A dual photonic–phononic crystal slot nanobeam with a gradient cavity for liquid sensing is proposed and analyzed using the finite-element method. Based on the photonic and phononic crystals with mode bandgaps, both optical and acoustic waves can be confined within the slot and holes to enhance interactions between sound/light and analyte solution. The incorporation of a gradient cavity can further concentrate energy in the cavity and reduce energy loss by avoiding abrupt changes in lattices. The newly designed sensor is aimed at determining both the refractive index and sound velocity of the analyte solution by utilizing optical and acoustic waves. The effect of the cavity gradient on the optical sensing performance of the nanobeam is thoroughly examined. By optimizing the design of the gradient cavity, the photonic–phononic sensor has significant sensing performances on the test of glucose solutions. The currently proposed device provides both optical and acoustic detections. The analyte can be cross-examined, which consequently will reduce the sample sensing uncertainty and increase the sensing precision. Full article

Organo-metallic europium complex tetrakis (dibenzoyl methide) triethylammonium (EuD₄TEA) shows a sharp emission spectrum, which makes it interesting for photonic applications. In this work, we embedded it into all-polymeric planar microcavities and investigated the effect of the photonic environment on its emission spectrum. To this end, submicron-sized EuD₄TEA crystals were loaded into a blend of polystyrene and carboxylic terminated polystyrene matrix, which served to stabilize the emitter in the polymer and to make the composite processable. The new composite was then casted by spin-coating as a defect layer in a polymeric planar microcavity. Spectroscopic studies demonstrate that fine spectral tuning of the cavity mode on the sharp organometal luminescence is possible and produces spectral redistribution of the fluorophore emission, along with a remarkable cavity quality factor. Full article

Photonic technologies are nowadays dominated by highly performing inorganic structures that are commonly fabricated via lithography or epitaxial growths. Unfortunately, the fabrication of these systems is costly, time consuming, and does not allow for the growth of large photonic structures. All-polymer photonic crystals could overcome this limitation thanks to easy solubility and melt processing. On the other hand, macromolecules often do not offer a dielectric contrast large enough to approach the performances of their inorganic counterparts. In this work, we demonstrate a new approach to achieve high dielectric contrast distributed Bragg reflectors with a photonic band gap that is tunable in a very broad spectral region. A highly transparent medium was developed through a blend of a commercial polymer with a high refractive index inverse vulcanized polymer that is rich in sulfur, where the large polarizability of the S–S bond provides refractive index values that are unconceivable with common non-conjugated polymers. This approach paves the way to the recycling of sulfur byproducts for new high added-value nano-structures. Full article

This paper deals with the structuring of polycrystalline diamond thin films using the technique of nanosphere lithography. The presented multistep approaches relied on a spin-coated self-assembled monolayer of polystyrene spheres, which served as a lithographic mask for the further custom nanofabrication steps. Various arrays of diamond nanostructures—close-packed and non-close-packed monolayers over substrates with various levels of surface roughness, noble metal films over nanosphere arrays, ordered arrays of holes, and unordered pores—were created using reactive ion etching, chemical vapour deposition, metallization, and/or lift-off processes. The size and shape of the lithographic mask was altered using oxygen plasma etching. The periodicity of the final structure was defined by the initial diameter of the spheres. The surface morphology of the samples was characterized using scanning electron microscopy. The advantages and limitations of the fabrication technique are discussed. Finally, the potential applications (e.g., photonics, plasmonics) of the obtained nanostructures are reviewed. Full article

We have been numerically demonstrated the mechanism of spatial beam filtering with autocloned photonic crystals. The spatial filtering through different configurations of the multilayered structures based on a harmonically modulated substrate profile is considered. The paper demonstrates a series of parameter studies to look for the best spatial beam filtering performance. The optimization results show that a beam spectral width of 39.2° can be reduced to that of 5.92°, leading to high potential applications for integrated optical microsystems. Full article

Light propagation in one-dimensional (1D) photonic crystals (PCs) enclosed in a rectangular waveguide is investigated in order to achieve a complete photonic band gap (PBG) while avoiding the difficulty in fabricating 3D PCs. This work complements our two previous articles (Phys. Rev. E) that quantitatively analyzed omnidirectional light propagation in 1D and 2D PCs, respectively, both showing that a complete PBG cannot exist if an evanescent wave propagation is involved. Here, we present a quantitative analysis of the transmission functions, the band structures, and the photon density of states (PDOS) for both the transverse electric (TE) and transverse magnetic (TM) polarization modes of the periodic multilayer heterostructure confined in a rectangular waveguide. The PDOS of the quasi-1D photonic crystal for both the TE and TM modes are obtained, respectively. It is demonstrated that a “complete PBG” can be obtained for some frequency ranges and categorized into three types: (1) below the cutoff frequency of the fundamental TE mode, (2) within the PBG of the fundamental TE mode but below the cutoff frequency of the next higher order mode, and (3) within an overlap of the PBGs of either TE modes, TM modes, or both. These results are of general importance and relevance to the dipole radiation or spontaneous emission by an atom in quasi-1D periodic structures and may have applications in future photonic quantum technologies. Full article

This paper presents a novel magneto-optical isolator based on an ultra-wideband and high efficiency photonic crystals (PCs) waveguide and gyromagnetic ferrites. The three-dimensional numerical simulation finds that the photonic crystals waveguide’s (PCW) transmission efficiency rises with its height and width. The corresponding experiments are performed by using a triangular lattice Al₂O₃ dielectric posts array in 5G millimeter wave band. The measured transmission efficiency is up to 90.78% for the optimal PCs waveguide structure, which has ultra-wide operating bandwidth from 23.45 to 31.25 GHz. The magneto-optical isolator is designed by inserting two rectangular gyromagnetic ferrites into the PCs waveguide. Due to the contrast between the effective permeability of the left and right circular polarization waves passing through the magnetized ferrite sheets, the ferromagnetic resonance absorption of the forward and reverse waves is different. By using finite element method, the isolation is optimized to be 49.49 dB for the isolator and its relative bandwidth reaches 8.85%. The high isolation, broadband, and easy integration indicate that our designed magneto-optical isolator has significant advantage in 5G communication systems. Full article

A simple scheme to generate an integrated, nanoscale optical frequency comb (OFC) is numerically studied. In this study, all optical intensity modulators based on photonic crystal (PhC) cavities are cascaded both in series and parallel. By adjusting the modulation parameters, such as the repetition rate, phase, and coupling efficiency of the modulating wave, it is possible to produce combs with a variety of different characteristics. Unique to PhC intensity modulators, in comparison with standard lithium niobate modulators, is the ability to control the amplitude of the light via a cavity rather than controlling the phase through one arm of a Mach–Zehnder interferometer. This opens up modulation-based OFC generation to new possibilities in both nanoscale operation and cavity-based schemes. Full article

In this paper, an all-optical photonic crystal-based switch containing a graphene resonant ring has been presented. The structure has been composed of 15 × 15 silicon rods for a fundamental lattice. Then, a resonant ring including 9 thick silicon rods and 24 graphene-SiO₂ rods was placed between two waveguides. The thick rods with a radius of 0.41a in the form of a 3 × 3 lattice were placed at the center of the ring. Graphene-SiO₂ rods with a radius of 0.2a were assumed around the thick rods. These rods were made of the graphene monolayers which were separated by SiO₂ disks. The size of the structure was about 70 µm² that was more compact than other works. Furthermore, the rise and fall times were obtained by 0.3 ps and 0.4 ps, respectively, which were less than other reports. Besides, the amount of the contrast ratio (the difference between the margin values for logics 1 and 0) for the proposed structure was calculated by about 82%. The correct switching operation, compactness, and ultra-fast response, as well as the high contrast ratio, make the presented switch for optical integrated circuits. Full article

In this study, an oscillator model of bubble-in-water is proposed to analyze the effective modulus of low-concentration bubbly water. We show that in a wide range of wave frequency the bubbly water acquires a negative effective modulus, while the effective density of the medium is still positive. These two properties imply the existence of a wide acoustic gap in which the propagation of acoustic waves in this medium is prohibited. The dispersion relation for the acoustic modes in this medium follows Lorentz type dispersion, which is of the same form as that of the phonon-polariton in an ionic crystal. Numerical results of the gap edge frequencies and the dispersion relation in the long-wavelength regime based on this effective theory are consistent with the sonic band results calculated with the plane-wave expansion method (PWEM). Our theory provides a simple mechanism for explaining the long-wavelength behavior of the bubbly water medium. Therefore, phenomena such as the high attenuation rate of sound or acoustic Anderson localization in bubbly water can be understood more intuitively. The effects of damping are also briefly discussed. This effective modulus theory may be generalized and applied to other bubble-in-soft-medium type sonic systems. Full article

Photonic crystal (PC) is usually realized in materials with high refractive indices contrast to achieve a photonic bandgap (PBG). In this work, we demonstrated an optimization of two-dimensional PCs using a low refractive index polymer material. An original idea of assembly of polymeric multiple rings in a hexagonal configuration allowed us to obtain a circular-like structure with higher symmetry, resulting in a larger PBG at a low refractive index of 1.6. The optical properties of such newly proposed structure are numerically calculated by using finite-difference time-domain (FDTD) method. The proposed structures were realized experimentally by using a direct laser writing technique based on low one-photon absorption method. Full article

Although the passively adjusting and actively tuning of pure longitudinal (primary (P-)) and pure transverse (secondary or shear (S-)) waves band structures in periodically laminated piezoelectric composites have been studied, the actively tuning of coupled elastic waves (such as P-SV, P-SH, SV-SH, and P-SV-SH waves), particularly as the coupling of wave modes is attributed to the material anisotropy, in these phononic crystals remains an untouched topic. This paper presents the analytical matrix method for solving the dispersion characteristics of coupled elastic waves along the thickness direction in periodically multilayered piezoelectric composites consisting of arbitrarily anisotropic materials and applied by four kinds of electrical boundaries. By switching among these four electrical boundaries—the electric-open, the external capacitance, the electric-short, and the external feedback control—and by altering the capacitance/gain coefficient in cases of the external capacitance/feedback-voltage boundaries, the tunability of the band properties of the coupled elastic waves along layering thickness in the concerned phononic multilayered crystals are investigated. First, the state space formalism is introduced to describe the three-dimensional elastodynamics of arbitrarily anisotropic elastic and piezoelectric layers. Second, based on the traveling wave solutions to the state vectors of all constituent layers in the unit cell, the transfer matrix method is used to derive the dispersion equation of characteristic coupled elastic waves in the whole periodically laminated anisotropic piezoelectric composites. Finally, the numerical examples are provided to demonstrate the dispersion properties of the coupled elastic waves, with their dependence on the anisotropy of piezoelectric constituent layers being emphasized. The influences of the electrical boundaries and the electrode thickness on the band structures of various kinds of coupled elastic waves are also studied through numerical examples. One main finding is that the frequencies corresponding to $qH=n\pi$ (with $qH$ the dimensionless characteristic wavenumber) are not always the demarcation between pass-bands and stop-bands for coupled elastic waves, although they are definitely the demarcation for pure P- and S-waves. The other main finding is that the coupled elastic waves are more sensitive to, if they are affected by, the electrical boundaries than the pure P- and S-wave modes, so that higher tunability efficiency should be achieved if coupled elastic waves instead of pure waves are exploited. Full article

We study energy harvesting in a binary phononic crystal (PC) beam at the defect mode. Specifically, we consider the placement of a mismatched unit cell related to the excitation point. The mismatched unit cell contains a perfect segment and a geometrically mismatched one with a lower flexural rigidity which serves as a point defect. We show that the strain in the defect PC beam is much larger than those in homogeneous beams with a defect segment. We suggest that the defect segment should be arranged in the first unit cell, but not directly connected to the excitation source, to achieve efficient less-attenuated localized energy harvesting. To harvest the energy, a polyvinylidene fluoride (PVDF) film is attached on top of the mismatched segment. Our numerical and experimental results indicate that the placement of the mismatched segment, which has not been addressed for PC beams under mechanical excitation, plays an important role in efficient energy harvesting based on the defect mode. Full article

We investigate theoretically and experimentally the creation of virtually any polymer-based photonic structure containing individual nonlinear KTiOPO ${}_4$ nanoparticles (KTP NPs) using low one-photon absorption (LOPA) direct laser writing (DLW) technique. The size and shape of polymeric microstructures and the position of the nonlinear KTP crystal inside the structures, were perfectly controlled at nanoscale and on demand. Furthermore, we demonstrated an enhancement of the second-harmonic generation (SHG) by a factor of 90 when a KTP NP was inserted in a polymeric pillar. The SHG enhancement is attributed to the resonance of the fundamental light in the cavity. This enhancement varied for different KTP NPs, because of the random orientation of the KTP NPs, which affects the light/matter interaction between the fundamental light and the NP as well as the collection efficiency of the SHG signal. The experimental result are further supported by a simulation model using Finite-Difference Time-Domain (FDTD) method. Full article

The differential quadrature method has been developed to calculate the elastic band gaps from the Bragg reflection mechanism in periodic structures efficiently and accurately. However, there have been no reports that this method has been successfully used to calculate the band gaps of locally resonant structures. This is because, in the process of using this method to calculate the band gaps of locally resonant structures, the non-linear term of frequency exists in the matrix equation, which makes it impossible to solve the dispersion relationship by using the conventional matrix-partitioning method. Hence, an accurate and efficient numerical method is proposed to calculate the flexural band gap of a locally resonant beam, with the aim of improving the calculation accuracy and computational efficiency. The proposed method is based on the differential quadrature method, an unconventional matrix-partitioning method, and a variable substitution method. A convergence study and validation indicate that the method has a fast convergence rate and good accuracy. In addition, compared with the plane wave expansion method and the finite element method, the present method demonstrates high accuracy and computational efficiency. Moreover, the parametric analysis shows that the width of the 1st band gap can be widened by increasing the mass ratio or the stiffness ratio or decreasing the lattice constant. One can decrease the lower edge of the 1st band gap by increasing the mass ratio or decreasing the stiffness ratio. The band gap frequency range calculated by the Timoshenko beam theory is lower than that calculated by the Euler-Bernoulli beam theory. The research results in this paper may provide a reference for the vibration reduction of beams in mechanical or civil engineering fields. Full article

In this work, an innovative vibration energy harvester is designed by using the point defect effect of two-dimensional (2D) magneto-elastic phononic crystals (PCs) and the piezoelectric effect of piezoelectric material. A point defect is formed by removing the central Tenfenol-D rod to confine and enhance vibration energy into a spot, after which the vibration energy is electromechanically converted into electrical energy by attaching a piezoelectric patch into the area of the point defect. Numerical analysis of the point defect can be carried out by the finite element method in combination with the supercell technique. A 3D Zheng-Liu (Z-L) model which accurately describes the magneto-mechanical coupling constitutive behavior of magnetostrictive material is adopted to obtain variable band structures by applied magnetic field and pre-stress along the z direction. The piezoelectric material is utilized to predict the output voltage and power based on the capacity to convert vibration energy into electrical energy. For the proposed tunable vibration energy harvesting system, numerical results illuminate that band gaps (BGs) and defect bands of the in-plane mixed wave modes (XY modes) can be adjusted to a great extent by applied magnetic field and pre-stress, and thus a much larger range of vibration frequency and more broad-distributed energy can be obtained. The defect bands in the anti-plane wave mode (Z mode), however, have a slight change with applied magnetic field, which leads to a certain frequency range of energy harvesting. These results can provide guidance for the intelligent control of vibration insulation and the active design of continuous power supply for low power devices in engineering. Full article

Photonic nanojets formed in the vicinity of the cylindrical graded-index lens with different types of index grading are numerically investigated based on the finite-difference time-domain method. The cylindrical lens with 1600 nm diameter is assembled by eighty-seven hexagonally arranged close-contact nanofibers with 160 nm diameter. Simulation and analysis results show that it is possible to engineer and elongate the photonic nanojet. Using differently graded-index nanofibers as building elements to compose this lens, the latitudinal and longitudinal sizes of the produced photonic nanojet can be flexibly adjusted. At an incident wavelength of 532 nm, the cylindrical lens with index grading = 2 can generate a photonic nanojet with a waist about 173 nm (0.32 wavelength). This lens could potentially contribute to the development of a novel device for breaking the diffraction limit in the field of optical nano-scope and bio-photonics. Full article

Orbital angular momentum (OAM) mode-division multiplexing (MDM) has recently been under intense investigations as a new way to increase the capacity of fiber communication. In this paper, a two-layer Erbium-doped fiber amplifier (EDFA) for an OAM multiplexing system is proposed. The amplifier is based on the circular photonic crystal fiber (C-PCF), which can maintain a stable transmission for 14 OAM modes by a large index difference between the fiber core and the cladding. Further, the two-layer doped region can balance the amplification performance of different modes. The relationship between the performance and the parameters of the amplifier is analyzed numerically to optimize the amplifier design. The optimized amplifier can amplify 18 modes (14 OAM modes) simultaneously over the C-band with a differential mode gain (DMG) lower than 0.1 dB while keeping the modal gain over 23 dB and noise figure below 4 dB. Finally, the fabrication tolerance and feasibility are discussed. The result shows a relatively large fabrication tolerance in the OAM EDFA parameters. Full article

Orbital angular momentum modes in optical fibers have polarization mode dispersion. The relationship between polarization mode dispersion and the birefringence vector can be deduced using an optical fiber dynamic equation. First, a mathematical model was established to formulate mode dispersion caused by stress-induced birefringence. Second, in the stress-induced birefringence simulation model, the finite element method was used to analyze the transmission characteristics of the hollow-core circular photonic crystal fiber. Finally, mode dispersion caused by stress-induced birefringence was obtained using theoretical derivation and simulation analyses. The results showed that the new fiber type has good transmission characteristics and strong stress sensitivity, which provide key theoretical support for optimizing the structural parameters of optical fiber and designing stress sensors. Full article

In this paper, the wave propagation in phononic crystal composed of auxetic star-shaped honeycomb matrix with negative Poisson’s ratio is presented. Two types of inclusions with circular and rectangular cross sections are considered and the band structures of the phononic crystals are also obtained by the finite element method. The band structure of the phononic crystal is affected significantly by the auxeticity of the star-shaped honeycomb. Some other interesting findings are also presented, such as the negative refraction and the self-collimation. The present study demonstrates the potential applications of the star-shaped honeycomb in phononic crystals, such as vibration isolation and the elastic waveguide. Full article

We propose a new polarization splitter (PS) based on Ti and liquid infiltrated photonic crystal fiber (PCF) with high birefringence. Impacts of parameters such as shape and size of the air holes in the cladding and filling material are investigated by using a vector beam propagation method. The results indicate that the PS offers an ultra-short length of 83.9 μm, a high extinction ratio of −44.05 dB, and a coupling loss of 0.0068 dB and at 1.55 μm. Moreover, an extinction ratio higher than −10 dB is achieved a bandwidth of 32.1 nm. Full article

In this study, a novel polarization converter (PC) based on square lattice photonic crystal fiber (PCF) is proposed and analyzed. For each square unit in the cladding, two identical circular air holes are arranged symmetrically along the $y=x$ axis. With the simple configuration structure, numerical simulations using the FDTD analysis demonstrate that the PC has a strong polarization conversion efficiency (PCE) of 99.4% with a device length of 53 $\mathsf{\mu }$ m, and the extinction ratio is −21.8 dB. Considering the current PCF fabrication technology, the structural tolerances of circular hole size and hole position have been discussed in detail. Moreover, it is expected that over the 1.2∼1.7 $\mathsf{\mu }$ m wavelength range, the PCE can be designed to be better than 99% and the corresponding extinction ratio is better than $-20\mathrm{dB}$ . Full article

Particle trapping and sensing serve as important tools for non-invasive studies of individual molecule or cell in bio-photonics. For such applications, it is required that the optical power to trap and detect particles is as low as possible, since large optical power would have side effects on biological particles. In this work, we proposed to deploy a nanobeam photonic crystal cavity for particle trapping and opto-mechanical sensing. For particles captured at 300 K, the input optical power was predicted to be as low as 48.8 μW by calculating the optical force and potential of a polystyrene particle with a radius of 150 nm when the trapping cavity was set in an aqueous environment. Moreover, both the optical and mechanical frequency shifts for particles with different sizes were calculated, which can be detected and distinguished by the optomechanical coupling between the particle and the designed cavity. The relative variation of the mechanical frequency achieved approximately 400%, which indicated better particle sensing compared with the variation of the optical frequency (±0.06%). Therefore, our proposed cavity shows promising potential as functional components in future particle trapping and manipulating applications in lab-on-chip. Full article

Colloidal photonic crystal (PC)-based anti-counterfeiting materials have been widely studied due to their inimitable structural colors and tunable photonic band gaps (PBGs) as well as their convenient identification methods. In this review, we summarize recent developments of colloidal PCs in the field of anti-counterfeiting from aspects of security strategies, design, and fabrication principles, and identification means. Firstly, an overview of the strategies for constructing PC anti-counterfeiting materials composed of variable color PC patterns, invisible PC prints, and several other PC anti-counterfeiting materials is presented. Then, the synthesis methods, working principles, security level, and specific identification means of these three types of PC materials are discussed in detail. Finally, the summary of strengths and challenges, as well as development prospects in the attractive research field, are presented. Full article