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Articles 1 - 30 of 47
Full-Text Articles in Engineering
Investigation Of Negative Refractive Index In Reciprocal Chiral Materials, Monish Ranjan Chatterjee, Partha P. Banerjee, Pradeep R. Anugula
Investigation Of Negative Refractive Index In Reciprocal Chiral Materials, Monish Ranjan Chatterjee, Partha P. Banerjee, Pradeep R. Anugula
Electrical and Computer Engineering Faculty Publications
It is well known that there exist both natural materials (such as milk or sugar solution) possessing chiral (or handed) properties, as well as an increasing list of man-made materials (such as sodium bromate) that exhibit chirality. One of the principal properties of chirality is that light of any arbitrary polarization, when propagating through a chiral material, splits up into two circular polarizations propagating in different directions. In the past decade or longer, researchers have investigated electromagnetic transverse (plane) wave propagation across a non-chiral/chiral interface, and determined the electromagnetic Fresnel coefficients for such propagation. Traditionally, such coefficients are derived under …
A Low-Phase-Noise 18-Ghz-Band Frequency Synthesizer With Low Frequency Step Size, B. Biglarbegian, F. Hodjat Kashani, Hossein Ameri Mahabadi
A Low-Phase-Noise 18-Ghz-Band Frequency Synthesizer With Low Frequency Step Size, B. Biglarbegian, F. Hodjat Kashani, Hossein Ameri Mahabadi
Hossein Ameri Mahabadi
Due to development of both wireless communication users and communication line users, utilization of high-speed communications has become a vital essence. High speed digital microwave radios have a great contribution in wireless telecommunications. Having a different and high capacitance, these radios can transmit and receive data in point to point links in far distances up to 30 km. Considering the high rate of utilization such digital microwave radios have in lower bands, it is imperative to utilize such kind of radios in upper bandsfor accessing more channels. One of the radios that plays a significant role in communications is digital …
Assessing The Potential For Improved Scramjet Performance Through Application Of Electromagnetic Flow Control, Martin F. Lindsey
Assessing The Potential For Improved Scramjet Performance Through Application Of Electromagnetic Flow Control, Martin F. Lindsey
Theses and Dissertations
Hypersonic flight using scramjet propulsion bridges the gap between turbojets and rockets. Recent efforts focus on magnetogasdynamic (MGD) flow control to mitigate the problems of high thermomechanical loads and low efficiencies associated with scramjets. This research is the first flight-scale, three-dimensional computational analysis of a realistic scramjet to assess how MGD flow control improves scramjet performance. Developing a quasi-one dimensional design tool culminated in the first open source scramjet geometry. This geometry was tested with the Air Force Research Laboratory's electromagnetic computational code. To increase fidelity, an algorithm was developed to incorporate thermochemistry, resulting in the only open-source model of …
Air Gap Error Compensation For Coaxial Transmission Line Method Of Electromagnetic Material Characterization, Ronald G. Fehlen
Air Gap Error Compensation For Coaxial Transmission Line Method Of Electromagnetic Material Characterization, Ronald G. Fehlen
Theses and Dissertations
This research analyzes material characterization measurements from 50 Mhz to 3.05 GHz where an axially symmetric air gap exists between the sample material and the inner or outer conductor. Higher order fields are excited by the air gap and are accounted for through modal analysis methods. A root search minimizes the difference between the calculated scattering parameters from the modal method and the experimentally measured scattering parameters. The root is the permittivity and permeability of the material. This method is tested with a non-magnetic material and a heavily loaded magnetic material. An error analysis based on dimension measurement uncertainty is …
Polar Phase Screens: A Comparison With Other Methods Of Random Phase Screen Generation, Rebecca J. Eckert
Polar Phase Screens: A Comparison With Other Methods Of Random Phase Screen Generation, Rebecca J. Eckert
Theses and Dissertations
This research provides the first organized comparison of random phase screen generation methods, including logarithmic polar Fourier series, using structure functions. Random phase screens are essential elements of simulating light propagation through turbulent media. In order to be effective, they must accurately reflect theory and be practical to implement. This research explains and evaluates three methods of generating random phase screens: using a Fourier series upon a polar frequency grid with logarithmic spacing; using the fast Fourier transform, with its Cartesian frequency grid; and using Zernike polynomials. It provides a comparison of the Polar Fourier Series technique with the two …
Determining The Resistivity Of Resistive Sheets Using Transmission Measurements, Milo W. Hyde Iv
Determining The Resistivity Of Resistive Sheets Using Transmission Measurements, Milo W. Hyde Iv
Theses and Dissertations
In September 2005, radar cross section (RCS) measurements were made of resistive sheets, or R-cards, wrapped around a polystyrene foam cylinder to compare with a newly developed theoretical RCS prediction technique. The resistivities of the R-cards were initially measured with a direct current (DC) four-point probe. When the RCS measurements were compared to the theoretical predictions, it became clear that DC resistivity alone is not sufficient to accurately predict the scattering from an R-card. This thesis presents alternating current (AC) methods for determining the resistivity of an R-card. Both freespace and waveguide techniques are presented. Experimental verification of the techniques …
A Study Of Near Field Data Transformed To The Far Field For A Canonical Pec Scatterer, E. Matthew Cady
A Study Of Near Field Data Transformed To The Far Field For A Canonical Pec Scatterer, E. Matthew Cady
Theses and Dissertations
The purpose of this research was to analyze the error associated with the Image Based Near Field to Far Field Transformation (IB NFFFT) for a canonical perfectly electrically conductive (PEC) scatterer. This research compares two groups of data: far field RCS predicted by the IB NFFFT and far field RCS predicted by X-Patch. The IB NFFFT requires a complete set of calibrated monostatic near field scattering data of the object. A detailed description is given of the configuration of the measurement facilities and procedures that were required to obtain the calibrated near field scattering data, as well as the process …
Comparison Of Computational Electromagnetic Codes For Prediction Of Low-Frequency Radar Cross Section, Paul C. Lash
Comparison Of Computational Electromagnetic Codes For Prediction Of Low-Frequency Radar Cross Section, Paul C. Lash
Theses and Dissertations
Radar cross section (RCS) prediction of full-scale aircraft is of interest to military planners for a variety of applications. Several computational electromagnetic codes for RCS prediction are available with differing features and capabilities. The goal of this research is to compare the capabilities of three computational electromagnetic codes for use in production of RCS signature assessments at low frequencies in terms of performance, accuracy, and features: Fast Illinois Solver Code (FISC), Code for Analysis of Radiators on Lossy Surfaces (CARLOS-3D), and Science Applications International Corporation Full-wave solver (SAF). The comparison is accomplished through analysis of predicted and measured RCS of …
Active Optical Tracking With Spatial Light Modulators, Steven R. Mawhorter
Active Optical Tracking With Spatial Light Modulators, Steven R. Mawhorter
Theses and Dissertations
Two spatial light modulators are utilized for beam splitting, steering and tracking. Both linear and holographic phase screens are used in a demonstration of technology to allow real time tracking to communicate in a one-to-several type scenario. One SLM is used to apply a linear phase modulation to steer multiple beams onto a detector. The spots that are produced represent the targets as they move around the field of view of the central communication node. A Gerchberg-Saxton algorithm will subsequently use the detected spots as the desired pointing locations. Using this as input, the Gerchberg-Saxton algorithm yields a phase only …
Investigation Of Frequency-Domain And Time-Domain Free-Space Material Measurements, Kirt J. Cassell
Investigation Of Frequency-Domain And Time-Domain Free-Space Material Measurements, Kirt J. Cassell
Theses and Dissertations
Electromagnetic material characterization is the process of determining the complex permittivity and permeability of a test sample. The primary goal of this thesis is to develop a new two-transmission material measurement method to decrease the error associated with using a reflection measurement. The transmission method uses a sample transmission measurement and an acrylic-backed sample transmission measurement. This technique is first demonstrated in a rectangular waveguide system then extended to frequency-domain and time-domain focus arch free-space systems. The frequency-domain free-space calibration process decreases accuracy at the band edges. The use of a digital oscilloscope with a time-domain reflectometer (TDR) module should …
Nanophotonics – From The Laboratory To Commercialization, Andrew Sarangan
Nanophotonics – From The Laboratory To Commercialization, Andrew Sarangan
Andrew Sarangan
No abstract provided.
Radiation Studies Of The Tin-Doped Microscopic Droplet Laser Plasma Light Source Specific To Euv Lithography, Chiew-Seng Koay
Radiation Studies Of The Tin-Doped Microscopic Droplet Laser Plasma Light Source Specific To Euv Lithography, Chiew-Seng Koay
Electronic Theses and Dissertations
Extreme ultraviolet lithography(EUVL) is being developed worldwide as the next generation technology to be inserted in ~ 2009 for the mass production of IC chips with feature sizes <35 nm. One major challenge to its implementation is the development of a 13.5 nm EUV source of radiation that meets the requirements of current roadmap designs of the source of illumination in commercial EUVL scanners. The light source must be debris-free, in a free-space environment with the imaging EUV optics that must provide sufficient, narrow spectral band EUV power to print 100 wafers/hr. To meet this need, extensive studies on emission from a laser plasma source utilizing tin-doped droplet target was conducted. Presented in this work, are the many optical techniques such as spectroscopy, radiometry, and imaging, that were employed to characterize and optimize emission from the laser plasma source State of the art EUV spectrographs were employed to observe the source's spectrum under various laser irradiation conditions. Comparing the experimental spectra to those from theory, has allowed the determination of the Sn ion stages responsible for emitting into the useful EUV bandwidth. Experimental results were compared to spectral simulations obtained using Collisional-Radiative Equilibrium (CRE) model, as well. Moreover, extensive measurements surveying source emission from 2 nm to 30 nm, which is the region of the electromagnetic spectrum defined as EUV, was accomplished. Absolutely calibrated metrology was employed with the Flying Circus instrument from which the source's conversion efficiency (CE)--from laser to the useful EUV energy--was characterized under various laser irradiation conditions. Hydrodynamic simulations of the plasma expansion together with the CRE model predicted the condition at which optimum conversion could be attained. The condition was demonstrated experimentally, with the highest CE to be slightly above 2%, which is the highest value among all EUV source contenders. In addition to laser intensity, the CE was found to depend on the laser wavelength. For better understanding, this observation is compared to results from simulations. Through a novel approach in imaging, the size of the plasma was characterized by recording images of the plasma within a narrow band, around 13.5 nm. The size, approximately 100 ìm, is safely within the etendue limit set by the optical elements in the EUV scanner. Finally, the notion of irradiating the target with multiple laser beams was explored for the possibility of improving the source's conversion efficiency.
Polarimetry Of Random Fields, Jeremy Ellis
Polarimetry Of Random Fields, Jeremy Ellis
Electronic Theses and Dissertations
On temporal, spatial and spectral scales which are small enough, all fields are fully polarized. In the optical regime, however, instantaneous fields can rarely be examined, and, instead, only average quantities are accessible. The study of polarimetry is concerned with both the description of electromagnetic fields and the characterization of media a field has interacted with. The polarimetric information is conventionally presented in terms of second order field correlations which are averaged over the ensemble of field realizations. Motivated by the deficiencies of classical polarimetry in dealing with specific practical situations, this dissertation expands the traditional polarimetric approaches to include …
Synchronization In Advanced Optical Communications, Inwoong Kim
Synchronization In Advanced Optical Communications, Inwoong Kim
Electronic Theses and Dissertations
The objective of this dissertation is to generate high power ultrashort optical pulses from an all-semiconductor mode-locked laser system. The limitations of semiconductor optical amplifier in high energy, ultrashort pulse amplification are reviewed. A method to overcome the fundamental limit of small stored energy inside semiconductor optical amplifier called "eXtreme Chirped Pulse Amplification (X-CPA)" is proposed and studied theoretically and experimentally. The key benefits of the concept of X-CPA are addressed. Based on theoretical and experimental study, an all-semiconductor mode-locked X-CPA system consisting of a mode-locked master oscillator, an optical pulse pre-stretcher, a semiconductor optical amplifier (SOA) pulse picker, an …
Integrated Inp Photonic Switches, Daniel May-Arrioja
Integrated Inp Photonic Switches, Daniel May-Arrioja
Electronic Theses and Dissertations
Photonic switches are becoming key components in advanced optical networks because of the large variety of applications that they can perform. One of the key advantages of photonic switches is that they redirect or convert light without having to make any optical to electronic conversions and vice versa, thus allowing networking functions to be lowered into the optical layer. InP-based switches are particularly attractive because of their small size, low electrical power consumption, and compatibility with integration of laser sources, photo-detectors, and electronic components. In this dissertation the development of integrated InP photonic switches using an area-selective zinc diffusion process …
Experimental Techniques For Nonlinear Material Characterization: A Nonlinear Spectrometer Using A White-Light Continuum Z-Scan, Mihaela Balu
Experimental Techniques For Nonlinear Material Characterization: A Nonlinear Spectrometer Using A White-Light Continuum Z-Scan, Mihaela Balu
Electronic Theses and Dissertations
The main goal of this dissertation is to introduce and demonstrate a new method for the rapid determination of the nonlinear absorption spectra and the dispersion of the nonlinear refraction of optical materials in the visible and near IR spectral regions. However, conventional methods like, white-light continuum pump-probe and Z-scan techniques were used to measure the peak 2PA cross-sections for a number of commercially available photoinitiators. In the new method mentioned above, a high energy, broadband femtosecond white-light continuum is used to replace the single wavelength source conventionally used in a Z-scan experiment. In a Z-scan experiment, the transmittance of …
Polarization-Independent Liquid Crystal Devices, Yi-Hsin Lin
Polarization-Independent Liquid Crystal Devices, Yi-Hsin Lin
Electronic Theses and Dissertations
Liquid crystal (LC) devices can be operated as amplitude modulators and phase modulators. LC amplitude modulation is commonly used in liquid crystal display (LCD) while phase-only modulation is useful for laser beam steering, tunable grating, prism, lens, and other photonic devices. Most LC devices are polarization dependent and require at least one polarizer. As a result, the optical efficiency is low. To enhance display brightness, a power hungry backlight has to be used leading to a high power consumption and short battery life. In a LC phase modulator, the polarization dependent property complicates the laser beam steering system. It is …
On The Use Of Variable Coherence In Inverse Scattering Problems, Erwan Baleine
On The Use Of Variable Coherence In Inverse Scattering Problems, Erwan Baleine
Electronic Theses and Dissertations
Even though most of the properties of optical fields, such as wavelength, polarization, wavefront curvature or angular spectrum, have been commonly manipulated in a variety of remote sensing procedures, controlling the degree of coherence of light did not find wide applications until recently. Since the emergence of optical coherence tomography, a growing number of scattering techniques have relied on temporal coherence gating which provides efficient target selectivity in a way achieved only by bulky short pulse measurements. The spatial counterpart of temporal coherence, however, has barely been exploited in sensing applications. This dissertation examines, in different scattering regimes, a variety …
Ultrashort, High Power, And Ultralow Noise Mode-Locked Optical Pulse Generation Using Quantum-Dot Semiconductor Lasers, Myoung-Taek Choi
Ultrashort, High Power, And Ultralow Noise Mode-Locked Optical Pulse Generation Using Quantum-Dot Semiconductor Lasers, Myoung-Taek Choi
Electronic Theses and Dissertations
This dissertation explores various aspects and potential of optical pulse generation based on active, passive, and hybrid mode-locked quantum dot semiconductor lasers with target applications such as optical interconnect and high speed signal processing. Design guidelines are developed for the single mode operation with suppressed reflection from waveguide discontinuities. The device fabrication procedure is explained, followed by characteristics of FP laser, SOA, and monolithic two-section devices. Short pulse generation from an external cavity mode-locked QD two-section diode laser is studied. High quality, sub-picosecond (960 fs), high peak power (1.2 W) pulse trains are obtained. The sign and magnitude of pulse …
Design And Optimization Of Nano-Optical Elements By Coupling Fabrication To Optical Behavior, Raymond Rumpf
Design And Optimization Of Nano-Optical Elements By Coupling Fabrication To Optical Behavior, Raymond Rumpf
Electronic Theses and Dissertations
Photonic crystals and nanophotonics have received a great deal of attention over the last decade, largely due to improved numerical modeling and advances in fabrication technologies. To this day, fabrication and optical behavior remain decoupled during the design phase and numerous assumptions are made about "perfect" geometry. As research moves from theory to real devices, predicting device behavior based on realistic geometry becomes critical. In this dissertation, a set of numerical tools was developed to model micro and nano fabrication processes. They were combined with equally capable tools to model optical performance of the simulated structures. Using these tools, it …
Probing Random Media With Singular Waves, Chaim Schwartz
Probing Random Media With Singular Waves, Chaim Schwartz
Electronic Theses and Dissertations
In recent years a resurgence of interest in wave singularities (of which optical vortices are a prominent example), light angular momentum and the relations between them has occurred. Many applications in various areas of linear and non-linear optics have been based on studying effects related to angular momentum and optical vortices. This dissertation examines the use of such wave singularities for studying the light propagation in highly inhomogeneous media and the relationship to angular momentum transfer. Angular momentum carried by light can be, in many cases, divided in two terms. The first one relates to the polarization of light and …
Low-Cost Wavelength Measurement Based On A Macrobending Single-Mode Fiber, Qian Wang, Gerald Farrell, Thomas Freir, Ginu Rajan, Pengfei Wang
Low-Cost Wavelength Measurement Based On A Macrobending Single-Mode Fiber, Qian Wang, Gerald Farrell, Thomas Freir, Ginu Rajan, Pengfei Wang
Articles
A low-cost all-fiber wavelength measurement technique is proposed and demonstrated. A macrobending standard single-mode fiber is developed as an edge filter with an optimal design and simple surface processing. A ratiometric wavelength measurement system employing the developed macrobending fiber filter demonstrates a resolution of∼10 pmin a wavelength range from1500to1560 nmwith ease of assembly and calibration.
Pocket Deformable Mirror For Adaptive Optics Applications, Leonid A. Beresnev, Mikhail Vorontsov, Peter Wangsness
Pocket Deformable Mirror For Adaptive Optics Applications, Leonid A. Beresnev, Mikhail Vorontsov, Peter Wangsness
Electrical and Computer Engineering Faculty Publications
Adaptive/active optical elements are designed to improve optical system performance in the presence of phase aberrations. For atmospheric optics and astronomical applications, an ideal deformable mirror should have sufficient frequency bandwidth for compensation of fast changing wave front aberrations induced by either atmospheric turbulences or by turbulent air flows surrounding a flying object (air optical effects). In many applications, such as atmospheric target tracking, remote sensing from flying aircraft, boundary layer imaging, laser communication and laser beam projection over near horizontal propagation paths the phase aberration frequency bandwidth can exceed several kHz. These fast-changing aberrations are currently compensated using relatively …
Adaptive Beam Director For A Tiled Fiber Array, Mikhail Vorontsov, Jim F. Riker, Ernst Polnau, Svetlana Lachinova, Venkata S. Rao Gudimetla
Adaptive Beam Director For A Tiled Fiber Array, Mikhail Vorontsov, Jim F. Riker, Ernst Polnau, Svetlana Lachinova, Venkata S. Rao Gudimetla
Electrical and Computer Engineering Faculty Publications
We present the concept development of a novel atmospheric compensation system based on adaptive tiled fiber array architecture operating with target-in-the-loop scenarios for directed beam applications. The adaptive tiled fiber array system is integrated with adaptive beam director (ABD). Wavefront control and sensing functions are performed directly on the beam director telescope primary mirror. The beam control of the adaptive tiled fiber array aims to compensate atmospheric turbulence-induced dynamic phase aberrations and results in a corresponding brightness increase on the illuminated extended object. The system is specifically designed for tiled fiber system architectures operating in strong intensity scintillation and speckle-modulation …
Enhanced Cerenkov Second-Harmonic Generation In Patterned Lithium Niobate, Cong Deng, Joseph W. Haus, Andrew Sarangan, Aziz Mahfoud, Concita Sibilia, Michael Scalora, Aleksei M. Zheltikov
Enhanced Cerenkov Second-Harmonic Generation In Patterned Lithium Niobate, Cong Deng, Joseph W. Haus, Andrew Sarangan, Aziz Mahfoud, Concita Sibilia, Michael Scalora, Aleksei M. Zheltikov
Electro-Optics and Photonics Faculty Publications
We present experimental results of second harmonic generation enhancement through the resonance of the band edge in a photonic crystal based on lithium niobate. Proton exchange technique was used to fabricate a waveguide near the surface of the lithium niobate substrate. The photonic crystal structure over the waveguide was made by UV laser interferometry. Subsequently experiments were designed to quantify the Cerenkov second-harmonic generation (CSHG) radiated into the substrate. The SHG radiated inside the waveguides was also experimentally investigated. In our experiments, the second guided mode of the waveguide was tuned to the band edge resonance to enhance the second …
External Cavity Multiwavelength Semiconductor Mode-Locked Laser Gain Dynamics, Luis Archundia-Berra
External Cavity Multiwavelength Semiconductor Mode-Locked Laser Gain Dynamics, Luis Archundia-Berra
Electronic Theses and Dissertations
External cavity semiconductor mode-locked lasers can produce pulses of a few picoseconds. The pulses from these lasers are inherently chirped with a predominant linear chirp component that can be compensated resulting in sub-picosecond pulses. External cavity semiconductor mode-locked lasers can be configured as multiwavelength pulse sources and are good candidates for time and wavelength division multiplexing applications. The gain medium in external cavity semiconductor mode-locked lasers is a semiconductor optical amplifier (SOA), and passive and hybrid mode-locked operation are achieved by the introduction of a saturable absorber (SA) in the laser cavity. Pump-probe techniques were used to measure the intracavity …
High Birefringence And Low Viscosity Liquid Crystals, Chien-Hui Wen
High Birefringence And Low Viscosity Liquid Crystals, Chien-Hui Wen
Electronic Theses and Dissertations
In this dissertation, liquid crystal (LC) materials and devices are investigated in order to meet the challenges for photonics and displays applications. We have studied three kinds of liquid crystal materials: positive dielectric anisotropic LCs, negative dielectric anisotropic LCs, and dual- frequency LCs. For the positive dielectric anisotropic LCs, we have developed some high birefringence isothiocyanato tolane LC compounds with birefringence ~0.4, and super high birefringence isothiocyanato biphenyl-bistolane LC compounds with birefringence as high as ~0.7. Moreover, we have studied the photostability of several high birefringence LC compounds, mixtures, and LC alignment layers in order to determine the failure mechanism …
Antenna-Coupled Infrared And Millimeter-Wave Detectors: Fabrication, Measurement And Optimization, Charles Middleton
Antenna-Coupled Infrared And Millimeter-Wave Detectors: Fabrication, Measurement And Optimization, Charles Middleton
Electronic Theses and Dissertations
Antenna-coupled detectors provide uncooled, cost-effective solutions for infrared and millimeter-wave imaging. This work describes the design, fabrication, measurement, and optimization of several types of antenna-coupled detectors for LWIR (8 - 12 µm) and 94 GHz radiation. Two types of millimeter-wave antenna-coupled detectors were fabricated and tested: a slot antenna coupled to a bolometer, and a patch antenna coupled to a SiC Schottky diode. Electromagnetic modeling of the antennas helped guide the design of antennas with better impedance matching to the detectors. Schottky diodes are discussed as detectors for millimeter-wave and infrared radiation, with the goal of increasing the cutoff frequency …
All-Semiconductor High Power Mode-Locked Laser System, Kyungbum Kim
All-Semiconductor High Power Mode-Locked Laser System, Kyungbum Kim
Electronic Theses and Dissertations
All-optical synchronization and its application in advanced optical communications have been investigated in this dissertation. Dynamics of all-optical timing synchronization (clock recovery) using multi-section gain-coupled distributed-feedback (MS-GC DFB) lasers are discussed. A record speed of 180-GHz timing synchronization has been demonstrated using this device. An all-optical carrier synchronization (phase and polarization recovery) scheme from PSK (phase shift keying) data is proposed and demonstrated for the first time. As an application of all-optical synchronization, the characterization of advanced modulation formats using a linear optical sampling technique was studied. The full characterization of 10-Gb/s RZ-BPSK (return-to-zero binary PSK) data has been demonstrated. …
Fast Response Liquid Crystal Devices, Yung-Hsun Wu
Fast Response Liquid Crystal Devices, Yung-Hsun Wu
Electronic Theses and Dissertations
Liquid crystal (LC) has been widely used for displays, spatial light modulators, variable optical attenuators (VOAs) and other tunable photonic devices. The response time of these devices is mainly determined by the employed liquid crystal material. How to obtain fast response for the LC devices is a fundamentally important and technically challenging task. In this dissertation, we investigate several methods to improve liquid crystal response time, for examples, using dual-frequency liquid crystals, polymer stabilized liquid crystals, and sheared polymer network liquid crystals. We discover a new class of material, denoted as sheared polymer network liquid crystal (SPNLC) which exhibits a …