We describe experiments on a quasi-two dimensional (2-D) optical system consisting of a triangular array of air cylinders etched through a laser-like Ga(Al)As waveguiding heterostructure. Such a configuration is shown to yield results very well approximated by the infinite 2-D photonic crystal (PC). We first present a set of measurements of the optical properties (transmission, reflection, and diffraction) of slabs of these photonic crystals, including the case of in-plane Fabry-Perot cavities formed between two such crystals. The measurement method makes use of the guided photoluminescence of embedded quantum wells or InAs quantum dots to generate an internal probe beam. Out-of-plant, scattering losses are evaluated by various means. In a second part, in-plane micrometer-sized photonic boxes bounded by circular trenches or by two-dimensional photonic crystal are probed by exciting spontaneous emission inside them. The high quality factors observed in such photon boxes demonstrate the excellent photon confinement attainable in these systems and allow to access the detail of the modal structure. Last, some perspectives for applications are offered.

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Optical and confinement properties of two-dimensional photonic crystals

We have investigated the fluorescence from R6G dye molecules embedded in fcc photonic crystals with a large range of lattice parameters. Both polystyrene opals and alumina inverse opals are studied, allowing us to compare direct and inverted structures. We observe clear stop bands in the fluorescence spectra, whose center positions, widths, and depths are analyzed and compared to stop bands from reflectivity measurements. In the frequency range of first-order stop gaps, the measured stop band centers and widths agree well with theoretical predictions. The depths are interpreted in terms of the mean free path (disorder) and the Bragg attenuation length (order). We observe intriguing enhanced emission at the blue side of the stop bands, which is attributed to the escape of diffuse light from the photonic crystal (related to both order and disorder). We perform the first experiments in the range of second-order stop gaps, which is the regime where the photonic band gap is anticipated. We observe complex multiple-Bragg features that correlate favorably with reflectivity peaks.

Directional fluorescence spectra of laser dye in opal and inverse opal photonic crystals.

The index of refraction of waveguide structures can be varied by altering carrier concentration. The waveguides preferably comprise semiconductors like silicon that are substantially optically transmissive at certain wavelengths. Variation of the carrier density in these semiconductors may be effectuated by inducing an electric field within the semiconductor for example by apply a voltage to electrodes associated with the semiconductor. Variable control of the index of refraction may be used to implement a variety of functionalites including, but not limited to, tunable waveguide gratings and resonant cavities, switchable couplers, modulators, and optical switches.

Tuning the index of a waveguide structure

Waveguide modes in two-dimensional (2-D) photonic crystals (PhCs) deeply etched through monomode slab waveguides, e.g., AlGaAs/GaAs, GaAs/AlOx, or InP/GaInAsP, suffer from radiation losses that are strongly affected by the air hole depth and shape. The issue of three-dimensional (3-D) out-of-plane losses is addressed analytically by means of an incoherent approximation. Assuming separability both for the dielectric map and for the electric field, this approach is valid for defects such as in-plane microcavities, PhC-based waveguides, bends and couplers. Out-of-plane scattering is translated into an effective imaginary index in the air holes, so that 3-D losses can be cast in a simple 2-D calculation. The case of cylindroconical holes is treated, and the validity of this approach is experimentally confirmed by transmission measurements through simple PhC slabs.

Radiation losses in planar photonic crystals: two- dimensional representation of hole depth and shape by an imaginary dielectric constant

The present I/O ports comprise (1) a layered structure comprising (a) an unpatterned superstrate having at least one layer, (b) an unpatterned substrate having at least one layer, and (c) at least one intermediate layer sandwiched between the unpatterned superstrate and the unpatterned substrate, (2) a coupling region that is within the at least one intermediate layer and that comprises an arrangement of at least one optical scattering element and (3) at least one output waveguide. The present I/O ports can be effectively used in balanced photonic circuits and unbalanced photonic circuits.

Photonic input/output port

We report on the measurement of the diffraction efficiency of two-dimensional photonic-bandgap lattices consisting of a triangular array of circular air holes etched in a semiconductor waveguide. We use the spontaneous emission of the material as an internal point source. Combined with previous reflectivity and transmission measurements, the diffraction data allow us to assess the total amount of out-of-plane losses experienced by a guided wave traversing the dielectric lattice, as a function of the lattice pitch. We found that these losses are particularly weak for some range of parameters, especially in the photonic bandgap of interest. We discuss the reasons why they can be substantial with other parameters.

Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices

We discuss the optical properties of semiconductor microcavities. We introduce to both weak and strong coupling regimes of the light—matter interaction. We discuss in the first part the modifications of the radiative emission rate in the weak coupling regime. In a second part we will give an overview the physics of cavity—polariton features in the strong coupling regime.

C. Weisbuch

Papers

Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices

Physics and devices with semiconductor microcavities