Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs

A theoretical model of disorder for the etched holes or pillars in a generic two-dimensional photonic crystal slab is presented. This model is employed to calculate the effects of size disorder on propagation losses in linear photonic crystal waveguides as well as on quality (Q)-factors in photonic crystal nano-cavities. The main results obtained by the present theory and shown in this work are: (a) large single-mode bandwidth and low-loss (<0.1 dB/mm) propagation of light is predicted for increased-width membrane-type photonic crystal waveguides, (b) pillar-based lattices show reduced sensitivity to size fluctuations than hole-based ones, (c) the effects of disorder on cavity Q-factors are quantitatively evaluated. An extension of the model is also introduced in order to take into account the side-wall micro-roughness of the perfectly vertical holes, and preliminary results of this more general approach are discussed.     

A novel technique to measure the sucrose concentration in hydrogel sucrose solution using two dimensional photonic crystal structures

We propose a novel technique to measure the concentration of sucrose in PAm-hydrogel sucrose solution using two dimensional photonic crystal structures consists of air holes. PAm-hydrogel is an organic hydrogels, which is used as biomedical applications. The principle of measurement is based on the linear variation of photonic band gap with the change of dielectric constant of the solution infiltrated in air holes of photonic crystal structure. Plane wave expansion method is used to find the band gap and linear variation (R² = 0.9949) of photonic band gap with respect to sucrose concentration is observed. Besides this, an excellent linear variation (R² = 0.9949) of transmitted intensity of light with respect to sucrose concentration is also seen. Since the simulation is based on optical principle, it gives accurate results. This suggests the possible use of 2-D photonic crystal structure as a sucrose sensor. Experimental procedure for measuring the concentration of sucrose is also mentioned.     

Multichannel W3 Y-branch filter in a two dimensional triangular-lattice photonic crystal slab

We demonstrate the design, fabrication and characterization of a highly efficient multichannel W3 Y-branch filter in a two dimensional triangular-lattice photonic crystal slab. The coupling properties between high-order waveguide modes and fundamental resonant modes are investigated. By finely adjusting the size of resonant cavities, four higher-order mode channels with different output wavelengths are experimentally realized, which is in agreement with the theoretical simulations. The results show that this kind of filter may be useful in optical integrated circuits with high coupling and transmission efficiency.     

Ultrahigh-Q of the L3 photonic crystal microcavity

In this paper, we theoretically investigate the L3 cavity with three missing holes in the center. They are of great interest for the realization of low threshold laser nanosources and for a strong interaction between the cavity and sources. In order to improve the transmission and Q factor simultaneously of these structure, by reducing unwanted reflection due to mismatch and through minimization of propagation losses, we modified L3 geometry: three missing holes in a line where both lateral displacement of the first hole adjacent to the cavity, d, and their radius, r, were changed. A photonic microcavity with a high Q factor of 1.8741 × 10⁷ and a modal volume V of 0.351 is demonstrated. We demonstrate that the calculated Q factor for the designed cavity increases by a factor of 49 relative to that for a cavity without displaced and reduced air holes, while the modal volume remains almost constant.     

2维光子晶体谐振腔的分析与模拟

 为指导光子晶体谐振腔的设计,运用3维电磁场仿真软件HFSS模拟了2维光子晶体谐振腔,分析了影响2维光子晶体谐振腔的主要特性参数,主要包括所插介质杆的排列结构、介电常数及其半径和间距。研究表明,在其它条件保持不变时,若增大介质杆半径,则同一模式频率没有同一的变化规律;若增大介质杆介电常数,则出现的规则模式减少,并且没有基模出现,同一个模式,频率明显降低;若增大介质杆间距,则计算的频率间隔减小,对其它参数影响不大,只是同一模式的频率略有减小。     

Lightwave splitting in two dimensional photonic crystal analogue of coupler

Two bent channels are created in an otherwise periodically arrayed photonic crystal structure by removing some dielectric pillars. If lightwave is introduced into one channel, a part of it would couple into the second channel and propagate down the guide. Factors deciding the amount of light couple from the first channel into the second channel are discussed thoroughly. This coupling scheme could be an important part for photonic integrated devices.     

Lateral shifting in one dimensional chiral photonic crystal

We report the lateral shifts of the transmitted waves in a one dimensional chiral photonic crystal by using the stationary-phase approach. It is revealed that two kinds of lateral shifts are observed due to the existence of cross coupling in chiral materials, which is different from what has been observed in previous non-chiral photonic crystals. Unlike the chiral slab, the positions of lateral shift peaks are closely related to the band edges of band gap characteristics of periodic structure and lateral shifts can be positive as well as negative. Besides, the lateral shifts show a strong dependence on the chiral factor, which varies the lateral shift peaks in both magnitudes and positions. These features are desirable for future device applications.     

Ultracompact refractive index sensor based on microcavity in the sandwiched photonic crystal waveguide structure

A refractive index (RI) sensor based on the two-dimensional photonic crystal is presented. The sensor is formed by a point-defect resonant cavity in the sandwiched waveguide structure. The transmission spectrums of the sensor with different ambient refractive indices ranging from n = 1.0 to n = 1.6 are calculated. The calculation results show that a change in ambient RI of Δn = 0.001 is apparent, the sensitivity of the sensor (Δλ/Δn) is achieved with 330 nm/RIU (when lattice constant a = 440 nm), where RIU means the refractive index unit; and the transmission efficiency in the RI range of 1.0-1.6 can reach about 40% to 70%, that make the detection of spectrum easy and feasible. The properties of the sensor are analyzed and calculated using the plane-wave expansion (PWE) method and simulated using the finite-difference time-domain (FDTD) method.     

T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal

We propose and numerically investigate a kind of high-efficiency T-shaped optical circulator in a two-dimensional square-lattice photonic crystal. In the T-shaped structure, the single-direction light transmission for 90° light-bending is achieved by coupling two magneto-optical rods. And aided with a side-coupled cavity, two paths of single-direction 90° light-bending are effectively combined, which realizes the nonreciprocal light transmission for two waveguides arranged and linked along a straight line. The optical properties of the system are investigated by finite element method. The circulator considered here can be used for isolating light reflections and improving system stabilization in designing photonic crystal integrated circuits.     

Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes

A small-size optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes is designed and theoretically simulated using plane wave expansion and finite-difference time-domain method. The interleaver is formed by two parallel and identical photonic crystal slab waveguides which are separated by three rows of air holes. The coupling region is designed below the light line to avoid vertical radiation. The simulated results show that the coupling coefficient is increased and the final length of the interleaver is decreased by enlarging the radius of the middle row of air holes. The transmission properties are analyzed after the interleaver’s structure is optimized, and around 100 GHz channel spacing can be got when the length of the interleaver is chosen as 40.5 μm.     

半径位置微扰对于不同光子晶体波导结构的影响

本文理论上分析了不同程度的位置半径微扰分别对于二维三角晶格不同空气孔形状的光子晶体波导结构透射率性能的影响。主要关注三个区域,低频带隙边缘,高频带隙边缘以及导模交叉点;三种空气孔形状,圆形,方形,椭圆形。仿真结果显示微扰对于交叉点影响最为严重。随着微扰程度变大,高低频边缘平坦的透射率区域逐渐变窄。相同形状相同微扰程度下,透射率对位置微扰更加敏感。不同形状比较发现,慢光区域正方空气孔对于位置微扰更稳健,圆形空气孔对于半径微扰更稳健。这对于光子晶体制作和实验过程中不可避免的位置和半径的随机微扰具有理论指导意义。     

Improved bends for two-dimensional photonic crystal waveguides

For two-dimensional photonic crystals involving infinitely long dielectric rods or air-holes on square or triangular lattices, a number of high performance 60° and 90° waveguide bends are obtained by solving optimization problems involving the radii of a few rods or air-holes as the degrees of freedom. In particular, the proposed 60° bends significantly outperform previous designs that insert three or five identical air-holes in the bend. The optimization problems are solved using a recently developed method based on the so-called Dirichlet-to-Neumann (DtN) maps of the unit cells.     

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.     

Waveguide arrays in selectively infiltrated photonic crystal fibres

The periodic array of air holes in the cladding of a photonic crystal fibre (PCF) provides a convenient scaffold for the introduction of an infiltrating liquid. In this paper we demonstrate a novel platform of one-dimensional tuneable nonlinear photonic lattices produced by selectively infiltrating a row of holes in a PCF. Such structures have been realised by blocking individual holes on one end of a PCF, leaving the desired infiltration pattern unblocked. Unblocked holes are then infiltrated by immersing the unblocked end of the fibre in a reservoir of the infiltrating liquid, allowing for the realisation of a wide variety of periodic structures. Such structures are studied for traditional linear and nonlinear effects in periodic systems.     

Photonic crystal waveguide directional couplers as wavelength selective optical filters

Waveguide directional couplers, formed by two closely spaced linear defect waveguides in a two-dimensional photonic crystal of air holes in a semiconductor matrix, are numerically studied using plane wave expansion and finite difference time domain methods. The coupling lengths are on a wavelength scale and show a strong wavelength dependence, allowing for the design of compact wavelength selective optical filters. Applications as a channel interleaver for the 1.55 μm wavelength range and as a micrometer sized 1.31/1.55 μm wavelength demultiplexer are presented.     

Large range of omni-directional reflection in 1D photonic crystal heterostructures

A simple design of one-dimensional omni-directional reflector based on photonic crystal heterostructures structure has been proposed. The proposed structure consists of a periodic array of alternate layers of SiO₂ and Te as the materials of low and high refractive indices, respectively. The structure considered here has three stacks of periodic structures having five layers each. The lattice period of successive stack is increased by a certain multiple (say gradual constant, δ) of the lattice period of the just preceding stack. For numerical computation, the method of transfer matrix method (TMM) has been employed. It is found that such a structure has wider reflection bands in comparison to a conventional dielectric PC structure and the width of the omni-directional reflection (ODR) bands can be enlarged by increasing the value of the gradual constant δ.     

Multi-wavelength filtering in side-coupled cascaded-cavities systems

We theoretically investigate an optical system, which consists of a waveguide side-coupled to a cascade of cavities, the filtering properties by the time domain coupled-mode theory. In such a system, the filter operating bandwidth and the width of transmission peaks are completely determined by the mutual coupling coefficients between the cavities. The characteristics are numerically demonstrated in photonic crystals by the finite-difference time-domain method.     

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.     

2维光子晶体谐振腔的分析与模拟

为指导光子晶体谐振腔的设计,运用3维电磁场仿真软件HFSS模拟了2维光子晶体谐振腔,分析了影响2维光子晶体谐振腔的主要特性参数,主要包括所插介质杆的排列结构、介电常数及其半径和间距。研究表明,在其它条件保持不变时,若增大介质杆半径,则同一模式频率没有同一的变化规律;若增大介质杆介电常数,则出现的规则模式减少,并且没有基模出现,同一个模式,频率明显降低;若增大介质杆间距,则计算的频率间隔减小,对其它参数影响不大,只是同一模式的频率略有减小。