## Abstract

Reservoir computing is a new bio-inspired computation paradigm. It exploits a dynamical system driven by a time-dependent input to carry out computation. For efficient information processing, only a few parameters of the reservoir needs to be tuned, which makes it a promising framework for hardware implementation. Recently, electronic, opto-electronic and all-optical experimental reservoir computers were reported. In those implementations, the nonlinear response of the reservoir is provided by active devices such as optoelectronic modulators or optical amplifiers. By contrast, we propose here the first reservoir computer based on a fully passive nonlinearity, namely the saturable absorption of a semiconductor mirror. Our experimental setup constitutes an important step towards the development of ultrafast low-consumption analog computers.

© 2014 Optical Society of America

## 1. Introduction

The term reservoir computing refers to a new class of recurrent neural networks introduced simultaneously by H. Jaeger [1,2] and W. Maas [3] a dozen years ago. A reservoir is a nonlinear dynamical system driven by the time-dependent input that one wants to process. The output of the reservoir is obtained through a linear combination of its many internal states. Contrary to other recurrent neural networks, a reservoir is only trained at its output: the only parameters that are optimized to train the reservoir are the weights determining the linear combination of the output. In order for a reservoir to be able to process information in an efficient way, only a few internal parameters of the dynamical system need to be tuned [1, 2, 4].

These characteristics make reservoir computing a unique paradigm for hardware implementation. Several experimental reservoir computers have recently been reported, including electronic [5], opto-electronic [6, 7], all-optical [8, 9] versions, all based on nonlinear delayed feedback structures. Those experimental setups exhibit performances that are comparable to digital implementations of reservoir computing.

For decades, optics has been viewed as a promising framework for implementing computation. Optics indeed naturally offers parallelism (frequency or space multiplexing) and speed. Moreover, since the advent of laser technologies, the field of nonlinear optics has witnessed a tremendous development. Consequently, a large number of optical nonlinearities are known and mastered. However, there has only been very limited success in building an optical computer because, despite huge progresses, optical nonlinearities remain weak, difficult to harness and to convert into logic gates.

For these reasons, reservoir computing constitutes an interesting framework to implement optical computing. Indeed there is much more freedom in the architecture because reservoir computing does not rely on logic gates. Recently, we reported the first all-optical reservoir computer [8]. It was based on a delayed feedback dynamical system and the nonlinearity was provided by the saturation of the gain of a semiconductor optical amplifier. This off-the-shelf component introduced noise in the reservoir, which led to a degradation of the performances as compared to our previous opto-electronic reservoir computer [6].

In ref. [9], an all-optical reservoir computer has been reported. It is based on a semiconductor laser submitted to feedback. Contrary to our all-optical implementation, the input of this dynamical system was synchronized with the delay time and it used the intrinsic time scale of the laser dynamics as coupling between the internal states. Optical reservoir computers based on networks of SOA’s or of micro ring resonators have also been studied in simulation in refs. [10–12]. More recently, a passive photonics chip-based reservoir computer has been demonstrated [13]. The reservoir itself is linear and is operated in the coherent regime to enrich its dynamics. The states of the reservoir undergo a nonlinear transformation at the readout level before the output is computed.

Here we report the first all-optical reservoir computer based on a passive nonlinear element, namely a semiconductor saturable absorber mirror (SESAM) whose structure is described in refs. [14, 15]. We tested our reservoir on benchmark tasks: performances are comparable or better than the ones reported with our previous experimental reservoir computers [6, 8] and comparable to state-of-the-art results of digital implementations.

The interest of this work is multifold: first, the nonlinearity that we use exhibits a fundamentally different behavior from the ones used in previous works. Up to now, experimental reservoir computers exploited nonlinear devices that mimic the node-inspired hyperbolic tangent response of the nodes in the standard digital implementations of reservoir computers (see e.g. [2, 4]). This should be opposed with the SESAM that exhibits a nonlinear behavior at low power and gets linear at high power. As a consequence, the present work shows that there is more freedom than originally anticipated for the choice of nonlinear functions to be exploited in reservoir computers.

Second, our work constitutes a first important step towards an entirely passive reservoir computer, a very desirable goal as it would eliminate the need to feed energy into the reservoir, while simultaneously suppressing an important source of noise in the reservoir itself.

Third, saturable absorption in semiconductors can be tuned through impurity concentration [16], and recovery times as small as a few picoseconds can be easily reached [15]. Our study thus opens up the route towards the realization of ultrafast all-optical reservoir computers.

Note however that, because of excessive losses in the setup, we had to include an amplifier in our nonlinear delay loop and our reservoir is thus not fully passive. Nevertheless, the amplifier has been used far from its saturation regime and its role was thus limited to pure linear loss compensation, which allows us to present our result as a genuine demonstration of the possibility to implement passive ultrafast all-optical reservoir.

In the next section we describe our experimental reservoir computer and all the devices used in our experiments. In section 3 we present our experimental results and compare our reservoir performances to state-of-the-art digital and experimental results. In section 4, we discuss the results and the interest of the passive nonlinearity for all-optical reservoir computing.

## 2. Hardware implementation

#### 2.1. Reservoir computing

A reservoir computer consists of a recurrent dynamical system described by some internal states *x _{i}* (typically called ”nodes” or, for historical reasons, ”neurons”) driven by a time dependent input sequence

*u*(

*n*). The core idea behind reservoir computing is that the perturbation that is brought in the dynamical system by the temporal features of

*u*(

*n*) can easily be picked up by a linear output layer. More specifically, the system evolves in discrete time according to Eq.

*N*is the number of internal variables,

*F*is a nonlinear function (the tanh function or other sigmoid functions are often used in digital implementations [2, 4]),

_{NL}*α*is the feedback gain,

*β*is the input gain and

*A*is the interconnection matrix. The node-dependent coefficients

*m*, collectively called the “input mask” serve the purpose of breaking the symmetries in the evolution of the node states, by dealing a different version of the input u(n) to each node

_{i}*x*.

_{i}The time-dependent output *y*(*n*) from the reservoir is a linear combination of the internal states of the reservoir:

*u*(

*n*). To do this, the reservoir is first trained by determining the output weight vector

*W*(for

_{i}*i*= 1, 2,...,

*N*) ensuring that the output

*y*(

*n*) of the reservoir is as close as possible to a target output

*ŷ*(

*n*). This is done by minimizing the normalized mean square error NMSE, defined by

*denotes the average on all discrete time steps. Once the weights are computed, they are left unchanged and the performances of the reservoir can be evaluated by feeding it with other input sequences and comparing the actual output to the desired output. The training of a reservoir computer is only performed at the level of the output weights*

_{n}*W*, although the parameters

_{i}*α*and

*β*must often be adjusted to obtain optimal performance.

The interconnection matrix *A* can be sparse and randomly generated [4]. However, the spectral radius of *αA* (i.e. the largest absolute value of the eigenvalues of *αA*) cannot be too high to avoid stability issues. In the case where *F _{NL}*(

*x*) = tanh(

*x*), this value is generally kept less than one.

It has been theoretically shown in refs. [17, 18] that a very simple interconnexion matrix *A* coupling a node *x _{i}* only to its direct neighbor

*x*

_{i−1}is sufficient to obtain interesting computation abilities. Such a matrix is easily implemented on hardware with the time-multiplexed approach that we used in this work and that is presented in the next section.

As discussed in the supplementary material of [6], many dynamical systems can be used as reservoir computers, and consequently there is a lot of freedom in designing good reservoirs, which is particularly interesting from the point of view of experimental implementations.

#### 2.2. Principle of the experimental implementation

The hardware implementation that we use is based on a delay loop allowing a time-multiplexing of the reservoir’s internal variable *x _{i}*. The desynchronization of the reservoir loop with respect to the input and output layers of the reservoir computer allows for the coupling of each internal variable

*x*to to one of its neighbors

_{i}*x*

_{i−k}. This configuration has already been extensively described in refs. [6, 8]. It differs from the one used in refs. [5, 7, 9] which is fully synchronized but uses bandwidth limitation of an element of the reservoir loop to connect neighboring nodes together.

To implement an experimental reservoir computer, we need to switch from the discrete time *n* used in Eq. 1 to continuous time *t*. As in previous works [5–9], each input is held for a time *T* = *Nθ* through a sample and hold procedure. Each interval of length *T* is subdivided into *N* intervals of length *θ* (the *node time*). The *i*-th interval of duration *θ* is associated with the input value *m _{i}u*(

*n*) where

*m*is the value of the input mask corresponding to the

_{i}*i*-th node. These values

*m*(

_{i}u*n*) drive the reservoir one after another.

Figure 1 presents a sketch of how time multiplexed dynamical systems can be used as reservoir computers. Coupling between internal variables is obtained by desynchronizing the round-trip time *T′* in the loop with respect to the input time *T*. By choosing *T′* = (*N* + *k*)*θ*, one obtains a coupling between *x _{i}* and

*x*

_{i}_{−}

*. This defines an interconnection matrix*

_{k}*A*similar to that proposed in refs. [17, 18]. We choose

*k*= 1 for all the experiments presented in this work. The corresponding evolution Eqs. are given by

#### 2.3. SESAM structure used as nonlinear element

In our experiment, the nonlinear function *F _{NL}* of Eq. (1) is provided by the saturation of the absorption of a SESAM device. This nonlinearity is qualitatively different from the ones used previously in experimental reservoir computers, namely the sine nonlinearity of a Mach-Zehnder intensity modulator [6, 7] and the saturation of the gain of a semiconductor optical amplifier (SOA) [8]. In Fig. 2, we present a comparison between the nonlinear behavior of the SOA used in ref. [8] and the nonlinear behavior of the SESAM used in the present work. For low input power, the SOA reacts in a linear way and becomes nonlinear at high powers (gain saturation). The SESAM exhibits an opposite behavior: it is nonlinear for low values of its input power and gets linear at higher input power. As a result, the response of the SESAM exhibits a desaturating positive curvature instead of the stabilizing negative curvature traditionally used in reservoir computers.

Our InP-based SESAM consists of a layered structure initially developed for extinction ratio enhancement of optical pulses [14] and all-optical 2R regeneration [15]. Its structure is depicted in Fig. 3. Compared to previous all-optical reservoirs [8, 9], this nonlinear element is passive, i.e. it is not fed by any external energy source. This represents a first step towards the design of all optical passive reservoir computers.

In Fig. 4 we present the experimentally measured evolution of the reflectivity *R* = *P _{out}*/

*P*of the SESAM as a function of its input power and we show the range of powers for which good results have been obtained on benchmark tasks. The SESAM used in our experiment presents linear losses of approximately 30% and an approximate recovery time of 2.5 nanoseconds.

_{in}#### 2.4. All optical implementation using semiconductor saturable absorber mirror (SESAM)

Our experimental set up depicted in Fig. 5 is closely inspired by the one described in [8]. The internal variables *x _{i}*(

*n*) of the dynamical systems are given by the optical power circulating inside the fiber. The reservoir itself consists of an erbium-doped fiber amplifier (Pritel PMFA-15), a semiconductor saturable absorber mirror (SESAM), a polarization controller and a fiber spool of 1.6 km.

Optical power is inserted in the reservoir by a superluminescent light emitting diode (SLED-Denselight DL-CS5254A) of 40 nm bandwidth centered at a wavelength of 1560 nm. This use of an incoherent source ensures that there are no interferences in the system [8]. An arbitrary waveform generator (AWG, National Instrument model PXI-5422) drives a Mach-Zehnder modulator (MZM, Photline model MXAN-LN-10) that modifies the power inserted into the reservoir, therefore creating the time-varying inputs to the reservoir. The input gain *β* is tuned by damping the maximum power injected in the reservoir using a controllable optical attenuator (Agilent, model 81571A).

Inside the feedback loop, we use an erbium-doped fiber amplifier to compensate for the losses (EDFA - Pritel PMFA-15). Modifying the pump current of the EDFA allows the tuning of the feedback attenuation. Input and feedback polarization controllers allows to adjust the polarization of the input and the feedback signals to match the polarization of the EDFA. The amplifier is used in a linear regime, i.e where there is no saturation of its gain. Consequently, the nonlinear response of the dynamical system is only caused by the SESAM. The round-trip time *T′* in the loop is 8.0073 *μs*. For a reservoir of *N* = 50 nodes (the value used in most of the experiments below) this corresponds to a node time *θ* = *T′*/(*N* + 1) of 157 ns and an input time *T* = *Nθ* of 7.85 *μ*s.

Light is focused on the SESAM using a lensed fiber. The reflected light is reinjected in the fiber using a circulator. A fraction of 20% of the signal is extracted from the loop by means of a coupler to record the evolution of the internal states of the reservoir using a photodiode (TTI TIA- 525, 125 MHz bandwidth), connected to a digitizer (National Instruments model PXI-5124) sending its output to a desktop computer for further post processing.

#### 2.5. Pre-processing: injecting information in the dynamical system

The information driving the reservoir is inserted as optical power. Consequently, one must convert the masked input *m _{i}u*(

*n*) into a positive value. To do this, this masked input sequence is first normalized to lie between −1 and 1. Then, this product is converted into a voltage driving the Mach-Zehnder modulator such that the output power from the modulator lies between 0 and a maximum power

*P*

_{0}.

The nonlinear sine response of the MZ intensity modulator is pre-compensated by applying a voltage
$V=\frac{{V}_{\pi}}{\pi}{\text{sin}}^{-1}({m}_{i}u(n))$. The applied voltage consequently spans the interval [
$-\frac{{V}_{\pi}}{2}$,
$\frac{{V}_{\pi}}{2}$], thereby completely exploiting the range of the modulator without any nonlinearity at the level of the input. Unless otherwise stated, the input mask elements *m _{i}* are uniformly distributed in the range [−1,+1].

#### 2.6. Post-processing: offline training and output computation

Information is processed analogically inside the reservoir. However, the training of the output weights and the computation of the output sequence from the reservoir *y*(*n*) is still performed offline using a desktop computer.

The internal states are defined by normalizing the intensity recorded in such a way that it lies between −1 and 1. As in our previous work, the internal states are measured by taking a temporal average of a window of length *θ*/2 around the middle of each window of length *θ* corresponding to each of the internal states.

Each input sequence is divided in three different subsequences. A first ”warm up” sequence is used to eliminate memory effects from the previous steady state before the reservoir was driven [8]. Then a training input sequence is fed into the reservoir. The reservoir states are recorded as explained above and the outputs weights *W _{i}* are determined using a least mean square algorithm that minimizes the NMSE defined in Eq. (3). Once the training is performed, the output weights are kept constant and the reservoir performances can be evaluated: a test input sequence is fed into the reservoir and drives the dynamical system whose internal states are recorded. The output is computed using the weights determined during the training phase. Finally, one computes the error between the actual output and the desired output to estimate the reservoir performances.

#### 2.7. Numerical simulations

A discrete-time numerical model of our reservoir was first used to validate our approach of using the nonlinearity of a SESAM in a reservoir computer. We integrated numerically the recurrence of Eqs. (4) with the nonlinear function *F _{NL}* replaced by a fit to the experimental response of the SESAM. This numerical model does not take into account neither the noise introduced by the SLED and the EDFA nor the bandpass effects due to electronics. We do not quote the results of these simulations in the rest of the paper except if relevant.

## 3. Results on benchmark tasks

We tested our experimental reservoir computer on several benchmark tasks usually employed to evaluate reservoir performances and compared our results to those of previous experimental and digital implementations.

#### 3.1. Memory capacities of the reservoir

The memory capacities evaluate the ability of a dynamical system to compute functions of its past inputs. For this task, the inputs *u*(*n*) are independent and identically distributed random variables in the interval [0,1]. The capacity of the reservoir to reconstruct the function *y*[*u*] of its past input *u* is defined as *C*[*y*] = 1 − *NMSE*[*y*].

In the case of the linear memory capacity, the function to reconstruct is simply *u*(*n* − *k*), its input shifted *k* time steps in the past [19]. The linear memory capacity is obtained by summing upon all values of the delay *k*. Hence, the linear memory capacity simply evaluates the way the dynamical system remembers its past inputs.

More recently, nonlinear memory capacities were introduced [20]. In this case, the function to reconstruct is a nonlinear transformation of the previous inputs. Here we only consider second order polynomials of the previous inputs. As in our previous work [8], we define the quadratic memory capacity as the ability to compute the second order Legendre polynomial of the input *k* time steps before: *y _{k}*[

*u*] = 3

*u*

^{2}(

*n*−

*k*)−1. The quadratic memory capacity is obtained upon summing on all values of the delay

*k*. Legendre polynomials constitute an orthogonal basis with respect to the

*L*

^{2}inner product; consequently there is no overlap between linear and nonlinear memory capacities. The cross memory capacity is obtained by considering the product of inputs at two different time steps in the past

*y*

_{k,k′}=

*u*(

*n*−

*k*) ×

*u*(

*n*−

*k′*). The summation upon all possible couples of (

*k*,

*k′*) with

*k*<

*k′*gives the cross memory capacity. The quadratic memory and cross memory capacities hence quantify how much the dynamical system is able to construct second order polynomials of its past inputs.

As shown in ref. [20], the total memory capacity (i.e. the sum of all the memory capacities) is bounded by the number of internal variables in the system *N*. Under certain conditions and by adding memory capacities of higher orders, the inequality can be saturated and the total memory capacity is then equal to the number of internal variables *N*.

In table 1, we present the best memory capacities we obtained with our reservoir made of *N* = 50 internal variables. We compare our results with the memory capacities of our previous optoelectronic and SOA based all-optical reservoir computers. Our results were obtained for a pump current of the EDFA of 110 mA. This corresponds to a feedback gain *α* of approximately 0.85 (This value takes into consideration all the losses in the delay loop). The optimum input gain *β* is determined independently for each of the computed memory capacities. The best results for the linear memory were obtained for an optical power of approximately 1.2 mW sent on the absorber. For the cross memory and quadratic memory capacities, the best results correspond to around 150 *μ*W of power focused on the SESAM.

Our reservoir based on saturable absorption exhibits a cross memory capacity twice as big as the one of our previous all-optical implementation. The linear memory capacity is also improved, even with respect to our optoelectronic reservoir computer of ref. [6]. Our total memory capacity is also improved with respect to our previous all-optical implementation. In our previous work, the degradation of the memory capacities of the SOA-based RC was attributed to the ASE noise generated by the amplifier and to polarization instability in the fiber loop. These effects are still present in our new reservoir based on a SESAM. However, the noise figure of the EDFA is less important than the one of the SOA. Moreover, the absorber removes part of the noise induced by the amplifier, especially for low input signals, i.e, in the exploited nonlinear range of the SESAM.

#### 3.2. Channel equalization task

This task was introduced in the context of reservoir computing by H. Jaeger [2]. We consider the transmission of a sequence *d*(*n*) of symbols randomly generated from the set {−3,−1,1,3} through a communication channel characterized by multi-symbol interferences and nonlinear distortions. The noisy distorted outputs *u*(*n*) of the communication channel are defined by the following Eqs.

*ν*(

*n*) is a white noise added to make the Signal-To-Noise Ratio (SNR) vary between 12 and 32 dB. The output

*u*(

*n*) of the channel is used as input to the reservoir. The desired output from the reservoir is the input sequence of the channel

*d*(

*n*).

For this task, performances of the reservoir are evaluated using the symbol error rate (SER), defined as the fraction of misclassified symbols. In Fig. 6, we compare the results obtained by our implementation using a SESAM with previous results obtained with our optoelectronic and SOA-based reservoir computers [6, 8]. The reservoir performances are evaluated during five successive experiments. Averaged results with standard deviations are presented in Fig. 6.

For each value of the SNR, the result is the best mean SER obtained over all the values of the input gain *β*. Our best results were obtained when the pump current of the EDFA was set to 82 mA. This corresponds to a feedback gain of 0.7 and to an approximate power of 150 *μ*W focused on the saturable absorber.

Our all-optical reservoir computer based on the saturation of absorption presents performances that are comparable to the ones obtained previously with our SOA-based reservoir computer. Results are even better for the highest values of the SNR. For SNR of 28 and 32 dB, our optical reservoir presents results similar to those of our optoelectronic reservoir [6] and performs as well as digital reservoirs. For instance, at 28 dB, the average SER obtained in ref. [2] is 10^{−4}, which is equivalent to our experimental result.

#### 3.3. Radar task

For this task, we consider the signal backscattered from the ocean surface and collected by the MacMaster University IPIX radar [21]. The reservoir is given this signal as input and the goal is to predict future values of this signal for prediction delays varying between 1 and 10. Two different samples are considered, the ”low sea state” (average wave height of 0.8 meters; maximum wave height of 1.8 meters) and the ”high sea state” (average wave height of 1.3 meters; maximum wave height of 2.9 meters). The performances on this task are evaluated using the NMSE.

For each prediction delay, we split the two thousands inputs of both samples in one train sequence and one test sequence of one thousand inputs each. Our best experimental NMSE results are presented in Fig. 7 and were obtained for a pump current of 100 mA. The feedback gain is consequently around 0.85. For each value of the prediction delay and for each of the two sea states, we find the optimum for the optical power focused on the absorber between 600 *μW* and 1.2 mW. Our results are comparable to the ones obtained by our previous hardware implementations of reservoir computers. They are also equivalent to results obtained by the digital implementation of ref. [18] where authors reported for the low sea state a NMSE of 1.15 · 10^{−3} for one-step prediction and 3.01 · 10^{−2} for 5-step prediction.

#### 3.4. Speech recognition

This task was introduced as a benchmark for reservoir computers in ref. [22]. The goal is to classify audio sequences. These audio sequences come from the National Institute of Standards and Technology (NIST) TI-46 corpus [23] and consist of digits between 0 and 9 pronounced by five different female speakers; each of the digits is pronounced 10 times. The audio sequence is sampled at 12.5 kHz, preprocessed using the Lyon cochlea ear model [24] and then sampled at regular intervals.

The input signal *u*(*n*) is an 86-dimensional state vector with up to 130 samplings for each sequence. For this task we used a reservoir made of *N* = 200 internal variables. The input mask is therefore a 200 × 86 matrix *m _{i j}* whose elements are randomly chosen with equal probabilities in the set {−0.1,0.1}. The sequence driving the reservoir is thus the

*N*-dimensional array ${\sum}_{j=1}^{86}{m}_{ij}{u}_{j}(n)$.

For the output layer, we train 10 different output weight vectors defining ten different output sequences *y _{k}*(

*n*), each of them being associated to one digit (

*k*= 0, 1,...,9). The desired output corresponding to a digit is 1 if this digit is being sent to the reservoir and −1 otherwise. For each sequence, each of the ten outputs is averaged over the sequence length; using a winner-take-all approach, the highest averaged classifier is then set to 1, and all other classifiers are set to −1. The task is evaluated using the word error rate (WER), i.e. the fraction of misclassified digits.

For this task, since the dataset contains only 500 sequences, five subsets of 100 sequences each are randomly chosen; the reservoir is trained over 4 subsets and tested over the last one. This procedure is repeated 5 times rotating the subsets, so that each subset is used once for the test. The results reported here are the average WERs and corresponding standard deviations over the 5 test subsets.

The best test WER we obtained with our reservoir based on a SESAM nonlinearity is of 2.6% with a standard deviation of 1.52%. This is two orders of magnitude worse than the experimental results obtained with our previous opto-electronic reservoir of ref. [?] but comparable to the results obtained with the SOA-based reservoir [8], for which performances degradation were attributed to the ASE-noise arising in the SOA. However, in our case, best simulation results gave a WER of 4.6% (standard deviation: 1.34 %), which means that even without noise, the performances are not very good. We attribute this lack of performances to the peculiar desaturating positive curvature of the SESAM nonlinear response (see section 2.3).

## 4. Conclusions

In this work we have presented an evolution of the first all-optical reservoir computer reported in ref. [8]. The challenge was to change the type of nonlinear response of the dynamical system in order to make the reservoir simpler and passive. Instead of the stabilizing saturated response of an optical amplifier we exploited the desaturating nonlinearity of a SESAM.

As the nonlinear behavior of the system drastically determines the dynamics of the reservoir, the outcome was unclear and required a deep numerical and experimental investigation. We undertook this investigation with success, showing that the concept of reservoir computing is surprisingly versatile. In particular, our study suggests that reservoir computing could lead to the realization of efficient low-noise, low-consumption ultrafast analog computers. However, to compensate for large losses in our system we had to include an erbium-doped amplifier in the reservoir which is therefore not totally passive. But, being used in its linear regime, this amplifier does not play a significant role in the dynamics of the reservoir and we can state that our experiment constitutes a genuine proof of principle.

We have tested our experimental optical reservoir on benchmark tasks in order to evaluate its performances. These performances are slightly lower than the ones obtained with our first opto-electronic reservoir [6]. However, these performances are comparable and for some tasks better than the ones obtained with our previous all-optical reservoir using gain saturation of ref. [8]. Hence, we have shown that passive nonlinear elements can be used to process information on relatively complex tasks.

In the near future we will undertake the experimental study of a fully passive low-noise reservoir based on saturable absorption in SESAM. This will constitute the basis of the development of an all-optical reservoir computer in which the parallelism and speed of optics will be exploited to reach record signal processing bandwidths.

## Acknowledgments

The authors acknowledge financial support from the
Fonds de la Recherche Scientifique FRS-FNRS under grant n^{o}
2.4611.10 and the Interuniversity Attraction Pole program of the
Belgian Science Policy Office under grant
IAP P7-35 photonics@be. Antoine Dejonckheere is a F.N.R.S. fellow and Frano̧is Duport is a postdoctoral researcher of the F.N.R.S.

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