The concept of bound states in the continuum (BIC) has been advancing light confinement technology in leaky environments. In this letter, we propose and numerically demonstrate a slow light waveguide based on a BIC mode. We considered a waveguide with a polymer core loaded on a plane slab, which supports a leaky guided mode coupled to the radiation continuum in the slab. We found that periodic modulation of the polymer core along the propagation direction can result in a high group index mode with a low propagation loss due to BIC confinement. The introduction of one-dimensional photonic crystals into the BIC waveguides will largely expand its functionality and applications in integrated photonics.
We describe theoretically and observe experimentally the formation of a surface state in a semi-infnite waveguide array with side-coupled waveguide, designed to simultaneously achieve Fano and Fabry-Perot resonances. We demonstrate that the surface mode is compact, with all energy concentrated in few waveguides at the edge and no field penetration beyond the side-coupled waveguide position. Furthermore, we show that by broadening the spectral band in the rest of the waveguide array it is possible to suppress exponentially localized modes, whereas the Fano state having the eigenvalue embedded i…
We study the effect of rotation on the propagation of electromagnetic waves in slow-light waveguide structures consisting of coupled micro-ring resonators. We show that such configurations exhibit new a type of the Sagnac effect which can be used for the realization of highly-compact integrated rotation sensors and gyroscopes.
We propose a scheme to realize controlled phase gate between two single photons through a single quantum dot in slow-light silicon photonic crystal waveguide. Enhanced Purcell factor and beta factor lead to high gate fidelity over broadband frequencies compared to cavity-assisted system. The excellent physical integration of this silicon photonic crystal waveguide system provides tremendous potential for large-scale quantum information processing.
We report the observations of spontaneous Raman scattering in silicon photonic crystal waveguides. Continuous-wave measurements of Stokes emission for both wavelength and power dependence is reported in single line-defect waveguides in hexagonal lattice photonic crystal silicon membranes. By utilizing the Bragg gap edge dispersion of the TM-like mode for pump enhancement and the TE-like fundamental mode-onset for Stokes enhancement, the Stokes emission was observed to increase by up to five times in the region of slow group velocity. The results show explicit nonlinear enhancement in a silicon…
Metamaterial is promising for enhancing the capability of plasmonic devices. We consider a cylindrical waveguide with three-level Λ atoms embedded in the dielectric core. By comparing metal cladding vs metamaterial cladding of a waveguide with Λ atoms in the core, we show that, for a fixed amount of slowing of light due to electromagnetically induced transparency, the metamaterial cladding outperforms in terms of the inherent loss.
We investigate bound states in the continuum (BICs) in a planar dielectric waveguide structure consisting of a gold grating on a dielectric layer with a back layer of metal. In this structure, Friedrich-Wintgen (FW) BICs caused by the destructive interference between the radiations from two waveguide modes appear near the anti-crossing point of the dispersion curves. In this study, it is revealed that the branch at which the BIC appears changes according to the polarization of incident radiation. Based on a temporal coupled mode theory, it is shown that the BIC branch is determined by the sign…
We identify a family of unusual slow-light modes occurring in lossy multi-mode grating waveguides, for which either the forward or backward mode components, or both, become degenerate. In the fully-degenerate case, by varying the wave amplitudes in a uniform input waveguide, one can modulate between coherent perfect absorption (zero reflection) and perfect reflection. The perfectly-absorbed wave has anomalously short absorption length, scaling as the inverse 1/3 power of the absorptivity.
We report optical transmission measurements on suspended silicon photonic-crystal waveguides, where one side of the photonic lattice is shifted by half a period along the waveguide axis. The combination of this glide symmetry and slow light leads to a strongly enhanced chiral light-matter interaction but the interplay between slow light and backscattering has not been investigated experimentally in such waveguides. We build photonic-crystal resonators consisting of glide-symmetric waveguides terminated by reflectors and use transmission measurements as well as evanescent coupling to map out th…
Four-wave mixing is observed in a silicon W1 photonic crystal waveguide. The dispersion dependence of the idler conversion efficiency is measured and shown to be enhanced at wavelengths exhibiting slow group velocities. A 12-dB increase in the conversion efficiency is observed. Concurrently, a decrease in the conversion bandwidth is observed due to the increase in group velocity dispersion in the slow-light regime. The experimentally observed conversion efficiencies agree with the numerically modeled results.
We reveal that slow-light enhanced optical forces between side-coupled photonic-crystal nanowire waveguides can be flexibly controlled by introducing a relative longitudinal shift. We predict that close to the photonic band-edge, where the group velocity is reduced, the transverse force can be tuned from repulse to attractive, and the force is suppressed for a particular shift value. Additionally the shift leads to symmetry breaking that can facilitate longitudinal forces acting on the waveguides, in contrast to unshifted structures where such forces vanish.
We investigate for the first time the enhancement of the stimulated Raman scattering in slow-light Silicon-on-Insulator (SOI) photonic crystal line defect waveguides. By applying the Bloch-Floquet formalism to the guided modes in a planar photonic crystal, we develop a formalism that relates the intensity of the down-shifted Stokes signal to the pump intensity and the modal group velocities. The formalism is then applied to two prospective schemes for enhanced stimulated Raman generation in slow-light photonic crystal waveguides. The results demonstrate a maximum factor of 10^4 (66,000) enhanc…
One-dimensional defect photonic crystal (Bragg waveguide) is studied from the viewpoint of the slow light problem. The calculations are presented showing that in the TiO$_2$/SiO$_2$-based Bragg waveguide one can obtain the group index of $\sim$ 1000 and spatial decay length of $\sim$ 3 mm for a nanosecond-scale pulse. Distortion of the pulse due to the group index dispersion proves to be acceptable for the relative pulse delay not exceeding 10. We also analyze propagation of the light pulse in the Bragg waveguide with a quantum well inside and provide arguments showing possibility of reaching …
Integrated optics provides a platform for the experimental implementation of highly complex and compact circuits for practical applications as well as for advances in the fundamental science of quantum optics. The lithium niobate (LN) waveguide is an important candidate for the construction of integrated optical circuits. Based on the bound state in the continuum (BIC) in a LN waveguide, we propose an efficient way to produce polarization-entangled photon pairs. The implementation of this method is simple and does not require the polarization process needed for periodically poled LN. The gener…
We demonstrate lasing in GaAs photonic crystal waveguides with InAs quantum dots as gain medium. Structural disorder is present due to fabrication imperfection and causes multiple scat- tering of light and localization of light. Lasing modes with varying spatial extend are observed at random locations along the guide. Lasing frequencies are determined by the local structure and occur within a narrow frequency band which coincides with the slow light regime of the waveguide mode. The three-dimensional numerical simulation reveals that the main loss channel for lasing modes located away from the…
The equations for Four-Wave-Mixing in a Photonic Crystal waveguide are derived accurately. The dispersive nature of slow-light enhancement, the impact of Bloch mode reshaping in the nonlinear overlap integrals and the tensor nature of the third order polarization are therefore taken into account. Numerical calculations reveal substantial differences with simpler models, which increase with decreasing group velocity. We predict that the gain for a 1.3 mm long, unoptimized GaInP waveguide will exceed 10 dB if the pump power exceeds 1 W.
The spectral dependence of a bending loss of cascaded 60-degree bends in photonic crystal (PhC) waveguides is explored in a slab-type silicon-on-insulator system. Ultra-low bending loss of (0.05+/-0.03)dB/bend is measured at wavelengths corresponding to the nearly dispersionless transmission regime. In contrast, the PhC bend is found to become completely opaque for wavelengths range corresponding to the slow light regime. A general strategy is presented and experimentally verified to optimize the bend design for improved slow light transmission.
We study the dispersion relations in slow-light waveguide structures consisting of coupled microdisk resonators. A group theoretical analysis of the symmetry properties of the propagating modes reveals an interesting phenomenon: The degeneracy of the CW and CCW rotating modes is removed, giving rise to two distinct transmission bands. This effect induces symmetry-based dispersion which may limit usable bandwidth of such structures. The properties of this band splitting and its impact on CROW performance for optical communications are studied in detail.
We study the energy propagation in subwavelength waveguides and demonstrate that the mechanism of material gain, previously suggested for loss compensation, is also a powerful tool to manipulate dispersion and propagation characteristics of electromagnetic pulses at the nanoscale. We show theoretically that the group velocity in lossy nano-waveguides can be controlled from slow to superluminal values by the material gain and waveguide geometry and develop an analytical description of the relevant physics. We utilize the developed formalism to show that gain-assisted dispersion management can b…
Slow light with electromagnetically induced transparency (EIT) in the core of cylindrical waveguide (CW) for an optical fiber system containing three-level atoms is investigated. The CW modes are treated in the weakly guiding approximation which renders the analysis into manageable form. The transparency window and permittivity profile of the waveguide due to the strong pump field in the EIT scheme is calculated. For a specific permittivity profile of the waveguide due to EIT, the propagation constant of the weak signal field and spatial shape of fundamental guided mode are calculated by solvi…
Bound states in the continuum (BICs) are trapped or guided modes with frequencies in radiation continua. They are associated with high-quality-factor resonances that give rise to strong local field enhancement and rapid variations in scattering spectra, and have found many valuable applications. A guided mode of an optical waveguide can also be a BIC, if there is a lateral structure supporting compatible waves propagating in the lateral direction, i.e., there is a channel for lateral leakage. A BIC is typically destroyed (becomes a resonant or a leaky mode) if the structure is slightly perturb…
We consider dielectric cavities whose radiation space is restricted by two parallel metallic planes. The TM solutions of the Maxwell equations of the system are equivalent to the solutions of periodical arrays of dielectric cavities. The system readily allows to achieve bound states in the continuum (BICs) of any type including topological BICs as dependent on position and orientation of the cavities relative to the planes. That extremely facilitates experimental studies in comparison to infinite arrays of the cavities. We show the effect of merging of topologically protected BICs that pushes …
We demonstrate how to control independently both spatial and temporal dynamics of slow light. We reveal that specially designed nonlinear waveguide arrays with phase-shifted Bragg gratings demonstrate the frequency-independent spatial diffraction near the edge of the photonic bandgap, where the group velocity of light can be strongly reduced. We show in numerical simulations that such structures allow a great flexibility in designing and controlling dispersion characteristics, and open a way for efficient spatiotemporal self-trapping and the formation of slow-light optical bullets.
Coupling of external light signals into a photonic crystal waveguide becomes increasingly inefficient as the group velocity of the waveguiding mode slows down. We have systematically studied the efficiency of coupling in the slow light regime for samples with different truncations of the photonic lattice at the coupling interface. Inverse power law dependence is found to best fit the experimental scaling of the coupling loss on the group index. Coupling efficiency is found to be significantly improved up to group indices of 100 for a truncation of the lattice that favors the appearance of the …
We analyze the resonant transmission of light through a photonic-crystal waveguide side coupled to a Kerr nonlinear cavity, and demonstrate how to design the structure geometry for achieving bistability and all-optical switching at ultra-low powers in the slow-light regime. We show that the resonance quality factor in such structures scales inversely proportional to the group velocity of light at the resonant frequency and thus grows indefinitely in the slow-light regime. Accordingly, the power threshold required for all-optical switching in such structures scales as a square of the group velo…
We present a semi-analytic method to calculate the dispersion curves and the group velocity of photonic crystal waveguide modes in two-dimensional geometries. We model the waveguide as a homogenous strip, surrounded by photonic crystal acting as diffracting mirrors. Following conventional guided-wave optics, the properties of the photonic crystal waveguide may be calculated from the phase upon propagation over the strip and the phase upon reflection. The cases of interest require a theory including the specular order and one other diffracted reflected order. The computational advantages let us…
We design an efficient coupler to transmit light from a strip waveguide into the flatband slow mode of a photonic crystal waveguide with ring-shaped holes. The coupler is a section of a photonic crystal waveguide with a higher group velocity, obtained by different ring dimensions. We demonstrate coupling efficiency in excess of 95% over the 8 nm wavelength range where the photonic crystal waveguide exhibits a quasi constant group velocity vg = c/37. An analysis based on the small Fabry-Pérot resonances in the simulated transmission spectra is introduced and used for studying the effect of the …
We present light transmission measurements and frequency-delay reflectometry maps for GaAs photonic crystal membranes, which show the transition from propagation with a well defined group velocity to a regime completely dominated by disorder-induced coherent scattering. Employing a self-consistent optical scattering theory, with only statistical functions to describe the structural disorder, we obtain an excellent agreement with the experiments using no fitting parameters. Our experiments and theory together provide clear physical insight into naturally occurring light localization and multipl…
By combining analytical and numerical approaches, we theoretically investigate the effect of fabrication imperfections, e.g. roughness at metal interfaces, on nanometer metal-insulator-metal waveguides supporting slow gap-plasmon modes. Realistic devices with vapor deposition- and chemically-grown metal films are considered. We obtain quantitative predictions for the attenuations induced by absorption and by backscattering, and analytically derive how both attenuations scale with respect to the group velocity. Depending on the material parameters and fabrication quality, roughness-induced back…
We demonstrate digital tuning of the slow-light regime in silicon photonic-crystal waveguides by performing atomic layer deposition of hafnium oxide. The high group-index regime was deterministically controlled (red-shift of 140 +/- 10 pm per atomic layer) without affecting the group-velocity dispersion and third-order dispersion. Additionally, differential tuning of 110 +/- 30 pm per monolayer of the slow-light TE-like and TM-like modes was observed. This passive post-fabrication process has potential applications including the tuning of chip-scale optical interconnects, as well as Raman and …
Bound states in the continuum (BICs) and exceptional points (EPs) have been the subjects of recent intensive research as they exhibit exotic phenomena that are significant for both fundamental physics and practical applications. We investigated the emergence of the Friedrich-Wintgen (FW) type BIC and the EP in a dielectric waveguide comprising a metal grating, focusing on their dependence on the grating thickness. The BIC emerges at a branch near the anti-crossing formed of the two waveguide modes, for a grating of any thickness. With the grating-thickness change, the anti-crossing gap varies …
Bound states in the continuum (BICs) have been extensively studied in various systems since its first proposal in quantum mechanics. Photonic BICs can enable optical mode confinement and provide field enhancement for nonlinear optics, but they have rarely been explored in nonlinear integrated photonic waveguides. Applying BICs in photonic integrated circuits enables low-loss light guidance and routing in low-refractive-index waveguides on high-refractive-index substrates, which is suitable for integrated photonics with nonlinear materials. Here, we report experimental demonstration of second-h…
Colloidal quantum dots (CQDs) are a promising gain material for solution-processed, wavelength-tunable lasers, with potential application in displays, communications, and biomedical devices. In this work, we combine a CQD film with an array of titanium dioxide (TiO2) nanoantennas to achieve lasing via bound states in the continuum (BICs), which are symmetry-protected cavity modes with giant quality factors. Here, the BICs arise from slab waveguide modes in the planar film, coupled to the periodic nanoantenna array. We engineer the thickness of the CQD film and size of the nanoantennas to achie…
In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wavevector for which there exist waves propagating to or from infinity in the surrounding media. For applications, it is important to analyze the high-$Q$ resonances that either exist naturally for wavevectors near that of the BIC or appear when the structure is perturbed. Existing theories provide quantitative results for the complex frequency (and the $Q$-factor) of resonant modes that appear/exist due to structural perturbations or wavevector variations. When a period…
Slow light is a fascinating physical effect, raising fundamental questions related to our understanding of light-matter interactions as well as offering new possibilities for photonic devices. From the first demonstrations of slow light propagation in ultra-cold atomic gasses, solid-state Ruby and photonic crystal structures, focus has shifted to applications, with slow light offering the ability to enhance and control light-matter interactions. The demonstration of tuneable delay lines, enhanced nonlinearities and spontaneous emission, enlarged spectral sensitivity and increased phase shifts …
We analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. Firstly, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete …
We investigate the diffraction of guided modes of a dielectric slab waveguide on a simple integrated structure consisting of a single dielectric ridge on the surface of the waveguide. Numerical simulations based on aperiodic rigorous coupled-wave analysis demonstrate the existence of sharp resonant features and bound states in the continuum (BICs) in the reflectance and the transmittance spectra occurring at oblique incidence of a TE-polarized guided mode on the ridge. Using the effective index method, we explain the resonances by the excitation of the cross-polarized modes of the ridge. The f…
We derive and validate a set of coupled Bloch wave equations for analyzing the reflection and transmission properties of active semiconductor photonic crystal waveguides. In such devices, slow-light propagation can be used to enhance the material gain per unit length, enabling, for example, the realization of short optical amplifiers compatible with photonic integration. The coupled wave analysis is compared to numerical approaches based on the Fourier modal method and a frequency domain finite element technique. The presence of material gain leads to the build-up of a backscattered field, whi…
Slow light has been widely utilized to obtain enhanced nonlinearities, enhanced spontaneous emissions, and increased phase shifts owing to its ability to promote light-matter interactions. By incorporating a graphene microheater on a slow-light silicon photonic crystal waveguide, we experimentally demonstrated an energy-efficient graphene microheater with a tuning efficiency of 1.07 nm/mW and power consumption per free spectral range of 3.99 mW. The rise and decay times (10% to 90%) were only 750 ns and 525 ns, which, to the best of our knowledge, are the fastest reported response times for mi…
In the past decades, many efforts have been devoted to the temporal manipulation of waves, especially focusing on slowing down their propagation. In electromagnetism, from microwave to optics, as well as in acoustics or for elastic waves, slow wave propagation indeed largely benefits both applied and fundamental physics. It is for instance essential in analog signal computing through the design of components such as delay lines and buffers, and it is one of the prerequisite for increased wave/matter interactions. Despite the interest of a broad community, researches have mostly been conducted …
We identify a broad class of phonon modes with persistent vortex fluxes at arbitrarily slow propagating velocities in periodic nano-waveguides. Such phonon vortices are associated with the split band-edges in dispersion dependencies, which can be engineered by waveguide design. Modulations introduced in such waveguides can support a pair of defect cavity phonon modes with an arbitrarily small frequency splitting. These features can find applications for sensing and nano-manipulation.
Photonic crystal waveguides are known to support C-points - point-like polarisation singularities with local chirality. Such points can couple with dipole-like emitters to produce highly directional emission, from which spin-photon entanglers can be built. Much is made of the promise of using slow-light modes to enhance this light-matter coupling. Here we explore the transition from travelling to standing waves for two different photonic crystal waveguide designs. We find that time-reversal symmetry and the reciprocal nature of light places constraints on using C-points in the slow-light regim…
We design photonic crystal waveguides with efficient chiral light--matter interfaces that can be integrated with solid-state quantum emitters. By using glide-plane-symmetric waveguides, we show that chiral light-matter interaction can exist even in the presence of slow light with slow-down factors of up to $100$ and therefore the light--matter interaction exhibits both strong Purcell enhancement and chirality. This allows for near-unity directional $β$-factors for a range of emitter positions and frequencies. Additionally, we design an efficient mode adapter to couple light from a standard nan…
We demonstrate the generation of quantum-correlated photon pairs from a Si photonic-crystal coupled-resonator optical waveguide. A slow-light supermode realized by the collective resonance of high-Q and small-mode-volume photonic-crystal cavities successfully enhanced the efficiency of the spontaneous four-wave mixing process. The generation rate of photon pairs was improved by two orders of magnitude compared with that of a photonic-crystal line defect waveguide without a slow-light effect.
Reflection at relativistically moving plasma mirrors is a well-known approach for frequency conversion as an alternative to nonlinear techniques. A key issue with plasma mirrors is the need for a high carrier concentration, of order 10^21 cm^-3, to achieve an appreciable reflectivity. To generate such high carrier concentrations, short laser pulses with extreme power densities of the order >10^15 W/cm^2 are required. Here, we introduce a novel waveguide-based method for generating relativistically moving plasma mirrors that requires much lower pump powers and much less carrier concentration. S…
Slow or even stop electromagnetic (EM) waves attract researchers' attentions for its potential applications in energy storage, optical buffer and nonlinearity enhancement. However, in most cases of the EM waves trapping, the EM waves are not truly trapped due to the existence of reflection. In this paper, a novel metal-semiconductor-semiconductor-metal (MSSM) structure, and a novel truly rainbow trapping in a tapered MSSM model at terahertz frequencies are demonstrated by theoretical analysis and numerical simulations. More importantly, functional devices such as optical buffer, optical switch…
The effect of the light group velocity reduction in dielectric Bragg reflection waveguide structures (SiO$_2$/TiO$_2$) in the vicinity of the cutoff frequency is studied experimentally. The effect of anti-mirror reflection, specific for the Bragg reflection waveguides, is described and employed for detection of "slow light". The experiments were performed with the use of the Ti:sapphire laser pulses ~ 100 fs in length. The group index $n_g \sim$ 30 with a fractional pulse delay (normalized to the pulse width) of $\sim$ 10 is demonstrated. The problems and prospects of implementation of the slo…
The atoms moving within the waveguide with a critical frequency higher than the resonant frequency of atoms are suggested for obtaining the "slow light". Due to the absence of the resonant mode in the guide the atoms conserves excitation and coherence. The speed of this mixed excitation (electromagnetic field + moving atom) can be very low or even zero. The atoms moving within the waveguide with a critical frequency higher than the resonant frequency of atoms are suggested for obtaining the "slow light". Due to the absence of the resonant mode in the guide the atoms conserves excitation and co…
We present slow-light photonic crystal waveguide designs that provide a $\times$8.6 improvement of the local density of optical states at a fully chiral point over previous designs.
Metamaterials, which are materials engineered to possess novel optical properties, have been increasingly studied. The ability to fabricate metamaterials has sparked an interest in determining possible applications. We investigate using a metamaterial for boundary engineering in waveguides. A metamaterial-clad cylindrical waveguide is used to provide confinement for an optical signal, thereby increasing the local electromagnetic energy density. We show that metamaterial-clad waveguides have unique optical properties, including new modes, which we call hybrid modes. These modes have properties …
Metamaterials with simultaneous negative permittivity and negative permeability (also called left-handed materials) open new avenues to achieving unprecedented physical properties and functionality unattainable with naturally occurring materials. It has been predicted that a metamaterial slab waveguide can slow down light significantly (even to zero velocity) as the thickness of the core layer approaches a critical thickness. Here we show that coupling between the forward and backward modes becomes significant near the critical thickness due to the good matching of the wavevectors and modal pr…
The optical properties of slab waveguides made of indefinite permittivity ($\vep$) materials (IEM) are considered. In this medium the transverse permittivity is negative while the longitudinal permittivity is positive. At any given frequency the waveguide supports an infinite number of transverse magnetic (TM) eigenmodes. For a slab waveguide with a fixed thickness, at most only one TM mode is forward-wave. The rest of them are backward waves which can have very large phase index. At a critical thickness, the waveguide supports degenerate forward- and backward-wave modes with zero group veloci…
We present a two-dimensional photonic crystal design with a microcavity of four defect dielectric rods with eigenfrequencies residing in the propagating band of directional waveguide. In the linear case for tuning of material parameters of defect rods the nonrobust bound state in the continuum (BSC) might occur. The BSC is a result of full destructive interference of resonant monopole and quadrupole modes with the same parity. % to trap light interior of the microcavity. A robust BSC arises in a self-adaptive way without necessity to tune the parameters of the microcavity with the Kerr effect.…
The ability to use coherent light for material science and applications is directly linked to our ability to measure short optical pulses. While free-space optical methods are well-established, achieving this on a chip would offer the greatest benefit in footprint, performance, flexibility and cost, and allow the integration with complementary signal processing devices. A key goal is to achieve operation at sub-Watt peak power levels and on sub-picosecond timescales. Previous integrated demonstrations require either a temporally synchronized reference pulse, an off-chip spectrometer, or long t…
