We analyze the fundamental impact of noise propagation in deep neural network (DNN) comprising nonlinear neurons and with connections optimized by training. Our motivation is to understand the impact of noise in analogue neural network realizations. We consider the influence of additive and multiplicative, correlated and uncorrelated types of internal noise in DNNs. We find general properties of the noise impact depending on the noise type, activation function, depth and the statistics of connection matrices and show that noise accumulation can be efficiently avoided. Our work is based on analytical methods predicting the noise levels in all layers of the network.
Analog neural networks are promising candidates for overcoming the sever energy challenges of digital Neural Network processors. However, noise is an inherent part of analogue circuitry independent if electronic, optical or electro-optical integration is the target. I will discuss fundamental aspects of noise in analogue circuits and will then introduce our analytical framwork describing noise propagation in fully trained deep neural networks comprising nonlinear neurons. Most importantly, we found that noise accumulation can be very efficiently supressed under realistic hardware conditions. As such, neural networks implemented in analog hardware should be very robust to internal noise, which is of fundamental importance for future hardware realizations.
Maximal computing performance can only be achieved if neural networks are fully hardware implemented. Besides the potentially large benefits, such parallel and analogue hardware platforms face new, fundamental challenges. An important concern is that such systems might ultimately succumb to the detrimental impact of noise. We study of noise propagation through deep neural networks with various neuron nonlinearities and trained via back-propagation for image recognition and time-series prediction. We consider correlated and uncorrelated, multiplicative and additive noise and use noise amplitudes extracted from a physical experiment. The developed analytical framework is of great relevance for future hardware neural networks. It allows predicting the noise level at the system’s output based on the properties of its constituents. As such it is an essential tool for future hardware neural network engineering and performance estimation.
We propose a novel implementation of autonomous photonic neural networks based on optically-addressed spatial light modulators (OASLMs). In our approach, the OASLM operates as a spatially non-uniform birefringent waveplate, the retardation of which nonlinearly depends on the incident light intensity. We develop a complete electrical and optical model of the device and investigate the optimal operational characteristics. We study both, feed-forward and recurrent neural networks and demonstrate that OASLMs are promising candidates for the implement of autonomous photonic neural networks with large numbers of neurons and ultra low energy consumption.
An experimental study of the variation of quality factor (Q-factor) of mm-size whispering-gallery mode (WGM) resonators manufactured with fluoride crystals as a function of surface roughness is proposed. Q-factors of the order of 1 billion are measured at 1550 nm. The experimental procedure needs repeated polishing steps, after which the surface roughness is measured by quantitative phase imaging, based on a white-light phase-shifting interferometry approach, while the Q-factors are determined using the cavity-ring-down method. This process allows us to reach an explicit curve linking the Q-factor of the disk-resonator to the surface roughness of the rim.
The variations of Q-factor as a function of surface roughness is universal, in the sense that it is globally independent of the bulk material under consideration. We used a white-light interferometer to investigate the dependency of Q-factors considering three different difluoride crystals as bulk materials; in all cases, we have found that a billion Q-factors at 1550 nm are achieved when the rms surface roughness has a nanometer order of magnitude.
We have also compared our experimental data with theoretical estimations. This comparison enabled us to highlight a mismatch, which can be explained by the many physical constraints imposed by the mechanical grinding and polishing protocol. We expect that our work will contribute to a better understanding of the Q-factor limitations for mm-size WGM resonators, which are finding applications in a broad range of areas.
We experimentally create a neural network via a spatial light modulator, implementing connections between 2025 in parallel based on diffractive coupling. We numerically validate the scheme for at least 34.000 photonic neurons. Based on a digital micro-mirror array we demonstrate photonic reinforcement learning and predict a chaotic time-series via our optical neural network. The prediction error efficiently converges. Finally, we give insight based on the first investigation of effects to be encountered in neural networks physically implemented in analogue substrates.
Crystalline whispering-gallery-mode disk resonators are finding an increasing number of applications in photonics. Their exceptional energy storage capacity is of great interest in the area of ultrastable oscillators for aerospace and communication engineerings as well as for sensing applications. Here, we investigate the physical properties of some unconventional crystalline materials. We show that these resonators can display quality factors higher than ten million at 1550 nm and we discuss their potential for various applications.
We investigate theoretically and experimentally the computational properties of an optoelectronic neuromorphic processor based on a complex nonlinear dynamics. This neuromorphic approach is based on a new paradigm of or reservoir computing, which is intrinsically different from the concept of Turing machines. It essentially 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, performed through a learning phase consisting of the resolution of a regression problem. We here investigate an architecture for photonic neuromorphic computing via these complex nonlinear dynamical transients. A versatile photonic nonlinear transient computer based on a multiple-delay is reported. Its hybrid analogue and digital architecture allows for an easy reconfiguration, and for direct implementation of in-line processing. Its computational efficiency in parameter space is also analyzed, and the computational performance of this system is successfully evaluated on a standard spoken digit recognition task. We then discuss the pathways that can lead to its effective integration.
We investigate the phase noise performance of an optoelectronic oscillator based on a calcium fluoride high quality
factor whispering gallery mode optical resonator (WGMR). In the oscillator setup, a particular attention is given to the
stabilization of the laser lightwave onto an optical resonance of the WGMR. Once the laser is stabilized, different
resonant optical modes are characterized in the microwave domain. Afterwards, phase noise spectra of different
oscillations at different modes of the WGMR are measured. Phase noise levels below -93 dBc/Hz and around
-90 dBc/Hz at 10 kHz offset frequency from 6.35 GHz and 12.7 GHz carriers are respectively obtained.
The theoretical understanding of Kerr combs has been the object of extensive efforts worldwide in the last ten years. Several insights have been provided since then into this problem and have enabled significant progress for the optimization and tailoring of these combs. Here, we investigate the formation of dissipative structures in crystalline whispering-gallery mode disk resonators that are pumped in different dispersion regimes. In the Fourier domain, these dissipative structures correspond to specific types of mode-locked Kerr optical frequency combs. Depending on the sign of the second-order chromatic dispersion and on the pumping conditions, we show that either bright or dark cavity solitons can emerge, and we show these two regimes are associated with characteristic spectral signatures that can be discriminated experimentally. We use the Lugiato-Lefever spatiotemporal formalism to investigate the temporal dynamics leading to the formation of these azimuthal solitons, as well as the emergence of Turing patterns. The theoretical results are in excellent agreement with experimental measurements that are obtained using calcium and magnesium fluoride disk resonators pumped near 1550 nm.
In this work, we present experimental results on an optoelectronic resonator (OEO) based on intensity modulation and a high-Q disk resonator. In our configuration, the crystalline whispering-gallery-mode resonator acts both as a frequency filter, selecting the microwave oscillating frequency, and as an optical storage element. In such a system, the oscillating frequency corresponds to the free spectral range of the resonator (between 10 GHz and 11 GHz), and therefore no delayinduced spurious peaks are present in the spectrum, in contrast to the case of the classical optoelectronic oscillator where the storage element consists of an optical fiber delay line. An other advantage of our system resides in its compactness allowing for efficient control of the temperature.
Based on a modal description of the evolution of the mode's amplitude in a whispering-gallery mode resonator, we numerically study the generation of Kerr combs. We show that a stable primary comb appear for pump power slightly above threshold, enabling potential applications in metrology. For high input power however, chaotic signals are observed.
Based on a modal description of the evolution Kerr combs in a whispering-gallery mode resonator, we numerically investigate the phase bhavior of the different spectral lines of the spectrum. We show that a stable phase relation exists between adjacent modes in primary combs. This result is of great interest for metrological applications where one phase noise is an issue. For high input power however, chaotic signals are observed.
The aim of this work is to compare advantages and disadvantages of different techniques for coupling a mini-discoptical-
resonator to determine quality factor of its resonance. Optical fiber coupled to a resonator consists in a mini disc
with whispering gallery modes at its circumference. We choose to work with three materials and design compact
miniresonators. Fused silica is found to be suitable for these applications thanks to its hardness in the range 6-7 and the
behavior to mechanical shocks, despite its sensitivity to water pollution. With its tetragonal crystal and a good behavior
with risk of water pollution, Calcium fluoride is a good candidate despite sensitivity to mechanical shocks. Magnesium
fluoride is the third material used. As a critical step, taper coupling is set with a 20nm resolution positioning system.
Miniresonator is excited from a system equipped with a tunable laser diode with a tunability from 1490 to 1640 nm and a
linewidth narrower than 300kHz. Light is coupled into the microsphere either from glass or fiber prism or with fiber
taper via evanescent field. We have also used a single frequency 660nm laser diode with a linewidth narrower than
100kHz which can be tuned about 10pm to test a single resonant peak. Both sources are used with either a tapered fiber
or a filed fiber. Resonance is observed and quality factor of the resonators is found to be in the range of 108.
The performance advances in communication systems like Radar system, precision navigation, space application and
time and frequency metrology require more stable frequency and low phase noise system. Here is presented a
configuration of phase noise measurement system operating in X- band using a photonic delay line as a frequency
discriminator. This system doesn't need any excellent frequency reference and works for any frequency between 8.2 and
12.4 GHz. Using cross correlation on 500 averages, noise floor of the instrument is respectively -150 and -170 dBc/Hz at
101 and 104 Hz from the 10 GHz carrier (-90 and -170 dBc/Hz including 2 km delay lines). This instrument is developed
in the context of association with the national french metrology institute (laboratoire national de métrologie et d'essais,
LNE). This calibration system is to be integrated in measurements means of the accredited laboratory to improve the
Calibration Metrology Capabilities (CMC) of the LNE.
Optoelectronic oscillators are ultra-pure microwave generators based on optical energy storage instead of high
finesse radio-frequency resonators. We present in this communication a new and compact architecture where the
optical energy storage is performed by trapping laser light into the ultra-high Q whispering gallery modes of a
millimeter-size disk resonator. As a proof of concept, we demonstrate the generation of a 10.7 GHz microwave
with a phase noise of -110 dBrad2/Hz at 100 kHz. We also discuss in detail the potential of this architecture
for the generation of microwaves with a frequency ranging from 50 to 200 GHz.
This study deals with a design, fabrication and characterization of compact optoelectronic oscillators (OEO). Resonator
behaves as a sphere because energy is trapped in whispering-gallery-modes in the equatorial region. For this purpose,
Fused-silica and MgF2 are suitable, due to their mechanical characteristics and their low attenuation at 1.55 μm
wavelength. In fact, 6-7 degrees Mohs hardness of these materials allows us to obtain a quite easy precision-processing.
Our prototype owns a quality factor of approximately 3×108, which is certainly limited by the available technology.
Resonator is coupled to an optical fiber including a taper-waveguide-based on a nm-position resolution. Microwave
carrier is generated by locking optical phase modulation to a free-spectral-range (FSR) resonator, which occurs in the X-band.
Moreover, this carrier is detected by a standard low-noise InGaAs p-i-n telecom photodiode. Oscillator prototype
is assembled on a 0.12 m2 optical breadboard. In principle, this surface can be reduced to those of the oscillator main
parts (resonator, laser, photodiode, amplifier and optical modulator). Oscillator phase noise measured by a dual-delay-line
instrument, which has been developed in Besançon, corresponds to -90 dBrad2/Hz at 10 kHz off carrier. According
to this result, oscillator suffers from severe noise-limitations due to several reasons: the thermal coefficient of the
resonator, the low power that the resonator can accept, and the small volume of the energy-confinement region in the
resonator (≈2×1014 m3) but our oscillator is packaged in a small volume, contrarily to classic OEO based on an optical fiber of a few km.
Chaotic wavelength transmitters based on a DBR laser submitted to optoelectronic feedback with periodic time delay are
considered. We investigate the retrieval of the periodic time delay function from experimental time series. Square-wave
and sinusoidal modulations are considered for the frequency clock of a delay module based on a First-In First-Out
memory. It is shown that the period of the time delay can be extracted from experimental data by using the mutual
information function. Different values of the nonlinearity are considered. Applying a modified filling factor method the
periodic time delay function is retrieved in the sinusoidal modulation case for different periods and modulation depths.
We study the identification of the delays of several chaotic optical cryptosystems subjected to one or two delayed feedbacks. We show that the delay of a single-delay system can be identified, even if highly complex chaos is used. For certain types of systems with two delays, the same identification techniques that work for single-delay systems also work for multiple-delay systems. These systems thus do not provide a significant increase of the security level. A careful choice of the architecture of multiple-delay system can, however, make these techniques fail. We propose some higher-dimensional techniques that lead to the identification of the delays for these architectures too. The increased complexity of these techniques means, however, that it takes a significantly longer time to identify the delays.
We present recent results obtained for an optical chaos communications system using optoelectronic devices. These devices are used to improve privacy and security in information transmission. Two kind of chaos based emitters and receivers are described: a semiconductor laser subject to all-optical feedback and operating in a non-linear regime and a semiconductor laser subject to non-linear electro-optical feedback and operating in a linear regime. We show that both configuration give very good synchronization properties and are suitable for message enconding/decoding at bit rates as high as Gbit/s.
We investigate the detrimental effect of chaotic noise on the performance of an optical chaos cryptosystem. Hyperchaos is generated in the emitter and receiver systems with Mach-Zehnder interferometers fed by semiconductor lasers and subjected to electro-optical feedback. In this optical chaos cryptosystem, (chaotic) noise originates from the mismatch in parameters between the emitter and the receiver. We therefore determine the amplitude of this noise as a fonction of the parameter mismatch, and we evaluate its effect on the bit error rate (BER) performance of the communication system. Analytical predictions are confirmed by numerical simulations and experimental results.
Chaos-based secure communication is intended to operate as an additional encryption mean at the physical layer, with the unique capability for operating at several 10s of Gb/s. Different chaos
generators have been recently explored for optical telecommunications, among which three setups were particularly interesting in terms of encryption speed capability: the all-optical external cavity semiconductor laser, the direct optoelectronic feedback semiconductor laser, and the nonlinear electrooptic
feedback. The latter solution was mainly investigated by our group during the last 5 years. We report its numerous advantages in terms of chaos complexity (attractor dimension as high as several hundreds have been obtained), architecture reliability (different chaos generator have been performed experimentally), encryption bandwidth
capability (more than 30GHz chaotic spectrum has been observed), stability, and decoding quality. The potential for high speed operation was recently demonstrated with an electrooptic chaos
generator at 3Gb/s, with BER as low as 10-9}.
Nonlinear delayed dynamics was first proposed in Optics by Kensuke Ikeda in 1979. Since then, many different setups based on similar dynamical principles were carried out experimentally, first to explore the numerous and various behaviours, and then to use the high complexity chaotic regimes for optical data encryption. After a brief review of the different setups and principles, we will report on 4 different optoelectronics realizations developed in our group, emphasizing on the characteric properties of each setup, and their implementation in chaos-based secure communication systems.
We present results on the state of the art in optoelectronic devices for chaos generation and message encryption/extraction. We concentrate on two kind of chaos based emitters and receivers: a semiconductor laser subject to all optical feedback and operating in a non linear regime and a semiconductor laser subject to nonlinear
electro optical feedback and operating in a linear regime. We show that both configuration give very good synchronization properties and are suitable for message enconding/decoding at bit rates as high as Gbit/s.
We propose a method to obtain intensity chaos of high dimensionality from a laser diode with a nonlinear delayed feedback. The core of the chaotic transmitter and receiver is formed by an electro-topic LiNbO3 modulator that is used to generate strong nonlinearities and chaotic waveforms. The method can be used for encrypting and decrypting a signal in a chaos-based communication system.
Severe communications based on chaos have been investigated for some years, especially in the area of radiofrequency transmissions. Signal decoding and decoding is then generally achieved using a RF carrier whose amplitude fluctuates chaotically. Recent advances have also been reported in the field of optical telecommunications. Optical chaos produced by random fluctuations of laser power is then used to encrypt signals. However most of the systems reported so far are plagued by their low flexibility which makes difficult the key to be changed easily. We report experiments in which chaos in wavelength, rather than in power, is advantageously used to encrypt signals. The latter are encrypted as chaotic fluctuations of the wavelength of a tunable semiconductor laser driven by a generator of chaos. Decoding makes use of another generator of chaos operating as a local oscillator synchronized on the first one. The first results are reported in the wavelength range of 1550 nm.
Secure communications based on chaos have been investigated for some years, especially in the area of radio frequency transmissions. Signal decoding and decoding is then generally achieved using a RF carrier whose amplitude fluctuates chaotically. Recent advances have also been reported in the field of optical telecommunications. Optical chaos produced by random fluctuations of laser power is the sued to encrypt signals. However most of the system reported so far are plagued by their low flexibility which makes difficult the key to be changed easily. We report experiments in which chaos in wavelength, rather than in power, is advantageously used to encrypt signals. The latter are encrypted as chaotic fluctuations of the wavelength of a tunable semiconductor laser driven by a generator of chaos. Decoding makes use of another generator of chaos operating as a local oscillator synchronized on the first one. The first results are reported in the wavelength range of 1550 nm.
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