Publications

The asterisk (*) on author names in publication entries indicates equal contribution to the work.

Preprints

  1. PT-Symmetric Topological Edge-Gain Effect
    Alex Y. Song, Xiao-Qi Sun, Avik Dutt, Momchil Minkov, Casey Wojcik, Haiwen Wang, Ian Williamson, Meir Orenstein, Shanhui Fan
    arXiv:1910.10946 [physics, physics:quant-ph]

    arXiv PDF

    We show that a uniform non-Hermitian material can exhibit a state where non-Hermicity, i.e. gain and loss, only manifests on the edge but not in the bulk. Such a state can generally exist in any topologically gapped structure formed by two sub-systems, e.g. a quantum spin Hall system, with a suitable non-Hermitian coupling between the spins. We also indicate a potential implementation of this effect for topological lasers.

  2. Parallel Fault-Tolerant Programming of an Arbitrary Feedforward Photonic Network
    Sunil Pai, Ian A. D. Williamson, Tyler W. Hughes, Momchil Minkov, Olav Solgaard, Shanhui Fan, David A. B. Miller
    arXiv:1909.06179 [physics]

    arXiv PDF

    Reconfigurable photonic mesh networks of tunable beamsplitter nodes can linearly transform \N\-dimensional vectors representing input modal amplitudes of light for applications such as energy-efficient machine learning hardware, quantum information processing, and mode demultiplexing. Such photonic meshes are typically programmed and/or calibrated by tuning or characterizing each beam splitter one-by-one, which can be time-consuming and can limit scaling to larger meshes. Here we introduce a graph-topological approach that defines the general class of feedforward networks commonly used in such applications and identifies columns of non-interacting nodes that can be adjusted simultaneously. By virtue of this approach, we can calculate the necessary input vectors to program entire columns of nodes in parallel by simultaneously nullifying the power in one output of each node via optoelectronic feedback onto adjustable phase shifters or couplers. This parallel nullification approach is fault-tolerant to fabrication errors, requiring no prior knowledge or calibration of the node parameters, and can reduce the programming time by a factor of order \N to being proportional to the optical depth (or number of node columns in the device). As a demonstration, we simulate our programming protocol on a feedforward optical neural network model trained to classify handwritten digit images from the MNIST dataset with up to 98% validation accuracy.

  3. Wave Physics as an Analog Recurrent Neural Network
    Tyler W. Hughes*, Ian A. D. Williamson*, Momchil Minkov, Shanhui Fan
    arXiv:1904.12831 [physics.comp-ph]

    arXiv PDF

    Analog machine learning hardware platforms promise to be faster and more energy-efficient than their digital counterparts. Wave physics, as found in acoustics and optics, is a natural candidate for building analog processors for time-varying signals. Here we identify a mapping between the dynamics of wave physics, and the computation in recurrent neural networks. This mapping indicates that physical wave systems can be trained to learn complex features in temporal data, using standard training techniques for neural networks. As a demonstration, we show that an inversely-designed inhomogeneous medium can perform vowel classification on raw audio data by simple propagation of waves through such a medium, achieving performance that is comparable to a standard digital implementation of a recurrent neural network. These findings pave the way for a new class of analog machine learning platforms, capable of fast and efficient processing of information in its native domain.

  4. Absence of Unidirectionally Propagating Surface Plasmon-Polaritons in Nonreciprocal Plasmonics
    Siddharth Buddhiraju, Yu Shi, Alex Song, Casey Wojcik, Momchil Minkov, Ian A. D. Williamson, Avik Dutt, Shanhui Fan
    arXiv:1809.05100 [physics]

    arXiv PDF

    In the presence of an external magnetic field, the surface plasmon polariton that exists at the metal-dielectric interface is believed to support a unidirectional frequency range near the surface plasmon frequency, where the surface plasmon polariton propagates along one but not the opposite direction. Recent works have pointed to some of the paradoxical consequences of such a unidirectional range, including in particular the violation of the time-bandwidth product constraint that should otherwise apply in general in static systems. Here we show that such a unidirectional frequency range is nonphysical, using both a general thermodynamic argument, and a detailed calculation based on a nonlocal hydrodynamic Drude model for the metal permittivity. Our calculation reveals that the surface plasmon-polariton remains bidirectional for all frequencies. This work overturns a long-held belief in nonreciprocal photonics, and highlights the importance of quantum plasmonic concepts for the understanding of nonreciprocal plasmonic effects.

  5. Fundamental Limits to Signal Integrity in Nonlinear Parametric Optical Circulators
    Ian A. D. Williamson, Zheng Wang
    arXiv:1711.02060 [physics]

    arXiv PDF

    We characterize the response of a parametric nonlinear optical circulator to realistic signals that have finite bandwidths. Our results show that intermodulation distortion (IMD), rather than pump depletion or compression, limits the maximal operating signal power and the dynamic range of nonlinear parametric circulators. This limitation holds even in the undepleted pump regime where nonlinear circulators are not constrained by dynamic reciprocity. With a realistic pump power, noise floor, and nonlinear waveguide, our numerical modeling demonstrates a maximally achievable spur-free dynamic range (SFDR) of 81 dB.

Journal articles

  1. Reprogrammable Electro-Optic Nonlinear Activation Functions for Optical Neural Networks
    Ian A. D. Williamson, Tyler W. Hughes, Momchil Minkov, Ben Bartlett, Sunil Pai, Shanhui Fan
    IEEE Journal of Selected Topics in Quantum Electronics, vol. 26, num. 1, pp. 1-12

    DOI PDF

    We introduce an electro-optic hardware platform for nonlinear activation functions in optical neural networks. The optical-to-optical nonlinearity operates by converting a small portion of the input optical signal into an analog electric signal, which is used to intensity -modulate the original optical signal with no reduction in processing speed. Our scheme allows for complete nonlinear on–off contrast in transmission at relatively low optical power thresholds and eliminates the requirement of having additional optical sources between each of the layers of the network Moreover, the activation function is reconfigurable via electrical bias, allowing it to be programmed or trained to synthesize a variety of nonlinear responses. Using numerical simulations, we demonstrate that this activation function significantly improves the expressiveness of optical neural networks, allowing them to perform well on two benchmark machine learning tasks: learning a multi-input exclusive-OR (XOR) logic function and classification of images of handwritten numbers from the MNIST dataset. The addition of the nonlinear activation function improves test accuracy on the MNIST task from 85% to 94%.

  2. Forward-Mode Differentiation of Maxwell’s Equations
    Tyler W Hughes, Ian A.D. Williamson, Momchil Minkov, Shanhui Fan
    ACS Photonics, vol. 6, num. 11, pp. 3010-3016

    DOI PDF PDF (supporting info)

    We present a previously unexplored ’forward-mode’ differentiation method for Maxwell’s equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable method, but provides a significant improvement in both memory and speed scaling for problems involving several output parameters, as we analyze in the context of finite-difference time-domain (FDTD) simulations. Furthermore, it provides an exact alternative to numerical derivative methods, based on finite-difference approximations. To demonstrate the usefulness of the method, we perform sensitivity analysis of two problems. First we compute how the spatial near-field intensity distribution of a scatterer changes with respect to its dielectric constant. Then, we compute how the spectral power and coupling efficiency of a surface grating coupler changes with respect to its fill factor.

  3. Penetration Depth Reduction with Plasmonic Metafilms
    Nathan Z. Zhao, Ian A. D. Williamson, Zhexin Zhao, Salim Boutami, Shanhui Fan
    ACS Photonics, vol. 6, num. 8, pp. 2049-2055

    DOI PDF

    In many optical systems, such as metal films, dielectric reflectors, and photonic crystals, electromagnetic waves experience evanescent decay. The spatial length scale of such a decay defines the penetration depth, and a number of technologically important applications in free-space and integrated optics benefit significantly from a small penetration depth. In this paper, we introduce an ultrathin metafilm consisting of alternating regions of metal and dielectric, which has a much smaller penetration depth than that of a corresponding metal thin film. We demonstrate that the reduction of the metafilm’s penetration depth is a direct result of the enhanced effective mass in its photonic band structure. Our results can lead to enhanced device performance in lightweight ultrahigh reflectivity reflectors and to an increased packing density of subwavelength plasmonic channel waveguides.

  4. Broadband Optical Switch Based on an Achromatic Photonic Gauge Potential in Dynamically Modulated Waveguides
    Ian A. D. Williamson, Shanhui Fan
    Physical Review Applied, vol. 11, num. 5, pp. 054035

    DOI PDF

    We demonstrate that a photonic gauge potential, which arises from the phase degree of freedom in dynamic refractive-index modulation and hence is achormatic, can be used to achieve a broadband optical switch using the configuration of a photonic Aharonov-Bohm interferometer (ABI). The resulting ABI switch has a far larger bandwidth and lower cross talk than the conventional Mach-Zehnder interferometer. Using coupled-mode theory and full-wave numerical modeling, we compare the response of the two interferometers in the presence of nonidealities. Our results indicate the importance of the photonic gauge potential for broadband optical signal processing.

  5. High Reflection from a One-Dimensional Array of Graphene Nanoribbons
    Nathan Zhao, Zhexin Zhao, Ian A. D. Williamson, Salim Boutami, Bo Zhao, Shanhui Fan
    ACS Photonics, vol. 6, num. 2, pp. 339-344

    DOI PDF

    We show that up to 90% reflectivity can be achieved by using guided plasmonic resonances in a one-dimensional periodic array of plasmonic nanoribbon. In general, to achieve strong reflection from a guided resonance system requires one to operate in the strongly overcoupled regime where the radiative decay rate dominates over the intrinsic loss rate of the resonances. Using an argument similar to what has been previously used to derive the Chu-Harrington limit for antennas, we show theoretically that there is no intrinsic limit for the radiative decay rate, even when the system has an atomic scale thickness, in contrast to the existence of such limits on antennas. We also show that the current distribution due to plasmonic resonance can be designed to achieve a very high external radiative rate. Our results show that high reflectivity can be achieved in an atomically thin graphene layer, pointing to a new opportunity for creating atomically thin optical devices.

  6. Adjoint Method and Inverse Design for Nonlinear Nanophotonic Devices
    Tyler W. Hughes*, Momchil Minkov*, Ian A. D. Williamson, Shanhui Fan
    ACS Photonics, vol. 5, num. 12, pp. 4781-4787

    DOI PDF PDF (supporting info)

    The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, nonintuitive structures with superior performance. Among various methods, large-scale, gradient-based optimization techniques have been one of the most important ways to design a structure containing a vast number of degrees of freedom. These techniques are made possible by the adjoint method, in which the gradient of an objective function with respect to all design degrees of freedom can be computed using only two full-field simulations. However, this approach has so far mostly been applied to linear photonic devices. Here, we present an extension of this method to modeling nonlinear devices in the frequency domain, with the nonlinear response directly included in the gradient computation. As illustrations, we use the method to devise compact photonic switches in a Kerr nonlinear material, in which low-power and high-power pulses are routed in different directions. Our technique may lead to the development of novel compact nonlinear photonic devices.

  7. Zero-Index Bound States in the Continuum
    Momchil Minkov, Ian A. D. Williamson, Meng Xiao, Shanhui Fan
    Physical Review Letters, vol. 121, num. 26, pp. 263901

    DOI PDF PDF (supporting info)

    Metamaterials with an effective zero refractive index associated with their electromagnetic response are sought for a number of applications in communications and nonlinear optics. A promising way that this can be achieved in all-dielectric photonic crystals is through the design of a Dirac cone at zero Bloch wave vector in the photonic band structure. In the optical frequency range, the natural way to implement this design is through the use of a photonic crystal slab. In the existing implementation, however, the zero-index photonic modes also radiate strongly into the environment due to intrinsic symmetry properties. This has resulted in large losses in recent experimental realizations of this zero-index paradigm. Here, we propose a photonic crystal slab with zero-index modes which are also symmetry-protected bound states in the continuum. Our approach thus eliminates the associated radiation loss. This could enable, for the first time, large-scale integration of zero-index materials in photonic devices.

  8. Dual-Carrier Floquet Circulator with Time-Modulated Optical Resonators
    Ian A. D. Williamson, S. Hossein Mousavi, Zheng Wang
    ACS Photonics, vol. 5, num. 9, pp. 3649-3657

    DOI PDF PDF (supporting info)

    Spatiotemporal modulation has shown great promise as a strong time-reversal symmetry breaking mechanism that enables integrated nonreciprocal devices and topological materials at optical frequencies. However, ideal circulator and isolator performance has relied on spatial symmetry or momentum matching between modulation and optical modes. The resulting systems have been challenging to experimentally realize, due to the prohibitively complex and lossy biasing networks and tight fabrication tolerances that maintain the desired rotational and mirror symmetries. In this work, we propose a microresonator Floquet circulator that leverages the previously untapped degrees of freedom of the modulation, through waveforms with strong harmonic components. The Floquet circulator response exhibits ideal on-resonance isolation and supports broadband forward transmission with no trade-off in insertion loss. We present a numerical demonstration in an on-chip photonic crystal platform with just two modulated resonators requiring no rotational symmetry. Moreover, this approach is general and can leverage a variety of modulation mechanisms while not being limited by pump depletion and signal distortion associated with parametric nonlinear systems.

  9. Large Cavity-Optomechanical Coupling with Graphene at Infrared and Terahertz Frequencies
    Ian A. D. Williamson, S. Hossein Mousavi, Zheng Wang
    ACS Photonics, vol. 3, num. 12, pp. 2353-2361

    DOI PDF PDF (supporting info)

    Graphene exhibits many unusual elastic properties, making it an intriguing material for mechanical measurement and actuation at the quantum limit. We theoretically examine the viability of graphene for cavity optomechanics from near-infrared to terahertz wavelengths, fully taking into account its large optical absorption and dispersion. A large optomechanical coupling coefficient, on the same order of that observed in state-of-the-art optomechanical materials, can be realized in the mid-infrared spectrum with highly doped graphene, a high optical quality factor, and optimal positioning of graphene. Around 100 THz, the dispersive coupling coefficient reaches 180 MHz/nm and 500 MHz/nm in the resolved and unresolved sideband regimes, respectively. We find that predominantly dispersive coupling requires a high graphene Fermi level and mid-infrared excitation, while predominantly dissipative coupling favors a moderate graphene Fermi level and near-infrared excitation.

  10. Extraordinary Wavelength Reduction in Terahertz Graphene-Cladded Photonic Crystal Slabs
    Ian A. D. Williamson, S. Hossein Mousavi, Zheng Wang
    Scientific Reports, vol. 6, pp. 25301

    DOI PDF PDF (supporting info)

    Photonic crystal slabs have been widely used in nanophotonics for light confinement, dispersion engineering, nonlinearity enhancement and other unusual effects arising from their structural periodicity. Sub-micron device sizes and mode volumes are routine for silicon-based photonic crystal slabs, however spectrally they are limited to operate in the near infrared. Here, we show that two single-layer graphene sheets allow silicon photonic crystal slabs with submicron periodicity to operate in the terahertz regime, with an extreme 100\texttimes wavelength reduction from graphene’s large kinetic inductance. The atomically thin graphene further leads to excellent out-of-plane confinement and consequently photonic-crystal-slab band structures that closely resemble those of ideal two-dimensional photonic crystals, with broad band gaps even when the slab thickness approaches zero. The overall photonic band structure not only scales with the graphene Fermi level, but more importantly scales to lower frequencies with reduced slab thickness. Just like ideal 2D photonic crystals, graphene-cladded photonic crystal slabs confine light along line defects, forming waveguides with the propagation lengths on the order of tens of lattice constants. The proposed structure opens up the possibility to dramatically reduce the size of terahertz photonic systems by orders of magnitude.

  11. Kinetic Inductance Driven Nanoscale 2D and 3D THz Transmission Lines
    S. Hossein Mousavi, Ian A. D. Williamson, Zheng Wang
    Scientific Reports, vol. 6, pp. 25303

    DOI PDF

    We examine the unusual dispersion and attenuation of transverse electromagnetic waves in the few-THz regime on nanoscale graphene and copper transmission lines. Conventionally, such propagation has been considered to be highly dispersive, due to the RC time constant-driven voltage diffusion below 1 THz and plasmonic effects at higher optical frequencies. Our numerical modeling across the microwave, THz and optical frequency ranges reveals that the conductor kinetic inductance creates an ultra-broadband linear-dispersion and constant-attenuation region in the THz regime. This so-called LC region is an ideal characteristic that is known to be absent in macro-scale transmission lines. The kinetic-LC frequency range is dictated by the structural dimensionality and the free-carrier scattering rate of the conductor material. Moreover, up to 40x wavelength reduction is observed in graphene transmission lines.

  12. Suppression of the Skin Effect in Radio Frequency Transmission Lines via Gridded Conductor Fibers
    Ian A. D. Williamson, Thien-An N. Nguyen, Zheng Wang
    Applied Physics Letters, vol. 108, num. 8, pp. 083502

    DOI PDF PDF (supporting info)

    Microwave propagation in transmission lines is fundamentally limited in bandwidth and reach by the skin and proximity effects. The resultant current crowding imparts a square-root frequency dependence on attenuation, and ultimately limits the spatial resolution of distributed transmission-line sensors and the data rate of communication systems. In this letter, we numerically analyze the microwave attenuation and impedance in μm-scale gridded fiber structures with currents arranged in a checkered pattern. The checkered lattice of currents significantly mitigates both the skin and proximity effects, and exhibits an unprecedented bandwidth (in excess of 1 GHz) of frequency-flat attenuation in a relatively small physical footprint (∼0.01 mm2).

Patents

  1. Multiple Sorting of Columns in a Displayed Table in a User Interactive Computer Display Interface through Sequential Radial Menus
    Rhys D. Ulerich, Ian A. Williamson
    US8161407 B2

    Google

    Multi-sorting of displayed columns representative of a tabular display is carried out by displaying a table of a plurality of columns, selectively displaying a first radial menu having a plurality of sectors, each sector representative of one of the plurality of columns, enabling a user to select one of the sectors, and responsive to a user selection of a sector for displaying a second radial menu of the plurality of sectors wherein the selected one sector is disabled, e.g. eliminated. This is continued through a sequence of subsequent radial menus until the user has selected the intended set of sequential columns for the multiple sorting.

Invited talks

  1. Workshop on Inverse Design and Automatic Differentiation
    Ian A. D. Williamson*, Momchil Minkov*
    Stanford University

    Slides

    Do you want to learn how to use algorithms to automatically design and optimize optical devices? This approach is called “inverse design,” and has become a very active area of research in recent years. Interestingly, the way that inverse design algorithms are able to efficiently compute gradients (through the adjoint variable method) is mathematically equivalent to the backpropagation algorithm used the machine learning community for training neural networks. Both approaches are instances of automatic differentiation! In this interactive workshop, we will explore these connections from a practical point of view by showing you how to optimize your very own nanophotonic devices by leveraging machine learning libraries. First, we will provide a brief crash course in optical device simulation. We will then spend most of the time discussing concepts in optimization and inverse design by walking through examples in a notebook format. All code will be made available publicly in advance of the workshop so attendees may follow along as we progress. The goal of this workshop will be to provide attendees with a broad understanding of the concepts involved in inverse design and automatic differentiation, while getting a hands-on feel for code and libraries that they can immediately adapt to their own research projects.

Conferences

  1. Wave Physics as an Analog Recurrent Neural Network
    Ian A. D. Williamson, Tyler W. Hughes, Momchil Minkov, Shanhui Fan
    International Symposium on Ultrafast Photonic Technologies & Special Symposium on Silicon Photonics of the Future

    Analog machine learning hardware platforms promise to be faster and more energy-efficient than their digital counterparts. Wave physics, as found in acoustics and optics, is a natural candidate for building analog processors for time-varying signals. Here we identify a mapping between the dynamics of wave physics, and the computation in recurrent neural networks. This mapping indicates that physical wave systems can be trained to learn complex features in temporal data, using standard training techniques for neural networks. As a demonstration, we show that an inversely-designed inhomogeneous medium can perform vowel classification on raw audio data by simple propagation of waves through such a medium, achieving performance that is comparable to a standard digital implementation of a recurrent neural network. These findings pave the way for a new class of analog machine learning platforms, capable of fast and efficient processing of information in its native domain.

  2. Adjoint-Based Inverse Design of Nonlinear Nanophotonic Devices
    Tyler W. Hughes, Momchil Minkov, Ian A. D. Williamson, Shanhui Fan
    Conference on Lasers and Electro-Optics (2019), Paper SW4J.7

    DOI

    We extend the frequency-domain adjoint method to nonlinear optical systems, which enables the gradient-based optimization and inverse design of novel devices. As illustrations, we devise compact photonic switches in a Kerr nonlinear material.

  3. Training of Photonic Neural Networks through In Situ Backpropagation
    Tyler W. Hughes, Momchil Minkov, Ian A. D. Williamson, Yu Shi, Shanhui Fan
    Conference on Lasers and Electro-Optics (2019), Paper JF3F.2

    DOI

    We provide a protocol for training photonic neural networks based on adjoint methods. The gradient of the network with respect to its tunable degrees of freedom is computed by physically backpropagating an optical error signal.

  4. Lossless Zero-Index Guided Modes via Bound States in the Continuum
    Momchil Minkov, Ian A. D. Williamson, Meng Xiao, Shanhui Fan
    Conference on Lasers and Electro-Optics (2019), Paper FM1B.2

    DOI

    Zero-index metamaterials are sought for a number of applications, but have thus far always been associated with significant optical loss. We overcome this shortcoming by designing non-radiative zero-index modes in an all-dielectric photonic crystal slab.

  5. High Reflection from a One-Dimensional Array of Graphene Nanoribbons
    Nathan Zhao, Zhexin Zhao, Ian A. D. Williamson, Salim Boutami, Bo Zhao, Shanhui Fan
    Conference on Lasers and Electro-Optics (2019), Paper FF2A.1

    DOI

    We show one-dimensional plasmonic systems such as graphene nanoribbons can be used to engineer extremely large bandwidth, high reflectivity resonances. Further, we prove that the underlying concept relies upon the general observation of the lack of Chu-Harrington limit in one-dimensional systems.

  6. Broadband Switches Using Photonic Aharonov-Bohm Interferometers and Dynamic Modulation
    Ian A. D. Williamson, Shanhui Fan
    Conference on Lasers and Electro-Optics (2019), Paper FF1B.5

    DOI

    We introduce an optical switch using an Aharonov-Bohm interferometer constructed from gauge potentials in dynamically modulated waveguides. Our results show that such a switch can have a far broader bandwidth than the conventional Mach-Zehnder interferometer.

  7. Absence of Frequency Ranges of Undirectional Propagation in Nonreciprocal Plasmonics
    Siddharth Buddhiraju, Yu Shi, Alex Song, Casey Wojcik, Momchil Minkov, Ian A. D. Williamson, Avik Dutt, Shanhui Fan
    Conference on Lasers and Electro-Optics (2019), Paper FM1C.7

    DOI

    Surface plasmon-polaritons at a metal-dielectric interface are believed to support a unidirectional frequency range under a magnetic field, where a violation of the time-bandwidth constraint is possible. We show that such unidirectionality is nonphysical.

  8. In-Situ Backpropagation in Photonic Neural Networks
    Momchil Minkov, Tyler W. Hughes, Yu Shi, Ian A. D. Williamson, Shanhui Fan
    Frontiers in Optics / Laser Science (2018), Paper FW1C.3

    DOI

    Recently, integrated optics has gained interest as a hardware platform for implementing machine learning algorithms. Here, we introduce a method that enables highly efficient, in situ training of a photonic artificial neural network. We use the adjoint variable method to derive the photonic analogue of the backpropagation algorithm, which is the standard method for computing gradients for conventional neural networks. We further show how these gradients can be obtained exactly through intensity measurements inside the device. Beyond the training of photonic machine learning implementations, our method may also be of broad interest to experimental sensitivity analysis of photonic systems and the optimization of reconfigurable optics platforms.

  9. Cascaded Floquet Resonators as Dual-Carrier Optical Circulators
    Ian Williamson, Zheng Wang
    Frontiers in Optics

    DOI

    Floquet resonances arising in temporally modulated resonators exhibit highly nonreciprocal responses when coupled to external photonic structures. We demonstrate a circulator response to a dual-carrier input compatible with on-chip photonic systems.

  10. Enhanced Dispersive and Dissipative Coupling Regimes in Graphene Optomechanics
    Ian Williamson, Hossein Mousavi, Zheng Wang
    Conference on Lasers and Electro-Optics

    DOI
  11. Strong Attractive Force Between Graphene Sheets at Terahertz Induced by Extraordinary Wavelength Reduction
    Danlu Wang, Ian Williamson, Hossein Mousavi, Zheng Wang
    Conference on Lasers and Electro-Optics

    DOI
  12. Dynamically Tunable Graphene/Dielectric Photonic Crystal Transmission Lines
    Ian Williamson, S. Hossein Mousavi, Zheng Wang
    APS March Meeting Abstracts

  13. Graphene Planar Interconnects: Dispersively- and Geometrically-Controlled Attenuation in RC, LC, and Skin-Depth Regimes
    S. Hossein Mousavi, Ian Williamson, Zheng Wang
    MRS Spring Meeting

  14. Dielectric Interconnects For THz Chip-to-Chip Communications
    Ian Williamson, Kristen N. Parrish, Andrea Alu, Deji Akinwande
    SRC Techcon