Nonlinear Dielectric Waveguide Research Articles

Evolution of optical harmonic generation near bound-states in the continuum in hybrid plasmonic-photonic structures.

We investigate the nonlinear optical harmonic generation behaviors near the bound-states in the continuum (BICs) in hybrid plasmonic-photonic structures. The hybrid structures are designed to consist of a plasmonic grating covered with a nonlinear dielectric waveguide layer, which support two distinct groups of BICs, i.e. the symmetry-protected BICs and Friedrich-Wintgen BICs. The evolution of second- and third-harmonic generation (SHG and THG) near the two groups of BICs was studied. The high dependence of nonlinear response on the local field distribution and tensor components of susceptibility of nonlinear materials was determined. Especially, there exists optimized angles of incidence for efficient SHG and THG response due to the interaction of photonic and plasmonic modes. The results are important to understand the nonlinear response behaviors in hybrid plasmonic-photonic structures and to design the nonlinear photonic devices.

Simple Analytical Solution of Čerenkov-Type Terahertz Wave Generation via Difference Frequency Generation in Dielectric Waveguides

We newly analyze the Cerenkov-type terahertz wave generation via the optical difference frequency generation in nonlinear dielectric waveguides based on the coupled-mode theory. The nonlinear coupled equations are derived, and the simple analytical solution for the terahertz wave is obtained in a closed form. The validity of our solution is also checked by the nonlinear beam propagation method. The analytical solution shows that for planar waveguides, the coupling coefficient has pole singularities at the propagation constants of the leaky modes at the terahertz frequency of the waveguides, and thus, the terahertz wave generation can be significantly enhanced as the phase-matching point approaches to the propagation constant of the lowest order leaky mode, whose imaginary part is very small compared to the real part of that.

On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular dielectric waveguide filled with nonlinear isotropic homogeneous medium

The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The problem is reduced to the new type of nonlinear eigenvalue problem. The analytical method of solving this problem is presented. New propagation regime is found.

Ultrafast self-action of surface-plasmon polaritons at an air/metal interface

We investigate both theoretically and experimentally the nonlinear propagation of surface-plasmon polaritons (SPP) on a single air/metal interface. Inspired by nonlinear dielectric waveguide theory, we analytically derive a model that describes the nonlinear propagation of SPPs, thus bridging the description of plasmonic and dielectric waveguides. The model, the numerical simulations, and the experiments, which are carried out in the 100 fs regime, reveal that the SPP undergoes strong ultrafast self-action which manifests itself through self-induced absorption. Our observations are consistent with a large, bulk, third-order nonlinear susceptibility $({\ensuremath{\chi}}^{(3)})$ of gold and provide a self-consistent theory of self-action of SPPs at an air/metal interface. Experimentally, we find $\mathrm{Im}{{\ensuremath{\chi}}^{\ensuremath{-}(3)}}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}/{\mathrm{V}}^{2}$. These findings have important implications in the nonlinear physics of plasmonics and metamaterials as they provide evidence that nonlinear absorption has a significant effect on the propagation of SPPs excited by intense optical pulses. This self-action is also expected to affect the anomalous absorption of light near subwavelength structures as well as the strength of desirable nonlinear processes such as third-harmonic generation and four-wave mixing, which will inevitably compete with nonlinear absorption.

Coupled electromagnetic transverse-electric–transverse magnetic wave propagation in a cylindrical waveguide with Kerr nonlinearity

Nonlinear coupled electromagnetic TE-TM wave propagation in a cylindrical nonlinear dielectric waveguide with circular cross section is considered. Nonlinearity inside the waveguide is described by Kerr law. Physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. It is proved that TE and TM waves that form (nonlinear) coupled TE-TM wave can propagate at different frequencies ωE and ωM, respectively. It is shown that nonlinear coupled TE-TM wave propagates at different frequencies ωE, ωM and with different propagation constants γE, γM in the waveguide. Frequencies ωE, ωM can be chosen independently. Existence of coupled surface TE-TM waves is proved. Intervals of localization of coupled eigenvalues (γE, γM) are found.

Dissipative Josephson junction of an optical soliton and a surface plasmon

We examine the dynamics of a dissipative photonic Josephson junction formed by the weak coupling of an optical soliton in a nonlinear dielectric waveguide and a co-propagating surface plasmon along a parallel metal surface with a linear dielectric spacer. We employ a heuristic model with a coupling function that depends on the soliton amplitude, and consider two phenomenological dissipation mechanisms separately: angular velocity dissipation and population imbalance dissipation. In the former dissipation mechanism, the system exhibits phase-slip phenomenon where the odd-\pi phase modes decay into even-\pi phase modes. The latter damping mechanism sculptures the phase-space significantly by introducing complex features, among which Hopf type bifurcations are notable. We show that some of the bifurcation points expand to stable limit cycles for certain regimes of the model parameters.

On the concept of a resonant tunneling photonic nanotriode

The concept of a resonant tunneling photonic nanotriode that allows the mutual all-optical control of cross-cut light flows is developed. The concept is based on the strong resonant interaction between the quasi-localized eigenmode of nonlinear planar dielectric waveguides and incident beams. It is demonstrated that small variations of input guided wave intensities may result in deep modulation of beam reflection and transmission coefficients.

Analysis of long-range surface plasmon polaritons in nonlinear plasmonic waveguides using pseudospectral method

A full-vectorial pseudospectral method is reported for solving the mode characteristics of nonlinear dielectric and plasmonic waveguides. The coupled equations are formulated in terms of transverse magnetic-field components, and self-consistent solutions are obtained through an iterative procedure. The proposed scheme applies in a saturable medium with biaxial anisotropy of practical interest. The accuracy and efficiency of this scheme are demonstrated by solving the mode bistability of a nonlinear dielectric optical waveguide, analyzed by the well-known finite-element-method-based imaginary-distance beam propagation method. Furthermore, the relationship between geometry and input power is studied by analyzing the power dispersion curve of the long-range surface plasmon polariton modes of a nonlinear plasmonic waveguide.

Pseudospectral mode solver for analyzing nonlinear optical waveguides

Numerical mode solver using a pseudospectral scheme is developed for solving various nonlinear dielectric and plasmonic waveguides with arbitrary nonlinear media. Two nonlinear iterative approaches that use this scheme are implemented; these approaches assign the mode power and effective index as extracted eigenvalues. However, to obtain the complete power dispersion curve including the stable and unstable modal solutions, assigning the mode power as an eigenvalue for a given effective index is required. Moreover, the biaxial feature of the nonlinear refractive index is considered for solving the transverse magnetic (TM) modes in materials of practical interest. Furthermore, the proposed scheme solves the problem of nonlinear surface plasmons guided by a thin metal film with nonlinear cladding, and the mode characteristics of long- and short-range surface plasmon polaritons are analyzed. We also apply the proposed scheme to a 2D strip waveguide with a nonlinear saturation substrate.

Nonlinear resonant control of cross-cut photonic flows

We introduce the concept of a resonant tunneling photonic nanotriode that makes possible the mutual control of cross-cut light flows. The idea of this concept is based on the strong resonant interaction between the nearly phase-matched quasi-localized eigenmode of nonlinear planar dielectric waveguides and incident beams. We demonstrate that by means of variation of input guided wave intensities even small nonlinear phase mismatches may switch the bistable system from one equilibrium state to another and back, resulting in deep modulation of beam reflection and transmission coefficients due to the exchange between trapped and free photons. The suggested nanosize device can also serve as light amplifier, light modulator, controlled coupler, light flows divider, etc.

Dynamical analysis of a weakly coupled nonlinear dielectric waveguide: Surface-plasmon model as another type of Josephson junction

We propose that a weakly coupled nonlinear dielectric waveguide surface-plasmon system can be formulated as another type of Josephson junction. Such a system can be realized along a metal-dielectric interface where the dielectric medium hosts a nonlinear waveguide (e.g., fiber) for soliton propagation. We demonstrate that the system is in close analogy to the bosonic Josephson junction of atomic condensates at very low temperatures, yet exhibits different dynamical features. In particular, the inherently dynamic coupling parameter between soliton and surface plasmon generates self-trapped oscillatory states at nonzero fractional populations with zero and $\ensuremath{\pi}$ time-averaged phase difference. The salient features of the dynamics are presented in the phase space.

Efficient second-harmonic generation in nonlinear plasmonic waveguide

We theoretically studied a nonlinear optical process in a hybrid plasmonic waveguide composed of a nonlinear dielectric waveguide and a metal film with a separation of a thin air gap. Owing to the hybridization effect of guided mode and surface plasmon polariton mode, this particular waveguide is able to confine the optical-field in a deep subwavelength scale together with low propagation loss. Based on this, efficient second-harmonic generations (SHG) were revealed at the fundamental wavelength of λ=1.55 μm with good field confinement. The SHG efficiency, as well as the coupling coefficient and mode area, were analyzed and discussed in detail with respect to the structural parameters.

Nonlinear plasmonic directional couplers

A study on the nonlinear modes of plasmonic directional couplers created by two nonlinear dielectric slot waveguides with metallic claddings is presented. The calculated power diagram shows substantial differences from the case of nonlinear dielectric couplers. The power-dependent switching and the effect of losses on the coupler performance are studied using finite-difference time-domain numerical simulations.

Goos-Hänchen Shift at the Interface of Nonlinear Left-Handed Metamaterials

The propagation characteristics of the electromagnetic wave incident from a linear conventional medium (RHM) into a nonlinear left-handed medium (LHM) and the Goos-Hänchen shift of total reflection at the interface are derived in this paper. The dependence of the lateral shift on the incident angle and incident field intensity is analyzed. It is found that the incident field intensity plays an important role in the propagation of the electromagnetic wave. If the incident field intensity is larger than the critical field intensity, total reflection condition is not satisfied and the incident beam penetrates into the nonlinear materials partly. Proposed nonlinear dielectric waveguide is of great value because it can not only regulate the lateral shift but also implement control over the incident field intensity.

Subwavelength Discrete Solitons in Nonlinear Metamaterials

We present the first study of subwavelength discrete solitons in nonlinear metamaterials: nanoscaled periodic structures consisting of metal and nonlinear dielectric slabs. The solitons supported by such media result from a balance between tunneling of surface plasmon modes and nonlinear self-trapping. The dynamics in such systems, arising from the threefold interplay between periodicity, nonlinearity, and surface plasmon polaritons, is substantially different from that in conventional nonlinear dielectric waveguide arrays. We expect these phenomena to inspire fundamental studies as well as potential applications of nonlinear metamaterials, particularly in subwavelength nonlinear optics.

Propagation of TE waves in cylindrical nonlinear dielectric waveguides

The propagation of TE-polarized electromagnetic waves along a Kerr-type nonlinear dielectric, nonabsorbing, nonmagnetic, and isotropic (circular) cylindrical waveguide is investigated. For axially (azimuthal) symmetric solutions the problem is reduced to a cubic-nonlinear integral equation that is solved by iteration leading to a sequence uniformly convergent to the solution of the integral equation. The dispersion relations associated to the exact and iterate solutions, respectively, are derived and solved, subject to certain constraints. The roots of the exact dispersion relation are approximated by the roots of the dispersion relations generated by the iterate solutions. All statements of existence and convergence are based on results of a previous paper. Numerical results (concerning solutions of dispersion relations, field patterns, dependence of the propagation constant and of the cutoff radius on the nonlinearity parameter, power flow) are included.

Integral Equation Approach for the Propagation of TE-Waves in a Nonlinear Dielectric Cylindrical Waveguide

We consider the propagation of TE-polarized electromagnetic waves in cylindrical dielectric waveguides of circular cross section filled with lossless, nonmagnetic, and isotropic medium exhibiting a local Kerr-type dielectric nonlinearity. We look for axially-symmetric solutions and reduce the problem to the analysis of the associated cubic-nonlinear equation. We show that the solution in the form of a TE-polarized electromagnetic wave exists and can be obtained by iterating a cubic-nonlinear integral equation. We derive the associated dispersion equation and prove that it has a root that determines this solution.

Simple analytical expression for the effect of initial interaction in - cerenkov second-harmonic generation

We analyze the nonlinear coupled-mode equations describing the Cerenkov second-harmonic generation in a nonlinear dielectric waveguide. An approximate analytic solution in a closed form is newly obtained for the pump depletion and nonlinear phase-shift of the fundamental field. Our solution, valid over the whole length, shows that the conversion efficiency is reduced by the feature of the initial process of the nonlinear interaction. It gives a simple expression for the efficiency with better accuracy for short device length. We have compared our solution with the previous analytic solutions derived by others. The validity of our solution is also checked by the nonlinear beam propagation method. Furthermore, the solution can be expressed in terms of a leaky mode phase-mismatch, and it shows explicitly that a resonant pump depletion and nonlinear phase-shift of the fundamental field occurs when the phase-matching to the lowest order leaky mode is accomplished. Extending our analysis method, we have also performed higher order numerical analysis for the nonlinear coupled-mode equations.

Full vectorial finite-element solution of nonlinear bistable optical waveguides

The accurate computation of the propagation constants and field distributions of different modes in nonlinear optical dielectric waveguides is addressed in this paper. Using the vector finite-element formulation of the beam propagation method, combined with the imaginary distance propagation technique, both linear and nonlinear modes can be accurately calculated. The proposed technique is applied to obtain the fundamental TE nonlinear mode of a strip-loaded waveguide, and the excellent agreement seen with published results shows its high numerical precision.

Analysis of dielectric waveguides by a modified Fourier decomposition method with adaptive mapping parameters

The adaptive modified Fourier decomposition method (A-MFDM), a recently proposed technique to perform the modal analysis of linear and nonlinear two-dimensional dielectric waveguides, is now extended to three-dimensional scalar structures for the first time. The method includes a strategy to automatically find quasioptimum numerical parameters of the technique, which, on the one hand, improves the accuracy in relation to the known Fourier decomposition method (FDM) and, on the other, makes the method self-adaptive. To validate the performance of the method, two linear dielectric waveguides with exact solutions have been defined and analyzed. Finally, the modal analysis of an asymmetrical rib waveguide directional coupler is carried out and the obtained results confirm the clear superiority of the A-MFDM in realistic situations.