Kurt Busch

Silicon-Based Photonic Crystals**

In semiconductors electrons propagate in a periodic poten-tial, which originates from the atomic lattice. This modifiesthe dispersion relation of free electrons and a band structurewith a bandgap occurs in the case of semiconductors. Theincorporation of electrically active defects allows the manipu-lation of the electronic properties, which gave birth to a largevariety of electronic devices. There are distinct electrical andelectro-optical properties of the different semiconductormaterials, the dominant and most studied semiconductorbeing silicon.For more than ten years, the optical analogues to electronicsemiconductors, the so-called photonic crystals, have been thesubject of intense international research efforts. Photoniccrystals are materials with a periodically varying index ofrefraction. This allows the control of the propagation of elec-tromagnetic waves, similar to electrons in a semiconductorcrystal. By analogy with semiconductors, the periodicity of theunderlying lattice structure is of the same order of magnitudeas the wavelength of the electromagnetic radiation.Despite the far-reaching analogies between electronicwaves in semiconductors and electromagnetic waves in pho-tonic crystals, there are pronounced differences between thetwo as is noticeable from the corresponding equations of mo-tion. Electrons are described by a scalar wavefield. In con-trast, the electromagnetic field is vectorial by nature. Further-more, the time-independent Schrodinger equation allowssolutions with negative energy eigenvalues, whereas the corre-sponding wave equation in electrodynamics contains only thesquare of the eigenfrequencies, hence negative eigenvaluesare excluded from the outset. It may be inferred from the fewphotonic crystals that appear in nature, in contrast to ubiqui-tous semiconductor materials, that these differences have adisadvantageous effect on the likelihood of the formation ofphotonic bandgaps. From the multitude of the optical phe-nomena only, for example, the colorful speckles of opals, somecrystallites on the wings of butterflies and the spine of the sea-mouse

Macroporous silicon with a complete two‐dimensional photonic band gap centered at 5 μm

We have fabricated a two‐dimensional photonic band structure based on macroporous silicon with a gap common to both polarizations and centered at 5 μm. A triangular lattice of circular air rods with a lattice constant of 2.3 μm was etched 75 μm deep in an n‐type silicon substrate by electrochemical pore formation in hydrofluoric acid. The porous layer was then micromechanically structured in such a way that 200 μm thick free‐standing bars of porous material were left over on the silicon substrate. These bars were then used for measuring the transmission of the photonic lattice. The results showed an excellent agreement with the theoretically calculated structure.

Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations

We fabricate three-dimensional photoresist templates by means of laser holography. In particular, fcc structures are achieved by placing a specially designed “prism” onto the photoresist surface. This solves the problem of previous work, in which the refraction at the air–photoresist interface made it impossible to obtain the required angles of the light wave vectors inside the photoresist. The photoresist templates are characterized by scanning electron microscopy as well as by optical transmission spectroscopy, which agree well with numerical band-structure calculations.

Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter

We report on the fabrication and optical characterization of a three-dimensional (3D) photonic crystal on the basis of macroporous silicon. The structure consists of a 2D array of air pores in silicon whose diameter is varied (modulated) periodically with depth. The bandstructure of the resulting 3D hexagonal photonic crystal is calculated and compared with transmission measurements. The described structure allows to adjust the dispersion relation along the pore axis almost independently from the dispersion relation in the plane perpendicular to the pore axis.

All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures.

We analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. First, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete equations derived using a Greens function method. We find that the discrete nature of the photonic crystal waveguides allows a geometry-driven enhancement of nonlinear effects by shifting the resonator location relative to the waveguide, thus providing an additional control of resonant waveguide transmission and Fano resonances. We further demonstrate that this enhancement may result in the lowering of the bistability threshold and switching power of nonlinear devices by several orders of magnitude. Finally, we show that employing such enhancements is of paramount importance for the design of all-optical devices based on slow-light photonic crystal waveguides.

Second-harmonic generation from split-ring resonators on a GaAs substrate

We study second-harmonic generation from gold split-ring resonators on a crystalline GaAs substrate. By systematically varying the relative orientation of the split-ring resonators with respect to the incident linear polarization of light and the GaAs crystallographic axes, we unambiguously identify a nonlinear contribution that originates specifically from the interplay of the local fields of the split-ring resonators and the bulk GaAs second-order nonlinear-susceptibility tensor. The experimental results are in good agreement with theoretical modeling.

Tunable photonic crystal circuits: concepts and designs based on single-pore infiltration.

We demonstrate that the infiltration of individual pores of certain two-dimensional photonic crystals with liquid crystals and (or) polymers provides an efficient platform for the realization of integrated photonic crystal circuitry. As an illustration of this principle, we present designs for monomode photonic crystal wave-guides and certain functional elements, such as waveguide bends, beam splitters, and waveguide intersections. These devices exhibit very low reflection over broad frequency ranges. In addition, we discuss the inherent tunability of these devices that originates in the tunability of the infiltrated material.

Few-Photon Transport in Low-Dimensional Systems: Interaction-Induced Radiation Trapping

We present a detailed analysis of the dynamics of photon transport in waveguiding systems in the presence of a two-level system. In these systems, quantum interference effects generate a strong effective optical nonlinearity on the few-photon level. We clarify the relevant physical mechanisms through an appropriate quantum many-body approach. Based on this, we demonstrate that a single-particle photon-atom bound state with an energy outside the band can be excited via multiparticle scattering processes. We further show that these trapping effects are robust and, therefore, will be useful for the control of photon entanglement in solid-state based quantum-optical systems.

The Wannier function approach to photonic crystal circuits

We introduce a novel approach to the accurate and efficient calculation of the optical properties of defect structures embedded in photonic crystals (PCs). This approach is based on an expansion of the electromagnetic field into optimally adapted photonic Wannier functions, which leads to effective lattice models of the PC structures. Calculations for eigenmode frequencies of simple and complex cavities as well as the dispersion relations for straight waveguides agree extremely well with the results from numerically exact supercell calculations. Similarly, calculations of the transmission through various waveguiding structures agree very well with the results of corresponding finite-difference time domain simulations. Besides being substantially more efficient than standard simulation tools, the Wannier function approach offers considerable insight into the nature of defect modes in PCs. With this approach, design studies and accurate simulation of optical anisotropic and non-linear defects as well as detailed investigations of disorder effects in higher-dimensional PCs become accessible.

Semiclassical theory of lasing in photonic crystals

We present a theoretical analysis of laser action within the bands of propagating modes of a photonic crystal. Using Bloch functions as carrier waves in conjunction with a multiscale analysis, we derive the generalized Maxwell–Bloch equations for an incoherently pumped atomic system in interaction with the electromagnetic reservoir of a photonic crystal. These general Maxwell–Bloch equations are similar to the conventional semiclassical laser equations but contain effective parameters that depend on the band structure of the linear photonic crystal. Through an investigation of steady-state laser behavior, we show that, near a photonic band edge, the rate of stimulated emission may be enhanced and the internal losses are reduced, which leads to an important lowering of the laser threshold. In addition, we find an increase of the laser output along with an additional narrowing of the linewidth at a photonic band edge.