Broadband computations using the Miro software

The light localization characteristics of the near-infrared triangular-lattice photonic crystal annular microcavity are studied theoretically in this paper. The photonic crystal has a lattice constant of <i>a</i>=540 and it is composed of silicon rods each with a radius of <i>r</i>=135 immersed in air background. The two kinds of annular microcavities are obtained by removing 12 silicon rods which are located respectively at a distance of 2a and at a distance of √<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i> to the central rod. Five resonant wavelengths and the corresponding eigen mode profiles of the microcavity are studied. A coupled resonant optical waveguide is formed by integrating the microcavities with a periodic length of 7<i>a</i> in space. The group velocity of light beam propagation within multiple guiding bands are analyzed by the tight-binding approximation method. The maximum and minimum velocity of 0.0028<i>c</i> and 0.00082<i>c</i> are obtained, where <i>c</i> is the light velocity in vacuum. The light transmittance values and spatial steady distributions of the electric field's amplitude through the structure at several wavelengths within the guiding bands are studied by the finite-difference time-domain method. The results are consistent with that calculated by the plane wave expand method. Interleaving circular microcavities perpendicular to the direction of optical transmission at a lateral distance of 2√<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i>, the coupling region between the adjacent microcavities is changed, the difference in group velocity between guiding bands apparently decreases and the transmittance values of two frequency bands are enhanced.<br/>Keeping the size of silicon rods unchanged, two kinds of microcavities are constructed by removing the six rods with the distances of 2<i>a</i> and √<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i> from the center of the central silicon rod, respectively. The resonant wavelengths supported by the above two microcavities are studied. Two coupled-resonant optical waveguides with a periodic length of 7<i>a</i> are proposed. Connecting these two coupled cavity optical waveguides with the W1-typed input/output waveguides, the selecting and sharing function of guiding band are finally achieved for wavelengths within different frequency bands. Keeping the group velocity slowing down, a maximum value of one guiding band reaches 0.00047<i>c</i>.

Ultrafast imaging is essential in physics and chemistry to investigate the femtosecond dynamics of nonuniform samples or of phenomena with strong spatial variations. It relies on observing the phenomena induced by an ultrashort laser pump pulse using an ultrashort probe pulse at a later time. Recent years have seen the emergence of very successful ultrafast imaging techniques of single non-reproducible events with extremely high frame rate, based on wavelength or spatial frequency encoding. However, further progress in ultrafast imaging towards high spatial resolution is hampered by the lack of characterization of weak probe beams. For pump–probe experiments realized within solids or liquids, because of the difference in group velocities between pump and probe, the determination of the absolute pump–probe delay depends on the sample position. In addition, pulse-front tilt is a widespread issue, unacceptable for ultrafast imaging, but which is conventionally very difficult to evaluate for the low-intensity probe pulses. Here we show that a pump-induced micro-grating generated from the electronic Kerr effect provides a detailed in-situ characterization of a weak probe pulse. It allows solving the two issues of absolute pump–probe delay determination and pulse-front tilt detection. Our approach is valid whatever the transparent medium with non-negligible Kerr index, whatever the probe pulse polarization and wavelength. Because it is nondestructive and fast to perform, this in-situ probe diagnostic can be repeated to calibrate experimental conditions, particularly in the case where complex wavelength, spatial frequency or polarization encoding is used. We anticipate that this technique will enable previously inaccessible spatiotemporal imaging in a number of fields of ultrafast science at the micro- and nanoscale.

Using a numerical model, the frequency dependence of the pump-to-signal RIN transfer in FOPAs has been investigated. The model includes fiber loss, pump depletion as well as difference in group velocity among interacting beams.

Enhancement of third harmonic generation by wave vector mismatch to counter phase-modulation

Group velocity matching has been observed in an optical fiber. The matching occurred in a fiber Raman oscillator pumped by mode-locked laser pulses. The group velocity difference between pump and Stokes pulses due to material dispersion was compensated for by the group delay between two different waveguide modes.

We analyze the dynamics of a two-component (vector) soliton in a model of a birefringent nonlinear optical fiber with a periodic spatial modulation of the birefringence parameter (group velocity difference). Evolution equations for the parameters of the vector soliton are derived by means of a variational technique. Numerical simulations of these equations demonstrate that the critical modulation amplitude necessary for splitting, regarded as a function of the soliton's energy, has a deep minimum very close to the point at which direct resonance takes place between the periodic modulation and an internal eigenmode of the vector soliton in the form of small relative oscillations of the centers of the two components. A shallower minimum, which can be related to another internal eigenmode of the vector soliton, is also found. We further briefly consider the internal vibrations of the vector soliton driven by a constant force, which corresponds to the birefringence growing linearly with propagation distance. The effect predicted has practical relevance to ultrashort (femtosecond) optical solitons, and it can be employed in the design of fiber-optical logic elements.

We demonstrate a simple method for infrared few optical-cycle pulse generation, which is based on collinear visible-to-infrared frequency conversion and involves difference-frequency generation and subsequent two-step optical parametric amplification. The numerical simulations and experiments using BBO crystals show an efficient frequency down conversion of visible ∼20 fs pulses from a commercial blue-pumped noncollinear optical parametric amplifier yielding 1.2–2.4 μm tunable sub-100 μJ pulses with duration of 3 to 5 optical-cycles. The proposed method could be readily extended to generate few optical-cycle pulses in the mid-infrared spectral range (up to 5.5 μm) using, e.g., LiIO3 and LiNbO3 crystals, as demonstrated by the numerical simulations. In these crystals, even shorter, two-optical-cycle mid-infrared pulses could be obtained at particular wavelengths where group velocity matching between the signal and idler waves is achieved.

We present a numerical simulation of parametric gain properties in GaInP PhC dispersion engineered waveguides in which the group velocity dispersion crosses zero twice and where the pump and the signal are 100 ps pulses. The simulations use the M-SSFT algorithm which incorporates dispersive nonlinear coefficients and losses. We concentrate on narrow band parametric gain which occurs for pump wavelengths in the normal group velocity dispersion regime. The effects of structural details, of pump wavelength and of losses are carefully analyzed.

Frequency up-conversion (∼10%) and compression (almost twofold) of a powerful (≤250 MW) microwave pulse in the propagating ionization front produced by the pulse itself in a gas-filled waveguide, is investigated experimentally and analyzed theoretically. Pulse envelope reshaping and group velocity increase manifest themselves in a propagation of the pulse faster than in the empty waveguide. A simple one-dimensional mathematical model allows the adequate interpretation of the experimental results.

Ultra-short optical pulse shaping using semiconductor optical amplifier

A matrix formalism for dispersive optical elements is applied to the study of laser cavities with dispersive elements such as gratings or prisms. The formalism consists of 3*3 matrices describing each element with complex coefficients to account for loss or gain. It is shown how to determine the frequency dependence of the beam center, propagation angle, gain, and transit time delay. In this manner, the linewidth selectivity, cavity group velocity dispersion, output spectral angular dispersion, and transverse walkoff of any arbitrary design can be determined. >

Strongly influenced by the advances in the semiconductor industry, the miniaturization and integration of optical circuits into smaller devices has stimulated considerable research efforts in recent decades. Among other structures, integrated interferometers play a prominent role in the development of photonic devices for on-chip applications ranging from optical communication networks to point-of-care analysis instruments. However, it has been a long-standing challenge to design extremely short interferometer schemes, as long interaction lengths are typically required for a complete modulation transition. Several approaches, including novel materials or sophisticated configurations, have been proposed to overcome some of these size limitations but at the expense of increasing fabrication complexity and cost. Here, we demonstrate for the first time slow light bimodal interferometric behaviour in an integrated single-channel one-dimensional photonic crystal. The proposed structure supports two electromagnetic modes of the same polarization that exhibit a large group velocity difference. Specifically, an over 20-fold reduction in the higher-order-mode group velocity is experimentally shown on a straightforward all-dielectric bimodal structure, leading to a remarkable optical path reduction compared to other conventional interferometers. Moreover, we experimentally demonstrate the significant performance improvement provided by the proposed bimodal photonic crystal interferometer in the creation of an ultra-compact optical modulator and a highly sensitive photonic sensor.

Recently solitary waves based on a quadratically nonlinear interaction attracted a lot of attention in nonlinear optics. They were found to exist as selfguided beams in planar waveguides [1]. Both spatial and temporal solitary waves are described by the same evolution Until now only a one-parameter family of such solutions is known. In the spatial case this corresponds to the fundamental and second harmonics propagating in the same direction. No spatial walk-off is induced, e.g. by birefringence. The spatial walk-off can be avoided in a planar waveguide, whereas in the temporal case the situation is much more complicated. The known one-parameter family of solitary wave solutions corresponds to a certain carrier frequency where the group velocities of the two pulses (fundamental and second harmonics) are equal. In most materials such a frequency does not exist. Here we concentrate on the more common situation where the two pulses may move away from each other due to a group velocity difference. The family of solitary wave solutions obtained is two-parametric and applies to the case of spatial walk-off as well.

Ultrafast lasers are of interest for applications in medicine, material processing and as drivers for mid-IR optical parametric frequency converters. Recently a sub-picosecond operation of Ho:YAG chirped pulse amplification (CPA) system was realized by extending the amplified pulse spectrum over two emission peaks centered at 2090 nm and 2096 nm [3], which required strong adaptive spectral shaping of the seed pulse to equalize spectral amplitude gain. In addition, dispersion management of the CPA was complicated due to the resonant spectral phase distortion and could only be accomplished by using an acousto-optic programmable dispersive filter (DAZZLER). The most intense emission line of Ho:YAG is centered at 2090 nm, and, without compensation of gain narrowing, supports amplified bandwidth of >1.5 nm corresponding to <; 4 ps pulses, an attractive pulse duration for the above-mentioned applications.

The threshold of polarization instability for solitons in birefringent fibers has been calculated analytically. The problem was studied when the polarization state of the soliton is oriented along one principal axis and the polarization state of the perturbation is oriented along the other. The instability threshold corresponds to the soliton field intensity which causes the exponential growing of the perturbation. The authors have shown for the first time that this problem can be solved exactly under the assumption that the influence of group velocity difference between the soliton and the perturbation on the instability threshold is negligible. Analytical expressions has been obtained for the threshold of the soliton instability and its duration. The polarization instability increment near threshold has also been calculated. It was shown that obtained analytical expressions are valid under a wide range of birefringent values. On the basis of these expressions, the general analysis of soliton propagation in birefringent fibers has been made and estimations of the instability threshold have been made. The results of this work can be used for the study of ultra-fast all optical switching as well as for the analyses of soliton propagation in optical fibers.