Polarization optimization in the interference of four umbrellalike symmetric beams for making three-dimensional periodic microstructures

A systematic and comprehensive analysis of the interference of four umbrellalike beams (lFUB) is provided based on the reciprocal space theory. The concept of pattern contrast is extended to the case of the IFUB, and it is indicated that a uniform contrast for all the interference terms can be obtained by properly choosing the beam ratio and the polarization of each beam. Different polarization combinations, including linear light and linear light, circular light and circular light, and linear light and circular light, have been discussed for the purpose of maximum uniform contrast. It is shown that the use of circular light may generally improve the uniform contrast. This study may lay a theoretical foundation for holographic fabrication of three-dimensional (3D) periodic microstructures, such as simple cubic, body-centered cubic, face-centered cubic, or trigonal lattice.     

Wave design and polarization optimization in the interference of four non-coplanar beams for making three-dimensional periodical microstructures

Abstract

A systematic analysis of the interference of four non-coplanar beams for the purpose of making three-dimensional periodical microstructures is described. A general relationship between the four wavevectors, the required wavelength and the desired 3D lattice is formulated based on the reciprocal space theory. A concept of uniform contrast is introduced to evaluate the modulation depth of the resultant pattern as a whole by properly choosing the beam ratio and polarization. A calculation algorithm is developed to determine the optimized polarization of each beam for a given lattice to reach the maximum uniform contrast. Specifically, the effect of non-uniqueness of the wavevector solution for a given lattice on the final result is investigated. It is shown that one can improve the uniform contrast by using a set of waves with less angular divergence.     

Formation of all fourteen Bravais lattices of three-dimensional photonic crystal structures by a dual beam multiple-exposure holographic technique

We make use of a dual beam multiple-exposure (DBME) holographic technique for the formation of all 14 Bravais lattices of three-dimensional photonic crystal microstructures. For simplicity of experimental implementation, the DBME method has been modified such that, prior to each exposure, once the proper angle between the wave vectors of the interfering beams is chosen, a single axis rotation of the recording medium gives the desired results. The parameters required for the generation of the lattice structures have been derived by appropriate modification of interference of four noncoplanar beams (IFNB) analysis for corresponding implementation in the DBME technique, and the results have been verified by computer simulations. After giving a comparative study of the results with the IFNB method, recording geometries for the DBME approach are also proposed in order to realize all 14 Bravais lattices experimentally.     

Beam splitter and beam bends based on self-collimation effect in two-dimensional photonic crystals

Basing on the self-collimation effect of photonic crystals, one-to-two beam splitter, beam bend and one-to-three beam splitter are, respectively, designed by introducing a different line defect along the same direction. From the equal-frequency contour plot which is calculated by the plane wave expansion method, we obtain the frequency and the propagate direction of the self-collimated beam. The self-collimated beam propagation in photonic crystals with different line defects is simulated by the two-dimensional finite-difference time-domain method with perfectly matched layer absorbing boundary conditions. The simulation results show that one-to-two beam splitter, beam bend and one-to-three beam splitter can be realized by appropriately arranging the line defect along the proper direction. Such devices can greatly enhance photonic crystals for use in high-density optical integrated circuits.     

Fabrication of three-dimensional photonic crystals with two-beam holographic lithography

A holographic technique used to fabricate three-dimensional photonic crystals with a two-beam interference method is presented. In the optical setup of fabrication one beam is incident on the recording plate in the direction of the plate normal and the other beam with an angle to the normal. Three exposures were taken. Between each exposure, the recording plate was rotated 120 degrees on axis until three exposures were completed. Good three-dimensional lattice structures have been obtained. Theoretical analysis, computer simulations, and experimental results are presented.     

Five-beam interference pattern controlled through phases and wave vectors for diamondlike photonic crystals

We demonstrate, for what is believed to be the first time, the design of diamondlike photonic crystals made by holographic lithography based on five-beam interference. All five beams are launched from the same half-space, and the exposure can easily be realized by a single diffractive optical element. The photonic structure can be constructed through the translation of the interference pattern controlled by the phase shift of laser beams. The proposed holographic lithography is capable of creating series photonic crystals with large photonic bandgaps by adjusting the phase and the wave vector of interfering beams.     

Tunable electro-optical 2 × 2 photonic crystal beam splitter

A tunable electro-optical 2?×?2 beam splitter based on two-dimensional rod-type photonic crystals is presented. The beam splitter consists of two orthogonally crossed linear waveguides and a single center rod in square lattice photonic crystals. In order to create a linear waveguide, the radius of a line of rods is reduced. A single center rod is positioned at the intersection of the linear waveguides to divide the input lightwave into output ports. The switching mechanism is a change in the conductance of the waveguide region and hence modulating the guided modes. The tunable beam splitter can be applied to photonic integrated circuits.     

Analysis of guided-resonance-based polarization beam splitting in photonic crystal slabs

We present an analysis of the phase and amplitude responses of guided resonances in a photonic crystal slab. Through this analysis, we obtain the general rules and conditions under which a photonic crystal slab can be employed as a general elliptical polarization beam splitter, separating an incoming beam equally into its two orthogonal constituents, so that half the power is reflected in one polarization state, and half the power is transmitted in the other state. We show that at normal incidence a photonic crystal slab acts as a dual quarter-wave retarder in which the fast and slow axes are switched for reflection and transmission. We also analyze the case where such a structure operates at oblique incidences. As a result we show that the effective dielectric constant of the photonic crystal slab imposes the Brewster angle as a boundary, separating two ranges of angles with different mechanisms of polarization beam splitting. We show that the diattenuation can be tuned from zero to one to make the structure a circular or linear polarization beam splitter. We verify our analytical analysis through finite-difference time-domain simulations and experimental measurements at infrared wavelengths.     

A tunable high-efficiency optical switch based on graphene coupled photonic crystals structure

A plasmonic device for high-efficiency optical switch is proposed based on graphene coupled photonic crystals structure. The finite-difference time-domain simulation results show that the transmission and reflection ratio can be controlled by tuning the parameters of the graphene strip, such as chemical potential or width. And the corresponding contrast ratio can be 25 and 26.8 for a single and double graphene strips coupled photonic crystals structure, respectively. The results in this paper will have potential application in nanosensors and integrated photonic circuits.     

Analysis of Photonic Band Gaps in a Two-Dimensional Triangular Lattice with Superconducting Hollow Rods

In this work, we use the plane wave expansion method to calculate photonic band structures in two-dimensional photonic crystals which consist of high-temperature superconducting hollow rods arranged in a triangular lattice. The variation of the photonic band structure with respect to both, the inner radius and the system temperature, is studied, taking into account temperatures below the critical temperature of the superconductor in the low frequencies regime and assuming E polarization of the incident light. Permittivity contrast and nontrivial geometry of the hollow rods lead to the appearance of new band gaps as compared with the case of solid cylinders. Such band gaps can be modulated by means of the inner radius and system temperature.     

Single-beam holography for Ag nanoparticle-embedded two-dimensional binary metallodielectric photonic crystals

Absolute photonic bandgaps of photonic crystals can be increased by reducing the structural symmetry and/or by enhancing the refractive index contrast. We have experimentally demonstrated a single-beam holography for creating Ag nanoparticle-embedded 2D binary photonic microstructures by adding a different diameter rod in the center of each original 2D honeycomb lattice for simultaneously realizing both symmetry reduction and the enhancement of the index contrast of PC structures.     

Optical properties of carbon nanofiber photonic crystals

Carbon nanofibers (CNFs) are used as components of planar photonic crystals. Square and rectangular lattices and random patterns of vertically aligned CNFs were fabricated and their properties studied using ellipsometry. We show that detailed information such as symmetry directions and the band structure of these novel materials can be extracted from considerations of the polarization state in the specular beam. The refractive index of the individual nanofibers was found to be n(CNF) = 4.1.     

Polarization filters with an autocloned symmetric structure

The process of fabricating photonic crystals comprised of alternately stacked high- and low-index dielectric materials on periodic substrates to form zigzag films is called the autocloning technique. In this study, we have fabricated TiO2/SiO2 two-dimensional polarization filters by using electron beam gun evaporation with ion-beam-assisted deposition. The shape of the zigzag structure is preserved, and the total thickness is 8?μm. The symmetric structural design can be utilized as an antireflection coating applied to reduce ripples and achieve a 200?nm working wavelength range.     

Polarization beam splitter based on honeycomb-lattice photonic crystal ring resonators

A new polarization beam splitter is proposed based on a photonic crystal ring resonator (PCRR) composed of honeycomb-lattice cylindrical silicon rods in air. By shrinking the width of the bus waveguide and adjusting the radii of two nearest-neighbor center rods of the PCRR, an unpolarized beam can be separated well into TE and TM polarization states, respectively, at the backward and forward output ports. Simulation results obtained by the two-dimensional finite-difference time-domain technique show that the insertion losses are 3.58 dB and 3.08 dB, and the polarization extinction ratios are 21.42 dB and 28.53 dB for TE and TM polarization, respectively, at a 1566.7 nm center wavelength. The excess loss is less than 0.34 dB and its dimensions are roughly 43.2 μm × 27.52 μm. These findings offer potential practical applications in high-density photonic integrated circuits.     

Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography

A comprehensive and fully three-dimensional model of holographic lithography is used to predict more rigorously the geometry and transmission spectra of photonic crystals formed in Epon SU-8 photoresist. It is the first effort known to the authors to incorporate physics of exposure, postexposure baking, and developing into three-dimensional models of photonic crystals. Optical absorption, reflections, standing waves, refraction, beam coherence, acid diffusion, resist shrinkage, and developing effects combine to distort lattices from their ideal geometry. These are completely neglected by intensity-threshold methods used throughout the literature to predict lattices. Numerical simulations compare remarkably well with experimental results for a face-centered-cube (FCC) photonic crystal. Absorption is shown to produce chirped lattices with broadened bandgaps. Reflections are shown to significantly alter lattice geometry and reduce image contrast. Through simulation, a diamond lattice is formed by multiple exposures, and a hybrid trigonal-FCC lattice is formed that exhibits properties of both component lattices.     

Fabrication of photonic crystals on several kinds of semiconductor materials by using focused-ion beam method

In this paper, we introduced the fabrication of photonic crystals on several kinds of semiconductor materials by using focused-ion beam machine, it shows that the method of focused-ion beam can fabricate two-dimensional photonic crystal and photonic crystal device efficiently, and the quality of the fabricated photonic crystal is high. Using the focused-ion beam method, we fabricate photonic crystal wavelength division multiplexer, and its characteristics are analyzed.     

Photonic crystal beam splitters

This work studies two-dimensional photonic crystal beam splitters with two input ports and two output ports. The beam splitter structure consists of two orthogonally crossed line defects and one point defect in square-lattice photonic crystals. The point defect is positioned at the intersection of the line defects to divide the input power into output ports. If the position and the size of the point defect are varied, the power of two output ports can be identical. The beam splitters can be used in photonic crystal Mach-Zehnder interferometers or switches. The simulation results show that a large bandwidth of the extinction ratio larger than 20 dB can be obtained while two beams are interfered in the beam splitters. This enables photonic crystal beam splitters to be used in fiber optic communication systems.     

Holographic creation of photonic crystals

We describe the creation of general photonic crystals by means of holography with an experimental demonstration. The recordings of periodic variations of amplitude and phase by the interference of coherent laser beams offer a natural means for the creation of one- two- or three-dimensional photonic crystals. Based on the principle of the interference of four noncoplanar beams, we present a comparative analysis of two different approaches for creating photonic crystals and use numerical simulated lattice structures to illustrate the differences between these two approaches. We then use a specific symmetrical optical architecture and select the proper approach to create holographic photonic crystals. The advantages and constraints of this holographic method are discussed.     

可见光区一维光子晶体纳米膜偏振带通滤波器的设计

应用一维时域有限差分方法研究各种条件下一维二元光子晶体的偏振带通滤波特性,具体数值分析了掺杂层位置、厚度、电磁参数、入射角度四种因素对偏振滤波特性的影响.数值结果表明传统意义上的光学多层膜是一维二元光子晶体在光学厚度满足四分之一波长时的特例;可见光区的偏振滤波器的窄带滤波特性与掺杂层的位置有关,掺杂层在整个膜中间位置时偏振分离效果好,掺杂层的厚度与周期层厚度相差越大则分离效果越好,两组元折射率相差越大越易形成禁带,入射角越大禁带越窄,偏振的分离度越好.特别是P偏振局域模更多;在线度参数相同的情况下介质电磁参数对禁带有较大影响,禁带只有在两组元折射率相差越大才能形成,介质损耗同样是不可忽略的因素;光源的入射角对禁带有重大影响.本文的研究对光子器件的设计有一定的指导作用.     

Phenomenological study of binding in optically trapped photonic crystals

We describe a phenomenological theory of the phenomenon of binding observed both experimentally and numerically when particles are trapped by an interference system in order to make a structure close to a photonic crystal. This theory leads to a very simple conclusion, which links the binding phenomenon to the bottom of the lowest bandgap of the trapped crystal in a given direction. The phenomenological theory allows one to calculate the period of the trapped crystal by using numerical tools on dispersion diagrams of photonic crystals. It emerges that the agreement of our theory with our rigorous numerical results given in a previous paper [J. Opt A8, 1059 (2006)] is better than 2% on the crystal period. Furthermore, it is shown that in two-dimensional problems and s polarization, all the optical forces derive from a scalar potential.