CN216286379U - Variable-coefficient differential equation photon calculation solving system - Google Patents
Variable-coefficient differential equation photon calculation solving system Download PDFInfo
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- CN216286379U CN216286379U CN202122625547.9U CN202122625547U CN216286379U CN 216286379 U CN216286379 U CN 216286379U CN 202122625547 U CN202122625547 U CN 202122625547U CN 216286379 U CN216286379 U CN 216286379U
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Abstract
The utility model discloses a variable coefficient differential equation photon calculation solving system, and belongs to the technical field of photon computers. The system comprises a laser, a first modulator, a second modulator, a first amplifier and a first filter which are sequentially connected in series; the first modulator is used for modulating the optical signal into a Gaussian function of a time domain; the second modulator is used for realizing pulse cutting and is driven by a 10GHz radio frequency signal emitted by the radio frequency source; the other end of the first filter is connected with an input port of the 3d coupler; one output port of the 3d coupler is connected with the first oscilloscope, and the other output port of the 3d coupler is sequentially connected with the silicon-based micro-ring modulator chip, the second amplifier, the second filter and the second oscilloscope. The utility model can realize the rapid solution of the differential equation, can realize the adjustment of the coefficient of the differential equation, and has high numerical value solution precision within the adjustable range of the coefficient.
Description
Technical Field
The utility model relates to the technical field of photon computers, in particular to a variable coefficient differential equation photon calculation solving system.
Background
In recent years, with the increasing development of CMOS based electronic chips, the size of the electronic chips has approached the physical limit, and moore's law has gradually begun to no longer apply. However, the demand for computing power is higher and higher due to the arrival of the current big data, artificial intelligence and the 5G era, and the praroni and the like at the university of Princeton in the United states in 2019 indicate that the demand for computing power is doubled every three and a half months in the big data era of artificial intelligence, which far exceeds the computing power supply predicted by the molar law. The scientific community seeks a new way to solve the computing power problem. The photon calculation method is one of the methods for solving the problem of the moore law predicament and insufficient calculation force by replacing the traditional electronic chip calculation with the photon calculation method, and is also one of the potential approaches for solving the power consumption problem.
The silicon-based photonic device integrated chip is developed rapidly by relying on a mature semiconductor process system, and the optical operation and information processing technology based on the silicon-based integrated photonic device is a mainstream method for solving the problem of ultrahigh-speed calculation and information processing of the future optical domain, and has very important application and market values. Among a plurality of silicon-based integrated photonic device structures, the silicon-based micro-resonator not only has the advantages of compact volume, flexible structure and easy large-scale expansion, but also has the characteristics of wavelength selectivity, high quality factor, resonance field intensity enhancement effect and the like, so that the silicon-based micro-resonator has very wide application in lasers, optical filters, electro-optical modulators, optical switches, optical delay lines, photoelectric detectors and sensors.
The differential equation is honored by large scientists newton as a language for describing the laws of nature, and has very wide application in modeling and analysis of natural science and engineering, and the application field covers many aspects such as classical mechanics, circuit theory, control theory, molecular dynamics, weather forecast and the like. The calculation and solution of differential equations is an important element of modern signal processing. Linear constant coefficient differential (ODE), the most basic differential equation, is widely applied to mathematical modeling and theoretical analysis of linear time invariant system (LTI) systems, and is the main research object of classical signal and system theory. The problem of solving the differential equation by using a digital electronic computer needs high complexity, and the improvement of the algorithm and the operation speed is still to be solved.
SUMMERY OF THE UTILITY MODEL
In view of the above, the present invention provides a variable coefficient differential equation photon calculation solving system. The system has good effect, easy realization, ultrahigh calculation speed and adjustable coefficient of the value of the optical differential equation
In order to achieve the purpose, the technical scheme adopted by the utility model is as follows:
a photon calculation solving system for a differential equation with variable coefficients comprises a laser, a first modulator, a second modulator, a first amplifier and a first filter which are sequentially connected in series; the first modulator is used for modulating the optical signal into a Gaussian function of a time domain; the second modulator is used for realizing pulse cutting and is driven by a 10GHz radio frequency signal emitted by a radio frequency source;
the other end of the first filter is connected with an input port of the 3d coupler; one output port of the 3d coupler is connected with a first oscilloscope, and the other output port of the 3d coupler is sequentially connected with a silicon-based micro-ring modulator chip, a second amplifier, a second filter and a second oscilloscope; the first oscilloscope is used for inputting time domain excitation of the differential equation, the second oscilloscope is used for outputting normalized numerical solution of the differential equation, and the silicon-based micro-ring modulator chip is used for performing numerical solution on the differential equation.
Further, the silicon-based micro-ring resonator chip comprises two parallel straight waveguides; a runway-type micro-ring resonator coplanar with the two straight waveguides is also arranged between the two straight waveguides; electrodes for voltage heating are arranged at included angles formed by the micro-ring resonators and the straight waveguides; the incidence end of the silicon-based micro-ring resonator is vertically coupled and packaged by an optical fiber array based on a grating, the electric packaging part is connected with a power supply, and the output end of the optical packaging part is connected with an oscilloscope.
Further, the 3d coupler may be replaced with a one-to-three beam splitter.
Furthermore, a first output end and a second output end of the three-in-one beam splitter are respectively connected with two corresponding output ends of the 3d coupler in the same way; and the third output end of the one-to-three beam splitter is connected with the third spectrometer.
Furthermore, the light packaging output end of the silicon-based micro-ring resonator chip is connected with the input end of a beam splitter, and two output ends of the beam splitter are respectively connected with the second oscilloscope and the second spectrometer.
Further, polarization controllers are arranged between the laser and the first modulator, between the first modulator and the second modulator, and between the 3d coupler and the silicon-based micro-ring resonator chip.
The utility model adopts the technical scheme to produce the beneficial effects that:
the utility model constructs a generation module of a photon differential equation input Gaussian pulse string, detects time domain and frequency domain spectral lines of an input optical signal, constructs a numerical solution system of the differential equation of a silicon-based micro-ring resonator, obtains the coefficient of the differential equation according to the output frequency domain spectral line by adopting a thermal regulation mode of the micro-ring resonator and an on-chip electrode and adopting a fiber array vertical coupling grating packaging mode, adopts a routing mode for electrical packaging, and obtains the normalized numerical solution of the differential equation after the output time domain spectral line is normalized.
Drawings
FIG. 1 is a schematic diagram of an embodiment of the present invention.
Fig. 2 is a schematic diagram of an add-drop multiplexing silicon-based microring resonator.
Fig. 3 is a schematic diagram of the silicon-based microring resonator chip of fig. 1.
Fig. 4 is a graph of coupling point temperature versus differential equation coefficients for a micro-ring modulator in an embodiment of the present invention.
Fig. 5 is a gaussian pulse diagram of a cascaded modulator obtained by simulation.
Fig. 6 is a simulation diagram of solving the differential equation of the gaussian pulse obtained by the simulation.
Fig. 7 is a basic configuration diagram of the ring resonator.
Fig. 8 is an add/drop multiplexing type micro-ring resonator.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific embodiments.
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
A variable-coefficient differential-equation photon computational solution system, with reference to fig. 1-3, comprising: the device comprises a laser, two modulators, a beam splitter, a filter, an amplifier, an oscilloscope and a spectrometer. Silicon-based microring resonator chip, comprising: straight waveguide, grating at two ends, electrode, micro-ring resonator and optical package and electric package of chip. And finally, installing an oscilloscope and a spectrometer for solving the differential equation coefficient and the detection numerical value.
The laser is connected with two modulators in cascade, an amplifier, a filter and a one-to-three beam splitter in sequence, a first output port of the one-to-three beam splitter is connected with an oscilloscope, a second output port of the one-to-three beam splitter is connected with a spectrometer, a third output port of the one-to-three beam splitter is connected with a polarization modulator and then connected with a packaged silicon-based micro-ring resonator chip, an electrical package of the silicon-based micro-ring resonator chip is connected with a multifunctional power supply, an output port of the optical package is connected with the beam splitter, and then the oscilloscope and the spectrometer are respectively connected.
The silicon-based micro-ring resonator chip is in a branching multiplexing mode and is in a runway type, an incident end is in optical fiber array vertical coupling packaging based on optical gratings, and electrodes are led to a PCB (printed circuit board) for packaging processing in an electrical packaging mode through wires.
The coefficient of the differential equation is obtained by the spectral lines measured by the two spectrometers, the frequency analysis of the transfer function of the whole micro-ring resonator is carried out according to the two corresponding frequency spectral lines at the same moment, and the value of the coefficient of the constant coefficient differential equation solved by the micro-ring resonator is obtained according to the obtained transfer function.
The input oscillograph in front of the silicon-based micro-ring resonator chip is the time-domain excitation of the input differential equation, and the output oscillograph after normalization is the normalized numerical solution of the output differential equation.
The silicon-based micro-ring resonator chip needs an alignment waveguide for waveguide alignment during packaging, a six-position adjusting frame is adjusted, a polarization controller in front of an output end is adjusted to adjust polarization, and dispensing is performed after alignment to package an optical fiber array.
The following concrete implementation steps are as follows:
step 1: and (4) constructing a differential equation photon calculation solving system with variable coefficients according to the above.
Step 2: and regulating the PPG and the radio frequency signal input by the modulator, and modulating the output signal into a Gaussian pulse of a time domain.
And step 3: aligning and packaging the silicon-based micro-ring resonator chip, accessing an input optical fiber array into a laser, connecting an output optical fiber array into a power meter, adjusting a polarization modulator, aligning the optical fiber array with a six-position adjusting frame to enable the obtained power to be maximum, and packaging.
And 4, step 4: and processing the frequency domain signal of the output signal of the resonator and the input frequency domain signal to obtain the coefficient of the solved differential equation.
And 5: and (4) normalizing the obtained time domain signal, namely solving a normalized differential equation.
The principle of the embodiment:
1.1 micro-ring coupled mode theory
The basic structural unit of the silicon-based micro-ring resonator is an optical waveguide which effectively binds and directionally transmits an optical field, and the theoretical basis of the silicon-based micro-ring resonator is a guided wave optical theory taking Maxwell equations as a core.
Referring to fig. 7, when the silicon-based micro-resonator operates in a linear condition, it can be equivalent to a linear analog filter, and thus, the time-domain coupling theory and the frequency-domain coupling theory can be modeled.
Since microring is a cyclic process of continuously dissipating light, and a mode with dissipation describes the equation for its dissipation:
this equation describes the process of the constant loss of energy of the mode, where τeRepresenting external losses, τiThe loss in the resonator is mainly caused by the waveguide length in the microring, so that the following equation is rewritten according to the microring resonator and the optical field input condition:
in the above formula, a is the energy amplitude in the ring, Ei(t) is the electric field strength of the externally excited light field input, τ is 1/(1/τ)i+1/τe) And μ is the conversion coefficient. The phase factor-j of μ can be arbitrarily chosen based on the chosen reference plane, here determined by the conformity with the general spatial coupling mode. Due to energy conservation, the output electric field and the output electric field have the following conversion relation:
E0(t)＝Ei(t)-jμa(t) (3)
when there is no light field input, i.e. EiWhen (t) is 0, and assuming initial energy W in the micro-ring resonator0The change of the energy in the resonator with time is known from the relation:
wherein Er(T) is the electric field strength in the resonator, TrFor the time it takes for the light to make one turn in the ring, the energy in the ring is continuously dissipated coupled into the straight waveguide, so the square of the electric field strength in the straight waveguide is the change in the energy in the ring over time:
where κ is the coupling coefficient of the resonator to the straight waveguide. Through the joint solution with the previous formula, the following results are obtained:
for a steady-state excitation signal Ei(t), taking Fourier transform of a (t) and then obtaining:
where FT is taken to mean fourier transform, then the above equation is put into the transfer function of the available resonator as:
the relationship between the loss factor and the quality factor in the above equation is:
referring to fig. 8, where η represents the loss rate of light traveling one turn in the micro-ring, and κ represents the amplitude coupling coefficient of transmission, the lower diagram is an add/drop multiplexing micro-ring resonator having two output ports, and the energy of the micro-ring is coupled into two straight waveguides respectively.
The following can be obtained through the same principle and derivation process as above:
wherein tau isiIs the time loss factor, tau, caused by the self-loss of the corresponding micro-ring resonatore1Is the time loss factor, τ, of the loss caused by the coupling of the microring resonator to the forward propagating waveguidee2Is the loss factor of the micro-ring resonator coupled to the reverse transmission waveguide. Qi、Qe1、Qe2Respectively, the quality factor of the resonator corresponding to the time loss factor.
2.2 micro-ring resonator and differential equation
For the micro-ring resonator, although the periodic change of light transmission cannot be intuitively reflected, the formula (12) is convenient for time-frequency conversion, is more suitable for analysis of a frequency domain and a time domain, and is suitable for analog light operation processing analysis. The inverse fourier transform is performed on the above equation to convert the transfer function to the time domain, so that the relationship between the input optical signal and the output optical signal can be obtained:
wherein, b0＝ω0/2Qi+ω0/2Qe2-ω0/2Qe1And a0＝ω0/2Qi+ω0/2Qe1+ω0/2Qe2Formula (II) is eliminated by finishing
This can then give:
the above formula is the structure of a first-order linear constant coefficient differential equation, and therefore, the equation is divided intoThe insertion multiplexing type silicon-based micro-ring resonator can be equivalent to a first-order constant coefficient linear differential equation, and the coefficient a of the differential equation0And b0The quality factor of the microring resonator is determined by the length, refractive index, and coupling coefficient of the resonator:
Qi＝-ω0ngL/[c ln(1-Y)] (15)
Qe1＝-ω0ngL/[c ln(1-K1)] (16)
Qe2＝-ω0ngL/[c ln(1-K2)] (17)
it can be derived from the above theory that the frequency domain transfer function of the micro-ring resonator is the same as that of the first-order linear time invariant system, so that the optical pulse can be input into the micro-ring resonator, and the output light is equivalent to the solution of the first constant coefficient differential equation of the input optical pulse. The coefficients of the differential equation to be solved are adjusted by changing the parameters of the micro-ring resonator. Temperature can affect the coupling coefficient, waveguide index,
therefore, the silicon-based micro-ring resonator can be heated in a mode of electrifying the electrode, so that the parameters of the first-order linear time-invariant system are adjusted, and the adjustment of the differential equation coefficient is realized.
The effects of the present invention can be further illustrated by the following simulations:
1. simulation software:
simulation of Lumerical device software, simulation of API system and Matlab numerical calculation
2. Simulation content and results:
in order to verify the influence of the designed electrode heating on the coupling coefficient of the micro-ring resonator and the Q value of the resonator cavity, the Lumerical designs a micro-ring coupler with the width of 500nm, the height of 220nm and the length of 310 um. The refractive index of the micro-ring resonator at different temperatures is obtained by simulation with FDTD. The coupling coefficient of the micro-ring and the waveguide with the gap being 0.25um is simulated by FDTD, and then the coefficients a0 and b0 of differential equations at different temperatures are plotted by Matlab according to the formula, as shown in FIG. 4.
The temperature of two coupling points of the branching multiplexing micro-ring resonator ranges from 10 ℃ to 110 ℃, and the adjustable a0 value ranges from: 1.5007e10-1.5562e 10. b ranges from 4.5343e9-5.6473e 9. It can be seen that the a0 value increases substantially linearly with increasing T1, and the a0 value increases substantially linearly with increasing T2. The b0 value decreased substantially linearly with increasing T1, and the a0 value increased substantially linearly with increasing T2. According to the fitting data, the coefficients of the resonator solving the differential equation can be changed by adding the electrodes.
In order to verify the effectiveness of the designed silicon-based resonator, VPI software is used for carrying out simulation according to a design drawing, firstly, a cascade modulator is used for generating a 10Gb/s Gaussian pulse train as shown in figure 5, then, a micro-ring resonator system with designed parameters is entered, and time domain spectral lines are carried out to be numerical solution of a differential equation. And extracting the Gaussian optical pulse data generated by the cascade modulator, performing numerical solution of a differential equation by using Matlab, and performing normalization on the data and output parameters of the micro-ring resonator, such as the data shown in FIG. 6.
According to the graph 6, the solution of the first-order linear time-invariant system of the Gaussian pulse obtained by VPI simulation is the same as that of the differential equation, the error is not more than 2%, and the method indicates that the designed micro-ring resonator can be applied to the solution of the photon differential equation, the precision is high, the differential equations with different coefficients can be solved in the adjusting range, and the speed is far higher than that of a digital computer.
While the principles of the utility model have been described in detail in connection with the preferred embodiments thereof, it will be understood by those skilled in the art that the foregoing embodiments are merely illustrative of exemplary implementations of the utility model and are not limiting of the scope of the utility model. The details of the embodiments are not to be interpreted as limiting the scope of the utility model, and any obvious changes, such as equivalent alterations, simple substitutions and the like, based on the technical solution of the utility model, can be interpreted without departing from the spirit and scope of the utility model.
Claims (6)
1. A photon calculation solving system for a differential equation with variable coefficients is characterized by comprising a laser, a first modulator, a second modulator, a first amplifier and a first filter which are sequentially connected in series; the first modulator is used for modulating the optical signal into a Gaussian function of a time domain; the second modulator is used for realizing pulse cutting and is driven by a 10GHz radio frequency signal emitted by a radio frequency source;
the other end of the first filter is connected with an input port of the 3d coupler; one output port of the 3d coupler is connected with a first oscilloscope, and the other output port of the 3d coupler is sequentially connected with a silicon-based micro-ring modulator chip, a second amplifier, a second filter and a second oscilloscope; the first oscilloscope is used for inputting time domain excitation of the differential equation, the second oscilloscope is used for outputting normalized numerical solution of the differential equation, and the silicon-based micro-ring modulator chip is used for performing numerical solution on the differential equation.
2. The system according to claim 1, wherein the silicon-based microring resonator chip comprises two parallel straight waveguides; a runway-type micro-ring resonator coplanar with the two straight waveguides is also arranged between the two straight waveguides; electrodes for voltage heating are arranged at included angles formed by the micro-ring resonators and the straight waveguides; the incidence end of the silicon-based micro-ring resonator is vertically coupled and packaged by an optical fiber array based on a grating, the electric packaging part is connected with a power supply, and the output end of the optical packaging part is connected with an oscilloscope.
3. The system according to claim 1, wherein the 3d coupler is replaced with a three-to-three beam splitter.
4. The system according to claim 3, wherein the first output end and the second output end of the three-in-one beam splitter are respectively connected with the two corresponding output ends of the 3d coupler in the same way; and the third output end of the one-to-three beam splitter is connected with the third spectrometer.
5. The system for solving the differential equation photon calculation of variable coefficients of claim 2, wherein the light package output end of the silicon-based microring resonator chip is connected with the input end of a beam splitter, and two output ends of the beam splitter are respectively connected with the second oscilloscope and the second spectrometer.
6. The system of claim 1, wherein polarization controllers are disposed between the laser and the first modulator, between the first modulator and the second modulator, and between the 3d coupler and the silicon-based microring resonator chip.
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