Three-dimensional Photonic Band Gap Crystals Research Articles

Three-dimensional photonic bandgap crystals of titania hollow spheres at visible wavelengths

A non-close-packed three-dimensional photonic crystal of titania hollow spheres has been fabricated. The fabricated process is based on the silica template technique, thermal sintering, and the sol–gel process. The band-structure calculations and optical measurements both indicate that a quasi-full three-dimensional photonic bandgap located at the visible wavelength has been presented between the eighth and ninth bands. This indicates that the non-close-packed structure of titania hollow spheres was easier to open the complete photonic bandgaps than other face-centered cubic structures made by self-assembling methods at the visible region.

Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals

We present ultrafast optical switching experiments on three-dimensional photonic band gap crystals. Switching the Si inverse opal is achieved by optically exciting free carriers by a two-photon process. We probe reflectivity in the frequency range of second order Bragg diffraction where the photonic band gap is predicted. We find good experimental switching conditions for free-carrier plasma frequencies between 0.3 and 0.7 times the optical frequency ω: we thus observe a large frequency shift of up to Δω∕ω=1.5% of all spectral features including the peak that corresponds to the photonic band gap. We deduce a corresponding large refractive index change of ΔnSi′∕nSi′=2.0%, where nSi′ is the refractive index of the silicon backbone of the crystal. The induced absorption length is longer than the sample thickness. We observe a fast decay time of 21 ps, which implies that switching could potentially be repeated at GHz rates. Such a high switching rate is relevant to future switching and modulation applications.

Diffraction in crystalline colloidal-array photonic crystals.

We characterized the diffraction and crystal structure of a crystalline colloidal array (CCA) photonic crystal composed of 270 nm diameter polystyrene spheres which have a nearest neighbor spacing of approximately 540 nm. This CCA diffracts light in first order at approximately 1200 nm and shows strong diffraction in the visible spectral region from higher order planes. We quantitatively examined the relative diffraction intensities of the putative fcc (111), (200), (220), and (311) planes. Comparing these intensities to those calculated theoretically we find that the crystal structure is fcc with significant stacking faults. Essentially, no light transmits at the Bragg angle for the fcc (111) planes even through thin approximately 40 microm thick CCA. However, much of this light is diffusely scattered about the Bragg angle due to crystal imperfections. Significant transmission occurs from thin samples oriented at the Bragg condition for the fcc (200), (220), and (311) planes. We also observe moderately intense two-dimensional diffraction from the first few layers at the crystal surfaces. We also examined the sample thickness dependence of diffraction from CCA photonic crystals prepared from approximately 120 nm polystyrene spheres whose fcc (111) planes diffract in the visible spectral region. These experimental observations, aided by calculations based upon a simple but flexible model of light scattering from an arbitrary collection of colloidal spheres, make clear that fabrication of three-dimensional photonic band gap crystals will be challenged by crystal imperfections.

Exceptionally directional sources with photonic-bandgap crystals

Three-dimensional photonic-bandgap crystals are used to design and fabricate uniquely directional sources and receivers. By utilizing the resonances of a Fabry–Perot cavity formed with photonic-bandgap crystals, we were able to create exceptionally directional sources by placing the sources within such a cavity. Very good agreement between finite-difference time-domain calculations and the experiment is obtained. Radiation patterns with half-power beam widths of less than 12 degrees were obtained.

Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals.

We present a blueprint for a three-dimensional photonic band gap (PBG) material that is amenable to large-scale microfabrication on the optical scale using glancing angle deposition methods. The proposed chiral crystal consists of square spiral posts on a tetragonal lattice. In the case of silicon posts in air (direct structure), the full PBG can be as large as 15% of the gap center frequency, whereas for air posts in a silicon background (inverted structure) the maximum PBG is 24% of the center frequency. This PBG occurs between the fourth and fifth bands of the photon dispersion relation and is very robust to variations (disorder) in the geometrical parameters of the crystal.

Full three-dimensional photonic bandgap crystals at near-infrared wavelengths

An artificial crystal structure has been fabricated exhibiting a full three-dimensional photonic bandgap effect at optical communication wavelengths. The photonic crystal was constructed by stacking 0.7-micrometer period semiconductor stripes with the accuracy of 30 nanometers by advanced wafer-fusion technique. A bandgap effect of more than 40 decibels (which corresponds to 99.99% reflection) was successfully achieved. The result encourages us to create an ultra-small optical integrated circuit including a three-dimensional photonic crystal waveguide with a sharp bend.

Interleaving two-dimensional lattices to create three-dimensional photonic bandgap structures

A two-dimensional lattice consists of an inhomogeneous dielectric medium which has periodic variations of permittivity along two linear directions, and is uniform in the third dimension. The paper considers a class of three-dimensional photonic band gap materials formed by the interleaving of a pair of two-dimensional lattices whose uniform directions are mutually orthogonal, the so-called 'woodpile' geometry. It is shown by numerical calculations that the strong polarisation discrimination exhibited by the constituent two-dimensional sublattices in their respective stopbands leads to a completely three-dimensional photonic bandgap crystal in all polarisations when the two sublattices are interleaved. For a general class of such synthetic crystals having arbitrary two-dimensional distributions in the sublattices, many properties of the three-dimensional interleaved crystal can be predicted directly from a knowledge of the properties of the sublattices, thereby radically reducing the computational cost of their determination.

Resonant cavity enhanced detectors embedded in photonic crystals

We report a resonant cavity enhanced (RCE) detector built around a three-dimensional photonic band gap crystal. The RCE detector was built by placing a monopole antenna within the localized modes of planar and boxlike defect structures. The enhanced electric field around these defect structures were then measured by a microwave detector and a network analyzer. We measured a power enhancement factor of 3450 for planar cavity structures. A Fabry–Perot cavity model was used to understand and predict resonant cavity enhancement in this structure. The tuning bandwidth of the RCE detector extends from 10.5 to 12.8 GHz, which corresponds to the full photonic band gap by the crystal. These RCE detectors have increased sensitivity and efficiency when compared to conventional detectors, and can be used for various applications.

Terahertz spectroscopy of three-dimensional photonic band-gap crystals

We have fabricated and built three-dimensional photonic band-gap crystals with band-gap frequencies larger than 500 GHz. We built the crystals by stacking micromachined (110) silicon wafers. The transmission and dispersion characteristics of the structures were measured by an all-electronic terahertz spectroscopy setup. The experimental results were in good agreement with theoretical calculations. To our knowledge, our new crystal has the highest reported photonic band-gap frequency.