A photonic reservoir computing system based on reflective semiconductor optical amplifier

Abstract

The application discloses a kind of photonic reservoir computing system based on reflective semiconductor optical amplifier, comprising: input layer, reservoir layer and output layer;Wherein, the pre-processing of signal is carried out in input layer, the masking process to input signal is completed, and the masked input signal is injected into reservoir layer;In the reservoir layer, the output light of RL is sampled at equal time interval, and N sampling points are obtained as the virtual nodes of reservoir;In the output layer, the state of all virtual nodes from RL to RSOA delay line is recorded, and the optimal readout weight is calculated by ridge regression algorithm, then the virtual node state and readout weight are linearly weighted and summed, to obtain the final result.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of reservoir computing, and more particularly relates to a photonic reservoir computing system based on a reflective semiconductor optical amplifier. BACKGROUND

[0002] Reservoir computing (RC) is derived from recurrent neural networks, and is a new type of neural network computing model that is easy to train and implement, and is suitable for processing time-dependent complex information, and has been widely applied to fields such as time series prediction, nonlinear channel equalization and robot control.

[0003] Light has the advantages of extremely fast operation speed, extremely high bandwidth and parallel processing in information processing, and a time-delay RC system has very low hardware implementation cost compared with a traditional RC system, so a RC system based on full-optical time delay has been widely studied.

[0004] At present, scholars at home and abroad have proposed various photonic RC systems based on various all-optical devices, for example: Xiang Shuiying et al. of Xi'an University of Electronic Science and Technology constructed a photonic time-delay RC system using a vertical cavity surface emitting laser (VCSEL), and explored the application of the RC system based on VCSEL in parallel task processing, high performance and high processing rate; Giovanni Donati et al. proposed a photonic RC system based on a micro ring resonator (MRR), and showed the prospect of MRR in scalable integrated photonic RC system; Romain Modeste Nguimdo not only constructed a high-performance photonic RC system using a quantum cascade laser (QCL), but also proposed a photonic RC system for parallel task processing based on a semiconductor ring laser (SRL); Takuma Tsurugaya et al. studied a low-power photonic RC system using the cross-gain modulation characteristics of a semiconductor optical amplifier (SOA), and revealed the application prospect of SOA in high-performance photonic RC system. Although the reflective semiconductor optical amplifier (RSOA) can achieve lower noise factor and higher optical gain at low driving current compared with the traditional SOA, there is no literature and patent reported that the performance of the photonic RC system is improved by using the nonlinearity caused by the gain saturation of the RSOA. SUMMARY

[0005] The present application aims to overcome the shortcomings of the prior art, and to design a photonic reservoir computing system based on a reflective semiconductor optical amplifier by using the nonlinear characteristics caused by the gain saturation of the RSOA, and to replace the ordinary mirror in the traditional time-delay feedback RC system with the RSOA, thereby enriching the nonlinearity of the system and improving the performance of the system.

[0006] To achieve the above object, the application discloses a photon reservoir pool computing system based on a reflective semiconductor optical amplifier, which comprises an input layer, a reservoir pool layer and an output layer.

[0007] The input layer comprises a driving laser DL and a phase modulator PM, and is used for pre-processing an input signal and completing a masking process of the input signal.

[0008] First, the input signal is sampled into a discrete signal u(n), and each sampling point of u(n) is kept for a time period T, then u(n) is multiplied by a masking signal m(t) and a scaling factor γ to obtain a masked input signal s(t), i.e., s(t) = u(n) x m(t) x γ.

[0009] Then, s(t) is modulated to a laser signal output by the DL through the PM to obtain a modulated signal E d (t), and E d (t) is injected into the reservoir pool layer; wherein the modulated signal E d (t) satisfies:

[0010]

[0011] Wherein I d represents a steady-state output light intensity of the DL.

[0012] The reservoir pool layer comprises a response laser RL and a reflective semiconductor optical amplifier RSOA.

[0013] In the reservoir pool layer, the modulated signal E d (t) from the input layer first affects the nonlinear dynamic characteristics of the RL, and changes the output of the RL; secondly, due to the gain saturation characteristics of the RSOA, the output signal of the RL is amplified and nonlinearly transformed by the RSOA to obtain a feedback signal E R (t), and the feedback signal E R (t) is fed back to the RL to affect the nonlinear dynamic characteristics of the RL again and change the output of the RL; then, a sampling time interval is set as θ, and the light signal output by the RL is sampled at equal intervals within a delay time τ to obtain N virtual nodes, wherein the i-th virtual node is denoted as x i (n), i = 1, 2,..., N.

[0014] The output layer records the state of the N virtual nodes, and takes the state value of each virtual node as an output value, and then minimizes the error between the output value and a preset target value through ridge regression algorithm, so as to calculate the optimal readout weight w i of each virtual node.

[0015] The virtual node x i (n) and the optimal readout weight w i are used to calculate the output signal of the reservoir pool layer.i performing linear weighted summation to obtain the final output result y(n) of the output layer;

[0016]

[0017] The application aims to achieve the following purposes:

[0018] The application is based on a photonic reservoir computing system of a reflective semiconductor optical amplifier, comprising an input layer, a reservoir layer and an output layer; wherein the input layer performs preprocessing of signals, completes a masking process of input signals, and injects the masked input signals into the reservoir layer; the reservoir layer performs equal-time-interval sampling on output light of the RL to obtain N sampling points as virtual nodes of the reservoir; the output layer records states of all virtual nodes on a delay line from the RL to the RSOA, and calculates optimal readout weights through ridge regression algorithm, and then performs linear weighted summation on the virtual node states and the readout weights to obtain a final result.

[0019] Meanwhile, the photonic reservoir computing system of the reflective semiconductor optical amplifier also has the following beneficial effects:

[0020] (1) By using the RSOA as an active mirror in the reservoir layer, the application has richer nonlinear characteristics and better performance compared with the traditional RC system using a common mirror;

[0021] (2) By using the RSOA, the application performs nonlinear transformation on feedback signals of the RL, widens the consistency region of the system, and improves the robustness of the system. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 is a block diagram of the photonic reservoir computing system of the reflective semiconductor optical amplifier according to the application;

[0023] Figure 2 is a simulation result diagram of a Santa Fe chaotic time series prediction task;

[0024] Figure 3 is a simulation result diagram of a nonlinear channel equalization task. DETAILED DESCRIPTION

[0025] The specific embodiments of the application will be described below with reference to the accompanying drawings, so that those skilled in the art can better understand the application. It should be particularly noted that in the following description, when detailed description of known functions and designs may obscure the main content of the application, these descriptions will be omitted here.

[0026] EMBODIMENT

[0027] Figure 1 is a block diagram of a photonic reservoir computing system based on reflective semiconductor optical amplifier according to the present application.

[0028] In the embodiment, as shown in the figure, the photonic reservoir computing system based on reflective semiconductor optical amplifier according to the present application comprises an input layer, a reservoir layer and an output layer. Figure 1

[0029] The input layer comprises a driving laser DL and a phase modulator PM; the input layer is used for pre-processing the input signal and completing the masking process of the input signal.

[0030] Firstly, the input signal is sampled into a discrete signal u(n), and each sampling point of u(n) keeps a time period T, then u(n) is multiplied by a masking signal m(t) and a scaling factor γ to obtain a masked input signal s(t), i.e. s(t) = u(n) x m(t) x γ; in the embodiment, a chaotic signal with a bandwidth of 7.45 GHz is used as the masking signal.

[0031] Then, s(t) is modulated by the PM to the laser signal output by the DL to obtain a modulated signal E d (t), and E d (t) is injected into the reservoir layer; wherein the modulated signal E d (t) satisfies:

[0032]

[0033] wherein I d represents the steady-state output light intensity of the DL.

[0034] The reservoir layer comprises a response laser RL and a reflective semiconductor optical amplifier RSOA; wherein the nonlinear dynamics of the RL is simultaneously affected by two signals, which are the modulated signal E d (t) from the input layer and the time-delay feedback signal E R (t) from the reflective semiconductor optical amplifier RSOA.

[0035] Specifically, the modulated signal E d (t) from the input layer firstly affects the nonlinear dynamics of the RL, changing the output of the RL; secondly, due to the gain saturation characteristics of the RSOA, the output signal of the RL is amplified and nonlinearly transformed by the RSOA to obtain the feedback signal E R (t).(t) and feedback to the RL to affect the nonlinear dynamics of the RL again and change the output of the RL; then, set the sampling time interval as θ, calculate the delay time τ = T + θ, where T = N x θ; sample the optical signal output by the RL at equal intervals within the delay time τ to obtain N virtual nodes, where the ith virtual node is denoted as x i (n), i = 1, 2, …, N;

[0036] In the embodiment, the nonlinear dynamics of the RL and the gain saturation characteristics of the RSOA need to meet certain conditions, which are usually described by rate equations, so in the embodiment, we establish the rate equation of the RL based on the rate equation of the traditional RC system using a common mirror by modifying the feedback term as follows:

[0037]

[0038]

[0039] where E(t) and N r (t) represent the slowly varying complex electric field amplitude and the carrier concentration of the RL, respectively, E R (t - τ) represents the feedback signal from the RSOA, α r is the linewidth enhancement factor of the RL, G is the gain coefficient, N0 is the transparent carrier concentration, ε is the gain saturation coefficient, τ p and τ c,r are the photon lifetime and the carrier lifetime of the RL, respectively, k inj is the injection intensity of the DL to the RL, k c is the mutual coupling intensity between the RL and the RSOA, J r is the injection current of the RL, ω is the angular frequency of the light output by the RL, Δω = 2πΔv represents the angular frequency mismatch between the DL and the RL, Δv is the frequency mismatch between the DL and the RL, χ(t) is Gaussian white noise, β r is the spontaneous emission rate.

[0040] Since the working mode of the RSOA is similar to the reflection mode of the vertical cavity semiconductor optical amplifier (VCSOA), the rate equation of the RSOA is established by modifying the rate equation of the VCSOA as follows:

[0041]

[0042]

[0043] where S(t) and N(t) represent the total photon concentration and the carrier concentration of the RSOA, respectively, P in(t) represents the injected optical power from RL to RSOA, h represents the Planck constant, v = c / λ is the center frequency of the optical signal, λ is the wavelength of the injected optical signal, V = WHL is the volume of the RSOA active region, β R is the spontaneous emission rate, α1= K0+ ΓK1N(t) is the internal loss of the active region, K0and K1represent the loss coefficient independent of the carrier and the loss coefficient dependent on the carrier, respectively, I is the injected current, q is the elementary charge, A rad and A nrad are the linear radiation and linear non-radiative recombination coefficients, respectively, B rad and B nrad are the bimolecular radiation and bimolecular non-radiative recombination coefficients, respectively, C aug is the Auger recombination coefficient.

[0044] Since the complex electric field amplitude E(t) and the optical power P(t) can be related by P(t) = |E(t)| 2 hv, and the optical power P(t) and the photon concentration S(t) can be related by S(t) = ΓP(t) / (hvv g WH), the feedback signal E R (t) from RSOA to RL and the injected optical power P in (t) from RL to RSOA can be expressed by the following formula:

[0045]

[0046] P in (t) = k c E(t-τ)exp(-iωτ) 2 hv

[0047] where S(t) is the photon concentration, W and H represent the width and height of the RSOA active region, respectively, v g = c / n g represents the group velocity, c is the speed of light in vacuum, n g is the refractive index of the RSOA active region; Γ is the confinement factor, φ is the phase shift generated by the propagation of the injected signal in the RSOA active region, and φ = π - α R Γg m L represents, α R is the linewidth enhancement factor of the RSOA, L represents the length of the RSOA active region, g m = g / (1+P out / P sat ) represents the RSOA material gain coefficient considering the gain saturation, g is the material gain coefficient of the RSOA, P out and P sat are the total output optical power and the saturated output optical power, respectively;

[0048] Further, the material gain coefficient g of the RSOA satisfies:

[0049]

[0050] where τ c,R is the carrier lifetime of the RSOA, m e is the effective mass of the electron in the conduction band, m hh is the effective mass of the heavy hole in the valence band, E g0 = q(a + by + cy 2 ) represents the bandgap energy without carrier injection, y is the mole fraction of arsenide in the active region, and a, b, and c are bandgap energy coefficients; ΔE g (N) = qK g N 3 / 2 represents the bandgap shrinkage with injection, K g is the bandgap shrinkage coefficient, f c (v) and f v (v) are the Fermi-Dirac probability distributions of the conduction band and the valence band, respectively.

[0051] The output layer first records the state of the N virtual nodes and takes the state value of each virtual node as an output value, and then minimizes the error between the output value and a preset target value through a ridge regression algorithm to calculate the optimal readout weight w i of each virtual node.

[0052] The virtual node x i (n) and the optimal readout weight w i are linearly weighted and summed to obtain the final output result y(n) of the output layer.

[0053]

[0054] Example simulation

[0055] In this embodiment, the performance of the system is evaluated by numerically simulating the Santa Fe chaotic time series prediction task and the nonlinear channel equalization task to verify the feasibility and technical advantages of the photonic reservoir computing (RC) system based on a reflective semiconductor optical amplifier (RSOA) of the present application.

[0056] In the Santa Fe chaotic time series prediction task, 3000 and 1000 data points are taken for weight training and performance testing, respectively, wherein the amplitude of the chaotic time series is adjusted to the interval range of 0 to 1. In addition, the scaling factor γ is set to 0.6, the virtual node interval θ is set to 0.01 ns, and the virtual node number N is set to 100; the mask signal is rescaled so that its mean value and variance value are adjusted to 0 and 1, respectively; the time period T is set to 1 ns, corresponding to an information processing rate of 1 Gbps; the simulation parameter values of the RL are as follows: α r = 3, N0= 1.4 x 10 24 m -3 , G = 8.4 x 10 -13 m 3 s -1 , ε = 2 x 10 -23 , τ p = 1.927 ps, τ c,r = 2.04 ns, I d = 6.56 x 10 20 , λ = 1550 nm, Δv = -4.0 GHz, J r = 1.037 x 10 33 m -3 s -1 , β r = 1.5 x 10 -6 ; the simulation parameters of the RSOA are as follows: Γ = 0.3, W = 0.4 μm, H = 0.4 μm, L = 700 μm, β R = 1.84 x 10 -5 , I = 80 mA, n g = 3.6, P sat = 3 dBm, K0= 6200 m -1 , K1= 7500 x 10 -24 m 2 , A rad = 1 x 10 7 s -1 , A nrad = 3.5 x 10 8 s -1 , B rad = 5.6 x 10 -16 m 3 s -1 , B nrad = 0, C aug = 3 x 10 -41 m 6 s -1 , τ c,R = 0.9 ns, m0= 9.11 x 10 -31 kg, m e= 0.045 x m0, m hh = 0.46 x m0, a = 1.35 eV, b = -0.775 eV, c = 0.149 eV, y = 0.89, a R = 7.632, K g = 9.8 x 10 -11 eVm.

[0057] Then the rate equations of the system are solved by using the fourth-order Runge-Kutta method to obtain the output of the system.

[0058] Figure 2 (a) shows the predicted values of the system in the Santa Fe chaotic time series prediction task, Figure 2 (b) shows the target values of the corresponding Santa Fe chaotic time series, Figure 2 (c) shows the error values of the system, wherein the injection strength k inj and the coupling strength k c are respectively set to 7.7 x 10 9 and 2 x 10 5 . It can be seen from Figure 2 that the predicted output of the system in the Santa Fe chaotic time series prediction task is basically consistent with the target output, and the value of the normalized mean square error (NMSE) is only 0.0077.

[0059] In the nonlinear channel equalization task, first, the original signal with 10 5 symbols is generated, then 3000 symbols are used to train the readout weight, and the remaining symbols are used to test the performance. In the numerical simulation, the scaling factor γ is set to 0.3, the virtual node interval θ is set to 0.02 ns, and the number of virtual nodes N is set to 50. Figure 3 shows the nonlinear channel equalization results of the system under different signal-to-noise ratio (SNR) conditions, wherein the injection strength k inj and the coupling strength k c are respectively set to 5 x 10 9 and 1.3 x 10 5 , and the SNR varies between 12 and 32 dB. The symbol error rate (SER) in the figure is the result obtained by 5 repeated tests. It can be seen from Figure 3 that the system can achieve a low SER under different SNRs, and the effect of nonlinear channel equalization is better as the SNR increases.

[0060] In summary, the RSOA-based photonic RC system designed in the application can effectively realize Santa Fe chaotic time series prediction and nonlinear channel equalization, wherein the information processing rate is 1 Gbps. Meanwhile, compared with the traditional photonic RC system using a common mirror, the application first uses the RSOA as a nonlinear mirror, and uses the nonlinearity caused by the gain saturation of the RSOA to improve the performance of the photonic RC system.

[0061] Although the above describes the specific embodiments of the present application in order to facilitate the understanding of the present application by those skilled in the art, it should be clear that the present application is not limited to the scope of the specific embodiments, and all the applications using the concept of the present application are within the scope of protection as long as various changes are obvious to those skilled in the art within the spirit and scope of the present application defined and determined by the appended claims.

Claims

1. A photon reservoir computing system based on a reflective semiconductor optical amplifier, characterized in that, include: Input layer, reservoir layer, and output layer; The input layer includes a driving laser DL and a phase modulator PM; The input layer is used to preprocess the input signal and complete the masking process of the input signal; First, the input signal is sampled into a discrete signal u(n), and each sampling point of u(n) is kept for a time period T. Then, u(n) is multiplied by the mask signal m(t) and the scaling factor γ to obtain the mask input signal s(t), that is, s(t) = u(n)×m(t)×γ. Then, s(t) is modulated onto the laser signal output by DL through PM to obtain the modulated signal. Then Injected into the reservoir layer; wherein, the modulation signal satisfy: ； Among them, I d This indicates the steady-state output light intensity of DL; The reservoir layer includes a responsive laser RL and a reflective semiconductor optical amplifier RSOA; In the reservoir layer, the modulation signal E from the input layer d (t) First, it affects the nonlinear dynamic characteristics of RL, changing the output of RL; second, due to the gain saturation characteristic of RSOA, the output signal of RL is amplified and nonlinearly transformed by RSOA to obtain the feedback signal. This feedback is then fed back into the RL, further influencing its nonlinear dynamic characteristics and altering its output. Then, with a sampling time interval of θ, the optical signal output by the RL is sampled at equal intervals within a delay time τ, resulting in N virtual nodes, where the _th_ ... Let x be a virtual node. i (n), ; The output layer first records the states of N virtual nodes and uses the state value of each virtual node as the output value. Then, based on a preset target value, it minimizes the error between the output value and the preset target value to calculate the optimal readout weight w for each virtual node. i ; Virtual node x i (n) and the optimal readout weight w i Perform a linear weighted summation to obtain the final output result y(n) of the output layer; 。 2. The photon reservoir computing system based on a reflective semiconductor optical amplifier according to claim 1, characterized in that, The mask signal m(t) is a chaotic signal with a bandwidth of 7.45 GHz.

3. The photon reservoir computing system based on a reflective semiconductor optical amplifier according to claim 1, characterized in that, The delay time τ = T+θ, where T = N×θ, and θ is the sampling time interval.

4. The photon reservoir computing system based on a reflective semiconductor optical amplifier according to claim 1, characterized in that, The feedback signal satisfy: ； Where S(t) is the photon concentration, W and H represent the width and height of the active region of RSOA, respectively, and v g = c / n g Let c represent the group velocity, and n be the speed of light in a vacuum. g Γ is the refractive index of the RSOA active region; Γ is the confinement factor; and ϕ is the phase shift caused by the injected signal propagating in the RSOA active region, given by ϕ = π - α. R Γg m L represents α R It is the linewidth enhancement factor of RSOA, where L represents the length of the active region of RSOA, and g m = g / (1+P out / P sat ) represents the material gain coefficient of RSOA considering gain saturation, g is the material gain coefficient of RSOA, and P out and P sat These are the total output optical power and the saturated output optical power, respectively.

5. The photon reservoir computing system based on a reflective semiconductor optical amplifier according to claim 4, characterized in that, The material gain coefficient g of the RSOA satisfies: ； Where h represents Planck's constant, v is the center frequency of the optical signal, q is the elementary charge, and τ is the t-value. c,R This is the carrier lifetime of RSOA, m e It is the effective mass of electrons in the conduction band, m hh It is the effective mass of heavy holes in the valence band, E g0 = q(a+by+cy 2 ) represents the bandgap energy without carrier injection, y is the mole fraction of arsenide in the active region, and a, b, and c are all bandgap energy coefficients; ΔE g (N) = qK g N 3 / 2 This indicates injected band gap contraction, K g It is the band gap shrinkage coefficient, f c (v) and f v (v) are the Fermi-Dirac probability distributions of the conduction band and valence band, respectively.

6. The photon reservoir computing system based on a reflective semiconductor optical amplifier according to claim 5, characterized in that, The nonlinear dynamic characteristics of the response laser RL satisfy: ； ； Where E(t) and N r (t) represent the amplitude of the slowly varying complex electric field of RL and the carrier concentration, respectively, E R (t-τ) represents the feedback signal from RSOA, α r τ is the linewidth enhancement factor of RL, G is the gain coefficient, N0 is the transparent carrier concentration, ε is the gain saturation coefficient, and τ is the gain enhancement factor. p and τ c,r These are the photon lifetime and carrier lifetime of RL, respectively, k inj It is the injection intensity from DL to RL, k c J is the mutual coupling strength between RL and RSOA. r ω is the injection current of RL, ω is the angular frequency of the output light of RL, Δω = 2πΔv represents the angular frequency detuning between DL and RL, Δv is the frequency detuning between DL and RL, χ(t) is Gaussian white noise, β r It is the spontaneous emission rate.

7. The photon reservoir computing system based on a reflective semiconductor optical amplifier according to claim 6, characterized in that, The gain saturation characteristic of the reflective semiconductor optical amplifier RSOA satisfies: ； ； Where S(t) and N(t) represent the total photon concentration and carrier concentration of RSOA, respectively, and P in (t) represents the injected optical power from RL to RSOA, h represents Planck's constant, v = c / λ is the center frequency of the optical signal, λ is the wavelength of the injected optical signal, V = WHL is the volume of the active region of RSOA, and β R It is the spontaneous emission rate, α1 = K0 + ΓK1N(t) is the internal loss of the active region, K0 and K1 represent the carrier-independent loss coefficient and the carrier-dependent loss coefficient, respectively, I is the injection current, q is the elementary charge, and A is the internal loss of the active region. rad and A nrad These are the linear radiative and linear nonradiative composite coefficients, B. rad and B nrad These are the bimolecular radiative and bimolecular nonradiative recombination coefficients, C. aug It is the Auger composite coefficient.

8. The photon reservoir computing system based on a reflective semiconductor optical amplifier according to claim 7, characterized in that, The injected optical power P in (t) satisfies: 。

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