On the enhancement of the nonlinear frequency transformation in periodic media

It is theoretically shown that an enhancement of the nonlinear frequency transformation in a periodic medium occurs under definite conditions if it is accompanied by light diffraction in this medium. The enhancement of the phase-matched frequency transformation occurs if the harmonic frequency ω approaches the stop band frequency ω_e. In the nondepleted pump approximation the corresponding increase of the harmonic intensity is proportional to ω_e(ω?ω_e)^?1 and is restricted by a quantity proportional to the fourth power of the sample thickness. The formulas for the enhancement of second harmonic generation are presented.     

Waves in periodic layered waveguides

Analytical expressions for EM-waves and evolutionary equations for the waves in geometric regular waveguides with layered nonstationary media are presented. A piecewise-homogeneous and periodic along the guide's axis medium is considered in detail. The analytical solution of the dispersion equation is invariant to both the guide's cross-section contour form and eigenwave type. The periodicity dispersion, particular resonances and an algorythm of the modeling application are discussed.     

Fundamental losses in planar Bragg waveguides

This paper considers a planar Bragg waveguide. The guided modes and their dissipation due to the fundamental absorption are described. In the interacting-wave approximation, an analytical relation between the characteristics of the modes and parameters of the Bragg-waveguide geometry was established. Absorption losses in hollow Bragg waveguides were shown to be significantly lower than in a regular waveguide fabricated from the same material. Quantitative estimates of the fundamental and radiation losses in Bragg waveguides are given for materials used at wavelengths of 1.55, 10.6, and 0.245 μm.     

Fundamental noise limitations to supercontinuum generation in microstructure fiber

Broadband noise on supercontinuum spectra generated in microstructure fiber is shown to lead to amplitude fluctuations as large as 50% for certain input laser pulse parameters. We study this noise using both experimental measurements and numerical simulations with a generalized stochastic nonlinear Schr?dinger equation, finding good quantitative agreement over a range of input-pulse energies and chirp values. This noise is shown to arise from nonlinear amplification of two quantum noise inputs: the input-pulse shot noise and the spontaneous Raman scattering down the fiber.     

Guided-mode resonances in multimode planar periodic waveguides

<正>Using the effective medium theory and the waveguide eigenvalue equation,we design a multimode planar periodic waveguide.When a plane wave illuminates the grating at the designed angle and wavelength, more than one leaky modes are excited coincidentally.Then the reflection efficiency around this designed angle and wavelength is investigated using a rigorous coupled wave analysis formulation and a gap of reflection peaks is found.Electric field distributions reveal that this high reflectivity gap is due to the coupling between these two coincidentally excited leaky modes.     

Unexpected light behaviour in periodic segmented waveguides

In this article, it is shown that multimode periodic segmented waveguides (PSW) are versatile optical systems in which properties of wave chaos can be highlighted. Numerical wave analysis reveals that structures of quantum phase space of PSW are similar to Poincare? sections which display a mixed phase space where stability islands are surrounded by a chaotic sea. Then, unexpected light behavior can occur such as, input gaussian beams do not diverge during the propagation in a highly multimode waveguide.     

Nonlinear absorption and Raman gain in helium-ion-implanted silicon waveguides

We study whether helium ion implantation can reduce the carrier lifetime and thus reduce the density of two-photon-absorption-generated free carriers. Our experiments and theoretical model show that helium ion implantation into silicon waveguides can successfully reduce the free-carrier losses and allow net gain to be attained by cw-pumped stimulated Raman scattering without requiring reverse bias to remove the photogenerated free carriers.     

Emission control in broad periodic waveguides and critical coupling

Broad periodic channel waveguides, with a corrugation on their edge, exhibit a remarkable structure in their dispersion diagram, in the form of stripes of minigaps, whose hyperbolic shape is demonstrated. Around the Brillouin zone edge, the contra-directional feedback borrows the geometry of Littrow diffraction. Spontaneous emission from a large subset of modes then acquires a strong modulation. Lasing on these modes, the so-called “Littrow lasing”, offers also the lowest lasing threshold of the open resonator system. Reviewing our recent studies of this system, we discuss slow light and critical coupling phenomena: for a properly adjusted contra-directional coupling, the bands become substantially flat in a sizable area of the dispersion diagram, opening various perspectives. The band engineering tools to master these phenomena and the physical implications in other domains are briefly reviewed.     

Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

Fundamental amplitude noise limitations to supercontinuum spectra generated in a microstructured fiber

Broadband supercontinuum spectra are generated in a microstructured fiber using femtosecond laser pulses. Noise properties of these spectra are studied through experiments and numerical simulations based on a generalized stochastic nonlinear Schrödinger equation. In particular, the relative intensity noise as a function of wavelength across the supercontinuum is measured over a wide range of input pulse parameters, and experimental results and simulations are shown to be in good quantitative agreement. For certain input pulse parameters, amplitude fluctuations as large as 50% are observed. The simulations clarify that the intensity noise on the supercontinuum arises from the amplification of two noise inputs during propagation – quantum-limited shot noise on the input pulse, and spontaneous Raman scattering in the fiber. The amplification factor is a sensitive function of the input pulse parameters. Short input pulses are critical for the generation of very broad supercontinua with low noise. PACS 42.50.Lc; 42.65.Re; 42.81.Dp; 02.60.CbAn Erratum to this article can be found at     

Nondiffracting beams in periodic media

We identify nondiffracting beams in two-dimensional periodic systems, exhibiting symmetry properties and phase structure characteristic of the band(s) they are associated with.     

A generic approach to boundary reflection in periodic media

Waves in periodic media, whose propagation is governed by nearest neighbour interaction, are investigated. The reflection and transmission coefficients are derived for a plane wave incident from medium 1 upon medium 2, without invoking common approximations. The derivation is valid for a class of waves including magneto- and electro-inductive waves, waves on short loaded dipoles, nanoparticles, coupled waveguides and acoustic waves in monatomic media. For this last case hitherto unknown microscopic reflection and transmission coefficients are derived and shown to reduce in the continuous limit to the well-known expressions in terms of acoustic impedances.     

Propagation of electromagnetic waves in two-dimensionally periodic thin-film waveguides

A simplified mathematical model of two-dimensionally(2D) periodic thin-film wavegmide is proposed and the characteristics of wave propagation are shown to be governed by a five-term recurrence relation with dyadic admittance coefficients. The generalized transverse resonance method can be used to analyze any complicated 2D periodic thin-film waveguide. The dispersion characteristics are described by both approximation analysis and numerical calculation. The theoretical explanation and physical understanding of the effecis of 2D periodic modulation provided by our analysis and resulis can give sound support to the engineering applications.     

Fractal properties of trivelpiece-gould waves in periodic plasma-filled waveguides

It is shown that dispersion curves describing a spectrum of Trivelpiece-Gould (TG) waves in periodic plasma-filled waveguides have a fractal nature. They are not solid lines as for other types of waves in periodic waveguides but suffer from discontinuities of the first kind at any k(z) = (P/Q) (2m+1)pi/d, where P and Q are integers, d is the period of the corrugation, and m is the transverse index of a mode. The gaps correspond to forbidden bands. The evaluation of the Hausdorf dimension of the dispersion curves is presented. Finally, qualitative consequences of the fractal nature of TG waves for plasma microwave electronics are discussed.     

Optical losses and gain in silicon-rich silica waveguides containing Er ions

Rib-loaded waveguides containing Er³⁺ coupled to Si-nc have been produced by magnetron sputtering and successive thermal annealing to investigate optical gain at 1535 nm. It has been shown that all Er ions are optically active, whereas the fraction that can be excited at high pump rates under non-resonant excitation is strongly limited by confined carrier absorption (CA), up-conversion processes, and mainly by the lack of coupling to the Si-nc. Er³⁺ absorption cross-section is found comparable to that of Er³⁺ in SiO₂, but a dependence with the effective refractive index has been found. Although the presence of Si-nc strongly improves the efficiency of Er³⁺ excitation, it introduces additional optical loss mechanisms, such as CA. These Si-nc losses affect the possibility of obtaining net optical gain. In the present study, they have been minimized by lowering the annealing time of the Er-doped Si-rich oxide. In pump-probe measurements it is shown that signal enhancement of the transmitted signal can be achieved at low pumping rate when the detrimental role of confined CA is attenuated by reducing the annealing time. A maximum signal enhancement of about 1.30 at 1535 nm was observed.     

Cavity mode control in side-coupled periodic waveguides: Theory and experiment

We demonstrate that the modes of coupled cavities created in periodic waveguides can depend critically on the longitudinal shift between the cavities. In the absence of such shift, the modes feature symmetric or antisymmetric profiles, and their frequency splitting generally increases as the cavities are brought closer. We show that the longitudinal shift enables flexible control over the fundamental modes, whose frequency detuning can be reduced down to zero. Our coupled-mode theory analysis reveals an intrinsic link between the mode tuning and the transformation of slow-light dispersion at the photonic band-edge. We illustrate our approach through numerical modeling of cavities created in arrays of dielectric rods, and confirm our predictions with experimental observations.     

Spectral broadening enhancement in silicon waveguides through pulse shaping

Spectral broadening in silicon waveguides is usually inhibited at telecom wavelengths due to some adverse effects related to semiconductor dynamics, namely, two-photon and free-carrier absorption (FCA). In this Letter, our numerical simulations show that it is possible to achieve a significant enhancement in spectral broadening when we properly preshape the input pulse to reduce the impact of FCA on spectral broadening. Our analysis suggests that the use of input pulses with the correct skewness and power level is crucial for this achievement.     

Dispersion of particles in periodic media

We discuss the long-time properties of the dispersion of particles in periodic media, using the random walk formalism. Exact asymptotic results are obtained for the average velocity and the diffusion coefficient, expressed in terms of the Green's function of the random walk inside the periodically repeated unit cell. We explicitly calculate the transport coefficients for several specific cases of interest, including a system with dead zones, a simple model for field-induced trapping, and a one-dimensional map leading to deterministic diffusion.