PBG properties of three-component 2D photonic crystals

In this paper we analyze theoretically how the introduction of the third component into the two-dimensional photonic crystal influences the photonic band structure and the density-of-states of the system. We consider the periodic array of cylindrical air rods in a dielectric, and the third medium is introduced as a ring-shaped intermediate layer of thickness d and dielectric constant _i between the air pores and the dielectric background. Using the plane wave method, we have obtained the band structures for the 2D triangular lattice photonic crystals. The dependencies of TE and TM band gaps’ widths and gaps’ edges position on the interlayer dielectric constant and interlayer thickness were analyzed. In the framework of this approach, we have estimated the influence of the surface oxide layer on the band structure of macroporous silicon. We observed the shift of the gaps’ edges to the higher or lower frequencies, depending on the interlayer thickness and dielectric constant. We have shown that the existence of a native oxide surface layer should be taken into consideration to understand the optical properties of 2D photonic crystals, particularly in macroporous silicon structures.     

Gap maps, diffraction losses, and exciton–polaritons in photonic crystal slabs

A theory of photonic crystal (PhC) slabs is described, which relies on an expansion in the basis of guided modes of an effective homogeneous waveguide and on treating the coupling to radiative modes and the resulting losses by perturbation theory. The following applications are discussed for the case of a high-index membrane: gap maps for photonic lattices in a waveguide; exciton–polariton states, when the PhC slab contains a quantum well with an excitonic resonance; propagation losses of line-defect modes in W1 waveguides, also in the presence of disorder; the quality factors of photonic nanocavities. In particular, we predict that disorder-induced losses below 0.2 dB/mm can be achieved in state-of-the-art samples by increasing the channel width of W1 waveguides.     

Resonant modes in quantum well structure of photonic crystals with different lattice constants

The resonant modes in a quantum well (QW) structure composed of three slabs of two dimensional (2D) photonic crystals with different lattice constants are analyzed with plane-wave-based transfer matrix method (TMM). It is found that the energy band of the well slab submerged into the band gap of barrier slab is discretized into quantized modes and the number of the resonant modes changes with the well slab thickness. A model structure of asymmetrical photonic QW consisting of two slabs of 2D photonic crystals with different lattice constants and one uniform dielectric slab in between is proposed and the resonant modes in it are investigated with the same method. A useful numerical simulation method for theoretical discussion as well as for practical application about photonic QW structure of photonic crystals with different lattice constants is proposed.     

不同晶格常数光子晶体构成的光量子阱中的共振模

用基于平面波的传输矩阵法分析由具有不同晶格常数的光子晶体材料构成的光量子阱结构中的共振模，发现湮没于垒层的阱层能带分离成共振模，且共振模的数目随阱层的厚度变化而改变。提出一种新型的非对称量子阱结构模型，由2块晶格常数不同的光子晶体材料和夹在光子晶体材料中间作为阱层的均匀介电材料构成，并对其中的共振模进行了分析。指出当阱层厚度达到构成垒层的光子晶体晶格常数的一半时出现一个共振模，若继续小量增加阱层厚度将使共振模频率出现红移。最后给出一种基于平面波的传输矩阵法，且对于不同晶格常数的光子晶体量子阱结构均有效的数值模拟方法，可用于研究由三维光子晶体材料或者色散材料组成的光子晶体量子阱结构。     

Two-dimensional Si photonic crystals on oxide using SOI substrate

Two-dimensional photonic crystals (2D-PhCs) on oxide can be easily incorporated into photonic integrated circuits. Although an asymmetrical structure (air/PhC/oxide) is advantageous in terms of ease of fabrication, it has been pointed out that such a structure may have no photonic band gap (PBG). To clarify the characteristics of the asymmetrical structure, we calculated the band structure using the three-dimensional (3D) FDTD method and measured the transmission characteristics of a fabricated 2D Si-PhC on oxide. The calculations show that we can use a quasi-PBG even in an asymmetrical structure when the PhC thickness satisfies the single-mode condition. The measured transmission characteristics correspond to the calculated band structure and reveal the existence of a quasi-PBG. These results show that the asymmetrical 2D Si-PhC-on-oxide structure can be applied to various optical devices.     

Roughness losses and volume-current methods in photonic-crystal waveguides

We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic “volume-current method” (Green’s functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.     

Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab

Strong coupling between localized particle plasmons and optical waveguide modes leads to drastic modifications of the transmission of metallic nanowire arrays on dielectric waveguide substrates. The coupling results in the formation of a new quasiparticle, a waveguide-plasmon polariton, with a surprisingly large Rabi splitting of 250 meV. Our experimental results agree well with scattering-matrix calculations and a polariton-type model. The effect provides an efficient tool for photonic band gap engineering in metallodielectric photonic crystal slabs. We show evidence of a full one-dimensional photonic band gap in resonant plasmon-waveguide structures.     

Transmission characteristics simulation of an erbium-doped lithium niobate film photonic crystal slab

A photonic crystal slab (PhC slab) which was constructed as a 2D hexagonal lattice with a finite depth was etched into an Er:LiNbO₃ film waveguide. The band diagrams and transmission spectra were simulated by plane wave expansion (PWE) and the finite-difference time-domain (FDTD) method. A high refractive index contrast of 0.5 enables strong light confinement in the vertical direction and a broad band gap. The simulated transmittance spectra indicate that the stop band is determined by lattice constant. The transmission spectra along ΓM of the PhC slab with a lattice constant 500 nm show a 250-nm broad stop band in the wavelength range from 1.33 to 1.58 μm and sharp band edge.     

Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides

Enhanced third harmonic (TH) generation from Silicon-On-Insulator (SOI) planar waveguides as well as SOI photonic crystal (PhC) slabs is studied in different angular configurations, both in the visible and infrared energy ranges. In the SOI planar waveguide, the multilayer structure causes the optical properties such as TH reflection to be different from those of bulk silicon samples. This behavior is well reproduced by calculations of TH reflectance.Measurements of third-harmonic reflection and diffraction from one-dimensional PhC slabs etched in the SOI waveguide are also reported. The angular positions of TH peaks at various diffraction orders agree well with those calculated from a nonlinear grating equation. Both reflection and diffraction processes contribute to enhanced TH generation efficiency in the PhC slabs.TH reflectance measurements performed on PhC slabs in the near infrared show a resonant interaction between the incident beam and the photonic structure, dependent on the angle of incidence. This leads to a nonlinear conversion efficiency which is strongly enhanced with respect to that of the SOI waveguide, due to the excitation of strong local fields associated with the presence of photonic modes in the PhC slab.     

Out-of-plane scattering in 1-D photonic crystal slabs

We present a detailed study of out-of-plane scattering losses in a 1D approximation of 2D photonic crystal slabs. In 2D photonic crystals with a waveguide structure in the third dimension, the periodic structure (in a lot of applications a 2D arrangement of holes etched through the core and cladding) will cause light to scatter out of the waveguide plane. We studied the out-of-plane scattering losses of these holes using a 2D approximation of this 3D structure, with etched slots instead of holes. Our simulation techniques included mode expansion with PML and FDTD. We will present the influence of the refractive index contrast between core and cladding of the layered structure. We show that the losses increase with higher index contrast between core and cladding, but that with very high index contrasts and under the right circumstances light can be coupled into lossless Bloch modes.     

Design,nano-fabrication and analysis of near-infrared 2D photonic crystal air-bridge structures

Selective wet etching is a technique that allows fabrication of freely suspended thin slabs in epitaxial heterostructures. This technique, together with high-aspect ratio dry etching, is used to create two-dimensional (2D) photonic crystals for near-infrared wavelengths in thin suspended AlGaAs membranes. The active photonic crystal areas contain hexagonal arrays of cylindrical holes completely perforating the membrane. For an appropriate selection of the slab thickness and the lattice parameter, dispersion relations for the guided modes are explicitly computed by solving the Maxwell equations in a geometry containing a 2D photonic crystal defined in the core layer of a dielectric waveguide structure. Measurements of the spectral transmittance in air-bridge samples show a narrow 30-dB-deep stop band for TM polarized incident light. The spectral position of the stop band shows a good agreement with theoretical band structure calculations when also the quasi-guided resonant modes outside the light cone are taken into account.     

Analysis and design of efficient coupling in photonic crystal circuits

A rigorous analysis and design of efficient coupling from photonic crystal (PhC) waveguides into conventional dielectric waveguides is reported. Closed-form expressions for the reflection and transmission matrices that completely characterize the scattering that occurs at the interface are derived based on an eigenmode expansion technique and a Bloch basis. Analytic expressions are used to analyze the reflection into PhC waveguides. We obtain that negligible reflection can be achieved by choosing a certain interface within a PhC unit cell. Furthermore, analytic expressions are used to design a novel and compact coupler structure in order to achieve high coupling efficiency when broad dielectric waveguides are considered. Thereby, transmission efficiencies near 100 from the fundamental guided Bloch mode into the fundamental waveguide mode are achieved.     

Tunable photonic crystals with semiconducting constituents

We propose that the photonic band structure (PBS) of semiconductor-based photonic crystals (PCs) can be made tunable if the free-carrier density is sufficiently high. In this case, the dielectric constant of the semiconductor, modeled as varepsilon(omega) = varepsilon(0)(1-omega(2)(p)/omega(2)), depends on the temperature T and on the impurity concentration N through the plasma frequency omega(p). Then the PBS is strongly T and N dependent; it is even possible to obliterate a photonic band gap. This is shown by calculating the 2D PBS for PCs that incorporate either intrinsic InSb or extrinsic Ge.     

Demonstration of temperature resilient properties of 2D silicon carbide photonic crystal structures and cavity modes

In this paper, photonic crystal (PhC) based on two dimensional (2D) square and hexagonal lattice periodic arrays of Silicon Carbide (SiC) rods in air structure have been investigated using plane wave expansion (PWE) method. The PhC designs have been optimized for telecommunication wavelength (λ = 1.55 μm) by varying the radius of the rods and lattice constant. The result obtained shows that a photonic band gap (PBG) exists for TE-mode propagation. First, the effect of temperature on the width of the photonic band gap in the 2D SiC PhC structure has been investigated and compared with Silicon (Si) PhC. Further, a cavity has been created in the proposed SiC PhC and carried out temperature resiliency study of the defect modes. The dispersion relation for the TE mode of a point defect A1 cavity for both SiC and Si PhC has been plotted. Quality factor (Q) for both these structures have been calculated using finite difference time domain (FDTD) method and found a maximum Q value of 224 for SiC and 213 for Si PhC cavity structures. These analyses are important for fabricating novel PhC cavity designs that may find application in temperature resilient devices.     

Modelling and design of complete photonic band gaps in two-dimensional photonic crystals

In this paper, we investigate the existence and variation of complete photonic band gap size with the introduction of asymmetry in the constituent dielectric rods with honeycomb lattices in two-dimensional photonic crystals (PhC) using the plane-wave expansion (PWE) method. Two examples, one consisting of elliptical rods and the other comprising of rectangular rods in honeycomb lattices are considered with a view to estimate the design parameters for maximizing the complete photonic band gap. Further, it has been shown that complete photonic band gap size changes with the variation in the orientation angle of the constituent dielectric rods.      

Band gap extension in honeycomb lattice two-dimensional plasma photonic crystals in the presence of dissipation

We investigate two types of honeycomb lattice two-dimensional plasma photonic crystals that possess large photonic band gaps in the presence of dissipation. We obtain a clear insight into the band structures and find imaginary parts of the eigenvalue band structure at the symmetry points display discontinuous behaviour when the filling factor of plasma in type-1 structure is low. Further more, we show how the photonic band gaps are affected by the normalized plasma frequency, radius of cylinder, dielectric constant and collision frequency. Our results demonstrate the band gap extension by increasing normalized plasma frequency in both type structures and radius of plasma cylinders in type-1 structure. The width of band gaps could also be enlarged by decreasing dielectric cylinder's radius. The bands shift toward lower frequencies when relative dielectric constant increases in both two types. These results may provide theoretical instructions to design new optoelectronic devices.     

Enhancement of photoluminescence from germanium by utilizing air-bridge-type photonic crystal slab

We fabricated germanium-based photonic crystal (PhC) slabs and characterized them by photoluminescence (PL) measurements at room temperature. Air-bridge-type Ge PhC slabs showed stronger PL than non-processed Ge layers on SiO₂ and than Ge PhC slabs on SiO₂. This enhancement is attributed to improved extraction efficiency due to the PhC patterns and to suppressed light leakage into the substrate by utilizing the air-suspended structure. In particular, when flat photonic band-edge modes around the Γ point are tuned to the Ge emission range, larger enhancement of integrated PL intensity was observed. A maximum enhancement ratio of integrated intensity up to 22 was demonstrated in an air-suspended Ge PhC slab with appropriate structural parameters. This is the largest enhancement factor of Ge PL using photonic nanostructures reported so far.     

Silicon-based two-dimensional photonic crystal waveguides

A review of the properties of silicon-based two-dimensional (2D) photonic crystals is given, essentially infinite 2D photonic crystals made from macroporous silicon and photonic crystal slabs based on silicon-on-insulator basis. We discuss the bulk photonic crystal properties with particular attention to the light cone and its impact on the band structure. The application for wave guiding is discussed for both material systems, and compared to classical waveguides based on index-guiding. Losses of resonant waveguide modes above the light line are discussed in detail.     

Photonic band gaps structure properties of two-dimensional function photonic crystals

The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.     

在高频区存在巨带隙的长方晶格二维光子晶体

本文利用降低光子晶体的对称性来提高绝对禁带宽度, 提出两种长方结构长方介质柱二维光子晶体, 用快速平面波展开法研究其高频区的带结构.经参数优化发现, 长方晶格包含一套介质柱时, 最大绝对禁带宽度Δω为0.1265ωe（ωe=2πc/a, a为晶格常数, c为光速）, 绝对禁带中心频率ωmid为1.9256ωe, Δω/ωmid=6.6%; 当长方晶格包含两套介质柱时, 最大绝对禁带宽度为0.203ωe, 绝对禁带中心频率为1.8597ωe, Δω/ωmid=10.9%.