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We recently proposed a mechanism for excitability in systems with a weakly broken Z2 symmetry, which includes optical units such as semiconductor ring lasers (SRLs). SRLs are a modern class of semiconductor lasers whose active cavity is characterized by a circular geometry. This enables the laser to support two counterpropagating modes, referred to as the clockwise (CW) and the counterclockwise (CCW) mode. The breaking of the Z2 symmetry is realized by making the linear coupling between the counterpropagating modes asymmetric. This can be achieved by increasing the reflection of, e.g., the CW mode into the CCW mode. This will stabilize lasing in the CCW mode and, when in the excitable regime, the SRL will fire optical pulses in the CW mode as a response to noise perturbations. In this contribution we experimentally and theoretically characterize these pulses. Our experiments reveal a statistical distribution of the characteristics of the optical pulses that is not observed in regular excitable systems. In particular, an inverse correlation exists between the pulse amplitude and duration. Numerical simulations and an interpretation in an asymptotic phase show that the observed distribution of the pulse amplitude and duration results from the characteristics of the excitability mechanism. Excitable behavior in optical systems has generally been shown to occur close to a fold bifurcation and a homoclinic bifurcation of a stable limit cycle. In these systems, the response to noise is governed by the presence of an accessible saddle point S embedded in the separatrix. Pulses are activated by noise-induced fluctuations that connect the resting state to S, and the large deterministic excursion takes place along the unstable manifold of S. However, in systems with a weakly broken Z2 symmetry, the accessible saddle is not embedded in the separatrix and the unstable manifold of S does not participate in the excitability mechanism. It is the folding of the stable manifold that participates in the pulse generation. The absence of a compressive flow between and perpendicular to this stable manifold explains the observed variety in pulse shapes. We also consider asymmetric SRLs coupled through a single bus waveguide. This is a first step towards an integrated optical neural network using semiconductor ring lasers as building blocks. We will show that for weak coupling, excitatory excursions still persist due to the similar phase space structure. Moreover, they can excite pulses in each other and can thus function as communicating neurons. This type of neural network can be fully integrated on chip and does not suffer from the drawback of needing extra-cavity measures, such as optical injection or saturable absorbers.

Semiconductor Ring Lasers (SRLs) are a novel class of semiconductor lasers whose active cavity is characterized by a circular geometry. SRLs have attracted attention due to the possibility of monolithical integration of thousands of them on the same chip in a cheap and reliable way. SRLs are interesting for applications that rely on the presence of two counter-propagating modes inside the optical cavity. For instance, fully symmetric coupled SRLs have been proposed as candidates for the realisation of small and fast all-optical memories. At the same time, a wealth of nonlinear and stochastic dynamics have been predicted and observed in symmetric SRLs which is a consequence of the underlying Z2-symmetry of the device. However, unavoidable fabrication defects, material roughness and chip-cleaving break the device symmetry in an uncontrolled and unpredictable way, which may result in a deterioration of the device's performance in applications such as all-optical signal-processing. Despite their importance, the effects of symmetry breaking in SRLs remain unaddressed. In this contribution we investigate theoretically and experimentally the stochastic dynamics of SRLs with weakly broken Z2-symmetry . We show how the symmetry of an SRL can be experimentally manipulated using the reflection from a cleaved facet of a multi-mode optical fibre and a control electrode on the bus waveguide. The experiments are performed on an InP-based multi-quantum well SRL operating in single-longitudinal mode regime. The power at the CCW output is collected using a fast photodiode connected to an oscilloscope with a sampling rate of 4.0 ns. For a not-too-weak symmetry breaking, we reveal that SRLs become excitable and therefore can emit large, deterministic power bursts as a response to stochastic fluctuations. The origin of excitability is explained by investigating the topology of the invariant manifolds of an asymptotic two-dimensional phase space model with broken Z2-invariance. The results of the experiments confirm the prediction of the theory.

Semiconductor ring lasers (SRLs) are a particular type of semiconductor lasers where the laser cavity consists of a ring-shaped waveguide. Due to their symmetry, SRLs can emit in one of two counter-propagating modes and are therefore recognized to be promising sources in photonic integrated circuits. In particular, this possibility of bistable directional operation has paved the way for encoding digital information in the emission direction of SRLs with record low values for switching times and energies [1]. We have applied a singular perturbation technique to reduce a set of rate equa- tions for a SRL to two equations for the relative modal intensity and the phase difference between the two counter-propagating modes [2]. Not only do these re- duced equations simplify the bifurcation analysis of the possible steady-state solu- tions considerably, they also allow for a two-dimensional phase-space description of the laser. In particular, the shape of the invariant manifolds of the saddle point in the system is studied and a full bifurcation analysis of this two-dimensional laser system is carried out. This approach also reveals that semiconductor ring lasers are an optical prototype of nonlinear systems with Z2 symmetry. We investigate both theoretically and experimentally the stochastic switching between two counter-propagating lasing modes of a SRL. Experimentally, the resi- dence time distribution cannot be described by a simple one parameter Arrhenius exponential law and reveals the presence of two different mode-hop scenarios with distinct time scales. The topological phase-space picture of the two-dimensional dynamical system gives insight into the observed features [3]. Expanding on the mode-hopping study in the bistable region, we also show how the operation of the device can be steered to multistable dynamical regimes, predicted by the two- dimensional model. By analyzing the phase-space in this model, we predict how the stochastic transitions between multiple stable states take place and confirm it experimentally [4]. Finally, we show theoretically and experimentally that by perturbing the Z2 symmetry, SRLs can be driven into a regime of excitability. The global shape of the invariant manifolds of the saddle in the vicinity of a homoclinic loop are shown to determine the origin of excitability and the features of the excitable pulses [5] [1] M. T. Hill et. al., Nature 432, 206-209 (2004). [2] G. Van der Sande et. al., J. Phys. B 41, 095402 (2008). [3] S. Beri et. al., Phys. Rev. Lett. 101, 093903 (2008). [4] L. Gelens et. al., Phys. Rev. Lett. 102, 193904 (2009). [5] S. Beri et. al., Phys. Lett. A 374, 739-743 (2010).

We present an investigation of excitability in a weakly asymmetric semiconductor ring laser (SRL). We simulate the injection of short optical trigger pulses in SRLs using a five-dimensional rate equation model and interpret the results in an asymptotic two-dimensional model. The response of the SRL to optical trigger pulses is characterized and we show that the phase difference between the injected field and the electric field inside the SRL plays an important role in determining the excitability threshold. A mechanism for exciting multiple consecutive pulses using a single trigger pulse will also be discussed. Finally, the variety of pulse shapes is investigated and compared with experiments.

We have investigated the label-free biosensing properties of grated silicon photonic wire (GSPW) waveguides with cross-sectional dimensions of 350 nm x 220 nm, fabricated using a 248-nm deep UV lithography process. The steep edges of the optical transmission spectrum of the GSPW enable detection of very small spectral shift, hence of small index changes. To obtain an antibody layer for the biosensing experiment, an immobilization process is required. We followed the standard immobilization process developed by Imenz B.V. The antibody immobilization process and the binding process of enzymes on an immobilized antibody layer have been monitored with the GSPW based sensor.

Multimode silicon-oxynitride (SiON) waveguide structures are investigated for probing fluorescence and backscattered light from samples of different thicknesses. The collection efficiency together with the resolution of such probes is compared to that of a conventional fiber probe. The simulation results show that, in case of low scattering samples, among the two types of probes the former present higher collection efficiencies when the sample thickness is below 85 µm. The analytical model developed to estimate the collection efficiency of the integrated probes was validated experimentally through fluorescence measurements carried out on a ruby rod. The model and the experimental results are both presented in this work.

Neodymium-doped Al2O3 layers were deposited on thermally oxidized Si substrates by reactive co-sputtering and channel waveguides were patterned using reactive-ion etching. Internal net gain on the Nd3+ transition at 1064 nm was experimentally investigated with various Nd3+ concentrations. With approximately 12 mW of launched pump power at 800 nm, a maximum gain of 4.0 dB/cm was demonstrated in a 1-cm-long Al2O3:Nd channel waveguide sample with a Nd3+ concentration of 1.68x1020 cm-3. Investigations of gain on the Nd3+ ground-state transition around 880 nm are under way. This wavelength range is of interest for amplification of signals transmitted through optical backplanes.

In this work plasma enhanced chemical vapor deposition (PECVD) were adopted to achieve boron/phosphorous (B/P) doped silicon oxynitride (SiON) layers. By adjusting the flow rates of corresponding gas precursor (PH3/Ar or B2H6/Ar), SiON layers with different B or P concentrations were obtained. Measurements by X-ray photoelectron spectroscopy (XPS) have shown that PH3 can result in more efficient doping in the layers than B2H6. Compared with B-doped samples, reduction of the hydrogen content can be more easily observed in P-doped SiON layers, as been confirmed by Fourier transform infrared spectroscopy. Hydrogen-related chemical bonds became undetectable after annealing of samples at temperatures as low as 700°C. These results are quite helpful to further research on B/P co-doped SiON layers in application of integrated optical waveguide devices.

Channel waveguides based on a polymer, 6-fluorinated-dianhydride/epoxy, which is actively doped with a rare-earth-ion-doped complex, Nd(thenoyltrifluoroacetone)3 1,10-phenanthroline, have been fabricated. Luminescence and loss spectra of the channel waveguides have been experimentally investigated. By optimization of the fabrication procedure of both, host material and optical structure, steady-state laser emission has been demonstrated from a channel waveguide near 1060 nm, which provides up to 440 µW of output power from the waveguide structures developed.

In this paper the design and modelling of an integrated Al2O3:Er3+ distributed feedback laser (DFB) is presented. The implemented laser model combines rate equations of the population mechanisms in the erbium ion with coupled-mode theory. The model enables the estimation of the optimum Bragg grating design that is required in order to realise such a DFB laser device. Based on the modelling results, the ideal grating geometry has been identified and fabricated by making use of laser interference lithography (LIL) and reactive ion etching (RIE). Optical characterisation experiments of the gratings are currently in progress.

High-quality crystalline KY(WO4)2:Yb3+ layers co-doped with large concentrations of optically inert Gd3+ and Lu3+ ions were grown by vertical liquid phase epitaxy. The codoping enhances the refractive index contrast between the active layer and the undoped KY(WO4)2 substrate to ~7.5×10-3. A K2W2O7 solvent was employed for the growth of layers onto undoped (010)-oriented KYW substrates. Single crystalline layers of thickness 5-10 µm were grown at low level of supersaturation and growth temperatures of 920-923°C. The layer quality was studied by X-ray diffraction. The composition of the grown layers was determined by laser-ablation inductively-coupled-plasma mass spectrometry (LA-ICP-MS). Planar waveguide lasers with low laser threshold of 18 mW, record-high slope efficiency of 82.3%, and maximum output power of 195 mW have been achieved.

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We review theoretical results on the dynamics of solitary single longitudinal mode and single transversal mode semiconductor ring lasers. These analyses are based on a rate equation model for the slowly varying envelopes of the counter-propagating fields in the ring cavity which has been proposed by Sorel et al. [Opt. Lett. 27, 1992 (2002); IEEE J. Quantum Electron. 39, 1187 (2003)]. The model shows several operating regimes. The lasers are found to operate bidirectionally up to twice the threshold, where unidirectional operation starts. Just above threshold, the lasers operate in a regime where the two counterpropagating modes are continuous wave, while as the injected current is increased, a regime appears where the intensities of the two counterpropagating modes undergo alternate sinusoidal oscillations. To understand these dynamical features, we discuss a reduction of this basic rate equation model derived by Van der Sande et al. [accepted for publication in J. Phys. B (2008)]. The reduction has been achieved using asymptotic methods based on the typical relative scaling of the dynamical time scales of the system. Physical conditions for the emergence of the operating regimes are assessed quantitatively in terms of nonlinear (saturation processes) and linear coupling (backscattering) between the counter-propagating modes.

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Fluctuational escape via an unstable limit cycle is investigated in stochastic flows and maps. A new topological method is suggested for analysis of the corresponding boundary value problems when the action functional has multiple local minima along the escape trajectories and the search for the global minimum is otherwise impossible. The method is applied to the analysis of the escape problem in the inverted Van der Pol oscillator and in the Henon map. An application of this technique to solution of the escape problem in chaotic maps with fractal boundaries, and in maps with chaotic saddles embedded within the basin of attraction, is discussed.