A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of (nonlinear) transformations to the solution of the linear differential equation. It is also shown that similar concepts apply to the nonlinear Schrödinger equation. The role of symmetry is discussed. Finally, the procedure which is followed in the one-dimensional cases is successfully applied to find special solutions of higher-dimensional nonlinear partial differential equations

Error-propagation in weakly nonlinear inverse problems

In applications of inversion methods to real data, nonlinear inverse problems are often simplied to more easily solvable linearized inverse problems. By doing so one introduces an error made by the linearization. Nonlinear inverse methods are more accurate because the methods that are used are more correct from a physical point of view. However, if data are used that have a statistical error, nonlinear inversion methods lead to a bias in the retrieved model parameters, caused the by nonlinear propagation of errors. If the bias in the estimated model parameters is larger than the linearization error, a linearized inverse problem leads to better estimation of the model parameter. In this paper the error-propagation is investigated for inversion methods that account the nonlinearity quadratically

Optical RF tone in-band labeling for large-scale and low-latency optical packet switches

We propose an RF tone in-band labeling technique that is able to support large-scale and low-latency optical packet switch. This approach is based on N in-band wavelengths, each carrying M radio frequency (RF) tones. The wavelengths and the tones have a binary value, and are able to encode 2N×M possible routing address. We develop an optical label processor for the RF tone in-band optical label based on parallel and asynchronous processing. It allows the optical packet switch with an exponential increase of number of ports at the expense of limited increase in the latency and the complexity. By using RF tone in-band labeling technique, we demonstrate error free (bit error rat

WDM monitoring technique using adaptive blind signal separation

We present a cost-effective method of monitoring the performance of wavelength-division-multiplexed (WDM) channels. The method is based on simple optical signal processing in combination with electronic signal processing. The photocurrent of a detected (multi-channel) optical signal is analysed using an adaptive blind signal separation method. A maximum data decorrelation criterion is used to separate the WDM channels. We show experimentally that four WDM channels can be reconstructed accurately by this numerical method

All-optical flip-flop based on coupled laser diodes

An all-optical set-reset flip-flop is presented that is based on two coupled lasers with separate cavities and lasing at different wavelengths. The lasers are coupled so that lasing in one of the lasers quenches lasing in the other laser. The flip-flop state is determined by the laser that is currently lasing. A rate-equation based model for the flip-flop is developed and used to obtain steady-state characteristics. Important properties of the system, such as the minimum coupling between lasers and the optical power required for switching, are derived from the model. These properties are primarily dependent on the laser mirror reflectivity, the inter-laser coupling, and the power emitted from one of the component lasers, affording the designer great control over the flip-flop properties. The flip-flop is experimentally demonstrated with two lasers constructed from identical semiconductor optical amplifiers (SOAs) and fiber Bragg gratings of different wavelengths. Good agreement between the theory and experiment is obtained. Furthermore, switching over a wide range of input wavelengths is shown; however, increased switching power is required for wavelengths far from the SOA gain peak

Wavelength conversion employing 120-fs optical pulses in a SOA-based nonlinear polarization switch

We demonstrate wavelength conversion based on nonlinear polarization rotation driven by ultrafast carrier relaxation in an InGaAsP-InGaAs multiquantum-well semiconductor optical amplifier. We use a continuous-wave (CW) probe beam at a center wavelength of 1555 nm, and a control pulse of duration of 120 fs at a center wavelength of 1520 nm. We have investigated wavelength conversion for different injection currents and for different control pulse energies. We show that a conversion efficiency of 12 dB can be obtained for control pulse energies of 10 pJ

All-optical label swapping of in-band addresses and 160 Gbit/s data packets

A 1×4 all-optical packet switch is presented, based on an optical label swapping technique that utilises a scalable label processor and a label rewriter with 'on the fly' operation. Experimental results show error-free packet switching with a data payload at 160Gbit/s. The label erasing and new label insertion operation introduces 0.5dB of power penalty. These results indicate a potential utilisation of the presented technique in a multi-hop packet switched network

All-optical label swapping techniques for data packets beyond 160 Gb/s

We present two paradigms to realize all-optical packet switches, and report experimental results showing the routing operation of the 160 Gb/s packets and beyond. Photonic integrated sub-systems required to implement the packet switch are reviewed. © 2009 IEEE