Photonic Crystal Lattice Research Articles

A Millimeter-Wave Y-Shaped Circulator Based on Magneto Photonic Crystals

In this paper, a millimeter-wave Y-shaped circulator based on magneto photonic crystals is demonstrated. The triangular lattice photonic crystal with Y-shaped line defect waveguide is constructed by Al2O3 ceramic posts. The magneto-optical cavity resonator in the junction of Y-shaped waveguide consists of two cylindrical ferrites and two triangular metal pedestals. The transmission characteristics of the circulator experimented under the external magnetic bias H0 = 300 Gs. In working frequency range 24∼28 GHz the isolation of circulator is better than 20 dB, and the best insertion loss is as low as 0.2 dB. The experimented results are well agreed with the simulation results.

Multiple topological transitions and topological edge states of triple-site honeycomb lattice photonic crystals

We propose a two-dimensional (2D) triple-site honeycomb lattice (TSHL) photonic crystal (PC) by rotating the three dielectric rods six times, forming unit cell, and then arraying the unit cells in the triangular lattice. The TSHL PC structure can achieve topological phase transitions in three ways, which are changing the position or size of the rods, and rotating the rods. By calculating the band structure under different parameters, the law of topological phase transition for TSHL PC is analyzed. The topological edge state can be adjusted by changing the rotation angle of the dielectric rods. Based on this, a frequency-selective beam splitter is designed. Compared with previous studies, this flexible topological system shows more abundant physical phenomena, enriches the implementation of topological photonics , and promotes the research of topological edge states and the development of topological insulators in practical applications. • We propose a two-dimensional triple-site honeycomb lattice photonic crystal, which has the high degrees of freedom. • The triple-site honeycomb lattice unit cell can achieve topological phase transitions in three ways, which are changing the position or size of the cylinders, and rotating the cylinders. • We design a frequency-selective beam splitter, by changing the rotation angle of the dielectric rods.

Self-collimation in the square lattice photonic crystals composed of multi-circular ring scatterers

In this paper, fractal supercells are constructed according to the Thue-Morse theory and arranged in a square lattice to form fractal photonic crystals (PCs), which are called the first-order (1st) and second-order (2nd) approximate of Thue-Morse structure. The multi-circular ring scatterers (MCRSs) are innovatively applied in them and the effect of the number (H) and width (W) variation of the rings on the equifrequency contours (EFCs) of PCs is investigated. To calculate the energy band diagrams and EFC mappings of the first-order (1st) and second-order (2nd) approximate of Thue-Morse structure, an improved plane wave expansion (PWE) method is also introduced. Then, the possibility of achieving polarization-insensitive self-collimation (PISC) in the approximate of Thue-Morse structure and conventional square lattice (CSL) PCs are explored. This phenomenon was verified by simulations at normalized frequencies of 0.128, 0.068, and 0.27 (ωa/2πc), respectively, and the phenomenon of vertical incidence self-collimation of light (VISCOL) was proposed on this basis. Finally, a reflection on the value of the multi-ring nested type of scatterers is presented. Replacing the circular rings in the PCs with square rings, it is found that the EFCs for TE polarization change less while the EFCs for TM polarization have larger variations, which leads to a reduction in the VISCOL frequency range and provides a possibility for beam splitter design.

Band gap properties and self-collimation in a tenfold quasicrystal structure photonic crystals applying multicircular ring scatterers

In this paper, a kind of tenfold photonic quasicrystals based on the Penrose puzzle theory with the application of multicircular ring scatterers (MCRSs) is presented. It is divided into four kinds of square supercells and employed in a square lattice to constitute the first-order (1st), second-order (2nd), third-order (3rd), and fourth-order (4th) tenfold quasicrystal structure photonic crystals (TFQCSPCs) accordingly. In an attempt to evaluate the dispersion maps and equifrequency contour (EFC) profiles of such long-range ordered but not really periodic TFQCSPCs, an enhanced plane wave expansion (PWE) method is adopted. The photonic crystals (PCs) discussed in this paper are first classified into two major categories, air hole and dielectric column types which will be referred to as type 1, type 2 respectively in the following. The varying features of photonic band gaps (PBGs) of TFQCSPCs are inquired about by changing the refractive index (n) of the relevant medium and the number of rings (H) of MCRSs under two broad prerequisites of type 1 and type 2 PCs. The results are also compared with the associated properties of PBGs of traditional square lattice PCs (TSLPCs) and traditional triangular lattice PCs (TTLPCs) which employ MCRSs. Then, the 1st and 2nd TFQCSPCs and TSLPCs are fabricated in the form of hollow air holes dug in the silicon plate, and the transformation of their PBGs and EFCs is researched when the width (W) and H of the ring are adjusted. The possibility of implementing the phenomenon of polarization-insensitive self-collimation (PISC) in TFQCSPCs and TSLPCs is explored by examining the smoothest EFCs in EFC mappings. Eventually, our work actualizes the PISC phenomenon at seven normalized frequency (NF) values of 0.074, 0.168, 0.170, 0.172, 0.265, 0.270, and 0.297, which fills the gap of the PISC phenomenon in the low-frequency domain.

Design and Simulation of Linear All-Optical Comparator Based on Square-Lattice Photonic Crystals

An optical comparator is an important logic circuit used in digital designs. Photonic crystals are among the platforms for implementing different kinds of gates and logic circuits, and they are structures with alternating refractive indices. In this paper, an optical comparator is designed and simulated based on a square lattice photonic crystal. In the design of this comparator, a small-sized structure is used. The simulation results show that in the proposed comparator, there is a high difference between logical values “0” and “1”, which are defined based on the optical power level. Due to the small size of this comparator and the adequate difference between logical values “0” and “1”, this structure suits photonic integrated circuits with high accuracy. The proposed structure footprint is 149.04 µm2, and the calculated rise time for this circuit is less than 0.4 ps.

Polariton Bose-Einstein condensate from a bound state in the continuum.

Bound states in the continuum (BICs)1-3 are peculiar topological states that, when realized in a planar photonic crystal lattice, are symmetry-protected from radiating in the far field despite lying within the light cone4. These BICs possess an invariant topological charge given by the winding number of the polarization vectors5, similar to vortices in quantum fluids such as superfluid helium and atomic Bose-Einstein condensates. In spite of several reports of optical BICs in patterned dielectric slabs with evidence of lasing, their potential as topologically protected states with theoretically infinite lifetime has not yet been fully exploited. Here we show non-equilibrium Bose-Einstein condensation of polaritons-hybrid light-matter excitations-occurring in a BIC thanks to its peculiar non-radiative nature, which favours polariton accumulation. The combination of the ultralong BIC lifetime and the tight confinement of the waveguide geometry enables the achievement of an extremely low threshold density for condensation, which is reachednot in the dispersion minimum but at a saddle point in reciprocal space. By bridging bosonic condensation and symmetry-protected radiation eigenmodes, we reveal ways of imparting topological properties onto macroscopic quantum states with unexplored dispersion features. Such an observation may open a route towards energy-efficient polariton condensation in cost-effective integrated devices, ultimately suited for the development of hybrid light-matter optical circuits.

Optical biosensors using plasmonic and photonic crystal band-gap structures for the detection of basal cell cancer

One of the most interesting topics in bio-optics is measuring the refractive index of tissues. Accordingly, two novel optical biosensor configurations for cancer cell detections have been proposed in this paper. These structures are composed of one-dimensional photonic crystal (PC) lattices coupled to two metal–insulator–metal (MIM) plasmonic waveguides. Also, the tapering method is used to improve the matching between the MIM plasmonic waveguides and PC structure in the second proposed topology. The PC lattices at the central part of the structures generate photonic bandgaps (PBGs) with sharp edges in the transmission spectra of the biosensors. These sharp edges are suitable candidates for sensing applications. On the other hand, the long distance between two PBG edges causes that when the low PBG edge is used for sensing mechanism, it does not have an overlapping with the high PBG edge by changing the refractive index of the analyte. Therefore, the proposed biosensors can be used for a wide wavelength range. The maximum obtained sensitivities and FOM values of the designed biosensors are equal to 718.6, 714.3 nm/RIU, and 156.217, 60.1 RIU−1, respectively. The metal and insulator materials which are used in the designed structures are silver, air, and GaAs, respectively. The finite-difference time-domain (FDTD) method is used for the numerical investigation of the proposed structures. Furthermore, the initial structure of the proposed biosensors is analyzed using the transmission line method to verify the FDTD simulations. The attractive and simple topologies of the proposed biosensors and their high sensitivities make them suitable candidates for biosensing applications.

All-optical half adder based on triangular lattice photonic crystals with uniform structural parameters

All-optical half adder based on triangular lattice photonic crystals with uniform structural parameters

Self-Collimation in the Square Lattice Photonic Crystals Composed of Multi-Circular Ring Scatterers

Self-Collimation in the Square Lattice Photonic Crystals Composed of Multi-Circular Ring Scatterers

Dimensional Optimization of TiO2 Nanodisk Photonic Crystals on Lead Iodide (MAPbI3) Perovskite Solar Cells by Using FDTD Simulations

Perovskite solar cells (PSC) are currently exhibiting reproducible high efficiency, low-cost manufacturing, and scalable electron transport layers (ETL), which are becoming increasingly important. The application of photonic crystals (PC) on solar cells has been proven to enhance light harvesting and lead solar cells to adjust the propagation and distribution of photons. In this paper, the optimization of a two-dimensional nanodisk PC introduced in ETL with an organic-inorganic lead-iodide perovskite (methylammonium lead-iodide, MAPbI3) as the absorber layer was studied. A finite-difference time-domain (FDTD) simulation was used to evaluate the optical performance of PSC with various lattice constants and a radius of nanodisk photonic crystals. According to the simulation, the optimum lattice constant and PC radius applied to ETL are 500 nm and 225 nm, respectively. This optimum design enhances PSC absorption performance by more than 94% of incident light.

High bit rate all-optical 4 to 1 multiplexer by cascading of AND and OR gates in two-dimensional photonic crystals

We present a design of an all-optical 4 to 1 multiplexer by cascading four stages of ψ-shaped three-input AND gates and a Y-shaped four-input OR gate on a square lattice photonic crystal with rods in air interface. The three-input AND gate was designed separately to achieve efficient logical output and integrated into the multiplexer, and the OR gate design was subsequently incorporated with the multiplexer design. The band diagram of the proposed structures was computed using the plane wave expansion method, and the electric field distributions were estimated using the finite-difference time-domain method. The all-optical three-input AND gate had a normalized intensity of 90% for logic “1” and 10% for logic “0,” a contrast ratio (CR) of 9.54 dB, a response time of 0.816 ps, and an operating bit rate of 1.224 Tb / s with a footprint of 189 μm2. The all-optical 4 to 1 multiplexer had a normalized intensity of 79% for logic “1” and 2% for logic “0,” a CR of 15.96 dB, a response time of 0.848 ps, and an operating bit rate of 1.179 Tb / s with a footprint of 1040 μm2. Therefore, the proposed 4 to 1 multiplexer design would be a desirable structure for optical signal processing and photonic integrated circuits.

Investigation of the Two-Mode Regime of Two-Gap Photonic-Crystal Resonance Systems Produced on a Printed Circuit Board with Fractal Elements "Minkowski Island

Introduction. The development of new amplifiers and generators of the Ku- and K-bands (12…27 GHz) for use in onboard equipment is increasingly attracting research interest. Low-voltage multi-beam klystrons (LMBK) can be a promising element base for such devices. Serious problems are associated with the need to suppress parasitic modes of oscillations in NMLK operating in the centimeter and millimeter range. A possible solution is to use double-gap photonic-crystal resonators (DPCR) in LMBK. Another promising direction for improving the characteristics of such resonators is to use resonant segments of strip lines with fractal elements. In this case, the strip lines are placed on a dielectric substrate in the interaction space. Such resonators exhibit new properties that are useful for klystrons (an increase in characteristic impedance, suppression of the spectrum of unwanted frequencies, a reduction in mass and dimensions).Aim. Determination of an optimal set of electrodynamic and electronic parameters of double-gap photonic-crystal resonance systems with fractal elements "Minkowski Island" when operated as part of the LMBK resonator system, excited on π- and 2π-modes of oscillation.Materials and methods. To calculate the electrodynamic parameters of resonators, the method of finite differences in the time domain was used. The well-known Wessel-Berg method was used to calculate electronic parameters, such as the Ge / G0 electronic conductivity and the coupling coefficient M.Results. The main electrodynamic parameters of the resonator – Q-factor, resonant frequency and characteristic impedance – were investigated. The electronic parameters of the resonator, the coefficient of coupling with the electron beam, and the relative electronic conductivity for π- and 2π-modes of oscillations were calculated. In this case, three variants of the resonator with zero, first and second iterations of the fractal element were investigated. The amplitude-frequency characteristics of the resonator were investigated with a change in the pitch of the photonic crystal lattice. An estimation of the inhomogeneity of the high-frequency field in the interaction spaces of the resonator was carried out. Operational conditions were determined simultaneously for two types of oscillations without self-excitation.Conclusion. The results can find application in the development of resonator systems for klystron-type devices in the centimeter and millimeter ranges.

Complete two-dimensional photonic bandgap in refractive-index ratio 2.1 photonic crystals due to high-order bands.

We find that in a suitably designed photonic crystal (PC) certain high-order photonic bands are less affected by the refractive-index ratio (RIR) than low-order bands, enabling the realization of a robust and complete two-dimensional (2D) photonic bandgap in a moderate refractive-index-ratio PC. A detailed theoretical investigation of low- and high-order bandgaps in a series of PCs with different configurations is performed that shows that high-order bands may favor substantial complete photonic bandgaps (CPBGs) for systems with a moderate RIR. Furthermore, the importance of the geometry and structural parameters on achieving a high-order CPBG is found. Specifically, a hexagonal lattice PC of annular-hole-peripheral connecting rods is proposed, which can support a CPBG with a refractive-index ratio (RIR) as low as nhigh:nlow=2.1; to the best of our knowledge, this is the lowest RIR used to obtain a 2D CPBG in a PC.

Dispersion Mapping in 3-Dimensional Core-Shell Photonic Crystal Lattices Capable of Negative Refraction in the Mid-Infrared.

Engineering of the dispersion properties of a photonic crystal (PhC) opens a new paradigm for the design and function of PhC devices. Exploiting the dispersion properties of PhCs allows control over wave propagation within a PhC. We describe the design, fabrication, and experimental observation of photonic bands for 3D PhCs capable of negative refraction in the mid-infrared. Band structure and equifrequency contours were calculated to inform the design of 3D polymer-germanium core-shell PhCs, which were fabricated using two-photon lithography direct laser writing and sputtering. We successfully characterized a polymer-Ge core-shell lattice and mapped its band structure, which we then used to calculate the PhC refraction behavior. An analysis of wave propagation revealed that this 3D core-shell PhC refracts light negatively and possesses an effective negative index of refraction in the experimentally observed region. These results suggest that architected nanolattices have the potential to serve as new optical components and devices across infrared frequencies.

Proposal of a Cascade Photonic Crystal XOR Logic Gate for Optical Integrated Circuits with Investigation of Fabrication Error and Optical Power Changes

A compact and simple structure is designed to create an all-optical XOR logic gate using a two-dimensional, photonic crystal lattice. The structure was implemented using three waveguides connected by two nano-resonators. The plane wave expansion method was used to obtain the photonic band gap and the finite-difference time-domain method was used to investigate the behavior of the electromagnetic field in the photonic crystal structure. Examining the high contrast ratio and high-speed cascade, all-optical XOR on a chip, the effects of fabrication error and the changes in the input optical power showed that the structure could be used in optical integrated circuits. The contrast ratio and data transfer rate of the cascade XOR logic gate were respectively obtained as 44.29 dB and 1.5 Tb/s. In addition, the designed structure had very small dimensions at 158.65 μm2 and required very low power to operate, which made it suitable for low-power circuits. This structure could also be used as a NOT logic gate. Therefore, an XNOR logic gate can be designed using XOR and NOT logic gates.

Transmission and reflection cloaking by using a zero-refractive-index photonic crystal in the microwave region.

We propose a rectangular column two-dimensional square lattice photonic crystal to realize zero refractive index. Through analysis of the energy band structure of the photonic crystal structure, the lattice constant and side length of the rectangular columns can be optimized, and the Dirac cone dispersion appears at the center of the Brillouin zone. The Dirac cone is formed by the interaction of a monopolar eigenstate and a dipolar eigenstate to form a triple accidental degenerate state. The effective medium theory is used to invert the effective electromagnetic parameters of the photonic crystal with a double zero refractive index. The zero-phase change and the focusing characteristic of the concave lens of this kind of zero-refractive-index material are verified. Importantly, we have achieved transmission and reflection cloaking with this zero-index medium. Through the analysis of the amplitude and phase distribution characteristics of the electromagnetic field, it is proved that the designed cloaking devices have obvious cloaking effect.

Fragile topology in double-site honeycomb lattice photonic crystal.

Fragile topology (FT) opens a new direction in topological photonics, but a new type of photonic crystal (PC) with FT remains to be proposed. In this Letter, the double-site honeycomb lattice (DSHL) PC is proposed by rotating the double dielectric rods (DDR) six times, forming unit cell, and then arraying the unit cells in a triangular lattice. Quantum spin Hall effect occurs by manipulating the DDR in the tangential and radial directions of the unit cell. First, the band structures of DSHL PCs with different structural parameters are calculated, and the laws of topological phase transition are analyzed statistically. Then, to prove the FT properties of two groups of topological nontrivial DSHL PCs, the Wannier-center positions of the bulk bands are calculated by the Wilson-Loop method. Finally, the topological edge states and two groups of topological corner states, which are in the same bulk-state bandgap, are realized successfully. The DSHL PC provides good platforms for both the research of topological photonics and the device design and application, which has a broad prospect.

Antichiral edge states and hinge states based on the Haldane model

Different from the chiral edge states, antichiral edge states propagating in the same direction on the opposite edges are theoretically proposed based on the modified Haldane model, which is recently experimentally realized in photonic crystal and electric lattice systems. Here, we instead present that the antichiral edge states in the two-dimensional system can also be achieved based on the original Haldane model by combining two subsystems with the opposite chirality. Most importantly, by stacking these two-dimensional systems into three-dimension, it is found that the copropagating antichiral hinge states localized on the two opposite diagonal hinge cases of the system can be implemented. Interestingly, the location of antichiral hinge states can be tuned via hopping parameters along the third dimension. By investigating the local Chern number/layer Chern number and transmission against random disorders, we confirm that the proposed antichiral edge states and hinge states are topologically protected and robust against disorders. Our proposed model systems are expected to be realized in photonic crystal and electric lattice systems.

Design of compact polarization-insensitive multimode interference triplexer

A compact polarization-insensitive multimode interference (MMI) triplexer is proposed. The triplexer can process signals among three wavelengths of 1310, 1490 and 1550 nm in the fibre-to-the-home (FTTH) systems. The polarization insensitivity is obtained by adjusting the refractive index of SiN x in the Si/SiN x /Si sandwiched structure. A triangular lattice array air-hole photonic crystal embedded in the MMI waveguide can transmit and reflect downstream and upstream signals, respectively. Furthermore, a cascaded MMI structure is used to separate two downstream signals. The performance parameters of the triplexer are analysed by three-dimensional finite-difference time-domain method. The results show that the size of the triplexer is only 5.5 × 234.5 µm2, the insertion loss and crosstalk are as low as 0.45 dB and −27.2 dB respectively. Besides, the triplexer has a large 3 dB bandwidth up to 105 nm, and it has potential application value in the FTTH systems.

Interface states in the rectangular lattice photonic crystals with identical dielectric rods

Interface states in photonic crystals (PCs) have attracted attention for the special properties, such as high transmission efficiency in bend waveguides, and their generation related to the topological phase. Previous works on interface states in PCs were mainly based on the square lattice, the honeycomb lattice or the triangular lattice, but with different materials, shapes, or sizes of rods resulting in the complicated structure. In this paper, an interface is constructed by two 2D PCs with different rectangular lattices, but the same materials, shapes, and sizes of dielectric rods, which generates interface states. The interface states are analyzed with respect to Zak phases and surface impedances. The retainability of the interface states in rectangular lattice PCs is investigated by studying the relationship between the length-width ratio of the rectangular lattice and the Zak phase. It is found that, when the interface states are generated by changing the length-width ratio of the rectangular lattice, the retainability of the interface states is related to the positions of the photonic bandgaps or the Zak phases of the bands. A more detailed examination indicates that these conclusions are applicable to the rectangular lattice PCs with other materials, shapes, and sizes of dielectric rods. These results can lead to new ways to generate interface states easily, with only one kind of dielectric rod. In addition, these outcomes may contribute to the understanding of the relationship between the geometry and the interface state.