microwave-photonics-systems-based-on-whispering-gallery-mode

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Microwave photonics systems rely fundamentally on the interaction between microwave and optical signals. These systems are extremely promising for various ...

FEMTO-ST Institute

We describe experimental studies of the dynamical behavior of a recently proposed electro-optic discrete time nonlinear delay oscillator. With appropriate choice of the oscillator loop parameters and external forcing of the dynamics using a pulsed laser source, the system allows for the physical realization of a high dimensional mathematical nonlinear mapping. The dynamical features observed with this new class of discrete time delay oscillator differ significantly from those observed with similar continuous time nonlinear delay feedback oscillators and reveal the intrinsic discrete time nature of the dynamics. We also discuss specific applications to chaos communications using regularly clocked binary data.

Experimental chaotic map generated by picosecond laser pulse-seeded electro-optic nonlinear delay dynamics.

The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time tau approximately 10 ps and by a low cutoff frequency with a response time theta approximately 1 micros. Moreover, the optoelectronic feedback also consists of a significant delay tauD of the order of 100 ns. Depending on two key physical parameters, the loop gain beta and the nonlinearity operating point Phi, a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations (DDEs), which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE (iDDE) that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants tau, theta, and tauD. We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of Phi. One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electro-optic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms (chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations).

Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators.

In this paper we propose group refractive index measurement with a spectral interferometric set-up using a broadband supercontinuum generated in an air-silica Microstructured Optical Fibre (MOF) pumped with a picosecond pulsed microchip laser. This source authorizes high fringes visibility for dispersion measurements by Spectroscopic Analysis of White Light Interferograms (SAWLI). Phase calculation is assumed by a wavelet transform procedure combined with a curve fit of the recorded channelled spectrum intensity. This approach provides high resolution and absolute group refractive index measurements along one line of the sample by recording a single 2D spectral interferogram without mechanical scanning.

High resolution group refractive index measurement by broadband supercontinuum interferometry and wavelet-transform analysis.

We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.

Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization.

Position-referenced microscopy (PRM) is based on smart sample holders that integrate a position reference pattern (PRP) in their depth, allowing the determination of the lateral coordinates with respect to the sample-holder itself. Regions of interest can thus be retrieved easily after culture dish transfers from a cell incubator to the microscope stage. Images recorded at different instants in time are superimposed in a common coordinate system with subpixel accuracy. This paper presents such smart Petri culture dishes and their use for live cell culture monitoring. The impact of the PRP on the light budget is discussed and performances are demonstrated. First results on the application of PRM to the observation of apoptotic body internalization are reported.

Position-referenced microscopy for live cell culture monitoring.

Whereas vision is an efficient way for noncontact sensing of many physical quantities, it assumes a cumbersome imaging system that may be very problematic in confined environments. In such contexts, the design of a compact vision probe can be based on digital holography that is a lensless imaging principle. In this interferometric method, object scenes are reconstructed numerically through wave propagation computations applied to a diffracted optical field recorded as an interferogram. We applied this approach to the visual positioning of a micropatterned glass plate. The pseudoperiodic pattern deposited on the surface is suited for absolute in-plane position determination as well as for fine object-feature interpolation leading to subpixel resolution. Results obtained demonstrate a lateral resolution of 0.1 Î¼m, corresponding to 1/20th of a pixel, from a 150 Î¼m period of the pseudoperiodic pattern and with a demonstrated excursion range of 1.6 cm. In the future, such position encoding could be applied to the backside of standardized sample holders for the easy localization of regions of interest when specimens are transferred from an instrument to another one, for instance in nanotechnology processes.

Lensless vision system for in-plane positioning of a patterned plate with subpixel resolution.

An electro-optic oscillator subject to two distinct delayed feedbacks has been designed to develop pronounced broadband chaotic output. Its route to chaos starts with regular pulsating gigahertz oscillations that we investigate both experimentally and theoretically. Of particular physical interest are the transitions to various crenelated fast time-periodic oscillations, prior to the onset of chaotic regimes. The two-delay problem is described mathematically by two coupled delay-differential equations, which we analyze by using multiple-time-scale methods. We show that the interplay of a large delay and a relatively small delay is responsible for the onset of fast oscillations modulated by a slowly varying square-wave envelope. As the bifurcation parameter progressively increases, this envelope undergoes a sequence of bifurcations that corresponds to successive fixed points of a sine map.

Crenelated fast oscillatory outputs of a two-delay electro-optic oscillator.

We report on the experimental demonstration of a hybrid optoelectronic neuromorphic computer based on a complex nonlinear wavelength dynamics including multiple delayed feedbacks with randomly defined weights. This neuromorphic approach is based on a new paradigm of a brain-inspired computational unit, intrinsically differing from Turing machines. This recent paradigm consists in expanding the input information to be processed into a higher dimensional phase space, through the nonlinear transient response of a complex dynamics excited by the input information. The computed output is then extracted via a linear separation of the transient trajectory in the complex phase space. The hyperplane separation is derived from a learning phase consisting of the resolution of a regression problem. The processing capability originates from the nonlinear transient, resulting in nonlinear transient computing. The computational performance is successfully evaluated on a standard benchmark test, namely, a spoken digit recognition task.

Photonic nonlinear transient computing with multiple-delay wavelength dynamics.

Time-delayed systems are known to exhibit symmetric square waves oscillating with a period close to twice the delay. Here, we show that strongly asymmetric square waves of a period close to one delay are possible. The plateau lengths can be tuned by changing a control parameter. The problem is investigated experimentally and numerically using a simple bandpass optoelectronic delay oscillator modeled by nonlinear delay integrodifferential equations. An asymptotic approximation of the square-wave periodic solution valid in the large delay limit allows an analytical description of its main properties (extrema and square pulse durations). A detailed numerical study of the bifurcation diagram indicates that the asymmetric square waves emerge from a Hopf bifurcation.

Article	Year
Experimental chaotic map generated by picosecond laser pulse-seeded electro-optic nonlinear delay dynamics. Chaos (Woodbury, N.Y.)\| PubMed ID: 18377061	2008
Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators. Physical review. E, Statistical, nonlinear, and soft matter physics\| PubMed ID: 19391821	2009
High resolution group refractive index measurement by broadband supercontinuum interferometry and wavelet-transform analysis. Optics express\| PubMed ID: 19532165	2006
Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization. Physical review. E, Statistical, nonlinear, and soft matter physics\| PubMed ID: 19792231	2009
Position-referenced microscopy for live cell culture monitoring. Biomedical optics express\| PubMed ID: 21559142	2011
Lensless vision system for in-plane positioning of a patterned plate with subpixel resolution. Journal of the Optical Society of America. A, Optics, image science, and vision\| PubMed ID: 22193262	2011
Crenelated fast oscillatory outputs of a two-delay electro-optic oscillator. Physical review. E, Statistical, nonlinear, and soft matter physics\| PubMed ID: 22463299	2012
Photonic nonlinear transient computing with multiple-delay wavelength dynamics. Physical review letters\| PubMed ID: 23004274	2012
Strongly asymmetric square waves in a time-delayed system. Physical review. E, Statistical, nonlinear, and soft matter physics\| PubMed ID: 23214834	2012

Maxime Jacquot

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