Cecile Jamois

Two- and three-dimensional photonic crystals made of macroporous silicon and liquid crystals

Variations of the refractive index can be utilized in order to shift the stop band in periodic structures, such as photonic crystals. We report on investigations about three-dimensional macroporous silicon structures that are filled with a liquid crystal. Fourier transform infrared measurements indicate that a shift of the photonic band edge can be induced by changing the temperature. The director field in macropores within the silicon structure is investigated by 2H-NMR spectroscopy and compared to director field simulations. The latter method indicates a preferred parallel orientation of the director in the nematic state. Based on this finding, we analyze the optical properties.

Tunable defect mode in a three-dimensional photonic crystal

Three-dimensionally periodic structures made of macroporous silicon with varying pore diameter show a photonic stop band in the middle infrared spectral range. A discontinuity of the periodic pore width modulation forms a planar optical resonator with a corresponding transmission peak in the stop band. Infiltration of the porous structure with a nematic liquid crystal and subsequent temperature changing cause a spectral shift of the defect mode. The experimental observations are in good agreement with theoretical calculations.

Silicon-based photonic crystal slabs: two concepts

We compare theoretically two different concepts of vertical light confinement in two-dimensional (2-D) silicon photonic crystals. Light guidance obtained by variation of the refractive index in an SiO/sub 2//Si/SiO/sub 2/ sandwich structure leads to a complete bandgap for all directions and polarizations with a gap-midgap ratio of about 8.5% and a bandgap for even modes only of about 27%. The complete bandgap is 50% smaller than for 2-D photonic crystals due to the lower confinement of light in the high-index material silicon and polarization mixing. Light guidance obtained by a vertical variation of the porosity, i.e., pore radius, leads under optimum conditions to a bandgap for even modes only, with a gap-midgap ratio of about 10%. The feasibility of such a structure is shown for macroporous silicon where the pore diameter can be varied with depth. In both cases, the optimum slab thickness can be approximated by classical waveguide optics, reducing the parameter space for optimization.

Photonic crystal gas sensors

The bandstructure of photonic crystals offers intriguing possibilities for the manipulation of electromagnetic waves. During the last years, research has mainly focussed on the application of these photonic crystal properties in the telecom area. We suggest utilization of photonic crystals for sensor applications such as qualitative and quantitative gas and liquid analysis. Taking advantage of the low group velocity and certain mode distributions for some k-points in the bandstructure of a photonic crystal should enable the realization of very compact sensor devices. We show different device configurations of a photonic crystal based on macroporous silicon that fulfill the demands to serve as a compact gas sensor.

Low Group Velocity Devices in Silicon Photonics

Two possible concepts to slow down the light are discussed: (coupled) cavities in comparison to the concept of low group velocities at flat bands in photonic crystals. Two devices using the second concept are presented.

Periodically arranged point defects in a 2D photonic crystal: the photonic analogue to a doped semiconductor

We present and characterize hexagonal point defects in a two dimensional photonic crystal based on macroporous silicon. These point defects are prepatterned periodically, forming a superstructure within the photonic crystal after electrochemical etching. Spatially resolved, optical investigations related to morphological properties, like defect concentration and pore radius, are compared to bandstructure calculations. The confined defect states are identified and their interaction is evaluated quantitatively.

Two-Dimensional Photonic Crystal Waveguides

In the last decades, a strong effort has been made to investigate and control the optical properties of materials, to confine light in specified areas, to prohibit its propagation, or to allow it to propagate only in certain directions and at certain frequencies. The introduction of components based on total internal reflection for light guidance, such as optical fibers or integrated ridge wave-guides, has already been a revolution in the telecommunication and optical industry. In parallel to that, another way of controlling light based on Bragg diffraction has already been used in many devices like dielectric mirrors. In 1987, the principle of dielectric mirrors leading to one-dimensional light reflection was generalized to two and three dimensions [1,2], founding a new class of materials: photonic crystals. Since then, this new field has gained continuously increasing interest [3]. Photonic crystals (PCs) are materials with a periodic dielectric constant. If the wavelength of light incident on the crystal is of the same order of magnitude as the periodicity, the multiple-scattered waves at the dielectric interfaces interfere, leading to a band structure for photons. If the difference between the dielectric constants of the materials composing the photonic crystal is high enough, a photonic band gap (i.e., a forbidden frequency range in a certain direction for a certain polarization) can occur. However, a complete photonic band gap (i.e., a forbidden frequency range in all directions for all polarizations) can occur only in three-dimensional (3-D) photonic crystals. Although these 3-D photonic crystals look very promising and have been theoretically widely studied, their experimental fabrication is still a challenge [4–7]. Therefore, a strong effort has been invested to study two-dimensional (2-D) photonic crystals, which are much easier to fabricate and which still present most of the interesting properties of their 3-D counterparts. In the ideal case, 2-D photonic crystals are infinitely extended structures with a dielectric constant that is periodic in a plane and homogeneous in the third dimension. However, experimental structures are always finite, leading to scattering losses in the third dimension [8]. More recently, the concept of photonic crystal slabs consisting of a thin 2-D photonic crystal surrounded by a lower-index material has emerged and is now widely studied, because it offers a compromise between two and three dimensions. Indeed, combining the index guiding in the vertical direction with the presence of the photonic crystal in the plane of periodicity, a 3-D control of light can be achieved [9–11]. Among the several interesting effects in photonic crystals that can be used for a multitude of applications, such as modification of spontaneous emission [12, 13] or effects based on the particular dispersion properties like birefringence [14], superprism effect, and negative refraction [15–17], one of the important effects relies on the existence of the band gap for waveguiding purposes. In this chapter, some properties of 2-D photonic crystals are studied, assuming first an infinite height (Section 2) and then a finite one (Section 3). Then, the influence of introducing a line defect into the photonic crystal lattice to build a waveguide is discussed, first in the case of infinite 2-D photonic crystals (Section 4) and finally in photonic crystal slabs (Section 5).

Photonic bandgap waveguide structures

Passive optical components based on high-index materials like silicon are becoming increasingly attractive because they allow dense integration. Photonic crystal waveguides support modes due to Bragg reflections as well as modes due to total internal reflection if the waveguide material is made out of the higher refractive medium. We have studied, based on macroporous silicon, the transmission through a 2D-photonic crystal waveguide. These structures are really two-dimensional since they exhibit aspect ratios of more than 100. Their transmission has strong spectral features, resulting from the coupling of index-guided modes with Bragg-guided modes. If both modes have the same symmetry, they interfere with each other and open up spectral gaps (Ministop bands). Moreover, the Bragg-guided modes can exhibit very small group velocities enabling their use for dispersion compensation or gas sensing devices.

Design of a New Taper for Light Coupling Between a Ridge Waveguide and a Photonic Crystal Waveguide

We propose the design of a new taper to improve light coupling between a photonic-crystalbased W1 waveguide and a ridge waveguide of similar width. The taper design is directly deduced from band structure calculations and allows an adiabatic mode conversion. The comparison between light propagation from the ridge waveguide through the W1 waveguide and through the taper, respectively, shows good improvement of the coupling efficiency.

Interaction of Periodically Arranged Point Defects in a Two Dimensional Photonic Crystal - The Photonic Analogue to a Doped Semiconductor

We present and characterize hexagonal point defects in a two dimensional photonic crystal based on macroporous silicon. These point defects are prepatterned periodically, forming a superstructure within the photonic crystal after electrochemical etching. Spatially resolved, optical investigations related to morphological properties, like defect concentration and pore radius, are compared to bandstructure calculations. The confined defect states are identified and their interaction is evaluated quantitatively.