Comparison of models of fast saturable absorption in passively modelocked lasers.

Fast saturable absorbers (FSAs) play a critical role in stabilizing many passively modelocked lasers. The most commonly used averaged model to study these lasers is the Haus modelocking equation (HME) that includes a third-order nonlinear FSA. However, it predicts a narrow region of stability that is inconsistent with experiments. To better replicate the laser physics, averaged laser models that include FSAs with higher-than-third-order nonlinearities have been introduced. Here, we compare three common FSA models to each other and to the HME using the recently-developed boundary tracking algorithms. The three FSA models are the cubic-quintic model, the sinusoidal model, and the algebraic model. We find that all three models predict the existence of a stable high-energy solution that is not present in the HME and have a much larger stable operating region. We also find that all three models predict qualitatively similar stability diagrams. We conclude that averaged laser models that include FSAs with higher-than-third-order nonlinearity should be used when studying the stability of passively modelocked lasers.

Information and control strategy to solve the degrees-of-freedom problem for nested locomotion-to-reach.

Locomoting-to-reach to a target is a common visuomotor approach behavior that consists of two nested component actions: locomotion and reaching. The information and control strategies that guide locomotion and reaching in isolation are well studied, but their interaction during locomoting-to-reach behavior has received little attention. We investigated the role of proportional rate control in unifying these components into one action. Individuals use this control strategy with hand-centric disparity-based τ information to guide seated reaching (Anderson and Bingham in Exp Brain Res 205:291-306. doi: 10.1007/s00221-010-2361-9 , 2010) and use it with sequential information to perform targeted locomotion to bring an outstretched arm and hand to a target; first with eye-centric τ information and then hand-centric τ information near the target (Anderson and Bingham in Exp Brain Res 214:631-644. doi: 10.1007/s00221-011-2865-y , 2011). In the current study, participants performed two tasks: locomoting to bring a rigidly outstretched arm and hand to a target (handout), and locomoting to initiate and guide a reach to a target (locomoting-to-reach). Movement trajectories were analyzed. Results show that participants used proportional rate control throughout both tasks, in the sequential manner that was found by Anderson and Bingham (Exp Brain Res 214:631-644. doi: 10.1007/s00221-011-2865-y , 2011). Individual differences were found in the moment at which this information switch occurred in the locomoting-to-reach task. Some participants appeared to switch to proportional rate control with hand-τ once the hand came into view and others switched once the reaching component was complete and the arm was fully outstretched. In the locomoting-to-reach task, participants consistently initiated reaches when eye-τ specified a time-to-contact of 1.0 s. Proportional rate control provides a solution to the degrees-of-freedom problem in the classic manner, by making multiple things one.

Pulse compression using a tapered microstructure optical fiber.

We calculate the pulse compression in a tapered microstructure optical fiber with four layers of holes. We show that the primary limitation on pulse compression is the loss due to mode leakage. As a fiber's diameter decreases due to the tapering, so does the air-hole diameter, and at a sufficiently small diameter the guided mode loss becomes unacceptably high. For the four-layer geometry we considered, a compression factor of 10 can be achieved by a pulse with an initial FWHM duration of 3 ps in a tapered fiber that is 28 m long. We find that there is little difference in the pulse compression between a linear taper profile and a Gaussian taper profile. More layers of air-holes allows the pitch to decrease considerably before losses become unacceptable, but only a moderate increase in the degree of pulse compression is obtained.

Autocorrelation function for polarization mode dispersion emulators with rotators.

We derive a recursion relation for the frequency autocorrelation function of the polarization dispersion vector for polarization mode dispersion emulators with rotators. The autocorrelation function has a nonzero background for an emulator with a fixed number of sections. This background diminishes slowly as the number of sections grows. Randomizing the section lengths removes the autocorrelation periodicity exhibited by an emulator with equal sections, but it does not remove the finite background.

Polarization-state evolution in recirculating loops with polarization-dependent loss.

We analyze the evolution of the polarization state of a signal in a recirculating loop with polarization-dependent loss. We show that the polarization-state evolution in experiments is in qualitative agreement with our analysis, and we discuss the relationship between the polarization-state evolution and the Q factor.