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Towards Low-Energy Electron High-Resolution Spectroscopy with Transition-Edge Sensors
Authors:
R. Ammendola,
A. Apponi,
G. Benato,
M. G. Betti,
R. Biondi,
P. Bos,
M. Cadeddu,
A. Casale,
O. Castellano,
G. Cavoto,
L. Cecchini,
E. Celasco,
M. Chirico,
W. Chung,
A. G. Cocco,
A. P. Colijn,
B. Corcione,
N. D'Ambrosio,
M. D'Incecco,
G. De Bellis,
M. De Deo,
N. de Groot,
A. Esposito,
M. Farino,
S. Farinon
, et al. (40 additional authors not shown)
Abstract:
We present a study of the energy resolution of transition-edge sensors (TESs) for the detection of electrons in the 100 eV kinetic energy range. The TES is a Ti-Au bilayer with an active area of $(60 \times 60)$ $μ\text{m}^2$ and a critical temperature of $\sim$ 80 mK. The electron source is based on vertically-aligned multiwall carbon nanotubes located inside the cryostat, with electrons generate…
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We present a study of the energy resolution of transition-edge sensors (TESs) for the detection of electrons in the 100 eV kinetic energy range. The TES is a Ti-Au bilayer with an active area of $(60 \times 60)$ $μ\text{m}^2$ and a critical temperature of $\sim$ 80 mK. The electron source is based on vertically-aligned multiwall carbon nanotubes located inside the cryostat, with electrons generated via field emission. For electrons in the (92 - 99) eV kinetic energy range, we obtain a Gaussian energy resolution for fully-absorbed electrons of (0.479 $\pm$ 0.041 $\pm$ 0.055) eV. When considering the full-width at half-maximum of the peak, the corresponding resolution is of (1.44 $\pm$ 0.17 $\pm$ 0.27) eV. The former represents an improvement of (46 - 60)% with respect to previous results, and is mainly attributed to the reduction in the TES active area. The latter is instead an improvement of over a factor of 20, and is mainly due to the reduction in the emitting area of the electron source, which significantly suppresses electron back-scattering in proximity of the TES. These results represent a major milestone toward high-precision spectroscopy on low-energy electrons, which is a key objective for the PTOLEMY experiment.
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Submitted 25 February, 2026;
originally announced February 2026.
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Ultra-high precision high voltage system for PTOLEMY
Authors:
R. Ammendola,
A. Apponi,
G. Benato,
M. G. Betti,
R. Biondim,
P. Bos,
G. Cavoto,
M. Cadeddu,
A. Casale,
O. Castellano,
E. Celasco,
L. Cecchini,
M. Chirico,
W. Chung,
A. G. Cocco,
A. P. Colijn,
B. Corcione,
N. D'Ambrosio,
M. D'Incecco,
G. De Bellis,
M. De Deo,
N. de Groot,
A. Esposito,
M. Farino,
S. Farinon
, et al. (41 additional authors not shown)
Abstract:
The PTOLEMY project is prototyping a novel electromagnetic filter for high-precision $β$ spectroscopy, with the ultimate and ambitious long-term goal of detecting the cosmic neutrino background through electron capture on tritium bound to graphene. Intermediate small-scale prototypes can achieve competitive sensitivity to the effective neutrino mass, even with reduced energy resolution. To reach a…
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The PTOLEMY project is prototyping a novel electromagnetic filter for high-precision $β$ spectroscopy, with the ultimate and ambitious long-term goal of detecting the cosmic neutrino background through electron capture on tritium bound to graphene. Intermediate small-scale prototypes can achieve competitive sensitivity to the effective neutrino mass, even with reduced energy resolution. To reach an energy resolution better than \SI{500}{meV} at the tritium $β$-spectrum endpoint of \SI{18.6}{keV}, and accounting for all uncertainties in the filtering chain, the electrode voltage must be controlled at the level of a few parts per million and monitored in real time. In this work, we present the first results obtained in this effort, using a chain of commercial ultra-high-precision voltage references, read out by precision multimeters and a \emph{field mill} device. The currently available precision on high voltage is, in the conservative case, as low as \SI{0.2}{ppm} per \SI{1}{kV} single board and $\lesssim$ \SI{50}{mV} over the \SI{10}{kV} series, presently limited by field mill read-out noise. However, assuming uncorrelated Gaussian noise extrapolation, the real precision could in principle be as low as \SI{0.05}{ppm} over \SI{20}{kV}.
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Submitted 22 December, 2025;
originally announced December 2025.
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A Demonstration of Slowed Electron ${\bf E} \times {\bf B}$ Drift for PTOLEMY
Authors:
M. Farino,
A. Tan,
A. Apponi,
M. Betti,
M. Borghesi,
A. Casale,
O. Castellano,
G. Cavoto,
L. Cecchini,
E. Celasco,
W. Chung,
A. G. Cocco,
A. Colijn,
B. Corcione,
N. D'Ambrosio,
N. de Groot,
S. el Morabit,
A. Esposito,
M. Faverzani,
A. D. Ferella,
E. Ferri,
L. Ficcadenti,
S. Gamba,
S. Gariazzo,
H. Garrone
, et al. (36 additional authors not shown)
Abstract:
To resolve the effective neutrino mass $m_β$ with an energy resolution of 50~meV, the PTOLEMY experiment has proposed a novel transverse electromagnetic filtering process. Substantially reducing the kinetic energy of tritium $β$-decay electrons by counteracting motion from ${\bf E}$ $\times$ ${\bf B}$ and $\nabla{\rm B}$ drift, the PTOLEMY filter requires an input of emitted electron kinematic inf…
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To resolve the effective neutrino mass $m_β$ with an energy resolution of 50~meV, the PTOLEMY experiment has proposed a novel transverse electromagnetic filtering process. Substantially reducing the kinetic energy of tritium $β$-decay electrons by counteracting motion from ${\bf E}$ $\times$ ${\bf B}$ and $\nabla{\rm B}$ drift, the PTOLEMY filter requires an input of emitted electron kinematic information to generate a tailored, suitable electric field for each candidate. The collaboration proposes to extract these quantities by using antennae to observe the relativistic frequency shift of emitted cyclotron radiation as an electron transits by ${\bf E}$ $\times$ ${\bf B}$ drift through a uniform magnetic field region preceding the filter. Electrons must be contained within this region long enough such that an adequate integrated radiated power signal is received to accurately estimate these kinematics. This necessitates a controlled, slowed drift speed. This paper presents the experimental design to vary ${\bf E}$ $\times$ ${\bf B}$ drift speed of carbon-14 $β$-decay electrons using a custom electrode field cage situated between the pole faces of an electromagnet. Matching our results with high-fidelity simulation, we deduce a capacity to increase particle time of flight by a factor of 5 in the field cage's slow drift region. Limited only by the dimensions of our system, we assert drift speed can be arbitrarily slowed to meet the needs of PTOLEMY's future detector. Actualizing such a system is a crucial milestone in developing the detector, enabling future cyclotron radiation measurements, filter implementation, and source injection.
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Submitted 10 July, 2025; v1 submitted 13 March, 2025;
originally announced March 2025.
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Detection of Low-Energy Electrons with Transition-Edge Sensors
Authors:
Carlo Pepe,
Benedetta Corcione,
Francesco Pandolfi,
Hobey Garrone,
Eugenio Monticone,
Ilaria Rago,
Gianluca Cavoto,
Alice Apponi,
Alessandro Ruocco,
Federico Malnati,
Danilo Serazio,
Mauro Rajteri
Abstract:
We present the first detection of electrons with kinetic energy in the 100 eV range with transition-edge sensors (TESs). This has been achieved with a $(100\times 100)$ $μ$m$^2$ Ti-Au bilayer TES, with a critical temperature of about 84 mK. The electrons are produced directly in the cryostat by an innovative cold source based on field emission from vertically-aligned multiwall carbon nanotubes. We…
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We present the first detection of electrons with kinetic energy in the 100 eV range with transition-edge sensors (TESs). This has been achieved with a $(100\times 100)$ $μ$m$^2$ Ti-Au bilayer TES, with a critical temperature of about 84 mK. The electrons are produced directly in the cryostat by an innovative cold source based on field emission from vertically-aligned multiwall carbon nanotubes. We obtain a Gaussian energy resolution between 0.8 and 1.8 eV for fully-absorbed electrons in the $(90-101)$ eV energy range, which is found to be compatible with the resolution of this same device for photons in the same energy range. This work opens new possibilities for high-precision energy measurements of low-energy electrons.
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Submitted 17 July, 2024; v1 submitted 29 May, 2024;
originally announced May 2024.
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Graphene phase modulators operating in the transparency regime
Authors:
H. F. Y. Watson,
A. Ruocco,
M. Tiberi,
J. E. Muench,
O. Balci,
S. M. Shinde,
S. Mignuzzi,
M. Pantouvaki,
D. Van Thourhout,
R. Sordan,
A. Tomadin,
M. Romagnoli,
A. C. Ferrari
Abstract:
Next-generation data networks need to support Tb/s rates. In-phase and quadrature (IQ) modulation combine phase and intensity information to increase the density of encoded data, reduce overall power consumption by minimising the number of channels, and increase noise tolerance. To reduce errors when decoding the received signal, intersymbol interference must be minimised. This is achieved with pu…
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Next-generation data networks need to support Tb/s rates. In-phase and quadrature (IQ) modulation combine phase and intensity information to increase the density of encoded data, reduce overall power consumption by minimising the number of channels, and increase noise tolerance. To reduce errors when decoding the received signal, intersymbol interference must be minimised. This is achieved with pure phase modulation, where the phase of the optical signal is controlled without changing its intensity. Phase modulators are characterised by the voltage required to achieve a $π$ phase shift V$_π$, the device length L, and their product V$_π$L. To reduce power consumption, IQ modulators are needed with$<$1V drive voltages and compact (sub-cm) dimensions, which translate in V$_π$L$<$1Vcm. Si and LiNbO$_3$ (LN) IQ modulators do not currently meet these requirements, because V$_π$L$>$1Vcm. Here, we report a double single-layer graphene (SLG) Mach-Zehnder modulator (MZM) with pure phase modulation in the transparent regime, where optical losses are minimised and remain constant with increasing voltage. Our device has $V_πL\sim$0.3Vcm, matching state-of-the-art SLG-based MZMs and plasmonic LN MZMs, but with pure phase modulation and low insertion loss ($\sim$5dB), essential for IQ modulation. Our $V_πL$ is$\sim$5 times lower than the lowest thin-film LN MZMs, and$\sim$3 times lower than the lowest Si MZMs. This enables devices with complementary metal-oxide semiconductor compatible V$_π$L ($<$1Vcm) and smaller footprint than LN or Si MZMs, improving circuit density and reducing power consumption by one order of magnitude.
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Submitted 25 December, 2023;
originally announced January 2024.
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Graphene-perovskite fibre photodetectors
Authors:
S. Akhavan,
A. Taheri Najafabadi,
S. Mignuzzi,
M. Abdi Jalebi,
A. Ruocco,
I. Paradisanos,
O. Balci,
Z. Andaji-Garmaroudi,
I. Goykhman,
L. G. Occhipinti,
E. Lidorikis,
S. D. Stranks,
A. C. Ferrari
Abstract:
The integration of optoelectronic devices, such as transistors and photodetectors (PDs), into wearables and textiles is of great interest for applications such as healthcare and physiological monitoring. These require flexible/wearable systems adaptable to body motions, thus materials conformable to non-planar surfaces, and able to maintain performance under mechanical distortions. Here, we prepar…
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The integration of optoelectronic devices, such as transistors and photodetectors (PDs), into wearables and textiles is of great interest for applications such as healthcare and physiological monitoring. These require flexible/wearable systems adaptable to body motions, thus materials conformable to non-planar surfaces, and able to maintain performance under mechanical distortions. Here, we prepare fibre PDs combining rolled graphene layers and photoactive perovskites. Conductive fibres ($\sim$500$Ω$/cm) are made by rolling single layer graphene (SLG) around silica fibres, followed by deposition of a dielectric layer (Al$_{2}$O$_{3}$ and parylene C), another rolled SLG as channel, and perovskite as photoactive component. The resulting gate-tunable PDs have response time$\sim$5ms, with an external responsivity$\sim$22kA/W at 488nm for 1V bias. The external responsivity is two orders of magnitude higher and the response time one order of magnitude faster than state-of-the-art wearable fibre based PDs. Under bending at 4mm radius, up to$\sim$80\% photocurrent is maintained. Washability tests show$\sim$72\% of initial photocurrent after 30 cycles, promising for wearable applications.
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Submitted 19 November, 2023;
originally announced November 2023.
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Absolute efficiency of a two-stage microchannel plate for electrons in the 30 - 900 eV energy range
Authors:
A. Apponi,
F. Pandolfi,
I. Rago,
G. Cavoto,
C. Mariani,
A. Ruocco
Abstract:
We report on an apparatus able to measure the absolute detection efficiency of a detector for electrons in the 30 - 900 eV range. In particular, we discuss the characterisation of a two-stage chevron microchannel plate (MCP). The measurements have been performed in the LASEC laboratory at Roma Tre University, whit a custom-made electron gun. The very good stability of the beam current in the fA ra…
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We report on an apparatus able to measure the absolute detection efficiency of a detector for electrons in the 30 - 900 eV range. In particular, we discuss the characterisation of a two-stage chevron microchannel plate (MCP). The measurements have been performed in the LASEC laboratory at Roma Tre University, whit a custom-made electron gun. The very good stability of the beam current in the fA range, together with the picoammeter nominal resolution of 0.01 fA, allowed the measurement of the MCP absolute efficiency $ε$. We found an $ε$ = (0.489 $\pm$ 0.003) with no evident energy dependence. We fully characterised the MCP pulse shape distribution, which is quasi-Gaussian with a well visible peak above the noise level. We measured a 68% variation of the average pulse height between 30 and 500 eV. Furthermore, with a deeper analysis of the pulse shape, and in particular of the correlation between pulse height, area and width, we found a method to discriminate single- and multi- electron events occurring within a 10 ns time window.
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Submitted 28 March, 2022;
originally announced March 2022.
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Implementation and Optimization of the PTOLEMY Transverse Drift Electromagnetic Filter
Authors:
A. Apponi,
M. G. Betti,
M. Borghesi,
A. Boscá,
F. Calle,
N. Canci,
G. Cavoto,
C. Chang,
W. Chung,
A. G. Cocco,
A. P. Colijn,
N. D'Ambrosio,
N. de Groot,
M. Faverzani,
A. Ferella,
E. Ferri,
L. Ficcadenti,
P. Garcia-Abia,
G. Garcia Gomez-Tejedor,
S. Gariazzo,
F. Gatti,
C. Gentile,
A. Giachero,
Y. Hochberg,
Y. Kahn
, et al. (31 additional authors not shown)
Abstract:
The PTOLEMY transverse drift filter is a new concept to enable precision analysis of the energy spectrum of electrons near the tritium beta-decay endpoint. This paper details the implementation and optimization methods for successful operation of the filter. We present the first demonstrator that produces the required magnetic field properties with an iron return-flux magnet. Two methods for the s…
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The PTOLEMY transverse drift filter is a new concept to enable precision analysis of the energy spectrum of electrons near the tritium beta-decay endpoint. This paper details the implementation and optimization methods for successful operation of the filter. We present the first demonstrator that produces the required magnetic field properties with an iron return-flux magnet. Two methods for the setting of filter electrode voltages are detailed. The challenges of low-energy electron transport in cases of low field are discussed, such as the growth of the cyclotron radius with decreasing magnetic field, which puts a ceiling on filter performance relative to fixed filter dimensions. Additionally, low pitch angle trajectories are dominated by motion parallel to the magnetic field lines and introduce non-adiabatic conditions and curvature drift. To minimize these effects and maximize electron acceptance into the filter, we present a three-potential-well design to simultaneously drain the parallel and transverse kinetic energies throughout the length of the filter. These optimizations are shown, in simulation, to achieve low-energy electron transport from a 1 T iron core (or 3 T superconducting) starting field with initial kinetic energy of 18.6 keV drained to <10 eV (<1 eV) in about 80 cm. This result for low field operation paves the way for the first demonstrator of the PTOLEMY spectrometer for measurement of electrons near the tritium endpoint to be constructed at the Gran Sasso National Laboratary (LNGS) in Italy.
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Submitted 24 January, 2022; v1 submitted 23 August, 2021;
originally announced August 2021.
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Response of Windowless Silicon Avalanche Photo-Diodes to Electrons in the 90-900 eV Range
Authors:
Alice Apponi,
Gianluca Cavoto,
Marco Iannone,
Carlo Mariani,
Francesco Pandolfi,
Daniele Paoloni,
Ilaria Rago,
Alessandro Ruocco
Abstract:
We report on the characterization of the response of windowless silicon avalanche photo-diodes to electrons in the 90-900 eV energy range. The electrons were provided by a monoenergetic electron gun present in the LASEC laboratories of University of Roma Tre. We find that the avalanche photo-diode generates a current proportional to the current of electrons hitting its active surface. The gain is…
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We report on the characterization of the response of windowless silicon avalanche photo-diodes to electrons in the 90-900 eV energy range. The electrons were provided by a monoenergetic electron gun present in the LASEC laboratories of University of Roma Tre. We find that the avalanche photo-diode generates a current proportional to the current of electrons hitting its active surface. The gain is found to depend on the electron energy $E_e$, and varies from $2.147 \pm 0.027$ (for $E_e = 90$ eV) to $385.8 \pm 3.3$ (for $E_e = 900$ eV), when operating the diode at a bias of $V_{apd} = 350$ V.} This is the first time silicon avalanche photo-diodes are employed to measure electrons with $E_e < 1$ keV.
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Submitted 29 September, 2020; v1 submitted 17 August, 2020;
originally announced August 2020.
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High-responsivity graphene photodetectors integrated on silicon microring resonators
Authors:
Simone Schuler,
Jakob E. Muench,
Alfonso Ruocco,
Osman Balci,
Dries van Thourhout,
Vito Sorianello,
Marco Romagnoli,
Kenji Watanabe,
Takashi Taniguchi,
Ilya Goykhman,
Andrea C. Ferrari,
Thomas Mueller
Abstract:
Graphene integrated photonics provides several advantages over conventional Si photonics. Single layer graphene (SLG) enables fast, broadband, and energy-efficient electro-optic modulators, optical switches and photodetectors (GPDs), and is compatible with any optical waveguide. The last major barrier to SLG-based optical receivers lies in the low responsivity - electrical output per optical input…
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Graphene integrated photonics provides several advantages over conventional Si photonics. Single layer graphene (SLG) enables fast, broadband, and energy-efficient electro-optic modulators, optical switches and photodetectors (GPDs), and is compatible with any optical waveguide. The last major barrier to SLG-based optical receivers lies in the low responsivity - electrical output per optical input - of GPDs compared to conventional PDs. Here we overcome this shortfall by integrating a photo-thermoelectric GPD with a Si microring resonator. Under critical coupling, we achieve $>$90% light absorption in a $\sim$6 $μ$m SLG channel along the Si waveguide. Exploiting the cavity-enhanced light-matter interaction, causing carriers in SLG to reach $\sim$400 K for an input power of $\sim$0.6 mW, we get a voltage responsivity $\sim$90 V/W, demonstrating the feasibility of our approach. Our device is capable of detecting data rates up to 20 Gbit/s, with a receiver sensitivity enabling it to operate at a 10$^{-9}$ bit-error rate, on par with mature semiconductor technology. The natural generation of a voltage rather than a current, removes the need for transimpedance amplification, with a reduction of the energy-per-bit cost and foot-print, when compared to a traditional semiconductor-based receiver.
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Submitted 6 July, 2020;
originally announced July 2020.
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Carbon nanotubes as anisotropic target for dark matter
Authors:
G Cavoto,
M G Betti,
C Mariani,
F Pandolfi,
A D Polosa,
I Rago,
A Ruocco
Abstract:
Directional detection of Dark Matter (DM) particles could be accomplished by studying either ion or electron recoils in large arrays of parallel carbon nanotubes. For instance, a MeV mass DM particle could scatter off a lattice electron, resulting in the transfer of sufficient energy to eject the electron from the nanotube surface. The electron can eventually be detected whenever an external elect…
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Directional detection of Dark Matter (DM) particles could be accomplished by studying either ion or electron recoils in large arrays of parallel carbon nanotubes. For instance, a MeV mass DM particle could scatter off a lattice electron, resulting in the transfer of sufficient energy to eject the electron from the nanotube surface. The electron can eventually be detected whenever an external electric field is added to drive it from the open ends of the array. This detection scheme would offer an anisotropic response and could be used to select an orientation of the target with respect to the DM wind. A compact sensor, in which the cathode element is substituted with a dense array of parallel carbon nanotubes, could serve as the basic detection unit which - if adequately replicated - would allow to explore a significant region of light DM mass and cross-section. A similar detection scheme could be used to detect DM particles with mass in the GeV range scattering off the surface of a CNT and ejecting a carbon ion. We report about the Monte Carlo simulations of such a system and the R&D towards a detector prototype.
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Submitted 4 November, 2019;
originally announced November 2019.
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Supercontinuum generation in varying-dispersion and birefringent silicon waveguide
Authors:
Neetesh Singh,
Diedrik Vermulen,
Alfonso Ruocco,
Nanxi Li,
Erich Ippen,
Franz X Kärtner,
Michael R Watts
Abstract:
Ability to selectively enhance the amplitude and maintain high coherence of the supercontinuum signal with long pulses is gaining significance. In this work an extra degree of freedom afforded by varying the dispersion profile of a waveguide is utilized to selectively enhance supercontinuum. As much as 16 dB signal enhancement in the telecom window and 100 nm of wavelength extension is achieved wi…
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Ability to selectively enhance the amplitude and maintain high coherence of the supercontinuum signal with long pulses is gaining significance. In this work an extra degree of freedom afforded by varying the dispersion profile of a waveguide is utilized to selectively enhance supercontinuum. As much as 16 dB signal enhancement in the telecom window and 100 nm of wavelength extension is achieved with a cascaded waveguide, compared to a fixed dispersion waveguide. Waveguide tapering, in particular with increasing width, is determined to have a flatter and more coherent supercontinuum than a fixed dispersion waveguide when longer input pulses are used. Furthermore, due to the strong birefringence of an asymmetric silicon waveguide the supercontinuum signal is broadened by pumping simultaneously with both quasitransverse electric (TE) and quasi-transverse magnetic (TM) mode in the anomalous dispersion regime. Thus, by controlling the dispersion for the two modes selective signal generation is obtained. Such waveguides offer several advantages over optical fiber as the variation in dispersion can be controlled with greater flexibility in an integrated platform. This work paves the way forward for various applications in fields ranging from medicine to telecom where specific wavelength windows need to be targeted.
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Submitted 27 May, 2019; v1 submitted 23 May, 2019;
originally announced May 2019.
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Waveguide-integrated, plasmonic enhanced graphene photodetectors
Authors:
J. E. Muench,
A. Ruocco,
M. A. Giambra,
V. Miseikis,
D. Zhang,
J. Wang,
H. F. Y. Watson,
G. C. Park,
S. Akhavan,
V. Sorianello,
M. Midrio,
A. Tomadin,
C. Coletti,
M. Romagnoli,
A. C. Ferrari,
I. Goykhman
Abstract:
We present a micrometer scale, on-chip integrated, plasmonic enhanced graphene photodetector (GPD) for telecom wavelengths operating at zero dark current. The GPD is designed and optimized to directly generate a photovoltage and has an external responsivity~12.2V/W with a 3dB bandwidth~42GHz. We utilize Au split-gates with a$\sim$100nm gap to electrostatically create a p-n-junction and simultaneou…
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We present a micrometer scale, on-chip integrated, plasmonic enhanced graphene photodetector (GPD) for telecom wavelengths operating at zero dark current. The GPD is designed and optimized to directly generate a photovoltage and has an external responsivity~12.2V/W with a 3dB bandwidth~42GHz. We utilize Au split-gates with a$\sim$100nm gap to electrostatically create a p-n-junction and simultaneously guide a surface plasmon polariton gap-mode. This increases light-graphene interaction and optical absorption and results in an increased electronic temperature and steeper temperature gradient across the GPD channel. This paves the way to compact, on-chip integrated, power-efficient graphene based photodetectors for receivers in tele and datacom modules
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Submitted 11 May, 2019;
originally announced May 2019.
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Interplay of the volume and surface plasmons in the electron energy loss spectra of C$_{60}$
Authors:
Alexey V. Verkhovtsev,
Andrei V. Korol,
Andrey V. Solov'yov,
Paola Bolognesi,
Alessandro Ruocco,
Lorenzo Avaldi
Abstract:
The results of a joint experimental and theoretical investigation of the C60 collective excitations in the process of inelastic scattering of electrons are presented. The shape of the electron energy loss spectrum is observed to vary when the scattering angle increases. This variation arising due to the electron diffraction of the fullerene shell is described by a new theoretical model which treat…
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The results of a joint experimental and theoretical investigation of the C60 collective excitations in the process of inelastic scattering of electrons are presented. The shape of the electron energy loss spectrum is observed to vary when the scattering angle increases. This variation arising due to the electron diffraction of the fullerene shell is described by a new theoretical model which treats the fullerene as a spherical shell of a finite width and accounts for the two modes of the surface plasmon and for the volume plasmon as well. It is shown that at small angles, the inelastic scattering cross section is determined mostly by the symmetric mode of the surface plasmon, while at larger angles, the contributions of the antisymmetric surface plasmon and the volume plasmon become prominent.
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Submitted 26 October, 2013; v1 submitted 29 February, 2012;
originally announced February 2012.