Low Frequency Dispersion Law for Two-Dimensional Metallic Photonic Crystals

Using the rigorous multiple-scattering theory, we study the dispersion relation of electromagnetic （EM） waves in two dimensional dielectric photonic crystals （PCs） and metallic photonic crystals （MPCs） in the low-frequency limit. Analytic formula for the effective velocity of EM waves in PCs and MPCs is obtained. Accuracy of our formula is checked by comparing the results with rigorous calculations. For PCs, our result is exactly the same as the coherent potential approximation （CPA）, which is accurate even when the filling fraction is high. But for MPCs, our approach demonstrates special advantages, while the CPA theory fails, in predicting the effective velocity of EM waves in MPCs at low frequency.

Comparative Study of the One Dimensional Dielectric and Metallic Photonic Crystals

The optical transmission properties of two types of photonic crystals have been analyzed by using the transfer matrix method. The first one is the dielectric photonic crystal (DPC), and the second is the metallic photonic crystal (MPC). We found the dielectric and metallic photonic crystals have different transmission spectra. The effect of the most prameters on the transmission spectra of the dielectric and metallic photonic crystals has been studied.

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.

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,

Existing conditions of full bandgaps and absolute negative refraction in metallic-dielectric photonic crystal

This paper has theoretically studied the characteristic frequencies of band structures in two-dimensional metallic- dielectric photonic crystals. It is demonstrated that a large filling fraction benefits the existence of absolute photonic band gap, while a smaller filling fraction benefits an absolute negative refraction band. In addition, it also finds that the relation between the cut-off frequency of E-polarized wave and the filling fraction exceeding 10% is content with a linear increasing function, whose coefficients are exponential to the normalized lattice constant. These investigations have significant implications for tuning the operational frequencies to desired applications and manufacturing photonic crystals.

Controlling the Bandgaps of One-Dimensional TiO2/SiO2, TiO2/SnO2, and SiO2/SnO2 Photonic Crystals Using the Transfer Matrix Method

One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has not been a comparative study of the three different 1D PhC structures to compare the influence of layer thickness, number, and refractive index on the ability of the PhCs to control light transmission. Herein, we use the transfer matrix method (TMM) to theoretically examine the transmission of 1D PhCs composed of layers of TiO2/SiO2, TiO2/SnO2, SiO2/SnO2, and combinations of the three with various top and bottom layer thicknesses to cover a substantial region of the electromagnetic spectrum (UV to NIR). With increasing layer numbers for TiO2/SiO2 and SiO2/SnO2, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO2/SiO2 layers had a high transmittance for a wide bandgap, allowing for wide-band optical filter applications. These different PhC architectures could enable a variety of applications, depending on the properties needed.

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.

Growth of Noncentrosymmetric Two-Dimensional Single Crystals

Among the various two-dimensional(2D)materials,more than 99%of them are noncentrosymmetric.However,since the commonly used substrates are generally centrosymmetric,antiparallel islands are usually inevitable in the growth of noncentrosymmetric 2D materials because of the energetic equivalency of these two kinds of antiparallel islands on centrosymmetric substrates.Therefore,achieving the growth of noncentrosymmetric 2D single crystals has long been a great challenge compared with the centrosymmetric ones like graphene.In this review,we presented the remarkable efforts and progress in the past decade,through precise chemical processes.We first discussed the great challenge and possible strategies in the growth of noncentrosymmetric 2D single crystals.Then,we focused on the advancements made in producing representative noncentrosymmetric 2D single crystals,including hexagonal boron nitride(hBN),transition metal dichalcogenides(TMDs),and other noncentrosymmetric 2D materials.At last,we summarized and looked forward to future research on the growth of layer-,stacking-,and twist-controlled noncentrosymmetric 2D single crystals and their heterostructures.

A Generalized Polymer Precursor Ink Design for 3D Printing of Functional Metal Oxides

Three-dimensional-structured metal oxides have myriad applications for optoelectronic devices.Comparing to conventional lithography-based manufacturing methods which face significant challenges for 3D device architectures,additive manufacturing approaches such as direct ink writing offer convenient,on-demand manufacturing of 3D oxides with high resolutions down to sub-micrometer scales.However,the lack of a universal ink design strategy greatly limits the choices of printable oxides.Here,a universal,facile synthetic strategy is developed for direct ink writable polymer precursor inks based on metal-polymer coordination effect.Specifically,polyethyleneimine functionalized by ethylenediaminetetraacetic acid is employed as the polymer matrix for adsorbing targeted metal ions.Next,glucose is introduced as a crosslinker for endowing the polymer precursor inks with a thermosetting property required for 3D printing via the Maillard reaction.For demonstrations,binary(i.e.,ZnO,CuO,In_(2)O_(3),Ga_(2)O_(3),TiO_(2),and Y_(2)O_(3)) and ternary metal oxides(i.e.,BaTiO_(3) and SrTiO_(3)) are printed into 3D architectures with sub-micrometer resolution by extruding the inks through ultrafine nozzles.Upon thermal crosslinking and pyrolysis,the 3D microarchitectures with woodpile geometries exhibit strong light-matter coupling in the mid-infrared region.The design strategy for printable inks opens a new pathway toward 3D-printed optoelectronic devices based on functional oxides.

The effect of array periodicity on the filtering characteristics of metal/dielectric photonic crystals

We present a both theoretical and experimental investigation into the effect of array periodicity on the filtering characteristics of metal/dielectric photonic crystals（MDPhCs） with hexagonal arrays of subwavelength holes in gold/silicon dioxide films,varying the array periodicity from 6 to 8μm every 1μm while the ratio of hole radius to array periodicity is kept constant（1/4）.The results indicate that the reflectance spectrum is highly dependent on the array periodicity.When the array periodicity increases,the reflectance spectrum exhibits a large redshift regularly.The finite difference time domain（FDTD） simulations agree well with the experimental results. By analyzing the relationship between the position of the reflectance minimum and the array periodicity,we find that the filtering characteristics of MDPhCs have an almost linear relationship with the array periodicity under the conditions of keeping the same ratio of hole radius to array periodicity（1/4）.This finding provides an effective way to control the filtering characteristics of MDPhCs,which have potential applications in optical filters,plasmonic thermal emitters and so on.

Two-dimensional near-infrared photonic crystal fabrication by generation of void channels in solid resin

Two-dimensional (2D) triangular void channel photonic crystals with different lattice constants stacked in two different directions were fabricated by using femtosecond laser micro-explosion in solid polymer material. Fundamental and higher-order stop gaps were observed both in the infrared transmission and reflection spectra. There is an approximately linear relationship between the gap position and the lattice constant. The suppression of the fundamental gap is as high as 70% for 24-layer structures stacked in the T-M direction.

High efficiency filtering using two-dimensional photonic crystal coupled cavity structures

Transmission spectra of coupled cavity structures （CCSs） in two-dimensional （2D） photonic crystals （PCs） are investigated using a coupled mode theory, and an optical filter based on CCS is proposed. The performance of the filter is investigated using finite-difference time-domain （FDTD） method, and the results show that within a very short coupling distance of about 3λ, where ）, is the wavelength of signal in vacuum, the incident signals with different frequencies are separated into different channels with a contrast ratio of 20 dB. The advantages of this kind of filter are small size and easily tunable operation frequencies.

Absolute band gaps in two-dimensional graphite photonic crystal

The off-plane propagation of electromagnetic (EM) waves in a two-dimensional (2D) graphite photonic crystal structure was studied using transfer matrix method. Transmission spectra calculations indicate that such a 2D structure has a common band gap from 0.202 to 0.2035 c/a for both H and E polarizations and for all off-plane angles form 0° up to 90°. The presence of such an absolute band gap implies that 2D graphite photonic crystal, which is much easier and more feasible to fabricate, can exhibit some properties of a three-dimensional (3D) photonic crystal.

Enhancement of light extraction efficiency in OLED with two-dimensional photonic crystal slabs

Light extraction efficiency of organic light emitting diode （OLED） based on various photonic crystal slab （PCS） structures was studied. By using the finite-difference time-domain （FDTD） method, we investigated the effect of several parameters, including filling factor and lattice constant, on the enhancement of light extraction efficiency of three basic PCSs, and got the most effective one. Two novel designs of ＂interlaced＂ and ＂double-interlaced＂ PCS structures based on the most effective basic PCS structure were introduced, and the ＂interlaced＂ one was proved to be even more efficient than its prototype. Large enhancement of light extraction efficiency resulted from the coupling to leaky modes in the expended light cone of a band structure, the diffraction in the space between columns, as well as the strong scattering at indium-tinoxide/glass interfaces.

Design and analysis of superlens based on complex two-dimensional square lattice photonic crystal

We theoretically demonstrate the imaging properties of a complex two-dimensional(2D) face-centered square lattice photonic crystal(PC) made from germanium cylinders in air background. The finitedifference time-domain(FDTD) method is employed to calculate the band structure and simulate image construction. The band diagram of the complex structure is significantly compressed. Negative refraction occurs in the second energy band with negative phase velocity at a frequency of 0.228(2πc/a), which is lower than results from previous studies. Lower negative refraction frequency leads to higher image resolution. Numerical results show that the spatial resolution of the system reaches 0.7296λ, which is lower than the incident wavelength.

金属银对光子晶体光吸收的增强效应

构造含金属银缺陷的光子晶体模型(AB)m AGA(BA)m,利用传输矩阵法理论,通过计算机计算仿真的方式,研究了金属银缺陷对光子晶体光吸收特性的增强效应,发现当光子晶体中引入金属银缺陷后,光子晶体的光反射率和吸收率均得到增强。在400~1400 nm范围内,平均反射率增强到93.87%,平均吸收率增强到6.13%,且吸收率大小和位置可调。随着周期数m或B介质层厚度d B增大,光子晶体的光吸收率均得到增强,当m=5时吸收率高达98.72%,当d B=118.52 nm时吸收率高达99.59%,且吸收峰的位置随m增大向短波方向移动,但随d B增大向长波方向移动。随着光入射角度θ增大,光子晶体的光吸收率先增强到极大值后再逐渐减弱,且吸收峰的位置随入射角θ增大向短波方向移动。随着A介质层厚度d A增大,光子晶体的光吸收率减弱,当d A=73.22 nm时吸收率为98.72%,且吸收峰的位置随d A增大向长波方向移动。含金属银缺陷光子晶体的光吸收特性,可为新型光学吸收器、太阳能电池、滤波器和全反射器等材料研究和选择提供理论参考。

Crystal phase control in two-dimensional materials

It is the nature of crystals to exist in different polymorphs. The recent emergence of two-dimensional(2 D) materials has evoked the discovery of a number of new crystal phases that are different from their bulk structures at ambient conditions, and revealed novel structure-dependent properties, which deserve in-depth understanding and further exploration. In this contribution, we review the recent development of crystal phase control in 2 D materials, including group V and VI. transition metal dichalcogenides(TMDs), group IVA metal chalcogenides and noble metals. For each group of materials, we begin with introducing the various existing crystal phases and their structure-related properties, followed by a detailed discussion on factors that influence these crystal structures and thus the possible strategies for phase control. Finally, after summarizing the whole paper, we present the challenges and opportunities in this research direction.

Enhanced absorption of solar cell made of photonic crystal by geometrical .design

In this paper, via numerical simulation we designed the geometry of solar cell made by onedimensional （1D） and two-dimensional （2D） photonic crystals with two kinds of materiel （silicon （Si） and hydrogenated amorphous silicon （a-Si：H）） in order to enhance its absorption. The absorption characteristics of light in the solar cell structures are simulated by using finite-difference time-domain （FDTD） method. The calculation results show that the enhancement of absorption in patterned structure is apparent comparing to the unpatterned one, which proves the ability of the structure to produce photonic crystal solar cell. We found solar cell geometries as a 2D photonic crystal enable to increase the absorption between 380 and 750 nm.