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NASA NTRS2009

Precise Stabilization of the Optical Frequency of WGMRs

Crystalline whispering gallery mode resonators (CWGMRs) made of crystals with axial symmetry have ordinary and extraordinary families of optical modes. These modes have substantially different thermo-refractive constants. This results in a very sharp dependence of differential detuning of optical frequency on effective temperature. This frequency difference compared with clock gives an error signal for precise compensation of the random fluctuations of optical frequency. Certain crystals, like MgF2, have turnover points where the thermo-refractive effect is completely nullified. An advantage for applications using WGMRs for frequency stabilization is in the possibility of manufacturing resonators out of practically any optically transparent crystal. It is known that there are crystals with negative and zero thermal expansion at some specific temperatures. Doping changes properties of the crystals and it is possible to create an optically transparent crystal with zero thermal expansion at room temperature. With this innovation s stabilization technique, the resultant WGMR will have absolute frequency stability The expansion of the resonator s body can be completely compensated for by nonlinear elements. This results in compensation of linear thermal expansion (see figure). In three-mode, the MgF2 resonator, if tuned at the turnover thermal point, can compensate for all types of random thermal-related frequency drift. Simplified dual-mode method is also available. This creates miniature optical resonators with good short- and long-term stability for passive secondary frequency ethalon and an active resonator for active secondary frequency standard (a narrowband laser with long-term stability).

Savchenkov, Anatoliy↗
NASA NTRS2009

Optical Device, System, and Method of Generating High Angular Momentum Beams

An optical device, optical system, and method of generating optical beams having high angular momenta are provided. The optical device includes a whispering gallery mode resonator defining a resonator radius and an elongated wavegWde having a length defined between a first end and a second end of the waveguide. The waveguide defines a waveguide radius which increases at least along a portion of the length of the waveguide in a direction from the first end to the second end. The waveguide radius at the first end of the waveguide is smaller than the resonator radius and the resonator is integrally formed with the first end of the waveguide.

Savchenkov, Anatoliy A.↗
NASA NTRS2007

NASA Tech Briefs, July 2007

Topics covered include: Miniature Intelligent Sensor Module; "Smart" Sensor Module; Portable Apparatus for Electrochemical Sensing of Ethylene; Increasing Linear Dynamic Range of a CMOS Image Sensor; Flight Qualified Micro Sun Sensor; Norbornene-Based Polymer Electrolytes for Lithium Cells; Making Single-Source Precursors of Ternary Semiconductors; Water-Free Proton-Conducting Membranes for Fuel Cells; Mo/Ti Diffusion Bonding for Making Thermoelectric Devices; Photodetectors on Coronagraph Mask for Pointing Control; High-Energy-Density, Low-Temperature Li/CFx Primary Cells; G4-FETs as Universal and Programmable Logic Gates; Fabrication of Buried Nanochannels From Nanowire Patterns; Diamond Smoothing Tools; Infrared Imaging System for Studying Brain Function; Rarefying Spectra of Whispering-Gallery-Mode Resonators; Large-Area Permanent-Magnet ECR Plasma Source; Slot-Antenna/Permanent-Magnet Device for Generating Plasma; Fiber-Optic Strain Gauge With High Resolution And Update Rate; Broadband Achromatic Telecentric Lens; Temperature-Corrected Model of Turbulence in Hot Jet Flows; Enhanced Elliptic Grid Generation; Automated Knowledge Discovery From Simulators; Electro-Optical Modulator Bias Control Using Bipolar Pulses; Generative Representations for Automated Design of Robots; Mars-Approach Navigation Using In Situ Orbiters; Efficient Optimization of Low-Thrust Spacecraft Trajectories; Cylindrical Asymmetrical Capacitors for Use in Outer Space; Protecting Against Faults in JPL Spacecraft; Algorithm Optimally Allocates Actuation of a Spacecraft; and Radar Interferometer for Topographic Mapping of Glaciers and Ice Sheets.

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NASA NTRS2006

NASA Tech Briefs, January 2006

Topics covered include: Semiautonomous Avionics-and-Sensors System for a UAV; Biomimetic/Optical Sensors for Detecting Bacterial Species; System Would Detect Foreign-Object Damage in Turbofan Engine; Detection of Water Hazards for Autonomous Robotic Vehicles; Fuel Cells Utilizing Oxygen From Air at Low Pressures; Hybrid Ion-Detector/Data-Acquisition System for a TOF-MS; Spontaneous-Desorption Ionizer for a TOF-MS; Equipment for On-Wafer Testing From 220 to 325 GHz; Computing Isentropic Flow Properties of Air/R-134a Mixtures; Java Mission Evaluation Workstation System; Using a Quadtree Algorithm To Assess Line of Sight; Software for Automated Generation of Cartesian Meshes; Optics Program Modified for Multithreaded Parallel Computing; Programs for Testing Processor-in-Memory Computing Systems; PVM Enhancement for Beowulf Multiple-Processor Nodes; Ion-Exclusion Chromatography for Analyzing Organics in Water; Selective Plasma Deposition of Fluorocarbon Films on SAMs; Water-Based Pressure-Sensitive Paints; System Finds Horizontal Location of Center of Gravity; Predicting Tail Buffet Loads of a Fighter Airplane; Water Containment Systems for Testing High-Speed Flywheels; Vapor-Compression Heat Pumps for Operation Aboard Spacecraft; Multistage Electrophoretic Separators; Recovering Residual Xenon Propellant for an Ion Propulsion System; Automated Solvent Seaming of Large Polyimide Membranes; Manufacturing Precise, Lightweight Paraboloidal Mirrors; Analysis of Membrane Lipids of Airborne Micro-Organisms; Noninvasive Diagnosis of Coronary Artery Disease Using 12-Lead High-Frequency Electrocardiograms; Dual-Laser-Pulse Ignition; Enhanced-Contrast Viewing of White-Hot Objects in Furnaces; Electrically Tunable Terahertz Quantum-Cascade Lasers; Few-Mode Whispering-Gallery-Mode Resonators; Conflict-Aware Scheduling Algorithm; and Real-Time Diagnosis of Faults Using a Bank of Kalman Filters.

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NASA NTRS2010

NASA Tech Briefs, May 2010

Topics covered include: Instrument for Analysis of Greenland's Glacier Mills Cryogenic Moisture Apparatus; A Transportable Gravity Gradiometer Based on Atom Interferometry; Three Methods of Detection of Hydrazines; Crossed, Small-Deflection Energy Analyzer for Wind/Temperature Spectrometer; Wavefront Correction for Large, Flexible Antenna Reflector; Novel Micro Strip-to-Waveguide Feed Employing a Double-Y Junction; Thin-Film Ferro Electric-Coupled Microstripline Phase Shifters With Reduced Device Hysteresis; Two-Stage, 90-GHz, Low-Noise Amplifier; A 311-GHz Fundamental Oscillator Using InP HBT Technology; FPGA Coprocessor Design for an Onboard Multi-Angle Spectro-Polarimetric Imager; Serrating Nozzle Surfaces for Complete Transfer of Droplets; Turbomolecular Pumps for Holding Gases in Open Containers; Triaxial Swirl Injector Element for Liquid-Fueled Engines; Integrated Budget Office Toolbox; PLOT3D Export Tool for Tecplot; Math Description Engine Software Development Kit; Astronaut Office Scheduling System Software; ISS Solar Array Management; Probabilistic Structural Analysis Program; SPOT Program; Integrated Hybrid System Architecture for Risk Analysis; System for Packaging Planetary Samples for Return to Earth; Offset Compound Gear Drive; Low-Dead-Volume Inlet for Vacuum Chamber; Simple Check Valves for Microfluidic Devices; A Capillary-Based Static Phase Separator for Highly Variable Wetting Conditions; Gimballing Spacecraft Thruster; Finned Carbon-Carbon Heat Pipe with Potassium Working Fluid; Lightweight Heat Pipes Made from Magnesium; Ceramic Rail-Race Ball Bearings; Improved OTEC System for a Submarine Robot; Reflector Surface Error Compensation in Dual-Reflector Antennas; Enriched Storable Oxidizers for Rocket Engines; Planar Submillimeter-Wave Mixer Technology with Integrated Antenna; Widely Tunable Mode-Hop-Free External-Cavity Quantum Cascade Laser; Non-Geiger-Mode Single-Photon Avalanche Detector with Low Excess Noise; Using Whispering-Gallery-Mode Resonators for Refractometry; RF Device for Acquiring Images of the Human Body; Reactive Collision Avoidance Algorithm; Fast Solution in Sparse LDA for Binary Classification; Modeling Common-Sense Decisions in Artificial Intelligence; Graph-Based Path-Planning for Titan Balloons; Nanolaminate Membranes as Cylindrical Telescope Reflectors; Air-Sea Spray Airborne Radar Profiler Characterizes Energy Fluxes in Hurricanes; Large Telescope Segmented Primary Mirror Alignment; and Simplified Night Sky Display System.

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NASA NTRS2012

Ring Image Analyzer

Ring Image Analyzer software analyzes images to recognize elliptical patterns. It determines the ellipse parameters (axes ratio, centroid coordinate, tilt angle). The program attempts to recognize elliptical fringes (e.g., Newton Rings) on a photograph and determine their centroid position, the short-to-long-axis ratio, and the angle of rotation of the long axis relative to the horizontal direction on the photograph. These capabilities are important in interferometric imaging and control of surfaces. In particular, this program has been developed and applied for determining the rim shape of precision-machined optical whispering gallery mode resonators. The program relies on a unique image recognition algorithm aimed at recognizing elliptical shapes, but can be easily adapted to other geometric shapes. It is robust against non-elliptical details of the image and against noise. Interferometric analysis of precision-machined surfaces remains an important technological instrument in hardware development and quality analysis. This software automates and increases the accuracy of this technique. The software has been developed for the needs of an R&TD-funded project and has become an important asset for the future research proposal to NASA as well as other agencies.

Strekalov, Dmitry V.↗
NASA NTRS2012

NASA Tech Briefs, February 2012

This issue contains the following briefs: (1) Optical Comb from a Whispering Gallery Mode Resonator for Spectroscopy and Astronomy Instruments Calibration (2) Real-Time Flight Envelope Monitoring System (3) Nemesis Autonomous Test System (4) Mirror Metrology Using Nano-Probe Supports (5) Automated Lab-on-a-Chip Electrophoresis System (6) Techniques for Down-Sampling a Measured Surface Height Map for Model Validation (7) Multi-Component, Multi-Point Interferometric Rayleigh/Mie Doppler Velocimeter (8) Frequency to Voltage Converter Analog Front-End Prototype (9) Dust-Tolerant Intelligent Electrical Connection System (10) Gigabit Ethernet Asynchronous Clock Compensation FIFO (11) High-Speed, Multi-Channel Serial ADC LVDS Interface for Xilinx Virtex-5 FPGA (12) Glovebox for GeoLab Subsystem in HDU1-PEM (13) Modified Process Reduces Porosity when Soldering in Reduced Gravity Environments (14) Use of Functionalized Carbon Nanotubes for Covalent Attachment of Nanotubes to Silicon (15) Flexible Plug Repair for Shuttle Wing Leading Edge (16) Three Dimensionally Interlinked, Dense, Solid Form of Single-Walled CNT Ropes (17) Axel Robotic Platform for Crater and Extreme Terrain Exploration (18) Site Tamper and Material Plow Tool - STAMP (19) Magnetic Interface for Segmented Mirror Assembly (20) Transpiration-Cooled Spacecraft-Insulation-Repair Fasteners (21) Fluorescence-Based Sensor for Monitoring Activation of Lunar Dust (22) Aperture Ion Source (23) Virtual Ultrasound Guidance for Inexperienced Operators (24) Model-Based Fault Diagnosis: Performing Root Cause and Impact Analyses in Real Time (25) Interactive Schematic Integration Within the Propellant System Modeling Environment (26) Magnetic and Electric Field Polarizations of Oblique Magnetospheric Chorus Waves (27) Variable Sampling Mapping.

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NASA NTRS2013

NASA Tech Briefs, January 2013

Topics include: Single-Photon-Sensitive HgCdTe Avalanche Photodiode Detector; Surface-Enhanced Raman Scattering Using Silica Whispering-Gallery Mode Resonators; 3D Hail Size Distribution Interpolation/Extrapolation Algorithm; Color-Changing Sensors for Detecting the Presence of Hypergolic Fuels; Artificial Intelligence Software for Assessing Postural Stability; Transformers: Shape-Changing Space Systems Built with Robotic Textiles; Fibrillar Adhesive for Climbing Robots; Using Pre-Melted Phase Change Material to Keep Payloads in Space Warm for Hours without Power; Development of a Centrifugal Technique for the Microbial Bioburden Analysis of Freon (CFC-11); Microwave Sinterator Freeform Additive Construction System (MS-FACS); DSP/FPGA Design for a High-Speed Programmable S-Band Space Transceiver; On-Chip Power-Combining for High-Power Schottky Diode-Based Frequency Multipliers; FPGA Vision Data Architecture; Memory Circuit Fault Simulator; Ultra-Compact Transputer-Based Controller for High-Level, Multi-Axis Coordination; Regolith Advanced Surface Systems Operations Robot Excavator; Magnetically Actuated Seal; Hybrid Electrostatic/Flextensional Mirror for Lightweight, Large-Aperture, and Cryogenic Space Telescopes; System for Contributing and Discovering Derived Mission and Science Data; Remote Viewer for Maritime Robotics Software; Stackfile Database; Reachability Maps for In Situ Operations; JPL Space Telecommunications Radio System Operating Environment; RFI-SIM: RFI Simulation Package; ION Configuration Editor; Dtest Testing Software; IMPaCT - Integration of Missions, Programs, and Core Technologies; Integrated Systems Health Management (ISHM) Toolkit; Wind-Driven Wireless Networked System of Mobile Sensors for Mars Exploration; In Situ Solid Particle Generator; Analysis of the Effects of Streamwise Lift Distribution on Sonic Boom Signature; Rad-Tolerant, Thermally Stable, High-Speed Fiber-Optic Network for Harsh Environments; Towed Subsurface Optical Communications Buoy; High-Collection-Efficiency Fluorescence Detection Cell; Ultra-Compact, Superconducting Spectrometer-on-a-Chip at Submillimeter Wavelengths; UV Resonant Raman Spectrometer with Multi-Line Laser Excitation; Medicine Delivery Device with Integrated Sterilization and Detection; Ionospheric Simulation System for Satellite Observations and Global Assimilative Model Experiments - ISOGAME; Airborne Tomographic Swath Ice Sounding Processing System; flexplan: Mission Planning System for the Lunar Reconnaissance Orbiter; Estimating Torque Imparted on Spacecraft Using Telemetry; PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils; Multiple-Frame Detection of Subpixel Targets in Thermal Image Sequences; Metric Learning to Enhance Hyperspectral Image Segmentation; Basic Operational Robotics Instructional System; Sheet Membrane Spacesuit Water Membrane Evaporator; Advanced Materials and Manufacturing for Low-Cost, High-Performance Liquid Rocket Combustion Chambers; Motor Qualification for Long-Duration Mars Missions.

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NASA NTRS2006

Optical vortices with large orbital momentum : generation and interference

We demonstrate a method for generation of beams of light with large angular momenta. The method utilizes whispering gallery mode resonators that transform a plane electromagnetic wave into high order Bessel beams. Interference pattern among the beams as well as shadow pictures induced by the beams are observed and studied.

Maleki, Lute↗
NASA NTRS2009

Phased-array optical whispering gallery mode modulation and method

A whispering gallery mode (WGM) resonator device and method capable of filtering sidebands of optical modulators are provided. The method includes providing an optical resonator adapted to support whispering gallery modes and forming a first field and a second field from a first location and a second location, respectively, at the circumference of the optical resonator and being separated by an arc angle, .alpha.. The method includes adjusting relative phase between the first field and the second field in accordance to a differential phase, .beta., and combining the first and the second fields into an output. Particular selection of the arc angle, .alpha., and the differential phase, .beta., can determine the function of the output.

Strekalov, Dmitry V.↗
NASA NTRS1993

Feasibility study: Monodisperse polymer particles containing laser-excitable dyes

The optical properties associated with small particles, which include aerosols, hydrosols and solid microspheres have an impact on several areas of science and engineering. Since the advent of high-speed computers and lasers, the interaction of light with matter in the form of small particles with a discontinuous optical boundary relative to the surroundings has been much better understood. Various nonlinear optical effects have been observed involving interaction of a laser beam with both solid microspheres and liquid microdroplets. These include observation of second and third harmonic generation, four wave mixing, optical visibility, two photon absorption, observation of stimulated emission and lasing, and Stimulated Raman Scattering. Many of these effects are observed with laser intensities which are orders of magnitude less than that required by threshold condition for interactions in macroscopic bulk medium. The primary reason for this is twofold. The front surface of the microsphere acts as a thick lens to enhance the internal intensity of the input laser radiation, and the spherical shape of the droplet acts as an optical cavity to provide feedback at specific wavelengths corresponding to the whispering gallery modes or the morphology dependent resonances (MDR's). The most interesting and significant recent finding in this field is undoubtedly the existence of resonance peaks in linear and nonlinear optical spectra. Such resonance peaks are only dependent on the particle morphology, which means the size, shape and refractive index of the particle. Because of the simultaneous presence of these resonances, they have been referred to by many names, including structural resonances, whispering modes or whispering gallery modes, creeping waves, circumferential waves, surfaces modes, and virtual modes. All of these names refer to the same phenomena, i.e. morphology dependent resonances (MDR's) which has already been described and predicted precisely by electromagnetic theory and Loentz-Mie theory since 1908. MDR's can become important when the particle size (radius a) approaches and exceeds the wavelength of the electromagnetic wave (lambda) and the refractive index of the particle is greater than that of the surrounding medium. Such resonances are easiest to observe from a single particle with high symmetry, such as a sphere, spheroid, or cylinder. MDR's correspond to solutions of the characteristic equations of the electromagnetic fields in the presence of a sphere.

Venkateswarlu, Putcha↗
NASA NTRS2008

Single-Mode WGM Resonators Fabricated by Diamond Turning

A diamond turning process has made possible a significant advance in the art of whispering-gallery-mode (WGM) optical resonators. By use of this process, it is possible to fashion crystalline materials into WGM resonators that have ultrahigh resonance quality factors (high Q values), are compact (ranging in size from millimeters down to tens of microns), and support single electromagnetic modes. This development combines and extends the developments reported in "Few- Mode Whispering-Gallery-Mode Resonators" (NPO-41256), NASA Tech Briefs, Vol. 30, No. 1 (January 2006), page 16a and "Fabrication of Submillimeter Axisymmetric Optical Components" (NPO-42056), NASA Tech Briefs, Vol. 31, No. 5 (May 2007), page 10a. To recapitulate from the first cited prior article: A WGM resonator of this special type consists of a rod, made of a suitable transparent material, from which protrudes a thin circumferential belt of the same material. The belt is integral with the rest of the rod and acts as a circumferential waveguide. If the depth and width of the belt are made appropriately small, then the belt acts as though it were the core of a single-mode optical fiber: the belt and the rod material adjacent to it support a single, circumferentially propagating mode or family of modes. To recapitulate from the second cited prior article: A major step in the fabrication of a WGM resonator of this special type is diamond turning or computer numerically controlled machining of a rod of a suitable transparent crystalline material on an ultrahigh-precision lathe. During the rotation of a spindle in which the rod is mounted, a diamond tool is used to cut the rod. A computer program is used to control stepping motors that move the diamond tool, thereby controlling the shape cut by the tool. Because the shape can be controlled via software, it is possible to choose a shape designed to optimize a resonator spectrum, including, if desired, to limit the resonator to supporting a single mode. After diamond turning, a resonator can be polished to increase its Q. By virtue of its largely automated, computer-controlled nature, the process is suitable for mass production of nominally identical single-mode WGM resonators. In a demonstration of the capabilities afforded by this development, a number of WGM resonators of various designs were fabricated side by side on the surface of a single CaF2 rod (see figure).

Grudinin, Ivan↗
NASA NTRS2012

A Solid State Ultraviolet Lasers Based on Cerium-Doped LiCaAIF(sub 6) Crystal Resonator

We report the first demonstration of a UV laser using a high-Q whispering gallery mode (WGM) resonator of Ce+: LiCaAlF6. We show that WGM resonators from LiCaAlF6 can achieve a Q of 2.6 x 10(sup 7) at UV. We demonstrated a UV laser at 290 nm with a pulsed pump laser at 266 nm. The experiments showed the low pump threshold intensity of 7.5 x 10(sup 9) W/m(sup 2) and slope efficiency of 25%. We have also observed lasing delay dynamics. These results are consistent with our modeling and theoretical estimates, and pave the way for a low threshold cw UV laser using WGM resonator cavity.

Whispering Gallery Mode Resonators↗
NASA NTRS2008

WGM Resonators for Terahertz-to-Optical Frequency Conversion

Progress has been made toward solving some practical problems in the implementation of terahertz-to-optical frequency converters utilizing whispering-gallery-mode (WGM) resonators. Such frequency converters are expected to be essential parts of non-cryogenic terahertz- radiation receivers that are, variously, under development or contemplated for a variety of applications in airborne and spaceborne instrumentation for astronomical and military uses. In most respects, the basic principles of terahertz-to-optical frequency conversion in WGM resonators are the same as those of microwave (sub-terahertz)-to-optical frequency conversion in WGM resonators, various aspects of which were discussed in the three preceeding articles. To recapitulate: In a receiver following this approach, a preamplified incoming microwave signal (in the present case, a terahertz signal) is up-converted to an optical signal by a technique that exploits the nonlinearity of the electromagnetic response of a whispering-gallery-mode (WGM) resonator made of LiNbO3 or another suitable electro-optical material. Upconversion takes place by three-wave mixing in the resonator. To ensure the required interaction among the optical and terahertz signals, the WGM resonator must be designed and fabricated to function as an electro-optical modulator while simultaneously exhibiting (1) resonance at the required microwave and optical operating frequencies and (2) phase matching among the microwave and optical signals circulating in the resonator. Downstream of the WGM resonator, the up-converted signal is processed photonically by use of a tunable optical filter or local oscillator and is then detected. The practical problems addressed in the present development effort are the following: Satisfaction of the optical and terahertz resonance-frequency requirement is a straightforward matter, inasmuch as the optical and terahertz spectra can be measured. However, satisfaction of the phase-matching requirement is more difficult. The approach followed in the present development is to perform computer simulations of the microwave and optical signals circulating in the resonator to test for phase matching. To enable excitation of the terahertz WGM resonator mode, it is also necessary to ensure phase matching between that mode and the incoming terahertz radiation. In the present development, the incoming signal is coupled into the WGM resonator via a tapered waveguide in the form of a fused silica rod. The phase-matching requirement is satisfied at one point along the taper; the rod is positioned with this point in proximity to the WGM resonator. To maximize the conversion efficiency, it is necessary to maximize the spatial overlap among the terahertz and optical modes in the WGM resonator. In the absence of a special design effort to address this issue, there would be little such overlap because, as a consequence of a large difference between wavelengths, the optical and terahertz modes would be concentrated at different depths from the rim of a WGM resonator. In the present development, overlap is ensured by constructing the WGM resonator as a ring (see figure) so thin that the optical and terahertz modes are effectively forced to overlap.

Strekalov,Dmitry↗
NASA NTRS2010

Optical Sidebands Multiplier

Optical sidebands have been generated with relative frequency tens to hundreds of GHz by using optical sidebands that are generated in a cascade process in high-quality optical resonators with Kerr nonlinearity, such as whispering gallery mode (WGM) resonators. For this purpose, the WGM resonator needs to be optically pumped at two frequencies matching its resonances. These two optical components can be one or several free spectral ranges (FSRs), equal to approximately 12 GHz, in this example, apart from each other, and can be easily derived from a monochromatic pump with an ordinary EOM (electro-optic modulation) operating at half the FSR frequency. With sufficient nonlinearity, an optical cascade process will convert the two pump frequencies into a comb-like structure extending many FSRs around the carrier frequency. This has a demonstratively efficient frequency conversion of this type with only a few milliwatt optical pump power. The concept of using Kerr nonlinearity in a resonator for non-degenerate wave mixing has been discussed before, but it was a common belief that this was a weak process requiring very high peak powers to be observable. It was not thought possible for this approach to compete with electro-optical modulators in CW applications, especially those at lower optical powers. By using the high-Q WGM resonators, the effective Kerr nonlinearity can be made so high that, using even weak seeding bands available from a conventional EOM, one can effectively multiply the optical sidebands, extending them into an otherwise inaccessible frequency range.

Strekalov, Dmitry V.↗
NASA NTRS2008

Delaying Trains of Short Light Pulses in WGM Resonators

Suitably configured whispering-gallery-mode (WGM) optical resonators have been proposed as delay lines for trains of short light pulses. Until now, it has been common practice to implement an optical delay line as a coiled long optical fiber, which is bulky and tends to be noisy. An alternative has been to implement an optical delay line as a coupled-resonator optical waveguide (a chain of coupled optical resonators), which is compact but limits the width of the pulse spectrum to the width of an optical resonance and thereby places a lower limit on the duration of a pulse. In contrast, a delay line according to the proposal could be implemented as a single WGM resonator, and the pulses delayed by the resonator could be so short that their spectral widths could greatly exceed the spectral width of any single resonance. The proposal emerged from theoretical and experimental studies of the propagation of a pulse train in a WGM resonator. An important element of the theoretical study was recognition that the traditional definition of group velocity in effect, the velocity of a single pulse comprising a packet of waves propagating in a medium, the responsivity of which is a monotonous function of frequency does not necessarily apply in the case of a WGM resonator or other medium having a spectrum consisting of discrete resonance peaks at different frequencies. A new definition of group velocity, applicable to a train of pulses propagating in such a medium, was introduced and found to lead to the discovery of previously unknown features of propagation. Notably, it was found that in a micro - sphere optical resonator that supports a suitable combination of WGM modes, the group velocity for a train of light pulses could be positive, zero, or negative. A positive group velocity could be so small that the delay could be much longer than the ring-down time of the resonator; a delay of such great length is impossible for a single pulse interacting with either a linearly responding lossless resonator or a coupled- resonator optical waveguide.

Matsko, Andrey↗