We present a new paradigm in the field of photonic crystals and metamaterials, applying the resonant-state expansion (RSE) to planar photonic-crystal structures. The RSE allows us to understand and quantify optical resonances in photonic-crystal structures in terms of the analytic resonant states of a homogeneous planar waveguide. The RSE provides an efficient and reliable tool for accurate calculation of a complete set of the resonant states of a photonic-crystal slab, which is required for the correct description and a better understanding of its optical spectra. For the proof of principle, numerical verification of the RSE, and demonstration of its unprecedented accuracy and convergence, an infinite planar photonic crystal slab periodic in one dimension is taken as an example. To illustrate the power of the present approach, we consider the mode evolution with the amplitude of the periodic modulation, revealing the role of the guided modes in the formation of bound states in the continuum.
A theory of light diffraction from planar quasicrystalline lattice with resonant scatterers is presented. Rich structure, absent in the periodic case, is found in specular reflection spectra, and interpreted as a specific kind of Wood anomalies, characteristic for quasicrystals. The theory is applied to semiconductor quantum dots arranged in Penrose tiling.
Second-order nonlinear effects, such as second-harmonic generation, can be strongly enhanced in nanofabricated photonic materials when both fundamental and harmonic frequencies are spatially and temporally confined. Practically designing low-volume and doubly resonant nanoresonators in conventional semiconductor compounds is challenging owing to their intrinsic refractive index dispersion. In this work we review a recently developed strategy to design doubly resonant nanocavities with low mode volume and large quality factor by localized defects in a photonic crystal structure. We build on thi…
We demonstrate off-resonant coupling between a single quantum dot and a nanobeam photonic crystal cavity, under resonant excitation of the quantum dot or the cavity. These results are consistent with previous descriptions of off-resonant coupling as an incoherent phonon-mediated process. The extension of this phenomenon to a nanobeam photonic crystal cavity presents interesting possibilities for coherent control of this interaction by tailoring the phonon density of states.
We investigate theoretically and numerically the photonic band structure in the optical domain of an array of core-shell metal-semiconductor nanowires. Corresponding negative-index photonic bands are calculated, showing isotropic equifrequency surfaces. The effective (negative) electric permittivity and magnetic permeability, retrieved from S parameters, are used to compare the performance of such nanowire arrays with homogeneous media in canonical examples, such as refraction through a prism and flat-lens focusing. Very good agreement is found, indeed confirming the effective medium behavior …
We reveal a triangular-lattice planar photonic crystal supports Bloch modes with radially and azimuthally symmetric electric field distributions at the top band-edge of the first photonic band. Bifurcated from the corresponding Bloch modes, two cylindrical vector resonant modes are achieved by simply enlarging the central air-hole of the planar photonic crystal, which have high quality factors around 3,000 and small mode volume. The far-field radiations of the two resonant modes present high-quality cylindrical vector beam profiles. The resonant modes could be optimized by modifying the six ne…
We report resonant features of novel controllable reflectarray which consists of meander-like graphene strips placed on a metal-backed dielectric substrate. The structure manifests two kinds of resonances appeared as sharp deeps of reflectivity. The first one exists because the strips of periodic cells of the structure have resonant sizes for induced surface plasmon-polaritons. The second kind of resonances is defined by excitation of TM eigenwaves of the whole structure as a plane photonic crystal. The latter resonances do not depend on whether the strips of the unit cells have resonant sizes…
We propose a concept of chiral photonic limiters utilising topologically protected localised midgap defect states in a photonic waveguide. The chiral symmetry alleviates the effects of structural imperfections and guaranties a high level of resonant transmission for low intensity radiation. At high intensity, the light-induced absorption can suppress the localised modes, along with the resonant transmission. In this case the entire photonic structure becomes highly reflective within a broad frequency range, thus increasing dramatically the damage threshold of the limiter. Here we demonstrate e…
Using a semi-analytic guided-mode expansion technique, we present theory and analysis of intrinsic propagation losses for topological photonic crystal slab waveguide structures with modified honeycomb lattices of circular or triangular holes. Although conventional photonic crystal waveguide structures, such as the W1 waveguide, have been designed to have lossless propagation modes, they are prone to disorder-induced losses and backscattering. Topological structures have been proposed to help mitigate this effect as their photonic edge states may allow for topological protection. However, the i…
Recently, huge attention has been drawn to improve optical sensing devices based on photonic resonators in the presence of graphene. In this paper, based on the transfer matrix approach and TE polarization for the incident electromagnetic waves, we numerically evaluate the transmission and reflection spectra for one-dimensional photonic resonators and surface plasmon resonances with strained graphene, respectively. We proved that a relatively small strain field in graphene can modulate linearly polarized resonant modes within the photonic bandgap of the defective crystal. Moreover, we study th…
Second-harmonic and sum-frequency mixing phenomena associated with 3D-localized photonic modes are studied in InP-based planar photonic crystal microcavities excited by short-pulse radiation near 1550 nm. Three-missing-hole microcavities that support two closely-spaced modes exhibit rich second-order scattering spectra that reflect intra- and inter-mode mixing via the bulk InP chi(2) during ring-down after excitation by the broadband, resonant pulse. Simultaneous excitation with a non-resonant source results in tunable second-order radiation from the microcavity.
Resonant splitting phenomena of photons in periodic T-shape waveguide structure are investigated by the Green's function method. It is found that, except for the (n-1)-fold resonant splitting in the low frequency region, (n-2)-fold resonant splitting occurs in the high frequency region of the transmission spectra. The (n-2)-fold resonant splitting peaks are induced by the high quasi-bound states where the photons are mainly localized in the constrictions rather than in the stubs. To this kind of quasi-bound state, the stub acts as a potential barrier rather than a well, which is the inverse of…
Polarization-resolved second-harmonic spectra are obtained from the resonant modes of a two-dimensional planar photonic crystal microcavity patterned in a free-standing InP slab. The photonic crystal microcavity is comprised of a single missing-hole defect in a hexagonal photonic crystal host formed with elliptically-shaped holes. The cavity supports two orthogonally-polarized resonant modes split by 60 wavenumbers. Sum-frequency data are reported from the nonlinear interaction of the two coherently excited modes, and the polarization dependence is explained in terms of the nonlinear susceptib…
We propose that a photonic array of resonant circular dielectric waveguides with subwavelength grating can be designed as a robust and sensitive topological chemical sensor. The device can detect trace amounts of a given chemical species through photonic edge modes that are impervious to most sources of disorder. We perform a simulation in the mid-infrared that accounts for the absorption loss introduced by chemical molecules in contact with a strongly coupled photonic lattice of resonators. Due to the topological nature of the device, its chemical sensitivity scales linearly with the system s…
We propose and experimentally demonstrate a photonic crystal nanocavity with multiple resonances that can be tuned nearly independently. The design is composed of two orthogonal intersecting nanobeam cavities. Experimentally, we measure cavity quality factors of 6,600 and 1000 for resonances separated by 382 nm; we measure a maximum separation between resonances of 506 nm. These structures are promising for enhancing efficiency in nonlinear optical processes such as sum/difference frequency and stimulated Raman scattering.
A fundamental quantity in multiple scattering is the transport mean free path the inverse of which describes the scattering strength of a sample. In this paper, we emphasize the importance of an appropriate description of the effective refractive index $n_{\mathrm{eff}}$ in multiple light scattering to accurately describe the light transport in dense photonic glasses. Using $n_{\mathrm{eff}}$ as calculated by the energy-density coherent potential approximation we are able to predict the transport mean free path of monodisperse photonic glasses. This model without any fit parameter is in qualit…
We propose a scheme for efficient cavity-enhanced nonlinear THz generation via difference-frequency generation (DFG) processes using a triply resonant system based on photonic crystal cavities. We show that high nonlinear overlap can be achieved by coupling a THz cavity to a doubly-resonant, dual-polarization near-infrared (e.g. telecom band) photonic-crystal nanobeam cavity, allowing the mixing of three mutually orthogonal fundamental cavity modes through a chi(2) nonlinearity. We demonstrate through coupled-mode theory that complete depletion of the pump frequency - i.e., quantum-limited con…
We design a polarization-sensitive resonator for use in midinfrared photodetectors, utilizing a photonic crystal cavity and a single or double-metal plasmonic waveguide to achieve enhanced detector efficiency due to superior optical confinement within the active region. As the cavity is highly frequency and polarization-sensitive, this resonator structure could be used in chip-based infrared spectrometers and cameras that can distinguish among different materials and temperatures to a high degree of precision.
We propose a novel method to generate vector beams in planar photonic crystal cavities with multiple missing-hole defects. Simulating the resonant modes in the cavities, we observe that the optical fields in each defect have different phase and polarization state distributions, which promise the compositions of vector beams by the scattered light from the defects. The far-field radiation patterns of the cavity modes calculated via the Sommerfeld diffraction theory present vector beams possessing hollow intensity profiles and polarization singularities. In addition, the extraction efficiencies …
We report the design of nonreciprocal resonant transmission/reflection using a one-dimensional photonic crystal (1DPC) adjacent to the magneto-optical (MO) metal film. The nonreciprocal surface modes are found at the interface between the PC and MO metal within the forbidden band of native PC structure. Breaking time-reversal symmetry using external magnetic field gives rise of such unique nonreciprocal properties. Quantitatively understanding of nonreciprocal resonant optical transmission/reflection behavior is performed using an effective admittance-matching theory. With excitation of the no…
We investigate resonant nonlinear optical interactions and demonstrate induced transparency in acetylene molecules in a hollow-core photonic band-gap fiber at 1.5$μ$m. The induced spectral transmission window is used to demonstrate slow-light effects, and we show that the observed broadening of the spectral features is due to collisions of the molecules with the inner walls of the fiber core. Our results illustrate that such fibers can be used to facilitate strong coherent light-matter interactions even when the optical response of the individual molecules is weak.
The dispersion properties of exciton polaritons in multiple-quantum-well based resonant photonic crystals are studied. In the case of structures with an elementary cell possessing a mirror symmetry with respect to its center, a powerful analytical method for deriving and analyzing dispersion laws of the respective normal modes is developed. The method is used to analyze band structure and dispersion properties of several types of resonant photonic crystals, which would not submit to analytical treatment by other approaches. These systems include multiple quantum well structures with an arbitra…
When the feature size of photonic structures becomes comparable or even smaller than the wavelength of light, the fabrication imperfections inevitably introduce disorder that may eliminate many functionalities of subwavelength photonic devices. Here we suggest a novel concept to achieve a robust bandgap which can endure disorder beyond 30 as a result of the transition from photonic crystals to Mie-resonant metamaterials. By utilizing Mie-resonant metamaterials with high refractive index, we demonstrate photonic waveguides and cavities with strong robustness to position disorder, thus providing…
An uncommon double-ray scenario of light resonant scattering by a periodic metasurface is proposed to provide strong non-specular reflection. The metasurface is constracted as an array of silicon nanodisks placed on thin silica-on-metal substrate. A low-lossy non-specular resonant reflection for any direction and any polarization of incident wave is revealed by a numerical simulation of light scattering. The conditions for the implementation of an autocollimation scheme of scattering and the observation of non-specular reflected ray that does not lie in the incidence plane are worked out. It i…
A technique is demonstrated which efficiently transfers light between a tapered standard single-mode optical fiber and a resonant mode of a high-Q photonic crystal cavity with mode volume less than a cubic wavelength in size. Cavity mode quality factors of 4.7 x 10^4 are measured, and a total fiber-to-cavity coupling efficiency of 44% is demonstrated.
Intensive light pulse interaction with a dense resonant medium is considered. The possibilities of optical switching and pulse compression at realistic parameters of the medium are analyzed. Pulse shape transformation in different photonic band gap structures containing a dense resonant medium is studied. In particular the effect of dispersion compensation due to nonlinear interaction with a medium is reported. The possibility of pulse control with another pulse is considered in the schemes of co- and counter-propagating pulses. It is shown that a photonic crystal makes controlling more effect…
Photonic Molecules made of dielectric cylinders assembled as two-dimensional octagons and decagons have been studied. These structures exhibit resonance states that change their intensity depending on the incident radiation angle. While most part of spectra present small or even null variation, one of the resonances in both structures presents a high-sensibility to the incidence angle. This strong variation is well described in terms of the electric field intensity distribution of this resonant state, which is composed of maxima with alternate polarities inside each cylinder. Experimental meas…
The red shifted solitonic resonant radiation is a fascinating phase matching phenomenon that occurs when an optical pulse, launched in the normal dispersion regime of photonic crystal fiber, radiates across the zero dispersion wavelength. The formation of such phase-matched radiation is independent of the generation of any optical soliton and mainly governed by the leading edge of input pump which forms a shock front. The radiation is generated at the anomalous dispersion regime and found to be confined both in time and frequency domain. We experimentally investigate the formation of such radi…
Gas-filled hollow-core photonic crystal fiber (PCF) is used for efficient nonlinear temporal compression of femtosecond laser pulses, two main schemes being direct soliton-effect self-compression, and spectral broadening followed by phase compensation. To obtain stable compressed pulses, it is crucial to avoid decoherence through modulational instability (MI) during spectral broadening. Here we show that changes in dispersion due to spectral anti-crossings between the fundamental core mode and core wall resonances in anti-resonant-guiding hollow-core PCF can strongly alter the MI gain spectrum…
The resonant-state expansion (RSE) provides a precise and computationally cheap tool to find resonant states in complex systems using the optical modes of a simpler system as a basis. We apply the RSE to a photonic crystal slab in order to identify and analyze its bound states in the continuum (BICs). We show that the RSE is a useful and reliable method for not only finding the BICs but also for differentiating between accidental and symmetry-protected BICs, as well as for understanding their formation from the basis modes and evolution with structural and material parameters of the system. Th…
We propose theoretically and demonstrate experimentally a coherent microwave photonic receiver operating at 35 GHz carrier frequency. The device is based on a lithium niobate or lithium tantalate optical whispering gallery mode resonator coupled to a microwave strip line resonator. Microwave local oscillator is fed into the microwave resonator along with the microwave signal. We show that the sensitivity of this receiver significantly exceeds the sensitivity of the incoherent quadratic receiver based on the same technology. The coherent receiver can possess a dynamic range in excess of 100 dB …
Topology-driven nonlinear light-matter effects open up new paradigms for both topological photonics and nonlinear optics. Here, we propose to achieve high-efficiency second-harmonic generation in a second-order photonic topological insulator. Such system hosts highly localized topological corner states with large quality factors for both fundamental and second harmonic waves, which could be matched perfectly in frequency by simply tuning the structural parameters. Through the nonlinear interaction of the doubly resonant topological corner states, unprecedented frequency conversion efficiency i…
Structural hierarchy and complex 3D architecture are characteristics of biological photonic designs that are challenging to reproduce in synthetic materials. Top-down lithography allows for designer patterning of arbitrary shapes, but is largely restricted to planar 2D structures. Self-assembly techniques facilitate easy fabrication of 3D photonic crystals, but controllable defect-integration is difficult. In this paper we combine the advantages of top-down and bottom-up fabrication, developing two techniques to deposit 2D-lithographically-patterned planar layers on top of or in between invers…
Enhanced Third-Harmonic Generation in Diamond Photonic Crystal Slabs via Doubly Resonant Quasi-Bound States in the Continuum
Research Institute for Semiconductor Engineering, Hiroshima University（广岛大学半导体工程研究所）；Research Center for Advanced Science and Technology, The University of Tokyo（东京大学先进科学技术研究中心）
We extend a recently developed Hamiltonian formalism for nonlinear wave interaction processes in spatially periodic dielectric structures to the far-off-resonant regime, and investigate numerically the three-wave resonance conditions in a one-dimensional optical medium with $χ^{(2)}$ nonlinearity. In particular, we demonstrate that the cascading of nonresonant wave interaction processes generates an effective $χ^{(3)}$ nonlinear response in these systems. We obtain the corresponding coupling coefficients through appropriate normal form transformations that formally lead to the Zakharov equatio…
We report on the existence of a novel kind of squeezing in photonic crystal fibers which is conceptually intermediate between the four-wave mixing induced squeezing, in which all the participant waves are monochromatic waves, and the self-phase modulation induced squeezing for a single pulse in a coherent state. This hybrid squeezing occurs when an arbitrary short soliton emits quasi-monochromatic resonant radiation near a zero group velocity dispersion point of the fiber. Photons around the resonant frequency become strongly correlated due to the presence of the classical soliton, and a reduc…
The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance d…
We demonstrate a free running 10GHz microresonator-based RF photonic hyper-parametric oscillator characterized with phase noise better than -60dBc/Hz at 10Hz, -90dBc/Hz at 100Hz, and -150dBc/Hz at 10MHz. The device consumes less than 25mW of optical power. A correlation between the frequency of the continuous wave laser pumping the nonlinear resonator and the generated RF frequency is confirmed. The performance of the device is compared with the performance of a standard optical fiber based coupled opto-electronic oscillator of OEwaves.
This paper proposes a novel multifunctional sensing platform based on multimode planar photonic crystals (PPCs). We analytically and numerically demonstrate that the reflection spectrum of PPCs exhibits multiple high-Q resonant modes, and the fundamental and higher-order modes respond distinctively to external mechanical and thermal perturbations, rendering the PPCs superior capability for detection and discrimination of multiple parameters. We further demonstrate simultaneous pressure and temperature sensing with a PPC sensor. Other advantages of PPC sensors include on-chip integration and wa…
We build ring resonators to assess the potentialities of Kagome Hollow-Core Photonic Crystal Fibers for future applications to resonant rotation sensing. The large mode diameter of Kagome fibers permits to reduce the free space fiber-to-fiber coupling losses, leading to cavities with finesses of about 30 for a diameter equal to 15 cm. Resonance linewidths of 3.2~MHz with contrasts as large as 89\% are obtained. Comparison with 7-cell photonic band gap (PBG) fiber leads to better finesse and contrast with Kagome fiber. Resonators based on such fibers are compatible with the angular random walk …
We consider propagation of light pulses detuned from the atomic resonance in a dense two-level medium and photonic structures with it. The large density of the medium is important to decrease spatial scale of such nonlinear effects as pulse compression, though it does not provide any fundamentally new phenomena as compared to dilute media. Frequency detuning decreases the effectivity of such nonlinear phenomena as pulse compression and dispersion spreading compensation as well. We propose simple logic gates based on interaction between two pulses in one-dimensional nonlinear photonic crystal. …
We identify different types of the photonic band gaps (PBGs) of two dimensional magnetic photonic crystals (MPCs) consisting of arrays of magnetic cylinders and study the different tunability (by an external static magnetic field) of these PBGs. One type of the band gaps comes from infinitely degenerate flat bands and is closely related to those in the study of plasmonics. In addition, such PBGs are magnetically tunable and robust against position disorder. We calcualte the transmission of the PBG's and found excellent agreement with the results of the photonic band structure calculation. Posi…
Photonic nanostructures simultaneously maximizing spectral and spatial overlap between fundamental and second-harmonic confined modes are highly desirable for enhancing second-order nonlinear effects in nonlinear media. These conditions have thus far remained challenging to satisfy in photonic crystal cavities because of the difficulty in designing a band gap at the second-harmonic frequency. Here, we solve this issue by using instead a bound state in the continuum at that frequency, and we design a doubly-resonant photonic crystal slab cavity with strongly improved figures of merit for nonlin…
We demonstrate tunable frequency-converted light mediated by a chi-(2) nonlinear photonic crystal nanocavity. The wavelength-scale InP-based cavity supports two closely-spaced localized modes near 1550 nm which are resonantly excited by a 130 fs laser pulse. The cavity is simultaneously irradiated with a non-resonant probe beam, giving rise to rich second-order scattering spectra reflecting nonlinear mixing of the different resonant and non-resonant components. In particular, we highlight the radiation at the sum frequencies of the probe beam and the respective cavity modes. This would be a us…
We develop the resonant mode coupling approximation to calculate the optical spectra of a stack of two photonic crystal slabs. The method is based on a derivation of the input and output resonant vectors in each slab in terms of the Fourier modal method in the scattering matrix form. We show that using the resonant mode coupling approximation of the scattering matrices of the upper and lower slabs, one can construct the total scattering matrix of the stack. The formation of the resonant output and input vectors of the stacked system is rigorously derived by means of an effective Hamiltonian. W…
We present a quantum model of two-level atoms localized in a 3D lattice, based on the Hopfield theory of exciton polaritons. In addition to a polaritonic gap at the exciton energy, a photonic bandgap opens up at the Brillouin zone boundary. Upon tuning the lattice period or angle of incidence to match the photonic gap with the exciton energy, one obtains a combined polaritonic and photonic gap as a generalization of Rabi splitting. For typical experimental parameters, the size of the combined gap is on the order of 25 cm^{-1}, up to 10^5 times the detuned gap size. The dispersion curve contain…
Results of research of resonant phenomena in planar periodic structures consisted of dielectric elements are presented. A problem of plane wave diffraction by a structure which a periodic cell is composed of two dielectric bars with different lengths has been solved. For the first time an existence of high Q-factor trapped mode resonances are revealed in these structures. The main difference of studied structure in contrast to the planar structure with a single dielectric bar in the unit cell is appearing of a great red shift of a trapped mode resonant wavelength. The red shift is caused by st…
Nonradiating sources of energy have traditionally been studied in quantum mechanics and astrophysics, while receiving a very little attention in the photonics community. This situation has changed recently due to a number of pioneering theoretical studies and remarkable experimental demonstrations of the exotic states of light in dielectric resonant photonic structures and metasurfaces, with the possibility to localize efficiently the electromagnetic fields of high intensities within small volumes of matter. These recent advances underpin novel concepts in nanophotonics, and provide a promisin…
We demonstrate, theoretically and experimentally, that a traveling electric charge passing from one photonic crystal into another generates edge waves -- electromagnetic modes with frequencies inside the common photonic bandgap localized at the interface -- via a process of transition edge-wave radiation (TER). A simple and intuitive expression for the TER spectral density is derived and then applied to a specific structure: two interfacing photonic topological insulators with opposite spin-Chern indices. We show that TER breaks the time-reversal symmetry and enables valley- and spin-polarized…
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close proximity of the spectral-angular range of interest. The developed approximation opens up possibilities for the fast calculation of the scattering matrix of these structures when describing the integral characteristics of spectra and dispersion curves containing high-Q resonances, such as bound states in the continuum.
