A discrete-group-graded sidewall etching waveguide Bragg grating and a design method thereof

Abstract

The present application belongs to the technical field of integrated photonics, and discloses a discrete grouping gradually changing sidewall etching waveguide Bragg grating and a design method thereof. The grating comprises a left gradually changing region, a center constant region and a right gradually changing region arranged in sequence along the light propagation direction, and the left gradually changing region and the right gradually changing region are mirror symmetric about the center constant region. The left gradually changing region and the right gradually changing region each comprise at least two gradually changing groups arranged along the light propagation direction, and at least two grating units in the same gradually changing group have the same lateral etching width and grating period. The design method determines the target coupling coefficient of each gradually changing group according to a preset target coupling coefficient distribution, inversely interpolates the lateral etching width of each gradually changing group based on the mapping relationship between the lateral etching width and the equivalent coupling coefficient, and determines the compensation period according to the local Bragg wavelength under the corresponding lateral etching width. The present application can reduce the reflection spectrum sidelobe, improve the sidelobe suppression ratio, and facilitate the layout discretization and manufacturing implementation.

Description

Technical Field

[0001] This invention relates to the field of integrated photonic devices and optical waveguide devices, and in particular to a discrete grouped graded sidewall etched waveguide Bragg grating and its design method. Background Technology

[0002] A waveguide Bragg grating is an optical waveguide device that selectively reflects light of a specific wavelength by forming a periodic effective refractive index modulation along the direction of light propagation, thereby satisfying the Bragg condition. Due to its small size, ease of on-chip integration, and ability to achieve wavelength-selective reflection, waveguide Bragg gratings can be used in on-chip mirrors, integrated lasers, optical filters, wavelength selectors, optical communication devices, and optical sensors.

[0003] Sidewall-etched waveguide Bragg gratings typically achieve periodic refractive index modulation by forming periodic etched structures on the waveguide sidewalls, resulting in different equivalent effective refractive indices in the etched and unetched areas of the local waveguide cross-section. The coupling coefficient of the grating and its distribution along the propagation direction affect spectral characteristics such as reflectivity, reflection bandwidth, sidelobes, and in-band ripple. To achieve predetermined reflection spectrum shaping or sidelobe suppression effects, geometric parameters such as the lateral etching width of the sidewalls can be varied to create a gradually changing coupling intensity distribution along the light propagation direction. However, the relationship between geometric parameters such as the lateral etching width and the coupling coefficient is typically influenced by various factors, including waveguide cross-sectional dimensions, material parameters, etching depth, duty cycle, grating period, operating mode, and operating wavelength, and may exhibit a nonlinear relationship. Therefore, linear or empirically derived gradual changes in geometric parameters cannot guarantee that the coupling coefficient changes according to the predetermined target envelope, potentially leading to a deviation of the actual coupling intensity distribution from the target distribution, thus affecting the reflection spectrum shape. Furthermore, variations in the lateral etching width of the sidewalls also alter the local effective refractive index and the local Bragg condition. If different transverse etching widths are used at different locations while the same grating period is still used, the local reflection center at different locations may shift, resulting in local Bragg detuning. This may also affect the coherent superposition of reflected light at different locations near the target operating wavelength, thereby affecting the position of the main peak of the reflection spectrum, the sidelobe suppression ratio, and the overall spectral shape.

[0004] Meanwhile, actual layout design and manufacturing are constrained by minimum linewidth, layout grid, and process deviations. The continuously varying theoretical lateral etching width usually needs to be quantized into a finite number of manufacturable discrete dimensions, and the quantized actual lateral etching width may further alter coupling characteristics and local Bragg conditions. On the other hand, setting different lateral etching widths and grating periods for each grating unit would increase layout complexity and manufacturing control difficulty.

[0005] Existing sidewall-etched waveguide Bragg gratings and their design methods still have the following shortcomings:

[0006] 1. Geometric parameters such as lateral etching width and coupling coefficient usually have a non-linear relationship, and it is difficult to obtain the preset target coupling coefficient distribution by directly using gradual changes in lateral etching width.

[0007] 2. The transverse etching width obtained by inverse interpolation of the target coupling coefficient will change the local effective refractive index and the local Bragg reflection center. If a uniform grating period is used at different positions, it may introduce local Bragg mismatch, affecting the coherent superposition of reflected light at different positions near the target working wavelength.

[0008] 3. The theoretical lateral etching width is constrained by the minimum manufacturable size and the layout grid. The quantized actual lateral etching width may change the local coupling characteristics and local Bragg conditions, and the corresponding compensation period needs to be re-determined based on the quantized actual lateral etching width.

[0009] 4. Setting different grating parameters for each cell increases the layout complexity and manufacturing control difficulty, while too few groups may reduce the approximation accuracy of the target coupling coefficient distribution.

[0010] Therefore, it is necessary to provide a waveguide Bragg grating and its design method that can achieve a gradual distribution of the target coupling coefficient under manufacturing constraints, while taking into account the local Bragg condition changes caused by different transverse etching widths and the layout complexity. Summary of the Invention

[0011] To address the challenges of achieving a predetermined target coupling coefficient distribution in existing sidewall-etched waveguide Bragg gratings by directly varying the lateral etching width, and the potential for local Bragg mismatch caused by different lateral etching widths, this invention proposes a discretely grouped, gradually varying sidewall-etched waveguide Bragg grating and its design method. This invention utilizes the coordinated control of the lateral etching width and compensation period of discrete groups to form a gradually varying coupling envelope. Under the same total grating period comparison conditions, it can reduce sidelobes in the reflection spectrum, improve the sidelobe suppression ratio, and minimize local Bragg mismatch caused by variations in lateral etching width, facilitating layout discretization and manufacturing.

[0012] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0013] This invention provides a discrete grouped gradient sidewall etched waveguide Bragg grating, comprising a left gradient region, a central constant region, and a right gradient region arranged sequentially along the light propagation direction. The left and right gradient regions are mirror-symmetrical about the central constant region. Each of the left and right gradient regions includes multiple gradient groups arranged along the light propagation direction. Each gradient group includes multiple consecutive grating units. Each grating unit within the same gradient group has the same lateral etching width and the same grating period. At least some different gradient groups have different lateral etching widths and compensation periods corresponding to the lateral etching widths.

[0014] This invention also provides a design method for discrete grouped gradient sidewall etched waveguide Bragg gratings, comprising: establishing a first mapping relationship between the lateral etching width and the equivalent coupling coefficient, and a second mapping relationship between the lateral etching width and the local Bragg wavelength; determining the target coupling coefficient of each gradient group according to a preset target coupling coefficient distribution; obtaining the theoretical lateral etching width of each gradient group by inverse interpolation based on the first mapping relationship, and quantizing the theoretical lateral etching width according to manufacturing constraints to obtain the actual lateral etching width; determining the corresponding local Bragg wavelength based on the quantized actual lateral etching width by the second mapping relationship, and determining the compensation period of the corresponding gradient group accordingly; generating grating patterns for the left gradient region, the central constant region, and the right gradient region according to the actual lateral etching width and the compensation period.

[0015] Compared with the prior art, the present invention has at least the following beneficial effects:

[0016] 1. This invention establishes a first mapping relationship between the unilateral lateral etching width and the equivalent coupling coefficient, and a second mapping relationship between the unilateral lateral etching width and the local Bragg wavelength. It determines the unilateral lateral etching width of each gradient group based on the target coupling coefficient distribution, and determines the compensation period based on the local Bragg wavelength under the corresponding unilateral lateral etching width. This can reduce the local Bragg mismatch caused by the change in unilateral lateral etching width while adjusting the coupling strength distribution.

[0017] 2. This invention divides the gradient region into multiple discrete gradient groups. Each grating unit within the same gradient group uses the same single-sided lateral etching width and grating period. While discretizing the distribution of the target coupling coefficient, it can reduce the number of changes in grating parameters along the propagation direction, which is beneficial for simplifying layout generation, reducing the amount of layout data, and reducing the manufacturing control complexity caused by periodic parameter changes. Since the parameters of each gradient group can be defined by the sidewall boundary and period coordinates in the same sidewall etching layer, it is easy to implement in manufacturing.

[0018] 3. This invention incorporates the minimum non-zero manufacturable single-sided lateral etching width and layout grid into the design process, and redetermines the local Bragg wavelength and compensation period after quantizing the single-sided lateral etching width, which helps to reduce the local Bragg mismatch caused by layout discretization and improve the consistency between design parameters and final layout parameters.

[0019] 4. The present invention adopts a structure that combines a left-right mirror-symmetrical gradient region with a central constant region, which can form a coupling intensity distribution from weak coupling to strong coupling and then back to weak coupling, which is beneficial to achieving reflection spectrum shaping and sidelobe suppression; and the reflection spectrum shape and sidelobe suppression characteristics can be designed and adjusted according to parameters such as the target coupling coefficient distribution, the number of gradient groups, the number of grating periods in each group, and the length of the central constant region.

[0020] 5. The design process of this invention can re-establish the mapping relationship between the single-sided lateral etching width and the equivalent coupling coefficient, as well as the mapping relationship between the single-sided lateral etching width and the local Bragg wavelength, given a material platform, waveguide cross section, operating wavelength and process conditions, thereby enabling the design of waveguide Bragg gratings under corresponding conditions. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the overall structure of the discrete grouped gradient Bragg grating of the present invention.

[0023] Figure 2 for Figure 1 The diagram shows a top view of a single grating unit.

[0024] Figure 3 This is a flowchart of the design method of the present invention.

[0025] Figure 4 The simulated reflectance spectrum of a uniform grating with 800 periods.

[0026] Figure 5 The simulated reflectance spectrum of a discrete grouped graded Bragg grating with 800 periods.

[0027] In the diagram, 1 represents the left gradient region, 2 represents the central constant region, and 3 represents the right gradient region. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Example 1

[0030] like Figure 1 As shown, a discretely grouped gradient sidewall etched waveguide Bragg grating includes a left gradient region 1, a central constant region 2, and a right gradient region 3 arranged sequentially along the light propagation direction. The left gradient region 1 and the right gradient region 3 are mirror-symmetrical about the central constant region 2. The left gradient region 1 is used to gradually transition the grating coupling strength from a weak coupling state at the grating end to a strong coupling state in the central constant region 2, thereby helping to reduce the sidelobes of the reflection spectrum caused by the abrupt coupling at the grating's starting end. The central constant region 2 has the same lateral etching width and grating period, providing the main Bragg reflection contribution and forming the main peak of the reflection spectrum near the target operating wavelength. The right gradient region 3 is used to gradually transition the grating coupling strength from the strong coupling state in the central constant region 2 to a weak coupling state at the other end of the grating, thereby helping to reduce the sidelobes and ripples of the reflection spectrum caused by the abrupt coupling at the grating's ending end. The left gradient region 1 and the right gradient region 3 are mirror-symmetric about the central constant region 2, so that the overall coupling strength envelope of the grating is symmetrically distributed in space, which is beneficial to improving the regularity of the reflection spectrum. At the same time, the mirror-symmetric structure can simplify the pattern parameter generation process. The lateral etching width and grating period of the right gradient region 3 can be obtained by reversing the parameters of the left gradient region 1.

[0031] Both the left gradient region 1 and the right gradient region 3 contain N gradient groups arranged along the light propagation direction, where N is an integer greater than or equal to 2; each gradient group includes M consecutive grating units, where M is an integer greater than or equal to 2. The central constant region 2 includes multiple consecutive grating units. Each grating unit in the central constant region 2 has the same single-sided lateral etching width and the same grating period, giving this region a substantially constant equivalent coupling coefficient, thereby providing the main cumulative coupling contribution within a finite grating length and forming a main reflection peak near the target operating wavelength. In a preferred embodiment, the number of periods in the central constant region 2 is not less than the number of periods in any single-sided gradient region; in a specific embodiment, the number of periods in the central constant region 2 can be greater than the sum of the number of periods in the left gradient region 1 and the right gradient region 3. The waveguide Bragg grating adopts a double-sided symmetrical etching structure. The parameters related to etching width mentioned below are all characterized by the single-sided lateral etching width, that is, the etching dimension extending from the waveguide sidewall into the core layer on each side.

[0032] Each gradient group in the gradient region has its unilateral lateral etching width and corresponding compensation period set according to a discrete gradient sequence. At least some different gradient groups have different unilateral lateral etching widths and corresponding compensation periods, thereby enabling the discrete mapping of the target coupling coefficient distribution onto the actual sidewall etching structure. This allows the coupling strength at both ends of the grating to gradually transition from weak to strong or from strong to weak, reducing the sidelobes of the reflection spectrum caused by abrupt coupling changes at the grating ends. Specifically, the grating period of each gradient group is set in association with its corresponding unilateral lateral etching width. Changes in the unilateral lateral etching width alter the local equivalent effective refractive index of the corresponding grating unit, resulting in different local Bragg wavelengths for different gradient groups. If different gradient groups use the same grating period, the difference in local equivalent effective refractive index caused by different unilateral lateral etching widths may cause a shift in the local Bragg reflection center of each gradient group, introducing local Bragg detuning and potentially affecting the position of the main peak of the reflection spectrum, the sidelobe suppression ratio, and the overall spectral shape. To improve the consistency between design parameters and actual layout parameters, the grating period of each gradient group is compensated according to the local Bragg wavelength shift corresponding to the lateral etching width on one side of the group. This allows different gradient groups to have different coupling strengths while helping to reduce the mismatch caused by the local Bragg condition deviating from the target operating wavelength.

[0033] Each grating unit within the same gradient group uses the same single-sided lateral etching width and grating period, enabling the gradient structure to be implemented in the form of piecewise constants. This helps to reduce the layout complexity and manufacturing difficulty of the continuously changing structure over periodic periods. The left and right gradient regions are set in a mirror symmetry, which keeps the overall grating coupling intensity distribution and periodic compensation distribution symmetrical, which helps to improve the regularity of the reflection spectrum and the sidelobe suppression effect.

[0034] Furthermore, the unilateral gradient region comprises N gradient groups arranged along the light propagation direction, with at least some different gradient groups corresponding to different target coupling coefficients, thus forming a piecewise discrete approximation of the preset target coupling coefficient distribution. The preset target coupling coefficient distribution uses the equivalent coupling coefficient corresponding to the unilateral lateral etching width of the central constant region 2 as the maximum target coupling coefficient. As the number of gradient groups N increases, the step-like discrete coupling coefficient distribution provides a more refined approximation of the coupling coefficient envelope of the continuous target, and the jump in coupling coefficient between adjacent gradient groups decreases, making the change in coupling coefficient along the light propagation direction smoother. However, increasing the number of gradient groups N also increases the number of discrete parameters and the number of inter-group transition boundaries, thereby increasing the requirements for layout generation, parameter verification, and manufacturing control. The number of gradient groups N can be determined based on the target reflection level, sidelobe suppression ratio, device length, minimum manufacturable feature size, layout grid, and process tolerance.

[0035] Each gradient group comprises M consecutive grating units, meaning that each grating unit within the same gradient group has the same single-sided lateral etching width and the same grating period. When the number of grating periods in a single-sided gradient region is T, and each gradient group contains the same number of grating units, the number of periods T in the single-sided gradient region, the number of gradient groups N, and the number of grating units M in each group satisfy the following condition: By setting the number M of grating units in each gradient group, a trade-off can be struck between the fineness of the discrete approximation of the target coupling coefficient distribution and the complexity of layout implementation. When M is small, with a fixed number of periods T in the single-sided gradient region, more gradient groups can be set, making the change in target coupling coefficient between adjacent gradient groups more refined, which helps to reduce reflection spectral ripple or sidelobes caused by abrupt changes in coupling coefficients; however, if M is too small, it will increase the number of gradient groups, the number of layout parameters, and the difficulty of manufacturing control. When M is large, the number of repeated grating units in the same gradient group increases, which helps to reduce the number of gradient groups, simplify the layout parameter configuration, reduce the amount of layout data, and improve structural repeatability and manufacturing control convenience; however, if M is too large, the number of gradient groups that can be set in the gradient region decreases, the degree of step distribution of coupling coefficients increases, and the approximation effect on the continuous target coupling coefficient distribution may be weakened. The specific value of the number M of grating units in each group can be determined according to the target reflection level, reflection spectral shape requirements, sidelobe suppression ratio, device length, minimum manufacturable feature size, layout grid, and manufacturing process tolerance.

[0036] In one embodiment, each grating unit sequentially includes an unetched region and an etched region along the light propagation direction. The etched region is formed by symmetrically etching the two sidewalls of the waveguide laterally toward the waveguide center, perpendicular to the light propagation direction. The width of the lateral etching on one side is the etching dimension extending from the sidewall toward the waveguide center, and the total lateral etching width on both sides is twice the width of the lateral etching on one side. Through symmetrical etching on both sides, the waveguide centerline of the etched region is kept consistent with that of the unetched region, which helps to reduce the lateral mode center shift and asymmetric mode perturbation caused by lateral etching, and allows the lateral etching width to serve as a definite geometric parameter for adjusting the local coupling coefficient.

[0037] In a preferred embodiment, the duty cycle D of the grating unit is 0.5, where D is the ratio of the length of the etched region along the light propagation direction to the grating period, i.e., the lengths of the etched and unetched regions along the light propagation direction are equal. For ideal binary periodic modulation, when the duty cycle is 0.5, the odd-order spatial Fourier modulation components remain non-zero, while the even-order spatial Fourier modulation components are suppressed, thus facilitating the formation and utilization of odd-order Bragg couplings. Simultaneously, since each gradient group uses the same duty cycle, the equivalent coupling coefficient and local Bragg wavelength can be primarily calibrated based on the lateral etching width, which simplifies the width inverse interpolation, compensation period calculation, and layout generation process.

[0038] Example 2

[0039] This embodiment provides a design method for discrete grouped gradient sidewall etched waveguide Bragg gratings. The method establishes a first mapping relationship between the single-sided lateral etching width and the equivalent coupling coefficient, and a second mapping relationship between the single-sided lateral etching width and the local Bragg wavelength. Based on a preset target coupling coefficient distribution, the theoretical single-sided lateral etching width of each gradient group is obtained through inverse interpolation. The theoretical single-sided lateral etching width is then quantized according to manufacturing rules. Subsequently, based on the quantized actual single-sided lateral etching width, the corresponding local Bragg wavelength is re-determined, and the compensation period is determined accordingly. This achieves the preset target coupling coefficient distribution while reducing the local Bragg mismatch caused by variations in single-sided etching width and width quantization, improving the consistency between design parameters and layout parameters, and contributing to improved reflection spectrum and sidelobe suppression ratio. The single-sided lateral etching width is the single-sided etching dimension perpendicular to the light propagation direction, extending from the waveguide sidewall into the core layer. Under double-sided symmetrical etching conditions, the total double-sided lateral etching width is twice the single-sided lateral etching width. The design method includes the following steps:

[0040] S1, determine the parameters of the central constant region and the reference grating period.

[0041] Determine the target operating wavelength Bragg order m, lateral etching width of the central constant region on one side The grating period corresponding to the central constant region is obtained and used as the reference grating period. .

[0042] Specifically, the target operating wavelength can be determined based on the required feedback wavelength or operating band. The single-sided transverse etching width of the central constant region is determined based on the preset main peak reflection level, maximum target coupling coefficient, waveguide cross-sectional dimensions, minimum manufacturable feature size, and process tolerance. According to the target operating wavelength The effective refractive index of the waveguide and the desired grating period range determine the Bragg order m; the target operating wavelength is then determined. Bragg order m and lateral etching width on one side of the central constant region Then, the reference grating period is determined based on the Bragg condition. .

[0043] S2, establish the mapping relationship between the unilateral lateral etching width, the equivalent coupling coefficient, and the local Bragg wavelength.

[0044] The reference grating period The equivalent coupling coefficient and local Bragg wavelength of the waveguide grating model corresponding to different single-sided lateral etching widths are obtained. A first mapping relationship between the single-sided lateral etching width and the equivalent coupling coefficient, and a second mapping relationship between the single-sided lateral etching width and the local Bragg wavelength are established.

[0045] Specifically, multiple candidate lateral etching widths are selected, and within the reference grating period... Under the conditions of a duty cycle of 0.5 and the same waveguide cross-section, corresponding uniform double-sided symmetrically etched waveguide Bragg grating models were constructed. The reflection spectrum corresponding to the lateral etching width of each candidate side was obtained by one or a combination of the intrinsic mode expansion method, finite element method, finite difference time-domain method, and experimental testing. The peak reflectivity and peak wavelength were then extracted from the reflection spectrum.

[0046] For a uniform grating, near the Bragg center, its peak reflectivity and equivalent coupling coefficient satisfy the following:

[0047] (kL);

[0048] From this, we can inversely deduce:

[0049] ;

[0050] in, Peak reflectivity This corresponds to the equivalent coupling coefficient under the lateral etching width on one side. For uniform grating length, It is the hyperbolic tangent function. It is the inverse hyperbolic tangent function.

[0051] The peak wavelength corresponding to each candidate single-sided lateral etching width is taken as the single-sided lateral etching width within the reference grating period. The local Bragg wavelength is determined, thus obtaining the first mapping relationship between the unilateral lateral etching width and the equivalent coupling coefficient, and the second mapping relationship between the unilateral lateral etching width and the local Bragg wavelength. For unilateral lateral etching widths not directly included in the candidate unilateral lateral etching width set, the corresponding equivalent coupling coefficient and local Bragg wavelength can be obtained through linear interpolation, monotonic spline interpolation, or fitting methods.

[0052] In some implementations, the first mapping relationship can be written as:

[0053] / ;

[0054] in, The width of the lateral etching on one side. Horizontal etching width on one side The corresponding equivalent coupling coefficient, The lateral etching width on one side of the central constant region The corresponding equivalent coupling coefficient.

[0055] The second mapping relationship can be expressed as:

[0056] ;

[0057] in, Horizontal etching width on one side During the reference grating period The corresponding local Bragg wavelength.

[0058] S3, determine the target coupling coefficient of each gradient group based on the target coupling coefficient distribution.

[0059] The target coupling coefficients of each gradient group in the left and right gradient regions are determined based on the preset target coupling coefficient distribution.

[0060] Suppose that the unilateral gradient region includes N gradient groups, and the th gradient group... The normalized center locations of the gradient groups are:

[0061] ;

[0062] in .

[0063] Selecting the envelope function of the normalized target coupling coefficient ,in: ;

[0064] and: ;

[0065] In this embodiment, the envelope function of the normalized target coupling coefficient is a raised cosine function:

[0066] ;

[0067] The lateral etching width on one side of the central constant region The corresponding equivalent coupling coefficient is used as the maximum target coupling coefficient. , No. The target coupling coefficients for each gradient group are: .

[0068] The target coupling coefficient sequence in the right gradient region is mirror-symmetric to that in the left gradient region.

[0069] In other embodiments, the target coupling coefficient distribution may also be a sine, cosine, Gaussian, Hanning window, linear, exponential, discrete distribution of the optimization algorithm output, or a combination of the above distributions.

[0070] S4, reverse interpolation is used to calculate the lateral etching width on one side and then quantize the manufacturing process.

[0071] Based on the first mapping relationship, the target coupling coefficient of each gradient group is back-interpolated to obtain the theoretical single-sided lateral etching width of each gradient group, and the manufacturing quantization of the theoretical single-sided lateral etching width is performed according to the minimum non-zero manufacturable etching width and the layout grid.

[0072] Specifically, in obtaining the first The target coupling coefficient of the gradient group Then, it is coupled with the maximum target coupling coefficient. Normalization yields the target normalized coupling coefficient: / ;

[0073] Based on the pre-established first mapping relationship: / ;

[0074] Inverse interpolation is performed within the monotonic interval of the first mapping relationship to obtain the theoretical single-sided lateral etching width that satisfies the following formula. ;in, For the first The theoretical single-sided transverse etching width of the gradient group.

[0075] Let the minimum non-zero manufacturable single-sided lateral etching width be... The width of the map grid is When the theoretical single-sided lateral etching width At that time, the quantized single-sided lateral etching width of the gradient group is set to: ;

[0076] This gradient group is treated as an etch-free waveguide section, and its period is taken as the reference grating period. .

[0077] When the theoretical single-sided transverse etching width At that time, Quantization to the minimum step size of the layout grid that can be adjusted within the layout The quantized single-sided lateral etching width is obtained by multiplying the integer multiple of the quantized value. For example, quantification can be performed in the following ways:

[0078] ;

[0079] in, () indicates taking the nearest integer.

[0080] Since the subsequent compensation cycle is based on the quantized single-sided lateral etching width used in the final layout, Determined, rather than based on theoretical single-sided lateral etching width This determination reduces the additional deviation caused by width quantization to local Bragg conditions, thus improving the consistency between theoretical design parameters and actual layout parameters.

[0081] S5, redetermine the local Bragg wavelength based on the quantized single-sided lateral etching width.

[0082] For gradient groups with a single-sided lateral etching width greater than zero after quantization, their position within the reference grating period is determined based on the second mapping relationship. The corresponding local Bragg wavelength.

[0083] Specifically, for the first The quantized single-sided lateral etching width is and The gradient group, according to the second mapping relationship:

[0084] ;

[0085] Determine the local Bragg wavelength corresponding to this gradient group: ;

[0086] For the quantized lateral etching width that is not directly included in the second mapping relationship, the corresponding local Bragg wavelength can be obtained by linear interpolation, monotonic spline interpolation, or fitting calculation.

[0087] For a gradient group with a single-sided lateral etching width of zero after quantization, this gradient group is treated as an unetched waveguide segment, and its period can be taken as the reference grating period. Furthermore, it is not used as an effective local Bragg reflection unit for compensation calculation.

[0088] S6, Determine the theoretical compensation period and quantify the period.

[0089] Based on the target operating wavelength and the local Bragg wavelength corresponding to each non-zero etching gradient group, the theoretical compensation period of each gradient group is determined, and the theoretical compensation period is quantized to an integer multiple of the preset period layout grid to obtain the quantized compensation period.

[0090] For the For a gradient group with a quantized single-sided transverse etching width greater than zero, its theoretical compensation period can be determined by the following formula:

[0091] ;

[0092] in, For the first The theoretical compensation period for a gradual change group For the reference grating period, For the target operating wavelength, For the first Each gradient group is within the reference grating period The corresponding local Bragg wavelength.

[0093] Theoretical compensation period Quantization to periodic layout grid The quantization compensation period is obtained by taking an integer multiple of the quantization compensation period. For example, quantification can be achieved in the following ways:

[0094] ;

[0095] In other embodiments, the theoretical compensation period can also be quantized to an integer multiple of the periodic layout grating using rounding up, rounding down, or optimized rounding. For gradient groups with a single-sided lateral etching width of zero after quantization, they are not used as effective grating modulation units for local Bragg period compensation; the period of this gradient group is taken as the reference grating period. .

[0096] S7 generates a discrete grouped gradient raster layout.

[0097] Based on the quantized lateral etching width of the central constant region and each gradient group, the corresponding quantization compensation period, and the number of grating periods contained in each gradient group, a waveguide Bragg grating layout including a left gradient region, a central constant region, and a right gradient region is generated, wherein the left gradient region and the right gradient region are mirror symmetric about the central constant region.

[0098] Suppose the left gradient region includes N gradient groups, and the... The gradient group includes If there are 1 grating period, then the number of grating periods contained in the left gradient region is: The right gradient region is mirror-symmetric to the left gradient region about the central constant region; therefore, the number of grating periods contained in the right gradient region is: The total number of grating periods satisfies: ;in, The number of grating periods contained in the central constant region.

[0099] A left gradient region, a central constant region, and a right gradient region are sequentially generated along the light propagation direction. The left gradient region, from the grating end to the central constant region, uses the quantized single-sided lateral etching width of the 1st to Nth gradient groups. Quantitative compensation cycle and number of cycles The central constant region uses a constant single-sided lateral etching width. Reference grating period and number of cycles The right gradient region uses parameters arranged in the reverse order of the left gradient region, making the right gradient region and the left gradient region mirror symmetrical about the central constant region.

[0100] The above method allows the lateral etching widths of the left and right gradient regions to be discretely gradiented according to the preset target coupling coefficient distribution. At the same time, it enables at least some non-zero etching gradient groups to have a quantization compensation period corresponding to their quantized lateral etching widths, thereby reducing the local Bragg mismatch caused by the change in lateral etching width. This makes the local reflection contribution of each gradient group more concentrated near the target operating wavelength, and is beneficial to reducing the sidelobes of the reflection spectrum and improving the sidelobe suppression ratio.

[0101] Example 3

[0102] like Figure 1 As shown, this embodiment provides a specific parameter implementation of a discrete grouped graded-sidewall etched waveguide Bragg grating. The sidewall etched waveguide Bragg grating uses a silicon oxide material system, with a core refractive index of 1.4740 and a cladding refractive index of 1.4444. The target operating wavelength is around 1550 nm, and the relative refractive index difference between the core and cladding is approximately 2%. The waveguide core cross-sectional dimensions are... .

[0103] The waveguide Bragg grating comprises a left gradient region 1, a central constant region 2, and a right gradient region 3, arranged sequentially along the light propagation direction. The left gradient region 1 and the right gradient region 3 are mirror-symmetrically arranged about the central constant region 2. Each grating period includes an unetched region and an etched region arranged sequentially along the light propagation direction, with a duty cycle of 0.5; that is, for the ... For each grating period in each gradient group, the length of the unetched region and the length of the etched region are respectively: , ,in, For the first The quantization compensation period used for each gradient group.

[0104] The etched area employs a bilaterally symmetrical lateral etching method. The width of each lateral etching side is a dimension perpendicular to the light propagation direction, extending from the waveguide sidewall into the core layer. For the first... A gradient group, if its quantized single-sided lateral etching width is Then the remaining lateral width of the waveguide core layer in the etched region is: ;

[0105] in, and The units are all in μm.

[0106] The lateral etching width on one side of the central constant region 2 is 0.5 μm, and the corresponding equivalent effective refractive index under the local waveguide cross-section of the etched region is approximately 1.4594. This embodiment uses a 15th-order Bragg grating, with a reference grating period of... The central constant region 2 contains 520 grating periods, and the left gradient region 1 and right gradient region 3 each contain 20 gradient groups, each containing 7 consecutive grating periods. Therefore, the left gradient region 1 and right gradient region 3 each contain 140 grating periods, and the total number of periods in the entire grating is 800.

[0107] The lateral etching width and grating period on one side are kept the same in each gradient group; the lateral etching width on one side of the left gradient region 1 increases discretely from the end of the grating to the central constant region 2 according to the preset target coupling coefficient distribution; the right gradient region 3 adopts parameters arranged in the reverse order of the left gradient region 1 to form a mirror symmetric structure.

[0108] To establish the first mapping relationship between the lateral etching width on one side and the equivalent coupling coefficient, and the second mapping relationship between the lateral etching width on one side and the local Bragg wavelength, uniform sidewall etched waveguide Bragg grating models with different lateral etching widths on one side were constructed under the conditions of a reference grating period of 7.966 μm, a duty cycle of 0.5, and a cross-section with a width and thickness of 3.8 μm. Each uniform grating model contains 800 grating periods, with a total length of: L = T × .

[0109] The reflection spectrum corresponding to the transverse etching width on each side was obtained through electromagnetic simulation, and the peak reflectivity was extracted. Local Bragg wavelength and 3dB bandwidth Δ For a uniform grating, near the Bragg center, its peak reflectivity and equivalent coupling coefficient satisfy the following:

[0110] (kL);

[0111] From this, we can inversely deduce:

[0112] ;

[0113] in, To represent the equivalent coupling coefficient under the single-sided lateral etching width, where L is the uniform grating length. It is the hyperbolic tangent function. This is the inverse hyperbolic tangent function. Normalizing the equivalent coupling coefficient k(w) corresponding to the transverse etching width on each side, we obtain k(w) / k( ),

[0114] in, Let be the lateral etching width of the central constant region 2 on one side. This yields the first mapping relationship between the lateral etching width and the equivalent coupling coefficient. Simultaneously, the peak wavelength of the reflection peak corresponding to each lateral etching width is taken as the local Bragg wavelength of that lateral etching width under the reference grating period, thus obtaining the second mapping relationship between the lateral etching width and the local Bragg wavelength.

[0115] Table 1 presents the simulation results of the reflection spectrum of the uniformly sidewall-etched waveguide Bragg grating under different single-sided lateral etching widths.

[0116] Table 1. Simulation results of reflection spectra of uniform sidewall-etched waveguide Bragg gratings under different single-sided lateral etching widths.

[0117]

[0118] As shown in Table 1, under the given waveguide cross-section, reference grating period, and duty cycle conditions in this embodiment, the equivalent coupling coefficient increases overall when the unilateral lateral etching width increases; simultaneously, changes in the unilateral lateral etching width cause local Bragg wavelength changes. Therefore, this embodiment first uses the first mapping relationship to inverse interpolate the theoretical unilateral lateral etching width of each gradient group in the gradient region, then uses the second mapping relationship to determine the local Bragg wavelength based on the actual unilateral lateral etching width after manufacturing quantization, and further calculates the quantization compensation period. Thus, while achieving the preset target coupling coefficient distribution, it reduces the local Bragg mismatch caused by changes in the unilateral lateral etching width, and provides manufacturable layout parameters for reflection spectrum shaping and sidelobe suppression.

[0119] This embodiment uses a group-centered sampling method to determine the target normalized coupling coefficient of each gradient group. Assume a single-sided gradient region includes 20 gradient groups, and the... The center-normalized positions of the gradient groups are:

[0120] ;

[0121] in .

[0122] The envelope function of the normalized target coupling coefficients adopts a raised cosine function:

[0123] , ;

[0124] Therefore, the first The target normalized coupling coefficients of the gradient groups are:

[0125] ;

[0126] The lateral etching width on one side of the central constant region The corresponding equivalent coupling coefficient is used as the maximum target coupling coefficient. , No. The target coupling coefficients for each gradient group are:

[0127] ;

[0128] Based on the target normalized coupling coefficient The normalized coupling coefficient k(w) / k(0.5) and the single-sided lateral etching width shown in Table 1 are... Inverse interpolation is performed on the first mapping relationship between them to obtain the second... The theoretical single-sided transverse etching width of each gradient group .

[0129] In this embodiment, the minimum non-zero manufacturable single-sided lateral etching width is: ;

[0130] The width of the map grid is: ;

[0131] The periodic layout grid is: ;

[0132] When the theoretical single-sided transverse etching width At that time, the quantized single-sided lateral etching width of the corresponding gradient group is set to 0, and the gradient group is treated as an unetched waveguide segment, with its period taken as the reference grating period. ;when At that time, the theoretical single-sided lateral etching width was determined. Quantize to width layout grid The quantized single-sided lateral etching width is obtained by multiplying the integer multiple of the quantized value. .

[0133] For gradient groups with a single-sided lateral etching width greater than zero after quantization, the corresponding local Bragg wavelength at a reference grating period of 7.966 μm and a duty cycle of 0.5 is determined according to the second mapping relationship shown in Table 1:

[0134] In this embodiment, the target operating wavelength ;

[0135] Then the first The theoretical compensation period for a non-zero etch gradient group is:

[0136] ;

[0137] The periodic layout grid size is 0.001 μm;

[0138] Theoretical compensation period The quantization compensation period is obtained by rounding to an integer multiple of the periodic layout raster. For gradient groups where the lateral etching width on one side is zero after quantization, no local Bragg compensation calculation is performed, and its period is taken as the reference grating period. .

[0139] Table 2 shows the grouping layout parameters of the left gradient region 1 in this embodiment. The right gradient region 2 adopts parameters arranged in reverse order with the left gradient region 1, and the central constant region 2 adopts a single-sided lateral etching width of 0.50 μm and a reference grating period of 7.966 μm.

[0140] Table 2 Grouping Parameters of the Left Gradient Zone

[0141]

[0142] Figure 4 The reflection spectrum of a uniformly sidewall-etched waveguide Bragg grating, used as a comparison structure, is shown. The uniform grating has a total of 800 periods, a fixed grating period of 7.966 μm, a fixed lateral etching width of 0.50 μm on one side, and a duty cycle of 0.5. Figure 5 The reflection spectrum of the discrete grouped graded-sidewall etched waveguide Bragg grating of this embodiment is shown. The total number of periods of the discrete grouped graded-sidewall etched waveguide Bragg grating is 800. The left graded region 1 and the right graded region 3 each include 20 graded groups, each graded group includes 7 consecutive grating periods, and the central constant region 2 includes 520 grating periods. Each graded group adopts the quantized single-sided lateral etching width and quantization compensation period shown in Table 2.

[0143] Both gratings were simulated using the intrinsic mode expansion method. Simulation results show that the center wavelength of the reflection peak of the uniformly sidewall-etched waveguide Bragg grating is approximately 1550.010 nm, the 3dB bandwidth is approximately 0.202 nm, and the sidelobe suppression ratio is approximately 13.37 dB. The center wavelength of the reflection peak of the discretely grouped graded-sidewall-etched waveguide Bragg grating in this embodiment is approximately 1550.040 nm, the 3dB bandwidth is approximately 0.216 nm, and the sidelobe suppression ratio is approximately 16.37 dB. Compared with the uniformly sidewall-etched waveguide Bragg grating, the sidelobe suppression ratio of the discretely grouped graded-sidewall-etched waveguide Bragg grating in this embodiment is improved by approximately 3.00 dB. From the reflection spectrum... Figure 4 The uniform grating shown has a prominent abrupt change in coupling strength at its ends, resulting in relatively obvious side lobes on both sides of its main reflection peak; while Figure 5The grating in this embodiment features discrete, grouped gradient regions at both ends. This allows the lateral etching width on one side and its corresponding equivalent coupling coefficient to gradually increase from the grating ends towards the central constant region, thereby reducing the impact of abrupt coupling changes at the ends on the sidelobes of the reflection spectrum. Simultaneously, the grating period for each non-zero etching gradient group is not uniformly fixed to the reference grating period, but rather determined based on the local Bragg wavelength corresponding to the quantized lateral etching width on one side. This reduces the local Bragg mismatch between different gradient groups, making the reflection contribution of each gradient group more concentrated near the target operating wavelength. Therefore, Figure 5 The reflected spectrum shown is relative to Figure 4 It features lower side lobes on both sides of the main peak and a higher side lobe suppression ratio, demonstrating the effect of the discrete grouping gradient etching width and quantization compensation period working together to shape the reflection spectrum.

[0144] It should be noted that the advantages of this embodiment are mainly reflected in reducing the side lobes on both sides of the main peak, improving the side lobe suppression ratio, and improving the reflection spectrum, rather than increasing the main peak reflectivity or narrowing the reflection bandwidth. Simulation results show that the main peak reflectivity of the grating in this embodiment is lower than that of the uniformly sidewalled etched waveguide Bragg grating, the 3dB bandwidth is slightly larger than that of the uniformly sidewalled etched waveguide Bragg grating, and the center wavelength of the reflection peak has a slight redshift of about 0.030 nm relative to the uniform grating reference.

[0145] Therefore, by designing a discretely grouped, gradually varying lateral etching width on one side and a quantization compensation period design associated with the quantized lateral etching width on one side, this embodiment achieves a reduction in sidelobes and an improvement in sidelobe suppression ratio on both sides of the main peak while still meeting the preset feedback requirements for the main peak reflection level. This result demonstrates that this embodiment can effectively shape the reflection spectrum under manufacturing quantization constraints and reduce the impact of local Bragg mismatch caused by etching width variations on the sidelobe characteristics of the reflection spectrum.

[0146] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A discrete grouped graded-sidewall etched waveguide Bragg grating, characterized in that, It includes a left gradient region (1), a central constant region (2) and a right gradient region (3) arranged sequentially along the direction of light propagation. The left gradient region (1) and the right gradient region (3) are mirror-symmetric about the central constant region (2). The waveguide Bragg grating adopts a double-sided symmetrical etching structure. Each grating unit includes an unetched area and an etched area arranged along the light propagation direction. The etched area is formed by symmetrical etching of the two sidewalls of the waveguide towards the center of the waveguide in a transverse direction perpendicular to the light propagation direction. The width of the transverse etching on one side is the etching dimension extending from the sidewall of the waveguide into the core layer on each side. The left gradient region (1) and the right gradient region (3) each include at least two gradient groups arranged along the light propagation direction. Each gradient group includes at least two consecutive grating units. Each grating unit in the same gradient group has the same single-sided lateral etching width and the same grating period. At least some different gradient groups have different single-sided lateral etching widths and quantization compensation periods corresponding to the single-sided lateral etching widths. The central constant region (2) includes at least two consecutive grating units, each of which has the same single-sided lateral etching width and the same grating period.

2. The discrete grouped graded sidewall etched waveguide Bragg grating according to claim 1, characterized in that, The single-sided lateral etching width is a discrete etching width determined according to the preset target coupling coefficient distribution, and the quantization compensation period is a grating period determined according to the offset of the local Bragg wavelength corresponding to the single-sided lateral etching width relative to the reference Bragg wavelength.

3. The discrete grouped graded sidewall etched waveguide Bragg grating according to claim 1, characterized in that, The etched areas in the left gradient region, the central constant region, and the right gradient region are located in the same sidewall etching plate layer. The lateral etching width of each gradient group in the left gradient region and the right gradient region, as well as the central constant region, is determined by the sidewall boundary position in the sidewall etching plate layer. The grating period of each gradient group in the left gradient region and the right gradient region, as well as the central constant region, is determined by the period coordinates along the light propagation direction.

4. A design method for discrete grouped graded sidewall etched waveguide Bragg gratings, characterized in that, Includes the following steps: S1, determine the target operating wavelength, Bragg order and the single-sided lateral etching width of the central constant region, obtain the grating period corresponding to the central constant region, and use the grating period as the reference grating period; S2, under the reference grating period, obtain the equivalent coupling coefficient and local Bragg wavelength of the waveguide grating model corresponding to different single-sided lateral etching widths, establish the first mapping relationship between the single-sided lateral etching width and the equivalent coupling coefficient, and the second mapping relationship between the single-sided lateral etching width and the local Bragg wavelength. S3, based on the preset target coupling coefficient distribution, determine the target coupling coefficient of each gradient group in the left gradient region and the right gradient region; S4. Based on the first mapping relationship, the target coupling coefficient of each gradient group is back-interpolated to obtain the theoretical single-sided lateral etching width of each gradient group. The theoretical single-sided lateral etching width is quantized according to the manufacturing rules to obtain the quantized single-sided lateral etching width of each gradient group. S5, for a gradient group whose single-sided lateral etching width is greater than zero after quantization, the local Bragg wavelength corresponding to the gradient group under the reference grating period is determined based on the second mapping relationship. S6. Determine the theoretical compensation period of each gradient group based on the target operating wavelength and the local Bragg wavelength, and quantize the theoretical compensation period to an integer multiple of the preset period layout grid to obtain the quantized compensation period. S7. Based on the quantized single-sided lateral etching width, quantization compensation period, and number of grating periods contained in each gradient group of the central constant region and each gradient group, a waveguide Bragg grating layout including the left gradient region, the central constant region, and the right gradient region is generated. The left gradient region and the right gradient region are mirror-symmetric about the central constant region.

5. The design method for discrete grouped graded sidewall etched waveguide Bragg gratings according to claim 4, characterized in that, The method for establishing the first and second mapping relationships includes: selecting at least two candidate single-sided lateral etching widths, and constructing corresponding uniform sidewall etched waveguide Bragg grating models under the conditions of reference grating period, same duty cycle, same waveguide cross section, and same grating length; obtaining the reflection spectrum corresponding to each candidate single-sided lateral etching width, and extracting the peak reflectivity and peak wavelength of the reflection spectrum; inverting the corresponding equivalent coupling coefficient based on the peak reflectivity, and using the peak wavelength as the local Bragg wavelength under the corresponding single-sided lateral etching width, thereby establishing the first mapping relationship between the single-sided lateral etching width and the equivalent coupling coefficient, and the second mapping relationship between the single-sided lateral etching width and the local Bragg wavelength.

6. The design method for discrete grouped graded sidewall etched waveguide Bragg gratings according to claim 4, characterized in that, The normalized envelope function of the preset target coupling coefficient distribution is a non-decreasing envelope function from the end of the grating to the central constant region, and is selected from one of the following: raised cosine type, sine square type, Gaussian half-window type, Hanning half-window type, linear type, exponential type, and discrete envelope output by the optimization algorithm.

7. The design method for discrete grouped graded sidewall etched waveguide Bragg gratings according to claim 4, characterized in that, The target coupling coefficient is determined by using the equivalent coupling coefficient corresponding to the single-sided etching width of the central constant region as the maximum target coupling coefficient. Suppose that the unilateral gradient region includes N gradient groups, and in the th... The center-normalized position of each gradient group: ,in, At the center normalized position Normalized envelope function for the pre-defined target coupling coefficient distribution Sampling was performed to obtain the first The target coupling coefficient of the gradient group .

8. The design method for discrete grouped graded sidewall etched waveguide Bragg gratings according to claim 4, characterized in that, The theoretical single-sided transverse etching width is determined as follows: A normalized first mapping relationship is established: / , Single-sided etching width The corresponding coupling coefficients; and inverse interpolation is performed within the monotonic interval of the normalized first mapping relationship to obtain the result satisfying: Theoretical single-sided transverse etching width .

9. The design method for discrete grouped graded sidewall etched waveguide Bragg gratings according to claim 4, characterized in that, The manufacturing quantification includes: setting the minimum non-zero manufacturable single-sided lateral etching width as... The map grid is When the first The theoretical single-sided transverse etching width of each gradient group When the gradient group is quantized, the lateral etching width on one side is set to 0, and the period of the gradient group is taken as the reference grating period; when At that time, the theoretical single-sided lateral etching width is... Quantized to the width of the layout grid The quantized single-sided lateral etching width is obtained by multiplying the integer multiple of the quantized value. The width of the pattern grid is determined based on the manufacturing resolution of the lateral etching width.

10. The design method for discrete grouped graded sidewall etched waveguide Bragg gratings according to claim 4, characterized in that, For each gradient group where the quantized single-sided lateral etching width is greater than zero, the quantized single-sided lateral etching width is obtained. Then, based on the second mapping relationship, the gradient group is determined in the reference grating period. The corresponding local Bragg wavelength According to the reference grating period Target operating wavelength and local Bragg wavelength Calculate the theoretical compensation period: and the theoretical compensation period Quantized to a preset periodic layout raster Integer multiples, to get the first The quantization compensation period used by each gradient group The periodic layout grid is determined based on the manufacturing resolution of the grating period.

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