Photonic Crystal Nanobeam Cavity Strongly Coupled to the Feeding Waveguide

A deterministic design of an ultrahigh Q, wavelength scale mode volume photonic crystal nanobeam cavity is proposed and experimentally demonstrated. Using this approach, cavities with Q>10^6 and on-resonance transmission T>90% are designed. The devices fabricated in Si and capped with low-index polymer, have Q=80,000 and T=73%. This is, to the best of our knowledge, the highest transmission measured in deterministically designed, wavelength scale high Q cavities

Radiation pattern of a classical dipole in a photonic crystal: photon focusing

The asymptotic analysis of the radiation pattern of a classical dipole in a photonic crystal possessing an incomplete photonic bandgap is presented. The far-field radiation pattern demonstrates a strong modification with respect to the dipole radiation pattern in vacuum. Radiated power is suppressed in the direction of the spatial stopband and strongly enhanced in the direction of the group velocity, which is stationary with respect to a small variation of the wave vector. An effect of radiated power enhancement is explained in terms of \emph{photon focusing}. Numerical example is given for a square-lattice two-dimensional photonic crystal. Predictions of asymptotic analysis are substantiated with finite-difference time-domain calculations, revealing a reasonable agreement.Comment: Submitted to Phys. Rev.

Radiation from elementary sources in a uniaxial wire medium

We investigate the radiation properties of two types of elementary sources embedded in a uniaxial wire medium: a short dipole parallel to the wires and a lumped voltage source connected across a gap in a generic metallic wire. It is demonstrated that the radiation pattern of these elementary sources have quite anomalous and unusual properties. Specifically, the radiation pattern of a short vertical dipole resembles that of an isotropic radiator close to the effective plasma frequency of the wire medium, whereas the radiation from the lumped voltage generator is characterized by an infinite directivity and a non-diffractive far-field distribution.Comment: 10 pages, 4 figure

Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method

According to a recent proposal [S. Takayama et al., Appl. Phys. Lett. 87, 061107 (2005)], the triangular lattice of triangular air holes may allow to achieve a complete photonic band gap in two-dimensional photonic crystal slabs. In this work we present a systematic theoretical study of this photonic lattice in a high-index membrane, and a comparison with the conventional triangular lattice of circular holes, by means of the guided-mode expansion method whose detailed formulation is described here. Photonic mode dispersion below and above the light line, gap maps, and intrinsic diffraction losses of quasi-guided modes are calculated for the periodic lattice as well as for line- and point-defects defined therein. The main results are summarized as follows: (i) the triangular lattice of triangular holes does indeed have a complete photonic band gap for the fundamental guided mode, but the useful region is generally limited by the presence of second-order waveguide modes; (ii) the lattice may support the usual photonic band gap for even modes (quasi-TE polarization) and several band gaps for odd modes (quasi-TM polarization), which could be tuned in order to achieve doubly-resonant frequency conversion between an even mode at the fundamental frequency and an odd mode at the second-harmonic frequency; (iii) diffraction losses of quasi-guided modes in the triangular lattices with circular and triangular holes, and in line-defect waveguides or point-defect cavities based on these geometries, are comparable. The results point to the interest of the triangular lattice of triangular holes for nonlinear optics, and show the usefulness of the guided-mode expansion method for calculating photonic band dispersion and diffraction losses, especially for higher-lying photonic modes.Comment: 16 pages, 11 figure

Shape control of QDs studied by cross-sectional scanning tunneling microscopy

In this cross-sectional scanning tunneling microscopy study we investigated various techniques to control the shape of self-assembled quantum dots (QDs) and wetting layers (WLs). The result shows that application of an indium flush during the growth of strained InGaAs/GaAs QD layers results in flattened QDs and a reduced WL. The height of the QDs and WLs could be controlled by varying the thickness of the first capping layer. Concerning the technique of antimony capping we show that the surfactant properties of Sb result in the preservation of the shape of strained InAs/InP QDs during overgrowth. This could be achieved by both a growth interrupt under Sb flux and capping with a thin GaAsSb layer prior to overgrowth of the uncapped QDs. The technique of droplet epitaxy was investigated by a structural analysis of strain free GaAs/AlGaAs QDs. We show that the QDs have a Gaussian shape, that the WL is less than 1 bilayer thick, and that minor intermixing of Al with the QDs takes place.Comment: 7 pages, 10 figure

Shape control of QDs studied by cross-sectional scanning tunneling microscopy

In this cross-sectional scanning tunneling microscopy study we investigated various techniques to control the shape of self-assembled quantum dots (QDs) and wetting layers (WLs). The result shows that application of an indium flush during the growth of strained InGaAs/GaAs QD layers results in flattened QDs and a reduced WL. The height of the QDs and WLs could be controlled by varying the thickness of the first capping layer. Concerning the technique of antimony capping we show that the surfactant properties of Sb result in the preservation of the shape of strained InAs/InP QDs during overgrowth. This could be achieved by both a growth interrupt under Sb flux and capping with a thin GaAsSb layer prior to overgrowth of the uncapped QDs. The technique of droplet epitaxy was investigated by a structural analysis of strain free GaAs/AlGaAs QDs. We show that the QDs have a Gaussian shape, that the WL is less than 1 bilayer thick, and that minor intermixing of Al with the QDs takes place.Comment: 7 pages, 10 figure

Size dependent line broadening in the emission spectra of single GaAs quantum dots: Impact of surface charges on spectral diffusion

Making use of droplet epitaxy, we systematically controlled the height of self-assembled GaAs quantum dots by more than one order of magnitude. The photoluminescence spectra of single quantum dots revealed the strong dependence of the spectral linewidth on the dot height. Tall dots with a height of ~30 nm showed broad spectral peaks with an average width as large as ~5 meV, but shallow dots with a height of ~2 nm showed resolution-limited spectral lines (<120 micro eV). The measured height dependence of the linewidths is in good agreement with Stark coefficients calculated for the experimental shape variation. We attribute the microscopic source of fluctuating electric fields to the random motion of surface charges at the vacuum-semiconductor interface. Our results offer guidelines for creating frequency-locked photon sources, which will serve as key devices for long-distance quantum key distribution.Comment: 6 pages, 6 figures; updated figs and their description

Boundary conditions for interfaces of electromagnetic (photonic) crystals and generalized Ewald-Oseen extinction principle

The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of incident wave, eigenmodes excited in the crystal and scattered spatial harmonics. Generalized Ewald-Oseen extinction principle is formulated on the base of deduced boundary conditions. The knowledge of properties of infinite crystal's eigenmodes provides option to solve the diffraction problem for the corresponding semi-infinite crystal numerically. In the case when the crystal is formed by small inclusions which can be treated as point dipolar scatterers with fixed direction the problem admits complete rigorous analytical solution. The amplitudes of excited modes and scattered spatial harmonics are expressed in terms of the wave vectors of the infinite crystal by closed-form analytical formulae. The result is applied for study of reflection properties of metamaterial formed by cubic lattice of split-ring resonators.Comment: 15 pages, 8 figures, submitted to PR

Properties of entangled photon pairs generated in one-dimensional nonlinear photonic-band-gap structures

We have developed a rigorous quantum model of spontaneous parametric down-conversion in a nonlinear 1D photonic-band-gap structure based upon expansion of the field into monochromatic plane waves. The model provides a two-photon amplitude of a created photon pair. The spectra of the signal and idler fields, their intensity profiles in the time domain, as well as the coincidence-count interference pattern in a Hong-Ou-Mandel interferometer are determined both for cw and pulsed pumping regimes in terms of the two-photon amplitude. A broad range of parameters characterizing the emitted down-converted fields can be used. As an example, a structure composed of 49 layers of GaN/AlN is analyzed as a suitable source of photon pairs having high efficiency.Comment: 14 pages, 23 figure

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.Comment: Accepted for publication in Phys. Rev.