3D Photonic Band Gap Research Articles

Spectroscopic assessment of rare-earth activated planar waveguides and microcavities

This paper deals with glass-based photonic structures, used to control and modify the optical and spectroscopic properties of rare earth ions. The spectroscopic assessment of sol–gel-derived planar waveguides and 1D photonic band gap structures is reported. The spectroscopic, optical, and structural properties of planar waveguides with (100 − x)SiO 2– xHfO 2– yErO 1.5 with y = 0.3, 0.01; and x = 10, 20, 30, 40 have been investigated by photoluminescence and Raman spectroscopy. The radiative quantum efficiency of the 4I 13/2 metastable state of Er 3+ ions is between 84 and 88% depending on the Si/Hf molar ratio. The sol–gel-derived one-dimensional cavity was realized by a Eu 3+-activated dielectric layer placed between distributed Bragg reflectors (DBRs).

Optical properties in 2D photonic crystal structure using fullerene and azafullerene thin films

Theoretical calculations via a transfer matrix method were performed to investigate the possibility of fullerene films acting as two-dimensional (2D) photonic band gap crystals. The response within and out of the periodic structure of 2D photonic crystals consisting of air rods drilled into C60 or (C59N)2 films was studied. PBG was found around 0.85–1.24eV in the near infrared region. We find that fullerene-based networks could be good candidates for absolute inhibition of transmission in the near infrared range for given orientations.

Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules, and simulations

We demonstrate on-chip, single-mode, waveguiding of light in air for a variety of 2D-3D photonic band gap (PBG) heterostructures. These include square spiral, woodpile, slanted pore, and inverse opal three-dimensional (3D) photonic crystals intercalated with a 2D (planar) photonic crystal microchip. Design rules are established to yield maximal single-mode waveguiding bandwidths of up to roughly 180 nanometers centered at a wavelength of 1.5 microns . This can be achieved with 3D PBG materials with gaps as small as 15% of the PBG center frequency. Finite-difference time-domain (FDTD) simulations of light flow in optical mirocircuits within such heterostructures reveal tolerance to layer misalignment and other fabrication-related structural disorder. We provide an interpretation of the universal mechanism for diffractionless light propagation in 2D-3D photonic crystal heterostructures. We demonstrate that planar, on-chip, optical microcircuitry similar to that of two-dimensional (2D) photonic crystals is almost universally achievable within the engineered electromagnetic vacuum of 3D PBG materials.

Optical properties of GaN Photonic Crystal Membrane Nanocavities at Blue Wavelengths

AbstractWe have investigated the design parameters for high-Q photonic-crystal (PC) bandgap modes in the emission wavelengths of InGaN/GaN multiple quantum wells. We demonstrate experimental schemes to realize 2D triangular-lattice PC membrane structures, which is essential to obtain photonic bandgap (PBG) modes, and the optical properties of L7 membrane nanocavities that consist of seven missing holes in the Γ-K direction. L7 cavities show pronounced resonances with Q factors of 300 to 800 in the PBG as well as the enhancement of light extraction of the broad InGaN/GaN multiple-quantum-well emission by the 2D PBG.

Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm

The fabrication and characterization of an all-solid photonic bandgap fiber is reported. The fiber presents a low-loss region (< 20 dB/km) around 1550 nm and can be used as single-mode even for a fiber core diameter as large as 20 microm. The fiber presents a zero dispersion at the short wavelength edge of the bandgap. The measured polarisation mode dispersion is wavelength dependent but remains small (few ps/km1/2). This fiber opens the possibility to realize low-loss large mode area bandgap fiber with a doped core and or Bragg gratings.

Square spiral 3D photonic bandgap crystals at telecommunications frequencies

We present evidence of complete, three-dimensional photonic bandgaps in obliquely deposited thin films with a porous microstructure of tetragonally arranged square spirals. We further present a capability to engineer the bandgap center to wavelengths as low as 1.65 mum, with bandgap widths of up to 10.9%. Using new deposition methods that provide detailed control over the photonic crystal dimensions and morphology, this approach allows advanced photonic crystal architectures to be realized over large scales with uncomplicated fabrication technology.

Theoretical characterization of multilayer photonic crystals having a 2D periodicity

We present a new, very accurate and fast model of photonic bandgap (PBG) structure characterized by a two-dimensional (2D) periodic change of the refractive index and finite height, therefore named quasi 3D PBG. The new model is based on the Floquet–Bloch formalism and allows to find all the propagation characteristics including the space harmonics and the total field distribution, the propagation constants, the guided and radiated power and modal loss induced by the 2D grating. A clear explanation of the physical phenomena occurring when a wave propagates inside the 2D periodic structure is presented, including the photonic bandgap formation and the radiation effects. The approach does not require any theoretical approximation, and can be applied to study rigorously any PBG-based multilayer structures. We have applied the model to investigate several structures for both optical and microwave applications. Copyright © 2005 John Wiley & Sons, Ltd.

Theoretical investigation of the reflectivity of fullerene-(C 60, C 70)/AlN multilayers in UV region

Theoretical calculations via a transfer matrix method (TMM) were performed to investigate the possibility of fullerene/AlN multilayer films acting as one-dimensional (1D) photonic band gap (PBG) crystals. The response within and out of the periodic plane of (C 60, C 70)/AlN multilayers was studied. (C 60, C 70)/AlN multilayer films presented incomplete PBG behavior in UV region. C 60/AlN multilayers with two pairs of 49 nm-C 60 and 21 nm-AlN layers exhibited a high reflectivity of 90.4% at a wavelength of about 200 nm. As a consequence, this photonic crystal may be important for achieving materials with an incomplete band gap in the UV region.

Photonic band gap enhancement in frequency-dependent dielectrics

We illustrate a general technique for evaluating photonic band structures in periodic d -dimensional microstructures in which the dielectric constant epsilon (omega) exhibits rapid variations with frequency omega . This technique involves the evaluation of generalized electromagnetic dispersion surfaces omega ( k--> ,epsilon) in a (d+1) -dimensional space consisting of the physical d -dimensional space of wave vectors k--> and an additional dimension defined by the continuous, independent, variable epsilon . The physical band structure for the photonic crystal is obtained by evaluating the intersection of the generalized dispersion surfaces with the "cutting surface" defined by the function epsilon (omega) . We apply this method to evaluate the band structure of both two- and three-dimensional (3D) periodic microstructures. We consider metallic photonic crystals with free carriers described by a simple Drude conductivity and verify the occurrence of electromagnetic pass bands below the plasma frequency of the bulk metal. We also evaluate the shift of the photonic band structure caused by free carrier injection into semiconductor-based photonic crystals. We apply our method to two models in which epsilon (omega) describes a resonant radiation-matter interaction. In the first model, we consider the addition of independent, resonant oscillators to a photonic crystal with an otherwise frequency-independent dielectric constant. We demonstrate that for an inhomogeneously broadened distribution of resonators impregnated within an inverse opal structure, the full 3D photonic band gap (PBG) can be considerably enhanced. In the second model, we consider a coupled resonant oscillator mode in a photonic crystal. When this mode is an optical phonon, there can be a synergetic interplay between the polaritonic resonance and the geometrical scattering resonances of the structured dielectric, leading to PBG enhancement. A similar effect may arise when resonant atoms that are coupled radiatively through resonance dipole-dipole interaction are placed in a photonic crystal.

Sculpting the vacuum in a photonic band gap micro-chip

We describe the engineering of the electromagnetic vacuum in a 2D–3D photonic bandgap (PBG) hetero-structure. This facilitates the development of novel active devices and the observation of novel quantum electrodynamic phenomena. We consider a specific architecture suitable as an all-optical micro-transistor capable of novel ultra-fast response with low switching power requirements. This relies on a unique collective atomic switching and population inversion achieved by coherent resonant pumping in a suitably engineered vacuum. Specific waveguide architectures within the 3D PBG micro-chip provide local density-of-states (LDOS) peaks near their cutoff frequency. These provide “building blocks” for electromagnetic vacuum engineering without recourse to conventional high Q-factor micro-cavities. For the all-optical micro-transistor, a fork shape LDOS within the micro-chip is desirable, using trimodal waveguide architecture. We delineate the functional robustness of these architectures to disorder caused by manufacturing errors within the PBG micro-chip.

Optical properties of two-dimensional photonic-bandgap crystals characterized by spectral ellipsometry

In this paper, we demonstrate a simple and non-destructive measuring method for both TE and TM bandgaps of two-dimensional (2D) silicon photonic bandgap (PBG) structures by using reflected spectral ellipsometry. Although this method measures the reflected light from samples, the transmitted signal of PBG layer can be measured by using reflecting signals. With large incident angles, planar PBG modulation effects and bandgap information can be obtained. To verify this method, we fabricated silicon arrays for 2D PBG by using electron-beam lithography. From SEM images, we can verify the geometry especially the radius of the cells, which is related to the bandgaps. With a specific set of radii and dielectric constants, we can get the band diagram with plane-wave expansion method. There are several bandgaps of both TE and TM modes, which can be used to detect multiple bandgaps by spectral ellipsometry.

Optical properties of two-dimensional photonic-bandgap crystals characterized by spectral ellipsometry

In this paper, we demonstrate a simple and non-destructive measuring method for both TE and TM bandgaps of two-dimensional (2D) silicon photonic bandgap (PBG) structures by using reflected spectral ellipsometry. Although this method measures the reflected light from samples, the transmitted signal of PBG layer can be measured by using reflecting signals. With large incident angles, planar PBG modulation effects and bandgap information can be obtained. To verify this method, we fabricated silicon arrays for 2D PBG by using electron-beam lithography. From SEM images, we can verify the geometry especially the radius of the cells, which is related to the bandgaps. With a specific set of radii and dielectric constants, we can get the band diagram with plane-wave expansion method. There are several bandgaps of both TE and TM modes, which can be used to detect multiple bandgaps by spectral ellipsometry.

Scaling properties of a tetragonal photonic crystal design having a large complete bandgap

Photonic crystal structures (PCs) of tetragonal lattice type are introduced and studied. They feature complete three-dimensional (3D) photonic bandgaps (PBGs). The PC design is based on two systems of ordered, parallel pores being perpendicular to each other. For increasing pore radii, the pore systems interpenetrate and an inverted woodpile geometry arises. The size of the 3D bandgaps depends on the ratio of the cell parameters L x , L y , and L z , the pore radii and the refractive index of the dielectric material. If realized as a silicon/air structure, the maximum 3D gap is larger than 25%. A possible fabrication route for the near-infrared is based on 2D macroporous silicon where perpendicular pores are drilled, e.g., by focused-ion-beam etching. The dispersion behaviour of the PCs is theoretically analysed (band structures, density-of-states), systematically varying all relevant parameters. The optimization of the PBG sizes as well as a possible tunability of the PBG energies are discussed.

Synthesis and Self-Assembly of Metal-Coated Nanoparticles

AbstractWe report theoretical and experimental studies on the metal-dielectric photonic crystal structure, which is constructed by the self-assembly of metal-coated nanoparticles. The finite- difference time-domain (FDTD) simulations were carried out to predict the width and position of the 3D photonic bandgap. For fabrication, we first prepared gold-embedded silica nanoparticles containing extremely small gold nanoparticles. The core particles are then immersed in a gold- containing solution in which the gold shells were formed by subsequent reduction. Formation of continuous shells was confirmed by scanning electron microscope (SEM) and the optical response due to the surface plasmons. We also performed self-assembly of both the gold- embedded core particles and metal-coated particles. SEM micrographs showed the formation highly ordered structures. The optical reflectance spectra exhibited shifts of the Bragg reflection peak due to the change in refractive index produced by gold nanoparticles.

Arrangements of four beams for any Bravais lattice.

A single geometric model based on a new concept of a reciprocal primitive pyramid (RPP) in reciprocal space is proposed for investigation of relationships between any three-dimensional (3D) lattice and arrangements of four beams (AFBs) that produce the lattice. A ternary linear equation set, described for the one-to-one correspondence between a RPP and AFB, can readily reveal all AFBs for the same lattice (AFBSLs). Quantitative AFBs for bcc and fcc real lattices are illustrated to show that various AFBSLs can modulate the properties of a photonic bandgap (PBG) both by tuning the lattice constant and by changing the lattice-point shape. This fact may yield the appropriate AFB for a complete 3D PBG with the desired center wavelength. The nonuniqueness of AFBSLs can provide abundant choices for persons who plan interference experiments, especially for holographic fabrication of 3D photonic crystals (PCs).

Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups.

The promise of photonic crystals and their potential applications has attracted considerable attention towards the establishment of periodic dielectric structures that in addition to possessing robust complete bandgaps, can be easily fabricated with current techniques. A number of theoretical structures have been proposed. To date, the best complete photonic bandgap structure is that of diamond networks having Fd3m symmetry (2-3 gap). The only other known complete bandgap in a face-centred-cubic (f.c.c.) lattice structure is that of air spheres in a dielectric matrix (8-9 gap; the so called 'inverse-opal' structure). Importantly, there is no systematic approach to discovering champion photonic crystal structures. Here we propose a level-set approach based on crystallography to systematically examine for photonic bandgap structures and illustrate this approach by applying it to the 11 f.c.c. groups. This approach gives us an insight into the effects of symmetry and connectivity. We classify the F-space groups into four fundamental geometries on the basis of the connectivity of high-symmetry Wyckoff sites. Three of the fundamental geometries studied display complete bandgaps--including two: the F-RD structure with Fm3m symmetry and a group 216 structure with F43m symmetry that have not been reported previously. By using this systematic approach we were able to open gaps between the 2-3, 5-6 and 8-9 bands in the f.c.c. systems.

A new compact 1D PBG microstrip structure with wider stopband based on semiconductor substrate

AbstractA new type of compact one dimensional (1D) microstrip photonic bandgap (PBG) used for filters is presented. A semiconductor‐based structure of a miniature band‐stop filter with three cells is simulated, realized, and measured. Basic agreement between the experimental and simulated results have been achieved. The filter with the proposed PBG structure exhibits wide, deep, and steep stop‐band characteristics, and also has less loss and ripples in the pass‐band. Thus, the new PBG structure can be used for low‐pass as well as high‐pass filters. The period of the PBG lattice is about (1/5 ∼ 1/4) λe (λe is the guiding wavelength at the center frequency of the stop‐band), or 0.08 λ0 (λ0 is the wavelength in air). The filter with the new PBG structure is much easier to fabricate and integrate with other circuits and is more compact than conventional filters. The results in our paper are based on semiconductor substrate and can be applied directly in MIC and MMIC. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 150–152, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11153

Proceedings of the 7th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS 7)

The 7th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS 7) was held at the Universität Karlsruhe (TH) from 24–28 February 2003. Topics of NOEKS 7 were: Ultrafast dynamics (coherent effects, coherent control, quantum kinetics, THz-experiments), photonic crystals (2D and 3D photonic band gap materials), quantum dot physics (quantum dots, quantum wires), spin effects (spin dephasing, spin transport), disorder-related effects, organic semiconductors, semiconductor quantum optics (luminescence, photon statistics), device physics (quantum cascade lasers, superlattices, interband lasers), and Bose-Einstein condensation of excitons.

Macroporous-silicon-based three-dimensional photonic crystal with a large complete band gap

A photonic crystal (PC) structure is described revealing a complete three-dimensional (3D) photonic band gap of about 25% if realized as a silicon/air structure. It is based on two systems of parallel circular pores being orthogonal to each other. The gap size depends on the degree of mutual penetration of the pore systems. A possible fabrication route is based on macroporous silicon (lattice constant a=0.5 μm), into which orthogonal pores are drilled, e.g., by focused-ion-beam etching. This yields a 3D photonic crystal with a complete band gap in the near infrared. The dispersion behavior of the PC is theoretically analyzed (band structure, density of states), varying the pore radii. We discuss the influence of pore shape variations and topological modifications on the size of the gap.

Papers presented at the 7th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS 7)

AbstractThe 7th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS 7) was held at Uni‐versit�t Karlsruhe from 24‐28 February 2003. Topics of NOEKS 7 were: Ultrafast dynamics (coherent effects, coherent control, quantum kinetics, THz‐experiments), photonic crystals (2D and 3D photonic band gap materials), quantum dot physics (quantum dots, quantum wires), spin effects (spin dephasing, spin transport), disorder‐related effects, organic semiconductors, semiconductor quantum optics (luminescence, photon statistics), device physics (quantum cascade lasers, superlattices, interband lasers), and Bose‐Einstein condensation of excitons.The cover picture is taken from Ref. [1] and shows the spatial pattern of the indirect exciton PL intensity in GaAs/AlGaAs coupled quantum wells. Around the laser excitation spot, it ex‐hibits an external ring structure with a periodic array of circular‐shaped structures which is due to the formation of an exciton gas with macroscopic coherence.The full proceedings of NOEKS 7, guest‐edited by Martin Wegener, are published in physica status solidi (c) 0, No. 5 (2003). Since 1988, all previous NOEKS proceedings have also appeared in physica status solidi.