Phoxonic Crystal Research Articles

Slit-Gradient Phoxonic Crystal Sensor for Detecting the Solution Concentration

Slit-Gradient Phoxonic Crystal Sensor for Detecting the Solution Concentration

Porous silicon opto-acoustic detector for ternary gas mixture

The use of porous phoxonic crystals with coupled optical and acoustic response has been proposed as a sensing device. Due to the porous nature of the crystal, each layer of the structure can be connected to the environment. As the optical and acoustic performances of the phoxonic crystal change when a gas permeates the pores due to modifications of the effective refractive index and density of the system, it results that these structures are suitable platforms for the detection of gases. The sensor designed following these premises can detect the composition of ternary gas mixtures through optical measurements, while an acoustic wave induces a structural oscillation. The amplified acoustic wave produces a mechanical deformation of the crystal layers that is maximized in the center a resonant microcavity. Therefore, under such experimental conditions, the sensitivity of the optical response is not only due to the optical property changes caused by the gas mixture in contact with the porous structure but also to changes in the mechanical deformations due to modifications of the acoustic properties. In this work, we discuss the device theoretical behavior as a multiparameter sensor that distinguishes the components and concentrations of a ternary gas mixture through the transfer matrix method. For a prototype combination of CO2−Air−CH4 mixture, the estimated resolution of the proposed device fabricated in porous silicon can be has high as 0.05% (500 ppm) in the concentration of each individual species.

Multispectral transmission through phoxonic crystal slot-waveguide at midwave infrared frequencies

We design a multispectral transmission waveguide based on phoxonic crystals at midwave infrared (MWIR) frequencies. The phoxonic crystal slot-waveguide architecture is realized using a germanium (Ge)-slot waveguide, surrounded by a supercell array of oxide holes in silicon–germanium (SiGe) membrane tailored photonic and phononic crystal bandgap. The plane wave simulations for both photonic and phononic crystal unit cells were performed to confirm the geometry of the phoxonic supercell. The bandgap analysis shows the capability of the proposed architecture to confine photons of the terahertz frequency range within the slot waveguide by isolating them from the phonons of gigahertz frequency range. The phononic and photonic bandgaps were simultaneously engineered by varying the periodic variation of the density function and dielectric permittivity, respectively. The computational approach shows the suppression in photon-phonon scattering as validated by a uniform transmission of ∼99.8 % over a broad range of 3 to 5 μm wavelengths. The designed phoxonic crystal waveguide can be fabricated with planar processing technology and used in many applications where multispectral control of mid-IR signals is required.

Acousto-optical coupling in two-dimensional air-slot phoxonic crystal heterostructure cavity

Phoxonic crystal is a periodic artificial structure that can manipulate optical and acoustic waves in the same temporal and spatial domain. It has broad application prospect in optical communication, optical mechanics sensor, quantum computations, phoxonic crystal integrated devices and so on. In this paper, we adopt a silicon-based two-dimensional square lattice structure, which can exhibit wide band gap of phonons and photons simultaneously. Then a periodic rectangular structure is introduced on the surface, the effects of the height and width of the rectangle on the optical and acoustic surface wave modes are analyzed. Based on the mode gap effect, a surface heterostructure composed of rectangles with different heights and widths is constructed. Then two identical surface heterostructures are placed face to face with an air slot in the middle, and connected with silicon substrate on both sides, which form an air slot heterostructure cavity. Five phononic cavity modes and three photonic cavity modes are obtained, the acousto-optical coupling rates between phononic and photonic cavity modes are calculated. The results show that the coupling rate between phononic and photonic cavity mode with the same symmetry and maximum overlap is the largest, and the coupling rates between the combination of phononic cavity modes α and β and photonic cavity modes can be adjusted by changing the phase difference φ of modes α and β. In this paper, the finite element method is used to simulate the calculation.

Dual Optical and Acoustic Negative Refraction in Phoxonic Crystals

We report dual optical and acoustic negative refraction based on a defect-free phoxonic crystal within a triangular lattice. The phoxonic negative refraction is achieved based on abnormal dispersion effect, by intentionally creating convex equal-frequency contours for both photonic and phononic modes. As a potential application, negative refraction imaging for both photonic and phononic modes is also achieved. Numerical simulations based on the finite element method demonstrate the coexistence of negative refraction and the resultant imaging for electromagnetic and acoustic waves. Compared with the defect-based bandgap effects that need low fault tolerance, phoxonic negative refraction relying on passbands has considerable advantages in realizing controllable propagation of waves. The new scheme for the simultaneous control of electromagnetic and acoustic waves provides a potential platform for designing novel phoxonic devices.

Coexistence of photonic and phononic corner states in a second-order topological phoxonic crystal

Recently, higher-order topological insulators (HOTIs) have been extended from the electronic system to classical wave systems. Beyond the conventional bulk-boundary correspondence, HOTIs can host zero-dimensional topologically protected corner states, which show the strong field localization and robustness against fabrication flaws. Here, we propose a second-order topological phoxonic crystal (PXC) based on a two-dimensional (2D) square lattice, of which different unit cell choices can show either a topologically trivial or non-trivial band structure characterized by the 2D Zak phase. The proposed PXC supports the coexistence of photonic and phononic topological corner states, and their robustness to disorders and defects is numerically demonstrated. Our work opens a venue for achieving simultaneous confinement of photons and phonons, which is potentially useful for exploring the interaction of photonic and phononic second-order topological states and for designing novel topological optomechanical devices.

Simultaneous slow light and sound rainbow trapping in phoxonic crystals.

In this paper, we use a phoxonic crystal (PxC) which can control the topological states of light and sound by breaking inversion symmetry and thus make it possible to achieve rainbow trapping of light and sound simultaneously. It is shown that topologically protected edge states can be obtained at the interfaces between PxCs with different topological phases. Thus, we designed a gradient structure to realize the topological rainbow trapping of light and sound by linearly modulating the structural parameter. In the proposed gradient structure, the edge states of light and sound modes with different frequencies are respectively trapped at different positions, owing to near zero group velocity. The topological rainbows of light and sound are simultaneously realized in one structure, which open a new, to the best of our knowledge, view and provide a feasible platform for the application of the topological optomechanical devices.

Topological edge and interface states in phoxonic crystal cavity chains

Topological states of classic waves are fascinating for both fundamental and practical purposes due to their unprecedented wave characteristics. In this paper, we realize the one-dimensional topological insulators for electromagnetic and mechanical waves simultaneously based on phoxonic crystal (PxC) cavity chains. The proposed PxC cavity chains are the analogs to the Su-Schrieffer-Heeger model in condensed-matter physics. The interaction between the neighboring PxC cavities can be described by the tight-binding model, where the coupling or hopping strength between the adjacent cavities can be tuned by varying their distance. Thus, the PxC cavity chains with topologically nontrivial and trivial phases are achieved by changing the cavity distances directly. The topological edge and interface states for the electromagnetic and elastic (or acoustic) waves are observed simultaneously in the finite-sized PxC cavity chains, which exhibit robustness against geometrical imperfections. The topological states of the proposed PxC cavity chains hold promise for designing robust devices in signal processing, sensing, and optomechanics.

Acousto-optical coupling of the side surface acoustic and optical waves in a two-dimensional phoxonic crystal slab hetero-structure cavity

Phoxonic crystal is a kind of artificial periodic structure which can manipulate light and sound in the same time and space domain. It has good application prospect in optical communication system and opto-mechnical sensor. In this paper, a two-dimensional silicon phoxonic crystal slab structure is proposed, which can exhibit large phononic and photonic bandgaps simultaneously. Then a periodic cylindrical structure is introduced on the side surface of the slab. The effects of the height and radius of the cylinder on the side surface wave modes are analyzed. On this basis, a phoxonic crystal hetero-structure cavity composed of cylinders with different radii and heights is constructed, which can simultaneously confine the acoustic and optical modes because of mode gap effect. Seven phononic cavity modes and two photonic cavity modes are obtained. The two photonic cavity modes are called dielectric mode and air mode respectively. Further, the acousto-optical coupling rates between the seven phononic cavity modes and dielectric mode are calculated. Finally, a gap is etched on each cylinder in hetero-structure cavity, which can increase the surface area of the cavity by 23%. Then two phononic cavity modes and photonic dielectric mode with higher coupling rates are considered. The results show that etching the z-direction gap in the center of the cylinder can effectively increase the acousto-optical coupling rates.

Geometric parameters optimization of a two-dimensional phoxonic crystal with dual forbidden band characteristics

In this paper, a novel phoxonic crystal (PxC) structure composed of silicon, with optimal dual phononic band gap (PNBG) and photonic band gap (PTBG), is presented. Using the finite element analysis method, both the transmission characteristics and dispersion relation of PNBG and PTBG are calculated, and the existence of dual BGs is demonstrated by the means of the analysis of transmission for the PxC structure. The influences of structural parameters on the dual forbidden band characteristics are further explored, the sensitive structure parameters can be determined: the width of elastic beams, the length of square silicon, and the length of square hole. Using the orthogonal test, 25 experimental runs based on 3-factor and 5-level experiment are performed to finish the numerical experimental design and analysis. Four functional relationships can be acquired between the three sensitive parameters and dual BGs. Finally, the unified objective function method is employed to perform the construction of the single objective optimization model for the purpose of obtaining the optimal dual BGs and the corresponding optimal parameter combinations of the PxC structure. Such scheme can be used as the potential optimization way, which may find wide application in the development and design of PxCs.

Dirac cones with zero refractive indices in phoxonic crystals.

In this paper, simultaneous zero refractive indices (ZRIs) for both sound and light are realized on the basis of a 2D triangular lattice phoxonic crystal (PxC) with C6v symmetry. For the phononic mode, accidental phononic Dirac degeneracy at the center of Brillouin zone (BZ) occurs at a relatively high frequency which leads to the failure of the efficient medium theory; hence, it is no longer applicable to the realization of acoustic ZRI. We thus turn to a low-frequency phononic Dirac cone located at K point, the corner of the BZ, which shows in-phase pressure field oscillations in expanded unit cells. Using zone folding, we further reveal the cause for the characteristic of acoustic ZRI. For the photonic mode, a low-frequency photonic Dirac-like cone can be achieved by adjusting the geometric parameter due to the high contrast permittivity between scatterers and the matrix. When the phononic and photonic low-frequency Dirac dispersions coexist, the PxC can be mapped into a zero-index material for both sound and light at the same time. The new mechanism for simultaneously controlling sound and light helps to achieve acousto-optic synchronous cloaking and unidirectional transmission, which are numerically demonstrated.

Acousto-optic cavity coupling in 2D phoxonic crystal with combined convex and concave holes

A two-dimensional cross-like phoxonic crystal (PxC) model is proposed, which exhibits simultaneously large complete photonic crystal (PtC) and phononic crystal (PnC) bandgaps. The most salient trait of the structure is the wide range of geometrical parameters compatible with large complete bandgaps. After geometrical optimization, photonic and phononic bandgaps with gap-to-midgap ratios of 11.5% and 90.7% are obtained, respectively. These values are close to the best topology-optimized reported values but are obtained with simple shapes compatible with nanoscale fabrication technology. These characteristics make the convex–concave topology a promising candidate for PxC devices. A cavity is then introduced by filling up one cross-like hole in the 7 × 7 super-cell. PtC and PnC bands with defects appear in the respective large complete bandgaps, confining phonons and photons in the same cavity. Acousto-optic (AO) coupling between photonic and phononic defect modes is further investigated by the finite element method, taking both photoelastic and moving interface mechanisms into consideration. The symmetries of both photonic and phononic modes play a dominant role in the coupling strength. Results show that the strongest linear coupling between a photonic transverse magnetic mode and phononic breathing mode is obtained due to the in-phase superposition in the x and y directions. A quadratic nonlinear coupling is observed when photonic modes are coupled with the phononic stretching mode due to the inverse superposition of x and y directions. Finally, the optomechanical coupling rates relative to zero-point motion are estimated.

Design and optimization of an opto-acoustic sensor based on porous silicon phoxonic crystals

We present the theoretical study of an opto-acoustic microdevice, a phoxonic crystal, made of porous silicon with a specific acoustic response in the range of tens of MHz and optical response in the visible and near-infrared range. We propose to control the opto-acoustic response of this device by spatially modulating the microstructure porosity. Based on this study, a multilayer microcavity is designed to have a strong coupling between the acoustic and optical response. The coupling mechanism is generated by exploiting the structural resonance due to the acoustic waves which produce maximum mechanical strains at the center of the cavity. The associated mechanical deformations of the central cavity change the optical response of the multilayer, allowing the mechanical response to be detected using optical techniques. In a phoxonic crystal, the acoustic and optic central gap frequencies are determined by the multilayer configuration which imposes a fixed relation between both resonant frequencies. This feature establishes a challenge for the microdevice design. To mitigate this problem, two microcavities, one inside the other in a matryoshka-like configuration is here proposed, placing an optical microcavity into the spacer of an acoustic microcavity. Consequently, the localized acoustic field generates a high perturbation of the optical microcavity structure. The optical microcavity is tuned at near-infrared frequencies, while the larger acoustic microcavity resonates at acoustic frequencies of the order of tens of MHz. The microdevice is designed to display a high optical response induced by acoustic deformation. Optical sensitivity to this effect is used to design a multiparametric sensor. Thanks to the porous structure of the device, it is possible to build a transducer sensitive to the presence of analytes in the environment that affect both its mechanical and optical response.

Strong quadratic acousto-optic coupling in 1D multilayer phoxonic crystal cavity

Abstract Four methods are applied to calculate the acousto-optic (AO) coupling in one-dimensional (1D) phoxonic crystal (PXC) cavity: transfer matrix method (TMM), finite element method (FEM), perturbation theory, and Born approximation. Two types of mechanisms, the photoelastic effect (PE) and the moving interface effect (MI), are investigated. Whether the AO coupling belongs to linear or quadratic, the results obtained by the perturbation theory are in good agreement with the numerical results. We show that the combination method of FEM and perturbation theory has some advantages over Born approximation. The dependence of linear and quadratic couplings on the symmetry of acoustic and optical modes has been discussed in detail. The linear coupling will vanish if the defect acoustic mode is even symmetry, but the quadratic effect may be enhanced. Based on second-order perturbation theory, the contribution of each optical eigenfrequency to quadratic coupling is clarified. Finally, the quadratic coupling is greatly enhanced by tuning the thickness of the defect layer, which is an order of magnitude larger than that of normal defect thickness. The enhancement mechanism of quadratic coupling is illustrated. The symmetry of the acoustic defect mode is transformed from odd to even, and two optical defect modes are modulated to be quasi-degenerated modes. This study opens up a possibility to achieve tunable phoxonic crystals on the basis of nonlinear AO effects.

High-performance phoxonic cavity designs for enhanced acousto-optical interaction.

Effective confinement of light and sound is achieved through a one-dimensional phoxonic crystal (PxC) cavity. In particular, co-localization of gigahertz phonons and infrared photons in a cavity created by introducing a defect inside a multilayer PxC has been performed. The incident elastic waves can control the refractive index variation of the dual phononic-photonic cavity layer. We also studied the acousto-optic (AO) effect in four AO materials, each located in the cavity layer between two identical Bragg mirrors. The cavities are designed to have high-quality factors for both photon and phonon resonances, which are proportional to their lifetime and allow for a much stronger photon-phonon interaction. The AO effect causes a shift in the optical mode of the photonic band gap. The values of the refractive index of the AO cavities layer are estimated as a function of time based on the elastic strain perturbation using the relevant photo-elastic relations. The phoxonic band gaps and transmission spectra for both unperturbed and elastically perturbed PxC structures are derived depending on the transfer matrix method. In our results, the selected AO cavity of PbMoO4 provided the strongest AO coupling, in which the maximum wavelength shift of the resonant photonic modes reached 113.3 nm. In addition, 11.9 nm is the maximum displacement amplitude of the confinement elastic wave of the same nanocavity. The TeO2 cavity provided the highest Q values for both photonic and phononic modes of 7093 and 175, respectively. We think this research could open the way to study the properties of linear elastic materials to design extremely miniaturized AO devices.

Dual band gaps optimization for a two-dimensional phoxonic crystal

A two-dimensional phoxonic crystal (PxC) with optimal dual phononic and photonic complete band gaps (BGs) is proposed and analyzed numerically. Using finite element simulations, the thickness of the frame and the length of square silicon as well as the length of the square scatterer are found to be the three key factors influencing the dual BGs of PxC. Based on the orthogonal test design, 3-factor and 5-level experiments are designed to determine the relationships between the total bandwidths of the photonic and phononic BGs, respectively, with the three key factors. Using the two functional relationships as the unified objective function, the optimal thickness of the frame, and the length of square silicon and square scatterer are obtained to open the optimal dual BGs of PxC. It is expected that the combination of orthogonal test design and finite element simulations is a helpful way to design PxCs.

Topological electromagnetic and elastic states in phoxonic crystal cavity arrays

AbstractIn this paper, we investigate the topological characteristics of the phoxonic crystal (PxC) arrays. For the PxC system, the electromagnetic transverse electric mode and the elastic in‐plane mode are considered. The PxC possesses the photonic and phononic bandgaps simultaneously. Based on the bandgaps, we design the PxC cavity which can confine the electromagnetic and elastic waves. The interaction strength between the neighboring PxC cavities can be tuned by changing the distance between these cavities. The PxC cavity arrays with the topologically non‐trivial and trivial phases are obtained. We combine the PxC arrays with the topologically non‐trivial and trivial phases together. The electromagnetic and elastic topological interface states can be simultaneously observed at the interface of the PxC cavity arrays.

Theoretical studies of dual optical and acoustic unidirectional filtering based on two-dimensional phoxonic crystals with rectangle defects

ABSTRACT Dual optical and acoustic unidirectional transmission in two-dimensional phoxonic crystal rectangular defect connected by two mutually perpendicular waveguides is theoretically achieved. The unidirectional filtering for both optical and acoustic waves is designed by altering the phoxonic crystal waveguides and cavity to obtain the modes’ match and mismatch via the finite element method. This kind of devices has the abilities of mode convertor, wavelength filtering and unidirectional propagation for both the optical and acoustic wave, and maybe potentially applied in simultaneously manipulating light and sound.

Simultaneous unidirectional reciprocal filters of electromagnetic and elastic waves based on the modal symmetry of phoxonic crystal waveguides and cavity

We theoretically achieve the simultaneous unidirectional reciprocal filter of electromagnetic (EM) and elastic waves in a single phoxonic crystal by the finite-element method. The functionality is achieved by matching and mismatching the modal symmetry between a resonant cavity and two mutually perpendicular waveguides. Suitable phoxonic cavity and waveguides are created to realize the match and mismatch of the modal symmetry for both EM and elastic waves. The proposed device has the abilities of phoxonic unidirectional filtering as well as providing great potential for enhancing acousto-optic coupling by simultaneously tailoring electromagnetic and elastic waves with an ultracompact footprint size.

Determination of 1-propanol, ethanol, and methanol concentrations in water based on a one-dimensional phoxonic crystal sensor.

In this research, the photonic and phononic response of one-dimensional multilayer phoxonic crystals (PxCs) with normal incident of electromagnetic and acoustic waves is discussed. The presented design can work as a highly sensitive sensor for measuring three binary alcohol/water mixtures (i.e., 1-propanol/water, ethanol/water, and methanol/water) for a wide range of concentrations. The PxC sensor is able to detect small changes in the refractive index and longitudinal sound velocity of the alcohol/water mixture with initially neglecting the acousto-optical interaction. The sensor design is a defective structure as [$({\rm Si}/{\rm SiO}_2)^4 (\rm mixture\;wt. \%) {({{\rm SiO}_2}/{\rm Si})^4}$(Si/SiO2)4(mixturewt.%)(SiO2/Si)4]. Also, we studied the effects of changing mixture concentrations from 0 wt. % to 100 wt. % on the physio-chemical parameters and resonant mode frequency. In our results, we have achieved high performance for the three alcohol mixtures in both phononic and photonic sensors especially for low concentrations. For example, in the photonic sensor we obtained sensitivity, $Q$Q value, and figure of merit of 873 nm/RIU, 755, and ${290}\;{{\rm RIU}^{ - 1}}$290RIU-1, respectively, for methanol of concentration 10% in water. The phononic sensor showed higher results compared with the photonic sensor, as for ethanol with concentration 26.8% in water we obtained sensitivity, $Q$Q value, and figure of merit of ${37}\;{{\rm MHz/ms}^{ - 1}}$37MHz/ms-1, 1604, and ${8.4}\;{({\rm m/s})^{ - 1}}$8.4(m/s)-1, respectively. The proposed structure has different merits: operation at high temperatures, compact size, ease of fabrication, and feasibility of alcohol detection with two different methods that could be used in many chemical applications.