The simulation and analysis of a temporal soliton perturbation (interaction) with a dispersive truncated Airy pulse traveling in a nonlinear fiber at the same center wavelength (or frequency). True Airy pulses remain self-similar while propagating along a ballistic trajectory. However, they are infinite in energy due to the infinite tail that prevents the energy integral from converging. In order to be realized, Airy pulses must therefore, be truncated. The truncation is carried out by apodizing the infinite Airy tail. Despite the truncation Airy pulses remain self-similar over extended ranges while the ballistic trajectory is completely preserved. This allows them to interact with a nearby soliton on account of the accelerating wavefront property. The interactions are governed by the Nonlinear Schrödinger equation for which no analytical solution currently exists for these initial conditions. Therefore, numerical simulations are required. The numerical method chosen is the split step Fourier method which is a mathematical algorithm for propagation of the pulses. By providing the simulation program with the initial launch conditions we are able to follow the interactions as they progress. Analysis of the simulation is carried out by tracking the fundamental parameters of the emergent soliton during propagation—time position, amplitude, phase and frequency—that alter due to the primary collision with the Airy main lobe and the continuous co-propagation with the dispersed Airy background. Following the collision, the soliton intensity oscillates as it relaxes in the dispersed Airy background, trying to settle in to a new soliton state. Further, by varying the initial parameters of the Airy pulse such as initial phase, amplitude and time position, different outcomes are witnessed which allows for a broader understanding of the interaction. Due to the spectral repositioning of the Airy spectrum by dispersion, the interaction is found to resemble coherent interactions at times and incoherent at others. The results indicate that in certain cases permanent change in frequency and intensity occurs, depending on the configuration of the initial parameters chosen. These changes are made apparent through changes in time position and in the accumulated phase of the soliton. Furthermore, according to the perturbation theory local changes in time position and phase can also occur independently from the frequency change and intensity change, respectively.
The expected permittivity and third order nonlinear susceptibility, of a low filling fraction composite consisting of semiconductor nanorods dispersed in a polymer host are derived, using the Maxwell-Garnett model for anisotropic nonlinear inclusions. The semiconductor nanorods are modeled both as prolate spheroids and more realistic capsule shapes. A new generalized model is presented for various nanorod axis orientation statistics, achieved by an aligning electric field. The angular distribution function of the nanorods is calculated for nanorods with a permanent electrical dipole moment, which assists the alignment of the nanorods. Using the angular distribution function, the composite macroscopic characteristics are found for a composite with random orientation, partially aligned and nematic array nanorods. As the alignment field strength increases, the composite optical properties asymptotically converge towards the nematic case. Different parameters relate to the nanorods geometry are examined, concluding that the main parameter influencing the alignment is the single NR volume, while for the nematic array the single nanorod axes aspect-ration is the major parameter. Due to the symmetry of the nanorods, the composite characteristics depend on the polarization of the optical electrical field, with a symmetry that resembles a uniaxial crystal. A nonlinear waveguide with a core made of such a composite is simulated, in order to find the nonlinear parameter of the waveguide. The model takes into account two electrodes for the alignment process, far enough from the waveguide core, in order to avoid losses to the optical mode. Significant optical response can be achieved even for randomly oriented nanorods composite, with a nonlinear parameter of 68(W×m)-1. The alignment process increases the nonlinear parameter significantly even at elevated temperature that are needed for polymerization of the polymer host, typically 150oC. Aligning field strength of 107 V/m results with very high value for the nonlinear parameter – 120(W×m)-1, much higher than ordinary glass based nonlinear optical fibers, that result with nonlinear parameter up to 50(W×m)-1.
An Airy pulse, a solution of the dispersion equation, manifests two unique properties while propagating in linear media. One is self-similarity, meaning the pulse has the same envelope throughout propagation in dispersive media and the second is acceleration in time- namely moving in parabolic trajectory with respect to a time frame that moves with the group velocity of the pulse. We simulate and analyze the propagation of truncated temporal Airy pulses in a single mode fiber in the presence of self-phase modulation (Kerr effect) and anomalous dispersion. Due to the presence of the nonlinear effect, the Airy is no longer a valid solution, such that the pulse evolution is no more predictable. By gradually increasing the launched Airy power we examine the nonlinearity influence on the Airy pulse evolution. For sufficient large launched intensity we observe soliton pulse shedding from the Airy main lobe, with the emergent soliton parameters dependent on the launched Airy pulse characteristics. The emergent soliton performs "breathing"- periodic oscillations of its parameters along the propagation distance due to interaction with background radiation, with the periodicity increasing with the launched power. Additionally, the soliton mean temporal position shifts to earlier times with higher launched powers due to an earlier shedding event and with greater energy in the Airy tail due to collisions with the accelerating lobes. In spite of the Airy energy loss to the shed Soliton, the Airy pulse continues to exhibit the unique property of acceleration in time and the main lobe recovers from the energy loss (healing property of Airy waveforms), but performs decaying oscillations of its peak power according to the interplay between the dispersion and the nonlinear effect. The influence of the truncation coefficient—required for limiting the Airy pulse to finite energy—on the Airy nonlinear propagation is also investigated. Small truncation degree increases the Airy tail energy, which has considerable influence on the soliton shedding distance, the soliton mean temporal position, and on the residual accelerating energy.
An optimization procedure for spatial mode multiplexing from individual single-mode fibers into a three-mode fiber based on a spatial aperture sampling concept has been developed. By placing space-variant imaging elements between the single-mode and few-mode fibers, each beam aperture can be shaped for lower loss coupling and low mode-dependent losses. The optimization achieves a record theoretical −1.5-dB insertion loss, improving on the previous theoretical −2-dB record.