Two-dimensional Photonic Bandgap Research Articles

Theory of Doppler-free spectroscopy with λ-thick vapor cells

Abstract A simple model of the Voigt spectral profile is employed to analyze the influence of the sizes of a vapor cell on the shape of the spectral contour of the linear susceptibility. The width of a resonant spectral line observed in transmission and absorption spectra measured with such a vapor cell is shown to tend to the natural width as one of the sizes of the vapor cell approaches the wavelength of the spectral line. The possibility of using λ -thick vapor cells, as well as one- and two-dimensional photonic band-gap structures for high resolution measurements is discussed.

Strain-tunable photonic band gap crystals

We have designed a two-dimensional strain-tunable photonic band gap crystal by distorting the symmetry of the crystal from a regular hexagonal to a quasihexagonal lattice by means of field driven strain using a piezoelectric material. Calculations predict that the original high symmetry energy bands split up into several strained energy bands depending on the magnitude and direction of the strain. In the proposed structures, we show that 2% (3%) shear strain can be used to tune ∼52% (73%) of the original undistorted absolute band gap of a two-dimensional photonic band gap crystal. These device structures can be used for optical switching and modulation.

Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study

In the present Letter, surface modes in two-dimensional dielectric and metallic photonic crystals are studied by a finite-difference time-domain method. The existence of surface modes in metallic photonic crystals is examined. The influence of surface waves on dielectric photonic crystal antennas is also studied.

Photonic bandgap structures in planar waveguides.

If a one-dimensional (1D) or two-dimensional (2D) photonic bandgap (PBG) structure is incorporated into a planar optical waveguide, the refractive-index nonuniformity in the direction perpendicular to the waveguide plane responsible for waveguiding may affect its behavior detrimentally. Such influence is demonstrated in the paper by numerical modeling of a deeply etched first-order waveguide Bragg grating. On the basis of physical considerations, a simple condition for the design of 1D and 2D waveguide PBG structures free of this degradation is formulated; it is, in fact the separability condition for the wave equation. Its positive effect is verified by numerical modeling of a modified waveguide Bragg grating that fulfills the separability condition.

Threshold gain and single-mode oscillation of two-dimensional photonic bandgap defect lasers

Defect laser behavior was simulated as a function of various parameters. When the crystal size was increased from 8/spl times/8 to 12/spl times/12 cylinders, the quality factor of the defect cavity increased from 6/spl times/10/sup 3/ to 5/spl times/10/sup 6/ while the threshold gain decreased by two orders of magnitude, It was predicted that a triangular-lattice photonic defect laser would be polarized in the /spl Gamma/-M direction. The defect laser studied usually showed multi-mode oscillation with a large defect radius, where the threshold gain was small. When the refractive indices of the cylinders and the defect, surrounded by air, were both 3.5, single-mode oscillation and a small threshold gain (4 cm/sup -1/) were, nevertheless, achieved at suitable device parameters that made the side-mode suppression ratio sufficiently large at 10/sup 3/. A single-mode oscillation and a small threshold gain (less than 20 cm(/sup -/1)) were also predicted over the entire defect radius range when the defect refractive index was decreased from 3.5 to 1.5.

Trapping and emission of photons by a single defect in a photonic bandgap structure

By introducing artificial defects and/or light-emitters into photonic bandgap structures, it should be possible to manipulate photons. For example, it has been predicted that strong localization (or trapping) of photons should occur in structures with single defects, and that the propagation of photons should be controllable using arrays of defects. But there has been little experimental progress in this regard, with the exception of a laser based on a single-defect photonic crystal. Here we demonstrate photon trapping by a single defect that has been created artificially inside a two-dimensional photonic bandgap structure. Photons propagating through a linear waveguide are trapped by the defect, which then emits them to free space. We envisage that this phenomenon may be used in ultra-small optical devices whose function is to selectively drop (or add) photons with various energies from (or to) optical communication traffic. More generally, our work should facilitate the development of all-optical circuits incorporating photonic bandgap waveguides and resonators.

Modified spontaneous emission from a two-dimensional photonic bandgap crystal slab

A two-dimensional photonic crystal patterned into a thin dielectric slab waveguide is shown to alter drastically the lifetime of spontaneous emission as well as the radiation pattern. This means that although the light extraction efficiency can be greatly enhanced, inhibited spontaneous emission within the photonic bandgap can result in low power output from such a structure. Strongly inhibited emission is found within the photonic bandgap as well as enhanced emission into the conduction band modes for certain geometries. Coupled with enhanced extraction efficiency in the photonic conduction band, this results in the possibility of a structure with increased total power efficiency.

Towards two-dimensional complete photonic bandgap structures below infrared wavelengths

Bandgaps in two- and three-dimensional photonic crystals are hard to achieve due to the limited contrast in the dielectric permeability available with conventional dielectric materials. The situation changes for periodic arrangements of scatterers consisting of materials with a Drude-like behaviour of the dielectric function. We show for two-dimensional square and triangular lattices that such systems have in-plane complete photonic bandgaps (CPBGs) below infrared wavelengths. Of the two geometries, the optimal one for ideal Drude-like behaviour is a square lattice, whereas for Drude-like behaviour in silver, using experimental data (Palik E D 1991 Handbook of Optical Constants of Solids vol 1 (San Diego: Academic)), the optimal geometry is a triangular lattice. If the lattice spacing is tuned to a characteristic plasma wavelength, several CPBGs open in the spectrum and their relative gap width can be as large as 36.9% (9.9% in a nonabsorptive window) even if the host dielectric constant eh = 1. Such structures can provide CPBG structures with bandgaps down to ultraviolet wavelengths.

Two-dimensional Kagome photonic bandgap waveguide

The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes is investigated with respect to the width of the 2D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out.

Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 μm

Thermally and mechanically dependable two-dimensional (2D) photonic band gap lasers are proposed and realized at room temperature. The thin slab photonic band gap laser structure is sandwiched between air and a drilled aluminum oxide layer provided by wafer fusion techniques. In this thin slab structure, the optical confinement of photons is achieved by 2D triangular photonic lattice in horizontal plane and total internal reflection in vertical direction. Pulsed lasing action is observed at 1.54 μm by optical pumping with duty cycle up to 10%. Polarization characteristics of two-dimensional photonic band gap defect modes are also studied below and above the lasing threshold.

Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials

By using two ab initio numerical methods we study the effects that disorder has on the spectral gaps and on wave localization in two-dimensional photonic band gap materials. We find that there are basically two different responses depending on the lattice realization (solid dielectric cylinders in air or vise versa), the wave polarization, and the particular form under which disorder is introduced. Two different pictures for the photonic states are employed, the ``nearly free'' photon and the ``strongly localized'' photon. These originate from the two different mechanisms responsible for the formation of the spectral gaps, ie. multiple scattering and single scatterer resonances, and they qualitatively explain our results.

Emission properties of a defect cavity in a two-dimensional photonic bandgap crystal slab

A single isolated defect within a two-dimensional photonic crystal semiconductor slab is shown to provide a lithographically tunable doubly degenerate emission resonance within the photonic bandgap, with a measured quality factor (Q) of 80–150, depending on the cavity geometry. Spontaneous emission outside the cavity linewidth is below the measurement limit of our system. Stimulated emission from this photonic crystal defect cavity is demonstrated at room temperature under pulsed optical pumping in spite of the large surface-to-volume ratio of this cavity and the associated large nonradiative surface recombination rate.

Photonic Crystal Nanocavity Lasers

When combined with high index constrast slabs in which light can be efficiently guided, microfabricated two-dimensional photonic bandgap mirrors provide us with the geometries needed to confine light into extremely small volumes. We show that these high Q cavities now make it possible to define microcavity lasers which function at room temperature and have mode volumes as small as 2.5 (λ/2nslab)3 or 0.03 μm3 in InGaAsP emitting at 1.55μm.

PHOTONIC CRYSTAL NANOCAVITY LASERS

When combined with high index constrast slabs in which light can be efficiently guided, microfabricated two-dimensional photonic bandgap mirrors provide us with the geometries needed to confine light into extremely small volumes. We show that these high Q cavities now make it possible to define microcavity lasers which function at room temperature and have mode volumes as small as 2.5 (λ/2nslab)3 or 0.03 μm3 in InGaAsP emitting at 1.55μm.

Photonic Crystal Nanocavity Lasers

When combined with high index contrast slabs in which light can be efficiently guided, microfabricated two-dimensional photonic bandgap mirrors provide us with the geometries needed to confine light into extremely small volumes. We show that these high Q cavities now make it possible to define microcavity lasers which function at room temperature and have mode volumes as small as 2.5 (X/2nsiab)3, or 0.03 urn3 in InGaAsP emitting at 1.55 u,m.

Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching

Fabrication process for sharp waveguide bends in a two-dimensional photonic band gap structure in silicon is developed. The waveguide bend is defined by removing a row of pillars in a two-dimensional photonic crystal of 5 μm long, 205 nm diameter pillars placed on a square lattice with a pitch of 570 nm. To meet the severe nanotolerance requirements in such a device the SF6/O2 electron cyclotron resonance plasma process at reduced temperature is tailored to extreme profile control. The impact of main plasma parameters—i.e., temperature, oxygen/fluorine content, and ion energy—on the sidewall passivation process is unraveled in detail. Crystallographic orientation preference in the etch rate is observed.

Spontaneous emission rate of an electric dipole in a general microcavity

A simple method to obtain the spontaneous emission rate of a dipole placed in a general microcavity is proposed and demonstrated. In our approach, Maxwell's equations are solved directly in real space instead of k space by the finite-difference time-domain method with a free-space boundary condition. It is advantageous that allowed eigenmodes need not be calculated and the total radiation rates to all the allowed modes are obtained from the beginning. All the localized modes, guided modes, and extended modes are inherently included in this formulation. The validity of the method is tested for a dipole placed in an ideal planar microcavity and the calculated results agree well with the closed-form analytic solutions. The enhancement and the inhibition of the spontaneous emission rate in several photonic band-gap structures are studied. Point dipole analyses show three-dimensional effects in two-dimensional in-plane photonic band gaps and the effects of localized, guided and extended modes on radiation rates.

Improved 2-D photonic bandgap structures in microstrip technology

By using tapering techniques in recently proposed two-dimensional (2-D) photonic bandgap (PBG) structures for microstrip lines, a great improvement in the sidelobe level of the frequency response is achieved. Simulations have been performed by using HPTM Momentum and, in accordance with the measurements, give promising potential for these structures. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 207–211, 1999

Measurement of spontaneous emission from a two-dimensional photonic band gap defined microcavity at near-infrared wavelengths

An active, photonic band gap-based microcavity emitter in the near infrared is demonstrated. We present direct measurement of the spontaneous emission power and spectrum from a microcavity formed using a two-dimensional photonic band gap structure in a half wavelength thick slab waveguide. The appearance of cavity resonance peaks in the spectrum correspond to the photonic band gap energy. For detuned band gaps, no resonances are observed. For devices with correctly tuned band gaps, a two-time enhancement of the extraction efficiency was demonstrated compared to detuned band gaps and unpatterned material.

Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems

It has recently been demonstrated that two-dimensional photonic band gaps can be realized in systems comprising of a quasiperiodic arrangement of dielectric cylinders. We show that waveguides crafted out of such photonic ``quasicrystals'' can be used to guide light around sharp corners, just as in the case of periodic photonic band-gap systems, but the quasiperiodic systems tend to be more frequency selective. Because of the absence of translational symmetry, these quasiperiodic photonic band-gap structures also display richer defect properties. Spectral gaps for both the TM and TE polarizations in the same frequency range can be realized in metallodielectric configurations.