Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Electro-optic modulators translate high-speed electronic signals into the optical domain and are critical components in modern telecommunication networks1,2 and microwave-photonic systems3,4. They are also expected to be building blocks for emerging applications such as quantum photonics5,6 and non-reciprocal optics7,8. All of these applications require chip-scale electro-optic modulators that operate at voltages compatible with complementary metal–oxide–semiconductor (CMOS) technology, have ultra-high electro-optic bandwidths and feature very low optical losses. Integrated modulator platforms based on materials such as silicon, indium phosphide or polymers have not yet been able to meet these requirements simultaneously because of the intrinsic limitations of the materials used. On the other hand, lithium niobate electro-optic modulators, the workhorse of the optoelectronic industry for decades9, have been challenging to integrate on-chip because of difficulties in microstructuring lithium niobate. The current generation of lithium niobate modulators are bulky, expensive, limited in bandwidth and require high drive voltages, and thus are unable to reach the full potential of the material. Here we overcome these limitations and demonstrate monolithically integrated lithium niobate electro-optic modulators that feature a CMOS-compatible drive voltage, support data rates up to 210 gigabits per second and show an on-chip optical loss of less than 0.5 decibels. We achieve this by engineering the microwave and photonic circuits to achieve high electro-optical efficiencies, ultra-low optical losses and group-velocity matching simultaneously. Our scalable modulator devices could provide cost-effective, low-power and ultra-high-speed solutions for next-generation optical communication networks and microwave photonic systems. Furthermore, our approach could lead to large-scale ultra-low-loss photonic circuits that are reconfigurable on a picosecond timescale, enabling a wide range of quantum and classical applications5,10,11 including feed-forward photonic quantum computation. Chip-scale lithium niobate electro-optic modulators that rapidly convert electrical to optical signals and use CMOS-compatible voltages could prove useful in optical communication networks, microwave photonic systems and photonic computation.

Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages

CRYSTALLINE MATERIALS Introduction Physical Properties Optical Properties Mechanical Properties Thermal Properties Magnetooptic Properties Electrooptic Properties Elastooptic Properties Nonlinear Optical Properties GLASSES Introduction Commercial Optical Glasses Specialty Optical Glasses Fused Silica Fluoride Glasses Chalcogenide Glasses Magnetooptic Properties Electrooptic Properties Elastooptic Properties Nonlinear Optical Properties Special Glasses POLYMERIC MATERIALS Optical Plastics Index of Refraction Nonlinear Optical Properties Thermal Properties Engineering Data METALS Physical Properties of Selected Metals Optical Properties Mechanical Properties Thermal Properties Mirror Substrate Materials LIQUIDS Introduction Water Physical Properties of Selected Liquids Index of Refraction Nonlinear Optical Properties Magnetooptic Properties Commercial Optical Liquids GASES Introduction Physical Properties of Selected Gases Index of Refraction Nonlinear Optical Properties Magnetooptic Properties Atomic Resonance Filters APPENDICES Safe Handling of Optical Materials Abbreviations, Acronyms, and Mineralogical or Common Names for Optical Materials Abbreviations for Methods of Preparing Optical Materials and Thin Films Fundamental Physical Constants Units and Conversion Factors

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Handbook of Optical Materials

Dark optical solitons: physics and applications

The absolute scale of the second-order nonlinear-optical coefficients of several important nonlinear-optical materials has been obtained with improved accuracy. Second-harmonic generation, parametric fluorescence, and difference-frequency generation measurements have been made at several wavelengths in the near-infrared region. The second-harmonic generation measurement was performed at the fundamental wavelengths of 1.548, 1.533, 1.313, 1.064, and 0.852 µm. The materials measured included congruent LiNbO3,1%MgO:LiNbO3,5%MgO:LiNbO3,LiTaO3,KNbO3,KTiOPO4,KH2PO4, quartz, GaAs, GaP, α-ZnS, CdS, ZnSe, and CdTe. We made the parametric fluorescence measurement to determine the nonlinear-optical coefficients of congruent LiNbO3 and 5%MgO:LiNbO3 at pump wavelengths of 0.532 and 0.488 µm. We made the difference-frequency generation measurement for congruent LiNbO3 at a pump wavelength of 0.532 µm. The second-harmonic generation, parametric fluorescence, and difference-frequency generation measurements yielded consistent data on the nonlinear-optical coefficients of the materials. We found that many of the currently accepted standard values are overestimated because of neglect of the multiple-reflection effect in (nearly) plane-parallel-plate samples. The dispersion of the nonlinear-optical coefficients showed that Miller’s Δ is barely constant over the wavelength range measured and thus that Miller’s rule is not so good as other methods for wavelength scaling of the nonlinear-optical coefficients.

Absolute scale of second-order nonlinear-optical coefficients

We demonstrate a new universal DSP receiver architecture for ground-based optical communications that autonomously identifies and decode TDHMFs in addition to conventional formats. The combination of a flexible and modular architecture with proper statistical tools has enabled successful validation of autonomous identification and demodulation, suggesting that these methods are extensible to any format including those not yet examined. Similar architectural concepts can be generalized to wireless communications, thus spanning the whole communication range of the avionics ecosystem.

Autonomous receivers for complex format identification and demodulation

Radio-frequency (RF) photonics is demonstrating superior performance in communication systems using discrete components. As systems establish an upgrade path balancing challenging bandwidth requirements with size, weight, and power constraints, the time is ripe for transition to a more efficient and cost-effective hybrid manufacturing technology. This technology has been applied to the construction of an optical coherent receiver for the down conversion of RF signals from 10–18 to 2 GHz. Light from a distributed feedback semiconductor laser is split between two lithium niobate Mach-Zehnder modulators, driven either by a tunable local oscillator tone or an RF signal coming, for example, from a receiving antenna. The modulated light signals are combined with an optical coupler and filtered by two fiber Bragg gratings that select one optical sideband from each signal. Detection of the filtered light by a balanced photo-detector produces an electrical signal at an intermediate frequency equal to the beat difference between the frequencies of the RF signal and the local oscillator. Packaging of optical and opto-electronic components within a common enclosure where light routing is performed by micro-optics has allowed a significant decrease in the size, weight, and power consumption of the receiver.

Hybrid Integration of RF Photonic Systems

A phased antenna array includes an array of antenna elements, and an electro-optic (EO) readout circuit coupled to the array of antenna elements. The EU readout circuit includes an optical source including a mode locked laser (MLL) configured to generate an optical carrier signal having beam carrier wavelengths, an EO modulator configured to modulate a signal from an antenna element based upon the optical carrier signal, a first WDM coupled downstream from the EO modulator, and optical-to-electrical converters coupled downstream from the first WDM. The first WDM is configured to multiplex each modulated beam carrier wavelength to a respective optical-to-electrical converter.

Phased antenna array with electro-optic readout circuit with multiplexing and mll and related methods

We propose a novel spectrum analyzer based on heterodyne down-conversion with two detuned optical frequency combs for rapid, wideband characterization of RF signals. The measurement bandwidth of ∼40GHz is limited by modulator speed and the system latency and frequency resolution are time-bandwidth limited.

Dual-comb spectrometer for fast wideband RF spectral analysis

We report on picosecond laser-induced damage experiments that were carried out on a natural type-IIa diamond and a thick specimen of high-quality chemically vapor-deposited (CVD) diamond. In conjunction with earlier measurements performed elsewhere on an `optically thick' single crystal, it is shown that for spot sizes (2 (omega) ) ranging from 3 to 60 micrometers , the breakdown field strength (E BD ) at the damage threshold of diamond obeys a pattern best described as follows: E BD approximately equals A/(root)2(omega) , where A equals 30.7 and 38.7 MV(mu) 1/2 /cm at 532 and 1064 nm, respectively. The case of CVD diamond demonstrates that, if problems arising from localized high absorption at the deposition surface can be avoided, this material should be of much promise for contemplated high-power free-electron laser window applications. We show that corrections for self- focusing in laser damage experiments depend not only on the peak pulse power but also on the position of the diffraction prefocus and the length of the Rayleigh range.

Richard DeSalvo

Papers

Autonomous receivers for complex format identification and demodulation

Hybrid Integration of RF Photonic Systems

Phased antenna array with electro-optic readout circuit with multiplexing and mll and related methods

Dual-comb spectrometer for fast wideband RF spectral analysis

Picosecond light-pulse-induced damage to diamond