Beam shaping optical system based on gradient refractive index lens and design method thereof

Abstract

The invention discloses a gradient refractive index lens-based beam shaping optical system and a design method thereof, the optical system comprises at least one divergent gradient refractive index lens and at least one convergent gradient refractive index lens, and the divergent gradient refractive index lens and the convergent gradient refractive index lens are combined and configured along the same optical axis. The arrangement sequence of the gradient refractive index lenses and the relative position relation of the gradient refractive index lenses in the optical axis direction are designed, so that the optical system forms an afocal light path structure on the whole. The optical system is used for carrying out transverse scale regulation and control on an incident light beam and realizing light beam expansion, light beam shrinkage and light beam shaping on the premise of keeping approximate collimation propagation characteristics of an output light beam. According to the structure, the thermal lens effect in high-power laser can be avoided, the stability and reliability of the system are improved, tight attachment, cascade expansion and direct coupling with optical fibers are supported, and miniaturization and integration application is facilitated.

Description

Technical Field

[0001] This invention relates to the field of optical device technology, and in particular to a beam shaping optical system based on a gradient refractive index lens and its design method, for controlling the lateral size and angular characteristics of a beam. Background Technology

[0002] In laser application systems, it is often necessary to adjust the lateral dimensions and divergence angle of the laser beam to meet the beam parameter requirements of different application scenarios. For example, in laser transmission, beam scanning, fiber coupling, and compact optoelectronic systems, it is usually necessary to expand the laser beam to reduce the beam divergence angle or match subsequent optical components with larger apertures. In other application scenarios, it is necessary to shrink the beam to achieve spot size compression or to match miniaturized optical devices, detectors, and integrated modules. Both beam expansion and beam shrinking are typical requirements for laser beam shaping.

[0003] In existing technologies, beam expansion or contraction is typically achieved using optical systems composed of multiple refractive lenses, such as Galilean or Keplerian optical structures. The size and divergence angle of the laser beam are adjusted through a combination of lenses with different focal lengths and spatial propagation between the lenses. These solutions rely on the refraction of the lens surfaces to achieve beam shaping, and while the structural form is mature, they usually require a certain axial length and multiple optical elements, thus limiting system miniaturization, assembly stability, and integration. Furthermore, multi-lens systems are sensitive to lens spacing and coaxiality; under conditions of vibration, shock, or temperature changes, optical axis misalignment or parameter drift can easily affect the beam shaping effect, limiting their use in high-stability, miniaturized applications.

[0004] Gradient-index lenses solve this problem. By creating a continuously varying refractive index distribution within the optical medium, gradient-index lenses gradually deflect light during propagation, thus enabling control over beam propagation characteristics without the need for complex surface curvature designs. This means that gradient-index lenses can have planar end faces, allowing multiple lenses to be closely fitted together or directly coupled to optical fibers. Compared to traditional optical systems that rely on multiple refractive surfaces and long free propagation distances, gradient-index lenses can control beam size variations and propagation direction distribution over a shorter physical length. This helps reduce the number of optical components in the system, lower axial dimensions, and improve the overall compactness and stability of the structure.

[0005] In practical applications, gradient refractive index lenses with different refractive index distribution characteristics exhibit different functional features in beam shaping. For example, gradient refractive index lenses with diverging characteristics can be used to control beam divergence, while those with contracting characteristics can be used to control beam convergence or reversal. By combining different types of gradient refractive index lenses, or by increasing the number of gradient refractive index lenses and selecting different gradient refractive index distribution parameters, diverse beam shaping needs can be met within a limited spatial scale. Summary of the Invention

[0006] This invention aims to provide a beam manipulation optical system based on gradient refractive index lenses and its design method. By combining and configuring different types of gradient refractive index lenses, a compact and axially aligned optical system is constructed. This system enables the manipulation of the lateral scale of the incident beam, including beam shaping functions such as beam expansion and beam contraction, while maintaining the approximately collimated propagation characteristics of the output beam. This optical system features simple structure, high stability, and ease of integration, making it suitable for miniaturization and system integration applications.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] In one aspect, the present invention proposes an optical system based on a gradient refractive index lens. The optical system includes at least one diverging gradient refractive index lens and at least one converging gradient refractive index lens. The diverging and converging gradient refractive index lenses are combined and configured along the same optical axis. By designing the arrangement order of each gradient refractive index lens and their relative positional relationship in the direction of the optical axis, the optical system as a whole forms a focal-free optical path structure similar to that of a Galilean telescope.

[0009] In the aforementioned afocal optical path structure, both the diverging gradient refractive index lens and the converging gradient refractive index lens are radial gradient refractive index lenses, and both types of lenses have flat end faces. The refractive index distribution of the diverging gradient refractive index lens increases from the optical axis towards the edge, causing the incident parallel beam of light to be deflected away from the optical axis. The refractive index distribution of the converging gradient refractive index lens decreases from the optical axis towards the edge, causing the incident parallel beam of light to be deflected towards the optical axis.

[0010] The diverging gradient refractive index lens and the converging gradient refractive index lens can be spaced apart from each other in the axial direction, directly connected to each other, or a combination of multiple gradient refractive index lenses to form an integrated optical structure; in some embodiments, the optical system can also be composed of multiple of the above-mentioned optical structures as sub-optical systems cascaded along the optical axis.

[0011] The diverging gradient refractive index lens and the converging gradient refractive index lens are spaced apart from each other in the axial direction. Specifically, the converging gradient refractive index lens and the diverging gradient refractive index lens are arranged sequentially along the same optical axis, with a dielectric layer between them. The dielectric layer is air or a transparent medium with a set refractive index. When a parallel beam of light is incident from the side of the converging gradient refractive index lens, it produces a beam shaping effect that reduces the incident beam. When a parallel beam of light is incident from the side of the diverging gradient refractive index lens, it produces a beam shaping effect that expands the incident beam.

[0012] By combining the two types of lenses, the parallel beam does not form an actual focal point inside the system, and the beam emitted after passing through the optical system still maintains a parallel propagation state, but its lateral aperture changes relative to the incident beam, thereby achieving scale control and wavefront shaping of the input beam.

[0013] Regardless of whether it is a single lens combination, a composite structure composed of multiple gradient refractive index lenses, or an overall structure formed by cascading multiple sub-optical systems, as long as its whole is equivalent to a first-order afocal optical structure without a real focus in the first-order optical sense, and can enable the incident parallel beam to exit in the form of a parallel beam after changing the lateral aperture, it falls within the protection scope of the optical system described in this invention.

[0014] In another aspect, the present invention also provides a design method for a beam shaping optical system based on a gradient refractive index lens, for realizing the above-mentioned beam shaping optical system based on a gradient refractive index lens.

[0015] The design method is based on a combination of at least one divergent gradient refractive index lens and at least one converging gradient refractive index lens. By arranging the divergent and converging gradient refractive index lenses along the same optical axis and designing the arrangement order and relative position of each gradient refractive index lens along the optical axis, the resulting optical system forms an optical path structure without a real focal point in the first-order optical sense, thereby achieving scale control of the incident beam.

[0016] In the design method described, the divergent and converging gradient refractive index lenses can be implemented in various ways along the axial direction, including being spaced apart from each other, directly connected to each other, or forming an integrated optical structure by combining multiple gradient refractive index lenses. In different implementation methods, adjacent gradient refractive index lenses can be separated by air or an intermediate medium with a predetermined refractive index, or they can be directly and tightly connected.

[0017] The design method further introduces first-order optical equivalent analysis, representing a single gradient refractive index lens as a first-order optical equivalent model. This first-order optical equivalent model consists of two optical spacers located on either side of the thin lens and an equivalent thin lens positioned between them. Specifically, the equivalent thin lens corresponding to a converging gradient refractive index lens has a positive equivalent focal length, while the equivalent thin lens corresponding to a diverging gradient refractive index lens has a negative equivalent focal length.

[0018] Based on the first-order optical equivalent analysis, by reasonably selecting the structural parameters of lenses with different refractive indices and the thickness and refractive index of possible intermediate media, the equivalent focal position of the equivalent positive thin lens and the equivalent focal position of the equivalent negative thin lens coincide in the optical axis direction, thus forming an optical structure without an actual focal point in an equivalent sense.

[0019] When the optical system contains multiple gradient refractive index lenses, the design method can also introduce a step-by-step merging equivalent processing approach. Specifically, each individual gradient refractive index lens is first equivalently represented as a first-order optical equivalent model; then, any two first-order optical equivalent models that are adjacent along the optical axis, together with any intermediate medium that may exist between them, are merged and equivalently represented as a single first-order optical merging equivalent unit.

[0020] By repeating the above-described stepwise merging equivalent processing, an optical system containing multiple gradient refractive index lenses can be gradually simplified into an equivalent representation composed of fewer merged equivalent units, until only the equivalent structure used for parameter design is retained, thereby completing the overall design of the beam shaping optical system.

[0021] In a further embodiment, the arrangement of the spaced-apart, directly interconnected, and multiple gradient refractive index lens combinations can also be implemented by arranging them in series along the optical axis in a predetermined order and connecting them to each other through an intermediate medium or by direct and tight connection, thereby forming an overall beam shaping optical system that satisfies the above-mentioned focalless optical path characteristics.

[0022] Beneficial effects of this invention:

[0023] The optical system proposed in this invention employs a focalless structure, eliminating the presence of a real focal point. This fundamentally avoids the "thermal lensing effect" common in high-power laser applications—the problem of localized temperature rise and undesirable refractive index changes in lenses due to highly concentrated beam energy, which negatively impacts system performance. This characteristic significantly improves the system's stability and reliability at high power. Furthermore, this structure can be cascaded with multiple focalless optical structures to achieve more extreme beamwidth ratios or more complex wavefront manipulation, demonstrating excellent scalability. Simultaneously, because the gradient refractive index lenses used can employ planar end-face structures, this optical system allows for close-fitting or integrated connections between multiple gradient refractive index lenses and direct coupling to fiber end faces. This reduces system assembly and adjustment complexity and improves the system's mechanical stability and environmental adaptability. Attached Figure Description

[0024] Figure 1 This is a structural diagram of the optical system described according to the first embodiment of the present invention;

[0025] Figure 2 This is an example of an optical system design method described according to the first embodiment of the present invention;

[0026] Figure 3 This is a structural diagram of the optical system described according to the second embodiment of the present invention;

[0027] Figure 4 This is an example of an optical system design method described according to the second embodiment of the present invention;

[0028] Figure 5 This is a structural diagram of the optical system described according to the third embodiment of the present invention;

[0029] Figure 6 This is an example of an optical system design method described according to the third embodiment of the present invention;

[0030] Figure 7 This is a structural diagram of the optical system described according to the fourth embodiment of the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0032] Implementation Method 1:

[0033] Figure 1 and Figure 2 The first embodiment of the present invention is shown.

[0034] like Figure 1 As shown, a beam-shaping optical system based on a gradient refractive index lens includes a converging gradient refractive index lens and a diverging gradient refractive index lens arranged sequentially along the same optical axis, with a dielectric layer between them. The dielectric layer can be air or a transparent medium with a specific refractive index, and its thickness can be set to a fixed value or designed as an adjustable structure to adapt to refractive index matching requirements under different operating wavelengths. In this optical system, when a parallel or nearly parallel beam is incident from the converging gradient refractive index lens side, the optical system produces a beam-shaping effect that reduces the incident beam; when a parallel beam is incident from the diverging gradient refractive index lens side, the optical system produces a beam-shaping effect that expands the incident beam.

[0035] To determine the structural parameters of the aforementioned optical system, the following design method can be used for analysis and calculation:

[0036] like Figure 2 As shown, this embodiment uses a first-order optical equivalent model to model the gradient refractive index lens.

[0037] Specifically, the converging gradient refractive index lens is equivalent to a converging gradient refractive index lens equivalent model. This equivalent model is a first-order optical model, consisting of two optical spaces of equal thickness and an equivalent positive thin lens sandwiched between the two optical spaces. The positive thin lens has a positive equivalent focal length. The equivalent thickness of the two optical gaps is .

[0038] Similarly, the diverging gradient refractive index lens can be equivalently represented by an equivalent model of a diverging gradient refractive index lens. This equivalent model is a first-order optical model, consisting of two optical spaces of equal thickness and an equivalent negative thin lens sandwiched between the two optical spaces. The negative thin lens has a negative equivalent focal length. The equivalent thickness of the two optical gaps is .

[0039] The equivalent model described above contains an intermediate medium with the same refractive index and thickness parameters as the medium in the actual optical system. This intermediate medium has a refractive index... ,thickness .

[0040] The equivalent model and the intermediate medium described above are still arranged sequentially along the optical axis according to the axial arrangement in the original optical system when representing the equivalent model. For the incident beam, a ray tracing analysis method under the first-order optical approximation condition can be used to perform an equivalent analysis of the propagation state of the light within the optical system. The first-order ray tracing method is an optical analysis technique known to those skilled in the art and will not be described in detail here.

[0041] In the equivalent models of converging and diverging gradient refractive index lenses, the equivalent focal length and the equivalent thickness of the two optical intervals can be determined by the refractive index gradient parameters of the corresponding gradient refractive index lens, the central refractive index of the lens, the refractive index of the intermediate medium, and the physical length of the lens, respectively, and their relationships are as follows:

[0042]

[0043] in, , For the refractive index gradient parameters of the corresponding gradient refractive index lens, For the central refractive index, , The length of the lens. The refractive index of the dielectric layer or reference medium. It is the tangent function. It is a cosecant function. It is the hyperbolic tangent function. It is a hyperbolic cosecant function.

[0044] Based on the above first-order optical equivalent model, the optical system can be equivalently represented as a number of optical action parts arranged sequentially along the optical axis under the first-order optical approximation conditions.

[0045] Specifically, the equivalent representation includes: a first optical interval located on the system input side, a positive thin lens disposed after the first optical interval, and a second optical interval disposed after the positive thin lens; an intermediate dielectric layer is disposed after the second optical interval; and a third optical interval, a negative thin lens, and a fourth optical interval are disposed sequentially after the intermediate dielectric layer, thereby collectively constituting the first-order optical equivalent representation of the optical system.

[0046] By rationally selecting the structural parameters of each gradient refractive index lens and setting the thickness of the medium between the gradient refractive index lenses, the equivalent focal position of the positive thin lens in the equivalent model of the converging gradient refractive index lens coincides with the equivalent focal position of the negative thin lens in the equivalent model of the diverging gradient refractive index lens in the optical axis direction.

[0047] Under these conditions, the equivalent focal length of the positive thin lens is greater than the absolute value of the equivalent focal length of the negative thin lens, thereby enabling the equivalent representation to constitute a type of first-order afocal optical structure without a real focal point in the first-order optical sense, thus completing the parameter design of the optical system.

[0048] The optical system obtained by the design method described in this embodiment has the following characteristics:

[0049] Under the above parameter configuration conditions, when the laser beam is incident from one side of the converging gradient refractive index lens, the optical system produces a beam shaping effect that reduces the incident beam.

[0050] In this operating state, the beam reduction factor of the optical system is jointly determined by the ratio between the equivalent focal length of the positive thin lens in the first-order optical equivalent model of the converging gradient index lens and the equivalent focal length of the negative thin lens in the first-order optical equivalent model of the diverging gradient index lens. The beam reduction factor is a positive value, used to characterize the reduction ratio of the lateral dimension of the output beam to the lateral dimension of the input beam.

[0051] Meanwhile, in this beam-shrinking working state, the angular distribution of the incident beam is magnified after passing through the optical system, and the magnification ratio is consistent with the beam-shrinking factor, thereby demonstrating the angular amplification and control effect of the optical system on the beam divergence angle.

[0052] When the laser beam is incident from one side of the divergent gradient refractive index lens, the optical system produces a beam-shaping effect that expands the incident beam.

[0053] In this operating state, the beam expansion factor of the optical system is also determined by the ratio between the equivalent positive thin lens focal length of the converging gradient refractive index lens and the equivalent negative thin lens focal length of the diverging gradient refractive index lens, which is used to characterize the magnification ratio of the output beam lateral dimension relative to the input beam lateral dimension.

[0054] Meanwhile, in this beam-expanding state, the angular distribution of the incident beam is compressed after passing through the optical system, and the compression ratio is the reciprocal of the beam-expanding factor, thus indicating that the optical system has the function of compressing and controlling the beam angular distribution during the beam-expanding process.

[0055] Implementation Method Two:

[0056] Figure 3 and Figure 4 A second embodiment of the present invention is shown.

[0057] like Figure 3As shown, the optical system in this embodiment includes a converging gradient refractive index lens and a diverging gradient refractive index lens arranged sequentially along the same optical axis. Unlike Embodiment 1, the converging and diverging gradient refractive index lenses do not have a separate intermediate medium layer; instead, they are directly connected to each other through welding, bonding, or pressing to form an integrated optical structure. In this optical system, when a parallel or nearly parallel beam is incident from the converging gradient refractive index lens, the optical system produces a beam-shaping effect that reduces the incident beam; when a parallel beam is incident from the diverging gradient refractive index lens, the optical system produces a beam-shaping effect that expands the incident beam.

[0058] To determine the structural parameters of the aforementioned optical system, the following design method can be used for analysis and calculation:

[0059] like Figure 4 As shown, in order to facilitate the parameter design of the above optical system, this embodiment also uses a first-order optical equivalent model to model the gradient refractive index lens. The modeling method and basic design idea are the same as those in Embodiment 1.

[0060] The difference lies in the fact that, since there is no independent dielectric layer between the converging gradient refractive index lens and the diverging gradient refractive index lens, it is not necessary to introduce intermediate dielectric refractive index parameters in the equivalent models of the converging and diverging gradient refractive index lenses. In this embodiment, the parameter can be treated as a constant, for example, set to 1 or other fixed values, and this setting does not affect the relative relationship and design conclusion of the equivalent model.

[0061] Based on the above first-order optical equivalent model, the optical system can be equivalently represented as a number of optical action parts arranged sequentially along the optical axis under the first-order optical approximation conditions.

[0062] Specifically, such as Figure 4 As shown, the equivalent representation includes: a first optical interval located on the system input side, a positive thin lens disposed after the first optical interval, and a second optical interval disposed after the positive thin lens; after the second optical interval, a third optical interval, a negative thin lens, and a fourth optical interval are disposed in sequence, thereby jointly constituting the first-order optical equivalent representation of the optical system.

[0063] By rationally selecting the structural parameters of each gradient refractive index lens, the equivalent focal position of the positive thin lens in the equivalent model of the converging gradient refractive index lens coincides with the equivalent focal position of the negative thin lens in the equivalent model of the diverging gradient refractive index lens along the optical axis.

[0064] Under these conditions, the equivalent focal length of the positive thin lens is greater than the absolute value of the equivalent focal length of the negative thin lens, thereby enabling the equivalent representation to constitute a type of afocal optical structure in the first-order optical sense, thus completing the parameter design of the optical system.

[0065] The optical system obtained by the design method described in this embodiment has the following characteristics:

[0066] Under the above parameter configuration conditions, when the laser beam is incident from one side of the converging gradient refractive index lens, the optical system produces a beam shaping effect that reduces the incident beam.

[0067] In this operating state, the beam reduction factor of the optical system is jointly determined by the ratio between the equivalent focal length of the positive thin lens in the first-order optical equivalent model of the converging gradient index lens and the equivalent focal length of the negative thin lens in the first-order optical equivalent model of the diverging gradient index lens. The beam reduction factor is a positive value, used to characterize the reduction ratio of the lateral dimension of the output beam to the lateral dimension of the input beam.

[0068] Meanwhile, in this beam-shrinking working state, the angular distribution of the incident beam is magnified after passing through the optical system, and the magnification ratio is consistent with the beam-shrinking factor, thereby demonstrating the angular amplification and control effect of the optical system on the beam divergence angle.

[0069] When the laser beam is incident from one side of the divergent gradient refractive index lens, the optical system produces a beam-shaping effect that expands the incident beam.

[0070] In this operating state, the beam expansion factor of the optical system is also determined by the ratio between the equivalent positive thin lens focal length of the converging gradient refractive index lens and the equivalent negative thin lens focal length of the diverging gradient refractive index lens, which is used to characterize the magnification ratio of the output beam lateral dimension relative to the input beam lateral dimension.

[0071] Meanwhile, in this beam-expanding state, the angular distribution of the incident beam is compressed after passing through the optical system, and the compression ratio is the reciprocal of the beam-expanding factor, thus indicating that the optical system has the function of compressing and controlling the beam angular distribution during the beam-expanding process.

[0072] Implementation Method 3:

[0073] like Figure 5 and Figure 6As shown, the optical system in this embodiment is a single, focal-free optical system composed of multiple gradient refractive index lenses. The optical system includes at least one converging gradient refractive index lens and at least one diverging gradient refractive index lens. These gradient refractive index lenses can be arranged sequentially along the same optical axis, and an intermediate dielectric layer can be provided between adjacent gradient refractive index lenses, or they can be directly and tightly connected to each other.

[0074] exist Figure 5 In the example shown, the optical system consists of two converging gradient index lenses and two diverging gradient index lenses, with an intermediate medium layer between the two converging gradient index lenses. This gap can be air or a transparent medium with a specific refractive index. However, it should be understood that this structure is only an example, and the number, type, and arrangement of the gradient index lenses can be adjusted as needed.

[0075] To determine the structural parameters of the aforementioned optical system, this embodiment proposes the following design method:

[0076] To facilitate parameter design for the above-mentioned optical system without a real focus, which consists of multiple gradient refractive index lenses, this embodiment adopts the first-order optical equivalent analysis method described in Embodiment 1, and introduces a step-by-step merging equivalent processing method to further simplify the first-order optical equivalent representation of the system.

[0077] Specifically, firstly, an equivalent processing method similar to that in Embodiment 1 is adopted to represent each individual gradient refractive index lens in the optical system as an equivalent first-order optical model. The first-order optical model consists of two optical intervals of equal thickness located on both sides of a thin lens, and a thin lens sandwiched between them, which is used to characterize the equivalent optical behavior of the corresponding gradient refractive index lens under the first-order optical approximation condition.

[0078] Subsequently, any two adjacent first-order optical equivalent models along the optical axis and any intermediate medium between them are treated as a whole and merged for equivalence processing. Under the first-order optical approximation conditions, they are equivalent to a single first-order optical merging equivalent unit. This merging equivalent unit also consists of two optical intervals and a thin lens between them, but the thicknesses of the two optical intervals on either side of the thin lens do not need to be equal. The merging equivalence processing refers to representing the two adjacent first-order optical equivalent models and the intermediate medium between them as a single first-order optical merging equivalent unit under the first-order optical approximation conditions. This first-order optical merging equivalent unit also consists of two optical intervals and a thin lens located between them, used to describe the equivalent first-order optical characteristics of the overall structure.

[0079] To provide a unified description of the two types of structures, in this embodiment, the first-order optical equivalent model and the first-order optical combined equivalent unit are collectively referred to as the first-order optical representation unit. Both have the same structural form, consisting of a thin lens and optical spacing on both sides. The difference lies in the fact that the former has equal spacing on both sides, while the latter's spacing on both sides is not necessarily equal.

[0080] During the merging and equivalent processing, the equivalent focal length of the thin lens and the optical spacing thickness on both sides in the obtained first-order optical merging equivalent unit are determined by the equivalent parameters of the two first-order optical representation units involved in the merging and the axial distance between them.

[0081] The axial distance refers to the distance along the optical axis between the thin lenses in the two first-order optical representation units to be merged before the merging equivalence processing is performed. This distance is composed of the optical spacing thickness on the right side of the thin lens of the left unit, the optical spacing thickness on the left side of the thin lens of the right unit, and the thickness of the intermediate medium that may exist between them. When there is no intermediate medium between the two first-order optical representation units, the axial distance is composed of the sum of the two optical spacing thicknesses mentioned above.

[0082] In one specific embodiment, to facilitate the explanation of the correspondence between the parameters, the equivalent parameters of the merged equivalent units can be described using the following relational expression:

[0083]

[0084] in, The thickness of the left optical spacing of the first-order optical representation unit on the left. This indicates the focal length of the thin lens in the first-order optical representation unit on the left. This indicates the right optical spacing thickness in the first-order optical representation unit on the right. This indicates the focal length of the thin lens in the first-order optical representation unit on the right. This indicates the aforementioned axial distance; , and These represent the optical spacing thickness on both sides of the merged unit and the equivalent focal length of its thin lens, respectively.

[0085] For example, such as Figure 6 As shown, the first-order optical equivalent models corresponding to the two converging gradient refractive index lenses set adjacent to each other on the left side of the system are combined and equivalent to form the first optical merging equivalent unit. The first-order optical equivalent models corresponding to the two diverging gradient refractive index lenses set adjacent to each other on the right side of the system are combined and equivalent to form the second merging equivalent unit.

[0086] If, after one merging and equivalence processing, there are still two or more first-order optical representation units arranged adjacent to each other along the optical axis in the system, further merging and equivalence processing can be performed on two adjacent first-order optical representation units along with any intermediate media that may exist between them. At this time, the object being equivalenced can be either the initial first-order optical equivalent model or the already formed first-order optical merging equivalent unit.

[0087] By repeating the above-described step-by-step merging equivalent process, the optical system can be gradually simplified into a system structure consisting of a smaller number of first-order optical representation units, until only two first-order optical representation units arranged adjacent to each other along the optical axis are ultimately retained for subsequent parameter design and analysis.

[0088] In the system structure after the above-mentioned step-by-step merging equivalent processing, the two first-order optical merging equivalent units that are finally retained are both composed of optical intervals located on both sides of the thin lens and the thin lens between them.

[0089] In the final equivalent structure described above, the two first-order optical representation units can be placed directly adjacent to each other, or the intermediate medium that was not involved in the equivalent processing in the original structure can be retained. By adjusting the presence, thickness, and refractive index of this intermediate medium, the axial equivalent parameter relationship of the system can be further adjusted.

[0090] Based on this, by reasonably selecting the structural parameters of each gradient refractive index lens and the thickness and refractive index of each medium layer, the equivalent focal points of the thin lenses in the two first-order optical representation units coincide with each other in the optical axis direction, so that the optical system forms a focalless optical path structure without actual focal points in the first-order optical sense, and the parameter design of the optical system can be completed.

[0091] The optical system obtained by the design method described in this embodiment has the following characteristics:

[0092] Under the above parameter configuration conditions, when the incident beam is incident from the actual optical structure end face corresponding to the side of the equivalent positive thin lens in the system structure after the merging and equivalent processing, the optical system produces a beam shaping effect that reduces the incident beam.

[0093] In this beam-shrinking operation state, the beam-shrinking factor of the optical system is determined by the ratio between the equivalent focal length of the equivalent positive thin lens and the equivalent focal length of the equivalent negative thin lens in the system structure after merging and equivalent processing. The beam-shrinking factor is a positive value used to characterize the reduction ratio of the lateral dimension of the output beam to the lateral dimension of the input beam.

[0094] Meanwhile, in this beam-shrinking working state, the angular distribution of the incident beam is magnified after passing through the optical system, and the degree of magnification corresponds to the beam-shrinking factor, thus indicating that the optical system has the function of angular amplification and control of the beam divergence angle during the beam-shrinking process.

[0095] When the incident beam is incident from the end face of the actual optical structure corresponding to the side where the equivalent negative thin lens is located in the system structure after the merging and equivalent processing, the optical system produces a beam shaping effect that expands the incident beam.

[0096] In this beam-expanding working state, the beam expansion factor of the optical system is also determined by the ratio between the equivalent focal length of the equivalent positive thin lens and the equivalent focal length of the equivalent negative thin lens, which is used to characterize the magnification ratio of the lateral dimension of the output beam relative to the lateral dimension of the input beam.

[0097] Meanwhile, in this beam-expanding state, the angular distribution of the incident beam is compressed after passing through the optical system, and the degree of compression corresponds to the beam expansion factor, thus indicating that the optical system has the ability to compress and control the beam angular distribution during the beam expansion process.

[0098] Implementation Method Four:

[0099] Figure 7 The fourth embodiment of the present invention is shown.

[0100] like Figure 7 As shown, the optical system in this embodiment is composed of multiple afocal optical path structures arranged sequentially along the same optical axis. Each afocal optical path structure is formed by combining divergent gradient refractive index lenses and converging gradient refractive index lenses according to a predetermined axial positional relationship, which satisfies the beam shaping function of not generating an actual focal point within the system and achieving scale transformation of parallel incident beams in the first-order optical sense.

[0101] The multiple afocal optical path structures can be arranged in series along the optical axis in a predetermined order to form an overall beam shaping optical system.

[0102] In terms of axial connection, an intermediate dielectric layer can be set between adjacent afocal optical path structures. The thickness and refractive index of the intermediate dielectric layer can be selected or adjusted according to design requirements. Alternatively, adjacent afocal optical path structures can be directly and tightly connected, for example, through optical contact, bonding, adhesive or integrated encapsulation.

[0103] With the above structural configuration, when a light beam is incident from one end face of the optical system, the beam passes sequentially through each afocal optical path structure along the optical axis and is subjected to beam shaping by the corresponding structure. Therefore, the overall beam shaping effect of the optical system on the incident beam is formed by the sequential accumulation of the beam shaping effects of each afocal optical path structure.

[0104] Specifically, the overall optical system's control effect on the lateral scale of the beam can be understood as the continuous superposition of the beam scale control ratios of each afocal optical path structure. Its overall beam expansion or contraction capability is equivalent to the stepwise product of the scale transformation ratios of each afocal optical path structure.

[0105] The scale modulation ratio of each afocal optical path structure on the incident beam reflects the degree to which the structure amplifies or reduces the lateral dimension of the beam.

[0106] Furthermore, since each of the aforementioned afocal optical path structures is based on a first-order, passive optical configuration without a real focal point, the overall optical system exhibits directional reversibility in its optical characteristics. That is, when the beam is incident from one side, it exhibits a beam-shrinking effect, and when it is incident from the opposite side, it will exhibit a corresponding beam-expanding effect, and vice versa.

Claims

1. A beam shaping optical system based on a gradient refractive index lens, characterized in that, The optical system includes at least one diverging gradient refractive index lens and at least one converging gradient refractive index lens. The diverging and converging gradient refractive index lenses are combined and configured along the same optical axis. By designing the arrangement order of each gradient refractive index lens and their relative positional relationship in the optical axis direction, the optical system as a whole forms a focalless optical path structure.

2. The beam shaping optical system based on a gradient refractive index lens according to claim 1, characterized in that, In the aforementioned afocal optical path structure, both the diverging gradient refractive index lens and the converging gradient refractive index lens are radial gradient refractive index lenses, and both types of lenses have flat end faces. The refractive index distribution of the diverging gradient refractive index lens increases from the optical axis to the edge, causing the incident parallel beam to bend away from the optical axis. The refractive index distribution of the converging gradient refractive index lens decreases from the optical axis to the edge, causing the incident parallel beam to bend towards the optical axis.

3. The beam shaping optical system based on a gradient refractive index lens according to claim 2, characterized in that, The divergent gradient refractive index lens and the converging gradient refractive index lens are arranged axially at intervals, directly connected to each other, or formed into an integrated optical structure through a combination of multiple gradient refractive index lenses.

4. The beam shaping optical system based on a gradient refractive index lens according to claim 3, characterized in that, The diverging gradient refractive index lens and the converging gradient refractive index lens are spaced apart from each other in the axial direction. Specifically, the converging gradient refractive index lens and the diverging gradient refractive index lens are arranged sequentially along the same optical axis, with a dielectric layer between them. The dielectric layer is air or a transparent medium with a set refractive index. When a parallel beam of light is incident from the side of the converging gradient refractive index lens, it produces a beam shaping effect that reduces the incident beam. When a parallel beam of light is incident from the side of the diverging gradient refractive index lens, it produces a beam shaping effect that expands the incident beam.

5. A method for designing a beam-shaping optical system based on a gradient refractive index lens, used to implement the beam-shaping optical system according to any one of claims 1 to 4, characterized in that, Includes the following processes: First, at least one diverging gradient refractive index lens and at least one converging gradient refractive index lens are combined and configured along the same optical axis. Secondly, by designing the arrangement order of lenses with different refractive indices and their relative positions along the optical axis, a focal-free optical path structure is formed.

6. The design method for a beam shaping optical system based on a gradient refractive index lens according to claim 5, characterized in that, The divergent gradient refractive index lens and the converging gradient refractive index lens are implemented axially in the following ways: spaced apart from each other, directly connected to each other, or a combination of multiple gradient refractive index lenses.

7. The design method for a beam shaping optical system based on a gradient refractive index lens according to claim 6, characterized in that, The diverging gradient refractive index lens and the converging gradient refractive index lens are axially spaced apart as follows: a first optical interval on the input side, a positive thin lens disposed after the first optical interval, and a second optical interval disposed after the positive thin lens; an intermediate dielectric layer is disposed after the second optical interval; after the intermediate dielectric layer, a third optical interval, a negative thin lens, and a fourth optical interval are disposed sequentially, together constituting the first-order optical equivalent representation of the optical system; the positive thin lens and the negative thin lens are specifically implemented as follows: A converging gradient refractive index lens can be represented by an equivalent model of a converging gradient refractive index lens. This equivalent model is a first-order optical model, consisting of two optical spaces of equal thickness and an equivalent positive thin lens sandwiched between the two optical spaces. The positive thin lens has a positive equivalent focal length, and the equivalent thickness of the two optical spaces is: The divergent gradient refractive index lens is equivalent to a divergent gradient refractive index lens equivalent model. The divergent gradient refractive index lens equivalent model is a first-order optical model, consisting of two optical spaces of equal thickness and an equivalent negative thin lens sandwiched between the two optical spaces. The negative thin lens has a negative equivalent focal length, and the equivalent thickness of the two optical spaces is equal. There is an intermediate medium between the equivalent models of converging gradient refractive index lenses and diverging gradient refractive index lenses; In the equivalent models of converging and diverging gradient refractive index lenses, the equivalent focal length and the equivalent thickness of the two optical intervals are determined by the refractive index gradient parameters of the corresponding gradient refractive index lens, the central refractive index of the lens, the refractive index of the intermediate medium, and the physical length of the lens, respectively. Ultimately, this makes the equivalent focal position of the positive thin lens in the equivalent model of the converging gradient refractive index lens coincide with the equivalent focal position of the negative thin lens in the equivalent model of the diverging gradient refractive index lens along the optical axis.

8. The design method for a beam shaping optical system based on a gradient refractive index lens according to claim 7, characterized in that, A diverging gradient refractive index lens and a converging gradient refractive index lens are directly connected to each other in the axial direction. Specifically, a converging gradient refractive index lens and a diverging gradient refractive index lens are arranged sequentially along the same optical axis. The converging gradient refractive index lens and the diverging gradient refractive index lens are directly bonded together to form an integrated optical structure, which specifically includes: a first optical interval located on the input side, a positive thin lens disposed after the first optical interval, and a second optical interval disposed after the positive thin lens. After the second optical interval, a third optical interval, a negative thin lens, and a fourth optical interval are arranged sequentially, which together constitute a first-order optical equivalent representation. The equivalent models of converging and diverging gradient index lenses do not introduce the refractive index parameter of the intermediate medium. This parameter is treated as a constant.

9. The design method for a beam shaping optical system based on a gradient refractive index lens according to claim 8, characterized in that, A combination of multiple gradient refractive index lenses along the axial direction, including at least one converging gradient refractive index lens and at least one diverging gradient refractive index lens, wherein each gradient refractive index lens is arranged sequentially along the same optical axis, and adjacent gradient refractive index lenses are connected by an intermediate dielectric layer or directly and tightly connected to each other. A step-by-step merging equivalent processing method is introduced to simplify the first-order optical equivalent representation. The simplification process is as follows: First, an equivalent treatment is adopted to represent each individual gradient refractive index lens as a first-order optical equivalent model; Subsequently, the first-order optical equivalent models of any two gradient refractive index lenses placed adjacent to each other along the optical axis are merged and equivalently processed as a whole. If there is an intermediate medium between the two gradient refractive index lenses, it is also merged and equivalently processed as a whole. The aforementioned merging equivalence processing refers to: under the first-order optical approximation condition, representing two adjacent first-order optical equivalent models and the intermediate medium between them as an equivalent first-order optical merging unit; the first-order optical merging equivalence unit is also composed of two optical intervals and a thin lens located between them; If, after one or more merging equivalent processing steps, there are still two or more merging equivalent units that are adjacent to each other along the optical axis, the merging equivalent units are selected again and merged until the entire optical system finally retains only two adjacent merging equivalent units for parameter design.

10. The design method for a beam shaping optical system based on a gradient refractive index lens according to claim 9, characterized in that, The axial implementation of the divergent gradient refractive index lens and the converging gradient refractive index lens also includes arranging three methods in series according to a set order: spacing, direct interconnection, or combination of multiple gradient refractive index lenses, to form an overall beam shaping optical system. The three methods of spacing, direct interconnection, and combination of multiple gradient refractive index lenses are achieved by setting an intermediate medium layer or by direct and tight connection.

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