As a step toward analyzing second-harmonic generation ͑SHG͒ from crystalline Si nanospheres in glass, we develop an anisotropic bond model ͑ABM͒ that expresses SHG in terms of physically meaningful parameters and provide a detailed understanding of the basic physics of SHG on the atomic scale. Nonlinear-optical ͑NLO͒ responses are calculated classically via the four fundamental steps of optics: evaluate the local field at a given bond site, solve the force equation for the acceleration of the charge, calculate the resulting radiation, then superpose the radiation from all charges. Because the emerging NLO signals are orders of magnitude weaker and occur at wavelengths different from that of the pump beam, these steps are independent. Paradoxically, the treatment of NLO is therefore simpler than that of linear optics ͑LO͒, where these calculations must be done self-consistently. The ABM goes beyond previous bond models by including the complete set of underlying contributions: retardation ͑RD͒, spatial-dispersion ͑SD͒, and magnetic ͑MG͒ effects, in addition to the anharmonic restoring force acting on the bond charge. Transverse as well as longitudinal motion is also considered. We apply the ABM to obtain analytic expressions for SHG from amorphous materials under Gaussian-beam excitation. These materials represent an interesting test case not only because they are ubiquitous but also because the anharmonic-force contribution that dominates the SHG response of crystalline materials and ordered interfaces vanishes by symmetry. The remaining contributions, and hence the SHG signals, are entirely functions of the LO response and beam geometry, so the only new information available is the anisotropy of the LO response at the bond level. The RD, SD, and MG contributions are all of the same order of magnitude, so none can be ignored. Diffraction is important in determining not only the pattern of the emerging beam but also the phases and amplitudes of the different terms. The plane-wave expansion that gives rise to electric quadrupole magnetic dipole effects in LO appears here as retardation. Using the paraxial-ray approximation, we reduce the results to the isotropic case in two limits, that where the linear restoring force dominates ͑glasses͒ and that where it is absent ͑metals͒. Both forward-and backscattering geometries are discussed. Estimated signal strengths and conversion efficiencies for fused silica appear to be in general agreement with data where available. Predictions that allow additional critical tests of these results are made.

Optoelectronic oscillators (OEOs) are promising sources of low phase noise radio frequency (RF) signals. However, at X-band frequencies, the long optical fiber delay line required for a high oscillator Q also leads to spurious modes (spurs) spaced too narrowly to be filtered by RF filters. The dual injection-locked OEO (DIL-OEO) has been proposed as a solution to this problem. In this work, we describe in detail the construction of a DIL-OEO. We also present experimental data from our systematic study of injection-locking in DIL-OEOs. With this data, we optimize the DIL-OEO, achieving both low phase noise and low spurs. Finally, we present data demonstrating a 60 dB suppression of the nearest-neighbor spur without increasing the phase noise within 1 kHz of the 10 GHz central oscillating mode.

Three optical ring resonator (ORR)-based integrated ultra-low-loss silicon nitride 1 × 4 optical beamforming networks (OBFNs) for millimeter-wave (mmW) beamsteering are reported. The group delay ripple of multi-ORR delay line was theoretically optimized and quantitatively studied by applying a genetic algorithm. The optimized 3-ORR delay true time delay (TTD) responses were experimentally achieved with 208.7 ps and 172.4 ps of delay tuning range for bandwidth of 6.3 GHz and 8.7 GHz, corresponding to a phase shift of 17.1π and 14.1π for 41 GHz mmW signal. The TTD performance of the 3-ORR delay line was also verified by controlling the delay of 3 Gbps data stream. A 22 • beamsteering angle equivalent OBFN delay distribution was achieved for 41 GHz half-wavelength dipole antenna array. Both the theoretical analysis and experiments exhibit that the topology with one ring shared could balance the system complexity and TTD bandwidth well. Using heterodyne up-conversion technology and a single delay path, 41 GHz mmW signal with 3 Gbps OOK NRZ data modulation was generated and delayed. Index Terms-Microwave photonics, photonic integrated circuits, true time delays, optical ring resonators, millimeter wave communication, phased arrays.

In-plane directional control of surface chemistry during interface formation can lead to new opportunities regarding device structures and applications. Control of this type requires techniques that can probe and hence provide feedback on the chemical reactivity of bonds not only in specific directions but also in real time. Here, we demonstrate both control and measurement of the oxidation of H-terminated (111) Si. Control is achieved by externally applying uniaxial strain, and measurement by second-harmonic generation (SHG) together with the anisotropic-bond model of nonlinear optics. In this system anisotropy results because bonds in the strain direction oxidize faster than those perpendicular to it, leading in addition to transient structural changes that can also be detected at the bond level by SHG.silicon | hyperpolarizability | ellipsometry | metrology | optical T he oxidation of silicon is one of the most technologically important chemical reactions. Because dangling bonds trap and/ or scatter carriers, well-organized bonding at Si∕SiO 2 interfaces is critical to device performance. Therefore, although Si oxidation has been studied for many years, the formation dynamics of Si∕SiO 2 interfaces continues to be of interest. The information provided to date regarding oxidation kinetics has been obtained primarily by standard spectroscopic and microscopic structuralanalysis techniques. For example, scanning tunneling microscopy and atomic force microscopy (AFM) studies have revealed the role of surface morphology during oxidation (1, 2). IR absorption experiments have probed the changes in vibrational modes during oxidation and have provided information about the chemical reactions involved in the process (3). Spectroscopic ellipsometry has provided data about growth rates (4). At the same time, considerable effort has been invested in manipulating Si oxidation kinetics. For example, uni-and biaxial strains have been used in manufacturing Si-based devices, taking advantage of the fact that tensile stress increases the overall oxidation rate of thermally grown oxides (5).The effect of strain on the morphology of clean vicinal and on-axis Si surfaces has been well studied by microscopic methods (6, 7). However, an atomic-level understanding of the specific effects of strain on surface chemistry is presently unknown. Here, we investigate oxidation of strained and unstrained H-terminated (111) Si in real time using second-harmonic generation (SHG), and we analyze these data with the anisotropic-bond model (ABM) of nonlinear optics. The bond-specific information that we obtain reveals two important aspects of the relevant chemical dynamics. First, strain changes the oxidation rates of Si─Si back bonds that are oriented in different directions, and second, the average back-bond directions themselves change as a result of this anisotropic oxidation. Fig. 1 provides an atomic-level view of the configuration, showing the bonding of the outermost bilayer of a (111) Si surface. Each outer-layer Si atom has one "up" bon...