We present a comprehensive theoretical analysis and computational study of four-wave mixing (FWM) of optical pulses co-propagating in one-dimensional silicon photonic crystal waveguides (Si-PhCWGs). Our theoretical analysis describes a very general set-up of the interacting optical pulses, namely we consider nondegenerate FWM in a configuration in which at each frequency there exists a superposition of guiding modes. We incorporate in our theoretical model all relevant linear optical effects, including waveguide loss, free-carrier (FC) dispersion and FC absorption, nonlinear optical effects such as self- and cross-phase modulation (SPM, XPM), two-photon absorption (TPA), and cross-absorption modulation (XAM), as well as the coupled dynamics of FCs and optical field. In particular, our theoretical analysis based on the coupled-mode theory provides rigorously derived formulae for linear dispersion coefficients of the guiding modes, linear coupling coefficients between these modes, as well as the nonlinear waveguide coefficients describing SPM, XPM, TPA, XAM, and FWM. In addition, our theoretical analysis and numerical simulations reveal key differences between the characteristics of FWM in the slow- and fast-light regimes, which could potentially have important implications to the design of ultra-compact active photonic devices.
We computationally study a subwavelength dielectric grating structure, show that slab waveguide modes can be used to obtain broadband high reflectivity, and analyze how slab waveguide modes influence reflection. A structure showing interference between Fabry-Perot modes, slab waveguide modes, and waveguide array modes is designed with ultra-broadband high reflectivity. Owing to the coupling of guided modes, the region with reflectivity R > 0.99 has an ultra-high bandwidth ( Δf/f > 30%). The incident-angle region with R > 0.99 extends over a range greater than 40°. Moreover, an asymmetric waveg…
Guided waves modes in a slab waveguide formed from the isotropic dielectric layer embedded by hyperbolic materials are investigated. Optical axis is normal to the slab plane. The dispersion relations for TE and TM waves are found. The differences between hyperbolic waveguide and conventional one are demonstrated. In particular, for each TM mode of hyperbolic waveguide there are two cut-off frequencies and the number of modes is limited. For the TE and TM modes Poynting vector component along the wave's propagation axis could be equal to zero.
Optical modes in anisotropic slab waveguides with topological and chiral magnetoelectric effects are investigated analytically, by deriving the closed-form characteristic equations of the modes and hence computing the dispersion-diagrams. In order to compute the characteristic equations, a vector-potential approach is introduced by incorporating a generalized Lorentz gauge, and the corresponding Helmholtz equations are derived correspondingly. It will be shown that the formation of the complex modes and hybridization of the optical modes in such slab waveguides is inevitable. Moreover, when th…
We demonstrate ultrafast all-optical deflection of spatial solitons in an AlGaAs slab waveguide using 190 fs, 1550 nm pulses which are used to generate and deflect the spatial soliton. The steering beam is focused onto the top of the waveguide near the soliton pathway and the soliton is steered due to refractive index changes induced by optical Kerr, or free carrier (Drude) effects. Angular deflections up to 8 mR are observed.
Motivated by the recent progress in analog computing [Science 343, 160 (2014)], a new approach to perform spatial integration is presented using a dielectric slab waveguide. Our approach is indeed based on the fact that the transmission coefficient of a simple dielectric slab waveguide at its mode excitation angle matches the Green's function of first order integration. Inspired by the mentioned dielectric-based integrator, we further demonstrate its graphene-based counterpart. The latter is not only reconfigurable but also highly miniaturized in contrast to the previously reported designs [Op…
We investigate a short (~1.5μm) partially-corrugated tapered waveguide structure for mode coupling from a silicon micro-slab to a plasmonic nano-gap waveguide at the optical communication frequency. More than 80% transmission efficiency is reported numerically for the first time. The result indicates that the corrugated waveguide structure should not only be helpful for realizing full on-chip silicon plasmonic devices but also a good choice for mode coupling enhancement from dielectric waveguides to plasmonic waveguides. Meanwhile, we point out that the coupling mechanism reported here is diff…
Nonlinear guided wave modes in an asymmetric slab waveguide formed by an isotropic dielectric layer placed on a linear or nonlinear substrate and covered by a hyperbolic material are investigated. Optical axis is normal to the slab plane. The dispersion relations for TM waves are found. It is shown that there are additional cut-off frequencies for each TM mode. The effects of the nonlinearity on the dispersion relations are investigated and discussed. There are the modes, which are corresponded with situation where the peak of electric field is localized in the nonlinear substrate. These modes…
Guided wave modes in a symmetric slab waveguide formed by an isotropic dielectric layer with cubic nonlinear response placed in the hyperbolic surrounding medium are investigated theoretically. Optical axis of the hyperbolic medium is normal to the slab plane. If dielectric permittivity of the waveguide core is more than extraordinary permittivity of the hyperbolic medium each TM mode has two cut-off frequencies. The dispersion relations for these modes are found and numerically solved for cases of focusing and defocussing medium of the core. Number of possible modes at given frequency depends…
Phoxonic crystal as a means of guiding and confining electromagnetic and elastic waves has already attracted attentions. Lack of exact knowledge on how these two types of waves interact inside this crystal and how electromagnetic wave evolves through this interaction has increased this field complexity. Here we explain how an elastic wave affects an electromagnetic wave through photo-elasticity and interface displacement mechanisms in a phoxonic crystal slab waveguide. We obtain a master equation which can describe electromagnetic wave evolution. In this equation we define a coupling parameter…
We propose a simple integrated narrowband filter consisting of two grooves on the surface of a slab waveguide. Spectral filtering is performed in transmission at oblique incidence due to excitation of an eigenmode of the structure localized at a ridge cavity between the grooves. For the considered parameters, strictly zero reflectance and unity transmittance are achieved at resonant conditions. Width and location of the transmittance peak can be controlled by changing the widths of the grooves and of the ridge, respectively. The proposed filter may find application in waveguide-integrated spec…
We report on systematic experimental mapping of the transmission properties of two-dimensional silicon-on-insulator photonic crystal waveguides for a broad range of hole radii, slab thicknesses and waveguide lengths for both TE and TM polarizations. Detailed analysis of numerous spectral features allows a direct comparison of experimental data with 3D plane wave and finite-difference time-domain calculations. We find, counter-intuitively, that the bandwidth for low-loss propagation completely vanishes for structural parameters where the photonic band gap is maximized. Our results demonstrate t…
In this paper we study and design quasi-2D optomechanical crystals, waveguides, and resonant cavities formed from patterned slabs. Two-dimensional periodicity allows for in-plane pseudo-bandgaps in frequency where resonant optical and mechanical excitations localized to the slab are forbidden. By tailoring the unit cell geometry, we show that it is possible to have a slab crystal with simultaneous optical and mechanical pseudo-bandgaps, and for which optical waveguiding is not compromised. We then use these crystals to design optomechanical cavities in which strongly interacting, co-localized …
A flexible and efficient method for fully vectorial modal analysis of 3D dielectric optical waveguides with arbitrary 2D cross-sections is proposed. The technique is based on expansion of each modal component in some a priori defined functions defined on one coordinate axis times some unknown coefficient-functions, defined on the other axis. By applying a variational restriction procedure the unknown coefficient-functions are determined, resulting in an optimum approximation of the true vectorial mode profile. This technique can be related to both Effective Index and Mode Matching methods. A c…
Sheets of slab waveguides with sharp corners are investigated. By means of rigorous numerical experiments, we look at oblique incidence of semi-guided plane waves. Radiation losses vanish beyond a certain critical angle of incidence. One can thus realize lossless propagation through 90-degree corner configurations, where the remaining guided waves are still subject to pronounced reflection and polarization conversion. A system of two corners can be viewed as a structure akin to a Fabry-Perot-interferometer. By adjusting the distance between the two partial reflectors, here the 90-degree corner…
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 derive formulas for Whispering Gallery Mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent waveguides. The derivation is based on a WKB treatment of Helmholtz equation and can in principle be extended to any number of concentric shells. A distinctive limit analytically arises in the analysis when two shells are brought at very close distance to one another. In that limit, the two shells act as a slot waveguide. If the two shells are sufficiently apart, we i…
The materials having negative permittivity and negative permeability, which are labeled as double-negative (DNG) materials, have attracted much attention because of their unusual physical properties, which are different from those of conventional double-positive (DPS) materials. Animations obtained by the finite-difference time-domain method (FDTD) are provided showing how a transient sinusoidal signal that starts at t=0 propagates in the DPS and DNG waveguides. Three types of waveguides are considered: a slab or grounded slab inside the cladding medium and a parallel-plate waveguide filled wi…
We show that a very simple structure consisting of a single subwavelength dielectric ridge on the surface of a slab waveguide enables spatial differentiation and integration of the profile of optical beams propagating in the waveguide. The differentiation and integration operations are performed in transmission and in reflection, respectively, at oblique incidence of the beam impinging on the ridge. The implementation of these operations is associated with the resonant excitation of a cross-polarized eigenmode of the ridge. At the considered parameters of the structure and incidence geometry, …
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…
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…
This study theoretically and experimentally investigates the transmission properties of a metamaterial slab comprised of two layers of metallic fish-scale structure arrays and a sandwiched dielectric layer. Calculations show that the asymmetric transmission can be tuned by varying the slab thickness, due to evanescent interlayer coupling. The spatial evolution of the local field inside the structure indicates that the slab functions as a perfect polarization transformer at certain frequencies in the manner of a waveguide twist. Measured transmission spectra are in good agreement with calculate…
We present a design of a one dimensional dielectric waveguide that can trap a broad band light pulse with different frequency component stored at different positions, effectively forming a "trapped rainbow"[1]. The spectrum of the rainbow covers the whole visible range. To do this, we first show that the dispersion of a $\text{SiO}_2$ waveguide with a Si grating placed on top can be engineered by the design parameter of the grating. Specifically, guided modes with zero group velocity(frozen modes) can be realized. Negative Goos-Hänchen shift along the surface of the grating is responsible for …
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 analyze planar electromagnetic waves confined by a slab waveguide formed by two perfect electrical conductors. Remarkably, 2D Maxwell equations describing transverse electromagnetic modes in such waveguides are exactly mapped onto equations for acoustic waves in fluids or gases. We show that interfaces between two slab waveguides with opposite-sign permeabilities support 1D edge modes, analogous to surface acoustic plasmons at interfaces with opposite-sign mass densities. We analyze this novel type of edge modes for the cases of isotropic media and anisotropic media with tensor permeabiliti…
We investigate a periodic array of aluminum nanoantennas embedded in a light-emitting slab waveguide. By varying the waveguide thickness we demonstrate the transition from weak to strong coupling between localized surface plasmons in the nanoantennas and refractive index guided modes in the waveguide. We experimentally observe a non-trivial relationship between extinction and emission dispersion diagrams across the weak to strong coupling transition. These results have implications for a broad class of photonic structures where sources are embedded within coupled resonators. For nanoantenna ar…
We consider the process of low-power light scattering by optical solitons in a slab waveguide with homogeneous and inhomogeneous refractive index core. We observe resonant reflection (Fano resonance) as well as resonant transmission of light by optical solitons at certain incident angles. The resonance position can be controlled experimentally by changing the soliton intensity and the relative frequency detuning between the soliton and the probe light beams.
We consider the propagation of broad optical beams through slab waveguides with a purely quadratic nonlinearity and containing linear and nonlinear long-period quasi-phase-matching gratings. An exact Floquet analysis on the periodic, plane-wave solution shows that the periodicity can drastically alter the growth rate of the modulational instability but that it never completely removes the instability. The results are confirmed by direct numerical simulation, as well as through a simpler, approximate theory for the averaged fields that accurately predicts the low-frequency part of the spectrum.
A coupled magnetic resonator waveguide, composed of a contacting gold nanosphere chain on a gold slab, is proposed and investigated. A broadband coherent magnetic plasmon mode can be excited in this one dimensional nanostructure. By employing the Lagrangian formalism and the Fourier transform method, the dispersion properties of the wave vector and group velocity of the magnetic plasmon mode are investigated. Small group velocity can be obtained from this system which can be applied as subwavelength slow wave waveguides.
Spatial and spectral properties of the pulsed second harmonic generation in a periodically-poled KTP waveguide exploiting simultaneously the first, second, and third harmonics of periodic nonlinear modulation are analyzed. Experimental results are interpreted using a model based on finite elements method. Correlations between spatial and spectral properties of the fundamental and second-harmonic fields are revealed. Individual nonlinear processes can be exploited combining spatial and spectral filtering. Also the influence of waveguide parameters to the second-harmonic spectra is addressed.
The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance d…
A photonic crystal (PhC) nanocavity formed in an optically very thick slab can support reasonably high-Q modes for lasing. Experimentally, we demonstrate room-temperature pulsed lasing operation from the PhC dipole mode emitting at 1324 nm, which is fabricated in an InGaAsP slab with thickness (T) of 606 nm. Numerical simulation reveals that, when T > 800 nm, over 90% of the laser output power couples to the PhC slab modes, suggesting a new route towards an efficient in-plane laser for photonic integrated circuits.
We report on III-nitride waveguides with c-plane GaN/AlGaN quantum wells in the strong light-matter coupling regime supporting propagating polaritons. They feature a normal mode splitting as large as 60 meV at low temperatures thanks to the large overlap between the optical mode and the active region, a polariton decay length up to 100 $μ$m for photon-like polaritons and lifetime of 1-2 ps; with the latter values being essentially limited by residual absorption occurring in the waveguide. The fully lattice-matched nature of the structure allows for very low disorder and high in-plane homogenei…
We photo-excite slab polymer waveguides doped with J-aggregating dye molecules and measure the leaky emission from strongly coupled waveguide exciton polariton modes at room temperature. We show that the momentum of the waveguide exciton polaritons can be controlled by modifying the thickness of the excitonic waveguide. Non-resonantly pumped excitons in the slab excitonic waveguide decay into transverse electric and transverse magnetic strongly coupled exciton waveguide modes with radial symmetry. These leak to cones of light with radial and azimuthal polarizations.
We analyze spectrum of waveguide modes of an arbitrary uniaxial anisotropic metamaterial slab with non-local electromagnetic response whose permittivity tensor could be described within Drude approximation. Spatial dispersion was introduced within the hydrodynamical model. Both anisotropy and spatial dispersion were considered as perturbations. This helps to distinguish their effect on the spectrum of the slab and to analyze lifting of the degeneracy of eigenmodes at plasma frequency in detail. Spatial dispersion is shown to result in break of the singularity in the den- sity of optical states…
e investigate both experimentally and theoretically the waveguiding properties of a novel double trench waveguide where a conventional single-mode strip waveguide is embedded in a two dimensional photonic crystal (PhC) slab formed in silicon on insulator (SOI) wafers. We demonstrate that the bandwidth for relatively low-loss (50dB/cm) waveguiding is significantly expanded to 250nm covering almost all the photonic band gap owing to nearly linear dispersion of the TE-like waveguiding mode. The flat transmission spectrum however is interrupted by numerous narrow stop bands. We found that these st…
Quantum pulsed second-subharmonic generation in a planar waveguide with a small periodic corrugation at the surface is studied. Back-scattering of the interacting fields on the corrugation enhances the nonlinear interaction giving larger values of squeezing. The problem of back-scattering is treated by perturbation theory, using the Fourier transform for non-dispersion propagation, and by numerical approach in the general case. Optimum spectral modes for squeezed-light generation are found using the Bloch-Messiah reduction. Improvement in squeezing and increase of numbers of generated photons …
A configuration to excite the Uller-Zenneck surface electromagnetic waves at the planar interfaces of homogeneous and isotropic dielectric materials is proposed and theoretically analyzed. The Uller-Zenneck waves are surface waves that can exist at the planar interface of two dissimilar dielectric materials of which at least one is a lossy dielectric material. In this work, a slab of a lossy dielectric material was taken with lossless dielectric materials on both sides. A canonical boundary-value problem was set up and solved to find the possible Uller-Zenneck waves and waveguide modes. The Ul…
We study the eigenmodes of a slab of a wire metamaterial and demonstrate that such a waveguiding structure supports deep-subwavelength propagating modes exhibiting properties of a single-mode waveguide at any fixed frequency below the plasma frequency of metal wires. We compare our analytical results with the dispersion relations extracted from the experimental measurements.
The use of an optically thick slab may provide versatile solutions for the realization of a current injection type laser using photonic crystals. Here, we show that a transversely higher-order defect mode can be designed to be confined by a photonic band gap in such a thick slab. Using simulations, we show that a high-Q of 10^5 is possible from a finely tuned second-order hexapole mode. Experimentally, we achieve optically pumped pulsed lasing at 1347 nm from the second-order hexapole mode with a peak threshold pump power of 88 uW.
We present a detailed study of oscillating modes in a slab waveguide with air core and anisotropic metamaterial cladding. It is shown that, under specific dielectric configurations, slow and even stopped electromagnetic wave can be supported by such an air waveguide. We propose a linearly tapped waveguide structure that could lead the propagating light to a complete standstill. Both the theoretical analysis and the proposed waveguide have been validated by full-wave simulation based on finite-difference time-domain method.
We investigate the connection between photonic local density of states and luminescent solar concentrator (LSC) performance in two manufacturable nanocavity LSC structures, a bilayer slab and a slab photonic crystal. Finite-difference time-domain electromagnetic simulations show that the waveguided luminescence photon flux can be enhanced up to 30% for the photonic crystal design over a conventional LSC operating in the ray optic limit assuming the same number of excited lumophores. Further photonic engineering could realize an increase of up to one order of magnitude in the flux of waveguided…
The effect of lattice termination on the surface states in a two-dimensional truncated photonic crystal slab is experimentally studied in a high index contrast silicon-on-insulator system. A single-mode silicon strip waveguide that is separated from the photonic crystal by a trench of variable width is used to evanescently couple to surface states in the surrounding lattice. It is demonstrated that the dispersion of the surface states depends strongly on the specific termination of the lattice.
We demonstrate that an array of discrete waveguides on a slab substrate, both featuring the $χ^{2}$ nonlinearity, supports stable solitons composed of discrete and continuous components. Two classes of fundamental composite solitons are identified: ones consisting of a discrete fundamental-frequency (FF) component in the waveguide array, coupled to a continuous second-harmonic (SH) component in the slab waveguide, and solitons with an inverted FF/SH structure. Twisted bound states of the fundamental solitons are found too. In contrast with usual systems, the \emph{intersite-centered} fundament…
Utilizing the underlying physics of evanescent wave amplification by a negative-refractive-index slab, it is shown that evanescent waves with specific spatial frequencies can also be amplified without any reflection simply by two dielectric planar waveguides. The simple configuration allows one to take advantage of the high resolution limit of a high-refractive-index material without contact with the object.
We study the electromagnetic force exerted on a pair of parallel slab waveguides by the light propagating through them. We have calculated the dependence of the force on the slab separation by means of the Maxwell--Stress tensor formalism and we have discussed its main features for the different propagation modes: spatially symmetric (antisymmetric) modes give rise to an attractive (repulsive) interaction. We have derived the asymptotic behaviors of the force at small and large separation and we have quantitatively estimated the mechanical deflection induced on a realistic air-bridge structure…
We construct families of optical semi-discrete composite solitons (SDCSs), with one or two independent propagation constants, supported by a planar slab waveguide, XPM-coupled to a periodic array of stripes. Both structures feature the cubic nonlinearity and support intrinsic modes with mutually orthogonal polarizations. We report three species of SDCSs, odd, even, and twisted ones, the first type being stable. Transverse motion of phase-tilted solitons, with potential applications to beam steering, is considered too.
