Anomalous Group Velocity Dispersion Region Research Articles

Soliton and dispersive wave generation with third-order dispersion and temporal boundary

We investigate the pulse evolution and energy conservation condition at the temporal boundary under third-order dispersion. When the fundamental soliton crosses the temporal boundary and forms two reflected pulses and one transmitted pulse, the power of the transmitted pulse first increases and then decreases as the incident spectrum shifts toward the blue side. If the transmitted spectrum lies in the anomalous group-velocity dispersion region, second-order soliton is formed and dispersive wave is radiated. We present a modified phase-matching condition to predict the resonance frequencies. The predicted results are in good agreement with the results obtained by numerically solving the nonlinear Schrödinger equation.

Nonparaxial solitons in air

In the present work the soliton regime of propagation in air of ultra-short long-wavelength infrared laser pulses is investigated. The dispersion of atmospheric air in mid-infrared and long-wavelength infrared shows anomalous group velocity dispersion regions for wavelengths in the ranges of 3.5 to 4.2μm and 9.3 to 13.5μm. In these spectral regions the atmospheric air is transparent. From other hand, the nonparaxiality leads to waveguiding regime of propagation for femtosecond pulses with shape of light disks (the transverse size is much bigger than the longitudinal one). It allows reducing this 3D + 1 task to 1D + 1 problem in the same manner as in optical fibers. The combination between anomalous group velocity dispersion and atmospheric nonlinearity is a base for the observation of optical solitons in the air transparency regions for the indicated wavelengths. The main equation in our research is the 1D + 1 nonlinear nonparaxial amplitude equation, written in Galilean and Laboratory coordinate systems. New analytical solution in the form of bright soliton is found. The critical power, needed for the observation of these solitons is of two orders of magnitudes less than the critical one for self-focusing. That is why there are no conditions for ionization of the media.

Gaussian Pulse Propagation via Bright and Dark Solitons through an Atomic Medium

We study the Gaussian pulse propagation and its absorption, dispersion, and distortion in an atomic medium for advanced optical technology. The output pulse intensity distribution in time and Rabi oscillations, as well as the phase of control fields, show significant dark and bright forms of soliton shapes. We investigate the localized intensity of dark and bright solitons with the intensity of control fields in time domain within the normal and anomalous group velocity dispersion regions. Uniform undistorted pulse intensity and bright soliton are noted in time domain with the phase variation of control fields. These theoretical results are useful for optical fibers due to their minimum losses of the signal quality.

Coherent, directional supercontinuum generation.

We demonstrate a novel approach to producing coherent, directional supercontinuum and cascaded dispersive waves using dispersion engineering in waveguides. By pumping in the normal group-velocity dispersion (GVD) regime, with two zero-GVD points to one side of the pump, pulse compression of the first dispersive wave generated in the anomalous GVD region results in the generation of a second dispersive wave beyond the second zero-GVD point in the normal GVD regime. As a result, we achieve an octave-spanning supercontinuum generated primarily to one side of the pump spectrum. We theoretically investigate the dynamics and show that the generated spectrum is highly coherent. We experimentally confirm this dynamical behavior and the coherence properties in silicon nitride waveguides by performing direct detection of the carrier-envelope-offset frequency of our femtosecond pump source using an f-2f interferometer. Our technique offers a path towards a stabilized, high-power, integrated supercontinuum source with low noise and high coherence, with applications including direct comb spectroscopy.

Carrier-envelope phase-stable spatiotemporal light bullets.

We present an extensive experimental investigation of the self-focusing and filamentation of intense 90fs, 1.8μm, carrier-envelope phase-stable laser pulses in fused silica in the anomalous group velocity dispersion region. Spectral measurements in a wedge-shaped sample uncover dynamics of spectral broadening, which captures the evolution of third-harmonic, resonant radiation, and supercontinuum spectra as a function of the propagation distance with unprecedented detail. The relevant events of spectral broadening are linked to the formation and propagation dynamics of spatiotemporal light bullets as measured by a three-dimensional imaging technique. We also show that at a higher input power, the light bullet splits into two bullets, which retain characteristic O-shaped spatiotemporal intensity distributions and propagate with different group velocities. Finally, we demonstrate that the light bullets have a stable carrier-envelope phase that is preserved even after the bullet splitting event, as verified by f-2f interferometric measurements.

Broadband parametric frequency comb generation with a 1-μm pump source

We report the first experimental demonstration of broadband frequency comb generation from a single-frequency pump laser at 1-μm using parametric oscillation in a high-Q silicon-nitride ring resonator. The resonator dispersion is engineered to have a broad anomalous group velocity dispersion region near the pump wavelength for efficient parametric four-wave mixing. The comb spans 55 THz with a 230-GHz free spectral range. These results demonstrate the powerful advantage of dispersion engineering in chip-based devices for producing combs with a wide range of pump wavelengths.

Theoretical analysis of the self-frequency shift near zero-dispersion points: Soliton spectral tunneling

Soliton dynamics under the action of higher-order dispersion and the Raman effect is analyzed. Though we consider a wide variety of parameters, a particularly interesting phenomenon occurs when the presence of cubic and quartic dispersion results in two regions of anomalous group velocity dispersion (GVD) separated by a region of normal dispersion. In this case a sharp switching of the soliton frequency from one anomalous GVD region to the other may exist. During such a transformation, the center of the soliton spectrum passes through the normal GVD region. We show that this switching occurs due to the phase matching between the soliton and the resonance frequency in the two anomalous GVD regions.

Third-Order Dispersion and Ultrafast-Pulse Propagation in Silicon Wire Waveguides

The dynamics of femtosecond (fs) pulse propagation in dispersion engineered silicon-on-insulator (SOI) photonic wires is investigated numerically. For fs pulses propagating in millimeter-long SOI waveguides, the interplay between nonlinear effects, group velocity dispersion (GVD), and the third-order dispersion (TOD) results in significant pulse reshaping. At the zero-GVD (ZGVD) wavelength, TOD causes strong pulse-shape asymmetry in both the temporal and spectral domains. In addition, in the anomalous GVD region near the ZGVD wavelength, soliton-like pulse dynamics is observed

Modulation instability in silicon photonic nanowires

We demonstrate that strong modulation instability (MI) of copropagating optical waves can be observed in Si photonic nanowires with a length of only a few millimeters. We consider two distinct cases, namely one in which one wave propagates in the normal group-velocity dispersion (GVD) region and the other one experiences anomalous GVD, and a second case in which both waves propagate in the anomalous GVD region. In both cases we show that, for comparable optical powers, the peak value of the MI gain spectrum is 2 to 3 orders of magnitude larger than that achieved in optical fibers.

Existence of optical solitons on wavelength division multiplexed beams in a nonlinear fiber.

A simple analytic expression for the initial fundamental optical solitons on wavelength division multiplexed (WDM) beams in a nonlinear fiber has been found. For an ideal fiber with no loss and uniform group-velocity dispersion (GVD) in the anomalous GVD region, the initial form is [1+2(M-1)](-1/2) sech(tau), where M is the number of WDM beams and tau is the normalized time. Computer simulation shows that these initial pulses on WDM beams in this fiber will propagate undistorted without change in their shapes for arbitrarily long distances. The discovery of the existence of solitons on WDM beams presents the ultimate goal for optical fiber communication on multiple wavelength beams in a single fiber.

Solitary waves for two and three coupled nonlinear Schrödinger equations

We present solitary-wave solutions of two and three coupled nonlinear Schr\odinger equations when the waves propagate in the normal and anomalous group-velocity dispersion regions. A wave of the form ${\mathrm{sech}}^{2}\ensuremath{\xi}\ensuremath{-}\frac{2}{3}$ is found, which, together with two known waves of the forms $\mathrm{tanh}\ensuremath{\xi}\mathrm{sech}\ensuremath{\xi}$ and ${\mathrm{sech}}^{2}\ensuremath{\xi},$ are shown to form a new generation of complementary waves. The implication of this wave set and its applications to coupled solitary-wave propagation is discussed.

Dark Solitary-Wave Solutions in Bulk Linear Media with Group Velocity Dispersion

A dark envelope solitary-wave solution in bulk dispersive linear media is obtained from the (3+1)-dimensional time-space coupled linear wave equation by taking account of the interplay between physical effects of transverse confinement and group velocity dispersion (GVD) effect under certain appropriate conditions. The characteristics of the solution are discussed in both normal and anomalous GVD regions.

Solitary Pulses in an Amplified Nonlinear Dispersive Medium in the Presence of Gain Saturation

Abstract The steady state solitary solution in a two-level homogeneously broadened amplifier with host nonlinearity and dispersion is perturbatively studied by consideration of gain saturation up to second-order energy terms normalized to the saturation energy of the transition. Carrier frequency shift occurs as a result of the saturation. The chirped solitary pulses derived exist in the anomalous group velocity dispersion region only.

Supercontinuum in the anomalous group-velocity dispersion region

We compute numerically the time-domain characteristics and the spectral distribution of an intense femtosecond pulse with its center frequency in the anomalous group-velocity dispersion region, that is, propagating in a one-spatial-dimension Kerr medium (optical fiber). We include in our calculations the effects of self-phase modulation, self-steepening, group-velocity dispersion, higher-order dispersion [β(3) term], and Raman scattering. We explicitly show the contributions of the different terms.