Engineering the light propagating features through the two-dimensional coupled-cavity photonic crystal waveguides

This paper studies the propagating characteristics of the electromagnetic waves through the coupled-resonator optical waveguides based on the two-dimensional square-lattice photonic crystals by the finite-difference time-domain method. When the traditional circular rods adjacent to the centre of the cavities are replaced by the oval rods, the simulated results show that the waveguide mode region can be adjusted only by the alteration of the oval rods＇ obliquity. When the obliquity of the oval rods around one cavity is different from the obliquity of that around the adjacent cavities, the group velocities of the waveguide modes can be greatly reduced and the information of different frequencies can be shared and chosen at the same time by the waveguide branches with different structures. If the obliquities of the oval rods around two adjacent cavities are equal and they alternate between two values, the group velocities can be further reduced and a maximum value of 0.0008c （c is the light velocity in vacuum） can be acquired.

Influence of disorder and deformation on the optical properties of a two-dimensional photonic crystal waveguide

We investigate the effect of disorder and mechanical deformation on a two-dimensional photonic crystal waveguide. The dispersion characteristics and transmittance of the waveguide are studied using the finite element method. Results show that the geometric change of the dielectric material perpendicular to the light propagation direction has a larger influence on the waveguide characteristics than that parallel to the light propagation direction. Mechanical deformation has an obvious influence on the performance of the waveguide. In particular, longitudinal deformed structure exhibits distinct optical characteristics from the ideal one. Studies on this work will provide useful guideline to the fabrication and practical applications based on photonic crystal waveguides.

The single-longitudinal-mode operation of a ridge waveguide laser based on two-dimensional photonic crystals

An electrically driven, single-longitudinal-mode GaAs based photonic crystal （PC） ridge waveguide （RWG） laser emitting at around 850 nm is demonstrated. The single-longitudinal-mode lasing characteristic is achieved by introducing the PC to the RWG laser. The triangle PC is etched on both sides of the ridge by photolithography and inductive coupled plasma （ICP） etching. The lasing spectra of the RWG lasers with and without the PC are studied, and the result shows that the PC purifies the longitudinal mode. The power per facet versus current and current-voltage characteristics have also been studied and compared.

The disorder effect on the performance of novel waveguides constructed in two-dimensional amorphous photonic materials

On the basis of two-dimensional amorphous photonic materials, we have designed a novel waveguide by inserting thinner cylindrical inclusions in the centre of basic hexagonal units of the amorphous structure along a given path. This waveguide in amorphous structure is similar to the coupled resonator optical waveguides in periodic photonic crystals. The transmission of this waveguide for S-polarized waves is investigated by a multiple-scattering method. Compared with the conventional waveguide by removing a line of cells from amorphous photonic materials, the guiding properties of this waveguide, including the transmissivity and bandwidth, are improved significantly. Then we study the effect of various types of positional disorder on the functionality of this device. Our results show that the waveguide performance is quite sensitive to the disorder located on the boundary layer of the waveguide, but robust against the disorder in the other area in amorphous structure except the waveguide border. This disorder effect in amorphous photonic materials is similar to the case in periodic photonic crystals.

Characteristics of local photonic state density in an infinite two-dimensional photonic crystal

The local density of photonic states （LDPS） of an infinite two-dimensional （2D） photonic crystal （PC） composed of rotated square-pillars in a 2D square lattice is calculated in terms of the plane-wave expansion method in a combination with the point group theory. The calculation results show that the LDPS strongly depends on the spatial positions. The variations of the LDPS as functions of the radial coordinate and frequency exhibit “mountain chain” structures with sharp peaks. The LDPS with large value spans a finite area and falls abruptly down to small value at the position corresponding to the interfaces between two different refractive index materials. The larger/lower LDPS occurs inward the lower/larger dielectric-constant medium. This feature can be well interpreted by the continuity of electricdisplacement vector at the interface. In the frequency range of the pseudo-PBG （photonic band gap）, the LDPS keeps very low value over the whole Wiger-Seitz cell. It indicates that the spontaneous emission in 2D PCs cannot be prohibited completely, but it can be inhibited intensively when the resonate frequency falls into the pseudo-PBG.

Photonic Band Modulation in a Two-Dimensional Photonic Crystal with a One-Dimensional Periodic Dielectric Background

A two-dimensional photonic crystal with a one-dimensional periodic dielectric background is proposed. The photonic band modulation effects due to the periodic background are investigated based on the plane wave expansion method. We find that periodic modulation of the dielectric background greatly alters photonic band structures, especially for the E-polarization modes. The number, width and position of the photonic band gaps （PBGs） sensitively depend on the structure parameters （the layer thicknesses and dielectric constants） of the one-dimensional periodic background,

Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.

Comment on “Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals” by Si-Qi Zhang et al.

Recently, Zhang et al. （Chin. Phys. B 26 024208 （2017）） investigated the band gap structures and semi-Dirac point of two-dimensional function photonic crystals, and the equations for the plane wave expansion method were induced to obtain the band structures. That report shows the band diagrams with the effects of function coefficient k and medium column ra under TE and TM waves. The proposed results look correct at first glance, but the authors made some mistakes in their report. Thus, the calculated results in their paper are incorrect. According to our calculations, the errors in their report are corrected, and the correct band structures also are presented in this paper.

THz-Wave Generation from GaP THz Photonic Crystal Waveguides under Difference-Frequency Mixing

GaP terahertz (THz) two-dimensional (2D) photonic crystal (PC) waveguides with line defects were fabricated using inductively-coupled plasma reactive-ion etching (ICP-RIE) in Ar/Cl2 gas chemistries. THz-wave generation from the fabricated PC waveguides was demonstrated under collinear phase-matched difference-frequency generation (DFG), using Cr:Forsterite (Cr:F) lasers as the incident source. We compared the THz-wave output characteristics of the PC waveguides with that of GaP planar waveguides. The collinear phase-matching conditions in the DFG process were satisfied for 300- and 500-μm-wide PC waveguide structures at 0.7 and 0.6 THz, respectively. The additional output peaks that appeared near the edge of the photonic band gap, around 0.5 THz, were attributed to the guiding modes in the PC waveguide;no such peaks appeared in the non-patterned ridge waveguides. These experimental results suggest that the phonon-polariton confinement in THz-PC waveguides based on the GaP crystal could be used to enhance the nonlinear optical effect for THz-wave generation.

A photonic crystal side-coupled waveguide based on a high-quality-factor resonator array

Based on the present coupled mode theory of the photonic crystal resonator array in this paper, we propose a novel side-coupled waveguide to achieve highly efficient coupling of photonic crystal devices. It is found that the coupling efficiency is sensitive to the interval, the total number and the quality factor of the resonator. Considering the coupling efficiency and the coupling region, we select five resonators with an interval of six lattice periods. By optimizing the structure parameters of the waveguide and resonator, the quality factors of the resonator can be modulated and the coupling efficiency of the side-coupled waveguide reaches 95.47% in theory. Compared with other coupling methods, the side-coupled waveguide can realize efficient coupling with a compact structure, a high level of integration and a low degree of operational difficulties.

A photonic crystal waveguide with silicon on insulator in the near-infrared band

A two-dimensional （2D） photonic crystal waveguide in the Г-K direction with triangular lattice on a silicon-on-insulator （SOI） substrate in the near-infrared band is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. Its transmission characteristics are analysed from the stimulated band diagram by the effective index and the 2D plane wave expansion （PWE） methods. In the experiment, the transmission band edge in a longer wavelength of the photonic crystal waveguide is about 1590 nm, which is in good qualitative agreement with the simulated value. However, there is a disagreement between the experimental and the simulated results when the wavelength ranges from 1607 to 1630 nm, which can be considered as due to the unpolarized source used in the transmission measurement.

Transmission Spectral Characteristics of Photonic Crystals Milled in Annealed Proton-Exchange LiNbO_3 Waveguide

Transmission spectra of triangular lattice photonic crystals milled in the top surface of an annealed proton- exchange waveguide are numerically simulated. The effects of the finite depth, conical shape, trapezoidal shape and hybrid shape of holes are theoretically analyzed. Due to the difficulty of milling high aspect-ratio cylindrical holes in lithium niobate （LiNbO3 ）, a compromised solution is proposed to improve the overlap between shallow holes and the waveguide mode, and useful transmission spectra with strong contrast and sharp band edges are achieved.

Design of tunable surface mode waveguide based on photonic crystal composite structure using organic liquid

With the method of replacing the surface layer of photonic crystal with tubes, a novel photonic crystal composite structure used as a tunable surface mode waveguide is designed. The tubes support tunable surface states. The tunable propagation capabilities of the structure are investigated by using the finite-difference time-domain. Simulation results show that the beam transmission distributions of the composite structure are sensitive to the frequency range of incident light and the surface morphology which can be modified by filling the tubes with different organic liquids. By adjusting the filler in tubes, the T-shaped, Y-shaped, and L-shaped propagations can be realized. The property can be applied to the tunable surface mode waveguide. Compared with a traditional single function photonic crystal waveguide, our designed structure not only has a small size, but also is a tunable device.

A ministop band in a single-defect photonic crystal waveguide based on silicon on insulator

This paper reports that a two-dimensional single-defect photonic crystal waveguide in the Г-K direction with triangular lattice on a silicon-on-insulator substrate is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. A ministop band （MSB） is observed by the measurement of transmission characteristics. It results from the coupling between the two modes with the same symmetry, which is analysed from the stimulated band diagram by the effective index and the two-dimensional plane wave expansion methods. The parameter working on the MSB is the ratio of the radius of air holes to the lattice constant, fla. It is obtained that the critical τ/a value determining the occurrence or disappearance of MSB is 0.36. When τ/a is larger than or equal to 0.36, the MSB occurs. However, when τ/a is smaller than 0.36, the MSB disappears.

Simulation and Design of a Low Crosstalk Hexagonal Photonic Crystal Crossover Waveguide

In this paper, an optical waveguide junction is introduced to reduce crosstalk based on a hexagonal structure of photonic crystals for TE modes. The wavelength is 1330 nm which is an important wavelength for optical fiber data transmission. Simulation results show that the proposed design exhibits a reduction of -50 dB in crosstalk. It translates to a considerable isolation improvement between two crossover waveguides. FDTD method is used to obtain the transmission coefficient.

Application of Padé Approximation in Simulating Photonic Crystals

To save finite-difference time-domain（FDTD） computing time, several methods are proposed to convert the time domain FDTD output into frequency domain. The Pad6 approximation with Baker＇s algorithm and the program are introduced to simulate photonic crystal structures. For a simple pole system with frequency 160THz and quality factor of 5000, the intensity spectrum obtained by the Padé approximation from a 2^8-item sequence output is more exact than that obtained by fast Fourier transformation from a 2^20-item sequence output. The mode frequencies and quality factors are calculated at different wave vectors for the photonic crystal slab from a much shorter FDTD output than that required by the FFT method, and then the band diagrams are obatined. In addition, mode frequencies and Q-factors are calculated for photonic crystal microcavity.

Optical properties of the direct-coupled Y-branch filters by using photonic crystal slabs

We fabricated a new type of two-dimensional photonic crystal slab filter. The resonant cavities were directly put into the waveguide arms. The optical transmissions of the filters were measured and the results show that the optimized two-channel filters give good intensity distribution at the output ports of the waveguide. A minimum wavelength spacing of 5 nm of the filter outputs is realized by accurately controlling the size of the resonant cavities.

Analysis of Optical Properties for Square, Circular and Hexagonal Photonic Crystal Fiber

This paper presents four rings square, circular, and hexagonal photonic crystal fiber (PCF) geometry for analyzing different optical properties in a wavelength ranging from 800 nm to 1600 nm. These three types of geometry have been used for analyzing Effective area, Propagation constant, Confinement loss and Waveguide dispersion. Silica glass is chosen as background material and the cladding region is made of four air hole layers. COMSOL Multiphysics (v.5) software is used to simulate these proposed PCF geometries. From the numerical analysis, it is found that the effective area is small for hexagonal PCF geometry and large for square PCF geometry (11.827 μm2, 10.588 μm2 and 9.405 μm2 for square, circular, and hexagonal PCF geometry respectively). From the analysis, the Confinement loss is approximately zero at wavelength ranges from 800 nm to 1250 nm and approximately zero waveguide dispersion is achieved from 900 nm to 1500 nm for all the three PCF structures. Again, negative dispersion approximately −30.354 ps/(nm⋅km) is achieved for circular PCF structure at the wavelength of 900 nm.

Implementation of all-optical tristate Pauli X, Y and Z gates based on two-dimensional photonic crystal

In this paper, we have designed and simulated all-optical tristate Pauli X, Y and Z gates using 2D photonic crystal. Simple line and point defects have been used to design the structure. The performance of the structure has been analyzed and investigated by plane wave expansion(PWE) and finite difference time domain(FDTD) methods. Different performance parameters, namely contrast ratio(CR), rise time, fall time, delay time, response time and bit rate, have been calculated. The main advantage of the proposed design is that all the Pauli gates have been realized from a single structure. Due to compact size, fast response time, good CR and high bit rate, the proposed structure can be highly useful for optical computing, data processing and optical integrated circuits.

Light propagation characteristics through the annular coupled-cavity waveguides based on the two-dimensional square-lattice photonic crystal

The light propagation characteristics through the annular coupled-resonator cavity waveguides are systematically analyzed by the finite-difference time-domain (FDTD) method. It is found that this kind of waveguide has more minbands owing to the increasing of the cavity’s size, compared with the traditional line-typed coupled-resonator waveguide. The group velocity of light propagation can be reduced for a further degree when the adjacent annular cavities are interlaced in the perpendicular direction, and a group velocity about 0.00067c (c is the light speed in vacuum) can be obtained.