Design and optimization method of electrodes for MZ electro-optic modulator

Abstract

The present invention is a design and optimization method for an MZ electro-optic modulator electrode. The design method is to select electrode materials, calculate electrode dimensions, and calculate relative electrode positions by given modulator performance, and finally obtain electrode parameters that meet the requirements of the modulator in combination with the size of the modulator. Before the electrode is designed, it should be ensured that the internal waveguide structure of the modulator without electrodes can normally realize the waveguide function. First, the theoretical steady state of the modulator is given, and the electric field strength required inside the modulator is determined by the steady-state parameters, and then the conditions required for the establishment of the electric field are obtained, so as to determine the relationship equation between the various size parameters of the electrode plate that meet the above requirements. According to the characteristics of the waveguide structure itself, the solution that meets the waveguide requirements is determined from the equation, and then the scope of the solution is narrowed according to the transient parameters. If the solution does not exist, it is necessary to modify the waveguide structure to correct the solution of the electrode. After the solution is obtained, the determined waveguide parameters and electrode parameters are modeled and simulated in finite element simulation software to check the effect of the designed modulator. The present invention provides a solution for the design of the electrode of the electro-optic modulator, which can effectively improve the polarization efficiency of the electrode to the material, thereby reducing the size of the photoelectric modulator and making the optical device more conducive to integration.

Description

Technical Field

[0001] The present invention relates to the field of silicon-based photonic chip integrated devices, and in particular to a design concept and optimization method for MZ electro-optic modulator electrodes. Background Art

[0002] Electro-optic modulator technology is a modulation technology that superimposes an electrical signal carrying information on a carrier light wave. Optical modulation can make certain parameters of the light wave, such as amplitude, frequency, phase, polarization state and duration, change according to certain rules. Electro-optic modulators are realized by the electro-optic effect of matter, including the Pockels Effect and the Kerr Effect. The relationship between the refractive index of a material and the electric field can be expressed as Where γ is the first-order photoelectric coefficient and ξ is the second-order photoelectric coefficient.

[0003] The MZ structure modulator is the most mature and widely used electro-optic modulator. The MZ modulator is an electro-optic modulator based on the Mach-Zehnder interference principle. It consists of two electro-optic phase modulators, two Y-branch waveguides and corresponding driving electrodes. The two phase modulators use the electro-optic effect of the crystal to achieve phase modulation of light, the two Y-branch waveguides complete the function of splitting and combining light, and the driving electrode provides the driving voltage required to achieve the electro-optic effect.

[0004] Scholars have developed many MZ electro-optical modulators, but the current MZ modulators have structural defects. There is a lack of in-depth analysis of the electrode parameters, and the electrode parameters have not been optimized. The electric field formed by the electrodes cannot be effectively utilized, which will make the modulator device size too large.

[0005] The invention discloses a design idea and optimization method for the electrodes of MZ electro-optic modulators. From the perspective of optical electromagnetic theory, the optimal electrode structure corresponding to a given MZ modulator is obtained, thereby reducing the size of the electro-optic modulator. The reduction in the size of optical devices allows more optical devices to be integrated on the same silicon substrate, which is very valuable for the development of integrated optics. Summary of the invention

[0006] The present invention is a method for designing and optimizing electrodes of an MZ electro-optical modulator. The design method is to select electrode materials, calculate electrode dimensions, and calculate relative electrode positions by given modulator performance, and finally obtain electrode parameters that meet modulator requirements in combination with the modulator dimensions.

[0007] The technical solution of the present invention is achieved in this way:

[0008] Step 1: Design a waveguide structure of an MZ electro-optic modulator based on the principle of optical waveguide. When designing, the wavelength of the incident wave, the waveguide material, the cladding material, and the waveguide size must be determined. A preliminary design can be made based on the total reflection theory in linear optics. The structure can be simulated in finite element simulation software. If the structure can form a guided mode, proceed to the next step. If it cannot form a guided mode, generally only the size of the waveguide is modified, while the material and cladding remain unchanged. Simulate again until a guided mode is formed.

[0009] Step 2: According to the electro-optic material characteristics and material dimensions of the modulator designed in the first step, the required electric field strength inside the electro-optic material is solved. Since the second-order and higher-order electro-optic effects of materials under weak light conditions are very weak, they are omitted. The relationship between the refractive index and the electric field strength in the electro-optic material can be obtained.

[0010]

[0011] Where n is the refractive index of the material when no electric field is applied. It should be noted that the refractive index is anisotropic and the electric field is directional. Only the electric field that satisfies the electro-optical effect of the material can affect the refractive index. The specific characteristics of the material need to be referred to. Suppose the phase of the required modulation is The length of the light modulation unit is L, the incident wavelength is λ0, and the electro-optic coefficient of the material is γ. Then the electric field required inside the material is

[0012]

[0013] The positive and negative represent the direction of the electric field.

[0014] Step 3: Solve the minimum cladding width as the constraint condition of the electrode plate size according to the waveguide optical model to ensure that the designed electrode does not affect the performance of the modulator. When light waves propagate in the waveguide, evanescent waves are generated, and their penetration depth is

[0015]

[0016] Where λ0 is the wavelength of the incident wave, n1 is the refractive index of the electro-optical material, and n2 is the refractive index of the cladding material. The distance between the electrodes should be slightly larger than the electro-optical material to avoid the penetration depth of the waveguide. The electric field distribution of the light wave in the cladding can also be deduced by Maxwell's equations, and the position of the electrode can be selected according to the distribution of the electric field of the light wave. According to the interference condition, the equation

[0017]

[0018] Calculate κ, and then use the waveguide electric field distribution equation

[0019]

[0020] The electric field distribution of the light wave in the cladding is obtained. Finite element simulation software can also be used to simulate the waveguide, directly view the distribution of light waves in the optical device, and select appropriate locations to place electrodes.

[0021] Step 4: Determine the constraints of the electrode plate that can establish the electric field mentioned in the second step based on the electrode electric field model. The electrode electric field model involves two relationships, one is the plate electric field distribution model

[0022] E center =f(x,y,E′)

[0023] It represents the relationship between the field strengths at various points around the electrode. The electric field at one point can be used to infer the electric field at nearby points. This model can be derived from the uniformly charged finite length thin straight rod model, and the field strength relationship at each point can be obtained by integrating the effect of the charge using Coulomb's law. It can also be simulated directly through finite element simulation modeling software to obtain the plate electric field distribution model. Another one is the flat plate capacitor electric field model U is the voltage applied to the electrode, and d is the distance between the plates. First, the relative position of the crystal and the electrode is used, and the plate electric field distribution model is used to set E′=E0 to obtain the electric field strength between the plates. Then, the plate capacitor electric field model is used to obtain the voltage of the electrode plates. If the voltage does not meet the design requirements, return to the previous wave to reposition the electrode or modify the electrode parameters.

[0024] Step 5: From the solutions of the constraints mentioned in step 4, determine the appropriate solution as the electrode parameters according to the waveguide structure. The solution under the constraints is a continuous domain, not an independent and unique solution. Considering the structure, shape, and other external factors of the waveguide, select a set of solutions from the domain and proceed to the next step. Most of the time, the solution is not optimal, and the subsequent steps will optimize the solution.

[0025] Step 6: Establish the optical waveguide model designed in step 1 and the electrode model determined in step 5 in the finite element simulation software, apply a driving voltage U to the electrode 3-1, and calculate the modulation of the waveguide 1 and the electrodes 3-1 and 3-2 on the light wave through the finite element simulation software. The driving voltage U applied is generally the voltage solved in the previous step. If the modulation effect is not ideal, the voltage can be fine-tuned. If the modulation effect does not meet the requirements, return to the previous step to select a new solution for simulation verification.

[0026] Step 7: The model in step 6 is abstracted into a resistance-capacitance circuit model, a step signal is applied to the optical modulator, and the response time is calculated by the basic circuit theorem. If the modulation time is too long and does not meet the design requirements, a suitable solution is found according to the solution set in step 5. The establishment of the circuit model can be done by using finite element simulation software to find the resistance-capacitance characteristics of the waveguide structure, or by using a simplified model, using a flat plate capacitor model to calculate the capacitance of the electrode, and using the material equation to find the resistance of the electrode. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a structural diagram of MZ electro-optical modulation.

[0028] Figure 2 This is a cross-sectional diagram of MZ electro-optical modulation.

[0029] Figure 3 It is a flow chart of the design and optimization method of MZ electro-optic modulator electrodes.

[0030] Figure 4 This is the electric field distribution diagram of a certain electrode simulated by COMSOL.

[0031] Figure 5 This is the relationship between the current of a certain electrode and time simulated by COMSOL. DETAILED DESCRIPTION

[0032] The present invention is described below with reference to specific embodiments.

[0033] Step 1: Design a waveguide structure of an MZ electro-optic modulator based on the principle of optical waveguide. The incident light wave is selected as 1.55um, the waveguide material is lithium niobate (LiNbO3), the waveguide height is 1.5um, and the waveguide width is 10um; the cladding material is silicon dioxide (SiO2), the cladding width is 60um, the cladding height is 10um, and the modulation area waveguide length is 200um. Use the "Electromagnetic Wave, Frequency Domain (ewfd)" interface of COMSOL software for simulation. Materials can be added from the COMSOL material library, or you can search for relevant literature to establish materials that meet your special needs. In order to reduce the simulation time, a two-dimensional model is used for simulation, that is, the waveguide width is assumed to be infinitely wide for simulation. It is obtained that the waveguide can form a guided mode, and the next step is carried out.

[0034] Step 2: Based on the electro-optic material properties and material dimensions of the modulator designed in the first step, calculate the required electric field strength inside the electro-optic material. Based on the material properties of lithium niobate (LiNbO3), n = 2.297, γ = 30.8 pm / V, substitute into the equation The relationship between the refractive index of lithium niobate and the electric field is obtained. The phase of the required modulation The length of the optical modulation unit L = 200um, the incident wavelength λ0 = 1.5um, the electro-optic coefficient γ of the material = 30.8pm / V, then the electric field required inside the material

[0035] Step 3: Solve the minimum cladding width as the constraint condition of the electrode plate size according to the waveguide optical model. Use the results of COMSOL simulation calculation of the model in step 1 to draw the field intensity distribution of the light wave. The field intensity at 0.5um is attenuated by half, and there is almost no light field at 2um. Therefore, the horizontal spacing between the electrode placement position and the waveguide is 2um, and the electrode spacing d = 64um.

[0036] Step 4: Determine the constraint conditions of the electrode plate that can establish the electric field in the second step based on the electrode electric field model. Assume that the height of the electrode is h = 20um, and use COMSOL software to simulate the distance d between the two electrodes and the height h e = 20um, the field distribution with infinite width, and the field strength E′ at each point in the space and the field strength E at the center of the plate are obtained center Relationship E center =f(x, y, E′), parallel plate capacitor electric field model U is the voltage applied to the electrodes, and d is the distance between the plates. The relationship between the plate voltage and the electric field at a certain point is obtained as U = dE center

[0037] Step 5: From the solution of the constraint conditions in step 4, determine the appropriate solution as the electrode parameters according to the waveguide structure. Assume that the electrode is located at h = 10um above the waveguide, and the plate spacing is d = 64um. From COMSOL simulation, we know that E center =1.37E', plate voltage U = dE center =87.68E', from the second step we know that E'=E0=0.2V / um. The plate voltage U=17.536V. If the voltage is too high and does not meet the requirements, redetermine the plate spacing and position parameters.

[0038] Step 6: Establish the optical waveguide model designed in step 1 and the electrode model determined in step 5 in the finite element simulation software, apply a driving voltage U=17.536V to the electrode 3-1, and calculate the modulation of the waveguide 1 and the electrodes 3-1 and 3-2 on the light wave through the finite element simulation software. If the modulation effect is not good, check the modulation condition by fine-tuning the voltage. If a suitable voltage cannot be found, return to the previous step and select a new solution for simulation verification.

[0039] Step 7: Abstract the model in step 6 into a resistor-capacitor circuit model, apply a step signal to the optical modulator, and calculate the response time using the basic circuit theorem. Use the "Current (ec)" and "Circuit (cir)" interfaces in COMSOL to set time slices to view the electromagnetic field distribution at different times to determine the dynamic characteristics of the device. Generate the "Time vs. Electric Field Strength" curve and the "Time vs. Current" curve, and get t = 1 × 10 -10s, the current is almost 0, the electrode is fully charged and enters a steady state. T = 1 / t = 10 GHz, and the designed electro-optic modulator can reach a modulation frequency of up to 10 GHz.

Claims

1. A design method for an MZ electro-optic modulator electrode, characterized in that: The method specifically comprises the following steps: S1: Designing the waveguide structure of the MZ electro-optic modulator according to optical theory, including the selection of the waveguide (1) material and the cladding (2) material, determining the size of the waveguide (1), and preliminarily determining the size of the modulator; the width and height of the waveguide (1) are 5 to 10 times the incident wavelength, the length has a wide range and needs to be greater than 100 times the wavelength, and needs to be determined according to the system's requirements for the device; the thickness of the cladding (2) is three times the thickness of the waveguide, the width is three times the total width of the waveguide, and the length is equal to the length of the waveguide (1); the waveguide material is an electro-optic material with a high electro-optic coefficient and a large refractive index, and the cladding is an electro-optic material with a small refractive index; S2: solving the required electric field strength inside the waveguide (1) of the modulator designed in step S1; given the phase to be modulated, the electric field strength is calculated using the electro-optic effect formula according to the length of the waveguide (1) in step S1, and the field strength is provided by the voltage applied by the electrodes (3-1) (3-2); S3: According to the evanescent wave theory of waveguide optics, the minimum width of the cladding (2) is solved. This width is the minimum distance to ensure that the electrodes (3-1) (3-2) will not affect the performance of the waveguide itself. The minimum width is related to the incident wavelength, that is, the material of the waveguide (1), the material of the cladding (2) and the incident wavelength; S4: According to the electrode electric field model established in S2, the relationship between the electric field and the distance d between the electrodes (3-1) (3-2), the height h of the electrodes (3-1) (3-2), and the driving voltage U is obtained; S5: From the domain that satisfies the minimum width constraint in S3 and the electric field establishment constraint in S4, select a suitable solution as the electrode spacing d, height h and driving voltage U according to the waveguide structure; S6: Establish the optical waveguide model designed by S1 and the electrode model determined by S5 in the finite element simulation software, apply a driving voltage U to the electrode (3-1), and calculate the modulation of the waveguide (1) and the electrode (3-1) (3-2) on the light wave through the finite element simulation software; S7: Use the model in S6 and abstract it into a resistor-capacitor circuit model. Apply a step signal to the optical modulator and calculate the response time using the basic circuit theorem. If the modulation time is too long and does not meet the design requirements, find a suitable solution based on the solution set in S5.

2. A design method for an MZ electro-optic modulator electrode according to claim 1, characterized in that In the aforementioned step S1, the MZ electro-optic modulator contains electro-optic effect material, and the optical axis direction of the material is known. To ensure that the designed MZ electro-optic modulator electrode can work normally, simulation is performed in finite element simulation software to ensure that a stable waveguide can be formed in the modulator under a given wavelength, and that the attenuation of the light wave in the waveguide is within an acceptable range.

3. A design method for an MZ electro-optic modulator electrode according to claim 1, characterized in that In the aforementioned step S2, the electro-optic effect formula is the relationship between the refractive index of the material and the applied electric field. Due to the difference in electro-optic materials, this relationship may be a first-order, second-order or higher-order function relationship. Since the electro-optic effect is sensitive to the direction of the electric field, the applied electric field is represented by a vector.

4. A design method for an MZ electro-optic modulator electrode according to claim 1, characterized in that In the aforementioned step S3, there are two methods for determining the minimum width of the cladding (2). One is to use the evanescent wave equation, and the other is to use Maxwell's equations to deduce the electromagnetic field distribution in the waveguide (1) and the cladding (2), and determine the minimum width of the cladding (2) based on the strength of the electromagnetic field.

5. A design method for MZ electro-optic modulator electrodes according to claim 1, characterized in that In the aforementioned step S4, the electric field model of the MZ electro-optic modulator electrode is obtained through two steps. The first step is to solve the electric field distribution near the MZ electro-optic modulator electrode using Maxwell's equations or finite element simulation software. The second step is to determine a simplified capacitance model based on the relative position of the waveguide (1) and the electrode (3-1) (3-2), calculate the electric field strength, and use the capacitance formula to calculate the relationship between the driving voltage U between the electrodes (3-1) (3-2) and the electrodes (3-1) (3-2), height h, electrodes (3-1) (3-2), and spacing d.

6. A design method for MZ electro-optic modulator electrodes according to claim 1, characterized in that In the said step S5, the solution under the condition of satisfying the minimum width constraint of S3 and the electric field establishment constraint of S4 is a continuous domain, rather than an independent and unique solution. Considering the structure, shape and other external factors of the waveguide, a set of solutions is selected from the domain and the next step is carried out. Most of the time, the solution is not optimal and the subsequent steps will optimize the solution.

7. A design method for an MZ electro-optic modulator electrode according to claim 1, characterized in that In the said step S6, due to the interaction between the cladding (2) and the electrodes (3-1) (3-2), or the influence on the performance of the original waveguide, the value of the applied driving voltage U is the solution in S5. If the modulation effect of the MZ electro-optic modulator electrode is not ideal, the driving voltage U is fine-tuned. If the modulation effect does not meet the requirements, return to S5 to select a new solution for simulation verification.

8. A design method for MZ electro-optic modulator electrodes according to claim 1, characterized in that In the said step S7, there are two ways to establish the RC circuit model. One is to obtain the RC characteristics of the waveguide structure through finite element simulation software. The other is to simplify the RC circuit model and use the flat capacitor model to calculate the capacitance of the MZ electro-optic modulator electrode and obtain the resistance of the MZ electro-optic modulator electrode through the material equation.

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