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We propose a time-resolved optical measurement scheme for sampling transient charge and spin currents in a bulk centrosymmetric semiconductor. The technique relies on emission of second harmonic light triggered by a pulsed below-gap optical excitation and a spontaneous intraband polarization arising from spin or charge motion, mediated by a $\chi^(3)$-based nonlinear optical process. Our proposal uses homodyne amplification to boost the weak second harmonic signal, making it detectable with conventional electronics, calculated for charge current in a room temperature GaAs semiconductor. This all-optical technique requires neither electrical contact nor bias fields and the signal is estimated at a few percent relative to the shot noise of the probe. This proposal motivates a novel method for exploring thermal and quantum fluctuations in the solid state in a non-invasive manner., Comment: 7 pages, 2 figures

Silicon photonics has many attractive features but faces a major issue: inefficient and slow photodetection in the telecom range. New metal-semiconductor Schottky photodetectors based on intraband absorption address this problem, but their efficiency remains low. We suggest that by creating a junction between silicon and a transparent oxide with appropriate doping, which results in a real permittivity close to zero (known as the epsilon near zero or ENZ regime), detection efficiency could increase by more than tenfold. Using Aluminum Zinc Oxide (AZO) as an example, we design an optimized AZO/Si slot photonic waveguide detector that could potentially reach an efficiency of several tens of percent, in contrast to a few percent for a metal/Si Schottky detector. This increase is primarily due to the lower density of states in AZO compared to metal, along with superior coupling efficiency and strong absorption within a 10 nm slot., Comment: 14 pages, 6 figures

The ability to manipulate the refractive index is a fundamental principle underlying numerous photonic devices. Various techniques exist to modify the refractive index across diverse materials, making performance comparison far from straightforward. In evaluating these methods, power consumption emerges as a key performance characteristic, alongside bandwidth and footprint. Here I undertake a comprehensive comparison of the energy and power requirements for the most well-known index change schemes. The findings reveal that while the energy per volume for index change remains within the same order of magnitude across different techniques and materials, the power consumption required to achieve switching, 100% modulation, or 100% frequency conversion can differ significantly, spanning many orders of magnitude. As it turns out, the material used has less influence on power reduction than the specific resonant or traveling wave scheme employed to enhance the interaction time between light and matter. Though this work is not intended to serve as a design guide, it does establish the limitations and trade-offs involved in index modulation, thus providing valuable insights for photonics practitioners.

Fully CMOS-compatible photonic memory holding devices hold a potential in a development of ultrafast artificial neural networks. Leveraging the benefits of photonics such as high-bandwidth, low latencies, low-energy interconnect and high speed they can overcome the existing limits of the electronic processing. To satisfy all these requirements a new photonic platform is proposed that combines low-loss nitride-rich silicon as a guide and low-loss transparent conductive oxides as an active material that can provide high nonlinearity and bistability under both electrical and optical signals., Comment: 13 pages, 8 figures

Photonics integrated circuits have a huge potential to serve as a framework for a new class of information processing machines and can enable ultrafast artificial neural networks. They can overcome the existing speed and power limits of the electronic processing elements and provide additional benefits of photonics such as high-bandwidth, sub-nanosecond latencies and low-energy interconnect credentials leading to a new paradigm called neuromorphic photonics. The main obstacle to realize such a task is a lack of proper material platform that imposes serious requirements on the architecture of the network. Here we suggest and justify that transparent conductive oxides can be an excellent candidate for such a task as they provide a nonlinearity and bistability under both optical and electrical inputs., Comment: 13 pages, 7 figures

Photonic Time crystals (PTC) arise in time-modulated media when the frequency of modulation of permittivity is on the order of twice the frequency of light and are manifested by the generation and amplification of so-called time reversed waves propagating in the direction opposite to the incoming light. Superficially, the observed phenomenon bears resemblance to the widely known phenomena of optical parametric generation (OPG) and amplification (OPA) using second or third order optical nonlinearities. I show that while indeed the same physical mechanism underpins both PTC and OPA , the difference arises from the boundary conditions. Thus , while dispersion for both PTC and OPA exhibit the same bandgap in momentum space, only in the case of PTC can one have propagation in that bandgap with exponential amplification. I also show that PTC can be engineered with both second and third order nonlinearities, and that rather unexpectedly, modulating permittivity on the ultrafast (few fs) rate is not a necessity, and that one can emulate all the PTC features using materials with a few picoseconds response time commensurate with the propagation time through the medium.

Optical isolators are indispensable components of optical networks. Magneto-optic isolators have excellent operating characteristics, including low-to-no power consumption, but are not well suited for on-chip integration. The technique of temporal modulation of dielectric constant offers an alternative way to achieve isolation without magnetic field but is not without its own drawbacks. In this work I examine diverse methods of optical isolation via temporal modulation and show that independent on whether modulation is achieved by carrier injection, Pockels and acousto-optic effects, or any other conceivable method, there is essentially the same set of constraints on footprint, modulation frequency, and, most important, on power consumption required to achieve full isolation without excessive insertion loss. This power is estimated to be on the order of at least a hundred of milliwatts and whether this requirement is acceptable will depend on ongoing progress of both magneto-optic and time modulated integrated technologies.

Photonic time-varying systems have attracted significant attention owing to their rich physics and potential opportunities for new and enhanced functionalities. In this context, the duality of space and time in wave physics has been particularly fruitful to uncover interesting physical effects in the temporal domain, such as reflection/refraction at temporal interfaces and momentum-bandgaps in time crystals. However, the characteristics of the temporal/frequency dimension, particularly its relation to causality and energy conservation ($\hbar \omega$ is energy, whereas $\hbar \boldsymbol{k}$ is momentum), create challenges and constraints that are unique to time-varying systems and are not present in their spatially varying counterparts. Here, we overview two key physical aspects of time-varying photonics that have only received marginal attention so far, namely temporal dispersion and external power requirements, and explore their implications. We discuss how temporal dispersion, an inherent property of any causal material, makes the fields evolve continuously at sharp temporal interfaces and may limit the strength of fast temporal modulations and of various resulting effects. Furthermore, we show that changing the refractive index in time always involves large amounts of energy. We derive power requirements to observe a time-crystal response in one of the most popular material platforms in time-varying photonics, i.e., transparent conducting oxides, and we argue that these effects are almost always obscured by less exotic nonlinear phenomena. These observations and findings shed light on the physics and constraints of time-varying photonics, and may guide the design and implementation of future time-modulated photonic systems., Comment: 14 pages, 3 figures

I present a simple view of nonlinear optcal phenomena as being determined mostly by the length of interaction time between photons and matter. This may explain why in the last decades the progress in developing better nonlinear materials has not been as rapid as wished. A few tentative routes towards possible improvements in the efficiency of nonlinear optical phenomena are suggested.

Monolayer transition metal dichalcogenides (TMDCs), like MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, feature direct bandgaps, strong spin-orbit coupling, and exciton-polariton interactions at the atomic scale, which could be harnessed for efficient light emission, valleytronics, and polaritonic lasing, respectively. Nevertheless, to build next-generation photonic devices that make use of these features, it is first essential to model the all-optical control mechanisms in TMDCs. Herein, a simple model is proposed to quantify the performance of a 35$\,$\textmu m long Si$_3$N$_4$ waveguide-integrated all-optical MoSe$_2$ modulator. Using this model, a switching energy of 14.6$\,$pJ is obtained for a transverse-magnetic (TM) and transverse-electric (TE) polarised pump signals at $\lambda =\,$480$\,$nm. Moreover, maximal extinction ratios of 20.6$\,$dB and 20.1$\,$dB are achieved for a TM and TE polarised probe signal at $\lambda =\,$500$\,$nm, respectively, with an ultra-low insertion loss of $<0.3\,$dB. Moreover, the device operates with an ultrafast recovery time of 50$\,$ps, while maintaining a high extinction ratio for practical applications. These findings facilitate modeling and designing novel TMDC-based photonic devices., Comment: \copyright 2022 Optica Publishing Group. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited

Permanent dipole moments of electronics states in non-centro-symmetric materials play pivotal role in many phenomena. Correctly evaluating them presents an arduous task and usually requires full knowledge of the band structure as well as understanding the intricate concepts of Berry curvature. Here we show that in a few cases (e.g. zinc blende and wurtzite) a rather facile first-principle analytical derivation of the permanent dipole moments using L Hopital rule can be performed, and the values and dispersion of these dipoles near high symmetry points can be found using just a couple of widely available material parameters. The results will hopefully contribute to better understanding of shift currents, optical rectification and other electro-optical phenomena.

Layered van der Waals materials offer a unique platform for creating atomic-void channels with sub-nanometer dimensions. Coupling light into these channels may further advance sensing, quantum information, and single molecule chemistries. Here we examine limits of light guiding in atomic-void channels and show that van der Waals materials exhibiting strong resonances - excitonic and polaritonic - are ideally suited for deeply subwavelength light guiding. We demonstrate that excitonic transition metal dichalcogenides can squeeze > 70% of optical power in just < {\lambda}/100 thick channel in the visible and near-infrared. We also show that polariton resonances of hexagonal boron nitride allow deeply subwavelength (< {\lambda}/500) guiding in the mid-infrared. We further reveal effects of natural material anisotropy and discuss the influence of losses. Our analysis shows van der Waals channel waveguides while offering extreme optical confinement exhibit significantly lower loss compared to plasmonic counterparts. Such atomic void waveguides pave the way to low loss and deeply subwavelength optics., Comment: 17 pages, 5 figures

Graphene has emerged as an ultrafast photonic material for on-chip all-optical modulation. However, its atomic thickness limits its interaction with guided optical modes, which results in a high switching energy per bit or low modulation efficiencies. Nonetheless, it is possible to enhance the interaction of guided light with graphene by nanophotonic means. Herein, we present a practical design of an all-optical modulator that is based on graphene and hexagonal boron nitride (hBN) heterostructures that are hybrid integrated into silicon slot waveguides. Using this device, a high extinction ratio (ER) of 7.3 dB, an ultralow insertion loss (IL) of <0.6 dB, and energy-efficient switching (<0.33 pJ/bit) are attainable for a 20{\mu}m long modulator with double layer graphene. In addition, the device performs ultrafast switching with a recovery time of <600 fs, and could potentially be employed as a high-performance all-optical modulator with an ultra-high bandwidth in the hundreds of GHz. Moreover, the modulation efficiency of the device is further enhanced by stacking additional layers of graphene-hBN heterostructures, while theoretically maintaining an ultrafast response. The proposed device exhibits highly promising performance metrics, which are expected to serve the needs of next-generation photonic computing systems., Comment: Accepted for publication in the IEEE Journal of Selected Topics in Quantum Electronics

Electro optic modulators being key for many signal processing systems must adhere to requirements given by both electrical and optical constrains. Distinguishing between charge driven (CD) and field driven (FD) designs, we answer the question of whether fundamental performance benefits can be claimed of modulators based on emerging electro-optic materials. Following primary metrics, we compare the performance of emerging electro-optic and electro-absorption modulators such as graphene, transparent conductive oxides, and Si, based on charge injection with that of the legacy FD modulators, such as those based on lithium niobate and quantum confined Stark effect. We show that for rather fundamental reasons, FD modulators always outperform CD ones in the conventional wavelength scale waveguides. However, for waveguide featuring a sub-wavelength optical mode, such as those assisted by plasmonics, the emerging CD devices are indeed highly competitive.

Electro-optic modulators provide a key function in optical transceivers and increasingly in photonic programmable Application Specific Integrated Circuits (ASICs) for machine learning and signal processing. However, both foundry ready silicon based modulators and conventional material based devices utilizing Lithium niobate fall short in simultaneously providing high chip packaging density and fast speed. Current driven ITO based modulators have the potential to achieve both enabled by efficient light matter interactions. Here, we introduce micrometer compact Mach Zehnder Interferometer (MZI) based modulators capable of exceeding 100 GHz switching rates. Integrating ITO thin films atop a photonic waveguide, spectrally broadband, and compact MZI phase shifter. Remarkably, this allows integrating more than 3500 of these modulators within the same chip area as only one single silicon MZI modulator. The modulator design introduced here features a holistic photonic, electronic, and RF-based optimization and includes an asymmetric MZI tuning step to optimize the Extinction Ratio (ER) to Insertion Loss (IL) and dielectric thickness sweep to balance the tradeoffs between ER and speed. Driven by CMOS compatible bias voltage levels, this device is the first to address next generation modulator demands for processors of the machine intelligence revolution, in addition to the edge and cloud computing demands as well as optical transceivers alike., Comment: 14 pages, 7 figures

Landau Damping (LD) mechanism of the Localized Surface Plasmon (LSP) decay is studied for the hybrid nanoplasmonic (metal core/dielectric shell) structures. It is shown that LD in hybrid structures is strongly affected by permittivity and electron effective mass in the dielectric shell in accordance with previous observations by Kreibig, and the strength of LD can be enhanced by an order of magnitude for some combinations of permittivity and effective mass. The physical reason for this effect is identified as electron spillover into the dielectric where electric field is higher than in the metal and the presence of quasi-discrete energy levels in the dielectric. The theory indicates that the transition absorption at the interface metal-dielectric is a dominant contribution to LD in such hybrid structures. Thus, by judicious selection of dielectric material and its thickness one can engineer decay rates and hot carrier production for important applications, such as photodetection and photochemistry.

While the photonic community is being occupied with exotic concepts portending a grand future and fame if not a fortune, I respectfully entertain the possibility that a humble concept of simply increasing refractive index by a modest factor may have a far greater payoff in many walks of life. With that in mind, I explore why higher index materials have not yet materialized, and point out a few tentative directions for the search of these elusive materials, be they natural or artificial.

The high demand for machine intelligence of doubling every three months is driving novel hardware solutions beyond charging of electrical wires given a resurrection to application specific integrated circuit (ASIC)-based accelerators. These innovations include photonic ASICs (P-ASIC) due to prospects of performing optical linear (and also nonlinear) operations, such as multiply-accumulate for vector matrix multiplications or convolutions, without iterative architectures. Such photonic linear algebra enables picosecond delay when photonic integrated circuits are utilized, via on-the-fly mathematics. However, the neurons full function includes providing a nonlinear activation function, knowns as thresholding, to enable decision making on inferred data. Many P-ASIC solutions performing this nonlinearity in the electronic domain, which brings challenges in terms of data throughput and delay, thus breaking the optical link and introducing increased system complexity via domain crossings. This work follows the notion of utilizing enhanced light-matter-interactions to provide efficient, compact, and engineerable electro-optic neuron nonlinearity. Here, we introduce and demonstrate a novel electro-optic device to engineer the shape of this optical nonlinearity to resemble a rectifying linear unit (ReLU) - the most-commonly used nonlinear activation function in neural networks. We combine the counter-directional transfer functions from heterostructures made out of two electro-optic materials to design a diode-like nonlinear response of the device. Integrating this nonlinearity into a photonic neural network, we show how the electrostatics of this thresholders gating junction improves machine learning inference accuracy and the energy efficiency of the neural network.

We appraise a waveguide-integrated plasmonic graphene photodetector based on the hot carrier photo-bolometric effect, with performance characterized simultaneously by high responsivity, on the scale of hundreds of AW-1, and high speed on the scale of 100s of GHz. Performance evaluation is based on a theory of bolometric effect originating from the band nonparabolicity of graphene. Results compare favorably with the state-of-the-art plasmonic bolometric photodetectors, predicting up to two orders of magnitude increase in a responsivity while keeping speed on the same level, defined by the electron-lattice scattering time in graphene., Comment: 18 pages, 9 figures. arXiv admin note: text overlap with arXiv:2002.04061

Electro-optic modulators are utilized ubiquitously ranging from applications in data communication to photonic neural networks. While tremendous progress has been made over the years, efficient phase-shifting modulators are challenged with fundamental tradeoffs, such as voltage-length, index change-losses or energy-bandwidth, and no single solution available checks all boxes. While voltage-driven phase modulators, such as based on lithium niobate, offer low loss and high speed operation, their footprint of 10's of cm-scale is prohibitively large, especially for density-critical applications, for example in photonic neural networks. Ignoring modulators for quantum applications, where loss is critical, here we distinguish between current versus voltage-driven modulators. We focus on the former, since current-based schemes of emerging thin electro-optical materials have shown unity-strong index modulation suitable for heterogeneous integration into foundry waveguides. Here, we provide an in-depth ab-initio analysis of obtainable modulator performance based on heterogeneously integrating low-dimensional materials, i.e. graphene, thin films of indium tin oxide, and transition metal dichalcogenide monolayers into a plurality of optical waveguide designs atop silicon photonics. Using the fundamental modulator tradeoff of energy-bandwidth-product as a design-quality quantifier, we show that a small modal cross section, such as given by plasmonic modes, enables high-performance operation, physically realized by arguments on charge-distribution and low electrical resistance. An in-depth design understanding of phase-modulator performance, beyond doped-junctions in silicon, offers opportunities for micrometer-compact yet energy-bandwidth-ratio constrained modulators with timely opportunities to hardware-accelerate applications beyond data communication towards photonic machine intelligence.

Novel materials, with enhanced light-matter interaction capabilities, play an essential role in achieving the lofty goals of nonlinear optics. Recently, Epsilon-Near-Zero (ENZ) media have emerged as a promising candidate to enable the enhancement of several nonlinear processes including refractive index modulation and harmonic generation. Here, we analyze the optical nonlinearity of ENZ media to clarify the commonalities with other nonlinear media and its unique properties. We focus on transparent conducting oxides (TCOs) as the family of ENZ media with near zero permittivity in the near-infrared (telecom) band. We investigate the instantaneous and delayed nonlinearities. By identifying their common origin from the band nonparabolicity, we show that their relative strength is entirely determined by a ratio of the energy and momentum relaxation (or dephasing) times. Using this framework, we compare ENZ materials against the many promising nonlinear media that have been investigated in literature and show that while ENZ materials do not radically outpace the strength of traditional materials in either the fast or slow nonlinearity, they pack key advantages such as an ideal response time, intrinsic slow light enhancement, and broadband nature in a compact platform making them a valuable tool for ultrafast photonics applications for decades to come.

Densely integrated active photonics is key for next generation on-chip networks for addressing both footprint and energy budget concerns. However, the weak light-matter interaction in traditional active Silicon optoelectronics mandates rather sizable device lengths. The ideal active material choice should avail high index modulation while being easily integrated into Silicon photonics platforms. Indium tin oxide (ITO) offers such functionalities and has shown promising modulation capacity recently. Interestingly, the nanometer-thin unity-strong index modulation of ITO synergistically combines the high group-index in hybrid plasmonic with nanoscale optical modes. Following this design paradigm, here, we demonstrate a spectrally broadband, GHz-fast Mach-Zehnder interferometric modulator, exhibiting a high efficiency signified by a miniscule VpL of 95 Vum, deploying an one-micrometer compact electrostatically tunable plasmonic phase-shifter, based on heterogeneously integrated ITO thin films into silicon photonics. Furthermore we show, that this device paradigm enables spectrally broadband operation across the entire telecommunication near infrared C-band. Such sub-wavelength short efficient and fast modulators monolithically integrated into Silicon platform open up new possibilities for high-density photonic circuitry, which is critical for high interconnect density of photonic neural networks or applications in GHz-fast optical phased-arrays, for example.

For decades, nonlinear optics has been used to control the frequency and propagation of light in unique ways enabling a wide range of applications such as ultrafast lasing, sub-wavelength imaging, and novel sensing methods. Through this, a key thread of research in the field has always been the development of new and improved nonlinear materials to empower these applications. Recently, epsilon-near-zero (ENZ) materials have emerged as a potential platform to enhanced nonlinear interactions, bolstered in large part due to the extreme refractive index tuning ({\Delta}n~ 0.1 - 1) of sub-micron thick films that has been demonstrated in literature. Despite this experimental success, the theory has lagged and is needed to guide future experimental efforts. Here, we construct a theoretical framework for the intensity-dependent refractive index of the most popular ENZ materials, heavily doped semiconductors. We demonstrate that the nonlinearity when excited below bandgap, is due to the modification of the effective mass of the electron sea which produces a shift in the plasma frequency. We discuss trends and trade-offs in the optimization of excitation conditions and material choice (such material loss, band structure, and index dispersion), and provide a figure of merit through which the performance of future materials may be evaluated. By illuminating the framework of the nonlinearity, we hope to propel future applications in this growing field.

We investigate waveguide-integrated plasmonic graphene photodetector operating based on the hot carrier photo-bolometric effect, which is characterized simultaneously by high responsivity on the scale of hundreds of AW-1 and high speed on the scale of 100s of GHz. We develop a theory of bolometric effect originating from the band nonparabolicity of graphene and estimate responsivity due to bolometric effect is shown to significantly surpass the responsivity of co-existing photo-conductive effect thus convincingly demonstrating the dominance of bolometric effect. Based on the theory we propose a novel detector configuration based on hybrid waveguide that allows for efficient absorption in the graphene over short distance and subsequently a large change of conductivity. The results demonstrate the potential of graphene for high-speed communication systems.

Plasmon-assisted hot carrier processes in metal nanoparticles can be described either classically or using the full strength of quantum mechanics. We reconfirm that from the practical applications point of view, when it comes to description of the decay of plasmons in nanoparticles, classical description is sufficiently adequate for all but the smallest of the nanoparticles. At the same time, the electron temperature rise in nanoparticles is discrete (quantized) and neglecting this fact can lead to significant underestimating of hot carrier assisted effects, such as photo-catalysis.

Evolution of the nonequilibrium carriers excited in the process of decay of surface plasmon polaritons in metal is described for each step, from the carrier generation to their extraction from the metal. The relative importance of various carrier generating mechanism is discussed. It is shown that both carrier generation and their decay are inherently quantum processes as for realistic illumination conditions no more than a single SPP per nanoparticle exists at a given time. As a result, the distribution of non-equilibrium carriers cannot be described by a single temperature. It is also shown that the originally excited carriers that have not undergone a single electron-electron scattering event, are practically the only ones that contribute to the injection. The role of the momentum conservation in the carrier extraction is discussed and it is shown that if all the momentum conservation rules are relaxed, it is the density of states in the semiconductor/dielectric that determines the ultimate injection efficiency. A set of recommendations aimed at improving the efficiency of plasmonic-assisted photodetection and (to a lesser degree) photocatalysis is made in the end.

We investigate adiabatic frequency conversion using epsilon near zero (ENZ) materials and show that while the maximum frequency conversion for a given change of permittivity does not exhibit increase in the vicinity of {\epsilon}=0 condition. However, that change can be achieved in a shorter length, and if the pump is also in the ENZ vicinity, at a lower pump intensity. This slow propagation effect makes the conversion efficiency in the ENZ material comparable to that in microresonators and other structured slow light schemes, but unlike the latter no nanofabrication is required for ENZ materials which constitutes their major advantage over alternative frequency conversion approaches.

Electro-optic modulation performs a technological relevant functionality such as for communication, beam steering, or neuromorphic computing through providing the nonlinear activation function of a perceptron. Wile Silicon photonics enabled the integration and hence miniaturization of optoelectronic devices, the weak electro-optic performance of Silicon renders these modulators to be bulky and power-hungry compared to a single switch functionality known from electronics. To gain deeper insights into the physics and operation of modulators hetero-generous integration of emerging electro-optically active materials could enable separating light passive and low-loss light routing from active light manipulation. Here we discuss and review our recent work on a) fundamental performance vectors of electro-optic modulators, and b) showcase recent development of heterogeneous-integrated emerging EO materials into Si-photonics to include an ITO-based MZM, a Graphene hybrid-plasmon and the first TMD-MRR modulator using a microring resonator. Our results indicate a viable path for energy efficient and compact Silicon photonic based modulators., Comment: arXiv admin note: text overlap with arXiv:1801.05046

Plasmonic structures are known to support the modes with subwavelength volumes in which the field matter interactions are greatly enhanced. Coupling between the molecular excitations and plasmons leading to formation of plexcitons has been investigated for a number of organic molecules. However, plasmon-exciton coupling in metal semiconductor structures have not experienced the same degree of attention. In this work we show that the very strong coupling regime in which the Rabi energy exceeds the exciton binding energy is attainable in semiconductor cladded plasmonic nanoparticles and leads to formation of Wannier Exciton Plasmon Polariton (WEPP) that is bound to the metal nanoparticle and characterized by dramatically smaller (by factor of few) excitonic radius and correspondingly higher ionization energy. This higher ionization energy exceeding approaching 100meV for the CdS/Ag structures may make room temperature Bose Einstein condensation and polariton lasing in plasmonic/semiconductor structures possible

A physically transparent unified theory of optically and plasmon induced hot carrier generation in metals is developed with all the relevant mechanisms included. Analytical expressions that estimate the carrier generation rates, their locations, energy and direction of motion are obtained. Among four mechanisms considered: interband absorption, phonon and defect assisted absorption, electron electron scattering assisted absorption, and surface collision assisted absorption (Landau damping), it is the last one that generates hot carriers which are most useful for practical applications in photo detection and photo catalysis.

For many applications Optical Frequency Combs (OFCs) require a high degree of temporal coherence (narrow linewidth). Commonly OFCs are generated in nonlinear media from a monochromatic narrow linewidth laser sources or from a mode-locked laser pulses but in the all-important mid-infrared (MIR) and terahertz (THz) regions of spectrum OFCs can be generated intrinsically by the free-running quantum cascade lasers (QCLs) with high efficiency. These combs do not look like conventional OFCs as the phases of each mode are different and in temporal domain the OFC is a seemingly random combination of amplitude- and phase-modulated signals rather than a short pulse. Despite this pseudo-randomness, the experimental evidence suggests that the linewidth of the QCL OFC is just as narrow as that of a QCL operating in the single mode. While universally acknowledged, this seemingly observation is not fully understood. In this work we rigorously prove this fact by deriving the expression for the Schawlow-Townes linewidth of QCL OFC and offer a transparent physical interpretation based on orthogonality of laser modes, indicating that despite their very different temporal profiles MIR and THz QCL OFCs are just as good for most applications as any other OFC.

Modern nonlinear optical materials allow light of one wavelength be efficiently converted into light at another wavelength. However, designing nonlinear optical materials to operate with ultrashort pulses is difficult, because it is necessary to match both the phase velocities and group velocities of the light. Here we show that self-organized nonlinear gratings can be formed with femtosecond pulses propagating through nanophotonic waveguides, providing simultaneous group-velocity matching and quasi-phase-matching for second harmonic generation. We record the first direct microscopy images of photo-induced nonlinear gratings, and demonstrate how these waveguides enable simultaneous $\chi^{(2)}$ and $\chi^{(3)}$ nonlinear processes, which we utilize to stabilize a laser frequency comb. Finally, we derive the equations that govern self-organized grating formation for femtosecond pulses and explain the crucial role of group-velocity matching. In the future, such nanophotonic waveguides could enable scalable, reconfigurable nonlinear optical systems., Comment: 19 pages, including Supplemental Information

Electrically-driven optical antennas can serve as compact sources of electromagnetic radiation operating at optical frequencies. In the most widely explored configurations, the radiation is generated by electrons tunneling between metallic parts of the structure when a bias voltage is applied across the tunneling gap. Rather than relying on an inherently inefficient inelastic light emission in the gap, we suggest to use a ballistic nanoconstriction as the feed element of an optical antenna supporting plasmonic modes. We discuss the underlying mechanisms responsible for the optical emission, and show that with such a nanoscale contact, one can reach quantum efficiency orders of magnitude larger than with standard light-emitting tunneling structures.

Electro-optic modulation is a technology-relevant function for signal keying, beam steering, or neuromorphic computing through providing the nonlinear activation function of a perceptron. With silicon-based modulators being bulky and inefficient, we here discuss graphene-based devices heterogeneously integrated. This study provides a critical and encompassing discussing of the physics and performance of graphene modulators rather than collecting relevant published work. We provide a holistic analysis of the underlying physics of modulators including the graphenes index tunability, the underlying optical mode, and discuss resulting performance vectors of this novel class of hybrid modulators. Our results show that the reducing the modal area, and reducing the effective broadening of the active material are key to improving device performance defined by the ratio of energy-bandwidth and footprint. We further show how the waveguides polarization must be in-plane with graphene such as given by plasmonic-slot structures. A high device performance can be obtained by introducing multi- or bi-layer graphene modulator designs. Lastly, we present recent results of a graphene-based hybrid-photon-plasmon modulator on a silicon platform, requiring near Boltzmann approximation (100mV) low drive voltages. Being physically compact this 100 aJ/bit modulator opens the path towards a new class of attojoule opto-electronics., Comment: arXiv admin note: text overlap with arXiv:1502.04672 by other authors

Electro-optic modulation is a key function for data communication. Given the vast amount of data handled, understanding the intricate physics and trade-offs of modulators on-chip allows revealing performance regimes not explored yet. Here we show a holistic performance analysis for waveguide-based electro-absorption modulators. Our approach centers around material properties revealing obtainable optical absorption leading to effective modal cross-section, and material broadening effects. Taken together both describe the modulator physical behavior entirely. We consider a plurality of material modulation classes to include two-level absorbers such as quantum dots, free carrier accumulation or depletion such as ITO or Silicon, two-dimensional electron gas in semiconductors such as quantum wells, Pauli blocking in Graphene, and excitons in two-dimensional atomic layered materials such as found in transition metal dichalcogendies. Our results show that reducing the modal area generally improves modulator performance defined by the amount of induced electrical charge, and hence the energy-per-bit function, required switching the signal. We find that broadening increases the amount of switching charge needed. While some material classes allow for reduced broadening such as quantum dots and 2-dimensional materials due to their reduced Coulomb screening leading to increased oscillator strengths, the sharpness of broadening is overshadowed by thermal effects independent of the material class. Further we find that plasmonics allows the switching charge and energy-per-bit function to be reduced by about one order of magnitude compared to bulk photonics. This analysis is aimed as a guide for the community to predict anticipated modulator performance based on both existing and emerging materials.

We present quantum yield measurements of single layer $\textrm{WSe}_2$ (1L-$\textrm{WSe}_2$) integrated with high-Q ($Q>10^6$) optical microdisk cavities, using an efficient ($\eta>$90%) near-field coupling scheme based on a tapered optical fiber. Coupling of the excitonic emission is achieved by placing 1L-WSe$_2$ to the evanescent cavity field. This preserves the microresonator high intrinsic quality factor ($Q>10^6$) below the bandgap of 1L-WSe$_2$. The nonlinear excitation power dependence of the cavity quantum yield is in agreement with an exciton-exciton annihilation model. The cavity quantum yield is $\textrm{QY}_\textrm{c}\sim10^{-3}$, consistent with operation in the \textit{broad emitter} regime (i.e. the emission lifetime of 1L-WSe$_2$ is significantly shorter than the bare cavity decay time). This scheme can serve as a precise measurement tool for the excitonic emission of layered materials into cavity modes, for both in plane and out of plane excitation.

Electrooptic modulation performs the conversion between the electrical and optical domain with applications in data communication for optical interconnects, but also for novel optical compute algorithms such as providing nonlinearity at the output stage of optical perceptrons in neuromorphic analogue optical computing. Since the clock frequency for photonics on chip has a power overhead sweet slot around 10s of GHz, ultrafast modulation may only be required in long distance communication, but not for short onchip links. Here we show a roadmap towards atto Joule per bit efficient modulators on chip as well as some experimental demonstrations of novel plasmon modulators with sub 1fJ per bit efficiencies. We then discuss the first experimental demonstration of a photon plasmon-hybrid Graphene-based electroabsorption modulator on silicon. The device shows a sub 1V steep switching enabled by near ideal electrostatics delivering a high 0.05dB per V um performance requiring only 110 aJ per bit. Improving on this design, we discuss a plasmonic slot based Graphene modulator design, where the polarization of the plasmonic mode matches with Graphenes inplane dimension. Here a push pull dual gating scheme enables 2dB per V um efficient modulation allowing the device to be just 770 nm short for 3dB small signal modulation. This in turn allows for a device-enabled two orders of magnitude improvement of electrical optical co integrated network on chips over electronic only architectures. The latter opens technological opportunities in in cognitive computing, dynamic data-driven applications system, and optical analogue compute engines to include neuromorphic photonic computing.

Graphene may be a fascinating material but at this time there exists no experimental or theoretical evidence that it can improve performance of practical nonlinear optical devices.

The common feature of various plasmonic schemes is their ability to confine optical fields of surface plasmon polaritons (SPPs) into sub-wavelength volumes and thus achieve a large enhancement of linear and nonlinear optical properties. This ability, however, is severely limited by the large ohmic loss inherent to even the best of metals. However, in the mid and far infrared ranges of the spectrum there exists a viable alternative to metals, polar dielectrics and semiconductors in which dielectric permittivity (the real part) turns negative in the Reststrahlen region. This feature engenders the so-called surface phonon polaritons (SPhPs) capable of confining the field in a way akin to their plasmonic analogues, the SPPs. Since the damping rate of polar phonons is substantially less than that of free electrons, it is not unreasonable to expect that phononic devices may outperform their plasmonic counterparts. Yet a more rigorous analysis of the comparative merits of phononics and plasmonics reveals a more nuanced answer, namely that while phononic schemes do exhibit narrower resonances and can achieve a very high degree of energy concentration, most of the energy is contained in the form of lattice vibrations so that enhancement of the electric field, and hence the Purcell factor, is rather small compared to what can be achieved with metal nanoantennas. Still, the sheer narrowness of phononic resonances is expected to make phononics viable in applications where frequency selectivity is important.

Rate of single-photon generation by quantum emitters (QEs) can be enhanced by placing a QE inside a resonant structure. This structure can represent an all-dielectric micro-resonator or waveguide and thus be characterized by ultra-low loss and dimensions on the order of wavelength. Or it can be a metal nanostructure supporting localized or propagating surface plasmon-polariton modes that are of subwavelength dimensions, but suffer from strong absorption. In this work, we develop a physically transparent analytical model of single-photon emission in resonant structures and show unambiguously that, notwithstanding the inherently high loss, the external emission rate can be enhanced with plasmonic nanostructures by two orders of magnitude compared to all-dielectric structures. Our analysis provides guidelines for developments of new plasmonic configurations and materials to be exploited in quantum plasmonics., Comment: 10 pages and 3 figures

In this paper, three different materials Si, ITO and graphene; and three different types of mode structures bulk, slot and hybrid; based on their electrooptical and electro absorptive aspects in performance are analyzed. The study focuses on three major characteristics of electrooptic tuning, i.e. material, modal and cavity dependency. The materials are characterized with established models and the allowed ranges for their key parameter spectra are analyzed with desired tuning in mind; categorizing into n and k dominant regions for plausible electrooptic and electro absorptive applications, respectively. A semi analytic approach, with the aid of FEM simulations for the eigenmode calculations, was used for this work. Electrooptic tuning i.e. resonance shift properties inside Fabry Perot cavities are investigated with modal and scaling concerns in mind. Tuning changes the effective complex refractive index of the mode dictated by the Kramers Kronig relations which subsequently suggest a tradeoff between the resonance shift and increasing losses. The electrical tuning properties of the different modes in the cavity are analyzed, and subsequently a figure of merit, delta-lambda/delta-alpha was chosen with respect to carrier concentration and cavity scaling to find prospective suitable regions for desired tuning effects., Comment: 31 pages, 5 figures, 1 table

We investigate the optical properties of sub-wavelength layered metal/dielectric structures, also known as hyperbolic metamaterials (HMMs), using exact analytical Kronig Penney (KP) model. We show that hyperbolic isofrequency surfaces exist for all combinations of layer permittivities and thicknesses, and the largest Purcell enhancements (PE) of spontaneous radiation are achieved away from the nominally hyperbolic region. Detailed comparison of field distributions, dispersion curves, and Purcell factors (PF) between the HMMs and Surface Plasmon Polaritons (SPPs) guided modes in metal/dielectric waveguides demonstrates that HMMs are nothing but weakly coupled gap or slab SPPs modes. Broadband PE is not specific to the HMMs and can be easily attained in single thin metallic layers. Furthermore, large wavevectors and PE are always combined with high loss, short propagation distances and large impedances; hence PE in HMMs is essentially a direct coupling of the energy into the free electron motion in the metal, or quenching of radiative lifetime. PE in HMMs is not related to the hyperbolicity per se but is simply the consequence of the strong dispersion of permittivity in the metals or polar dielectrics, as our conclusions are relevant also for the infrared HMMs occurring in nature. When it comes to enhancement of radiating processes and field concentrations, HMMs are not superior to far simpler plasmonic structures., Comment: 13 pages 15 figures

Noble metals that currently dominate the fields of plasmonics and metamaterials suffer from large ohmic losses. New plasmonic materials, such as doped oxides and nitrides, have smaller material loss, and, using them in place of metals carries promise of reduced-loss plasmonic and metamaterial structures, with sharper resonances and higher field concentration. This promise is put to a rigorous analytical test in this work which reveals that having low material loss is not sufficient to have a reduced modal loss in plasmonic structures. To reduce the modal loss it is absolutely necessary for the plasma frequency to be significantly higher than the operational frequency. Using examples of nanoparticle plasmons and gap plasmons one comes to the conclusion that even in the mid-infrared spectrum metals continue to hold advantage over the alternative media. The new materials may still find application niche where the high absorption loss is beneficial, e.g. in medicine and thermal photovoltaics.

A rigorous theory of photon emission accompanied inelastic tunnelling inside the gap of plasmonic nanoantennas has been developed. The disappointingly low efficiency of the electrical excitation of surface plasmon polaritons in these structures can be increased by orders of magnitude when a resonant tunnelling structure is incorporated inside the gap. Resonant tunnelling assisted surface plasmon emitter may become a key element in future electrically-driven nanoplasmonic circuits., Comment: 7 pages, 6 figures

We show that density-dependent velocity saturation in a GaN High Electron Mobility Transistor (HEMT) can be related to the stimulated emission of longitudinal optical (LO) phonons. As the drift velocity of electrons increases, the drift of the Fermi distribution in reciprocal space produces population inversion and gain for the LO phonons. Once this gain reaches a threshold value, the avalanche-like increase of LO emission causes a rapid loss of electron energy and momentum and leads to drift velocity saturation. Our simple model correctly predicts both the general trend of the saturation velocity decreasing with increasing electron density and the values of saturation velocity measured in our experiments.