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

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 EO readout circuit includes an optical source having a first wavelength division multiplexer (WDM) configured to generate an optical carrier signal including beam carrier wavelengths, a first EO modulator configured to modulate a signal from an antenna element based upon the optical carrier signal, a second WDM coupled downstream from the first EO modulator, and optical-to-electrical converters coupled downstream from the second WDM. The second 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 related methods

Compact lithium niobate electrooptic Mach-Zehnder modulators on silicon with 18 dB extinction ratio and record-low 3.1 V.cm half-wave voltage-length product are characterized up to 20 GHz, rendering them suitable for high-speed datacom applications.

Lithium niobate modulators on silicon beyond 20 GHz

We describe an analog optical link using amplitude modulation and coherent detection for high SFDR, gain, and low noise figure. We then address the dominant performance-limiting parameters and discuss several approaches to overcome these limitations.

System impacts of modulation technology and phase noise on coherent analog optical links

A silicon microwave photonic down-converter

Radio frequency (RF) photonics can provide high performance at a lower size, weight, and power than traditional electrical systems. The implementation of RF photonics technology is paramount to meet the demands of future Department of Defense and commercial systems. This paper will cover some key performance aspects and discuss future investments to meet performance challenges.

Richard DeSalvo

Papers

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

Lithium niobate modulators on silicon beyond 20 GHz

System impacts of modulation technology and phase noise on coherent analog optical links

A silicon microwave photonic down-converter

Directions in radio frequency photonic systems