Method for improving transmission efficiency of Cassegrain optical antenna

Abstract

The invention discloses a method for improving the transmission efficiency of a Cassegrain optical antenna. The method comprises the following steps: 1) designing a beam shaping system; 2) arranging a beam shaping system between the semiconductor laser and the Cassegrain optical antenna; (3) optimizing the distance d2 between the subsystem I (1) and the subsystem II (2) by taking the direction, parallel to the optical axis, of the annular collimated light beam output by the subsystem II (2) as a target; and 4) converting the astigmatic elliptical divergent beam generated by the semiconductor laser into an annular collimated beam by using the beam shaping system, and transmitting the annular collimated beam to the Cassegrain optical antennae. The invention provides a structure optimization method for improving the transmission efficiency of the system.

Description

Technical Field

[0001] This invention relates to the field of optical transmission, specifically a method for improving the transmission efficiency of a Cassegrain optical antenna. Background Technology

[0002] Semiconductor lasers (laser diodes) are compact, efficient, and reliable light sources in many scientific and engineering applications. However, their potential applications are limited by poor output beam quality. High-power semiconductor lasers typically emit beams with large divergence angles and astigmatism, resulting in complex far-field distributions that require appropriate models to describe their characteristics. Semiconductor lasers, with their high power, small size, light weight, and high-speed modulation capabilities, are well-suited for use as light sources in long-distance space optical communication. However, the poor beam quality of high-power semiconductor lasers necessitates appropriate beam shaping systems to obtain a circular, appropriately sized laser beam with a small divergence angle to meet the needs of long-distance optical communication. Cassegrain antennas, commonly used in reflective transceiver antennas, are widely used due to their simple structure, ease of manufacture, large aperture, long-distance transmission capability, lack of dispersion, and wide bandwidth. However, they suffer from central energy loss due to secondary mirror obstruction, significantly reducing their efficiency in transmitting solid beams. Therefore, designing an optical shaping system that can simultaneously improve antenna transmission efficiency and semiconductor laser beam quality has significant theoretical and practical value.

[0003] Cassegrain optical antennas are widely used due to their simple structure, ease of manufacture, and lack of aberrations. However, Cassegrain antennas suffer from significant central energy loss, which greatly reduces the transmission efficiency of optical antenna systems in space optical communication. To improve the transmission efficiency of optical antennas, many researchers have modified the structure of optical antennas: optimizing the structure of the primary or secondary mirror or designing off-axis antennas. While transmission efficiency has been improved, this has introduced the problem of manufacturing complex surface antenna mirrors. Other researchers have used hollow beams to avoid central energy loss, such as Laguerre-Gaussian (LG) beams and hollow beams generated by conical lenses. However, generating LG beams using computer holography results in energy loss due to the use of numerous optical components.

[0004] Semiconductor lasers (LDs) are commonly used as light sources in optical communication systems due to their advantages such as small size, high input-output conversion efficiency, low cost, and long lifespan. However, the output beam of a semiconductor laser is typically an elliptical diverging beam with some astigmatism. Some researchers use freeform surface lenses or gradient refractive index lenses to collimate the beam, but freeform surfaces usually lack mathematical expressions, making them difficult to fabricate, while the fabrication process of gradient refractive index lenses is complex, making it difficult to achieve ideal collimation results. Some researchers use microlens arrays, step mirrors, or plane mirrors to split and rearrange the beam from the semiconductor laser to achieve beam shaping and homogenization. Among these, microlens arrays are lightweight and small, but the incident beam is split into small beams that overlap on the homogenization plane, forming interference patterns that severely affect the shaping effect. Summary of the Invention

[0005] The purpose of this invention is to provide a method for improving the transmission efficiency of a Cassegrain optical antenna, comprising the following steps:

[0006] 1) Design a beam shaping system, including subsystem I and subsystem II;

[0007] Subsystem I is an aspherical cylindrical lens; subsystem II includes an aspherical lens and a truncated cone.

[0008] The aspherical cylindrical lens is used for astigmatism correction and beam circularization; the aspherical lens and the truncated cone are used to achieve beam collimation and generate a hollow beam.

[0009] 2) Position the beam shaping system between the semiconductor laser and the Cassegrain optical antenna;

[0010] 3) Optimize the distance d2 between subsystem I and subsystem II with the goal of ensuring that the annular collimated beam output by subsystem II is parallel to the optical axis;

[0011] 4) The elliptical diverging beam with astigmatism generated by the semiconductor laser is converted into a ring collimated beam using a beam shaping system, and the ring collimated beam is transmitted to the Cassegrain optical antenna.

[0012] Furthermore, the divergence angle of the outgoing beam from the aspherical cylindrical lens in the zy plane and zx plane of the o-xyz coordinate system is equal to... The o-xyz coordinate system has its origin at the center of the front surface of the aspherical cylindrical lens.

[0013] Furthermore, the semiconductor laser emits fast-axis and slow-axis beams outwards;

[0014] The fast-axis beam diverges at an angle of θ in the zy plane. The virtual source point is located on the output surface of the semiconductor laser.

[0015] The divergence angle of the slow-axis beam in the zx plane is The distance between the virtual source point and the output surface of the semiconductor laser is .

[0016] Furthermore, the distance between the aspherical cylindrical lens and the emitting end face of the semiconductor laser is d0;

[0017] The distance d0 satisfies the following constraints:

[0018] (1)

[0019] In the formula, Let be the divergence angle of the fast-axis beam in the zy plane; This is the distance between the virtual source point of the slow-axis beam and the output end face of the semiconductor laser; Let be the angle between the normal to the tangent plane at point A and the z-axis.

[0020] Furthermore, the beam after astigmatism correction via subsystem I is set to originate from the virtual source point. The emitted beam of light is a diverging circular beam;

[0021] Virtual Source Distance from the front surface of subsystem II As shown below:

[0022] (2)

[0023] In the formula, The distance between subsystem I and subsystem II; denoted as , where is the length of subsystem I; and is the refractive index.

[0024] Furthermore, the front surface of subsystem II is a rotationally symmetric hyperboloid, and the bottom surface is of height [missing information]. half-width is The inner cone;

[0025] The angle between the outer contour of the subsystem II truncated cone and the optical axis is equal to half the angle of the inner cone;

[0026] The collimated beam entering subsystem II undergoes two total internal reflections at the glass-air interface, and then exits from the rear surface of subsystem II in a direction parallel to the optical axis.

[0027] Furthermore, the collimated beam radius entering subsystem II As shown below:

[0028] (3)

[0029] Furthermore, the hollow radius of the emitted beam from subsystem II is shown below:

[0030] , (4)

[0031] In the formula, k is a constant; L is the thickness of the base of the truncated cone;

[0032] Among them, angle The following constraints must be met:

[0033] , (5)

[0034] Height of the inner cone As shown below:

[0035] (6)

[0036] Furthermore, subsystem II is symmetrical to the Cassegrain optical antenna about the optical axis center; the focal coordinates of the primary and secondary mirrors of the Cassegrain optical antenna are the same, that is... ; The thickness of the base of the truncated cone; The height of the hollowed-out bottom of subsystem II (2) is half-width is The radius of the circle at the base of the cone is L1 = dtanθ;

[0037] Point G With point F The ordinate of the intersection point E of the line and the secondary mirror surface is ; It is the focal length of the secondary lens; z1 is the coordinate value of point G on the z-axis; This represents the z-axis coordinate of the antenna primary mirror center.

[0038] Furthermore, the thickness of the truncated cone base of subsystem II ,as well as Determined by the following equation:

[0039] (7)

[0040] In the formula, and y1 and y2 are the focal lengths of the secondary and primary mirrors, respectively; y3 is the y-coordinate of point N; point N is the point where the light ray is reflected from point M to the primary mirror.

[0041] Furthermore, the transmission efficiency of the beam shaping system As shown below:

[0042] (9)

[0043] In the formula, r1 is the beam radius of the collimated beam entering subsystem II (2); E1 is the normalized intensity distribution of the hollow beam passing through system EA. It refers to the internal transmittance of the glass.

[0044] The technical effectiveness of this invention is undeniable. This invention designs an EA system that converts an elliptical, diffuse beam emitted by a semiconductor laser into a ring-shaped, collimated beam, achieving four functions: aberration correction, beam circularization, beam collimation, and hollow beam generation. Based on the vector catadioptric theorem and Fermat's principle, the parameters of part-1 and part-2 constituting the EA system, as well as the corresponding transmitting antenna structural parameters, were designed and calculated. Theoretical analysis and simulation results show that the larger the distance between part-1 and part-2 of the EA system, the wider the hollow beam. Based on this conclusion, a structural optimization method to improve the system's transmission efficiency is proposed. After comprehensively considering several practical factors that may lead to losses in the entire system, such as truncation loss, inner cone chamfer, and glass dielectric transmittance, the transmission efficiency of the entire system can reach 93.91% at a wavelength of 1550 nm. Considering material dispersion, the transmission efficiency can still be maintained above 90.00% in the wavelength range of 500–1647 nm, indicating that the system can operate over a wide wavelength range. Attached Figure Description

[0045] Figure 1 A schematic diagram of the Cassegrain optical transmitting antenna using the EA system;

[0046] Figure 2 This is a schematic diagram of the part-1 shaping principle;

[0047] Figure 3 The following are ray tracing diagrams of the laser beam passing through part-1. (a) Three-dimensional ray tracing diagram; (b) Ray tracing diagram along the fast axis; (c) Ray tracing diagram along the slow axis;

[0048] Figure 4 This is a schematic diagram of the cross-section of part-2 and a model diagram in two directions.

[0049] Figure 5 This is a schematic diagram of the Cassegrain transmitting antenna and part-2.

[0050] Figure 6 This is a schematic diagram of part-2 with chamfered edges.

[0051] Figure 7 This is a three-dimensional ray tracing diagram of a Cassegrain antenna with an EA system.

[0052] Figure 8 This is a transmission efficiency curve considering different practical factors.

[0053] Figure 9 (a) shows the beam waist variation of different wavelength beams in an EA system designed for a wavelength of 1550 nm. The lower right box is a schematic diagram of the normalized energy distribution of the beam reaching the antenna secondary mirror. The annular area surrounded by two gray dashed rings corresponds to... Figure 8 Zhong Cong Click (a) The ring region of the secondary mirror at the point, with the red line corresponding to the maximum energy; (b) Transmission efficiency curves of EA systems designed for wavelengths of 850nm, 1310nm and 1550nm respectively. Detailed Implementation

[0054] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0055] Example 1:

[0056] A method for improving the transmission efficiency of a Cassegrain optical antenna includes the following steps:

[0057] 1) Design a beam shaping system, including subsystem I1 and subsystem II2;

[0058] Subsystem I1 is an aspherical cylindrical lens; subsystem II2 includes an aspherical lens and a truncated cone.

[0059] The aspherical cylindrical lens is used for astigmatism correction and beam circularization; the aspherical lens and the truncated cone are used to achieve beam collimation and generate a hollow beam.

[0060] 2) Position the beam shaping system between the semiconductor laser and the Cassegrain optical antenna;

[0061] 3) Optimize the distance d2 between subsystem I1 and subsystem II2 with the goal that the annular collimated beam output by subsystem II2 is parallel to the optical axis;

[0062] 4) The elliptical diverging beam with astigmatism generated by the semiconductor laser is converted into a ring collimated beam using a beam shaping system, and the ring collimated beam is transmitted to the Cassegrain optical antenna.

[0063] Example 2:

[0064] A method for improving the transmission efficiency of a Cassegrain optical antenna, with the same technical content as in Embodiment 1, further wherein the divergence angle of the emitted beam from the aspherical cylindrical lens in the zy plane and zx plane of the o-xyz coordinate system is equal to The o-xyz coordinate system has its origin at the center of the front surface of the aspherical cylindrical lens.

[0065] Example 3:

[0066] A method for improving the transmission efficiency of a Cassegrain optical antenna, the technical content of which is the same as any one of Embodiment 2, further comprising a semiconductor laser emitting a fast-axis beam and a slow-axis beam;

[0067] The fast-axis beam diverges at an angle of θ in the zy plane. The virtual source point is located on the output surface of the semiconductor laser.

[0068] The divergence angle of the slow-axis beam in the zx plane is The distance between the virtual source point and the output surface of the semiconductor laser is .

[0069] Example 4:

[0070] A method for improving the transmission efficiency of a Cassegrain optical antenna, the technical content of which is the same as any one of Embodiment 3, further wherein the distance between the aspherical cylindrical lens and the emitting end face of the semiconductor laser is d0;

[0071] The distance d0 satisfies the following constraints:

[0072] (1)

[0073] In the formula, Let be the divergence angle of the fast-axis beam in the zy plane; This is the distance between the virtual source point of the slow-axis beam and the output end face of the semiconductor laser; Let be the angle between the normal to the tangent plane at point A and the z-axis.

[0074] Example 5:

[0075] A method for improving the transmission efficiency of a Cassegrain optical antenna, with the same technical content as any one of Embodiment 4, further wherein the beam after astigmatism correction via subsystem I1 is set to originate from a virtual source point. The emitted beam of light is a diverging circular beam;

[0076] Virtual Source Distance from the front surface of subsystem II2 As shown below:

[0077] (2)

[0078] In the formula, The distance between subsystem I1 and subsystem II2; denoted as the length of subsystem I1; n is the refractive index.

[0079] Example 6:

[0080] A method for improving the transmission efficiency of a Cassegrain optical antenna, with the same technical content as any one of Embodiment 5, further wherein the front surface of subsystem II2 is a rotationally symmetric hyperboloid, and the bottom is a surface with a height of half-width is The inner cone;

[0081] The angle between the outer contour of the subsystem II2 truncated cone and the optical axis is equal to half the angle of the inner cone;

[0082] The collimated beam entering subsystem II2 undergoes two total internal reflections at the glass-air interface, and then exits from the rear surface of subsystem II2 in a direction parallel to the optical axis.

[0083] Example 7:

[0084] A method for improving the transmission efficiency of a Cassegrain optical antenna, with the same technical content as any one of Embodiment 6, further comprising: the collimated beam radius entering subsystem II2... As shown below:

[0085] (3)

[0086] Example 8:

[0087] A method for improving the transmission efficiency of a Cassegrain optical antenna, with the same technical content as any one of Embodiment 7, further wherein the hollow radius of the emitted beam from subsystem II2 is as follows:

[0088] , (4)

[0089] In the formula, k is a constant; L is the thickness of the base of the truncated cone;

[0090] Among them, angle The following constraints must be met:

[0091] , (5)

[0092] Height of the inner cone As shown below:

[0093] (6)

[0094] Example 9:

[0095] A method for improving the transmission efficiency of a Cassegrain optical antenna, with the same technical content as any one of Embodiment 8, further comprising the following: subsystem II2 is symmetrical to the Cassegrain optical antenna about the optical axis center; the focal coordinates of the primary and secondary mirrors of the Cassegrain optical antenna are the same, i.e. ; The thickness of the base of the truncated cone; The height of the hollowed-out bottom of subsystem II (2) is half-width is The radius of the circle at the base of the cone is L1 = dtanθ;

[0096] Point G With point F The ordinate of the intersection point E of the line and the secondary mirror surface is ; It is the focal length of the secondary lens; z1 is the coordinate value of point G on the z-axis; This represents the z-axis coordinate of the antenna primary mirror center.

[0097] Example 10:

[0098] A method for improving the transmission efficiency of a Cassegrain optical antenna, with the same technical content as any one of Embodiment 9, further comprising: the thickness of the truncated cone base of subsystem II2. ,as well as Determined by the following equation:

[0099] (7)

[0100] In the formula, and y1 and y2 are the focal lengths of the secondary and primary mirrors, respectively; y3 is the y-coordinate of point N; point N is the point where the light ray is reflected from point M to the primary mirror.

[0101] Example 11:

[0102] A method for improving the transmission efficiency of a Cassegrain optical antenna, with the same technical content as any one of Embodiment 10, further comprising improving the transmission efficiency of the beam shaping system. As shown below:

[0103] (9)

[0104] In the formula, r1 is the beam radius of the collimated beam entering subsystem II (2); E1 is the normalized intensity distribution of the hollow beam passing through system EA. It refers to the internal transmittance of the glass.

[0105] Example 12:

[0106] A method for improving the transmission efficiency of a Cassegrain optical antenna is described below:

[0107] Semiconductor lasers emit elliptical diverging beams with a degree of astigmatism. A novel beam-shaping system is proposed to convert the astigmatically divergent elliptical beam generated by a semiconductor laser into a ring-collimated beam. This system is placed between the semiconductor laser and a Cassegrain optical antenna, such as... Figure 1 As shown. To facilitate discussion and emphasize the effect of beam shaping from an elliptical astigmatic beam to a circularly collimated beam, it is referred to as the EA system. This system consists of two parts: part 1 is an aspherical cylindrical lens, and part 2 consists of an aspherical lens and a truncated cone. Part 1 is specifically designed for astigmatism correction and beam circularization; the corrected beam can be considered as a non-astigmatic circular beam emanating from a single point. Part 2 aims to achieve beam collimation and produce a hollow beam.

[0108] Based on the characteristics of the emitted beam of the semiconductor laser described above, as follows... Figure 2 The mathematical model is constructed as shown, assuming the optical axis is along the z-axis and the divergence angle on the zy-plane is... The virtual source point of the fast-axis beam is located on the output end face of the semiconductor laser, and the divergence angle on the zx plane is... The other virtual source point of the slow-axis beam is located at the output end face. The beam emitted from a semiconductor laser travels in the opposite direction to the emitted beam. Therefore, the emitted beam exhibits inherent astigmatism. Furthermore, the divergence angles of the zy-plane and zx-plane differ significantly, making the output beam from the semiconductor laser unsuitable as a light source for space optical communication. Therefore, part-1 is designed to correct the astigmatically divergent elliptical beam into a circular beam. This means that the divergence angles of the output beam from part-1 should be the same in both planes, and both should be equal to... .

[0109] Part-1 is placed at a distance d0 from the emitting end face of the semiconductor laser. The total length of part-1 is d1. The divergence angle in the fast-axis beam is... The light rays intersect part-1 at point. Then, starting from point B, according to Snell's law of reflection, we know... Figure 2 The geometric relations in can be expressed as

[0110] (1)

[0111] Let the equation of the generatrix of the hyperbolic cylinder be...

[0112] (2)

[0113] In the formula For conic coefficients of the quadratic surface, is a constant coefficient.

[0114] By solving the above system of equations, the parameters of the hyperbolic cylindrical surface can be expressed as follows:

[0115] (3)

[0116] and Therefore, d0 needs to satisfy the following inequality

[0117] (4)

[0118] The surface equation can be written in the following form (the cylindrical equation does not contain x).

[0119] (5)

[0120] In the formula .

[0121] Using MATLAB simulation software, based on the vector theory of reflection and refraction and combined with the cylindrical equation (5), the coordinates of the intersection points of the laser beam with the front and rear surfaces of part-1 can be obtained. Furthermore, the ray tracing diagram of the laser beam passing through part-1 can be obtained, as shown below. Figure 3 As shown. By Figure 3 (b) and Figure 3 (c) It can be seen that the divergence angle and radius of the emitted beam in the x direction are the same as those in the y direction, indicating that astigmatism correction and beam circularization functions have been realized.

[0122] The system design for generating a collimated hollow beam, i.e., part-2, is as follows. Figure 4 As shown, the dashed boxes represent the model diagrams of part-2 from two directions. The front surface of part-2 is a rotationally symmetric hyperboloid, and the bottom is a hollowed-out area with a height of [missing information]. half-width is The thickness of the base of the truncated cone is The entire structure is rotationally symmetrical along the optical axis; therefore, only the cross-section of part-2 in the meridional plane is used to illustrate how light passes through part-2. The beam after astigmatism correction via part-1 can be considered as originating from a virtual source point. The emitted divergent circular beam is then collimated by rotating the hyperbolic surface, and finally undergoes two total internal reflections on the outer contour of the truncated cone before exiting vertically from the bottom of the truncated cone.

[0123] Let the distance between the virtual source point and the front surface of part-2 be...

[0124] (6)

[0125] In the formula Let be the distance between part-1 and part-2. To ensure that the diverging light energy entering part-2 propagates parallel to the optical axis, according to Fermat's law...

[0126] (7)

[0127] (8)

[0128] Therefore, the surface equation can be written in the form of a quadratic surface, i.e.

[0129] (9)

[0130] In the formula, c2 and k2 are the conic coefficient and constant coefficient of the quadratic surface, respectively, and their values ​​are...

[0131] (10)

[0132] Therefore, when the parameters of the incident beam, the position of the element, and the refractive index are determined, the parameters of the hyperboloid of revolution can be determined. The radius of the collimated beam entering part-2 is expressed as...

[0133] (11)

[0134] As discussed earlier, the light beam entering the hyperboloid at the front end of part-2 will propagate in a direction parallel to the optical axis. Since the angle between the outer contour of the truncated cone portion of part-2 and the optical axis is equal to the half-angle of the inner cone, ... Figure 4 As shown, under certain conditions, after the collimated beam enters part-2, it will undergo two total internal reflections at the glass-air interface and finally exit from the rear surface of part-2 in a direction parallel to the optical axis.

[0135] like Figure 4 The geometric relationship shown indicates that the hollow radius of the emitted beam can be expressed as:

[0136] , (12)

[0137] The conditions for total internal reflection and backward propagation must be met, i.e.

[0138] , (13)

[0139] If you want the light trail to look like Figure 4 As pre-set, then the height of the inner cone Need to meet

[0140] (14)

[0141] After passing through the EA system, the laser beam will be collimated; therefore, the primary and secondary mirror structures of the Cassegrain optical antenna will employ a double parabolic surface. Due to the antenna's rotational symmetry, analysis in the yz plane is sufficient.

[0142] Referring to some basic principles and designs of Cassegrain optical antennas, in order to avoid the problem of energy loss at the center of the secondary mirror in Cassegrain optical antennas, the antenna design follows these principles:

[0143] Part-2 is symmetrical with respect to the antenna about the optical axis, and the focal coordinates of the primary and secondary mirrors are the same.

[0144] .

[0145] .Wire The ordinate of the intersection point E with the secondary mirror surface is

[0146] A schematic diagram of the cross-section of the designed Cassegrain transmitting antenna is shown below. Figure 5 As shown.

[0147] from Dot and Parallel beams reflected from the annular region of the secondary mirror between points will reach the primary mirror and exit from the primary mirror in a direction parallel to the optical axis, while beams transmitted to the secondary mirror from the center point to... The beam of light will not reach the primary mirror in the central region of the point. Figure 5 The geometric relationship in can be expressed as:

[0148] (15)

[0149] Based on the above principles, the ratio of f1 to f2 and the coordinate value of y3 can be obtained:

[0150] (16)

[0151] and These are the focal lengths of the secondary mirror and the primary mirror, respectively. Once these two values ​​are determined, the basic structural parameters of the antenna are determined. Conversely, given specific antenna structural parameters, part-2 can also be determined according to equation (16). and parameter.

[0152] Due to the limited lens size, part of the beam may not reach the EA system; therefore, this portion of the transmission efficiency loss and the antenna transmission efficiency loss can both be collectively referred to as truncation loss. The incident beam in part-1 is the beam waist. A Gaussian beam, when the half-height of part-1 is greater than... When only considering truncation loss, the transmission efficiency of part-1 can be assumed to be... It reached 100%. The incident light in part-2 is at the waist... For Gaussian light, considering only the truncated part-2, the transmission efficiency is:

[0153] (17)

[0154] The normalized energy distribution of the hollow beam passing through the EA system is:

[0155] (18)

[0156] The central beam cannot be reflected by the secondary mirror of the antenna to the primary mirror; it can only reach the beam from the secondary mirror. arrive The beam can be transmitted through the ring region of the secondary mirror; therefore, considering only the transmission efficiency loss due to truncation, the antenna's transmission efficiency is...

[0157] (19)

[0158] The cutoff loss includes the cutoff loss of the EA system and the cutoff loss of the antenna; therefore, the overall transmission efficiency considering the cutoff loss is:

[0159] (20)

[0160] Considering that it is impossible to machine an ideal inner cone angle in reality, a chamfer is used to replace the inner cone angle of part-2. For example... Figure 6 As shown. The inner cone angle is tangent to the circle at point. , Point coordinates can be represented as , It is half of the inner cone angle.

[0161] The transmission efficiency of the Gaussian beam through the chamfered part-2 is:

[0162] (twenty one)

[0163] Observing equation (21), it can be seen that the transmission efficiency loss caused by factors such as truncation and chamfering is related to the system parameters. , and They are related, and the following relationship exists between them. / The smaller the ratio, the smaller the cutoff loss; / The larger the ratio, the smaller the chamfer loss. Due to limitations in machining accuracy, It cannot be zero, and It needs to satisfy equation (13), so when taking At a maximum angle of 45°, There is a minimum value. If only one variable is used to optimize the system structure, then... It is more reasonable to consider it as a variable, because Increasing the size of part-2 will lead to an increase in production costs, while adjusting... It can achieve flexible changes The purpose, The adjustment can be achieved by moving part-1 and part-2. Further details will follow. It is used as a control variable to optimize the overall structure and improve transmission efficiency.

[0164] During beam propagation in an EA system, energy loss occurs due to Fresnel reflection at the interface and absorption of light within the glass; therefore, both must be considered when analyzing transmittance. Selecting glass with high transmittance at the laser's operating wavelength is crucial for reducing system transmission loss. However, due to the non-negligible path length of the beam during propagation in the EA system, absorption loss cannot be ignored even in high-transmittance glass. Applying an antireflection coating to the glass surface can reduce reflection loss. When selecting an antireflection coating, in addition to matching the glass's refractive index, it is desirable that it exhibits good performance over a wide frequency band, especially in commonly used optical communication bands. Assuming the use of an antireflection coating, a porous film prepared in a humid environment by spin-coating a cellulose acetate butyrate (CAB) solution in tetrahydrofuran, taking an average reflectance of 0.88% as an example, the overall transmittance after coating on the front and back surfaces of part-1 and part-2 (total internal reflection occurs inside and outside the truncated cone, no coating is required) is...

[0165] (twenty two)

[0166] In the formula It is the transmittance of a light beam through glass with a spin-coated CAB film. It refers to the number of coating layers. It refers to the internal transmittance of the glass. Because both the front and back surfaces of both parts have coatings, the value is... .

[0167] As is well known, the refractive index of a medium varies with wavelength. The refractive index of optical glass materials in the near-infrared band can be approximated by the Sellmeier formula. As a common optical glass, Schott N-BAK1 glass has a refractive index that matches the selected antireflective coating and exhibits high transmittance in the 0.4μm–1.5μm band. Therefore, when using Schott N-BAK1 glass to fabricate an antireflective coating (EA) system, the refractive index can be expressed as:

[0168] (twenty three)

[0169] In the formula It is the wavelength in a vacuum.

[0170] Based on the above analysis and taking into account practical factors, the transmission efficiency of the entire system is (ignoring energy loss caused by antenna reflection and diffraction):

[0171] (twenty four)

[0172] Based on the preceding analysis, the adjustment was determined. Methods to improve transmission efficiency. The steps for determining the parameters of the incident beam, EA system, and antenna are as follows:

[0173] Determine the parameters of the laser semiconductor output beam, the refractive index of the glass material, and the size and distance parameters of part-1 and part-2.

[0174] Determine the surface equations and parameters for part-1 and part-2 based on Table 1.

[0175] Determine the surface equation and parameters of the antenna based on Table 2.

[0176] To illustrate the effect of the overall system transmission efficiency... The changes are illustrated with a specific example. The specific parameters for this example are shown in Table 1. Based on the parameters in Table 1, the three-dimensional ray tracing simulation results of the entire optical antenna with the EA system when the transmission distance is 6000mm are as follows: Figure 7 As shown.

[0177] Table 1. Surface equations and parameters of the entire system

[0178] Efficiency curve follows Changes such as Figure 8 As shown, in Figure 8 In the diagram, the solid green line represents the transmission efficiency considering only the chamfer factor, while the blue line with an X represents the transmission efficiency considering only the truncation factor. The trends of the two curves validate the analysis of the impact of system parameters on transmission efficiency. After considering both the chamfer and truncation factors simultaneously, in... The maximum transmission efficiency of 99.72% can be obtained at this point, as shown by the orange dashed curve. Furthermore, after considering the transmittance of the glass material, the transmittance of the entire system considering all practical factors is obtained, as shown by the yellow curve with dots. The transmission efficiency reaches a maximum of 93.91%. Compared to the theoretical transmission efficiency of 75.46% for a traditional Cassegrain optical antenna, the EA system's transmission efficiency is improved by 18.45%. Furthermore, after optimizing the EA system's structure, the transmission efficiency losses caused by truncation and chamfering factors can be very small. In this case, the upper limit of the overall system's transmission efficiency mainly depends on the transmittance of the glass dielectric material. Therefore, if a glass with higher transmittance can be selected or a more effective method can be used to reduce reflection losses on the lens surface, the overall system's transmission efficiency can be further improved.

[0179] Apart from In addition, changes in wavelength will also lead to changes in transmission efficiency. The above discussion is based on the premise that the incident beam wavelength is 1550nm, and the system parameters are designed for a transmitted beam with a wavelength of 1550nm. However, when the wavelength changes, the beam waist and transmittance will also change, ultimately leading to changes in transmission efficiency. Figure 9 (a) shows the beam waist variation diagram for using beams of different wavelengths in an EA system designed for a 1550 nm wavelength, where w x01 w y01 It is the waist of the beam when it reaches part-2, w x02 w y02 This refers to the beam waist in the xz and yz directions when the light beam reaches the secondary mirror of the antenna. Once both parts are fabricated, the surface equations of the EA system are fixed. Therefore, when light beams of different wavelengths enter the lens, due to changes in refractive index, the surface equations no longer match the incident beam, ultimately causing changes in the beam waist and divergence angle of the outgoing beam. Since the front surface of part-1 is cylindrical, the change in the beam waist in the xz direction is less than the change in the yz direction.

[0180] With the help of equation (27) and considering practical factors, the transmission efficiency curves of different wavelengths in the EA system designed for wavelengths of 850nm, 1310nm and 1550nm are as follows: Figure 9 As shown in (b), the variation in system transmission efficiency is affected by the combined effects of variations in refractive index and transmittance.

[0181] Figure 9 (a) Beam waist variation diagram for different wavelength beams in an EA system designed for a 1550 nm wavelength. The lower right box shows the normalized energy distribution of the beam reaching the antenna secondary mirror. The annular region surrounded by two gray dashed rings corresponds to... Figure 8 Zhong Cong Click (a) The annular region of the secondary mirror, with the red line corresponding to the maximum energy; (b) Transmission efficiency curves of EA systems designed for wavelengths of 850nm, 1310nm, and 1550nm respectively.

[0182] The main reason for the reduced transmission efficiency due to dispersion is that the existence of the divergence angle prevents some beams from reaching the secondary mirror, resulting in energy loss. The beam within the annular region surrounded by the two gray dashed rings can be reflected by the secondary mirror and then reach the primary mirror; the energy of the beam that cannot reach the annular region is considered the lost energy. According to the structural parameters of part-2 in Table 1, the energy is concentrated at the red line in the schematic diagram, and the energy distribution outside the annular region is very small; therefore, the energy loss caused by dispersion is minimal. At that time, the maximum overall system efficiency of the system designed for a wavelength of 850nm was 95.80%. When the wavelength of the incident beam is greater than 1550nm, the transmission efficiency drops rapidly, but in the wavelength range of 500~1647nm, the overall transmission efficiency can still be maintained above 90.00%.

Claims

1. A method for improving the transmission efficiency of a Cassegrain optical antenna, characterized in that, Includes the following steps: Step 1) Design a beam shaping system, including subsystem I (1) and subsystem II (2); Subsystem I (1) is an aspherical cylindrical lens; subsystem II (2) includes an aspherical lens and a truncated cone; The aspherical cylindrical lens is used for astigmatism correction and beam circularization; the aspherical lens and the truncated cone are used to achieve beam collimation and generate a hollow beam. Step 2) Position the beam shaping system between the semiconductor laser and the Cassegrain optical antenna; Step 3) Optimize the distance d2 between subsystem I (1) and subsystem II (2) with the goal that the annular collimated beam output by subsystem II (2) is parallel to the optical axis direction; Step 4) Use a beam shaping system to convert the elliptical diverging beam with astigmatism generated by the semiconductor laser into a ring collimated beam, and then transmit the ring collimated beam to the Cassegrain optical antenna.

2. The method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 1, characterized in that, The divergence angle of the outgoing beam from an aspherical cylindrical lens in the o-xyz coordinate system on both the zy plane and the zx plane is equal to... The o-xyz coordinate system has its origin at the center of the front surface of the aspherical cylindrical lens.

3. The method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 2, characterized in that, Semiconductor lasers emit fast-axis and slow-axis beams. The fast-axis beam diverges at an angle of θ in the zy plane. The virtual source point is located on the output surface of the semiconductor laser. The divergence angle of the slow-axis beam in the zx plane is The distance between the virtual source point and the output surface of the semiconductor laser is .

4. The method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 1, characterized in that, The distance between the aspherical cylindrical lens and the emitting end face of the semiconductor laser is d0; The distance d0 satisfies the following constraints: (1) In the formula, Let be the divergence angle of the fast-axis beam in the zy plane; This is the distance between the virtual source point of the slow-axis beam and the output end face of the semiconductor laser; Let be the angle between the normal to the tangent plane at point A and the z-axis.

5. The method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 1, characterized in that, The beam after astigmatism correction via subsystem I (1) is set to originate from the virtual source point. The emitted beam of light is a diverging circular beam; Virtual Source Distance from the front surface of subsystem II (2) As shown below: (2) In the formula, The distance between subsystem I (1) and subsystem II (2); is the length of subsystem I(1); n is the refractive index.

6. The method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 1, characterized in that, Subsystem II (2) has a front surface that is rotationally symmetric hyperboloid and a bottom surface with a height of half-width is The inner cone; Subsystem II (2) The angle between the outer contour of the truncated cone and the optical axis is equal to half the angle of the inner cone; The collimated beam entering subsystem II (2) undergoes two total internal reflections at the glass-air interface, and then exits from the rear surface of subsystem II (2) in a direction parallel to the optical axis.

7. A method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 6, characterized in that, Collimated beam radius entering subsystem II (2) As shown below: (3) The hollow radius R of the emitted beam from subsystem II (2) is shown below: ， (4) In the formula, k is a constant; L is the thickness of the base of the truncated cone; Among them, angle The following constraints must be met: ， (5) Height of the inner cone As shown below: (6)。 8. A method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 6, characterized in that, Subsystem II (2) is symmetrical to the Cassegrain optical antenna about the optical axis center; the focal coordinates of the primary and secondary mirrors of the Cassegrain optical antenna are the same, that is ; The thickness of the base of the truncated cone; The height of the hollowed-out bottom of subsystem II (2) is half-width is The radius of the circle at the base of the cone is L1 = dtanθ; Point G With point F The ordinate of the intersection point E of the line and the secondary mirror surface is ; It is the focal length of the secondary mirror; z1 is the coordinate value of point G on the z-axis; This represents the z-axis coordinate of the antenna primary mirror center.

9. The method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 1, characterized in that, Subsystem II (2) Thickness of the truncated cone base ,as well as Determined by the following equation: (7) In the formula, and y1 and y2 are the focal lengths of the secondary and primary mirrors, respectively; y3 is the y-coordinate of point N; point N is the point where the light ray is reflected from point M to the primary mirror.

10. A method for improving the transmission efficiency of a Cassegrain optical antenna according to claim 1, characterized in that, Transmission efficiency of beam shaping system As shown below: (9) In the formula, r1 is the beam radius of the collimated beam entering subsystem II (2); E1 is the normalized intensity distribution of the hollow beam passing through system EA. It refers to the internal transmittance of the glass.

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