Rational design of an integrated directional coupler for wideband operation.

We consider a design procedure for directional couplers for which the coupling length is approximately wavelength-independent over a wide bandwidth. We show analytically that two coupled planar waveguides exhibit a maximum in the coupling strength, which ensures both wideband transmission and minimal device footprint. This acts as a starting point for mapping out the relevant part of phase space. This analysis is then generalized to the fully three-dimensional geometry of rib waveguides using an effective medium approximation. This forms an excellent starting point for fully numerical calculations and leads to designs with unprecedented bandwidths and compactness.

Microwave analogy of Förster resonance energy transfer and effect of finite antenna length.

The near-field interaction between quantum emitters, governed by Förster resonance energy transfer (FRET), plays a pivotal role in nanoscale energy transfer mechanisms. However, FRET measurements in the optical regime are challenging as they require nanoscale control of the position and orientation of the emitters. To overcome these challenges, microwave measurements were proposed for enhanced spatial resolution and precise orientation control. However, unlike in optical systems for which the dipole can be taken to be infinitesimal in size, the finite size of microwave antennas can affect energy transfer measurements, especially at short distances. This highlights the necessity to consider the finite antenna length to obtain accurate results. In this study, we advance the understanding of dipole-dipole energy transfer in the microwave regime by developing an analytical model that explicitly considers finite antennas. Unlike previous works, our model calculates the mutual impedance of finite-length thin-wire dipole antennas without assuming a uniform current distribution. We validate our analytical model through experiments investigating energy transfer between antennas placed adjacent to a perfect electric conductor mirror. This allows us to provide clear guidelines for designing microwave experiments, distinguishing conditions where finite-size effects can be neglected and where they must be taken into account. Our study not only contributes to the fundamental physics of energy transfer but also opens avenues for microwave antenna impedance-based measurements to complement optical FRET experiments and quantitatively explore dipole-dipole energy transfer in a wider range of conditions.

Modulation instability with high-order dispersion: fundamental limitations of pattern formation.

We theoretically and numerically investigate modulation instability in the presence of even, high-order dispersion, focusing on general trends rather than on specific results for a particular dispersion order. We show that high-order dispersion leads to increasingly poor phase matching between the three central waves (i.e. the pump and the ±1 sidebands) and the higher sideband orders, inhibiting in effect four-wave mixing frequency generation. For sufficiently large dispersion orders, the problem in effect can reduce to a three-wave system. Our predictions are in excellent agreement with numerical simulations and show that high-order dispersion imposes a fundamental limit on modulation instability dynamics.

Experimental observation of linear pulses affected by high-order dispersion.

We experimentally study the linear propagation of optical pulses affected by high-order dispersion. We use a programmable spectral pulse-shaper that applies a phase that equals that which would result from dispersive propagation. The temporal intensity profiles of the pulses are characterized using phase-resolved measurements. Our results are in very good agreement with previous numerical and theoretical results, confirming that for high dispersion orders m the central part of the pulses follow the same evolution, with m only determining the rate of evolution.

Plasmonic Sensors beyond the Phase Matching Condition: A Simplified Approach.

The conventional approach to optimising plasmonic sensors is typically based entirely on ensuring phase matching between the excitation wave and the surface plasmon supported by the metallic structure. However, this leads to suboptimal performance, even in the simplest sensor configuration based on the Otto geometry. We present a simplified coupled mode theory approach for evaluating and optimizing the sensing properties of plasmonic waveguide refractive index sensors. It only requires the calculation of propagation constants, without the need for calculating mode overlap integrals. We apply our method by evaluating the wavelength-, device length- and refractive index-dependent transmission spectra for an example silicon-on-insulator-based sensor of finite length. This reveals all salient spectral features which are consistent with full-field finite element calculations. This work provides a rapid and convenient framework for designing dielectric-plasmonic sensor prototypes-its applicability to the case of fibre plasmonic sensors is also discussed.

Omnidirectional field enhancements drive giant nonlinearities in epsilon-near-zero waveguides.

Bulk materials with a relative electric permittivity ε close to zero exhibit giant Kerr nonlinearities. However, harnessing this response in guided-wave geometries is not straightforward, due to the extreme and counterintuitive properties of such epsilon-near-zero materials. Here we investigate, through rigorous calculations of the nonlinear coefficient, how the remarkable nonlinear properties of such materials can be exploited in several structures, including bulk films, plasmonic nanowires, and metal nanoapertures. We find the largest nonlinear response when the modal area and group velocity are simultaneously minimized, leading to omnidirectional field enhancement. This insight will be key for understanding nonlinear nanophotonic systems with extreme nonlinearities and points to new design paradigms.

Self-similar propagation of optical pulses in fibers with positive quartic dispersion.

We study the propagation of ultrashort pulses in optical fiber with gain and positive (or normal) quartic dispersion by self-similarity analysis of the modified nonlinear Schrödinger equation. We find an exact asymptotic solution, corresponding to a triangle-like T4/3 intensity profile, with a T1/3 chirp, which is confirmed by numerical simulations. This solution follows different amplitude and width scaling compared to the conventional case with quadratic dispersion. We also suggest, and numerically investigate, a fiber laser consisting of components with positive quartic dispersion that emits quartic self-similar pulses.

Modular nonlinear hybrid plasmonic circuit.

Photonic integrated circuits (PICs) are revolutionizing nanotechnology, with far-reaching applications in telecommunications, molecular sensing, and quantum information. PIC designs rely on mature nanofabrication processes and readily available and optimised photonic components (gratings, splitters, couplers). Hybrid plasmonic elements can enhance PIC functionality (e.g., wavelength-scale polarization rotation, nanoscale optical volumes, and enhanced nonlinearities), but most PIC-compatible designs use single plasmonic elements, with more complex circuits typically requiring ab initio designs. Here we demonstrate a modular approach to post-processes off-the-shelf silicon-on-insulator (SOI) waveguides into hybrid plasmonic integrated circuits. These consist of a plasmonic rotator and a nanofocusser, which generate the second harmonic frequency of the incoming light. We characterize each component's performance on the SOI waveguide, experimentally demonstrating intensity enhancements of more than 200 in an inferred mode area of 100 nm2, at a pump wavelength of 1320 nm. This modular approach to plasmonic circuitry makes the applications of this technology more practical.

Simple model for orthogonal and angled coupling in dielectric-plasmonic waveguides.

We numerically and analytically study orthogonal and angled coupling schemes between a dielectric slab waveguide and a plasmonic slot waveguide for a large range of geometric and material parameters. We obtain high orthogonal coupling transmission efficiencies (up to 78% for 2D calculations, and 54% for 3D calculations) over a wide range of refractive indices, and provide simple analytic arguments that explain the underlying trends. The insights obtained point to angled couplers with even higher coupling efficiencies (up to 86% in 2D, and 61% in 3D). We find that angled plasmonic coupling is well suited for large dielectric waveguides at the phase matching angle. These results suggest new capabilities for efficient dielectric-plasmonic interconnects that can be applied to a wide variety of material combinations and geometries.

A theory of waveguide design for plasmonic nanolasers.

We propose a theory for the waveguide design and analysis for plasmonic nanolasers by reformulating the fundamental waveguide requirements. This theory does not rely on further optimizing previously used structures, but examines each possible design without prejudice. Our exploration of one-dimensional (i.e., layered) plasmonic nanowaveguide geometries and the subsequent extension to 2D structures not only provides a deep understanding of the characteristics of currently used designs, but also leads to superior structures with the potential to address long-standing challenges in plasmonic nanolasers. In addition, we discover analogies between the reformulated fundamental requirements for the waveguide for nanolasers and nanoscale four-wave mixing (FWM) devices. Therefore, after a slight modification, our theory can also be applied to the waveguide design for plasmonic FWM devices.

Analysis and design of fibers for pure-quartic solitons.

The recently discovered pure-quartic solitons, arising from the interaction of quartic dispersion and Kerr nonlinearity, open the door to unexplored soliton regimes and ultrafast laser science. Here, we report a general analysis of the dispersion and nonlinear properties necessary to observe pure-quartic solitons in optical platforms. We apply this analysis, in combination with numerical calculations, to the design of pure-quartic soliton supporting microstructured optical fibers. The designs presented here, which have realistic fabrication tolerances, support unperturbed pure-quartic soliton propagation providing access to an unmatched platform to study novel soliton physics.

Pure-quartic solitons.

Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction of negative fourth-order dispersion and self-phase modulation, which can occur even for normal group-velocity dispersion. We provide experimental and numerical evidence of shape-preserving propagation and flat temporal phase for the fundamental pure-quartic soliton and periodically modulated propagation for the higher-order pure-quartic solitons. We derive the approximate shape of the fundamental pure-quartic soliton and discover that is surprisingly Gaussian, exhibiting excellent agreement with our experimental observations. Our discovery, enabled by precise dispersion engineering, could find applications in communications, frequency combs and ultrafast lasers.

Fano resonances of dielectric gratings: symmetries and broadband filtering.

The guided mode resonances (GMRs) of diffraction gratings surrounded by low index materials can be designed to produce broadband regions of near perfect reflection and near perfect transmission. These have many applications, including in optical isolators, in hybrid lasers cavities and in photovoltaics. The excitation of rapid GMRs occurs in a background of slowly varying Fabry-Perot oscillation, which produces Fano resonances. We demonstrate the critical role of the polarity of adjacent Fano resonances in the formation of the broadband features. We design gratings for photovoltaic applications that operate at wavelengths where material absorption must be considered and where light is incident at non-normal angles.

New avenues for phase matching in nonlinear hyperbolic metamaterials.

Nonlinear optical processes, which are of paramount importance in science and technology, involve the generation of new frequencies. This requires phase matching to avoid that light generated at different positions interferes destructively. Of the two original approaches to achieve this, one relies on birefringence in optical crystals, and is therefore limited by the dispersion of naturally occurring materials, whereas the other, quasi-phase-matching, requires direct modulation of material properties, which is not universally possible. To overcome these limitations, we propose to exploit the unique dispersion afforded by hyperbolic metamaterials, where the refractive index can be arbitrarily large. We systematically analyse the ensuing opportunities and demonstrate that hyperbolic phase matching can be achieved with a wide range of material parameters, offering access to the use of nonlinear media for which phase matching cannot be achieved by other means. With the rapid development in the fabrication of hyperbolic metamaterials, our approach is destined to bring significant advantages over conventional techniques for the phase matching of a variety of nonlinear processes.

Coherent perfect absorption and reflection in slow-light waveguides.

We identify a family of unusual slow-light modes occurring in lossy multimode grating waveguides, for which either the forward or backward mode components, or both, are degenerate. In the fully degenerate case, the response can be modulated between coherent perfect absorption (zero reflection) and perfect reflection by varying the wave amplitudes in a uniform input waveguide. The perfectly absorbed wave has anomalously short absorption length, scaling as the inverse one-third power of the absorptivity.

Cavity Optical Pulse Extraction: ultra-short pulse generation as seeded Hawking radiation.

We show that light trapped in an optical cavity can be extracted from that cavity in an ultrashort burst by means of a trigger pulse. We find a simple analytic description of this process and show that while the extracted pulse inherits its pulse length from that of the trigger pulse, its wavelength can be completely different. Cavity Optical Pulse Extraction is thus well suited for the development of ultrashort laser sources in new wavelength ranges. We discuss similarities between this process and the generation of Hawking radiation at the optical analogue of an event horizon with extremely high Hawking temperature. Our analytic predictions are confirmed by thorough numerical simulations.

Understanding the contribution of mode area and slow light to the effective Kerr nonlinearity of waveguides.

We resolve the ambiguity in existing definitions of the effective area of a waveguide mode that have been reported in the literature by examining which definition leads to an accurate evaluation of the effective Kerr nonlinearity. We show that the effective nonlinear coefficient of a waveguide mode can be written as the product of a suitable average of the nonlinear coefficients of the waveguide's constituent materials, the mode's group velocity and a new suitably defined effective mode area. None of these parameters on their own completely describe the strength of the nonlinear effects of a waveguide.

Degenerate band edge resonances in coupled periodic silicon optical waveguides.

Using full three-dimensional analysis we show that coupled periodic optical waveguides can exhibit a giant slow light resonance associated with a degenerate photonic band edge. We consider the silicon-on-insulator material system for implementation in silicon photonics at optical telecommunications wavelengths. The coupling of the resonance mode with the input light can be controlled continuously by varying the input power ratio and the phase difference between the two input arms. Near unity transmission efficiency through the degenerate band edge structure can be achieved, enabling exploitation of the advantages of the giant slow wave resonance.

Reconfigurable, defect-free, ultrahigh-Q photonic crystal microcavities for sensing.

We propose a new approach for creating reconfigurable high-Q cavities in defect-free photonic crystal slabs (PCSs). The approach relies on selective air-hole infiltration in otherwise defect-free PCSs. We show that using this method we can design ultrahigh-Q microcavities, with Q~10(6). Numerical calculations indicate a large number of high-Q modes with high sensitivity, which are ideal for simultaneous, multi-parameter refractive index-based sensing.