A non-equal-interval silicon-based optical phased array low-sidelobe two-dimensional scanning method and system

Abstract

This disclosure provides a low-sidelobe two-dimensional scanning method and system for non-equidistant silicon-based optical phased arrays, relating to the field of optical phased array control technology. The method includes: acquiring the target scanning direction, including the target azimuth and elevation angles, and array constraints; establishing a far-field light intensity model based on the phase delay relationship between the array element positions, array element phases, and far-field direction angles; under array constraints, iteratively determining the non-equidistant array element position sequence with the goal of suppressing sidelobes and grating lobes and increasing the main lobe energy concentration; determining the target operating wavelength of the input light based on the target elevation angle; determining the phase control quantity of each grating antenna element based on the target azimuth, target operating wavelength, and non-equidistant array element position sequence, and mapping it to a driving voltage; achieving azimuth scanning through the driving voltage, and elevation scanning through the target operating wavelength and the dispersion of the grating antenna elements. This disclosure can suppress sidelobes and grating lobes in non-target directions, achieving non-mechanical beam scanning.

Description

Technical Field

[0001] This disclosure relates to the field of optical phased array control technology, and in particular to a method and system for low sidelobe two-dimensional scanning of a non-equidistant silicon-based optical phased array. Background Technology

[0002] Silicon-based optical phased arrays achieve non-mechanical beam scanning by controlling the relative phase of multiple antenna elements. Equally spaced arrays generate grating lobes when the spacing is large, while smaller spacing increases crosstalk and fabrication difficulty. Sidelobe suppression, scanning field of view, and process constraints are mutually restrictive, and phase deviation is difficult to compensate for, affecting far-field beam quality and two-dimensional scanning performance. Summary of the Invention

[0003] To overcome the problems existing in related technologies, this disclosure provides a two-dimensional scanning method and system for low sidelobes of non-equidistant silicon-based optical phased arrays.

[0004] According to a first aspect of the present disclosure, a low sidelobe two-dimensional scanning method for a non-equidistant silicon-based optical phased array is provided, applied to a silicon-based optical phased array, wherein the silicon-based optical phased array includes a beam splitter network, multiple silicon-based waveguides, multiple phase shifters, and multiple grating antenna elements, comprising: Obtain the target scanning direction and array constraints; the target scanning direction includes the target azimuth angle and the target elevation angle. A far-field light intensity model is established based on the phase delay relationship between the array element position, array element phase and far-field direction angle; Under the array constraints, with the goal of suppressing sidelobes and grating lobes in non-target directions and increasing the energy concentration of the main lobe, the non-equidistant array element position sequence is determined iteratively based on the far-field light intensity model; the non-equidistant array element position sequence represents the arrangement position of the multiple grating antenna array elements. Based on the target elevation angle, the target operating wavelength of the input light is determined. Based on the target azimuth angle, the target operating wavelength, and the non-equidistant array element position sequence, the phase control quantity of each grating antenna array element is determined, and the phase control quantity is mapped to the driving voltage of the multiple phase shifters. The input light is adjusted to the target operating wavelength, and the adjusted input light is distributed to the multi-channel silicon waveguide via the beam splitter network; The driving voltage is applied to the plurality of phase shifters to achieve azimuth scanning through the phase difference between adjacent grating antenna elements; By utilizing the input light adjusted to the target operating wavelength and the dispersion of the grating antenna array elements, the elevation emission angle is made to correspond to the target elevation angle, thereby achieving elevation scanning.

[0005] In some embodiments, establishing a far-field light intensity model based on the phase delay relationship between the array element position, array element phase, and far-field azimuth angle includes: The array factor is constructed based on the amplitude weight, position, and phase control of each grating antenna element; The far-field light intensity distribution is determined based on the array factor and the single-element field pattern; Wherein, the array factor satisfies: ; The far-field light intensity distribution satisfies: ; in, For array factor, For far-field light intensity distribution, This is a single-element field pattern. The far-field direction angle, For the operating wavelength, , , The first The amplitude weights, position and phase control parameters of each grating antenna element , The refractive index of the exit-side medium. The imaginary unit, The number of elements in the grating antenna array.

[0006] In some embodiments, the array constraints include adjacent element spacing constraints, array aperture constraints, and element crosstalk constraints; the step of determining the non-equidistant element position sequence based on the far-field intensity model iteratively, with the goal of suppressing sidelobes and grating lobes in non-target directions and increasing the main lobe energy concentration under the array constraints, includes: An evaluation function is constructed based on the far-field light intensity distribution; the evaluation function includes at least a peak sidelobe term and a main lobe energy concentration term, and also includes at least one of an array element crosstalk penalty term and a constraint penalty term; wherein, the peak sidelobe term is determined based on the maximum light intensity outside the main lobe angular domain, and the main lobe energy concentration term is determined based on the energy proportion within the main lobe angular domain; the main lobe angular domain is the angular domain surrounding the target azimuth angle; With the goal of reducing the peak sidelobe term and increasing the main lobe energy concentration term, the candidate array element position sequence is iteratively updated; The candidate array element position sequence that satisfies the array constraints is determined as the non-equally spaced array element position sequence.

[0007] In some embodiments, the iterative update of the candidate array element position sequence includes: The positions of the array elements with equal spacing are used as the initial array element positions; Keeping the positions of the two end array elements fixed, position perturbation is introduced into at least some of the grating antenna array elements other than the end array elements to obtain a candidate array element position sequence; Under the conditions of satisfying the adjacent element spacing constraint, the array aperture constraint, and the element crosstalk constraint, the position perturbation amount is iteratively updated until the evaluation function converges or reaches the preset number of iterations.

[0008] In some embodiments, determining the phase control amount of each grating antenna element based on the target azimuth angle, the target operating wavelength, and the non-equidistant array element position sequence includes: Based on the target azimuth angle, the target operating wavelength, and the non-equidistant array element position sequence, calculate the... Ideal phase of each grating antenna element: ; in, The target azimuth angle is... The target operating wavelength, For the first The position of each grating antenna element The wave number in the exit medium. For the first The ideal phase of each grating antenna element; With the goal of further reducing the non-target direction sidelobes and grating lobes obtained based on the far-field intensity model, a phase correction is searched near the ideal phase. ; Based on the ideal phase and the phase correction amount, the corrected phase control amount is obtained: ; in, For the first Phase control quantity after correction for each grating antenna element For the first Phase correction amount of each grating antenna element This indicates a modulo operation; the phase correction amount is used to compensate for phase deviations caused by at least one of the following: manufacturing errors, optical path transmission errors, and thermal crosstalk.

[0009] In some embodiments, the plurality of phase shifters are plurality of thermo-optical phase shifters; mapping the phase control quantity to the driving voltage of the plurality of phase shifters includes: Based on simulation or calibration results, a phase voltage mapping table between the phase change and driving voltage of each thermo-optical phase shifter is established. Based on the phase control value of each grating antenna element, the corresponding driving voltage is called in the phase voltage mapping table; Among them, the The phase change of the aforementioned thermo-optical phase shifter satisfies: ; in, The target operating wavelength, For the first The effective refractive index change of a silicon-based waveguide under driving voltage. For the first The effective phase shift length of a thermo-optical phase shifter.

[0010] In some embodiments, determining the target operating wavelength of the input light based on the target pitch angle includes: The target operating wavelength is determined based on the target pitch angle and the grating phase matching relationship; The grating phase matching relationship satisfies: ; in, Let be the waveguide propagation constant. , The refractive index of the exit-side medium. The pitch launch angle corresponds to the target pitch angle. For diffraction orders, The period is the grating period.

[0011] According to a second aspect of the present disclosure, a non-equidistant silicon-based optical phased array low sidelobe two-dimensional scanning system is provided for performing the method described in the first aspect of the present disclosure, comprising: a tunable laser, a beam splitter network, a multi-channel silicon-based waveguide, a plurality of phase shifters, a plurality of grating antenna elements, a multi-channel voltage controller, and a controller. The plurality of grating antenna elements are arranged in a non-equidistant element position sequence; at least two adjacent elements in the non-equidistant element position sequence have different spacing; the non-equidistant element position sequence is a sequence determined in advance based on a far-field light intensity model and under array constraints with the goal of suppressing sidelobes and grating lobes in non-target directions. The tunable laser is used to output input light to the beam splitter network; The beam splitter network is used to distribute the input light to the multiple silicon-based waveguides; The multiple phase shifters are respectively disposed on the multiple silicon-based waveguides and correspond to the multiple grating antenna array elements; The multi-channel voltage controller is connected to the plurality of phase shifters respectively, and is used to apply independent drive voltages to the plurality of phase shifters; The controller is connected to the tunable laser and the multi-channel voltage controller respectively. The controller is used to receive the target scanning direction, determine the target operating wavelength of the tunable laser according to the target elevation angle in the target scanning direction, determine the phase control quantity of each phase shifter according to the target azimuth angle in the target scanning direction, the target operating wavelength and the non-equidistant array element position sequence, and convert the phase control quantity into the independent driving voltage so as to achieve azimuth scanning through the phase difference between adjacent grating antenna array elements, and achieve elevation scanning through the tuning of the target operating wavelength.

[0012] In some embodiments, the beam splitting network is a multimode interferometric beam splitting network; the multimode interferometric beam splitting network includes multiple cascaded 1×2 multimode interferometric beam splitting units; each 1×2 multimode interferometric beam splitting unit includes a multimode interferometric region, an input waveguide, and an output waveguide; at least one of the input waveguide and the output waveguide is provided with a tapered transition section; the length of the multimode interferometric region is determined according to the self-imaging conditions and adjusted by field strength distribution scanning.

[0013] In some embodiments, the number of output channels of the multimode interferometric beam splitter network is not less than 16; the length of the multimode interferometric region of each 1×2 multimode interferometric beam splitter unit is... The spacing between the output waveguides is ; The plurality of phase shifters are thermo-optical phase shifters, each including a metal electrode disposed adjacent to a corresponding silicon-based waveguide; the driving voltage output by the multi-channel voltage controller to the metal electrode ranges as follows: to ; The number of the plurality of grating antenna elements is not less than 16, and the grating period is [missing information]. The grating width is The grating etching depth is ; The center wavelength of the tunable laser is The wavelength tuning range is .

[0014] The scheme provided in this disclosure can obtain the target scanning direction and array constraints. A far-field light intensity model is established based on the phase delay relationship between the element positions, element phases, and far-field azimuth angles. Under array constraints, the non-equidistant element position sequence is iteratively determined with the goal of suppressing sidelobes and grating lobes and improving the main lobe energy concentration. The target operating wavelength is determined based on the target elevation angle, and the phase control quantity is determined based on the target azimuth angle, target operating wavelength, and non-equidistant element position sequence. Azimuth scanning is achieved through driving voltage, and elevation scanning is achieved through wavelength tuning and grating dispersion. By combining non-equidistant element position optimization with phase correction, this disclosure can suppress sidelobes and grating lobes during the scanning process while considering element crosstalk and layout constraints. Simultaneously, the dispersion characteristics of the grating antenna are utilized to achieve elevation beam deflection through wavelength tuning, thereby forming a two-dimensional non-mechanical beam scanning, which is beneficial for improving far-field beam quality and scanning performance. Attached Figure Description

[0015] Figure 1 The diagram shows a flowchart of a low sidelobe two-dimensional scanning method for a non-equally spaced silicon-based optical phased array according to an embodiment of the present disclosure.

[0016] Figure 2 A flowchart illustrating the method for establishing a far-field light intensity model in an embodiment of this disclosure is shown.

[0017] Figure 3 A flowchart illustrating the method for iteratively determining the position sequence of non-equidistant array elements in an embodiment of this disclosure is shown.

[0018] Figure 4 A flowchart illustrating the method for iteratively updating the candidate array element position sequence in an embodiment of this disclosure is shown.

[0019] Figure 5 This diagram illustrates a flowchart of a method for determining the phase control amount of each grating antenna element in an embodiment of this disclosure.

[0020] Figure 6 This diagram illustrates a method for mapping phase control quantities to drive voltages in an embodiment of this disclosure.

[0021] Figure 7 This diagram illustrates the principle of two-dimensional scanning achieved through the coordinated use of phase adjustment and wavelength tuning in an embodiment of this disclosure.

[0022] Figure 8 This diagram illustrates a non-equally spaced grating antenna array and independent phase modulation in an embodiment of this disclosure.

[0023] Figure 9 The diagram shows a comparison of directional field strength under different element spacings in the embodiments of this disclosure.

[0024] Figure 10The far-field radiation pattern and far-field longitudinal section of the grating antenna array in the embodiments of this disclosure are shown.

[0025] Figure 11 This diagram illustrates the structure of a non-equidistant silicon-based optical phased array low sidelobe two-dimensional scanning system according to an embodiment of the present disclosure.

[0026] Figure 12 A schematic diagram of the structure of the multimode interference beam splitter network in an embodiment of this disclosure is shown.

[0027] Figure 13 The simulation results of the field strength distribution of the multimode interferometric beam splitter in the embodiments of this disclosure are shown. Detailed Implementation

[0028] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0029] Before describing the specific embodiments of this disclosure in detail, the core concepts and basic principles involved in this disclosure will first be explained.

[0030] Optical phased arrays are a technology that achieves beam deflection without relying on mechanical moving parts by controlling the relative phase of the radiated light fields of multiple antenna array elements to coherently superimpose the light fields in the target direction. Compared with traditional mechanical scanning methods, optical phased arrays do not require mechanical components such as rotating mechanisms, oscillating mechanisms, or scanning mirrors, thus offering advantages such as high scanning speed, high reliability, small size, and vibration resistance. Silicon-based optical phased arrays are based on silicon-based photonic integration platforms and manufactured using complementary metal-oxide-semiconductor (CMOS) technology. They feature small size, high integration, low cost, and ease of mass production, enabling applications in fields such as all-solid-state lidar, space optical communication, laser imaging, target detection, and intelligent transportation.

[0031] Silicon-based optical phased arrays typically consist of a beam-splitting network, multiple silicon waveguides, a phase shifter array, and a grating antenna array. The input light is distributed to the multiple silicon waveguides by the beam-splitting network, and the phase shifters alter the phase of each path before the light is radiated into free space by multiple grating antenna elements. By changing the phase difference between adjacent elements, the azimuth beam direction can be adjusted; by changing the input light wavelength and utilizing the dispersion characteristics of the grating antennas, the elevation exit angle can be adjusted, thus achieving two-dimensional beam scanning.

[0032] However, for equidistant arrays, grating lobes tend to appear in the far-field pattern when the spacing between adjacent elements is large; when the spacing between adjacent elements is too small, coupling and crosstalk between adjacent waveguides increase, increasing the difficulty of layout design and fabrication. Non-equidistant arrays can disperse the energy of periodic grating lobes by adjusting the positional relationship of different elements, but optimizing the element positions alone is still insufficient to fully compensate for phase deviations caused by fabrication errors, thermal crosstalk, and optical transmission errors in each path. On the other hand, large-scale phased arrays require stable and uniform multi-path beam splitting networks and independently controllable phase shifter arrays. This disclosure combines non-equidistant array layout optimization, phase correction, multi-path independent driving, and wavelength tuning to provide a low-sidelobe two-dimensional scanning control method and system.

[0033] Next, with reference to specific embodiments, the low sidelobe two-dimensional scanning method for non-equidistant silicon-based optical phased arrays provided in this disclosure will be described in detail.

[0034] Figure 1 This diagram illustrates a flow chart of a low sidelobe two-dimensional scanning method for a non-equally spaced silicon-based optical phased array according to an embodiment of the present disclosure. This method can be applied to silicon-based optical phased arrays, which include a beam splitter network, multiple silicon waveguides, multiple phase shifters, and multiple grating antenna elements. Figure 1 As shown, the method includes the following steps S101 to S107: S101, obtain the target scanning direction and array constraints.

[0035] The target scanning direction includes the target azimuth angle and the target elevation angle. The target azimuth angle indicates the angle to which the beam needs to be deflected in the horizontal plane, and the target elevation angle indicates the angle to which the beam needs to be deflected in the vertical plane. In practical applications, the target scanning direction can be input by the host computer or the user according to the current scanning requirements, or it can be automatically generated by the system according to a preset scanning strategy. For example, in all-solid-state lidar applications, the target scanning direction can be determined based on the spatial area to be detected at the current moment.

[0036] Array constraints refer to the physical and design limitations that must be met when determining the arrangement of grating antenna elements. Array constraints may include restrictions on the spacing between adjacent elements, restrictions on the overall array aperture size, and restrictions on the level of crosstalk between adjacent elements. The setting of array constraints needs to comprehensively consider factors such as chip manufacturing process capabilities, layout area limitations, and electromagnetic coupling effects between grating antenna elements to ensure that the optimized element position sequence is feasible in actual manufacturing and that severe crosstalk problems are not caused by excessively small element spacing.

[0037] In some applications, the target scanning direction can be a discrete angle point or a continuously changing sequence of angles. When a point-by-point scan of a field of view is required, the system can sequentially acquire multiple target scanning directions and execute subsequent steps for each target scanning direction, thereby achieving beam scanning within the entire field of view.

[0038] S102, based on the phase delay relationship between the array element position, array element phase and far-field direction angle, establishes a far-field light intensity model.

[0039] In a silicon-based optical phased array, each grating antenna element radiates a light field into free space, and the light fields radiated by different elements interfere and superimpose in the far-field space. Since the elements are positioned differently in the array, and the output phase of each element can be adjusted by a phase shifter, the light fields from different elements have different phase delays at a certain far-field azimuth angle. When the phase difference of these light fields satisfies the coherent superposition condition, a main lobe is formed in that direction; when the phase difference does not satisfy the coherent superposition condition, the light fields cancel each other out or partially cancel each other out, forming side lobes or a zero-radiation direction.

[0040] The far-field intensity model describes the intensity distribution at various directional angles in the far-field space under given element positions, element amplitude weights, and element phase control parameters. This model forms the basis for subsequent element position optimization and phase control parameter calculations, enabling quantitative evaluation of far-field beam quality under different element arrangement schemes and phase configurations. Using the far-field intensity model, different element position sequences and phase control schemes can be simulated and evaluated without actual chip fabrication, thus allowing for the selection of the optimal solution.

[0041] The phase delay relationship reflects the spatial phase accumulation law between the element position and the far-field azimuth angle. Specifically, for a given far-field azimuth angle, the light field radiated by elements farther from the reference point will experience an additional spatial propagation path compared to the light field radiated by elements closer to the reference point, thus resulting in a corresponding phase delay. This phase delay is related to the element position, the far-field azimuth angle, and the wavenumber in the exit medium. Based on this phase delay relationship, the radiation contributions of each element can be vector-superimposed in the far-field space to obtain the far-field intensity distribution.

[0042] S103, under array constraints, aims to suppress side lobes and grating lobes in non-target directions and improve the energy concentration of the main lobe. The position sequence of non-equidistant array elements is determined iteratively based on the far-field light intensity model.

[0043] The non-equal-spacing array element position sequence represents the arrangement of multiple grating antenna elements. Unlike traditional equal-spacing arrays, the spacing between adjacent elements in a non-equal-spacing array is not exactly the same. This non-periodic arrangement can effectively disperse the grating lobe energy caused by the periodic structure of the equal-spacing array, allowing the grating lobe energy to be dispersed over a wider angular range, thereby reducing the peak level of the grating lobes.

[0044] Determining the non-equidistant array element position sequence requires considering multiple optimization objectives and constraints simultaneously. Optimization objectives primarily include suppressing sidelobe and grating lobe levels in non-target directions, while simultaneously increasing energy concentration in the main lobe corner domain, concentrating more radiated energy near the target scanning direction. Constraints include physical size limitations of the array, manufacturing process requirements for minimum spacing, and limitations on crosstalk levels between adjacent elements. Through iterative optimization, the optimal element position sequence is sought that achieves the comprehensive optimization objectives while satisfying all constraints.

[0045] The iterative process of determining the non-equidistant element position sequence can be completed during the chip design phase. The optimized non-equidistant element position sequence can be used to guide the actual arrangement of grating antenna elements on the chip layout, ensuring that the chip after tape-out has the predetermined non-equidistant element layout. Since this layout has been optimized through simulation before chip manufacturing, there is no need to adjust the element positions after tape-out, which helps reduce R&D costs and shorten the R&D cycle.

[0046] S104: Based on the target elevation angle, determine the target operating wavelength of the input light; based on the target azimuth angle, the target operating wavelength, and the non-equidistant array element position sequence, determine the phase control quantity of each grating antenna element, and map the phase control quantity to the driving voltage of multiple phase shifters.

[0047] In silicon-based optical phased arrays, elevation beam deflection is achieved by altering the operating wavelength of the input light and utilizing the dispersion characteristics of the grating antenna elements. A definite correspondence exists between the emission angle of the grating antenna elements and the operating wavelength; therefore, the required target operating wavelength can be deduced from the target elevation angle. Azimuth beam deflection is achieved by adjusting the phase difference between adjacent grating antenna elements. After determining the non-equidistant element position sequence and the target operating wavelength, the required phase control amount for each element can be calculated based on the target azimuth angle, causing the far-field beams to coherently superimpose in the target azimuth direction to form the main lobe. The calculated phase control amount needs to be further mapped to the driving voltage of each phase shifter so that the phase shifters can be controlled by electrical signals to produce the required phase change.

[0048] Phase control parameters can be understood as the phase value that each grating antenna element should have in the emitted light field. This phase value determines the superposition of the radiated light fields of each element in the far-field space. By properly setting the phase control parameters of each element, a high-gain main lobe can be formed in the target azimuth direction of the far-field beam, while suppressing side lobes and grating lobes in other directions.

[0049] The driving voltage is an electrical signal applied to the phase shifter to control it and produce a predetermined phase change. Different phase shifters can receive different driving voltages, thus enabling independent phase control for each array element. The correspondence between the driving voltage and the phase change can be established in advance through simulation or experimental calibration, and determined during actual scanning by looking up tables or calculations.

[0050] S105 adjusts the input light to the target operating wavelength and distributes the adjusted input light to multiple silicon-based waveguides via a beam splitter network.

[0051] After determining the target operating wavelength, the output wavelength of the tunable laser is adjusted to ensure that the wavelength of the input light precisely corresponds to the target operating wavelength. The adjusted input light enters a beam splitter network, which uniformly distributes one input light into multiple output lights, each coupled to its corresponding silicon waveguide. The number of output channels of the beam splitter network corresponds to the number of grating antenna elements, ensuring that each grating antenna element receives a coherent input light. The beam splitting uniformity of the beam splitter network directly affects the amplitude consistency of the radiated light field of each element, and thus affects the sidelobe performance of the far-field radiation pattern.

[0052] In some embodiments, the beam splitter network can adopt a multimode interference beam splitter structure, or a star coupler, cascaded directional coupler structure, or other structures capable of multi-path beam splitting. Regardless of the structure used, the beam splitter network needs to ensure a stable phase relationship and as consistent an amplitude as possible between the output beams to meet the requirements of the phased array for coherent input beams.

[0053] S106 applies a driving voltage to multiple phase shifters to achieve azimuth scanning through the phase difference between adjacent grating antenna elements.

[0054] Phase shifters are mounted on multiple silicon-based waveguides, with each phase shifter corresponding to a grating antenna element. When a driving voltage is applied to a phase shifter, it changes the phase of the transmitted optical signal in the corresponding silicon-based waveguide, thereby changing the output phase of the corresponding grating antenna element. By applying different driving voltages to different phase shifters, a preset phase difference distribution can be formed between adjacent grating antenna elements. According to the far-field light intensity model, when the phase control quantity of each grating antenna element satisfies a linear distribution relationship with its position—that is, when the phase control quantity compensates for the spatial phase delay of each element in the target azimuth angle—the far-field beam will form a main lobe in the target azimuth angle direction, achieving azimuth beam deflection. By changing the magnitude of the driving voltage, the phase difference distribution can be changed, thereby achieving continuous scanning in the azimuth direction.

[0055] Azimuth scanning can be understood as the deflection process of a light beam in the horizontal plane. By sequentially changing the driving voltage of each phase shifter, the far-field main lobe can be continuously moved within a preset azimuth angle range, thereby achieving point-by-point or line-by-line scanning of the target's field of view. Due to the fast response speed of the phase shifters, azimuth scanning can be completed in a short time, which is beneficial for improving the scanning frame rate.

[0056] S107 utilizes the input light adjusted to the target operating wavelength and the dispersion of the grating antenna array elements to make the elevation output angle correspond to the target elevation angle, thereby achieving elevation scanning.

[0057] Grating antenna elements exhibit dispersive characteristics, meaning that light of different wavelengths has different propagation constants and exit angles within the grating antenna element. When the operating wavelength of the input light changes, the waveguide propagation constant changes accordingly, causing a deflection of the elevation exit angle of the grating antenna element. By precisely adjusting the input light to the target operating wavelength corresponding to the target elevation angle, the elevation exit angle can accurately correspond to the target elevation angle, thus achieving beam deflection in the elevation direction. Combining azimuth and elevation scanning allows for non-mechanical beam scanning in two-dimensional space.

[0058] Pitch scanning can be understood as the deflection process of a light beam in the vertical plane. Since pitch scanning depends on wavelength tuning, the scanning speed and accuracy are closely related to the tuning performance of the tunable laser. In practical applications, the output wavelength can be adjusted by controlling the drive current or temperature of the tunable laser, thereby controlling the pitch angle.

[0059] This embodiment first establishes a far-field light intensity model, iteratively optimizes the position sequence of non-equidistant array elements under array constraints, then determines the working wavelength and phase control quantity according to the target scanning direction, and finally achieves azimuth scanning through phase shifter driving voltage and elevation scanning through wavelength tuning. By combining non-equidistant array layout optimization with phase correction and wavelength tuning, it can effectively suppress side lobes and grating lobes and improve the main lobe energy concentration under the conditions of considering process constraints and crosstalk limitations, thus realizing two-dimensional non-mechanical beam scanning of silicon-based optical phased arrays.

[0060] The overall flow of the low sidelobe two-dimensional scanning method provided in this disclosure has been described above. Next, the key technical details involved in each step will be described in detail.

[0061] Please refer to Figure 2 , Figure 2 A flowchart illustrating the method for establishing a far-field light intensity model in an embodiment of this disclosure is shown. Figure 2 As shown, the far-field light intensity model established in S102 above, based on the phase delay relationship between the array element position, array element phase, and far-field direction angle, includes the following steps S201 to S202: S201, construct the array factor based on the amplitude weight, position and phase control of each grating antenna element.

[0062] The array factor is a mathematical expression describing the contribution of each element in the array to the far-field radiation. It reflects the combined influence of element position, amplitude weighting, and phase control on the far-field radiation pattern. Let the number of elements in the grating antenna be... , No. The amplitude weights of the grating antenna elements are: The location is The phase control quantity is The refractive index of the exit-side medium is The operating wavelength is The far-field direction angle is Then the wave number in the exiting medium is: ; The array factor can be expressed as: ; in, For array factor, The far-field direction angle, For the operating wavelength, The imaginary unit, Within the index item Indicates the first Each array element relative to the reference array element (usually the first element) has a far-field directional angle. Spatial phase delay on Indicates the first The phase control quantity introduced by the phase shifter for each array element. When the phase difference of the emitted light from adjacent array elements at a certain far-field directional angle is... When the value is an integer multiple of the array factor, the array factor reaches its maximum value in that direction, forming the main lobe or grating lobe.

[0063] Amplitude weight This reflects the amplitude differences in the radiated light fields of each array element. In practical systems, due to the limited beam splitting uniformity of the beam splitter network, the imperfect uniformity of waveguide transmission loss, and the slight differences in the coupling efficiency of the grating antenna, the radiation amplitudes of each array element are not exactly the same. By introducing amplitude weights into the far-field intensity model, the far-field radiation characteristics of the actual system can be simulated more accurately. Ideally, the amplitude weights of each array element can be considered equal, i.e.: ; In more accurate models, the amplitude weights can be set based on the output amplitude distribution of the beam splitter network or measured results.

[0064] Array element position Indicates the first The coordinates of each grating antenna element in the array arrangement direction. For a one-dimensional linear array, the element position can be represented by one-dimensional coordinates; for a two-dimensional area array, the element position can be represented by two-dimensional coordinates. In this embodiment, an azimuth-oriented one-dimensional linear array is used as an example for explanation, i.e., the element position... The array elements are distributed along the azimuth direction. The elements can be evenly spaced or non-evenly spaced. In a non-evenly spaced array, the spacing between adjacent elements is not exactly equal.

[0065] Phase control quantity Indicates the first Each array element has an adjustable phase introduced by a phase shifter. The range of values ​​for the phase control quantity is typically [value missing]. The phase control quantity can be continuously or discretely adjusted using a phase shifter. During the scanning process, the phase control quantity is updated according to the target azimuth angle, thereby changing the direction of the far-field main lobe.

[0066] S202 determines the far-field light intensity distribution based on the array factor and the field pattern of a single array element.

[0067] The far-field light intensity distribution depends not only on the array factor but also on the radiation characteristics of each individual grating antenna element. (Single element field pattern) This describes the radiation intensity distribution of a single grating antenna element at different far-field azimuth angles, determined by the specific structural parameters of the grating antenna (such as grating period, grating width, etching depth, etc.). According to antenna theory, the far-field light intensity distribution of the array is equal to the product of the square of the modulus of the single element's field pattern and the square of the modulus of the array factor: ; in, This reflects the envelope modulation effect of the radiation characteristics of a single grating antenna element on the far-field light intensity. This reflects the modulation effect of multi-element interference superposition on far-field light intensity. When the input power is fixed, this formula is used to characterize the relative far-field light intensity distribution in different scanning directions.

[0068] In practical calculations, the field pattern of a single element can be pre-calculated using full-wave simulation software (such as the finite-time difference method or the finite element method) or obtained through experimental measurement. In subsequent element position optimization and phase optimization processes, the field pattern of a single element is usually treated as a known quantity, and the far-field light intensity distribution is optimized mainly by adjusting the element positions and phase control quantities in the array factor.

[0069] Far-field direction angle The value range can be determined based on the actual scanning field of view. For example, when the azimuth scanning range is... At that time, it can be The calculation range is set to Or a wider range, to fully assess the distribution of the main lobe, side lobes, and grating lobes. During optimization, attention is typically paid to the side lobe levels outside the main lobe angular domain and the possible locations of grating lobes to ensure that there are no interfering high-level side lobes within the scanning field of view.

[0070] This disclosure establishes a complete far-field light intensity model by constructing an array factor and combining it with the field pattern of a single array element. This model can quantitatively describe the light intensity distribution at various directional angles in the far-field space under different array element positions, amplitude weights, and phase control parameters. This model provides a reliable theoretical basis for subsequent optimization of non-equidistant array element positions and calculation of phase control parameters, enabling the optimization process to be performed efficiently in a simulation environment without repeated tape-out verification. This helps reduce design costs and shorten the development cycle.

[0071] Please refer to Figure 3 , Figure 3 This diagram illustrates a flowchart of a method for iteratively determining the position sequence of non-equidistant array elements according to an embodiment of this disclosure. Figure 3 As shown, in S103 above, under array constraints, with the goal of suppressing sidelobes and grating lobes in non-target directions and increasing the energy concentration of the main lobe, the non-equally spaced array element position sequence is determined iteratively based on the far-field light intensity model, including the following steps S301 to S303: S301, construct an evaluation function based on the far-field light intensity distribution.

[0072] The evaluation function is used to quantitatively assess the far-field radiation performance of candidate element position sequences and is the objective function in the iterative optimization process. The evaluation function includes at least a peak sidelobe term and a main lobe energy concentration term, and also includes at least one of an element crosstalk penalty term and a constraint penalty term.

[0073] Specifically, the array constraints include adjacent element spacing constraints, array aperture constraints, and element crosstalk constraints. Among them, the adjacent element spacing constraint requires the spacing between any two adjacent elements. satisfy: ; in, Minimum allowable spacing, For the maximum allowable spacing, For the first Each element and the first The spacing between array elements. Array aperture constraints require a certain total aperture of the array. satisfy: ; in, , The maximum permissible array aperture is specified. Element crosstalk constraints require that mode coupling crosstalk between adjacent silicon waveguides does not exceed a preset threshold.

[0074] The evaluation function can be expressed as: ; in, ( The weighting factor () is a non-negative weighting coefficient used to adjust the relative importance of each optimization term. The value of the weighting factor can be adjusted according to specific design requirements. For example, when the design focus is on reducing sidelobe levels, the weighting factor can be increased. The value of can be increased when the design focus is on improving the energy concentration of the main lobe. The value of can be increased when crosstalk control is critical. The value of .

[0075] Peak sidelobe term Determined based on the maximum light intensity outside the main lobe angular domain, i.e., the peak-to-side-lobe ratio: ; in, The main lobe angle domain, i.e., the area surrounding the target azimuth. angular domain; The sidelobe angular domain refers to the angular domain outside the main lobe angular domain. When it needs to be characterized in decibels, the peak sidelobe level can be written as: ; A lower peak-to-sidelobe ratio indicates a lower amplitude of the largest sidelobe outside the main lobe relative to the main lobe, resulting in stronger anti-interference capability of the far-field pattern. In low-sidelobe designs, it is generally desirable to control the peak-to-sidelobe ratio at a low level, for example... Below, even the following.

[0076] Main lobe energy concentration term Determined based on the energy percentage within the main lobe corner region: ; in, To calculate the angular domain, a higher main lobe energy concentration indicates that more radiation energy is concentrated near the target scanning direction, resulting in better beam quality. The range of main lobe energy concentration values ​​is... When it approaches This indicates that almost all the radiated energy is concentrated in the main lobe angular domain.

[0077] Array element crosstalk penalty item It can be represented as: ; in, The crosstalk function is established based on the simulation results or experimental calibration results of mode coupling between adjacent silicon-based waveguides, and is used to characterize the spacing between adjacent array elements. The crosstalk level at that time. When the spacing between adjacent array elements is small, the mode coupling between waveguides increases, and the crosstalk level rises. A crosstalk penalty term can be used to penalize excessively small array element spacing. Crosstalk function It typically decreases monotonically as the spacing increases, which can be obtained through coupled-mode theory simulation or experimental measurement.

[0078] Constraints and penalties The method used to penalize violations of array constraints can be expressed as: ; Among them, the element spacing constraint penalty term It can be represented as: ; Array aperture constraint penalty term It can be represented as: ; When the spacing between adjacent array elements or the array aperture violates the constraints, the corresponding penalty term takes a positive value, which increases the evaluation function and guides the optimization process to search in the direction that satisfies the constraints. When the constraints are satisfied, the corresponding penalty term is zero and will not have any additional effect on the evaluation function.

[0079] S302 aims to reduce the peak sidelobe term and increase the main lobe energy concentration term by iteratively updating the candidate array element position sequence.

[0080] After constructing the evaluation function, the optimization process aims to reduce the evaluation function value by iteratively updating the candidate element position sequence. In each iteration, based on the current candidate element position sequence, the corresponding far-field light intensity distribution is calculated using the far-field light intensity model. Peak sidelobe terms, main lobe energy concentration terms, element crosstalk penalty terms, and constraint penalty terms are extracted, and the evaluation function value is calculated. Subsequently, according to the update strategy of the optimization algorithm, the candidate element position sequence is adjusted to generate a new candidate element position sequence, and the evaluation function value is recalculated. This process is repeated iteratively until the evaluation function converges or the preset number of iterations is reached.

[0081] In iterative optimization, one or more of swarm intelligence optimization algorithms or heuristic optimization algorithms can be employed. For example, particle swarm optimization (PSO), genetic algorithms, non-dominated sorting genetic algorithms, or simulated annealing algorithms can be used. Different optimization algorithms have different search strategies and convergence characteristics, and can be selected based on the specific optimization problem size and computational resources. PSO, by simulating bird flock foraging behavior, updates the position of candidate solutions using individual and group experience, making it suitable for continuous optimization problems with relatively fast convergence. Genetic algorithms simulate biological evolution through selection, crossover, and mutation operations, making them suitable for discrete or mixed optimization problems with strong global search capabilities. Non-dominated sorting genetic algorithms are suitable for multi-objective optimization problems, capable of finding Pareto optimal solutions among multiple optimization objectives. Simulated annealing, by simulating the annealing process of metal, accepts inferior solutions with a certain probability, effectively avoiding local optima, but its convergence speed is relatively slow. In practical applications, multiple algorithms can also be combined to leverage their respective advantages.

[0082] S303 determines the candidate array element position sequence that satisfies the array constraints as a non-equally spaced array element position sequence.

[0083] After the iterative optimization process is completed, the sequence with the optimal evaluation function value is selected from the candidate element position sequences that satisfy the array constraints, and this sequence is taken as the final non-equidistant element position sequence. In this non-equidistant element position sequence, the spacing between at least two adjacent elements is different, that is, the element arrangement is not periodic. This sequence will be used to guide the actual arrangement of the grating antenna elements on the chip.

[0084] After determining the non-equidistant array element position sequence, further verification and analysis can be performed on this sequence. For example, the far-field light intensity distribution can be recalculated based on this sequence to check whether indicators such as peak sidelobe level, main lobe energy concentration, and the presence of grating lobes meet the design requirements. If the indicators do not meet the requirements, the weighting coefficients or constraints can be adjusted and the optimization can be performed again. After successful verification, the non-equidistant array element position sequence can be used for subsequent phase control quantity calculations and chip layout design.

[0085] This disclosure discloses an embodiment that constructs a comprehensive evaluation function including a peak sidelobe term, a main lobe energy concentration term, an element crosstalk penalty term, and a constraint penalty term. Under the conditions of satisfying adjacent element spacing constraints, array aperture constraints, and element crosstalk constraints, iterative optimization is used to determine the non-equidistant element position sequence. This approach can effectively suppress sidelobes and grating lobes in non-target directions and improve the main lobe energy concentration, while considering practical constraints such as layout size, process spacing, and element crosstalk, thus laying the foundation for subsequent high-performance two-dimensional scanning.

[0086] Please refer to Figure 4 , Figure 4 This diagram illustrates a flowchart of a method for iteratively updating the candidate array element position sequence in an embodiment of this disclosure. Figure 4 As shown, the iterative update of the candidate array element position sequence in S302 above includes the following steps S401 to S403: S401 uses the equally spaced array element positions as the initial array element positions.

[0087] Before optimization, the initial element position sequence needs to be determined. Equally spaced element positions are used as the initial positions; that is, within the array aperture range, all grating antenna elements are uniformly arranged with equal spacing. The initial position sequence of the equally spaced array has clear physical meaning and symmetry, serving as a reasonable starting point for the optimization process. The spacing of the equally spaced array can be initially determined based on the array aperture and the number of elements; that is, the initial spacing is: ; in, The initial spacing is set to an equal spacing. The selection of the initial spacing needs to balance lobe suppression and crosstalk control. When the initial spacing is too large, the equal-spacing array will produce noticeable lobes, requiring significant positional perturbations during optimization to disperse the lobe energy. When the initial spacing is too small, crosstalk between array elements is strong, requiring the spacing to be increased to reduce crosstalk during optimization. Therefore, the initial spacing is usually selected as an intermediate value within the allowable range of the manufacturing process.

[0088] S402, keeping the positions of the two end array elements fixed, introduce position perturbation amounts into at least some of the grating antenna array elements other than the end array elements to obtain a candidate array element position sequence.

[0089] Based on the initial positions of the array elements at equal intervals, keep the first array element ( ) and the last array element ( The positions of the array elements are kept fixed, and positional perturbations are introduced into the intermediate array elements, excluding the end elements. The positional perturbation represents the offset of each intermediate element relative to its initial, equally spaced position, and can be a positive value (offset towards increasing array aperture) or a negative value (offset towards decreasing array aperture). By introducing positional perturbations, the equally spaced array is adjusted to a non-equally spaced array, resulting in a sequence of candidate array element positions.

[0090] The reason for keeping the end element positions fixed is that the position of the end elements determines the total aperture of the array, which is usually limited by the chip layout size. Fixing the end elements ensures that the total array aperture does not exceed the allowable range during optimization, while reducing the number of optimization variables and improving optimization efficiency. The introduction of positional perturbations can be random or based on a specific strategy. For example, perturbations can be introduced only on some of the middle elements, or perturbations of different ranges can be introduced on elements at different positions.

[0091] The range of values ​​for the position perturbation needs to be limited by the spacing between adjacent array elements. Specifically, the spacing between any adjacent array elements must satisfy: ; in, Minimum allowable spacing, The maximum permissible spacing is determined by the minimum linewidth of the manufacturing process and the crosstalk requirements between adjacent waveguides; the maximum permissible spacing is determined by the array aperture limitation and the requirement to avoid excessively large grating lobes.

[0092] S403, under the conditions of satisfying the adjacent element spacing constraints, array aperture constraints and element crosstalk constraints, iteratively updates the position perturbation amount until the evaluation function converges or reaches the preset number of iterations.

[0093] During the optimization iteration process, after each update of the position perturbation, it is necessary to check whether the updated array element position sequence satisfies all constraints. Specifically, it is necessary to verify whether the spacing between adjacent array elements is within the specified range. Within the range, does the total aperture of the array not exceed... And whether the crosstalk level between adjacent array elements is within an acceptable range. For combinations of positional perturbations that do not meet the constraints, they can be reflected in the evaluation function through constraint penalty terms, or the combination can be directly discarded and regenerated.

[0094] The optimization process iterates continuously until the change in the evaluation function value is less than a preset convergence threshold, or the preset maximum number of iterations is reached. After convergence, the current array element position sequence is the non-equidistant array element position sequence that satisfies the constraints.

[0095] In an executable optimization example, first in the preset... and Multiple array element position sequences are randomly initialized within the range; then, the far-field light intensity distribution corresponding to each position sequence is calculated according to the array factor formula and the far-field light intensity distribution formula, the maximum side lobe outside the target main lobe window is extracted, and the evaluation function is calculated by combining the main lobe energy ratio and crosstalk penalty term; then, the candidate position sequence is updated using the optimization algorithm until the evaluation function converges or the preset number of iterations is reached.

[0096] This embodiment of the present disclosure, by taking the positions of equally spaced array elements as the starting point, fixing the end array elements, introducing position perturbation amounts to the middle array elements, and iteratively optimizing under constraints, can effectively explore the design space of non-equally spaced array element arrangement while ensuring that the array aperture does not exceed the limit, and obtain a non-equally spaced array element position sequence with excellent sidelobe and grating lobe suppression effects.

[0097] The determination method for the position sequence of non-equidistant array elements has been explained in detail above. Next, with reference to specific embodiments, the determination method for the phase control quantities of each grating antenna element will be described in detail.

[0098] Please refer to Figure 5 , Figure 5 This diagram illustrates a flowchart of a method for determining the phase control amount of each grating antenna element in an embodiment of this disclosure. Figure 5 As shown, in the above S104, the phase control quantity of each grating antenna element is determined according to the target azimuth angle, the target operating wavelength, and the non-equidistant array element position sequence, including the following steps S501 to S503.

[0099] S501, based on the target azimuth, target operating wavelength, and non-equidistant array element position sequence, calculate the... The ideal phase of each grating antenna element.

[0100] After the non-equidistant array element position sequence is determined, the position of each grating antenna element is fixed. To ensure the far-field beam is aligned with the target azimuth... The main lobe is formed by coherent superposition in the direction of the radiation. It is necessary to calculate the ideal phase of each array element. The ideal phase refers to the phase control amount required to ensure that the radiated light fields of all array elements are in phase in the target azimuth direction, without considering any error factors. The ideal phase of a grating antenna element can be expressed as: ; in, The target azimuth angle, For the target operating wavelength, For the first The position of each grating antenna element The wave number in the exit medium. For the first The ideal phase of the nth grating antenna element. The physical meaning of this formula is that the nth... Each element in the far-field direction angle The spatial phase delay on is To ensure that the radiated light field of this array element is in phase with that of the reference array element in the target direction, it is necessary to apply... The phase control quantity is used to compensate for the spatial phase delay.

[0101] The calculation of the ideal phase is based on the phase delay relationship in the far-field light intensity model. When all array elements are set with phase control values ​​according to the above formula, the array factor at the target azimuth angle... The direction reaches its maximum value, and the main lobe in the far-field light intensity distribution points to the target azimuth. At this point, if processing errors and other non-ideal factors are not considered, the far-field radiation pattern will reach its theoretical optimal state.

[0102] S502 aims to further reduce the non-target direction sidelobes and grating lobes obtained based on the far-field light intensity model, and searches for phase correction near the ideal phase.

[0103] In practical systems, due to factors such as fabrication errors, optical path transmission errors, and thermal crosstalk, the actual output phase of each array element may deviate from the ideal phase. Fabrication errors include waveguide width deviations, grating etching depth deviations, and positional deviations; optical path transmission errors include inconsistent waveguide transmission loss and phase accumulation deviations; thermal crosstalk includes the thermal coupling effect between adjacent phase shifters. These phase deviations lead to increased sidelobe levels in the far-field pattern, reducing beam quality.

[0104] To compensate for the aforementioned phase deviation, a phase correction is searched for near the ideal phase. The search process for phase corrections can be based on a far-field intensity model. This involves adjusting the phase of each array element within a preset range near the ideal phase, with the goal of further reducing sidelobes and grating lobes in non-target directions, to find the optimal combination of phase corrections for the far-field intensity distribution. This search process can also be implemented using optimization algorithms, such as particle swarm optimization, genetic algorithms, or simulated annealing.

[0105] The search range for the phase correction can be determined based on the magnitude of the actual phase deviation. For example, the search range can be set to... or An excessively large search range may increase the difficulty of optimization, while an excessively small search range may fail to adequately compensate for phase deviation. During the optimization process, the search range can be gradually reduced to improve optimization accuracy.

[0106] S503, based on the ideal phase and the phase correction amount, obtains the corrected phase control amount.

[0107] After determining the phase correction amount, the ideal phase is superimposed with the phase correction amount, and the phase control amount is limited to a certain value through modulo operation. Within the range, the corrected phase control quantity is obtained: ; in, For the first Phase control quantity after correction for each grating antenna element For the first Phase correction amount of each grating antenna element This represents the modulo operation, which calculates the remainder of the sum of the ideal phase and the phase correction divided by 2π, ensuring the phase value falls within the range... Within the range, to avoid phase values ​​exceeding... This results in phase ambiguity. The corrected phase control quantity. It contains both the ideal phase information required for coherent superposition of far-field beams in the target azimuth direction and correction information for compensating for phase deviations caused by processing errors, optical path transmission errors and thermal crosstalk. This enables more accurate control of the output phase of each array element and further reduces the sidelobe and grating lobe levels in non-target directions.

[0108] During phase optimization, the array layout (i.e., the sequence of non-equidistant element positions) remains fixed, with only the phase correction as the optimization variable. This two-stage optimization approach (optimizing element positions first, then phase) reduces the dimensionality of the optimization problem and improves the convergence speed. Furthermore, since the element positions have already been optimized, phase optimization can further enhance far-field performance based on a better element layout.

[0109] The embodiments disclosed herein search for a phase correction amount based on an ideal phase and superimpose the two to obtain the final phase control amount. This can effectively compensate for phase deviations caused by processing errors, optical path transmission errors, and thermal crosstalk, further improve the quality of the far-field beam, reduce the sidelobe and grating lobe levels in non-target directions, and enable the silicon-based optical phased array to maintain a low sidelobe level during scanning.

[0110] Please refer to Figure 6 , Figure 6 This diagram illustrates a flow chart of a method for mapping phase control quantities to drive voltages according to an embodiment of this disclosure. Figure 6 As shown, in the above S104, the phase control quantity is mapped to the driving voltage of multiple phase shifters, wherein the multiple phase shifters are multiple thermo-optical phase shifters, including the following steps S601 to S602: S601, based on simulation or calibration results, establish a phase voltage mapping table between the phase change and driving voltage of each thermo-optical phase shifter.

[0111] Thermo-optic phase shifters utilize the thermo-optic effect of silicon to alter the effective refractive index of a silicon-based waveguide, thereby changing the phase of the optical signal transmitted through the waveguide. Specifically, the thermo-optic phase shifter includes metal electrodes positioned adjacent to the corresponding silicon-based waveguide. When a driving voltage is applied to the metal electrodes, Joule heating is generated, causing a local temperature increase in the silicon-based waveguide. Due to the thermo-optic effect of silicon, the increased temperature leads to a change in the effective refractive index of the silicon-based waveguide, thus altering the transmission phase of the optical signal. The phase change of each thermo-optical phase shifter satisfies: ; in, For the target operating wavelength, For the first The effective refractive index change of a silicon-based waveguide under driving voltage. For the first The effective phase shift length of the thermo-optical phase shifter. Within a small temperature rise range, the change in effective refractive index is approximately linear with the temperature change, i.e.: ; in, The temperature coefficient of the effective refractive index of a silicon-based waveguide. This represents the change in temperature.

[0112] A phase-voltage mapping table is used to establish the correspondence between the phase changes of each thermo-optical phase shifter and the driving voltage. This mapping table can be obtained through thermo-electro-optical coupling simulation, i.e., by simulating the temperature distribution, effective refractive index change, and phase change of the silicon-based waveguide under different driving voltages, establishing the correspondence between phase change and driving voltage. Alternatively, this mapping table can be obtained through experimental calibration after chip fabrication, i.e., by measuring the actual phase changes of each thermo-optical phase shifter under different driving voltages using methods such as interferometry, thereby establishing the mapping table. Due to potential process variations between different thermo-optical phase shifters, the phase-voltage mapping table is usually established separately for each thermo-optical phase shifter to improve the accuracy of phase control.

[0113] The phase voltage mapping table can be stored in the controller as a lookup table. The horizontal axis of the lookup table represents the phase control quantity, and the vertical axis represents the driving voltage. During the actual scanning process, the controller looks up the corresponding driving voltage based on the target phase control quantity and outputs it through a multi-channel voltage controller. To improve phase control accuracy, the lookup table can be set with sufficiently dense sampling points, and linear interpolation can be used between adjacent sampling points.

[0114] S602 retrieves the corresponding driving voltage from the phase voltage mapping table based on the phase control quantity of each grating antenna element.

[0115] After determining the phase control values ​​of each grating antenna element Next, based on the phase voltage mapping table, the driving voltage corresponding to each phase control quantity is found. That is, the first The driving voltage of the first thermo-optical phase shifter. Specifically, for the first... A thermo-optical phase shifter, based on its target phase control quantity The closest driving voltage value is found in the corresponding phase voltage mapping table and used as the driving voltage for the thermo-optical phase shifter. The found driving voltage is applied to the corresponding metal electrode through a multiplexer voltage controller, causing the thermo-optical phase shifter to produce the required phase change, thereby causing each grating antenna element to emit light signals according to the preset phase control amount.

[0116] The range of the driving voltage can be determined based on the design parameters of the thermo-optical phase shifter and the thermo-optical characteristics of the silicon-based waveguide. As an example, the driving voltage range can be set to... to This range ensures sufficient phase tuning range while avoiding excessive power consumption in the thermo-optical phase shifter or excessive temperature in the silicon waveguide due to excessively high driving voltage. In practical applications, the driving voltage range can also be adjusted according to the phase shift length of the thermo-optical phase shifter, the resistance of the metal electrodes, and heat dissipation conditions.

[0117] This embodiment of the present disclosure can achieve precise phase control of the thermo-optical phase shifter by establishing a phase voltage mapping table and calling the corresponding driving voltage according to the phase control quantity, so that the output phase of each grating antenna element accurately corresponds to the preset phase control quantity, providing a reliable phase control basis for azimuth scanning.

[0118] The determination of the phase control quantity and the mapping of the driving voltage have been explained in detail above. Next, the method for determining the target operating wavelength will be described. The process of determining the target operating wavelength of the input light based on the target elevation angle in S104 above is as follows.

[0119] The relationship between the elevation emission angle of a grating antenna element and the operating wavelength is determined by the grating phase matching relationship. Under a chosen diffraction direction, the elevation emission angle of the grating antenna element... The following phase matching relationship is satisfied: ; in, Let be the waveguide propagation constant, and , The effective refractive index of the waveguide; For free space wavenumber; The refractive index of the exit-side medium is typically the refractive index of air (approximately...). ); The elevation angle is the angle of attack. For diffraction orders; The period is the grating period.

[0120] The physical meaning of this formula is that the guided mode transmitted in the grating antenna array elements undergoes diffraction under the periodic perturbation of the grating structure. When the difference between the propagation constant of the guided mode and the wave vector component of the diffracted light in free space along the grating direction is equal to an integer multiple of the grating reciprocal lattice vector, the phase matching condition is satisfied, and light couples and radiates from the waveguide into free space. This is because the waveguide propagation constant... It is a function of wavelength; when the wavelength of the input light changes, the elevation-to-emitter angle that satisfies the phase-matching condition is... This also changes accordingly, thus achieving beam deflection in the pitch direction.

[0121] After determining the target's pitch angle, the pitch direction can be adjusted to the launch angle. Set the value to the corresponding target elevation angle, and then deduce the required target operating wavelength through the grating phase matching relationship. Due to the waveguide propagation constant The relationship with wavelength is usually non-linear, and the target operating wavelength can be determined by numerical solution or table lookup. After determining the target operating wavelength, adjusting the output wavelength of the tunable laser to that target operating wavelength will make the elevation output angle correspond to the target elevation angle, thus achieving elevation scanning.

[0122] As a control target, the center wavelength of the input light can be set to... The wavelength tuning range can be set to ,Right now to Within this wavelength tuning range, a certain range of elevation-direction exit angle deflection can be achieved through the dispersion characteristics of the grating antenna. The elevation scanning range is closely related to the grating period, the effective refractive index of the waveguide, and the wavelength tuning range; the required elevation scanning range can be obtained by rationally designing the grating parameters.

[0123] Please refer to Figure 7 , Figure 7 This diagram illustrates the principle of two-dimensional scanning achieved through the coordinated use of phase adjustment and wavelength tuning in an embodiment of this disclosure. Figure 7 As shown, azimuth scanning is achieved by changing the phase difference between adjacent grating antenna elements. Specifically, by adjusting the driving voltage of each thermo-optical phase shifter, the output phase difference between adjacent elements is changed, causing the far-field main lobe to deflect within the azimuth plane. As a control target, the azimuth scanning range can be set to... Pitch scanning is achieved by changing the operating wavelength of the input light. Specifically, utilizing the dispersion characteristics of the grating antenna elements, when the input light wavelength changes, the phase matching condition of the grating changes, causing a corresponding change in the pitch exit angle, thereby achieving beam deflection within the pitch plane. As a control target, the input light wavelength can be... The beam can be adjusted within a certain range, and the elevation exit angle can be changed by using grating dispersion. The azimuth phase adjustment and the elevation wavelength tuning are independent of each other but work together to achieve non-mechanical beam scanning in two-dimensional space.

[0124] Please refer to Figure 8 , Figure 8 This diagram illustrates a non-equally spaced grating antenna array and independent phase modulation in an embodiment of this disclosure. (See attached diagram.) Figure 8 As shown, the non-equidistant grating antenna array includes The grating antenna array element, the first The position of each array element is recorded as The spacing between adjacent array elements is . Figure 8 The diagram uses eight array elements as an example, with the positions of each element as follows: The spacing between adjacent array elements is as follows: The element spacing is not all equal, but is determined during the structural optimization stage under constraints of manufacturing dimensions, inter-element crosstalk, and array aperture, allowing for different spacings between adjacent elements. A thermo-optical phase shifter is placed adjacent to each silicon-based waveguide, and each thermo-optical phase shifter independently applies the phase. This allows for independent control of the output phase of each element. The thermo-optical phase shifter includes metal electrodes. When a driving voltage is applied, the metal electrodes generate Joule heating and change the local temperature of the silicon-based waveguide, causing a change in the effective refractive index, thereby altering the output phase of the corresponding element. By independently controlling the phase of each element and combining this with a non-equidistant element arrangement, a low-sidelobe beam pattern can be formed in the far field.

[0125] To illustrate the impact of element spacing on the far-field radiation pattern, simulation analysis can be performed on the far-field radiation pattern under different equidistant element spacings. Please refer to... Figure 9 , Figure 9 This diagram illustrates a comparison of directional field strength under different element spacings in embodiments of this disclosure. The diagram serves as a schematic simulation result illustrating the influence of element spacing on the far-field radiation pattern. Figure 9 As shown, the element spacing is , and The comparison results of the directional field intensity at different times show that the sidelobes and additional peaks in the far-field pattern change with the element spacing. When the element spacing increases to a certain value... At that time, a more obvious additional peak, namely the grating lobe, appeared in the figure. This further verifies the necessity and effectiveness of using a non-equidistant array element position sequence to reduce the impact of periodic grating lobes on the effective field of view.

[0126] Regarding the grating antenna structure, the grating period can be set to... The grating width can be set to The etching depth can be set to A local subarray can be simulated with eight elements across the entire wavelength to study the effects of grating period, grating width, and element spacing on far-field radiation. The number of elements in the complete scanning system can be set to 16 or more. The azimuth scanning range can be set to... Pitch scanning is achieved by changing the operating wavelength of the input light, which can be... Adjustable within the range, and the pitch exit angle is changed by using grating dispersion.

[0127] Please refer to Figure 10 , Figure 10 The far-field radiation pattern and far-field longitudinal section view of the grating antenna array in an embodiment of this disclosure are shown. Figure 10 As shown, the far-field radiation pattern reflects the light intensity distribution of the grating antenna array in the far-field space, while the far-field longitudinal profile reflects the distribution characteristics of the far-field light intensity in the elevation direction. Through the far-field radiation pattern and the far-field longitudinal profile, the main lobe pointing, side lobe levels, and grating lobe distribution can be observed intuitively, thereby verifying the optimization effect of the non-equidistant element position sequence and phase control quantities. The simulation results show that after using the non-equidistant element position sequence combined with phase correction, the side lobe level in the far-field radiation pattern is effectively suppressed, and the main lobe energy concentration is improved.

[0128] To facilitate understanding of the overall execution process of the low sidelobe two-dimensional scanning method provided in this disclosure, the scanning control flow is explained below with reference to a specific application example.

[0129] In an executable scanning control process, the target scanning angle and array constraints are first input. The target scanning angle includes the target azimuth and elevation angles, and the array constraints include minimum and maximum spacing between adjacent elements, array aperture, and element crosstalk limitations. Subsequently, an array factor and far-field light intensity distribution model are established, i.e., a far-field light intensity model is constructed based on the array factor formula and the far-field light intensity distribution formula. Next, structural optimization is performed, i.e., an evaluation function is constructed using the peak-to-sidelobe ratio, main lobe energy ratio, crosstalk penalty term, and constraint penalty term, and the non-equidistant element position sequence is solved through iterative optimization. After structural optimization, phase optimization is performed, i.e., under a fixed array layout, the ideal phase and phase correction amount are solved for the target azimuth angle to obtain the corrected phase control amount. Then, the driving voltages for each path are generated based on the phase voltage mapping table. In the actual scanning phase, coherent optical signals are input to each element via a beam splitter network, and independent driving voltages are applied. Azimuth scanning is achieved through phase adjustment; simultaneously, the input wavelength is changed, and elevation scanning is achieved using grating dispersion. This process combines structural optimization and phase optimization in stages, and integrates phase adjustment and wavelength tuning in actual scanning, enabling stable low-sidelobe two-dimensional beam scanning.

[0130] During the structural optimization phase, the array element position sequence is... As optimization variables, an evaluation function is constructed using the peak-to-sidelobe ratio, main lobe energy proportion, crosstalk penalty term, and constraint penalty term. The phase optimization stage... After fixing, for the target azimuth angle Solving for the phase correction This reduces sidelobes in non-target directions and compensates for phase errors. This two-stage optimization approach reduces the complexity of the optimization problem and improves convergence efficiency.

[0131] Based on the same inventive concept, this disclosure also provides a low-sidelobe two-dimensional scanning system for a non-equidistant silicon-based optical phased array, used to execute the low-sidelobe two-dimensional scanning method for a non-equidistant silicon-based optical phased array provided in this disclosure. Since the principle by which this system embodiment solves the problem is similar to that of the above-described method embodiment, the implementation of this system embodiment can refer to the implementation of the above-described method embodiment, and repeated details will not be elaborated further.

[0132] Please refer to Figure 11 , Figure 11 This diagram illustrates the structure of a low-sidelobe two-dimensional scanning system based on a non-equidistant silicon-based optical phased array, according to an embodiment of this disclosure. Figure 11 As shown, the system includes a tunable laser, a beam splitter network, multiple silicon-based waveguides, multiple phase shifters (i.e., independent thermo-optical phase shifter arrays), multiple grating antenna elements (i.e., non-equally spaced grating antenna arrays), multiple voltage controllers, and a controller.

[0133] Specifically, the input light in the communication optical band of the tunable laser output is set to a center wavelength of... The input light is distributed to multiple silicon-based waveguides via a beam splitter network and propagates along different optical paths to the corresponding grating antenna elements. Each of the multiple silicon-based waveguides is equipped with a thermo-optical phase shifter, and the array of thermo-optical phase shifters independently adjusts the phase of each optical signal. The elements in the non-equidistant grating antenna array are arranged according to an optimized non-equidistant position sequence, radiating the phase-adjusted optical signal into free space. A multi-channel voltage controller provides independent drive voltages to each thermo-optical phase shifter. The controller is connected to both the tunable laser and the multi-channel voltage controller to determine the operating wavelength of the input light and the drive voltage of each thermo-optical phase shifter based on the target scanning direction, achieving coordinated output of wavelength control and drive parameters.

[0134] Multiple grating antenna elements are arranged in a non-equidistant element position sequence. In this non-equidistant element position sequence, at least two adjacent elements have different spacing. The non-equidistant element position sequence is pre-determined based on a far-field light intensity model and under array constraints, with the goal of suppressing sidelobes and grating lobes in non-target directions. The method for determining the non-equidistant element position sequence can be found in the detailed description of the aforementioned method embodiments, and will not be repeated here.

[0135] Tunable lasers are used to output input light to a beam splitter network. A tunable laser allows the output wavelength to be adjusted within a preset wavelength range. As an example, the center wavelength of a tunable laser can be set to... The wavelength tuning range can be set to Tunable lasers can be produced by combining distributed feedback lasers with temperature tuning, or by using external cavity tunable lasers or other laser structures capable of wavelength tuning.

[0136] Beam splitters are used to distribute input light to multiple silicon waveguides. A beam splitter uniformly distributes one input beam into multiple output beams, each of which is coupled to its corresponding silicon waveguide. The number of output channels in the beam splitter corresponds to the number of grating antenna elements. The beam splitting uniformity of the beam splitter directly affects the amplitude consistency of the radiated light field of each element, significantly influencing the sidelobe performance of the far-field radiation pattern.

[0137] Multiple phase shifters are disposed on multiple silicon-based waveguides, each corresponding to multiple grating antenna elements. Each phase shifter is used to adjust the phase of the transmitted optical signal in the corresponding silicon-based waveguide, thereby changing the output phase of the corresponding grating antenna element. In the case of thermo-optical phase shifters, each thermo-optical phase shifter includes a metal electrode disposed adjacent to the corresponding silicon-based waveguide. By applying a driving voltage to the metal electrode to generate Joule heating, the local temperature and effective refractive index of the silicon-based waveguide are changed, thereby achieving phase adjustment.

[0138] A multi-channel voltage controller is connected to multiple phase shifters to apply independent drive voltages to them. The controller can simultaneously output multiple independent drive voltage signals, each applied to its corresponding phase shifter, enabling independent control of each shifter. The number of channels in the multi-channel voltage controller corresponds to the number of phase shifters, and each drive voltage can be adjusted independently.

[0139] The controller is connected to both the tunable laser and the multiplex voltage controller. The controller receives the target scanning direction, determines the target operating wavelength of the tunable laser based on the target elevation angle in the scanning direction, determines the phase control quantity of each phase shifter based on the target azimuth angle, target operating wavelength, and the non-equidistant array element position sequence in the scanning direction, and converts the phase control quantity into independent driving voltages. This allows for azimuth scanning through the phase difference between adjacent grating antenna elements, and elevation scanning through tuning the target operating wavelength.

[0140] In some embodiments, the controller may include an array layout parameter storage module, a phase voltage mapping table storage module, and a scan control module. The array layout parameter storage module stores the sequence of non-equidistant array element positions and related array parameter information, such as element position coordinates, spacing between adjacent elements, and array aperture. The phase voltage mapping table storage module stores the phase voltage mapping table for each thermo-optical phase shifter, which can be obtained through simulation or calibration. The scan control module calls the corresponding phase control quantity based on the target azimuth angle and the corresponding input light operating wavelength based on the target elevation angle, thereby achieving real-time scan control of the silicon-based optical phased array. The scan control module can quickly generate driving voltage and wavelength control signals based on a lookup table to meet the requirements of real-time scanning.

[0141] The non-equidistant silicon-based optical phased array low-sidelobe two-dimensional scanning system provided in this disclosure suppresses sidelobes and grating lobes through the design of the non-equidistant array element position sequence, achieves azimuth beam deflection by generating a controllable phase difference through multiple independent thermo-optical phase shifters, and achieves elevation beam deflection through wavelength tuning and grating dispersion, thereby realizing two-dimensional beam scanning without the use of mechanical scanning components. This system is suitable for silicon-based photonic integrated platforms and can be used in applications such as all-solid-state lidar, optical communication, laser imaging, and target detection.

[0142] Please refer to Figure 12 , Figure 12 A schematic diagram of the structure of the multimode interferometric beam splitter network in an embodiment of this disclosure is shown. Figure 12 As shown, in some embodiments, the beam-splitting network is a multimode interferometric beam-splitting network. The multimode interferometric beam-splitting network includes multiple cascaded... Multimode interference beam splitter unit. Each The multimode interferometric beam splitter works based on the self-imaging effect in the multimode waveguide.

[0143] Each The multimode interferometric beam splitter unit includes a multimode interferometer region, an input waveguide, and an output waveguide. At least one of the input waveguide and the output waveguide is provided with a tapered transition section. The tapered transition section is used to improve the mode matching of the input light from the single-mode waveguide to the multimode interferometer region and from the multimode interferometer region to the output waveguide, reduce the insertion loss and return loss caused by mode mismatch, and improve the beam splitting uniformity.

[0144] The length of the multimode interference region is determined based on the self-imaging condition and adjusted by scanning the field intensity distribution. The self-imaging effect refers to the ability of the optical field in a multimode waveguide to reproduce the image of the input field after a specific propagation distance. The initial length of the multimode interference region can be calculated using mode solvers based on the self-imaging condition. Specifically, the propagation constants of the lower-order modes in the multimode interference region are first calculated using mode solver software, and then the initial length of the interference region is obtained based on the self-imaging condition. Subsequently, the field intensity distribution in the interference region is scanned using full-wave simulation software to fine-tune the length of the interference region, achieving optimal splitting uniformity and the lowest insertion loss.

[0145] As one embodiment, a three-level cascade can be used. Multimode interferometric beam-splitting units form an 8-way beam-splitting sub-network, serving as the modeling and simulation input for the local sub-array. When the complete optical phased array contains no fewer than 16 grating antenna elements, 16 outputs can be formed by adding a cascaded stage, or the number of cascaded stages can be further expanded. In a specific design example, each The length of the multimode interference region of the multimode interference beam splitter unit is The spacing between the output waveguides is The length of the multimode interference region can be determined by the initial design. Adjusted after field strength distribution scanning To optimize beam splitting uniformity, tapered transition sections are incorporated into both the input and output waveguides to improve beam splitting uniformity and reduce return loss.

[0146] Please refer to Figure 13 , Figure 13 The simulation results of the field strength distribution of the multimode interferometric beam splitter in the embodiments of this disclosure are shown. Figure 13 As shown, the field intensity distribution of the multimode interferometric beamsplitter at the operating wavelength exhibits clear self-imaging characteristics. After mode interference within the multimode interference region, the input light forms a uniform image point at the output waveguide position. The simulation results demonstrate that the multimode interferometric beamsplitter can achieve uniform optical field distribution, and the tapered transition section design helps reduce mode mismatch and return loss. Adjusting the length of the multimode interference region by scanning the field intensity distribution can further optimize the beam splitting uniformity and reduce amplitude differences between different output channels.

[0147] The multimode interferometric beam splitter network has at least 16 output channels. The length of the multimode interference region of the multimode interference beam splitter unit is The spacing between the output waveguides is Multiple phase shifters are thermo-optical phase shifters, each including a metal electrode positioned adjacent to the corresponding silicon-based waveguide. The drive voltage range output by the multi-channel voltage controller to the metal electrode is... to The number of grating antenna elements is no less than 16, and the grating period is... The grating width is The grating etching depth is The center wavelength of the tunable laser is The wavelength tuning range is .

[0148] This embodiment employs a multimode interferometric beam splitter network to provide coherent input light to multiple array elements. Optimization of the tapered transition section and the length of the multimode interferometric region improves the multi-path splitting performance, which helps reduce amplitude differences between different array elements. Furthermore, through the specific structural parameter design described above, high-performance, low-sidelobe two-dimensional scanning can be achieved on a silicon-based photonic integration platform.

[0149] To more fully illustrate the technical solution of this disclosure, the application of silicon-based all-solid-state lidar is described below. The non-equidistant silicon-based optical phased array low-sidelobe two-dimensional scanning system provided in this disclosure can be applied to silicon-based all-solid-state lidar. In this application, the silicon-based all-solid-state lidar includes the aforementioned non-equidistant silicon-based optical phased array low-sidelobe two-dimensional scanning system. It acquires information such as the target's range, azimuth, and spatial topography by emitting a scanning beam and receiving the target echo. Because this system uses a non-mechanical scanning method and does not contain mechanical moving parts such as rotating or oscillating mechanisms, it has advantages such as small size, high reliability, and fast scanning speed, making it suitable for various application scenarios such as vehicle-mounted lidar, UAV-borne lidar, and fixed lidar.

[0150] During the operation of the all-solid-state lidar, the controller generates a target scanning direction sequence according to the scanning strategy and sequentially controls the tunable laser to output input light of the corresponding operating wavelength. Simultaneously, a multi-channel voltage controller applies corresponding driving voltages to each thermo-optical phase shifter. The emitted beam is radiated to the target scene via a grating antenna array. The target echo is collected by the receiving optical system and sent to the detection module. Target distance information is obtained through time-of-flight ranging or coherent detection. Combined with the current scanning direction, the three-dimensional spatial coordinates of the target can be obtained, thereby constructing a point cloud image of the target scene. Because the scanning system provided in this disclosure can suppress sidelobes and grating lobes, it can reduce stray light interference from non-target directions, improving the signal-to-noise ratio and ranging accuracy of the lidar.

[0151] In other embodiments, the number of stages, number of array elements, array element position sequence, grating parameters, driving voltage range, and input light wavelength range of the multimode interferometric beam splitter can be adjusted according to the chip manufacturing process, silicon waveguide cross-section, grating antenna coupling efficiency, thermo-optical phase shifter power consumption, and crosstalk calibration results. This disclosure does not limit these aspects.

[0152] The above are merely preferred embodiments of this disclosure. For those skilled in the art, any equivalent substitutions or changes made to the number of array elements, element positions, beam splitter network structure, phase shifter structure, driving method, and optimization algorithm without departing from the technical concept of this disclosure should fall within the scope of protection of this disclosure. Other embodiments of this disclosure will be readily apparent to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This disclosure is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A low-sidelobe two-dimensional scanning method for a non-equidistant silicon-based optical phased array, applied to a silicon-based optical phased array, wherein the silicon-based optical phased array includes a beam splitter network, multiple silicon-based waveguides, multiple phase shifters, and multiple grating antenna elements, characterized in that, include: Obtain the target scanning direction and array constraints; The target scanning direction includes the target azimuth angle and the target elevation angle; A far-field light intensity model is established based on the phase delay relationship between the array element position, array element phase and far-field direction angle; Under the array constraints, with the goal of suppressing sidelobes and grating lobes in non-target directions and increasing the energy concentration of the main lobe, the non-equidistant array element position sequence is determined iteratively based on the far-field light intensity model; the non-equidistant array element position sequence represents the arrangement position of the multiple grating antenna array elements. Based on the target elevation angle, the target operating wavelength of the input light is determined. Based on the target azimuth angle, the target operating wavelength, and the non-equidistant array element position sequence, the phase control quantity of each grating antenna array element is determined, and the phase control quantity is mapped to the driving voltage of the multiple phase shifters. The input light is adjusted to the target operating wavelength, and the adjusted input light is distributed to the multi-channel silicon waveguide via the beam splitter network; The driving voltage is applied to the plurality of phase shifters to achieve azimuth scanning through the phase difference between adjacent grating antenna elements; By utilizing the input light adjusted to the target operating wavelength and the dispersion of the grating antenna array elements, the elevation emission angle is made to correspond to the target elevation angle, thereby achieving elevation scanning.

2. The method according to claim 1, characterized in that, The establishment of a far-field light intensity model based on the phase delay relationship between array element position, array element phase, and far-field azimuth angle includes: The array factor is constructed based on the amplitude weight, position, and phase control of each grating antenna element; The far-field light intensity distribution is determined based on the array factor and the single-element field pattern; Wherein, the array factor satisfies: ； The far-field light intensity distribution satisfies: ； in, For array factor, For far-field light intensity distribution, This is a single-element field pattern. The far-field direction angle, For the operating wavelength, , , The first The amplitude weights, position and phase control parameters of each grating antenna element , The refractive index of the exit-side medium. The imaginary unit, The number of elements in the grating antenna array.

3. The method according to claim 2, characterized in that, The array constraints include adjacent element spacing constraints, array aperture constraints, and element crosstalk constraints; under these array constraints, with the goal of suppressing sidelobes and grating lobes in non-target directions and increasing the main lobe energy concentration, the non-equidistant element position sequence is determined iteratively based on the far-field intensity model, including: An evaluation function is constructed based on the far-field light intensity distribution; the evaluation function includes at least a peak sidelobe term and a main lobe energy concentration term, and also includes at least one of an array element crosstalk penalty term and a constraint penalty term; wherein, the peak sidelobe term is determined based on the maximum light intensity outside the main lobe angular domain, and the main lobe energy concentration term is determined based on the energy proportion within the main lobe angular domain; the main lobe angular domain is the angular domain surrounding the target azimuth angle; With the goal of reducing the peak sidelobe term and increasing the main lobe energy concentration term, the candidate array element position sequence is iteratively updated; The candidate array element position sequence that satisfies the array constraints is determined as the non-equally spaced array element position sequence.

4. The method according to claim 3, characterized in that, The iterative update of the candidate array element position sequence includes: The positions of the array elements with equal spacing are used as the initial array element positions; Keeping the positions of the two end array elements fixed, position perturbation is introduced into at least some of the grating antenna array elements other than the end array elements to obtain a candidate array element position sequence; Under the conditions of satisfying the adjacent element spacing constraint, the array aperture constraint, and the element crosstalk constraint, the position perturbation amount is iteratively updated until the evaluation function converges or reaches the preset number of iterations.

5. The method according to claim 2, characterized in that, The step of determining the phase control quantity of each grating antenna element based on the target azimuth angle, the target operating wavelength, and the non-equidistant array element position sequence includes: Based on the target azimuth angle, the target operating wavelength, and the non-equidistant array element position sequence, calculate the... Ideal phase of each grating antenna element: ； in, The target azimuth angle is... The target operating wavelength, For the first The position of each grating antenna element The wave number in the exit medium. For the first The ideal phase of each grating antenna element; With the goal of further reducing the non-target direction sidelobes and grating lobes obtained based on the far-field intensity model, a phase correction is searched near the ideal phase. ; Based on the ideal phase and the phase correction amount, the corrected phase control amount is obtained: ； in, For the first Phase control quantity after correction for each grating antenna element For the first Phase correction amount of each grating antenna element This indicates a modulo operation; the phase correction amount is used to compensate for phase deviations caused by at least one of the following: manufacturing errors, optical path transmission errors, and thermal crosstalk.

6. The method according to claim 5, characterized in that, The plurality of phase shifters are plurality of thermo-optical phase shifters; the mapping of the phase control quantity to the driving voltage of the plurality of phase shifters includes: Based on simulation or calibration results, a phase voltage mapping table between the phase change and driving voltage of each thermo-optical phase shifter is established. Based on the phase control value of each grating antenna element, the corresponding driving voltage is called in the phase voltage mapping table; Among them, the The phase change of the aforementioned thermo-optical phase shifter satisfies: ； in, The target operating wavelength, For the first The effective refractive index change of a silicon-based waveguide under driving voltage. For the first The effective phase shift length of a thermo-optical phase shifter.

7. The method according to claim 1, characterized in that, Determining the target operating wavelength of the input light based on the target elevation angle includes: The target operating wavelength is determined based on the target pitch angle and the grating phase matching relationship; The grating phase matching relationship satisfies: ； in, Let be the waveguide propagation constant. , The refractive index of the exit-side medium. The pitch-direction launch angle corresponds to the target pitch angle. For diffraction orders, The grating period.

8. A low-sidelobe two-dimensional scanning system for a non-equidistant silicon-based optical phased array, characterized in that, The method for performing the method as described in any one of claims 1 to 7 includes: a tunable laser, a beam splitter network, a multi-channel silicon waveguide, a plurality of phase shifters, a plurality of grating antenna elements, a multi-channel voltage controller, and a controller. The plurality of grating antenna elements are arranged in a non-equidistant element position sequence; at least two adjacent elements in the non-equidistant element position sequence have different spacing; the non-equidistant element position sequence is a sequence determined in advance based on a far-field light intensity model and under array constraints with the goal of suppressing sidelobes and grating lobes in non-target directions. The tunable laser is used to output input light to the beam splitter network; The beam splitter network is used to distribute the input light to the multiple silicon-based waveguides; The multiple phase shifters are respectively disposed on the multiple silicon-based waveguides and correspond to the multiple grating antenna array elements; The multi-channel voltage controller is connected to the plurality of phase shifters respectively, and is used to apply independent drive voltages to the plurality of phase shifters; The controller is connected to the tunable laser and the multi-channel voltage controller respectively. The controller is used to receive the target scanning direction, determine the target operating wavelength of the tunable laser according to the target elevation angle in the target scanning direction, determine the phase control quantity of each phase shifter according to the target azimuth angle in the target scanning direction, the target operating wavelength and the non-equidistant array element position sequence, and convert the phase control quantity into the independent driving voltage so as to achieve azimuth scanning through the phase difference between adjacent grating antenna array elements, and achieve elevation scanning through the tuning of the target operating wavelength.

9. The system according to claim 8, characterized in that, The beam splitting network is a multimode interferometric beam splitting network; the multimode interferometric beam splitting network includes multiple cascaded 1×2 multimode interferometric beam splitting units; each 1×2 multimode interferometric beam splitting unit includes a multimode interferometric region, an input waveguide, and an output waveguide; at least one of the input waveguide and the output waveguide is provided with a tapered transition section; the length of the multimode interferometric region is determined according to the self-imaging conditions and adjusted by field strength distribution scanning.

10. The system according to claim 9, characterized in that, The multimode interferometric beam splitter network has no fewer than 16 output channels; the length of the multimode interferometric region of each 1×2 multimode interferometric beam splitter unit is... The spacing between the output waveguides is ; The plurality of phase shifters are thermo-optical phase shifters, each including a metal electrode disposed adjacent to a corresponding silicon-based waveguide; the driving voltage output by the multi-channel voltage controller to the metal electrode ranges as follows: to ; The number of the plurality of grating antenna elements is not less than 16, and the grating period is [missing information]. The grating width is The grating etching depth is ; The center wavelength of the tunable laser is The wavelength tuning range is .

Images