Experimental observation of superluminal group velocities in bulk two-dimensional photonic bandgap crystals

The authors have experimentally observed superluminal, negative, and infinite group velocities in bulk hexagonal two-dimensional photonic bandgap crystals with bandgaps in the microwave region. The group velocities depend on the polarization of the incident radiation and the air-filling fraction of the crystal.     

Notes on waves with negative phase velocity

Negative refraction is a wave phenomenon beyond geometrical optics - it depends on the way waves behave when their phase velocity reaches a zero. Various forms of linear wave processes in media can be concisely described in one wave equation that is inspired by the interpretation of a medium as an effective space-time geometry. Depending on the conformal factor of the effective metric, the waves may show positive or negative refraction. For electromagnetic waves in two-dimensional dielectrics the conformal factor corresponds to the impedance.     

Superluminal pulse propagation in linear and nonlinear photonic grating structures

Optical pulse propagation in photonic grating structures can show anomalous (i.e., superluminal or negative) group velocities under certain circumstances owing to the anomalous dispersive properties induced by the periodic grating structure. Such phenomena can be observed for either linear pulse propagation in passive dielectric grating structures, such as in fiber Bragg gratings (FBGs), as well as in frequency-conversion processes exploiting second-order cascading effects in quasi-phase-matched (QPM) nonlinear crystals. Engineering of the grating structure can be exploited to observe a wide variety of anomalous pulse transmission and reflection behaviors. In this article, we review the main recent experimental and theoretical achievements obtained by our group in this field. In particular, we report on superluminal propagation of picosecond optical pulses at the 1.5-/spl mu/m wavelength of optical communications in FBGs, both in transmission and reflection configurations, with the observation of group velocities as large as /spl sim/5c/sub 0/. We also show that the phenomenon of transparent pulse propagation at a negative group velocity in a gain doublet atomic amplifier, recently observed in cesium vapor by Wang and co-workers (L. J. Wang, A. Kuzmich, and A. Dogariu, Nature vol.406, p.277-9, 2000), can be achieved as well in a photonic parametric amplifier by exploiting the anomalous dispersive properties of the amplifier induced by a suitably designed QPM grating profile.     

Wave propagation through a photonic crystal in a negative phase refractive-index region

The wave propagation through a photonic crystal with a triangular lattice of air holes realized in the InP-InGaAsP heterostructure are studied theoretically for the transverse magnetic modes. The photonic crystal possesses a negative refractive index, and the self-focus of the beam is successfully observed. The weak side beams are observed due to high-order Bloch waves in the photonic crystal. The coupling efficiency for the outgoing waves to a waveguide is also studied.     

Numerical study of the effect of defect layer on unmagnetized plasma photonic crystals

In this paper an explicit finite-difference time domain scheme developed in staggered grids is used to solve the Maxwell’s equations in Drude medium. Besides the preservation of discrete zero-divergence condition in electric and magnetic fields, we also aim to conserve the inherent conservation laws in simple medium all the time using the temporally second-order accurate explicit symplectic partitioned Runge-Kutta scheme. Within the framework of a semidiscretized method, the first-order spatial derivative terms in Faraday’s and Ampère’s equations are approximated to get an accurate numerical dispersion relation equation. The derived numerical angular frequency is accurately related to the wavenumber of Maxwell’s equations for the space centered scheme of fourth-order accuracy. The resulting symplectic finite difference scheme developed in the time domain minimizes the difference between the exact and numerical group velocities. This newly proposed scheme is applied to model EM waves in the unmagnetized plasma crystal which contains a defect layer in photonic crystal. Our purpose is to numerically study the effects of defect layers on the propagation insight.     

Analysis of band gap of non-bravais lattice photonic crystal fiber

This article designs a novel type of non-bravais lattice photonic crystal fiber. To form the nesting complexperiod with positive and negative refractive index materials respectively, a cylinder with the same radius and negative refractive index is introduced into the center of each lattice unit cell in the traditional square lattice air-holes photonic crystal fiber. The photonic band-gap of the photonic crystal fiber is calculated numerically by the plane wave expansion method. The result shows that compared with the traditional square photonic band-gap fiber (PBGF), when R/Λ is 0.35, the refractive index of the substrate, airhole, and medium-column are 1.30, 1.0, and −1:0, respectively. This new PBGF can transmit signal by the photonic band-gap effect. When the lattice constant Λ varies from 1:5 μm to 3:0 μm, the range of the wavelength ranges from 880 nm to 2300 nm. __________ Translated from Optoelectronic Technology, 2007, 27(4): 257–260 [译自: 光电子技术]     

Light localizations in photonic crystal line defect waveguides

In this paper, we discuss unique light localizations in photonic crystal line defect waveguides based on two different concepts. The first concept is an additional defect doping that breaks the symmetry of the line defect. Even though such a defect is open to the line defect, the optical field is well confined around the defect at cutoff frequencies of the line defect. This expands the design flexibility of microcavities and allows effective mode controls such as the single-mode operation. The lasing action of such cavities in a GaInAsP photonic crystal slab was experimentally observed by photopumping at room temperature. The second concept is a chirping of the waveguide structure. The photonic band of a waveguide mode has a band edge, at which the group velocity becomes zero. The band-edge condition shifts in a chirped line defect waveguide, so guided light reaches a zero group velocity point and is localized. A macroscopic behavior of this phenomenon was experimentally observed in a waveguide fabricated into a silicon-on-insulator substrate. In addition, a microscopic behavior was theoretically investigated, which suggested its applicability to a group delay device.     

InP bonded membrane photonics components and circuits: toward 2.5 dimensional micro-nano-photonics

The general objective of this presentation is to demonstrate the great potential of III-V semiconductor -membrane photonic devices, with a special emphasis on InP and related materials in the prospect of new developments in the field of micro-nano-photonics. Various classes devices will be presented, which will have the communality of being based on the use of high index contrast structuration of semiconductor materials. The structuration is achieved vertically for the first class, by forming thin semiconductor membranes surrounded by low optical index material, or laterally for the second class via a two-dimensional (2-D) lateral structuration of the membranes (thus, resulting in 2-D photonic crystal (PC) structures); both structurations are also combined, according to a "2.5-dimensional" approach, which should broaden considerably the combinations of functionality beyond those presently contemplated with the two first classes. The general technological scheme of the membrane approach is fully compatible with planar technology which is widely in use in the world of silicon microelectronics and with heterogeneous integration of III-V active microphotonic devices with silicon microphotonics and microelectronics (e.g., molecular bonding of InP active membranes on silica on silicon substrate). A variety of devices will be presented, featuring micro-lasers based on 2-D PC micro-cavities as well as on 2-D Bloch modes (2-D distributed-feed-back micro-laser) for in plane and surface emission.     

Self-collimation in planar photonic crystals

We analyze, in three dimensions, the dispersion properties of dielectric slabs perforated with two-dimensional photonic crystals (PCs) of square symmetry. The band diagrams are calculated for all k-vectors in the first Brillouin zone, and not only along the characteristic high-symmetry directions. We have analyzed the equal-frequency contours of the first two bands, and we found that the square lattice planar photonic crystal is a good candidate for the self-collimation of light beams. We map out the group velocities for the second band of a square lattice planar PC and show that the group velocity is the highest in the region of maximum self-collimation. Such a self-collimated beam is predicted to show beating patterns due to the specific shape of the equal-frequency contours. A geometrical transformation maps the region of the first and second photonic bands where self-collimation takes place one onto the other and gives additional insights on the structural similarities of self-collimation in those two bands.     

Two-dimensional photonic crystal semiconductor lasers: computational design, fabrication, and characterization

We have designed, fabricated, and tested two-dimensional (2-D) slab photonic crystal semiconductor lasers at communication wavelengths. Wavelength-size microresonators defined on the 2-D slab photonic crystal have been effective in photon confinement and functioned well as ultra-small lasers by optical pumping. The photonic crystal laser structures that we have tested have shown large quality factors and low thresholds.     

Physical Mechanism of p-i-n-Diode-Based Photonic Crystal Silicon Electrooptic Modulators for Gigahertz Operation

In this paper, the physical mechanism governing the optical modulation in a p-i-n-diode-embedded photonic crystal (PC) silicon Mach-Zehnder interferometer modulator is examined. Optical simulations have been performed to study how the slow group velocity of the photonic crystal waveguides enables a significant reduction of device size. The theoretical speed limitation in a PC-based silicon modulator is also explored. The 2-D semiconductor device simulator MEDICI has been employed to analyze the transient behavior of the p-i-n-diode-embedded silicon modulator. Electrical simulations have revealed a significant improvement in modulation speed upon the enhancement of current density in a downscaled PC device. High-speed optical modulation at 1 Gmiddots^-1 has been experimentally demonstrated. The performance degradation in optical modulation at the low-frequency operation region attributed to the thermooptic effect is identified and discussed. Simulations have also revealed that the modulation speed of our device can be improved up to 10 GHz by further reducing the device dimensions with little penalty of the increased optical loss.     

On the localized superluminal solutions to the Maxwell equations

The various experimental sectors of physics in which superluminal motions seem to appear are briefly mentioned. In particular, a bird's-eye view is presented of the experiments with evanescent waves (and/or tunneling photons) and with the "localized superluminal solutions" (SLS) to the wave equation, like the so-called X-shaped beams. The authors also present a series of new SLSs to the Maxwell equations, suitable for arbitrary frequencies and arbitrary bandwidths, some of them endowed with finite total energy. Among the others, the authors set forth an infinite family of generalizations of the classical X-shaped wave and show how to deal with the case of a dispersive medium. Results of this kind may find application in other fields in which an essential role is played by a wave equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.).     

Wide Range Tuning of Slow Light Pulse in SOI Photonic Crystal Coupled Waveguide via Folded Chirping

In this paper, we demonstrate state-of-the-art slow light in silicon-on-insulator photonic crystal coupled waveguide, which allows slow light pulse transmission and its tunable delay by means of structural chirping. The key idea of this study is the application of a folded chirping profile to the structure, instead of the conventional monotonous chirping. It suppresses unwanted spectral oscillation caused by structural disordering and expands the tuning range. By postprocessing an airhole-diameter-chirped device, we show that 0.9-ps-wide slow light pulses are delayed for 72 ps, corresponding to a buffering capacity of 80 bits. In a separate, unchirped device, we demonstrate a tunable delay by applying thermally induced index chirping. Here, a maximum tuning range of 103 ps and a tunable capacity of 22 bits are obtained.      

Femtosecond optical pulse generation using quasi-velocity-matchedelectrooptic phase modulator

Ultrashort optical pulses in the femtosecond range were generated from a continuous-wave (CW) narrow linewidth laser by using the chirping compression method with a highly efficient electrooptic phase modulator. Before the femtosecond pulse generation, a high modulation index electrooptic modulator specially designed was fabricated by employing the quasi-velocity-matching. In the pulse generation experiment, the electrooptic modulator and a grating pair as a negative group delay dispersion element were used for a 514.5-nm CW Ar laser. As a result, the sideband spectrum of 2.0 THz full-width half-maximum (FWHM) was produced and 560-fs optical pulses with 16.25-GHz repetition rate was successfully obtained. For this electrooptic pulse compression method is applicable to the negative group delay dispersion element as well as the positive group delay dispersion     

A brief intro to metamaterials

Metamaterials are new artificial materials with unusual electromagnetic properties that are not found in naturally occurring materials. All "natural" materials such as glass, diamond and such have positive electrical permittivity, magnetic permeability and an index of refraction. In these new artificially fabricated materials - termed as negative index materials (NIM) or double negative (ONG) media or left handed (LH) materials or backward wave (BW) media - all these material parameters are negative. With these unusual material parameters, new kinds of miniaturized antennas and microwave components/devices can be created for the wireless communications and the defense industries. The electrical permittivity and the magnetic permeability are the main determinants of a material's response to electromagnetic (EM) waves. In metamaterials, both these material parameters are negative. Correspondingly, the refractive index of the metamaterials is also negative. Another strange property of metamaterials is its reverse Doppler effect.     

Templating and Replication of Spiral Photonic Crystals for Silicon Photonics

This paper describes femtosecond laser lithography of 3-D photonic crystal templates in commercial photoresist SU-8 and replication of these templates with silicon. Using this approach, silicon-based photonic crystals having 3-D square spiral architecture and exhibiting photonic stop gaps near the 2.5- mum wavelength were fabricated. Possibilities to use a multiple-beam interference technique for two-photon absorption templating of photonic crystals are explored.     

High-Power Low-Beam Divergence Edge-Emitting Semiconductor Lasers with 1- and 2-D Photonic Bandgap Crystal Waveguide

We report on edge-emitting lasers based on the 1- and 2-D longitudinal photonic bandgap crystal concept. The longitudinal photonic bandgap crystal (PBC) design allows a robust and controllable extension of the fundamental mode over a thick multilayer waveguide to obtain a very large vertical mode spot size and a narrow vertical beam divergence.     

Focused ion beam nanopatterning for optoelectronic device fabrication

Recent photonic device structures, including distributed Bragg reflectors (DBRs), one-dimensional (1-D) or two-dimensional (2-D) photonic crystals, and surface plasmon devices, often require nanoscale lithography techniques for their device fabrication. Focused ion beam (FIB) etching has been used as a nanolithographic tool for the creation of these nanostructures. We report the use of FIB etching as a lithographic tool that enables sub-100-nm resolution. The FIB patterning of nanoscale holes on an epitaxially grown GaAs layer is characterized. To eliminate redeposition of sputtered materials during FIB patterning, we have developed a process using a dielectric mask and subsequent dry etching. This approach creates patterns with vertical and smooth sidewalls. A thin titanium layer can be deposited on the dielectric layer to avoid surface charging effects during the FIB process. This FIB nanopatterning technique can be applied to fabricate optoelectronic devices, and we show examples of 1-D gratings in optical fibers for sensing applications, photonic crystal vertical cavity lasers, and photonic crystal defect lasers.     

A simple demonstration of numerical dispersion under FDTD [for EMfield calculations]

The method of finite differences in the time domain (FDTD) has become of growing importance for solving electromagnetic problems due to its simplicity, versatility and the available of inexpensive and powerful computers. In this work, the authors try to demonstrate in an understandable way the characteristic of numerical dispersion of the algorithm. For this purpose, they simulate the one-dimensional propagation of different wave shapes under FDTD. In order to enhance the fact that the dispersion arises as a consequence of the different phase and group velocities for monochromatic waves, they decompose the signals into spectral components and, after propagation at the phase speed given by FDTD, they reconstruct the signals. This computation gives the same results as FDTD. Finally, they compute the propagation assuming that the phase speed its truly the speed in vacuum. In this case, no dispersion its observed at all     

The effect of media parameters on wave propagation in a chiral metamaterials slab using FDTD

Because the permittivity, permeability, and chirality parameters of chiral metamaterials (CMMs) are frequency dependent, the wave equations that describe the characters of electromagnetic wave propagation in CMMs are presented and discretized on the basis of auxiliary differential equation technique in finite‐difference time‐domain method. The total‐field/scattered‐field, Mur's first‐order absorbing and dielectric boundary conditions for CMMs slab are discussed in the paper. Numerical results show that the cross‐polarized reflected coefficient of the CMMs slab is zero. Negative index of refraction phenomenon and optical property of giant optical activity in CMMs slabs are illustrated with 1D auxiliary differential equation–finite‐difference time‐domain method. The effects to positive or negative phase velocity caused by media parameters of CMMs are studied. Copyright © 2013 John Wiley & Sons, Ltd.