provides a new approach for realizing and tuning dual-frequency BICs,offering expanded possibilities for applications in multimode lasers,nonlinear optics,multi-channel filtering,and optical sensing.展开更多
A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quali...A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quality factor(Q-factor)can be supported by such a grating when perfect reflection is introduced at its boundaries.If geometrical perturbations are introduced into the structure,the dark BICs transform into bright quasi-BICs with finite Q-factor,maintaining spectral characteristics nearly identical to those of quasi-BICs supported by infinite gratings.When the boundaries are replaced with high-reflectivity metallic mirrors,the Q-factor of the resonant mode is reduced to be finite;however,it can be much larger than that in the corresponding nanostructure with open boundaries and can be tuned over a large range by varying the number of unit cells or boundary conditions.展开更多
The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium s...The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium systems.In this work,we study the possible bound states in the triple-ηcand triple-J/ψsystems with J^(PC)=0^(-+)and 1^(--),respectively.In quantum chromodynamics sum rules,we calculate the two-point correlation functions and spectral functions up to the dimension-four gluon condensate.We use the iterative dispersion relation approach to deal with the five-loop banana integrals,which significantly improves computational efficiency.Our results show that the masses of triple-ηcand triple-J/ψstates lie below the corresponding mass thresholds,supporting the existence of such three-body bound states.展开更多
This paper demonstrated the generation of multi-wavelength bound state noise-like pulse(BNLP)in a dispersion-managed composite-filtered fiber laser consisting of nonlinear polarization rotation(NPR)and loop.In the cas...This paper demonstrated the generation of multi-wavelength bound state noise-like pulse(BNLP)in a dispersion-managed composite-filtered fiber laser consisting of nonlinear polarization rotation(NPR)and loop.In the case of BNLP,the generation is caused by the interaction between two noise-like pulses(NLPs)induced by the comb-filtering effect,and bound state level can be artificially controlled in the researches.Our work provides a new method for generating low-coherence pulses and establishes a research idea for the study of the comb-filtering effects.展开更多
Two types of bound states in continuum(BICs),symmetry-protected and Brillouin zone folding driven,are identified in hollow Si nanorod arrays.By modulating the direction and distance of the air holes from the center of...Two types of bound states in continuum(BICs),symmetry-protected and Brillouin zone folding driven,are identified in hollow Si nanorod arrays.By modulating the direction and distance of the air holes from the center of the nanorods,it is possible to achieve either a single quasi-BIC or three quasi-BICs.The transmission spectra exhibit ultra-narrow lines,and the quasi-BICs demonstrate ultra-high Q factors.Additionally,efficient third-harmonic generation occurs at low pump intensities.The results indicate that the proposed nanostructures of two types of BICs with a flexible modulation hold great potential applications for nonlinear photonic devices.展开更多
We report the bifurcation of bound states in the continuum(BICs) in a dissipative cavity magnonic system, where a BIC splits into a pair of BICs. We theoretically analyze BICs in a dissipative cavity magnonic system a...We report the bifurcation of bound states in the continuum(BICs) in a dissipative cavity magnonic system, where a BIC splits into a pair of BICs. We theoretically analyze BICs in a dissipative cavity magnonic system and derive the critical condition for BICs bifurcation. Based on the theoretical results, we experimentally tune the dissipative photon–magnon coupling strength and demonstrate precise control over the detuning and number of BICs. When the dissipative coupling strength reaches a critical value, we observe the bifurcation of BICs, which is consistent with the theoretical prediction. Our systematic investigation of the evolution of BICs concerning the dissipative coupling strength and the discovery of the BIC bifurcation may enhance the sensitivity of BICs to external perturbations, potentially enabling applications in ultrasensitive detection.展开更多
The realization of high-Q resonances in a silicon metasurface with various broken-symmetry blocks is reported. Theoretical analysis reveals that the sharp resonances in the metasurfaces originate from symmetry-protect...The realization of high-Q resonances in a silicon metasurface with various broken-symmetry blocks is reported. Theoretical analysis reveals that the sharp resonances in the metasurfaces originate from symmetry-protected bound in the continuum(BIC) and the magnetic dipole dominates these peculiar states. A smaller size of the defect in the broken-symmetry block gives rise to the resonance with a larger Q factor. Importantly, this relationship can be tuned by changing the structural parameter, resulting from the modulation of the topological configuration of BICs. Consequently, a Q factor of more than 3,000 can be easily achieved by optimizing dimensions of the nanostructure. At this sharp resonance, the intensity of the third harmonic generation signal in the patterned structure can be 368 times larger than that of the flat silicon film. The proposed strategy and underlying theory can open up new avenues to realize ultrasharp resonances, which may promote the development of the potential meta-devices for nonlinearity, lasing action, and sensing.展开更多
We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] prov...We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0展开更多
Bound states in the continuum(BICs)have exhibited extraordinary properties in photonics for enhanced light-matter interactions that enable appealing applications in nonlinear optics,biosensors,and ultrafast optical sw...Bound states in the continuum(BICs)have exhibited extraordinary properties in photonics for enhanced light-matter interactions that enable appealing applications in nonlinear optics,biosensors,and ultrafast optical switches.The most common strategy to apply BICs in a metasurface is by breaking symmetry of resonators in the uniform array that leaks the otherwise uncoupled mode to free space and exhibits an inverse quadratic relationship between quality factor(Q)and asymmetry.Here,we propose a scheme to further reduce scattering losses and improve the robustness of symmetry-protected BICs by decreasing the radiation density with a hybrid BIC lattice.We observe a significant increase of radiative Q in the hybrid lattice compared to the uniform lattice with a factor larger than 14.6.In the hybrid BIC lattice,modes are transferred toГpoint inherited from high symmetric X,Y,and M points in the Brillouin zone that reveal as multiple Fano resonances in the far field and would find applications in hyperspectral sensing.This work initiates a novel and generalized path toward reducing scattering losses and improving the robustness of BICs in terms of lattice engineering that would release the rigid requirements of fabrication accuracy and benefit applications of photonics and optoelectronic devices.展开更多
Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Current...Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Currently,symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry,but few cases are achieved by breaking the material symmetry.This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry.Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to-980 times the resonance wavelength,and the maximum GH shift is located at the reflection peak with unity reflectance.This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future.展开更多
The emergence of two dimensional(2D)materials has opened new possibilities for exhibiting second harmonic genera-tion(SHG)at the nanoscale,due to their remarkable optical response related to stable excitons at room te...The emergence of two dimensional(2D)materials has opened new possibilities for exhibiting second harmonic genera-tion(SHG)at the nanoscale,due to their remarkable optical response related to stable excitons at room temperature.However,the ultimate atomic-scale interaction length with light makes the SHG of Transition Metal Dichalcogenides(TM-Ds)monolayers naturally weak.Here,we propose coupling a monolayer of TMDs with a photonic grating slab that works with doubly resonant bound states in the continuum(BIC).The BIC slabs are designed to exhibit a pair of BICs,reson-ant with both the fundamental wave(FW)and the second harmonic wave(SHW).Firstly,the spatial mode matching can be fulfilled by tilting FW's incident angle.We theoretically demonstrate that this strategy leads to more than four orders of magnitude enhancement of SHG efficiency than a sole monolayer of TMDs,under a pump light intensity of 0.1 GW/cm^(2).Moreover,we demonstrate that patterning the TMDs monolayer can further enhance the spatial overlap coefficient,which leads to an extra three orders of magnitude enhancement of SHG efficiency.These results demonstrate remarkable pos-sibilities for enhancing SHG with nonlinear 2D materials,opening many opportunities for chip-based light sources,nano-lasers,imaging,and biochemical sensing.展开更多
Andreev reflection （AR） in a normal-metal/quantum-dot/superconductor （N-QD-S） system with coupled Majorana bound states （MBSs） is investigated theoretically. We find that in the N--QD-S system, the AR can be enh...Andreev reflection （AR） in a normal-metal/quantum-dot/superconductor （N-QD-S） system with coupled Majorana bound states （MBSs） is investigated theoretically. We find that in the N--QD-S system, the AR can be enhanced when coupling to the MBSs is incorporated. Fano line-shapes can be observed in the AR conductance spectrum when there is an appropriate QD-MBS coupling or MBS-MBS coupling. The AR conductance is always e2/2h at the zero Fermi energy point when only QD--MBSs coupling is considered. In addition, the resonant AR occurs when the MBS-MBS coupling roughly equals to the QD energy level. We also find that an AR antiresonance appears when the QD energy level approximately equals to the sum of the QD-MBS coupling and the MBS-MBS coupling. These features may serve as characteristic signatures for the probe of MBSs.展开更多
A theoretical study on discrete vortex bound states is carried out near a vortex core in the presence of a van Hove singularity(VHS) near the Fermi level by solving Bogoliubov–de Gennes(Bd G) equations. When the VHS ...A theoretical study on discrete vortex bound states is carried out near a vortex core in the presence of a van Hove singularity(VHS) near the Fermi level by solving Bogoliubov–de Gennes(Bd G) equations. When the VHS lies exactly at the Fermi level and also at the middle of the band, a zero-energy state and other higher-energy states whose energy ratios follow integer numbers emerge. These discrete vortex bound state peaks undergo a splitting behavior when the VHS or Fermi level moves away from the middle of the band. Such splitting behavior will eventually lead to a new arrangement of quantized vortex core states whose energy ratios follow half-odd-integer numbers.展开更多
We consider the following nonlinear Schroodinger equations -ε^2△u ＋ u = Q（x）｜u｜^p-2u in R^N, u ∈ H^1（R^N）,where ε is a small positive parameter, N ≥ 2, 2 〈 p 〈 ∞ for N = 2 and 2 〈 p 〈2N/N-2 for N ≥ 3...We consider the following nonlinear Schroodinger equations -ε^2△u ＋ u = Q（x）｜u｜^p-2u in R^N, u ∈ H^1（R^N）,where ε is a small positive parameter, N ≥ 2, 2 〈 p 〈 ∞ for N = 2 and 2 〈 p 〈2N/N-2 for N ≥ 3. We prove that this problem has sign-changing（nodal） semi-classical bound states with clustered spikes for sufficiently small ε under some additional conditions on Q（x）.Moreover, the number of this type of solutions will go to infinity as ε→ 0^＋.展开更多
We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of...We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of the equation is instantaneous ＂occasionally＂）. The obtained rigorous instantaneous formulation, in fact, is expressed as an operator sandwiched by two ＂reduced BS wave functions＂ properly, while the reduced BS wave functions appearing in the formulation are the rigorous solutions of the instantaneous BS equation, and they may relate to Schroedinger wave functions straightforwardly. We also show that the rigorous instantaneous formulation is gauge-invariant with respect to the Uem（1） transformation precisely, if the concerned transitions are radiative. Some applications of the formulation are outlined.展开更多
The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is sti...The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is still debatable. When it is at rest, the space-like separation between the constituent particles is the primary variable. When the bound state moves, this space-like separation picks up the time-like separation. The time-separation is not a measurable variable in the present form of quantum mechanics. The only way to deal with this un-observable variable is to treat it statistically. This leads to rise of the statistical variables such entropy and temperature. Paul A. M. Dirac made efforts to construct bound-state wave functions in Einstein’s Lorentz-covariant world. In 1927, he noted that the c-number time-energy relation should be incorporated in the relativistic world. In 1945, he constructed four-dimensional oscillator wave functions with one time coordinate in addition to the three-dimensional space. In 1949, Dirac introduced the light-cone coordinate system for Lorentz transformations. It is then possible to integrate these contributions made by Dirac to construct the Lorentz-covariant harmonic oscillator wave functions. This oscillator system can explain the proton as a bound state of the quarks when it is at rest, and explain the Feynman’s parton picture when it moves with a speed close to that of light. While the un-measurable time-like separation becomes equal to the space-like separation at this speed, the statistical variables become prominent. The entropy and the temperature of this covariant harmonic oscillator are calculated. It is shown that they rise rapidly as the proton speed approaches that of light.展开更多
We study the existence and non-existence of bound states （i.e., solutions in W1,P（RN）） for a class of quasilinear scalar field equations of the for -△pu＋V（x）｜u｜p-2u=a（x）｜u｜q-2u,x∈RN,1〈P〈N,mwhen the po...We study the existence and non-existence of bound states （i.e., solutions in W1,P（RN）） for a class of quasilinear scalar field equations of the for -△pu＋V（x）｜u｜p-2u=a（x）｜u｜q-2u,x∈RN,1〈P〈N,mwhen the potentials V（.）≥ 0 and a（.） decay to zero at infinity.展开更多
The one-dimensional Dirac particle for equal scalar and vector asymmetric q-parameter hyperbolic PschlTeller potential (qHPT) is solved in terms of hypergeometric functions. The scattering and bound states are obtaine...The one-dimensional Dirac particle for equal scalar and vector asymmetric q-parameter hyperbolic PschlTeller potential (qHPT) is solved in terms of hypergeometric functions. The scattering and bound states are obtained by using the properties of the equation of continuity of the wave functions. We calculat in details the transmission and reflection coefficients.展开更多
In this study, we present the analytical solutions of bound states for the Schrodinger equation with the mulfiparameter potential containing the different types of physical potentials via the asymptotic iteration meth...In this study, we present the analytical solutions of bound states for the Schrodinger equation with the mulfiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l （states） quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues. Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12175315 and 12205385)。
文摘We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrieffer-Heeger chains.The formation of topological Floquet BICs can be adjusted only by tuning the driving amplitude or frequency,regardless of whether the static system has BICs or not.The interchain bias can only change the localization property of topological Floquet BICs,and a bigger bias can lead to transforming topological Floquet BICs into bound states out of the continuum(BOCs).But it does not change the topological properties of these topological Floquet states.Based on the repulsion effect of edge states,we propose to detect occurrence of topological Floquet BICs and transition point between topological Floquet BICs and BOCs using quantum walk.Our work provided a convenient and realistic approach for the experimental realization and manipulation of BICs in a single-particle quantum system.
文摘Compared to traditional single-frequency bound states in the continuum(BIC),dual-band BIC of-fers higher degrees of freedom and functionality.Moveover,implementing independent control of dual-band BICs can further enhance their advantages and maximize their performance.This study presents a design for a dielectric metasurface that achieves dual-band BICs in the terahertz(THz)range.By adjusting two asym-metry parameters of the structure,independent control of the two symmetry-protected BICs is achieved.Fur-thermore,by varying the shape of the silicon holes,the design's robustness to geometric variations is demon-strated.Finally,the test results show that the figures of merit(FOMs)for both BICs reach 109.This work provides a new approach for realizing and tuning dual-frequency BICs,offering expanded possibilities for applications in multimode lasers,nonlinear optics,multi-channel filtering,and optical sensing.
基金supported by the National Natural Science Foundation of China(Grant Nos.11874270 and 12174228)the Shenzhen Basic Research Special Project(Grant No.JCYJ20240813141606009)。
文摘A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quality factor(Q-factor)can be supported by such a grating when perfect reflection is introduced at its boundaries.If geometrical perturbations are introduced into the structure,the dark BICs transform into bright quasi-BICs with finite Q-factor,maintaining spectral characteristics nearly identical to those of quasi-BICs supported by infinite gratings.When the boundaries are replaced with high-reflectivity metallic mirrors,the Q-factor of the resonant mode is reduced to be finite;however,it can be much larger than that in the corresponding nanostructure with open boundaries and can be tuned over a large range by varying the number of unit cells or boundary conditions.
基金supported by the National Natural Science Foundation of China(Grant No.12175318)the Natural Science Foundation of Guangdong Province of China(Grant No.2023A1515011704)。
文摘The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium systems.In this work,we study the possible bound states in the triple-ηcand triple-J/ψsystems with J^(PC)=0^(-+)and 1^(--),respectively.In quantum chromodynamics sum rules,we calculate the two-point correlation functions and spectral functions up to the dimension-four gluon condensate.We use the iterative dispersion relation approach to deal with the five-loop banana integrals,which significantly improves computational efficiency.Our results show that the masses of triple-ηcand triple-J/ψstates lie below the corresponding mass thresholds,supporting the existence of such three-body bound states.
基金supported by the Research Fund of Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology(No.2020B1212030010)。
文摘This paper demonstrated the generation of multi-wavelength bound state noise-like pulse(BNLP)in a dispersion-managed composite-filtered fiber laser consisting of nonlinear polarization rotation(NPR)and loop.In the case of BNLP,the generation is caused by the interaction between two noise-like pulses(NLPs)induced by the comb-filtering effect,and bound state level can be artificially controlled in the researches.Our work provides a new method for generating low-coherence pulses and establishes a research idea for the study of the comb-filtering effects.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12174228 and 12274271)。
文摘Two types of bound states in continuum(BICs),symmetry-protected and Brillouin zone folding driven,are identified in hollow Si nanorod arrays.By modulating the direction and distance of the air holes from the center of the nanorods,it is possible to achieve either a single quasi-BIC or three quasi-BICs.The transmission spectra exhibit ultra-narrow lines,and the quasi-BICs demonstrate ultra-high Q factors.Additionally,efficient third-harmonic generation occurs at low pump intensities.The results indicate that the proposed nanostructures of two types of BICs with a flexible modulation hold great potential applications for nonlinear photonic devices.
基金Project supported by the National Key Research and Development Program of China (Grant No. 2023YFA1406604)the National Natural Science Foundation of China (Grant Nos. 12274260, 12204306, 12122413, and 12474120)+1 种基金the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2024YQ001)the Qilu Young Scholar Programs of Shandong University。
文摘We report the bifurcation of bound states in the continuum(BICs) in a dissipative cavity magnonic system, where a BIC splits into a pair of BICs. We theoretically analyze BICs in a dissipative cavity magnonic system and derive the critical condition for BICs bifurcation. Based on the theoretical results, we experimentally tune the dissipative photon–magnon coupling strength and demonstrate precise control over the detuning and number of BICs. When the dissipative coupling strength reaches a critical value, we observe the bifurcation of BICs, which is consistent with the theoretical prediction. Our systematic investigation of the evolution of BICs concerning the dissipative coupling strength and the discovery of the BIC bifurcation may enhance the sensitivity of BICs to external perturbations, potentially enabling applications in ultrasensitive detection.
基金support from the National Key Research and Development Project (Grant No. 2018YFB2200500, 2018YFB2202800)National Natural Science Foundation of China (Grant No. 61534004, 91964202, 61874081, 61851406, 91950119, and 61905196)。
文摘The realization of high-Q resonances in a silicon metasurface with various broken-symmetry blocks is reported. Theoretical analysis reveals that the sharp resonances in the metasurfaces originate from symmetry-protected bound in the continuum(BIC) and the magnetic dipole dominates these peculiar states. A smaller size of the defect in the broken-symmetry block gives rise to the resonance with a larger Q factor. Importantly, this relationship can be tuned by changing the structural parameter, resulting from the modulation of the topological configuration of BICs. Consequently, a Q factor of more than 3,000 can be easily achieved by optimizing dimensions of the nanostructure. At this sharp resonance, the intensity of the third harmonic generation signal in the patterned structure can be 368 times larger than that of the flat silicon film. The proposed strategy and underlying theory can open up new avenues to realize ultrasharp resonances, which may promote the development of the potential meta-devices for nonlinearity, lasing action, and sensing.
基金Supported by NSFC(10631030) and CAS-KJCX3-SYW-S03
文摘We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0
基金This work was supported by the National Natural Science Foundation of China(Award No.62175099)Guangdong Basic and Applied Basic Research Foundation(Award No.2023A1515011085)+1 种基金Stable Support Program for Higher Education Institutions from Shenzhen Science,Technology&Innovation Commission(Award No.20220815151149004)Global recruitment program of young experts of China,and startup funding of Southern University of Science and Technology.The authors acknowledge the assistance of SUSTech Core Research Facilities and thank Yao Wang for helpful discussions on fabrication.
文摘Bound states in the continuum(BICs)have exhibited extraordinary properties in photonics for enhanced light-matter interactions that enable appealing applications in nonlinear optics,biosensors,and ultrafast optical switches.The most common strategy to apply BICs in a metasurface is by breaking symmetry of resonators in the uniform array that leaks the otherwise uncoupled mode to free space and exhibits an inverse quadratic relationship between quality factor(Q)and asymmetry.Here,we propose a scheme to further reduce scattering losses and improve the robustness of symmetry-protected BICs by decreasing the radiation density with a hybrid BIC lattice.We observe a significant increase of radiative Q in the hybrid lattice compared to the uniform lattice with a factor larger than 14.6.In the hybrid BIC lattice,modes are transferred toГpoint inherited from high symmetric X,Y,and M points in the Brillouin zone that reveal as multiple Fano resonances in the far field and would find applications in hyperspectral sensing.This work initiates a novel and generalized path toward reducing scattering losses and improving the robustness of BICs in terms of lattice engineering that would release the rigid requirements of fabrication accuracy and benefit applications of photonics and optoelectronic devices.
基金Project supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ23F040001)the National Natural Science Foundation of China(Grant No.12204446)+1 种基金the Public Welfare Technology Research Project of Zhejiang Province(Grant No.LGC22E050006)the Quzhou Science and Technology Project of China(Grant No.2022K104).
文摘Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Currently,symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry,but few cases are achieved by breaking the material symmetry.This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry.Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to-980 times the resonance wavelength,and the maximum GH shift is located at the reflection peak with unity reflectance.This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future.
基金financial supports from the National Natural Science Foundation of China(Grant No.11604150)Fundamental Research Funds for the Central Universities of China(Grant No.ZYGX2020J010)M.Rahmani.acknowledges support from the UK Research and Innovation Future Leaders Fellowship(MR/T040513/1)。
文摘The emergence of two dimensional(2D)materials has opened new possibilities for exhibiting second harmonic genera-tion(SHG)at the nanoscale,due to their remarkable optical response related to stable excitons at room temperature.However,the ultimate atomic-scale interaction length with light makes the SHG of Transition Metal Dichalcogenides(TM-Ds)monolayers naturally weak.Here,we propose coupling a monolayer of TMDs with a photonic grating slab that works with doubly resonant bound states in the continuum(BIC).The BIC slabs are designed to exhibit a pair of BICs,reson-ant with both the fundamental wave(FW)and the second harmonic wave(SHW).Firstly,the spatial mode matching can be fulfilled by tilting FW's incident angle.We theoretically demonstrate that this strategy leads to more than four orders of magnitude enhancement of SHG efficiency than a sole monolayer of TMDs,under a pump light intensity of 0.1 GW/cm^(2).Moreover,we demonstrate that patterning the TMDs monolayer can further enhance the spatial overlap coefficient,which leads to an extra three orders of magnitude enhancement of SHG efficiency.These results demonstrate remarkable pos-sibilities for enhancing SHG with nonlinear 2D materials,opening many opportunities for chip-based light sources,nano-lasers,imaging,and biochemical sensing.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61176089 and 10974043)the Natural Science Foundation of Hebei Province,China(Grant Nos.A2011205092 and 2014205005)the Fund for Hebei Normal University for Nationalities,China(Grant No.201109)
文摘Andreev reflection （AR） in a normal-metal/quantum-dot/superconductor （N-QD-S） system with coupled Majorana bound states （MBSs） is investigated theoretically. We find that in the N--QD-S system, the AR can be enhanced when coupling to the MBSs is incorporated. Fano line-shapes can be observed in the AR conductance spectrum when there is an appropriate QD-MBS coupling or MBS-MBS coupling. The AR conductance is always e2/2h at the zero Fermi energy point when only QD--MBSs coupling is considered. In addition, the resonant AR occurs when the MBS-MBS coupling roughly equals to the QD energy level. We also find that an AR antiresonance appears when the QD energy level approximately equals to the sum of the QD-MBS coupling and the MBS-MBS coupling. These features may serve as characteristic signatures for the probe of MBSs.
基金the National Natural Science Foundation of China (Grant No. 11804154)the Scientific Research Foundation of NJIT (Grant Nos. YKJ201853 and CKJA201807)。
文摘A theoretical study on discrete vortex bound states is carried out near a vortex core in the presence of a van Hove singularity(VHS) near the Fermi level by solving Bogoliubov–de Gennes(Bd G) equations. When the VHS lies exactly at the Fermi level and also at the middle of the band, a zero-energy state and other higher-energy states whose energy ratios follow integer numbers emerge. These discrete vortex bound state peaks undergo a splitting behavior when the VHS or Fermi level moves away from the middle of the band. Such splitting behavior will eventually lead to a new arrangement of quantized vortex core states whose energy ratios follow half-odd-integer numbers.
基金supported by NSFC(11301204)supported by program for outstanding young Technology Innovative team in universities of Hubei Province(T2014212)
文摘We consider the following nonlinear Schroodinger equations -ε^2△u ＋ u = Q（x）｜u｜^p-2u in R^N, u ∈ H^1（R^N）,where ε is a small positive parameter, N ≥ 2, 2 〈 p 〈 ∞ for N = 2 and 2 〈 p 〈2N/N-2 for N ≥ 3. We prove that this problem has sign-changing（nodal） semi-classical bound states with clustered spikes for sufficiently small ε under some additional conditions on Q（x）.Moreover, the number of this type of solutions will go to infinity as ε→ 0^＋.
基金The project supported in part by National Natural Science Foundation of China
文摘We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of the equation is instantaneous ＂occasionally＂）. The obtained rigorous instantaneous formulation, in fact, is expressed as an operator sandwiched by two ＂reduced BS wave functions＂ properly, while the reduced BS wave functions appearing in the formulation are the rigorous solutions of the instantaneous BS equation, and they may relate to Schroedinger wave functions straightforwardly. We also show that the rigorous instantaneous formulation is gauge-invariant with respect to the Uem（1） transformation precisely, if the concerned transitions are radiative. Some applications of the formulation are outlined.
文摘The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is still debatable. When it is at rest, the space-like separation between the constituent particles is the primary variable. When the bound state moves, this space-like separation picks up the time-like separation. The time-separation is not a measurable variable in the present form of quantum mechanics. The only way to deal with this un-observable variable is to treat it statistically. This leads to rise of the statistical variables such entropy and temperature. Paul A. M. Dirac made efforts to construct bound-state wave functions in Einstein’s Lorentz-covariant world. In 1927, he noted that the c-number time-energy relation should be incorporated in the relativistic world. In 1945, he constructed four-dimensional oscillator wave functions with one time coordinate in addition to the three-dimensional space. In 1949, Dirac introduced the light-cone coordinate system for Lorentz transformations. It is then possible to integrate these contributions made by Dirac to construct the Lorentz-covariant harmonic oscillator wave functions. This oscillator system can explain the proton as a bound state of the quarks when it is at rest, and explain the Feynman’s parton picture when it moves with a speed close to that of light. While the un-measurable time-like separation becomes equal to the space-like separation at this speed, the statistical variables become prominent. The entropy and the temperature of this covariant harmonic oscillator are calculated. It is shown that they rise rapidly as the proton speed approaches that of light.
文摘We study the existence and non-existence of bound states （i.e., solutions in W1,P（RN）） for a class of quasilinear scalar field equations of the for -△pu＋V（x）｜u｜p-2u=a（x）｜u｜q-2u,x∈RN,1〈P〈N,mwhen the potentials V（.）≥ 0 and a（.） decay to zero at infinity.
文摘The one-dimensional Dirac particle for equal scalar and vector asymmetric q-parameter hyperbolic PschlTeller potential (qHPT) is solved in terms of hypergeometric functions. The scattering and bound states are obtained by using the properties of the equation of continuity of the wave functions. We calculat in details the transmission and reflection coefficients.
文摘In this study, we present the analytical solutions of bound states for the Schrodinger equation with the mulfiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l （states） quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues. Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.
