Strong coupling between resonantly matched surface plasmons of metals and excitons of quantum emitters results in the formation of new plasmon-exciton hybridized energy states.In plasmon-exciton strong coupling,plasmo...Strong coupling between resonantly matched surface plasmons of metals and excitons of quantum emitters results in the formation of new plasmon-exciton hybridized energy states.In plasmon-exciton strong coupling,plasmonic nanocavities play a significant role due to their ability to confine light in an ultrasmall volume.Additionally,two-dimensional transition metal dichalcogenides(TMDCs) have a significant exciton binding energy and remain stable at ambient conditions,making them an excellent alternative for investigating light-matter interactions.As a result,strong plasmon-exciton coupling has been reported by introducing a single metallic cavity.However,single nanoparticles have lower spatial confinement of electromagnetic fields and limited tunability to match the excitonic resonance.Here,we introduce the concept of catenary-shaped optical fields induced by plasmonic metamaterial cavities to scale the strength of plasmon-exciton coupling.The demonstrated plasmon modes of metallic metamaterial cavities offer high confinement and tunability and can match with the excitons of TMDCs to exhibit a strong coupling regime by tuning either the size of the cavity gap or thickness.The calculated Rabi splitting of Au-MoSe_2 and Au-WSe_2 heterostructures strongly depends on the catenary-like field enhancement induced by the Au cavity,resulting in room-temperature Rabi splitting ranging between 77.86 and 320 me V.These plasmonic metamaterial cavities can pave the way for manipulating excitons in TMDCs and operating active nanophotonic devices at ambient temperature.展开更多
Dielectric metasurfaces play an increasingly important role in enhancing optical nonlinear generations owing to their ability to support strong light-matter interactions based on Mie-type multipolar resonances.Compare...Dielectric metasurfaces play an increasingly important role in enhancing optical nonlinear generations owing to their ability to support strong light-matter interactions based on Mie-type multipolar resonances.Compared to metasurfaces composed of the periodic arrangement of nanoparticles,inverse,so-called,membrane metasurfaces offer unique possibilities for supporting multipolar resonances,while maintaining small unit cell size,large mode volume and high field enhancement for enhancing nonlinear frequency conversion.Here,we theoretically and experimentally investigate the formation of bound states in the continuum(BICs)from silicon dimer-hole membrane metasurfaces.We demonstrate that our BIC-formed resonance features a strong and tailorable electric near-field confinement inside the silicon membrane films.Furthermore,we show that by tuning the gap between the holes,one can open a leaky channel to transform these regular BICs into quasi-BICs,which can be excited directly under normal plane wave incidence.To prove the capabilities of such metasurfaces,we demonstrate the conversion of an infrared image to the visible range,based on the Third-harmonic generation(THG)process with the resonant membrane metasurfaces.Our results suggest a new paradigm for realising efficient nonlinear photonics metadevices and hold promise for extending the applications of nonlinear structuring surfaces to new types of all-optical near-infrared imaging technologies.展开更多
Bound states in the continuum(BICs)are perfectly localized resonances despite embedding in the continuum spectrum.However,an isolated BIC is very sensitive to the structure perturbation.Here,we report merging acoustic...Bound states in the continuum(BICs)are perfectly localized resonances despite embedding in the continuum spectrum.However,an isolated BIC is very sensitive to the structure perturbation.Here,we report merging acoustic BICs in a single open resonator,robust against the structure perturbation.We find that both symmetry-protected BIC and Friedrich-Wintgen BIC are sustained in a single coupled waveguide-resonator system.By varying the height and length of the resonator,these two BICs move toward each other and merge into a single one at a critical dimension.Compared to an individual BIC,the merged BIC is robust against fabrication error because its Q-factor is proportional toΔL^(−4),whereΔL embodies the structure perturbation.The essence of this extraordinary phenomenon is perfectly explained by the two-and three-level approximations of the effective non-Hermitian Hamiltonian.Finally,we present direct experimental demonstrations of the moving and merging of BICs in a coupled 3D waveguide-resonator,which are evidenced by the vanishing of the linewidth of Fano resonance in the transmission spectra.Our results may find exciting applications in designing high-quality acoustic sources,sensors and filters.展开更多
Nonlinear metasurfaces have experienced rapid growth recently due to their potential in various applications,including infrared imaging and spectroscopy.However,due to the low conversion efficiencies of metasurfaces,s...Nonlinear metasurfaces have experienced rapid growth recently due to their potential in various applications,including infrared imaging and spectroscopy.However,due to the low conversion efficiencies of metasurfaces,several strategies have been adopted to enhance their performances,including employing resonances at signal or nonlinear emission wavelengths.This strategy results in a narrow operational band of the nonlinear metasurfaces,which has bottlenecked many applications,including nonlinear holography,image encoding,and nonlinear metalenses.Here,we overcome this issue by introducing a new nonlinear imaging platform utilizing a pump beam to enhance signal conversion through four-wave mixing(FWM),whereby the metasurface is resonant at the pump wavelength rather than the signal or nonlinear emissions.As a result,we demonstrate broadband nonlinear imaging for arbitrary objects using metasurfaces.A silicon disk-on-slab metasurface is introduced with an excitable guided-mode resonance at the pump wavelength.This enabled direct conversion of a broad IR image ranging from>1000 to 4000 nm into visible.Importantly,adopting FWM substantially reduces the dependence on high-power signal inputs or resonant features at the signal beam of nonlinear imaging by utilizing the quadratic relationship between the pump beam intensity and the signal conversion efficiency.Our results,therefore,unlock the potential for broadband infrared imaging capabilities with metasurfaces,making a promising advancement for next-generation all-optical infrared imaging techniques with chip-scale photonic devices.展开更多
We demonstrate that a dielectric anapole resonator on a metallic mirror can enhance the third harmonic emission by two orders of magnitude compared to a typical anapole resonator on an insulator substrate.By employing...We demonstrate that a dielectric anapole resonator on a metallic mirror can enhance the third harmonic emission by two orders of magnitude compared to a typical anapole resonator on an insulator substrate.By employing a gold mirror under a silicon nanodisk,we introduce a novel characteristic of the anapole mode through the spatial overlap of resonantly excited Cartesian electric and toroidal dipole modes.This is a remarkable improvement on the early demonstrations of the anapole mode in which the electric and toroidal modes interfere off-resonantly.Therefore,our system produces a significant near-field enhancement,facilitating the nonlinear process.Moreover,the mirror surface boosts the nonlinear emission via the free-charge oscillations within the interface,equivalent to producing a mirror image of the nonlinear source and the pump beneath the interface.We found that these improvements result in an extremely high experimentally obtained efficiency of 0.01%.展开更多
A key concept underlying the specific functionalities of metasurfaces is the use of constituent components to shape the wavefront of the light on demand.Metasurfaces are versatile,novel platforms for manipulating the ...A key concept underlying the specific functionalities of metasurfaces is the use of constituent components to shape the wavefront of the light on demand.Metasurfaces are versatile,novel platforms for manipulating the scattering,color,phase,or intensity of light.Currently,one of the typical approaches for designing a metasurface is to optimize one or two variables among a vast number of fixed parameters,such as various materials’properties and coupling effects,as well as the geometrical parameters.Ideally,this would require multidimensional space optimization through direct numerical simulations.Recently,an alternative,popular approach allows for reducing the computational cost significantly based on a deep-learning-assisted method.We utilize a deep-learning approach for obtaining high-quality factor(high-Q)resonances with desired characteristics,such as linewidth,amplitude,and spectral position.We exploit such high-Q resonances for enhancedlight–matter interaction in nonlinearoptical metasurfaces and optomechanical vibrations,simultaneously.We demonstrate that optimized metasurfaces achieve up to 400-fold enhancement of the third-harmonic generation;at the same time,they also contribute to 100-fold enhancement of the amplitude of optomechanical vibrations.This approach can be further used to realize structures with unconventional scattering responses.展开更多
Infrared imaging is a crucial technique in a multitude of applications,including night vision,autonomous vehicle navigation,optical tomography,and food quality control.Conventional infrared imaging technologies,howeve...Infrared imaging is a crucial technique in a multitude of applications,including night vision,autonomous vehicle navigation,optical tomography,and food quality control.Conventional infrared imaging technologies,however,require the use of materials such as narrow bandgap semiconductors,which are sensitive to thermal noise and often require cryogenic cooling.We demonstrate a compact all-optical alternative to perform infrared imaging in a metasurface composed of GaAs semiconductor nanoantennas,using a nonlinear wave-mixing process.We experimentally show the upconversion of short-wave infrared wavelengths via the coherent parametric process of sum-frequency generation.In this process,an infrared image of a target is mixed inside the metasurface with a strong pump beam,translating the image from the infrared to the visible in a nanoscale ultrathin imaging device.Our results open up new opportunities for the development of compact infrared imaging devices with applications in infrared vision and life sciences.展开更多
Bound states in the continuum(BICs)have emerged as an efficient tool for trapping light at the nanoscale,promising several exciting applications in photonics.Breaking the structural symmetry has been proposed as an ef...Bound states in the continuum(BICs)have emerged as an efficient tool for trapping light at the nanoscale,promising several exciting applications in photonics.Breaking the structural symmetry has been proposed as an effective way of exciting quasiBICs(QBICs)and generating high-Q resonances.Herein,we demonstrate that QBICs can be excited in an all-dielectric metasurface by scaling the lattice of the metasurface,causing translational symmetry breaking.The corresponding BICs arise from band folding from the band edge to the Γ point in the first Brillouin zone.Multipole analysis reveals that the toroidal dipole dominates these QBICs.Furthermore,scaling the lattice along different directions provides additional freedom for tailoring QBICs,enabling polarization-dependent or-independent QBICs.In addition,this allows the realization of two QBICs at different wavelengths using plane-wave illumination with different polarizations on the metasurface.We experimentally demonstrated the existence of these BICs by fabricating silicon metasurfaces with scaled lattices and measuring their transmission spectra.The vanished resonant linewidth identifies BICs in the transmission spectrum,and the QBICs are characterized by highQ Fano resonances with the Q-factor reaching 2000.Our results have potential applications in enhancing light-matter interaction,such as laser,nonlinear harmonic generation,and strong coupling.展开更多
As an elementary particle,a photon that carries information in frequency,polarization,phase,and amplitude,plays a crucial role in modern science and technology.However,how to retrieve the full information of unknown p...As an elementary particle,a photon that carries information in frequency,polarization,phase,and amplitude,plays a crucial role in modern science and technology.However,how to retrieve the full information of unknown photons in.an ultracompact manner over broad bandwidth remains a challenging task with growing importance.Here,we demonstrate a versatile photonic slide rule based on an ll-silicon metasurface that enables uS to reconstruct incident photons'frequency and polarization state.The underlying mechanism relies on the coherent interactions of frequency-driven phase diagrams which rotate at various angular velocities within broad bandwidth.The rotation direction and speed are determined by the topological charge and phase dispersion.Specificall,our metasurface leverages both achromatically focusing and azimuthally evolving phases with topological charges+1 and-1 to ensure the confocal annular intensity ditributions.The combination of geometric phase and interference holography allows the joint manipulations of two distinct group delay coverages to realize angle-resolved in-pair spots in a.transverse manner-a behavior that would disperse along longitudinal direction in conventional implementations.The spin-orbital coupling between the incident photons and vortex phases provides routing for the simultaneous identifcation of the photons'frequency and circular polarization state through recognizing the spots'locations.Our work provides an analog of the conventional slide rule to flexibly characterize the photons in an ultracompact and multifunctional way and may find applications in integrated optical circuits or pocketable devices.展开更多
基金supported by the Australian Research Council (DP200101353)。
文摘Strong coupling between resonantly matched surface plasmons of metals and excitons of quantum emitters results in the formation of new plasmon-exciton hybridized energy states.In plasmon-exciton strong coupling,plasmonic nanocavities play a significant role due to their ability to confine light in an ultrasmall volume.Additionally,two-dimensional transition metal dichalcogenides(TMDCs) have a significant exciton binding energy and remain stable at ambient conditions,making them an excellent alternative for investigating light-matter interactions.As a result,strong plasmon-exciton coupling has been reported by introducing a single metallic cavity.However,single nanoparticles have lower spatial confinement of electromagnetic fields and limited tunability to match the excitonic resonance.Here,we introduce the concept of catenary-shaped optical fields induced by plasmonic metamaterial cavities to scale the strength of plasmon-exciton coupling.The demonstrated plasmon modes of metallic metamaterial cavities offer high confinement and tunability and can match with the excitons of TMDCs to exhibit a strong coupling regime by tuning either the size of the cavity gap or thickness.The calculated Rabi splitting of Au-MoSe_2 and Au-WSe_2 heterostructures strongly depends on the catenary-like field enhancement induced by the Au cavity,resulting in room-temperature Rabi splitting ranging between 77.86 and 320 me V.These plasmonic metamaterial cavities can pave the way for manipulating excitons in TMDCs and operating active nanophotonic devices at ambient temperature.
基金the support from the Royal Society scholarshipsupport from the UK Research and Innovation Future Leaders Fellowship (MR/T040513/1).
文摘Dielectric metasurfaces play an increasingly important role in enhancing optical nonlinear generations owing to their ability to support strong light-matter interactions based on Mie-type multipolar resonances.Compared to metasurfaces composed of the periodic arrangement of nanoparticles,inverse,so-called,membrane metasurfaces offer unique possibilities for supporting multipolar resonances,while maintaining small unit cell size,large mode volume and high field enhancement for enhancing nonlinear frequency conversion.Here,we theoretically and experimentally investigate the formation of bound states in the continuum(BICs)from silicon dimer-hole membrane metasurfaces.We demonstrate that our BIC-formed resonance features a strong and tailorable electric near-field confinement inside the silicon membrane films.Furthermore,we show that by tuning the gap between the holes,one can open a leaky channel to transform these regular BICs into quasi-BICs,which can be excited directly under normal plane wave incidence.To prove the capabilities of such metasurfaces,we demonstrate the conversion of an infrared image to the visible range,based on the Third-harmonic generation(THG)process with the resonant membrane metasurfaces.Our results suggest a new paradigm for realising efficient nonlinear photonics metadevices and hold promise for extending the applications of nonlinear structuring surfaces to new types of all-optical near-infrared imaging technologies.
基金supported by the National Natural Science Foundation of China(Grant No.12074286)Shanghai Science and Technology Committee(Grant No.21JC1405600)+1 种基金supported by the Australian Research Council Discovery Project(Grant No.DP200101353)supported by Russian Science Foundation(Grant No.22-12-00070)。
文摘Bound states in the continuum(BICs)are perfectly localized resonances despite embedding in the continuum spectrum.However,an isolated BIC is very sensitive to the structure perturbation.Here,we report merging acoustic BICs in a single open resonator,robust against the structure perturbation.We find that both symmetry-protected BIC and Friedrich-Wintgen BIC are sustained in a single coupled waveguide-resonator system.By varying the height and length of the resonator,these two BICs move toward each other and merge into a single one at a critical dimension.Compared to an individual BIC,the merged BIC is robust against fabrication error because its Q-factor is proportional toΔL^(−4),whereΔL embodies the structure perturbation.The essence of this extraordinary phenomenon is perfectly explained by the two-and three-level approximations of the effective non-Hermitian Hamiltonian.Finally,we present direct experimental demonstrations of the moving and merging of BICs in a coupled 3D waveguide-resonator,which are evidenced by the vanishing of the linewidth of Fano resonance in the transmission spectra.Our results may find exciting applications in designing high-quality acoustic sources,sensors and filters.
基金the Royal Society scholarshipG.S.acknowledges support from Biotechnology and Biological Council Doctoral Training Programme(BBSRC DTP)+1 种基金D.S.and D.N.N.acknowledge the support by the Australian Research Council(CE200100010 and FT230100058)L.Xu and M.Rahmani acknowledge support from the UK Research and Innovation Future Leaders Fellowship(MR/T040513/1)。
文摘Nonlinear metasurfaces have experienced rapid growth recently due to their potential in various applications,including infrared imaging and spectroscopy.However,due to the low conversion efficiencies of metasurfaces,several strategies have been adopted to enhance their performances,including employing resonances at signal or nonlinear emission wavelengths.This strategy results in a narrow operational band of the nonlinear metasurfaces,which has bottlenecked many applications,including nonlinear holography,image encoding,and nonlinear metalenses.Here,we overcome this issue by introducing a new nonlinear imaging platform utilizing a pump beam to enhance signal conversion through four-wave mixing(FWM),whereby the metasurface is resonant at the pump wavelength rather than the signal or nonlinear emissions.As a result,we demonstrate broadband nonlinear imaging for arbitrary objects using metasurfaces.A silicon disk-on-slab metasurface is introduced with an excitable guided-mode resonance at the pump wavelength.This enabled direct conversion of a broad IR image ranging from>1000 to 4000 nm into visible.Importantly,adopting FWM substantially reduces the dependence on high-power signal inputs or resonant features at the signal beam of nonlinear imaging by utilizing the quadratic relationship between the pump beam intensity and the signal conversion efficiency.Our results,therefore,unlock the potential for broadband infrared imaging capabilities with metasurfaces,making a promising advancement for next-generation all-optical infrared imaging techniques with chip-scale photonic devices.
基金support provided by the Australian Research Council(ARC)and participation in the Erasmus Mundus NANOPHI project,contract number 20135659/002-001from an ARC Discovery Early Career Research Fellowship(DE170100250)+4 种基金supported by a UNSW Scientia Fellowshipfunding from the Australia-Germany Joint Research Cooperation Schemefrom Consejo Nacional de Ciencia y Tecnologıa(CONACYT)the financial support by NSFC(No.11774182,No.91750204)support by the German Research Foundation(STA 1426/2-1)。
文摘We demonstrate that a dielectric anapole resonator on a metallic mirror can enhance the third harmonic emission by two orders of magnitude compared to a typical anapole resonator on an insulator substrate.By employing a gold mirror under a silicon nanodisk,we introduce a novel characteristic of the anapole mode through the spatial overlap of resonantly excited Cartesian electric and toroidal dipole modes.This is a remarkable improvement on the early demonstrations of the anapole mode in which the electric and toroidal modes interfere off-resonantly.Therefore,our system produces a significant near-field enhancement,facilitating the nonlinear process.Moreover,the mirror surface boosts the nonlinear emission via the free-charge oscillations within the interface,equivalent to producing a mirror image of the nonlinear source and the pump beneath the interface.We found that these improvements result in an extremely high experimentally obtained efficiency of 0.01%.
基金supported by UNSW Scientia Fellowship and ARC Discovery Project(DP170103778)funding from ARC Discovery Early Career Research Fellowship(DE170100250)+1 种基金financial support from the Russian Foundation for Basic Research(Grants Nos.18-02-00381 and 19-02-00261)the Australian Research Council(DE19010043).
文摘A key concept underlying the specific functionalities of metasurfaces is the use of constituent components to shape the wavefront of the light on demand.Metasurfaces are versatile,novel platforms for manipulating the scattering,color,phase,or intensity of light.Currently,one of the typical approaches for designing a metasurface is to optimize one or two variables among a vast number of fixed parameters,such as various materials’properties and coupling effects,as well as the geometrical parameters.Ideally,this would require multidimensional space optimization through direct numerical simulations.Recently,an alternative,popular approach allows for reducing the computational cost significantly based on a deep-learning-assisted method.We utilize a deep-learning approach for obtaining high-quality factor(high-Q)resonances with desired characteristics,such as linewidth,amplitude,and spectral position.We exploit such high-Q resonances for enhancedlight–matter interaction in nonlinearoptical metasurfaces and optomechanical vibrations,simultaneously.We demonstrate that optimized metasurfaces achieve up to 400-fold enhancement of the third-harmonic generation;at the same time,they also contribute to 100-fold enhancement of the amplitude of optomechanical vibrations.This approach can be further used to realize structures with unconventional scattering responses.
基金The authors acknowledge the use of the Australian National Fabrication Facility(ANFF),ACT Node.Rocio CamachoMorales acknowledges a grant from the Consejo Nacional de Ciencia y Tecnología(CONACYT),MexicoNikolay Dimitrov and Lyubomir Stoyanov acknowledge a grant from the EU Marie-Curie RISE program NOCTURNO+1 种基金Mohsen Rahmani acknowledges support from the UK Research and Innovation Future Leaders Fellowship(MR/T040513/1)Dragomir N.Neshev acknowledges a grant from the Australian Research Council(CE20010001,DP190101559).
文摘Infrared imaging is a crucial technique in a multitude of applications,including night vision,autonomous vehicle navigation,optical tomography,and food quality control.Conventional infrared imaging technologies,however,require the use of materials such as narrow bandgap semiconductors,which are sensitive to thermal noise and often require cryogenic cooling.We demonstrate a compact all-optical alternative to perform infrared imaging in a metasurface composed of GaAs semiconductor nanoantennas,using a nonlinear wave-mixing process.We experimentally show the upconversion of short-wave infrared wavelengths via the coherent parametric process of sum-frequency generation.In this process,an infrared image of a target is mixed inside the metasurface with a strong pump beam,translating the image from the infrared to the visible in a nanoscale ultrathin imaging device.Our results open up new opportunities for the development of compact infrared imaging devices with applications in infrared vision and life sciences.
基金supported by the National Natural Science Foundation of China(Grant Nos.12004084,12164008,and 62261008)the Guizhou Provincial Science and Technology Projects(Grant No.ZK[2021]030)+8 种基金the Science and Technology Innovation Team Project of Guizhou Colleges and Universities(Grant No.[2023]060)the Science and Technology Talent Support Project of the Department of Education in the Guizhou Province(Grant No.KY[2018]043)the Construction Project of Characteristic Key Laboratory in Guizhou Colleges and Universities(Grant No.Y[2021]003)the Key Laboratory of Guizhou Minzu University(Grant No.GZMUSYS[2021]03)the Australian Research Council Discovery Project(Grant No.DP200101353)the UNSW Scientia Fellowship Programand the Shanghai Pujiang Program(Grant No.22PJ1402900)support from the Royal Societythe Wolfson Foundation。
文摘Bound states in the continuum(BICs)have emerged as an efficient tool for trapping light at the nanoscale,promising several exciting applications in photonics.Breaking the structural symmetry has been proposed as an effective way of exciting quasiBICs(QBICs)and generating high-Q resonances.Herein,we demonstrate that QBICs can be excited in an all-dielectric metasurface by scaling the lattice of the metasurface,causing translational symmetry breaking.The corresponding BICs arise from band folding from the band edge to the Γ point in the first Brillouin zone.Multipole analysis reveals that the toroidal dipole dominates these QBICs.Furthermore,scaling the lattice along different directions provides additional freedom for tailoring QBICs,enabling polarization-dependent or-independent QBICs.In addition,this allows the realization of two QBICs at different wavelengths using plane-wave illumination with different polarizations on the metasurface.We experimentally demonstrated the existence of these BICs by fabricating silicon metasurfaces with scaled lattices and measuring their transmission spectra.The vanished resonant linewidth identifies BICs in the transmission spectrum,and the QBICs are characterized by highQ Fano resonances with the Q-factor reaching 2000.Our results have potential applications in enhancing light-matter interaction,such as laser,nonlinear harmonic generation,and strong coupling.
基金the National Key Research and Development Program of China under Grant 2018YFA0306200 and Grant 2017YFA0205800the National Natural Science Foundation of China under Grant 61875218,Grant 61991440,and Grant 91850208+5 种基金the Youth Innovation Promotion Association of Chinese Academy of Sciences under Grant 2017285the Strategic Priority Research Program of Chinese Academy of Sciences under Grant XDB43010200the Shanghai Rising-Star Program under Grant 20QA1410400the Shanghai Science and Technology Committee under Grant 20JC1416000the Natural Science Foundation of Zhejiang Province under Grant LR22F050004the Shanghai Municipal Science and Technology Major Projea under Grant 2019SHZDZX01.
文摘As an elementary particle,a photon that carries information in frequency,polarization,phase,and amplitude,plays a crucial role in modern science and technology.However,how to retrieve the full information of unknown photons in.an ultracompact manner over broad bandwidth remains a challenging task with growing importance.Here,we demonstrate a versatile photonic slide rule based on an ll-silicon metasurface that enables uS to reconstruct incident photons'frequency and polarization state.The underlying mechanism relies on the coherent interactions of frequency-driven phase diagrams which rotate at various angular velocities within broad bandwidth.The rotation direction and speed are determined by the topological charge and phase dispersion.Specificall,our metasurface leverages both achromatically focusing and azimuthally evolving phases with topological charges+1 and-1 to ensure the confocal annular intensity ditributions.The combination of geometric phase and interference holography allows the joint manipulations of two distinct group delay coverages to realize angle-resolved in-pair spots in a.transverse manner-a behavior that would disperse along longitudinal direction in conventional implementations.The spin-orbital coupling between the incident photons and vortex phases provides routing for the simultaneous identifcation of the photons'frequency and circular polarization state through recognizing the spots'locations.Our work provides an analog of the conventional slide rule to flexibly characterize the photons in an ultracompact and multifunctional way and may find applications in integrated optical circuits or pocketable devices.
