Photonic Crystal Defect Research Articles

Influence of filling fraction on the defect mode and gap closing of a one-dimensional photonic crystal: An analytical approach

Study of the optical properties of the one-dimensional defective photonic crystals using the gap map is improving through the emergence of new analytical methods, which are easy and without any physical restrictions. Gap map is able to monitor the changes in the defect mode frequencies and photonic band gap regions as a function of filling fractions, and all visible spectra in a single graphic presentation. In this paper, by utilizing a novel technique based on Green’s function method for analyzing the defect modes, the gap map and gap closing point of a one-dimensional defective photonic crystal have been demonstrated. This method enables study of the defect modes inside the omnidirectional band gap, which is an important object in the designing of the optical filters. Moreover, as a designing criterion, obtaining the gap closing points inside the gap map enables finding of some filling fraction intervals that each one contains several distinct omnidirectional band gaps simultaneously, using a single photonic crystal. This method has been employed for the design of an optical filter at 1.3 and 1.55 μm, which is applicable for telecommunication.

Heterogeneous integration and precise alignment of InP-based photonic crystal lasers to complementary metal-oxide semiconductor fabricated silicon-on-insulator wire waveguides

The integration of two-dimensional III-V InP-based photonic crystal and silicon wire waveguides is achieved through an accurate alignment of the two optical levels using mix-and-match deep ultraviolet (DUV)/electron beam lithography. The adhesively bonded structures exhibit an enhancement of light emission at frequencies where low group velocity modes of the photonic crystal line defect waveguides occur. Pulsed laser operation is obtained from these modes at room temperature under optical pumping. The laser light is coupled out of the Si waveguide via grating couplers directly to single mode fiber.

Fabrication and optical properties of two‐dimensional photonic crystal of ZnO pillars

AbstractTwo‐dimensional (2D) photonic crystal of ZnO pillars was synthesized on silicon substrate by the combination of template method and vapor‐phase transport method. The microstructure and morphology of the ZnO photonic crystal was evaluated by using scanning electron microscope (SEM) and X‐ray diffraction (XRD). Large‐area specular reflectance measurements showed the presence of photonic stop band. The effect of the photonic band gap and the special structure on the photoluminescence (PL) properties of ZnO photonic crystal has been investigated. Both suppression and enhancement in the PL were observed. Raman scattering analyses demonstrated that the defect of ZnO photonic crystal exists in this experiment. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Transmission and reflection spectra of a photonic crystal with a Raman defects

Features of Raman gain of probe radiation in three-level atoms placed in a defect of a one-dimensional photonic crystal in the presence of laser radiation (pump) at an adjacent high-frequency transition have been theoretically investigated. It has been shown that there is a pump intensity range where narrow peaks (resonances) simultaneously appear in the transmission and reflection spectra of the probe field. Beyond this region, the peak in the transmission spectrum is transformed to a narrow dip. The spectral position of these peaks is determined by the Raman resonance and the transmittance and reflectance can be larger than unity at pump intensities from several microwatts per square centimeter to several tens of milliwatts per square centimeter. The nature of narrow peaks is due to a sharp dispersion of a nonlinear refractive index near the Raman resonance; this dispersion is responsible for a strong decrease in the group velocity of probe radiation. The proposed scheme makes it possible to obtain controlled ultranarrow resonances in the transmission and reflection spectra of the photonic crystal.

Sensitive temperature sensor based on phase properties of photonic crystal

It is revealed in the present paper that the reflectance around the defect mode of one-dimensional defective photonic crystal (PC) in an asymmetric structure approaches to 1, while the phase-shift depends on the number of the coupled-defect layers, i.e., the phase shift is 2π for every sub-peak of the defect mode. When the defect layer is a temperature sensitive material, very small change of temperature will cause a significant phase change. Secondly, it is demonstrated that the relationship of phase and temperature has a linear range. According to the above characteristics, a highly sensitive temperature sensor is designed based on the phase property of photonic crystal. Moreover, this principle of PC phase sensing can be extended to study other sensors, such as the two-dimensional PC, which is suitable for optical integration.

PROPERTIES OF DEFECT MODES IN ONE-DIMENSIONAL PHOTONIC CRYSTALS

A theoretical analysis of the properties of the defect modes in a one-dimensional defective photonic crystal (PC) is given. Two defective PCs stacked in symmetric and asymmetric geometries are considered. The defect modes are investigated by the calculated wavelength-dependent transmittance for both TE and TM waves. It is found that there exists a single defect mode within the photonic band gap (PBG) in the asymmetric PC. There are, however, two defect modes within the PBG in the symmetric one. The dependences of defect modes on the angle of incidence are illustrated. Additionally, the efiect of defect thickness on the number of defect modes is also examined.

Group index and dispersion properties of photonic crystal waveguides with circular and square air-holes

The slow light and group velocity dispersion properties of 2D triangular lattice photonic crystal line defect waveguide (PCW) with square and circular air-holes are numerically investigated with the plane-wave expansion method. The simulation results show that the guided mode is impacted slightly by the cross section’s shape of the air-holes of the same filling ratio. Adjusting two rows of the inner-hole adjacent to the waveguide and modifying the waveguide width can bring in low-group velocity and low-dispersion (LVLD) region, in which the group index of the square holes can reach 210 which is far better than the circular-holes. At the same air-hole size and waveguide width, the PCW with the square holes can support higher bit rate of the signal up to 35 Gb/s. These results provide important theoretical basis for realizing of optical buffering and optical logic devices in all-optical network.

Applications of Heavy Ion Irradiation in Photonic CrystalResearch

Photonic crystals (PC) have received extensive attention for the photonic band gap (PBG). The polystyrene (PS) particles bottom-up approach is a productive method for photonic crystal manufacture, this kind of photonic crystals having an unique PBG that depends on the particle's shape, sizes and defects. Heavy ion irradiation is a very useful method to induce defects in PC and change the shapes of the particles to tune the PBG. MeV heavy ion irradiation leads to an anisotropic deformation of the particles from spherical to ellipsoidal, the aspect ratio of which can be precisely controlled by using the ion energy and flux. Sub-micrometer PS particles were deposited on a Cu substrate and were irradiated at 230 K by using heavy ion energy and fluence in the range from 2 to 10 MeV and 1 x 10(14) cm(-2) to 1 x 10(15) cm(-2); respectively.

Polarization- and direction-independent defect modes in a wide incident-angle range within Bragg gaps by photonic heterostructures containing negative-index materials

We propose a type of photonic heterostructure by combining dielectric one-dimensional (1D) defective photonic crystals (PCs) and magnetic 1D defective PCs. Both of the two PCs consist of alternating positive-index-material (PIM) layers with a negative-index-material (NIM) defect layer. It is demonstrated by transfer matrix method that there is a polarization- and direction-independent defect mode in a wide incident-angle range within Bragg gaps in the heterostructure. The field distributions prove that the dielectric 1D defective PC benefits to achieve the approximately omnidirectional defect mode for TE waves while the magnetic 1D defective PC benefits for TM waves. Such a structure is useful for designing polarization-independent and omnidirectional or large incident angle narrow-passband filters in optical devices.

Ultranarrow resonance peaks in the transmission and reflection spectra of a photonic crystal cavity with Raman gain

The Raman gain of a probe light in a three-state $\ensuremath{\Lambda}$ scheme placed into a defect of a one-dimensional photonic crystal is studied theoretically. We show that there exists a pump intensity range, where the transmission and reflection spectra of the probe field exhibit simultaneously occurring narrow peaks (resonances) whose position is determined by the Raman resonance. Transmission and reflection coefficients can be larger than unity at pump intensities on the order of tens of $\ensuremath{\mu}\text{W}/{\text{cm}}^{2}$. When the pump intensity is outside this region, the peak in the transmission spectrum turns into a narrow dip. The nature of narrow resonances is attributed to a drastic dispersion of the nonlinear refractive index in the vicinity of the Raman transition, which leads to a significant reduction in the group velocity of the probe wave.

Modal Behavior of Photonic Crystal Tapers for Improved Coupling Toward Cleaved-Facet Single-Mode Fiber

We report simulation and experiment results of modal behaviors of photonic crystal (PhC) tapers on InP-based materials designed to improve coupling efficiency of the PhC waveguide mode into a cleaved-facet single-mode fiber. The modal distributions of transmitted power are simulated by two-dimensional finite difference time domain (2D-FDTD) calculation and the measured far-field patterns are in agreement with these calculations. The 34.4 mum-long PhC taper with Gaussian curve geometry is demonstrated to have an enhancement of coupling efficiency by a factor of four compared to the direct coupling from a W3 PhC defect waveguide.

RESONANT LIGHT SCATTERING AND HIGHER HARMONIC GENERATION BY PERIODIC SUBWAVELENGTH ARRAYS

Scattering of light on periodic subwavelength arrays is studied in the framework of the resonant scattering theory. With various examples of periodic structures it is demonstrated that: (i) an enhanced reflectance or transmittance is associated with the existence of trapped modes (quasi-stationary modes of light confined in the vicinity of the scattering structure); (ii) scattering structures may have trapped modes due to peculiarities their geometry (geometrical modes) and the dispersive properties of their material (material modes); a practical criterion based on the scaling symmetry of Maxwell's equations is proposed to distinguish them; (iii) the trapped mode field can be significantly amplified, as compared to the incident wave amplitude, in some regions of the structure; (iv) the amplification increases with increasing the lifetime of the trapped mode; (v) this effect can be used to enhance nonlinear optical effects (a resonant higher harmonic generation is studied in detail as an example). The theory of coupled resonances is developed and used to prove that there exist bound states of light in the radiation continuum (resonances with the vanishing width) in periodic arrays. The bound states are neither modes in metal cavities nor modes in photonic crystal defects. Structures supporting the bound states of light can be used to enhance and control nonlinear optical effects in subwavelength periodic arrays.

Coupled mode analysis of nonlinear defects in photonic crystals

We present a general analysis of the coupling of nonlinear photonic crystal cavities using coupled-mode theory. The nonlinear transmission properties of two coupled nonlinear cavities have been investigated. We validate the analysis by comparing the theoretical result with rigorous numerical simulations based on finite-difference time-domain techniques. A device consisting of two nonidentical photonic crystal cavities is proposed, by which we demonstrate that this theory can be employed for designing high-contrast all-optical switches or diodes.

Silicon nitride membrane photonics

We propose a concept for realizing large area nanophotonic circuits in a silicon nitride membrane. Light is coupled into the membrane using a novel metallic photonic crystal grating coupler. A coupling loss of 5.5 dB is predicted for TE polarized light at 1550 nm. Waveguiding at telecoms wavelengths is achieved by using low loss photonic crystal defect waveguides. The propagation losses of the photonic crystal waveguides are estimated at 8.6 dB mm−1, comparable to early silicon photonic crystal waveguides. Using the proposed approach, photonic circuits can be fabricated using a single lithography and etching step. Thus the design scheme shows a route to low-cost fabrication.

Five beam holographic lithography for simultaneous fabrication of three dimensional photonic crystal templates and line defects using phase tunable diffractive optical element

This paper demonstrates an approach for laser holographic patterning of three-dimensional photonic lattice structures using a single diffractive optical element. The diffractive optical element is fabricated by recording gratings in a photosensitive polymer using a two-beam interference method and has four diffraction gratings oriented with four-fold symmetry around a central opening. Four first-order diffracted beams from the gratings and one non-diffracted central beam overlap and form a three-dimensional interference pattern. The phase of one side beam is delayed by inserting a thin piece of microscope glass slide into the beam. By rotating the glass slide, thus tuning the phase of the side beam, the five beam interference pattern changes from face-center tetragonal symmetry into diamond-like lattice symmetry with an optimal bandgap. Three-dimensional photonic crystal templates are produced in a photoresist and show the phase tuning effect for bandgap optimization. Furthermore, by integrating an amplitude mask in the central opening, line defects are produced within the photonic crystal template. This paper presents the first experimental demonstration on the holographic fabrication approach of three-dimensional photonic crystal templates with functional defects by a single laser exposure using a single optical element.

Manipulating emission of CdSe/ZnS nanocrystals embedded in synthetic opals

Photonic crystals (PCs) are the object of great interest due to the possibility, for appropriate PCs, to modify and control light propagation and even to influence the emission properties of an emitter, such as its emission diagram and its life time. One of the most common approaches to prepare 3D PCs takes advantage of the spontaneous self-organisation of spherical colloidal particles. Various self-assembly techniques such as sedimentation, convective or Langmuir-Blodgett ones have been studied as they provide a low cost and relatively easy protocol to obtain artificial opals. SiO2 opals exhibit a pseudo-band gap. Nevertheless the coupling of II–VI nanocrystal emitters in such PCs allows one to recognize and study some basic problems. Large opals have been prepared by the sedimentation method and the size of the balls has been adjusted so that the pseudo-band gap of those PCs lies in the same region as the emission band of CdSe/ZnS nanocrystals. Diagrams of radiation and the modification of the spontaneous life time of the embedded nanocrystals will be presented and discussed. Introducing well-defined defects in PCs which are necessary to guide the photons through the crystal remains a hard technological challenge. Several top-down methods have been investigated. We will present different bottom-up routes proposed by different groups to engineer planar defects into colloidal PCs.

Van derWaals enhancement of optical atom potentials via resonant coupling to surface polaritons

Contemporary experiments in cavity quantum electrodynamics (cavity QED) with gas-phase neutral atoms rely increasingly on laser cooling and optical, magneto-optical or magnetostatic trapping methods to provide atomic localization with sub-micron uncertainty. Difficult to achieve in free space, this goal is further frustrated by atom-surface interactions if the desired atomic placement approaches within several hundred nanometers of a solid surface, as can be the case in setups incorporating monolithic dielectric optical resonators such as microspheres, microtoroids, microdisks or photonic crystal defect cavities. Typically in such scenarios, the smallest atom-surface separation at which the van der Waals interaction can be neglected is taken to be the optimal localization point for associated trapping schemes, but this sort of conservative strategy generally compromises the achievable cavity QED coupling strength. Here we suggest a new approach to the design of optical dipole traps for atom confinement near surfaces that exploits strong surface interactions, rather than avoiding them, and present the results of a numerical study based on (39)K atoms and indium tin oxide (ITO). Our theoretical framework points to the possibility of utilizing nanopatterning methods to engineer novel modifications of atom-surface interactions.

High Polarization Single Mode Photonic Crystal Microlaser

Generally, dipole mode is a doubly degenerate mode. Theoretical calculations have indicated that the single dipole mode of two-dimensional photonic crystal single point defect cavity shows high polarization property. We present a structure with elongated lattice, which only supports a single y-dipole mode. With this structure we can eliminate the degeneracy, control the lasing action of the cavity and demonstrate the high polarization property of the single dipole mode. In our experiment, the polarization extinction ratio of the y-dipole mode is as high as 51:1.

Modes of symmetric composite defects in two-dimensional photonic crystals

We consider the modal fields and resonance frequencies of composite defects in two-dimensional photonic crystals (PCs). Using an asymptotic method based on Green's functions, we show that the coupling matrices for the composite defect can be represented as circulant or block-circulant matrices. Using the properties of these matrices, specifically that their eigenvectors are independent of the values of the matrix elements, we obtain modal properties such as dispersion relations, modal cutoff, degeneracy, and symmetry of the mode fields. Using our formulation, we investigate defects arranged on the vertices of regular polygons as well as PC ring resonators with defects arranged on the edges of polygons. Finally, we discuss the impact of band-edge degeneracies on composite-defect modes.

Comprehensive theory of plane-wave expansion based eigenmode method for scattering-matrix analysis of photonic structures

A plane-wave-based eigenmode method for scattering-matrix propagation of waves through layered photonic structures is presented. Mode matching using plane-wave-based eigenmode expansion requires a balance between the number of plane waves for the expansion of fields and the number of modes (number of eigensolutions) for mode matching. A matrix-free Fourier operator can handle the increase in the number of plane waves for large structures independently of the number of eigenmodes needed for the scattering-matrix analysis. A convergence analysis of the reflection and transmission of photonic crystal and photonic crystal defect structures as a function of the number of plane waves and the number of eigenmodes is carried out.