Two-dimensional Square-lattice Photonic Crystal Research Articles

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.

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.

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).

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°.

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.

Compact, low-loss and broadband photonic crystal circulator based on a star-type ferrite rod

Abstract We propose and investigate a compact, low-loss and broadband circulator based on a star-type ferrite rod in two-dimensional square-lattice photonic crystals. Only one ferrite rod is required to be inserted in our structure. Firstly, the performances of circulator based on the star-type, circle, and square ferrite rod are compared, showing that the circulator with the star-type ferrite rod performs better than the other two ones. And then, based on the star-type ferrite rod circulator, four cases of improvement, in which the background rods around the center ferrite rod are replaced respectively by the backward-triangle, forward-triangle, backward-semicircle, and forward-semicircle rods, are investigated to modulate the coupling between the center magneto-optical micro-cavity and the corresponding waveguides. The results show that, with proper parameters, all the four cases can greatly improve the output properties of the circulator, and different cases have its own advantages. The mechanism behind these improvements is also discussed. Finite-element method is used to calculate the characteristics of the circulator and Nelder-Mead optimization method is employed to obtain the optimized parameters. The ideas presented here are useful for designing broadband, low insertion loss, and high-isolation circulators which have potential application in integrated photonic crystal devices.

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.

Design and simulation of linear logic gates in the two-dimensional square-lattice photonic crystals

We have proposed all-optical three-port AND, OR, XOR and NOT photonic crystal logic gates, based on modified symmetric T-branch combiners. Using the temporal coupled-mode theory the operation of the symmetric T-branch combiner has been investigated and the conditions which lead to a maximum power at the output port have been obtained. At the output port of the proposed devices, the logics 1 and 0 are defined as a more than 42% and a less than 14% of the transmission, respectively. The minimum intensity contrast ratio of the suggested logic gates is about 4.77dB. The operations of the proposed devices are examined using time-domain transition-response simulations which have been performed using two dimensional finite-difference time-domain method.

All-optical controllable channel-drop filters in two-dimensional square-lattice photonic crystals

A novel all-optical controllable channel-drop filter in photonic crystals (PC) of square lattice is presented. We show that using a resonant-cavity-based add-drop filter with a wavelength-selective reflection feedback and a single-control switching module which is based on nonlinear PC microcavities, the dropped channel can be routed to the drop port or returned to the bus waveguide. Using the temporal coupled-mode theory and two-dimensional nonlinear finite-difference time-domain method, the performance of the proposed device is investigated and the simulation results show the validity of the proposed design.

Three-visible-light wave combiner based on photonic crystal microcavities

We propose a three-visible-light wave combiner based on two-dimensional square-lattice photonic crystal (PhC) microcavities. A coupled-cavity waveguide is introduced to reduce the insertion losses for the three waves in the combiner. The transmission characteristic of light waves in PhCs with point defects is analyzed. As an example, a combiner for combining light waves of 488, 532, and 635nm, which are commonly used as the three primary colors in laser display systems, is designed and demonstrated through the finite-difference time-domain method. The three visible light waves of 488, 532, and 635nm are output at the same output port with transmittances of 97.6%, 98.1%, and 90.0%, respectively. The results show that the proposed device can perform efficient synthesis and the designing method can be applied in building other combiners based on PhCs made of dispersion materials.

Photonic band gaps of two-dimensional square-lattice photonic crystals based on 8-shaped scatters

A novel photonic crystals (PhC) based on 8-shaped scatters with two-dimensional (2-D) square-lattice is presented. By employing the MIT photonic bands (MPB), the relationship between the structural parameters of the PhC and the properties of photonic band gaps (PBG) are investigated. The calculation results of 8-shaped scatters with 2-D square-lattice demonstrate that the reduction of scatters’ symmetry can produce larger number of PBG and broaden the width of PBG only for TM mode, and reversely for TE mode. The peculiarity would meet the distinguish employment of different mode. By optimizing the structural parameters, the maximum absolute PBG 0.1028(ωa/2πc) at R=0.3, ɛr=11.56, θ=45° is obtained and six absolute PBGs is got at R=0.3, θ=115°, ɛr∈[32.3, 33.5].

Y-type polarization beam splitter based on polarization-selective defects within crystal waveguides in a square-lattice photonic crystal with solid rods

We propose a Y-type polarization beam splitter based on internal polarization-selective defects within crystal waveguides in a two-dimensional square-lattice photonic crystal with solid rods. When the nonpolarized light launches from the input port, different polarizations will be separated and can only transmit through their own channel. It is demonstrated by finite element method that the proposed structure can achieve good performance for both the transverse electric and transverse magnetic polarizations in a wide range of wavelength, with the polarization extinction ratio more than 25 dB, the degree of polarization nearly 1, and the insert loss less than 0.5 dB, respectively.

Multi-channel slow light coupled-resonant waveguides based on photonic crystal with rectangular microcavities

The light transmission characteristics through the coupled-resonator optical waveguides (CROWs) based on the two-dimensional square-lattice photonic crystal with rectangular microcavities are systematically studied by the finite-difference time-domain method. Owing to the multiple spatial symmetries of the defective modes localized by the rectangular microcavities, the guiding bands can be adjusted by changing the coupling region between the CROW and the traditional W1-typed input and output channels, and their corresponding group velocities can be quite different from each other through the same CROW structure. Through optimizing the coupling regions between the CROW and three output channels, a kind of device with both the abilities of light beam splitting and frequency selection can be obtained, which has potential applications in the future complex all-optical circuits.

Wide-angle reflection-mode spatial filtering and splitting with photonic crystal gratings and single-layer rod gratings

New diffractive optical elements offering a frequency tolerant, very efficient, high-pass and bandpass spatial filtering over a broad range of incidence angles are demonstrated by numerical simulations. The device operates in reflection mode owing to the (nearly) perfect blazing. It relies on two-dimensional square-lattice photonic crystals composed of dielectric rods with simple corrugations at the interface. Similar performance can be obtained with gratings composed of a single rod layer placed in the near field of a metal mirror, indicating a route to geometries that can be easily fabricated with modern nanotechnologies. Also equal splitting between zero and first negative orders can be obtained for incidence-angle variations that are wider than 60°.

A Two-Dimensional Square-Lattice Photonic Crystal with Rotated Square Cylinders and Cross Thin Plates Exhibiting Wide Photonic Bandgap

A new type of two-dimensional square-lattice photonic crystal structure made of rotated square cylinders and cross thin plates is presented and numerically investigated using the plane-wave expansion method. The largest absolute photonic bandgap (APBG) reaches 14.3%. The proposed structure can have promising application for its large APBG and convenience in designing optical circuits.

PHOTONIC DIRAC CONES REALIZED BY ACCIDENTAL DEGENERACY ON THE BRILLOUIN-ZONE BOUNDARY

The condition for the formation of Dirac cones at arbitrary points in the Brillouin zone by the accidental degeneracy of two photonic bands was examined by the degenerate perturbation theory and group theory based on the spatial symmetry of two modes. The analysis was applied to a two-dimensional square-lattice photonic crystal with C4v symmetry and the dispersion relation in the vicinity of the M point was examined. Exact agreement between the analytical and numerical calculation was obtained.

Near-infrared Subwavelength Imaging and Focusing Analysis of a Square Lattice Photonic Crystal Made from Partitioned Cylinders

We study the focusing properties of a two-dimensional square-lattice photonic crystal (PC) comprising silica and germanium partitioned cylinders in air background. The finite difference time domain (FDTD) method with periodic boundary condition is utilized to calculate the dispersion band diagram and the FDTD method incorporating the perfectly matched layer boundary condition is employed to simulate the image formation. In contrast to the common square PCs in which the negative refraction effect occurs in the first photonic band without negative phase propagation, in our suggested model system, the frequency with negative refraction exists in the second band and in near-infrared region. In this case, the wave propagates with a negative phase velocity and the evanescent waves can be supported. We also discuss the dependency of the image resolution and its location on surface termination, source location, and slab thickness. According to the simulation results, spatial resolution of the proposed PC lens is below the radiation wavelength.

Unidirectional reciprocal wavelength filters based on the square-lattice photonic crystal structures with the rectangular defects

The novel all-optical unidirectional wavelength filters are studied by the finite-difference time-domain method, which are based on the two-dimensional square-lattice photonic crystal with the rectangular defects. Owing to the modes' match and mismatch between the defect and the adjacent waveguides, the unidirectional propagation of the fundamental-mode light beam resonant at a certain frequency is obtained. Through merely altering the coupling region between the defect and the input waveguide, a unidirectional dual-branch waveguide filter is designed. This kind of devices has both the abilities of wavelength filtering and unidirectional light propagation, and may be potentially applied in the future all-optical complex integrated circuits.