Segmented modeling method based on symmetrical segmentation of travelling-wave electro-optic modulator

Abstract

A segmented modeling method based on symmetrical segmentation of a travelling-wave electro-optic modulator, comprising steps: performing modeling simulation on electrical properties of an electro-optic modulation material of a silicon photonic modulator, and extracting electrical parameter data; performing optical simulation on a laser waveguide formed by the preprocessed electro-optic modulation material, and extracting optical waveguide parameter data; performing modeling simulation on an unloaded traveling-wave electrode, and extracting transmission line parameter data; performing small signal modeling analysis and calculation, and performing step-by-step segmentation processing on a medium-loaded traveling-wave electrode in a symmetrical segmentation manner, and performing data analysis and extraction on a simulation result to obtain a parameter result of system design; and the like. The problems of large amount of calculation, low speed and low efficiency can be solved.

Description

A segmented modeling method based on a symmetrically partitioned traveling-wave electrode electro-optic modulator Technical Field

[0001] This invention relates to the field of data information transmission technology, mainly to optical communication electro-optic modulators and dielectric-loaded microwave transmission line technology, specifically to a segmented modeling method based on a symmetrically partitioned traveling wave electrode electro-optic modulator. Background Technology

[0002] High-performance and high-bandwidth optical fiber communication is an important component of modern communication technology, providing a high-speed, high-capacity, and stable and reliable solution for data transmission. External modulation techniques and traveling-wave electrode models are widely used for broadband and high-performance optical fiber communication.

[0003] External modulation technology is used in long-relay, high-capacity optical fiber communication networks and high-speed optical signal processing systems. Compared to internal modulation, it eliminates chirp and offers higher modulation rates, larger bandwidths, and deeper modulation depths, thus possessing significant advantages. External electro-optic modulators include LiNbO3 Mach-Zehnder modulators (MZMs), electro-absorption modulators (EAMs), gallium arsenide MZMs, quantum well-type InP MZMs, thin-film MZMs, and silicon photonics MZMs. Traveling-wave electrode models are used in microwave and radio frequency fields and are widely applied in various high-frequency devices such as radar and communication systems. They can effectively transmit high-frequency signals and perform signal amplification, modulation, and demodulation. Traveling-wave electrodes typically require impedance matching, velocity matching, and low microwave loss. Low microwave loss can be achieved based on simple geometric structures, such as the use of coplanar strip-shaped traveling-wave electrodes. Therefore, achieving impedance matching and optical / electrical signal group velocity matching is one of the main requirements for improving modulator bandwidth in dielectric-loaded traveling wave electrode design.

[0004] Currently, silicon photonic modulators, a hot research topic, are similar to gallium arsenide (GaAs) and InP modulators in that their traveling-wave electrode design must consider the speed matching problem between optical and electrical signals. For silicon photonic modulators, signal speed matching is usually achieved by leaving a gap in the optical transmission direction of the dielectric-loaded PN junction or, as described in the paper "High Baud Rate All-Silicon Photonics Carrier Depletion Modulators" (IEEE JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL.38, NO.2, JANUARY 2020), by adjusting the PN junction doping concentration. Because dielectric-loaded electro-optic modulators based on traveling-wave electrodes involve multiple physical processes such as electrical (microwave), optical, and electro-optic coupling, there are numerous modeling and design parameters, such as coplanar strip-shaped traveling-wave electrodes, PN doping concentration, PN junction structure, and various geometric parameters, all of which have multiple key parameters. The joint optimization of these parameters is a major challenge in the modeling and design of electro-optic modulators: for example, when there are 9 parameters that need to be jointly optimized, each parameter taking 10 values, the simulation calculations required to traverse all combinations reach 10^60. 9 That is, 1 billion times, which requires a huge amount of computation and time.

[0005] A traveling wave signal loaded on a coplanar strip electrode, when the electrode is unloaded, constitutes a linear transmission system. However, in a PN junction or other semiconductor load electrode, voltage changes alter the electrical properties of the transmission line in real time, such as resistance and capacitance. In this case, the microwave transmission system is nonlinear. However, as described in the paper "A finite-difference time-domain large signal model for Silicon photonics modulators" (IEEE Photonics Technology Letters, VOL.31, NO.13, July 2019), the nonlinear large-signal method can accurately model and simulate such nonlinear transmission systems. However, as mentioned earlier, joint optimization of multiple parameters is difficult to apply in practice due to the high computational complexity of the nonlinear large-signal method. Therefore, linearizing the nonlinear large signal to obtain a small-signal model for modeling, simulating, and optimizing electro-optic modulators has become a fundamental method used in industry and academia.

[0006] However, even under small-signal models, joint optimization of multiple parameters still requires traversing a huge parameter space, resulting in enormous computational load and lengthy computation time. This leads to problems of high computational cost, slow speed, and low efficiency, severely restricting the design efficiency and optimization performance of electro-optic modulators as key devices in optical communication and optical sensing fields. Therefore, to solve these problems, it is necessary to further improve the computational efficiency of small-signal models, involving efficient and reasonable modeling and simulation methods to achieve high-speed traversal of the parameter space. This is of great significance for the modeling, simulation, and optimization design of silicon photonic modulators and other electro-optic modulators with semiconductor or thin-film loaded traveling-wave electrodes, as well as for a wider range of electro-optic devices with dielectric-loaded traveling-wave electrodes.

[0007] Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a segmented modeling method for electro-optic modulators based on symmetrically partitioned traveling wave electrodes. This method overcomes the shortcomings of low simulation efficiency and long optimization design time of silicon photonic modulators, electro-optic modulators, and electro-optic devices with dielectric-loaded traveling wave electrodes, and solves the problems of large computational load, slow speed, and low efficiency.

[0009] This invention provides a segmented modeling method for a symmetrically partitioned traveling-wave electrode electro-optic modulator, specifically including the following steps:

[0010] (1) Model and simulate the electrical properties of the electro-optic modulation material of the silicon photonic modulator, extract the electrical parameter data, and calculate different capacitance and resistance values.

[0011] (2) Perform optical simulation on the laser waveguide formed by the pretreated electro-optic modulation material and extract the optical waveguide parameter data. The pretreated electro-optic modulation material includes at least a doped PN junction.

[0012] (3) Model and simulate the unloaded traveling wave electrode and extract the transmission line parameter data;

[0013] (4) Perform small-signal modeling analysis and calculation on the traveling wave electrode with dielectric load to obtain group velocity matching information parameter data of dielectric load impedance and phase matching.

[0014] (5) The traveling wave electrode with dielectric load is segmented step by step in a symmetrical segmentation manner, a mathematical and physical model of phase shift of symmetrical segmentation is established, the simulation formula and algorithm based on the model are obtained, and simulation calculation is carried out.

[0015] (6) Perform data analysis and extraction on the simulation results to obtain the parameter results of the system design; among which, the parameter results include the transmission line electrical frequency domain response parameters and the electro-optic frequency domain response parameters of the electro-optic modulator;

[0016] Among them, the silicon photonic modulator has a load microwave transmission line, that is, the silicon photonic modulator has a coplanar strip traveling wave electrode.

[0017] Step (2) includes obtaining the fundamental mode distribution and calculating the transmission parameters by overlapping integral. The transmission parameters include the optical loss coefficient and the dispersion relation.

[0018] Specifically, step (3) includes the following steps:

[0019] (3.1) Microwave electrical performance simulation of unloaded traveling wave electrodes is performed using electromagnetic solvers based on FDTD or FEM to obtain S-parameters based on electrode structure.

[0020] (3.2) Convert the S-parameters to the ABCD parameters of the unloaded traveling wave electrode;

[0021] Among them, Z 01 and Z 02 These are the source and terminating load impedance parameters, R. 01 and R 02 Z 01 and Z 02 The real part;

[0022] (3.3) Use the ABCD parameters to obtain the attenuation coefficient and dispersion relationship in the propagation coefficient, and on this basis, obtain the RLGC parameter value per unit length of the unloaded transmission line.

[0023] Specifically, step (4) includes the following steps:

[0024] (4.1) Extract the characteristic impedance microwave exponential frequency domain parameters of the unloaded microwave transmission line, and extract the unloaded impedance Z from the ABCD parameters. 0ul and transmission parameter γ ul The pulRLGC parameters are calculated.

[0025] (4.2) Extract the characteristic impedance microwave exponential frequency domain parameters of microwave transmission lines with dielectric loads.

[0026] (4.3) Use the results of step (4.2) to perform group velocity matching. If the matching requirements are not met, optimize and iterate the design of the microwave transmission line with no load and / or the PN doping concentration and structure to achieve group velocity matching of optical signal and microwave voltage signal transmission, as well as terminal load matching of the traveling wave electrode with load.

[0027] Specifically, step (5) includes the following steps:

[0028] (5.1) Dielectric-loaded traveling wave electrodes are mathematically divided into multiple segments, such as N segments, in the direction of electrical and optical signal transmission, with each segment having a length of Δz;

[0029] (5.2) The traveling wave electrode with dielectric load, each segment of length Δz, is divided into three segments based on the mathematical model;

[0030] (5.3) Connect all the symmetrically divided Δz segments in series;

[0031] (5.4) Each transmission line and dielectric load is equivalent to a unit length lumped circuit model of pul, and the physical quantities corresponding to each segment are obtained by matrix operation.

[0032] In step (5.2), the three-segment structure is divided according to the first segment Δz / 2, the second segment Δz, and the third segment Δz / 2; the mathematical model can be represented as LPN. Δz / 2 UTL Δz LPN Δz / 2 , or UTL Δz / 2 LPN Δz UTL Δz / 2 .

[0033] Specifically, step (6) further includes solving the electro-optic response in the following manner:

[0034] Where V is the voltage value, N is the number of segments, R is the resistance, C is the capacitance, and the subscripts indicate the corresponding relationships.

[0035] In step (6), the average value of the voltage across each segment after segmentation is taken as the voltage value of the electro-optic response of that segment: (V n +V n-1 ) / 2.

[0036] The process also includes step (7): using the system model of the electro-optic modulator to obtain system simulation formulas and algorithms for system-level simulation and calculation.

[0037] The segmented modeling method for a traveling-wave electrode electro-optic modulator based on symmetrical partitioning of the present invention is the first to use symmetrical partitioning to progressively segment the traveling-wave electrode with a dielectric load, which can achieve:

[0038] (1) In the simulation calculation of silicon photonic modulators, electro-optic modulators and electro-optic devices with dielectric-loaded traveling wave electrodes, the problem of low computational efficiency and long optimization design time caused by the current general first-order precision modeling and simulation calculation method is solved. It provides a new symmetrical segmented modeling and calculation method to build a high-speed and efficient simulation design method for the field of high-speed electro-optic modulators and high-speed dielectric-loaded microwave transmission lines in optical communication.

[0039] (2) The segmented traveling wave electrode with dielectric load is symmetrically divided so that the segmented unloaded traveling wave electrode and dielectric load are symmetrically distributed with respect to the center point along half the segment length Δz / 2. The symmetrical distribution lays the foundation for the second-order accuracy of this invention and is a significant improvement on the simple segmented model with first-order accuracy in the prior art.

[0040] (3) By symmetrically partitioning the dielectric-loaded traveling wave electrodes, the first-order error term is eliminated, thereby improving the simulation accuracy and computational efficiency by orders of magnitude. This allows for more realistic modeling and faster simulation of complex electro-optic devices, and increases the number of optimization iterations by orders of magnitude within a limited time. This can greatly improve the performance indicators of the designed high-speed electro-optic modulator for optical communication and related electro-optic devices of high-speed dielectric-loaded microwave transmission lines. Attached Figure Description

[0041] Figure 1 is a schematic diagram of the silicon photonic modulator structure;

[0042] Figure 2 is a schematic diagram of the cross-sectional structure of the PN junction and the distribution of the carrier cross-section, including the depletion layer.

[0043] Figures 3(a)-3(c) are schematic diagrams of the numerical calculation results of PN junction electrical parameters, PN junction optical properties and unloaded microwave transmission line RLGC, respectively.

[0044] Figures 4(a)-4(b) are schematic diagrams showing the characteristic impedance and microwave dispersion results of microwave transmission lines with PN junction loads.

[0045] Figures 5(a)-5(b) are schematic diagrams of the mathematical and physical models established by asymmetric segmentation for a loaded traveling wave electrode.

[0046] Figure 6 is a schematic diagram of the mathematical and physical model of a loaded traveling wave electrode established by symmetrical segmentation.

[0047] Figure 7 is a schematic diagram of the electro-optic adjustment mechanism, large signal, and small signal mechanism;

[0048] Figure 8 is a flowchart of the modeling and simulation design of a silicon photonic modulator based on a symmetrically segmented, loaded traveling-wave electrode.

[0049] Figure 9 shows a schematic diagram of different precisions of small signal calculation results and a summary diagram of calculation precision and efficiency. Detailed Implementation

[0050] The specific implementation of the present invention will be described in detail below. It should be noted that the following implementation is only for further illustration of the present invention and should not be construed as a limitation on the scope of protection of the present invention. Some non-essential improvements and adjustments made to the present invention by those skilled in the art based on the above description of the present invention still fall within the scope of protection of the present invention.

[0051] This invention provides a segmented modeling method for electro-optic modulators based on symmetrically partitioned traveling-wave electrodes. The specific implementation and data content are shown in Figures 1-9. This invention provides a novel, high-speed, and efficient simulation design method for optical communication electro-optic modulators and dielectric-loaded microwave transmission lines by symmetrically partitioning and modeling segments. This invention achieves second-order accuracy. Compared to the simple first-order accurate segmented models used in existing technologies, this invention eliminates first-order error terms by symmetrically partitioning dielectric-loaded traveling-wave electrodes, significantly improving simulation accuracy and computational efficiency. This allows for more realistic modeling and faster simulation of complex electro-optic devices, significantly increasing the number of optimization iterations and parameter traversal space within a finite time. This can greatly improve the performance indicators of the designed optical communication electro-optic modulators and related electro-optic devices with dielectric-loaded microwave transmission lines.

[0052] The following section provides a detailed introduction to the segmented modeling method for symmetrically partitioned traveling wave electrode electro-optic modulators.

[0053] This invention provides a segmented modeling method for a symmetrically partitioned traveling-wave electrode electro-optic modulator, comprising the following steps:

[0054] First, the electrical properties of the electro-optic modulation material in the silicon photonic modulator are modeled and simulated, and electrical parameter data are extracted to calculate different capacitance and resistance values. The silicon photonic modulator has a load microwave transmission line, meaning it has a coplanar strip-shaped traveling wave electrode. Preferably, the electro-optic modulation material includes at least a PN junction, but may also include other electro-optic modulation materials.

[0055] Figure 1 shows a silicon optical modulator structure with a loaded microwave transmission line (coplanar traveling-wave electrode), illustrating the signal loading process. As shown in Figure 1, the silicon optical modulator includes a PN junction optical waveguide, a transmission line load, a coplanar traveling-wave electrode transmission line, a laser optical path transmission section, a high-speed microwave voltage signal loading section, a phase modulation section, and an MZM electro-optic modulation section. It should be noted that in Figure 1:

[0056] Grounding;

[0057] Coplanar strip traveling wave electrode: CPS (coplanar strip) traveling wave electrode;

[0058] n-doping: n, n+, n++ represent three types of doping concentration from low to high;

[0059] p-doping: n, n+, n++ represent three types of doping concentration from low to high;

[0060] Box: is silicon dioxide (SiO2);

[0061] Vg and Rg: source voltage and source resistance;

[0062] Vbias: Bias voltage;

[0063] optical signal enters;

[0064] optical out (optical signal output);

[0065] Si substrate: silicon substrate;

[0066] RL: Terminal load resistance

[0067] As shown in Figure 2, for a silicon photonic modulator, the cross-sectional structure of the PN junction and the distribution of the carrier cross-section, including the depletion layer, are obtained by semiconductor FDTD or FEM simulation under different bias voltages, depending on a certain doping concentration and method.

[0068] Figures 3(a)-3(c) are schematic diagrams of the numerical calculation results of the PN junction electrical parameters, PN junction optical properties, and unloaded microwave transmission line RLGC, respectively. The PN junction optical parameters in Figure 3(a) are: α eff V is the optical loss parameter; π L is the modulator V π Voltage-distance product. As shown in Figure 3, different capacitance and resistance values ​​are obtained through calculation.

[0069] Secondly, optical simulation is performed on the laser waveguide formed by the pretreated electro-optic modulation material, and the optical waveguide parameter data is extracted. Specifically, the fundamental mode distribution is obtained, and the transmission parameters, including the optical loss coefficient and dispersion relation, are calculated using an overlap integral. Preferably, the pretreated electro-optic modulation material includes at least a doped PN junction, but may also include other electro-optic modulation materials. As shown in Figure 3, specifically for silicon photonic modulators, the fundamental mode distribution is obtained, and the transmission parameters, including the optical loss coefficient and dispersion relation, are calculated using an overlap integral.

[0070] Next, the unloaded traveling wave electrode is modeled and simulated, and transmission line parameter data is extracted. The unloaded traveling wave electrode includes a coplanar strip-shaped traveling wave electrode. Specifically, the steps are as follows:

[0071] (1) Microwave electrical performance simulation of unloaded traveling wave electrodes (including coplanar strip traveling wave electrodes) is performed using electromagnetic solvers based on FDTD or FEM to obtain S-parameters based on electrode structure.

[0072] (2) Convert the S-parameters into the ABCD parameters of the unloaded traveling wave electrode;

[0073] In the formula, Z 01 and Z 02 These are the source and terminating load impedance parameters, R. 01 and R 02 Z 01 and Z 02 The real part.

[0074] (3) Use the ABCD parameters to obtain the attenuation coefficient and dispersion relationship in the propagation coefficient, and on this basis, obtain the RLGC parameter values ​​per unit length of the unloaded transmission line, where the RLGC parameter values ​​include resistance, inductance, conductance and capacitance.

[0075] Specifically, after the S-parameter to ABCD parameter conversion and subsequent extraction, the no-load impedance and transmission parameters are obtained: that is, the no-load impedance is obtained. Transmission parameter γ ul d=α ul d+jβ ul d = cosh -1 (A). Therefore, the parameters of pulRLGC can be obtained as follows: R′=real(Z 0ul γ ul ), L′=imag(Z 0ul γ ul ) / ω, G′=real(γ ul / Z 0ul ), and C′=real(γ ul / Z 0ul ) / ω. For silicon photonic modulators, the pulRLGC of the unloaded coplanar traveling wave strip electrode is shown in Figure 3(c).

[0076] Then, small-signal modeling analysis and calculation are performed on the dielectric-loaded traveling wave electrode to obtain dielectric load impedance and phase matching (group velocity matching) parameter data. The dielectric-loaded traveling wave electrode includes a coplanar strip-shaped traveling wave electrode. Specifically, the following steps are included:

[0077] (1) Extract the characteristic impedance microwave exponential frequency domain parameters of the unloaded microwave transmission line, that is, extract the unloaded impedance Z from the ABCD parameters. 0ul and transmission parameter γ ul This step is an auxiliary step;

[0078] (2) Extracting the characteristic impedance and microwave index frequency domain parameters of microwave transmission lines with dielectric loads. Specifically, taking a silicon photonic modulator as an example, the results are shown in Figure 4. Figure 4(a) is a frequency domain schematic diagram of the characteristic impedance (char.impendance) of a microwave transmission line with a PN junction load under a bias voltage of 0 to 4 volts. Figure 4(b) is a frequency domain schematic diagram of the microwave group velocity (microwave index) of a microwave transmission line with a PN junction load under a bias voltage of 0 to 4 volts.

[0079] (3) If the results of the above steps cannot meet the matching requirements, the microwave transmission line with no load and / or the PN doping concentration and structure are optimized and iteratively designed to achieve the group speed matching of optical signal and microwave voltage signal transmission, as well as the terminal load matching of the traveling wave electrode with load.

[0080] Subsequently, the traveling wave electrode with dielectric load is progressively segmented symmetrically to establish a mathematical and physical model of phase shift based on the symmetrical segmentation. Simulation formulas and algorithms based on this model are then obtained, and simulation calculations are implemented in hardware and / or software. Specifically, the steps include the following:

[0081] (1) The traveling-wave electrode with dielectric load is mathematically divided into multiple segments, such as N segments, in the direction of electrical and optical signal transmission (e.g., the z-direction), each segment having a length of Δz. Up to this point, the mathematical model is accurate for the physical process. In each Δz segment, the microwave electrical signal electric field (or voltage, current) propagates simultaneously and in the same location on the traveling-wave electrode and within the dielectric load. In this example of the silicon photonic modulator, the microwave electrical signal voltage propagates simultaneously and in the same location on the coplanar strip-shaped traveling-wave electrode and within the PN dielectric load. Referring to Figure 5(a), a schematic diagram of the silicon photonic modulator circuit model and the non-uniform Δz segment partitioning model is shown, where:

[0082] E i，opt Incident laser electric field;

[0083] E i，opt : Emitted laser electric field;

[0084] V RF Transmission line voltage;

[0085] TL: Unloaded traveling wave electrode transmission line;

[0086] PN: PN junction dielectric load;

[0087] (2) The traveling-wave electrode with dielectric load, each segment of length Δz, is divided into three segments based on a mathematical model. These segments are Δz / 2, Δz, and Δz / 2. Physically, each Δz segment has a dielectric load, meaning the traveling-wave electrode transmission line (i.e., the unloaded traveling-wave electrode, including the coplanar strip-shaped traveling-wave electrode) and the semiconductor or other electro-optic medium (i.e., the dielectric load) between the electrodes overlap in the z-direction. In one preferred embodiment, the mathematical model simulates the first Δz / 2 segment as the dielectric load, the second Δz segment as the unloaded traveling-wave electrode transmission line, and the third Δz / 2 segment as the dielectric load. In another preferred embodiment, the mathematical model simulates the first Δz / 2 segment as the unloaded traveling-wave electrode transmission line, the second Δz segment as the dielectric load, and the third Δz / 2 segment as the unloaded traveling-wave electrode transmission line. The above modeling method for dividing the Δz segment into mathematical models is the preferred method for dividing and modeling symmetrical dielectric-loaded electrode transmission lines.

[0088] Here, relative to the microwave voltage signal, the effect of the unloaded traveling wave electrode transmission line can be represented by the mathematical operator UTL, and the effect of the dielectric load (a dielectric load with applied bias voltage) can be represented by the mathematical operator LPN. To represent the segmented length, if a segment length is Δz / 2, the operator superscript is Δz / 2; if a segment length is Δz, the operator superscript is Δz.

[0089] Preferably, the preferred mathematical model in step (2) can be described as LPN. Δz / 2 UTL Δz LPN Δz / 2 , or UTL Δz / 2 LPN Δz UTL Δz / 2 Because of LPN Δz / 2 UTL Δz LPN Δz / 2 =LPN Δz / 2 UTL Δz / 2 UTL Δz / 2LPN Δz / 2 , or UTL Δz / 2 LPN Δz UTL Δz / 2 =UTL Δz / 2 LPN Δz / 2LPN Δz / 2 UTL Δz / 2 This can be called the symmetrical partitioning method.

[0090] It should be noted that, in contrast to the three-segment structure, the mathematical model of a traveling wave electrode with a dielectric load, where each segment of length Δz is divided into a two-segment structure, where both segments are Δz and Δz. Based on the essence of the mathematical model, the first segment Δz is simulated as an unloaded traveling wave electrode transmission line, and the second segment Δz is simulated as a dielectric load; or, the first segment Δz is simulated as a dielectric load, and the second segment Δz is simulated as an unloaded traveling wave electrode transmission line. This modeling method of dividing the mathematical model for the Δz segment is called the asymmetric dielectric-loaded electrode transmission line partitioning modeling method. The mathematical model under this method can be described as a UTL (Uneven Transmission Line). Δz LPN Δz or LPN Δz UTL Δz .

[0091] The above, including both asymmetric partitioning and the symmetric partitioning involved in this invention, lead to an approximation of the mathematical model relative to the physical process, and the degree of approximation increases as Δz decreases.

[0092] (3) Connect all the symmetrically divided Δz segments in series.

[0093] For an N-segment dielectric-loaded traveling wave electrode transmission line, the preferred mathematical model is:

[0094] LPN Δz / 2 UTL Δz LPN Δz / 2 LPN Δz / 2 UTL Δz LPN Δz / 2 ...LPN Δz / 2 UTL Δz LPN Δz / 2 (N segments) = LPN Δz / 2 UTL Δz LPN Δz UTL Δz LPN Δz ...UTL Δz LPN Δz UTL Δz LPN Δz / 2 ;

[0095] Therefore, LPN Δz / 2 LPN Δz / 2 =LPN Δz It can be simplified by applying it.

[0096] In the right-hand side of the above formula, except for the first term LPN... Δz / 2 And the last item UTL Δz LPN Δz / 2 In addition, there are N-1 UTLs in the middle. Δz LPN ΔzWhen N is large (e.g., N > 10), the UTL of these N-1 terms can be approximated. Δz LPN Δz And the two-segment structure N-term UTL described in step (2) above Δz LPN Δz The numerical methods they represent have comparable computational complexity.

[0097] For an N-segment dielectric-loaded traveling wave electrode transmission line, the preferred mathematical model can also be:

[0098] UTL Δz / 2 LPN Δz UTL Δz / 2 UTL Δz / 2 LPN Δz UTL Δz / 2 ...UTL Δz / 2LPN Δz UTL Δz / 2 (N paragraph)=UTL Δz / 2 LPN Δz UTL Δz LPN Δz UTL Δz ...LPN Δz UTL Δz LPN Δz UTL Δz / 2

[0099] Therefore, UTL Δz / 2 UTL Δz / 2 =UTL Δz It can be simplified by applying it.

[0100] In the right-hand side of the above formula, except for the first term UTL Δz / 2 And the last item LPN Δz UTL Δz / 2 In addition, there are N-1 LPNs in the middle. Δz UTL Δz When N is large (e.g., N > 10), this N-1 term LPN can be approximated. Δz UTL Δz And the two-segment structure N-term LPN described in step (2) Δz UTL Δz The numerical methods they represent have comparable computational complexity.

[0101] In contrast, for all symmetrically partitioned Δz segments, the asymmetric dielectric-loaded electrode transmission line partitioning model (divided into the first Δz segment, the second Δz segment, etc.) is cascaded. For an N-segment dielectric-loaded traveling wave electrode transmission line, the resulting mathematical model is:

[0102] UTLΔz LPN Δz UTL Δz LPN Δz ...TL Δz LPN Δz ,

[0103] or LPN Δz UTL Δz LPN Δz UTL Δz ...LPN Δz UTL Δz

[0104] The numerical computational complexity represented is N-term UTL. Δz LPN Δz or N LPN Δz UTL Δz The numerical computational complexity represented by the preferred mathematical model is comparable when N is large.

[0105] It should be noted that the symmetrical dielectric-loaded electrode transmission line partitioning modeling method used in this invention has second-order accuracy. Compared with the first-order accuracy of the traditional asymmetrical dielectric-loaded electrode transmission line partitioning modeling method, this invention eliminates the first-order error term by symmetrically partitioning the dielectric-loaded traveling wave electrode, thereby improving the simulation accuracy by orders of magnitude. It can also improve the computational efficiency by orders of magnitude by reducing the number of segments N at the same simulation accuracy.

[0106] (4) Each transmission line and dielectric load is equivalent to a unit length (pul) lumped circuit model, and the physical quantities corresponding to each segment, such as voltage and current values, are obtained through matrix operations.

[0107] In this model, all the stacked and partitioned Δz segments (divided into the first segment Δz / 2, the second segment Δz, and the third segment Δz / 2) are equivalent to a PLU circuit model. This yields the transmission lines for the corresponding Δz and Δz / 2 segments, as well as the resistance, inductance, and capacitance of the dielectric load within those transmission lines. Taking the capacitance of the dielectric load in a traveling-wave electrode silicon photonic modulator as an example, the capacitance values ​​for the Δz and Δz / 2 segments are C1 and C2, respectively. s =C pn ·Δz and C s =C pn ·Δz / 2.

[0108] Using matrix operations, the unloaded transmission line operator matrix is ​​obtained as follows (to save space, the T0 operator represents UTL here). Δz )

[0109] Among them, Z μ With γ μ=α μ +jβ μ Here, Δz represents the impedance and propagation constant of the transmission line, respectively, and Δz is the length of the segment. When Δz / 2 is the length of the segment, T2 is used here to represent the unloaded transmission line operator. The matrix simulating the dielectric load is as follows for dielectric loads of length Δz / 2 and length Δz:

[0110] and

[0111] Among them, R s and C s Here, ω represents the resistance and unit capacitance parameters of the PN junction dielectric load, respectively, and ω is the electric field angular frequency.

[0112] Based on the above matrix, we can obtain the ABCD matrix of a medium-loaded transmission line system. Preferably, the LPN is symmetrically segmented. Δz / 2 UTL Δz LPN Δz / 2 LPN Δz / 2 UTL Δz LPN Δz / 2 ...LPN Δz / 2 UTL Δz / 2 LPN Δz / 2 For example

[0113] Its simplified formula is:

[0114] T3 and T4 are the unused transmission line matrices at the source and terminal load ends, respectively.

[0115] The corresponding physical quantities are solved through matrix operations and by combining them with boundary conditions, which are as follows:

[0116] V S =V w +I w Z S ;

[0117] V T =I T Z T ;

[0118] Where V S Z S These are the source voltage and impedance, respectively, V T Z T I T These represent the voltage, impedance, and current at the terminal load, respectively, V w I w These are the operating point voltage and current on the transmission line, respectively.

[0119] Solving the above equation yields:

[0120] In V T I T Once obtained, V can be derived sequentially using the matrix. N V N-1 ...V1, ...V0;

[0121] The accuracy of the voltage value obtained by this invention is second-order, which greatly improves the calculation efficiency and accuracy compared to the first-order accuracy of non-uniform segmentation.

[0122] The following is a detailed introduction. In the specific implementation, the traveling wave electrode with dielectric load is first mathematically divided into multiple segments, such as N segments, in the direction of electrical signal and optical signal transmission, such as the z direction, with each segment having a length of Δz.

[0123] Up to this point, the mathematical model is accurate for the physical process: in each Δz segment, the microwave electrical signal electric field (or voltage, current) propagates simultaneously and in the same location on the traveling wave electrode and within the dielectric load. In this silicon photonic modulator example, the microwave electrical signal voltage propagates simultaneously and in the same location on the coplanar strip traveling wave electrode and within the PN dielectric load.

[0124] However, the above mathematical model has no analytical solution for any signal, so it is first divided into several Δz segments. Then, in the next step, in current academic research and product development, each segment of the traveling wave electrode with a dielectric load of length Δz is mathematically divided into a two-segment structure, as shown in Figure 5. The first segment Δz and the second segment are both Δz. The first segment Δz is simulated as an unloaded traveling wave electrode transmission line, and the second segment Δz is simulated as a dielectric load; or, the first segment Δz is simulated as a dielectric load, and the second segment Δz is simulated as an unloaded traveling wave electrode transmission line. This asymmetric dielectric load electrode transmission line subdivision modeling method approximates the transmission of the microwave electrical signal voltage in Figure 5(a) through a segment of length Δz passing through both the traveling wave electrode and the dielectric load as either first passing through an unloaded traveling wave electrode transmission line of length Δz and then through a dielectric load of length Δz, or vice versa. The approximation is obvious because it alters the actual physical transmission mechanism, thus causing computational simulation errors. The mathematical model under this method, as described in step 5.2, can be described as UTL. Δz LPN Δz or LPN Δz UTL Δz Or, the corresponding abbreviation is T1T b or Tb T1. When Δz decreases, the simulation error decreases while the simulation accuracy increases. When Δz approaches 0, the simulation error gradually disappears. However, when Δz decreases, the total number of calculation steps increases. When Δz decreases to 0, the total number of calculation steps approaches infinity, making calculation, simulation, and optimization impossible.

[0125] During the research process of this invention, it was discovered that the asymmetric partitioning method of the Δz segment described above is a first-order method, meaning that for every 2-fold decrease in Δz, the simulation error decreases by a 2-fold. To achieve a certain level of simulation accuracy, the required Δz is generally very small, resulting in a large number of calculation steps, leading to long simulation times and low efficiency.

[0126] As shown in Figure 6, the symmetrical segmentation method of the Δz segment proposed in this invention is a second-order method, which divides each segment of the traveling wave electrode with dielectric load of length Δz into a three-segment structure on the mathematical model, wherein the first segment is Δz / 2, the second segment is Δz, and the third segment is Δz / 2.

[0127] As shown in Figure 6, when the symmetrical partitioning method concatenates the same intermediate operators, when n is large (e.g., n > 10), it can be approximated that the computational complexity of this method and the asymmetric partitioning method is basically equivalent in the same n steps, i.e., when the device length d and Δz are equal. However, the symmetrical dielectric-loaded electrode transmission line partitioning modeling method (this invention) has second-order accuracy. Compared with the first-order accuracy of the asymmetric dielectric-loaded electrode transmission line partitioning modeling method, this invention eliminates the first-order error term by symmetrically partitioning the dielectric-loaded traveling wave electrode, thereby improving the simulation accuracy by orders of magnitude. Therefore, at the same simulation accuracy, the computational efficiency can be improved by orders of magnitude by reducing the number of segments N.

[0128] Specifically, for the second-order method, for every 2-fold decrease in Δz, the simulation error decreases by 2. 2 = 4 times; for every 10-fold decrease in Δz, the simulation error decreases by 10. 2 =100 times. To achieve a certain level of high simulation accuracy, a larger Δz is required, resulting in fewer calculation steps, shorter simulation time, and significantly improved computational efficiency compared to the first-order method.

[0129] It is important to emphasize that this invention uses the average voltage across each segment as the voltage value of the electro-optic response for that segment, resulting in a second-order accuracy. In contrast, the response of non-uniformly segmented data, even when using the average voltage, only achieves first-order accuracy. The second-order accuracy achieved by this invention is primarily due to the partitioning of the symmetrical dielectric-loaded electrode transmission line. The algorithm derived from this partitioning has been detailed in the preceding steps.

[0130] Then, the simulation results are analyzed and extracted to obtain the parameter results of the system design. The parameter results include the transmission line electrical frequency domain response parameters and the electro-optic frequency domain response parameters of the electro-optic modulator. The average value of the voltage at both ends of each segment is taken as the voltage value of the electro-optic response of this segment. Therefore, the obtained response is second-order accurate, while the response of non-uniform segmentation is only first-order accurate.

[0131] The electro-optic response, which includes the integral, cumulative voltage, and photoelectric phase matching, obtained by this invention, is calculated using the following formula.

[0132] Based on this, the electro-optic frequency domain response can be solved. It is important to note that the key point of this invention lies in the formula, where the average voltage across each segment is taken as (V). n +V n-1 ) / 2.

[0133] Finally, the system simulation formulas and algorithms are obtained using the system model of the electro-optic modulator for system-level simulation and calculation.

[0134] As shown in Figure 7, when the electrical small signal, i.e., the small amplitude peak-to-peak microwave information signal V s Apply a bias voltage V bias Driving the phase shift arm in the MZM modulator will result in a small optical output signal. The electro-optic response M(ω) is defined conventionally as the response with a bias voltage of V. π / 2 Or Δφ = π / 2. Thus, the ratio of optical output power at different frequencies is...

[0135] Therefore, the EO response can be defined, and the commonly used unit is dBe or dBo.

[0136] The modeling and simulation design process for silicon photonic modulators based on symmetrically segmented, loaded traveling-wave electrodes is shown in Figure 8. This invention includes PN junction simulation, optical waveguide mode solving, mode overlap integration, traveling-wave electrode waveguide simulation, equivalent PLU circuit modeling, analytical approximation modeling of the load electrode transmission line and calculation of impedance and phase matching, symmetrical dielectric load electrode transmission line partitioning modeling, symmetrically segmented PN-loaded traveling-wave electrode transmission line modeling, frequency domain small-signal model simulation, electro-optic response calculation, and the final step, step 7, MZM waveform simulation. Performance analysis in MZM device-level development often stops at electro-optic response calculation. MZM waveform simulation relies on mature technology and will not be detailed further in this invention.

[0137] In a specific embodiment, the segmented modeling method of the present invention based on symmetrically partitioned traveling wave electrode electro-optic modulator is verified by numerical simulation, and compared with the traditional method based on asymmetric partitioning.

[0138] For simplicity, assume the unloaded transmission line parameters are pulR′ = 2.5 kΩ / m, L′ = 684.8 nH / m, G′ = 0, and C′ = 86.6 pF / m. However, even using the frequency-dependent RLGC parameters in Figure 3, the conclusion remains the same. The reverse bias voltage is set to -2V, and the modulator length is d = 3.1 mm. The PN junction uses a moderate level of doping. Both the source impedance and load impedance are matched to the characteristic impedance of the load at 30 GHz. The PN fill factor is assumed to be 100%. During the simulation, the mid-range voltage V(f, d / 2) on the dielectric-loaded transmission line was recorded, and Vf on the PN junction was also recorded. pn (f, d / 2), note that its numerical precision depends on the chosen Δz. Also note that f is the frequency. Here, the asymmetric step-size splitting method is represented as "split1", and the symmetric splitting method as "split2". Finally, the small-signal modulator EO response M(f) is calculated, which is compared with all individual V values ​​calculated at a distance nΔz. pn The sum of (f, nΔz) is involved, then multiplied by the phase mismatch factor. The normalized standard deviation (nsd), as described in the paper "Symmetrized SSF scheme to control global simulation accuracy in fiber optic communication systems" (IEEE JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL.26, NO.2, JANUARY 2008), is used as the global error. The metric is defined as the approximate solution with a specific step size Δz and a very small Δz or a very large total number of steps N. steps The difference between the obtained "true solutions".

[0139] First, use the split1 method and N. steps =4608 is used to simulate the definition of the medium-distance voltage V. pn The true electrical response (EE) of (d, d / 2) is shown in Figure 9, plotting the N responses for two different partitioning methods. steps The electro-optic (EO) response was plotted. Compared to the asymmetric partitioning method, the symmetric partitioning method produces results closer to the "true solution". Furthermore, the electro-optic (EO) response amplitudes for the three cases were plotted in the figure, along with the EO phase response, yielding similar conclusions: that under the same total number of steps, the symmetric partitioning method produces results closer to the "true solution" compared to the asymmetric partitioning method.

[0140] Simulation steps N steps Global error with NSD The relationship is shown in Figures 9 to 9, indicating that for 1) the voltage V(f, d / 2) on the transmission line with a dielectric load, 2) the voltage V on the PN junction... pn (d, d / 2), and 3) the modulator EO response M(f), which is related to the phase factor modulated V. pn The sum of (d, d / 2) is proportional to the result. The symmetric partitioning method, i.e., split 2, has been proven by simulation results to be a second-order method: when the step size is halved, the NSD error decreases to 1 / 4. The asymmetric partitioning method, also i.e., split 2, has been proven to be a first-order method; to achieve the same NSD, it requires more simulation steps. At the desired accuracy or error level, symmetric partitioning methods require 1 / 5 to 1 / 4 of the number of steps compared to asymmetric partitioning methods; At the required accuracy level, symmetric partitioning methods require approximately 1 / 10 of the number of steps compared to asymmetric methods. In optical communication employing high-capability error-correcting codes, where higher accuracy is required, symmetric partitioning methods may be tens of times faster than asymmetric methods.

[0141] In the main processes mentioned above, this invention, through segmented processing and data analysis of simulation results, extracts specific electro-optic frequency domain responses and electro-optic frequency domain responses. Compared with previous modeling, simulation, and design methods, this invention significantly improves the computational efficiency of electro-optic modulator optimization design at the same precision. Furthermore, the above embodiments are merely illustrative of this invention and should not be construed as limiting the scope of protection of this invention. For example, while the implementation example is a silicon photonic modulator, the core process of this invention involves progressively segmenting the loaded traveling-wave electrode in a symmetrical manner to establish a symmetrical segmented phase shift mathematical and physical model and obtain simulation formulas and algorithms based on this model. This symmetrical segmentation modeling, simulation, and calculation model is applicable to traveling-wave electrodes using other electro-optic materials besides silicon photonics as loads. More specifically, the core process of this invention includes modeling, simulation, and calculation of transmission lines containing dielectric load materials whose dielectric properties vary with transmission line voltage or current. Any non-essential improvements and adjustments made to this invention by those skilled in the art based on the above description are still within the scope of protection of this invention.

[0142] Although exemplary embodiments of the invention have been described for illustrative purposes, those skilled in the art will understand that various modifications, additions, and substitutions in form and detail may be made without departing from the scope and spirit of the invention disclosed in the appended claims, and all such modifications and substitutions should fall within the scope of protection of the appended claims. Furthermore, the various parts of the product and the various steps of the method claimed in this invention can be combined in any combination. Therefore, the description of the embodiments disclosed in this invention is not intended to limit the scope of the invention, but rather to describe the invention. Accordingly, the scope of the invention is not limited by the above embodiments, but is defined by the claims or their equivalents.

Claims

1. A segmented modeling method for a symmetrically partitioned traveling-wave electrode electro-optic modulator, characterized in that, Includes the following steps: (1) Model and simulate the electrical properties of the electro-optic modulation material of the silicon photonic modulator, extract the electrical parameter data, and calculate different capacitance and resistance values. (2) Perform optical simulation on the laser waveguide formed by the pretreated electro-optic modulation material and extract the optical waveguide parameter data. The pretreated electro-optic modulation material includes at least a doped PN junction. (3) Model and simulate the unloaded traveling wave electrode and extract the transmission line parameter data; (4) Perform small-signal modeling analysis and calculation on the traveling wave electrode with dielectric load to obtain group velocity matching information parameter data of dielectric load impedance and phase matching. (5) The traveling wave electrode with dielectric load is segmented step by step in a symmetrical segmentation manner, a mathematical and physical model of phase shift of symmetrical segmentation is established, the simulation formula and algorithm based on the model are obtained, and simulation calculation is carried out. (6) Perform data analysis and extraction on the simulation results to obtain the parameter results of the system design; among which, the parameter results include the transmission line electrical frequency domain response parameters and the electro-optic frequency domain response parameters of the electro-optic modulator.

2. The method as described in claim 1, characterized in that: The silicon photonic modulator has a load microwave transmission line, that is, the silicon photonic modulator has a coplanar strip traveling wave electrode.

3. The method as described in claim 2, characterized in that: Step (2) includes obtaining the fundamental mode distribution and calculating the transmission parameters by overlapping integral. The transmission parameters include the optical loss coefficient and the dispersion relation.

4. The method as described in claim 1 or 3, characterized in that: Step (3) specifically includes the following steps: (3.1) Microwave treatment of unloaded traveling wave electrodes using an electromagnetic solver based on FDTD or FEM. Electrical performance simulation was performed to obtain S-parameters based on the electrode structure. (3.2) Convert the S-parameters to the ABCD parameters of the unloaded traveling wave electrode; Among them, Z 01 and Z 02 These are the source and terminating load impedance parameters, R. 01 and R 02 Z 01 and Z 02 The real part; (3.3) Use the ABCD parameters to obtain the attenuation coefficient and dispersion relationship in the propagation coefficient, and on this basis, obtain the RLGC parameter value per unit length of the unloaded transmission line.

5. The method as described in claim 4, characterized in that: Step (4) specifically includes the following steps: (4.1) Extract the characteristic impedance microwave exponential frequency domain parameters of the unloaded microwave transmission line, and extract the unloaded impedance Z from the ABCD parameters. 0ul and transmission parameter γ ul The pulRLGC parameters are calculated. (4.2) Extract the characteristic impedance microwave exponential frequency domain parameters of microwave transmission lines with dielectric loads. (4.3) Use the results of step (4.2) to perform group velocity matching. If the matching requirements are not met, optimize and iterate the design of the microwave transmission line with no load and / or the PN doping concentration and structure to achieve group velocity matching of optical signal and microwave voltage signal transmission, as well as terminal load matching of the traveling wave electrode with load.

6. The method as described in claim 1 or 5, characterized in that: Step (5) specifically includes the following steps: (5.1) The traveling wave electrode with dielectric load is mathematically divided into multiple segments, such as N segments, in the direction of electrical signal and optical signal transmission, with each segment having a length of Δz. (5.2) The traveling wave electrode with dielectric load, each segment of length Δz, is divided into three segments based on the mathematical model; (5.3) Connect all the symmetrically divided Δz segments in series; (5.4) Each transmission line and dielectric load is equivalent to a unit length lumped circuit model of pul, and the physical quantities corresponding to each segment are obtained by matrix operation.

7. The method as described in claim 6, characterized in that: In step (5.2), the three-segment structure is divided according to the first segment Δz / 2, the second segment Δz, and the third segment Δz / 2; the mathematical model can be represented as LPN. Δz / 2 UTL Δz LPN Δz / 2 , or UTL Δz / 2 LPN Δz UTL Δz / 2 .

8. The method as described in claim 1 or 7, characterized in that: Step (6) further includes solving the electro-optic response in the following ways: Where V is the voltage value, N is the number of segments, R is the resistance, C is the capacitance, and the subscripts indicate the corresponding relationships.

9. The method as described in claim 8, characterized in that: In step (6), the average value of the voltage across each segment after segmentation is taken as the voltage value of the electro-optic response of that segment: (V n +V n-1 ) / 2.

10. The method as described in claim 1 or 9, characterized in that, It also includes step (7): using the system model of the electro-optic modulator to obtain system simulation formulas and algorithms for system-level simulation and calculation.

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