Square Lattice Photonic Crystal Research Articles

Large transmittance contrast via 90-degree sharp bends in square lattice glide-symmetric photonic crystal waveguides.

We demonstrate an intriguing transmittance contrast in a glide-symmetric square-lattice photonic crystal waveguide with a 90-degree sharp bend. The glide-symmetry gives rise to a degeneracy point in the band structure and separates a high-frequency and a low-frequency band. Previously, a similar large transmittance contrast between these two bands has been observed in glide-symmetric triangular- or honeycomb-lattice photonic crystals without inversion symmetry, and this phenomenon has been attributed to the valley-photonic effect. In this study, we demonstrate the first example of this phenomenon in square-lattice photonic crystals, which do not possess the valley effect. Our result sheds new light onto unexplored properties of glide-symmetric waveguides. We show that this phenomenon is related to the spatial distribution of circular polarization singularities in glide-symmetric waveguides. This work expands the possible designs of low-loss photonic circuits and provides a new understanding of light transmission via sharp bends in photonic crystal waveguides.

Design of All-Optical Logic Half-Adder Based on Photonic Crystal Multi-Ring Resonator

In this paper, a novel design of an all-optical half-adder (HA) based on two two-ring resonators in a two-dimensional square-lattice photonic crystal (PC) structure without nonlinear materials is proposed. The all-optical HA comprises AND and XOR gates where each gate is composed of cross-shaped waveguides and two-ring resonators in a 2D square-lattice PC that are filled with silicon (Si) rods in silica (SiO2). The AND and XOR gates are analyzed and simulated using plane-wave expansion (PWE) and finite-difference time-domain (FDTD) methods. Simulation results show that light guiding inside the device functions as AND and XOR gates. Thus, the proposed device has the potential for use in optical arithmetic logic units for digital computing circuits. The structure comprises an optical AND gate and an optical XOR gate that were designed to work at the C-band spectrum. Results show that there is a clear distinction between logic states 1 and 0 with a narrow power range that leads to a better robust decision on the receiver side for minimized logic errors in the photonic decision circuit. Thus, the proposed HA can be a key component for designing a photonic arithmetic logic unit.

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.

Topological Properties of a Two-Dimensional Photonic Square Lattice without C4 and Mx(y) Symmetries

Rich topological phenomena, edge states and two types of corner states, are unveiled in a two-dimensional square-lattice dielectric photonic crystal without both $C_4$ and $M_{x(y)}$ symmetries. Specifically, non-trivial type-I corner states, which do not exist in systems with $C_4$ and $M_{x(y)}$ since the degeneracy, are protected by non-zero quadrupole moment, no longer quantized to but less than $0.5$. Excellent properties, e.g. sub-wavelength localization and air-concentrated field distribution, are presented. Type-II corner states, induced by long-range interactions, are easier realized due to asymmetry. This work broadens the topological physics for the symmetries-broken systems and provides potential applications.

Improved power and far-field pattern of surface-emitting quantum cascade lasers with strain compensation to operate at 4.3 μm

We fabricated surface-emitting quantum cascade lasers with photonic crystal resonators whose active layers were strain-compensated InGaAs/AlInAs multiple quantum wells to operate at 4.3 μm. We tested two kinds of square-lattice photonic crystals consisting of circular and pentagonal InGaAs cylinders as a unit structure. We examined their output power and far-field pattern to find that both of them were improved by lowering the photonic-crystal symmetry to achieve a high extraction efficiency. The maximum output power was 50 mW at 77 K and the far-field pattern was a single peak with a divergence angle smaller than 1° for the pentagonal cylinder structure. In addition, we attributed the lasing mode to a B2-symmetric (quadrupole) eigenstate on the Γ point for the circular cylinder structure by observing the polarization dependence of the far-field pattern and comparing it with calculations by the k · p perturbation method.

Band gap of silicon photonic crystal with square-lattice and windmill-shaped defects

A new type of 2D square-lattice photonic crystal with different windmill-shaped defects is proposed. Based on the plane wave expansion method and super cell theory, the band gaps of defect models are numerically analyzed according to the symmetry. We aim at further reducing the defect symmetry of photonic crystals compared to previous studies and researching the effect of translation and rotation of different windmill-shaped defect structures on the transverse magnetic (TM) band gap. The results reveal that the translation distance of defects brings great impacts on the band gap of 2D square-lattice photonic crystals and the width of the TM band gap can be further expanded after rotating on the basis of translation. In addition, we discovery that the band gap of the model with even-numbered fan-shaped defects is wider than that of the model with odd-numbered fan-shaped defects. Among the five different defect models (three-wings, four-wings, five-wings, six-wings, rotating-cross), the four-wing windmill defect model produces the largest band gap, which reaches 5.307 × 10−2 (ɷa/2πc). This research is helpful to understand the band gap characteristics of photonic crystals, which will contribute to the design of photonic crystal devices.

A study of the origin of supercollimation in two-dimensional square-lattice photonic crystals

The origin of the supercollimation (SC) phenomenon in two-dimensional photonic crystals (PhCs), which is generated by a weak periodic modulation of the dielectric constant, is studied by the plane-wave expansion (PWE) method. We find that the smallest order of PWE required in order to obtain the SC phenomenon is the second order. The distance in k-space and the frequency difference between the SC point and the M point are proportional to the square of the periodic modulation strength. These results strongly imply that the SC phenomenon originates from second-order Bragg scattering. In addition, we rotate the coordinates and study the SC phenomenon using a model which is physically the same as the original model but has a unit cell two times larger and a folded Brillouin zone. In such a rotated model, the mathematical form of the eigenequation becomes much simpler and the SC phenomenon can be obtained with the first-order expansion alone. By neglecting the smaller off-diagonal terms, we can block diagonalize the matrix, which then corresponds to a layered model. Since the layered model is strictly solvable, we derive that a curvature-reversion (CR) point must exist for equi-frequency contours because of the robust asymptotic behavior in the small region. Theoretically and numerically, we also prove that the CR point of the layered model has similar properties to those of the SC point of a square-lattice PhC and infer that the physical origin of these properties is second-order Bragg scattering.

A highly efficient asymmetric transmission device for arbitrary linearly polarized light

In this paper, we theoretically demonstrate a nanophotonic optical asymmetric transmission device (NOATD) for arbitrary linear polarization, which is composed of two two-dimensional (2D) square-lattice photonic crystals (PhCs) with different effective refractive indices. In this way, the NOATD achieves asymmetric transmission based on the generalized total reflection principle, which is able to realize a high forward transmittance (>0.6) and contrast ratio (>0.9) for arbitrary linearly polarized light in a broad wavelength range (>100 nm).

Multifunctional beam steering via switchable negative refraction, self-collimation, and zero refraction effects in conventional and annular photonic crystals.

Negative refraction (NR), self-collimation (SC), and zero refraction (ZR) effects of photonic crystals play an important role in beam steering. In this work, we report a multifunctional beam steering concept in photonic crystals, i.e., integrating two or three of the NR, SC, and ZR effects together at the same frequency. We find the square-lattice dielectric ring photonic crystal is an ideal candidate to realize the switchable function of ZR-SC while the square-lattice dielectric ring photonic crystal is more suitable for realizing the ZR-SC, ZR-NR, and ZR-SC-NR functions. The photonic band theory and an equivalent waveguide model are employed to explain these switchable functions in conventional and annular photonic crystals.

Logical discrimination of multiple disease-markers in an ultra-compact nano-pillar lab-in-a-photonic-crystal

We present a theoretical prescription for a physically realizable Lab-in-a-Photonic-Crystal optical biosensor that can instantaneously detect and discriminate multiple analytes, both quantitatively and combinatorially, in a single spectroscopic measurement. Unlike other biosensors that utilize simple resonance modes, our fundamental operating principle is the analyte-induced hybridization of waveguide modes and surface modes in a photonic bandgap, leading to a complex spectral fingerprint. Our real-world liquid-infiltrated photonic crystal sensor supplants two-dimensional conceptual paradigms proposed earlier with realistic features and a path to implementation. A square-lattice photonic crystal of nanopillars with fixed height but differentiated cross sections within a narrow flow-channel is used for cascaded transmission of light through the photonic bandgap. The nanopillar array is placed on a thin layer of high-refractive-index backing material resting on a glass substrate with fluid and biomarker flow along the waveguide direction. Using finite-difference time-domain simulations of light transmission perpendicular to the waveguide, a variety of spectral fingerprints are identified as various disease-marker combinations bind to specific lines of nanopillars. Various diseases or various stages of a given disease are detected and differentiated through the interplay of central-waveguide resonances with edge modes and three-dimensional index-guided bulk modes. This offers a distinctive mechanism for instantaneous disease diagnosis using a minimal volume of fluid sample.

Effect of windmill-like-shaped defect on TM photonic band gaps of two-dimensional square-lattice photonic crystals

A novel windmill-like-shaped defect was introduced in two-dimensional square-lattice photonic crystals consisting of circular dielectric rods. The photonic band gap (PBG) and defect modes were numerically analyzed using the plane wave expansion method. We studied the influence of the translation distance and the rotation angle of defect on the photonic band gap. The results show that the symmetry of defect may affect the width of PBG. The transverse magnetic (TM) band-gap first increases and then decreases with increased translation distance. For a translation distance of 0.66a, the width of TM band-gap reached it’s widest value of 0.05057 (ωa/2πc). Additionally, we studied the influence of the rotation angle of the defect on the TM band-gap with a fixed translation distance of 0.66a. We discovered that square-lattice photonic crystals with a rotated windmill-like-shaped defect can generate a larger photonic band gap, and the largest width can reach up to 0.05307 (ωa/2πc) with a rotated angle of 10°.

Design and analysis of a 09 Tb/s six-channel WDM filter based on photonic crystal waveguides

A six-channel wavelength-division multiplexing filter is proposed in this paper, based on a two-dimensional rods-in-air square-lattice photonic crystal (PhC) slab structure. The plane wave expansion method is applied to compute the band structure of the PhC. Three-dimensional finite-difference time-domain simulation methodology is used to measure and analyze the performance of the filter. Performances for both the 2D and 3D designs of the structure are analyzed. The analyses show that the device is capable of filtering six different wavelengths, i.e., 1310 nm, 1415 nm, 1455 nm, 1550 nm, 1725 nm, and 1770 nm. Owing to its linear optical operation, the device is able to operate at low power and also offers a high data rate in the range of $ \approx 0.9\,\,{\rm Tb/s} $≈0.9Tb/s to $ \approx 4\,\,{\rm Tb/s} $≈4Tb/s. Moreover, the footprint area of the proposed device is on the order of $ {165}\,\,{{\unicode{x00B5}{\rm m}}^2} $165µm2, which is suitable for high-density integration of photonic circuits.

Room‐Temperature InGaAs Nanowire Array Band‐Edge Lasers on Patterned Silicon‐on‐Insulator Platforms (Phys. Status Solidi RRL 3/2019)

The back-cover image represents lasing from square-lattice nanowire array photonic crystals on silicon-on-insulator (SOI) platforms. Integration of light sources on silicon platforms is regarded as a crucial requirement for various nanophotonic applications, but the lattice mismatch between III–V materials and silicon has been one of the major challenges to realize this. Here, Hyunseok Kim et al. (article no. 1800489) employed bottom-up integrated nanowires to overcome this issue and realize highquality III.V materials on silicon. InGaAs/InP core/shell nanowires form photonic crystals with a footprint of only 3.0×3.0 μm2, and a high Q factor of 23,000 is achieved by integrating these nanowires on two-dimensional silicon gratings. Roomtemperature lasing is observed from a fundamental band-edge mode at 1290 nm, which is the O-band of the telecommunication wavelength. These results represent a meaningful step toward ultracompact and monolithic III–V lasers on silicon photonic platforms.

Design of terahertz reconfigurable devices by locally controlling topological phases of square gyro-electric rod arrays

In topological photonics, there is a class of designing approaches that usually tunes topological phase from trivial to non-trivial in a magneto-optical photonic crystal by applying an external magnetic field to break time reversal symmetry. Here we theoretically realize topological phase transition by rotating square gyro-electric rods with broken time reversal symmetry. By calculating band structures and Chern numbers, in a simple square-lattice photonic crystal, we demonstrate the topological phase transition at a specific orientation angle of the rods. Based on the dependence of topological phase on the orientation angle, we propose several terahertz devices including an isolator, circulator and splitter in a 50x50 reconfigurable rod array by locally controlling topological phases of the rods. These results may have potential applications in producing reconfigurable terahertz topological devices.

Polarization-independent one-way transmission of silicon annular photonic crystal heterojunctions

To realize the one-way transmission is a key point in optical integration. As a step to this goal, heterojunctions composed of two 2D square-lattice silicon annular photonic crystals are constructed and expected to realize polarization-independent optical diodes. Band structures are calculated by the plane wave expansion method, and the transmission characteristics are analyzed using the finite-different time-domain method. The directional bandgap difference causes the one-way transmission behavior, and an overlapping one-way transmission frequency range for TE and TM modes is observed. Moreover, the transmission spectra, contrast ratio and field distributions for two polarizations demonstrate polarization-independent one-way transmission. The transmission performance is further enhanced and the equal forward transmittance for two polarizations reaches 45%.

Multiple wavelength-selecting and beam-splitting photonic crystal functional device based on the mode coupling between the central microcavity and the adjacent waveguides.

The beam-splitting and wavelength selecting characteristics of the two-dimensional square-lattice photonic crystal with a rectangular microcavity and adjacent W1-type waveguides are studied. Based on the abundant defective modes with different symmetries supported by the central microcavity, a multiple-functional device with the abilities of beam splitting and wavelength selecting is achieved. Through altering the connecting location between the input/output channels and the central microcavity, the proposed device can achieve three kinds of functions at different wavelengths within an ultra-small wavelength band of about 3nm, a maximum transmittance of 0.57, and signal-to-noise ratio of 149 are achieved for the one-channel selecting, 0.31 and 146 for two-channel splitting, and a maximum transmittance of 0.24 for the three-channel light beam sharing. The corresponding forward directions of light propagation along the output channels can also be flexibly adjusted.

Effects of hydrostatic pressure on the band structure in two-dimensional semiconductor square photonic lattice with defect

Using the plane wave expansion method, we studied the effects of hydrostatic pressure on the structure of TM bands in two-dimensional square-lattice photonic crystals. These crystals are composed of infinite cylindrical rods of GaAs embedded in air background. Initially, we studied regular photonic crystals (without defects) and found that by increasing the hydrostatic pressure at a fixed temperature, the band structure shows a shift at high frequencies due to the decrease of the radius of the rods and the dielectric constant of the GaAs semiconductor. On the other hand, using the supercell technique, a point defect L1 is introduced, which consists in the missing of a GaAs post in the photonic crystal. We found a defect mode inside the photonic band gap, which shows a shift at high frequencies as the hydrostatic pressure increases at a fixed temperature.

One-way optical transmission in silicon photonic crystal heterojunction with circular and square scatterers

A 2D orthogonal square-lattice photonic crystal (PC) heterojunction consisting of circular and square air holes in silicon is presented. Band structures are calculated using the plane wave expansion method, and the transmission properties are investigated by the finite-different time-domain simulations. Thanks to the higher diffraction orders excited when the circular and square holes are interlaced along the interface, one-way transmission phenomena can exist within wide frequency regions. The higher order diffraction is further enhanced through two different interface optimization designs proposed by modifying the PC structure of the hetero-interface. An orthogonal PC heterojunction for wide-band and efficient one-way transmission is constructed, and the maximum transmissivity is up to 78%.

Mid-infrared T-shaped photonic crystal waveguide for optical refractive index sensing

In this paper, we propose and design a new type of an integrated optical sensor that performs sensing in a wide wavelength range corresponding to mid-infrared (mid-IR) spectrum. By engineering the structural parameters of square-lattice photonic crystal (PC) slab incorporated with a T-shaped air-slot, strong light confinement and interaction with the analytes are assured. Numerical analyses in the time and frequency domain are conducted to determine the structural parameters of the design. The direct interaction between the slot waveguide mode and the analyte infiltrated into the slot gives rise to highly sensitive refractive index sensors. The highest sensitivity of the proposed T-slotted PC sensor is 1040nm/RIU within the range of analytes’ refractive indices n=1.05–1.10, and the overall sensitivity corresponding to the higher refractive index range of n=1.10–1.30 is around 500nm/RIU. Moreover, for a realistic PC slab structure, we determined an average refractive index sensitivity of 530nm/RIU within the range of n=1.10–1.25 and an average sensitivity of 390nm/RIU within the range of n=1.00–1.30. Furthermore, we speculate on the possible approach for the fabrication and the optical characterization of the device. The assets of the device include being compact, having a feasible measurement and fabrication technique, and possessing label-free sensing characteristic. We expect that the presented work may lead to the further development of the mid-IR label-free biochemical sensor devices for detection of various materials and gases in the near future.

Study on unidirectional transmission in silicon photonic crystal heterojunctions

Electronic diode plays an important role in electronic circuits owing to its capability of unidirectional movement of the current flux. An optical diode offers unidirectional propagation of light beams, which plays key roles in the all-optical integrated circuits. Unidirectional wave propagation requires either time-reversal or spatial inversion symmetry breaking. The former can be achieved with the help of nonlinear materials, magnetic-optical materials and so on. The realization of these schemes all needs the external conditions (electric field, magnetic field or light field), and thus their applications are limited. In contrast, spatial inversion symmetry breaking can make up for this shortcoming and has been widely studied. Through breaking the structure's spatial inversion symmetry, much research demonstrated that the unidirectional light propagation could be achieved in a photonic crystal structure. Specially, the optical diode based on the photonic crystal heterojunction has been drawing much attention. Though relevant studies have been reported, how to find a more simple structure to realize high-efficiency optical diodes is always pursued by people. The previous design of optical diode is generally based on the orthogonal or non-orthogonal photonic crystal heterojunctions. However, the comparative analysis of the two types of heterojunctions has not been systematically carried out. The transmission characteristics of two-dimensional orthogonal and non-orthogonal silicon photonic crystal heterojunctions are obtained and compared. Firstly, the directional band gap mismatch of two-dimensional square-lattice silicon photonic crystals with the same lattice constant but different air hole radii is calculated by the plane wave expansion method. The band structure indicates that in a certain frequency range, one photonic crystal is the omni-directional pass band, while the other has directional band gap. This is just the necessary condition for the unidirectional light transmission through the photonic crystal heterojunctions. Therefore, the heterojunction constructed by the two photonic crystals is expected to achieve optical diode. Based on this, the orthogonal and the non-orthogonal heterojunctions are proposed. Their transmission spectra and field distributions are calculated by the finite-difference time-domain method. The results show that the unidirectional light transmission can be realized by the non-orthogonal heterojunction structure (unidirectional transmission efficiency reaches 45%) but not the orthogonal heterojunction structure. That is to say, the realization of unidirectional transmission is closely related to the orientation of the hetero-interface. Moreover, the non-orthogonal photonic crystal hetero-interface is optimized. It is found that the unidirectional transmission efficiency increases to 54% and the overall increases by 10%. More importantly, it greatly improves the performance of optical diode for its simple structure and small size, and provides another more effective design method.