A quantum signal transceiving optical system polarization aberration optimization method

Abstract

The application discloses a quantum signal transceiving optical system polarization aberration optimization method and relates to the field of quantum communication.The application fully considers the influence of factors such as large-angle incidence, material birefringence and optical element surface curvature, obtains the influence of an optical system on the polarization state of incident signal light through strict calculation by establishing a polarization signal transmission model on the element surface, and reduces the influence of the optical system on the polarization state of the signal by optimizing system parameters.The method can guide optical system designers to optimize the polarization aberration, avoids the use of a polarization detection system and a compensation device, and has better economic benefits.

Description

Technical Field

[0001] This invention relates to the field of quantum communication, and more particularly to a method for optimizing polarization aberration in a quantum signal transceiver optical system. Background Technology

[0002] Quantum communication technology has important applications in secure data transmission, and space quantum communication technology is one of the core technologies for constructing three-dimensional quantum communication networks. The performance of quantum communication systems, such as continuous-variable quantum key distribution systems and polarization-modulated discrete-variable quantum key distribution systems, is closely related to the polarization state of the quantum signal, and the optical system has a significant impact on the polarization characteristics of the quantum signal. To ensure the transmission efficiency of quantum signals, it is necessary to quantitatively analyze and optimize the polarization aberration of the optical system. This paper proposes an analytical optimization method for the polarization aberration of the optical system by analyzing the signal transmission characteristics of space quantum communication systems. This method comprehensively considers the influence of factors such as large-angle incident angle, component surface curvature, and material birefringence on the polarization aberration of the optical system. Based on obtaining the accurate polarization aberration of the optical system, the polarization aberration is optimized by adjusting the system parameters.

[0003] Currently, polarization aberration analysis and optimization of large numerical aperture optical systems mainly utilize polarization aberration detection systems to measure the polarization aberration of the optical system, and then design corresponding compensation modules to compensate for the polarization aberration based on the measurement results. This method requires the design of complex polarization aberration detection systems, and the design of compensation modules is challenging due to the spatial distribution characteristics of polarization aberrations. By fully integrating theories such as ray tracing, Fresnel theory, and Snell's theorem, polarization aberration analysis of the optical system can be achieved during the design phase, thereby guiding the design optimization of the optical system. Existing polarization aberration analysis methods mostly perform aberration analysis under special conditions and based on appropriate approximations or assumptions. Space quantum communication optical systems often involve large-angle incident light during the focusing process, and the surfaces of optical system components are mostly curved and made of various materials. While assuming that the front and rear surfaces of the device are parallel planes and that the optical axis is parallel to the device surface can significantly simplify the analysis process, it often does not conform to the actual quantum communication optical system and cannot achieve accurate analysis and optimization of the optical system's polarization aberration. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the aforementioned background technology by proposing a polarization aberration optimization method for quantum signal transceiver optical systems. This method comprehensively considers the influence of factors such as optical element surface shape, optical axis orientation, film layers, and light incident angle on the polarization aberration of the optical system. It can achieve accurate analysis of polarization aberrations of different types of optical systems and provide optimization results for polarization aberration parameters.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for optimizing polarization aberration in a quantum signal transceiver optical system includes the following steps:

[0007] (1) Establish device coordinate systems for all transmission and reflection elements in the optical system in sequence. For reflection elements, establish a device coordinate system with the center of curvature of the front surface of the element as the origin. For transmission elements, establish a device coordinate system with the center of curvature of the front surface of the element and the center of curvature of the rear surface of the element as the origin respectively. In the device coordinate system, the Z-axis makes an acute angle with the incident direction of the light. When the element is an isotropic material, the X-axis and Y-axis are established according to the right-hand Cartesian coordinate system. When the element is an anisotropic material, select the X-axis or Y-axis to coincide with the optical axis of the element.

[0008] (2) Define the device coordinate system as the system coordinate system, which is established with the curvature center of the first element of the optical system as the origin.

[0009] (3) Starting from the first element in the optical system, the polarization components of the incident signal on the surface of each element are represented in the device coordinate system of the corresponding element surface in turn, and the orthogonal polarization components of the outgoing signal on the surface of the element are calculated.

[0010] (4) Represent the orthogonal polarization component of the signal emitted from the surface of the last element of the optical system in the system coordinate system, and calculate the integral sum of the orthogonal polarization components of the emitted signal to obtain the signal depolarization degree of the emitted signal of the entire optical system relative to the incident signal.

[0011] (5) Using the polarization state of the incident quantum signal, the optical axis orientation of the optical system components, and the refractive index of the film as independent variables, the optimization algorithm is used to minimize the signal depolarization of the entire optical system, thereby optimizing the polarization aberration of the optical system.

[0012] Furthermore, the front surface of the component is the signal incident surface of the entire component, and the rear surface of the component is the signal exit surface of the entire component.

[0013] Furthermore, signal depolarization = 1 - the proportion of the outgoing signal component in the polarization direction of the incident signal.

[0014] Furthermore, the optimization algorithm is the gradient descent algorithm.

[0015] Compared with existing technologies, the advantages of this invention are as follows:

[0016] 1. This invention analyzes the polarization characteristics of each element in an optical system based on Fresnel and Snell theories under oblique incidence conditions, thereby obtaining the accurate polarization aberration of the system.

[0017] 2. The analysis process of this invention does not employ approximation processing or impose any restrictions on the incident light and the state of the optical system components. Therefore, it can achieve accurate analysis of polarization aberrations of different types of optical systems and optimize polarization aberrations by optimizing the system's own parameters without the need for additional compensation devices. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0019] Figure 2 This is the optical path diagram of the optical system selected in the embodiments of the present invention.

[0020] Figure 3 This is a schematic diagram of the device coordinate system used for analyzing a single optical element in an embodiment of the present invention. Detailed Implementation

[0021] The implementation process of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0022] A method for optimizing polarization aberration in a quantum signal transceiver optical system, flowchart as follows: Figure 1 As shown, it mainly includes the following key steps:

[0023] (1) Establish a system coordinate system and represent the polarization state of the light signal incident on the optical system in the system coordinate system;

[0024] (2) For the first optical element of the optical system, establish a device coordinate system, represent the polarization state of the incident signal light in the device coordinate system, and obtain the polarization state of the output signal light in the device coordinate system;

[0025] (3) The polarization states of the input and output signals of the subsequent components of the optical system are obtained sequentially using a similar process, and the polarization state of the output signal of the last component is represented in the system coordinate system;

[0026] (4) Obtain the polarization aberration of the entire optical system, and reduce the polarization aberration of the system by optimizing parameters such as the polarization state of the incident light, the refractive index of the element film, and the orientation of the element optical axis.

[0027] The origin of the device coordinate system is set as the center of curvature sphere of the component surface. If the optical signal passes through two surfaces of the component, the device coordinate system needs to be constructed separately.

[0028] For transmissive devices, only the transmission component is calculated; for reflective devices, only the reflection component is calculated; and for semi-transmissive and semi-reflective devices, both the transmission and reflection components are calculated.

[0029] Generally, the curvature centers of the front and rear surfaces of the same optical element do not coincide, but the coordinate systems of two devices of the same optical element can be made to coincide through translation.

[0030] Given that the thickness of the film layer on the component surface is very small, the film layer can be treated as a single-surface device.

[0031] The parameter optimization process can be implemented using any optimization algorithm, such as gradient descent.

[0032] The following example, using the polarization aberration analysis optimization of a two-element quantum signal transceiver optical system, illustrates the detailed implementation process of this method. The first and second elements are a biconvex lens and a plane mirror, respectively. Without loss of generality, the polarization aberration analysis of the optical system is performed using the signal reception process as an example; the polarization aberration analysis process for the signal transmission process is similar.

[0033] like Figure 2 As shown, when the quantum signal light emitted from the other end is incident on the first element of the optical system, the signal light received by the system can be considered as a plane wave. A system coordinate system is constructed, coinciding with the device coordinate system corresponding to the front surface of the convex lens. Quantum communication systems often utilize linearly polarized light as the signal modulation quantum state or initial coherent state, focusing on the amplitude and phase differences introduced by the optical system to the two orthogonal components of the signal light.

[0034] like Figure 3 As shown, when designing an optical system, most optical components are curved surfaces. Therefore, it cannot be assumed that the optical axis of the component is parallel to the component surface, and the relationship between the optical axis and the incident surface changes with the angle of the incident light. Regardless of the type of optical component, under the condition that the rules for establishing the device coordinate system are determined, it is possible to make the optical axis of the component parallel to a certain axis of the coordinate system during optical design.

[0035] When the signal light is incident on the front surface of the convex lens, a device coordinate system is established, and the optical axis is kept parallel to the Y-axis of the device coordinate system. The optical axis vector is... In this invention, θ and... Let represent the angles between the vector and the Z-axis and X-axis of the coordinate system, respectively. Assume the incident light direction vector is... The direction vector of the incident photoelectric field vibration is The refractive indices of air and the film are 1 and n, respectively. if Then the light vector components within the film layer on the front surface of the convex lens are

[0036]

[0037]

[0038] Where, θ in and θ if These are the angle of incidence and the angle of refraction, sinθ in =n if sinθif E s and E p These are the s-component and p-component of the incident light, respectively. For the incident point on the front surface of the convex lens... The incident light signal at point , the coordinates of the incident point are r1 is the radius of curvature of the front surface, and the above components can be obtained by the following formula.

[0039]

[0040]

[0041]

[0042] Here, it is assumed that the incident light energy is 1.

[0043] The convex lens uses a uniaxial crystal material, so birefringence of the signal needs to be considered. Assume that the angles between the wave normals of the o-ray and e-ray after refraction by the coating layer on the front surface of the lens and the normal to the front surface of the lens are θ. o and θ e ,have

[0044] sinθ in =n o ·sinθ o

[0045] sinθ in =n ep ·sinθ e

[0046] Where, n ep The refractive index of the lens with respect to the normal of the e-ray wave can be expressed as:

[0047]

[0048] Where, n o and n e Here, φ represents the refractive index of the o-ray and e-ray, respectively. eA Let be the angle between the e-wave normal and the optical axis. To obtain the direction vectors of the normals for the o-wave and e-wave, assume that the directions of the normals for the o-wave and e-wave are respectively... and have

[0049]

[0050]

[0051] Combining the two equations above, we can obtain the wave normal direction of the o-ray. The ray direction of the o-ray coincides with its wave normal direction. After obtaining the wave normal direction of the o-ray, the wave normal direction of the e-ray can be easily obtained.

[0052]

[0053]

[0054] To obtain the phase difference between the o-ray and e-ray, it is necessary to determine the intersection point of their wave normals with the rear surface of the convex lens. A coordinate system is constructed with the center of curvature of the rear surface of the convex lens as the origin. In this coordinate system, the coordinates of the exit point of the ray on the front surface of the convex lens are: z'=r1 cosθ p +r1+r2-d, where r1 and r2 are the radii of curvature of the front and rear surfaces of the convex lens, respectively, and d is the center thickness of the lens. Assume the unit vectors of the intersection points of the o-ray and e-ray normals with the rear surface relative to the origin of the coordinate system are respectively... and but

[0055]

[0056]

[0057] Combining the two equations above, we can obtain the trajectory of the normal to the o-wave in the convex lens; similarly, we can also obtain the trajectory of the normal to the e-wave in the convex lens. Then, the phase difference between the two components of the signal after passing through the convex lens is...

[0058]

[0059] The direction of the o-ray coincides with the wave normal, therefore the direction of the o-ray is known. To obtain the polarization component of the e-ray, we need to determine its direction. Assume the propagation vector of the e-ray is... Therefore, the angles between the e-wave normal and the ray and the optical axis of the lens are respectively...

[0060]

[0061]

[0062] From the relationship between the e-ray normal and the angle between the ray and the optical axis, we have:

[0063]

[0064] Furthermore, since the wave normal, ray, and optic axis of the e-ray are coplanar, therefore:

[0065]

[0066] From the above three equations, we can obtain two equations about θ. et and From the equation, we can obtain the propagation direction vector of the e-ray.

[0067] After obtaining the phase difference introduced by the lens for the o-ray and e-ray, the two orthogonal components of the signal are calculated. Based on the definitions of s-ray and p-ray, the vibration direction of the s-ray is... p-optic vibration direction s-optical vibration intensity D s and p-light vibration intensity D p Given that the vibration direction of the o-ray is perpendicular to its principal plane, and the vibration direction of the e-ray lies within the principal plane, we can obtain the rectangular coordinate representation of the vibration vector directions of the o-ray and e-ray after determining their ray directions.

[0068]

[0069]

[0070] Therefore, the amplitudes of the o-ray and e-ray can be obtained as follows:

[0071]

[0072]

[0073] Where, φ es φ os φ ep and φ op All are less than 90°, and satisfy the following conditions:

[0074]

[0075]

[0076]

[0077]

[0078] After analyzing the transmission of the signal light within the lens, we will now analyze its exit process at the rear surface of the convex lens. In the previous analysis, we obtained the coordinates of the exit point on the rear surface and the incident direction of the light ray, as well as the incident angle θ of the ray at the rear surface. oi2 satisfy

[0079]

[0080] Assume the refractive index of the back surface film and the refractive index of air are respectively n of If and 1, then the s-component and p-component of the optical signal in the back surface film are respectively

[0081]

[0082]

[0083] Where, θ of2 E is the refraction angle of the film. os E op Let the incident light have s and p components, then

[0084] n o sinθ oi2 =n of sinθ of2

[0085]

[0086]

[0087] Similarly, when the o-ray is refracted between the emitting film layer and the air, it satisfies

[0088] n of2 sinθ of2 =sinθ oo

[0089]

[0090]

[0091] Where, θ oo Let E be the angle of refraction of the o-ray on the back surface. oos and E oop These are the s-component and p-component of the emitted signal.

[0092] Assume the unit vector of the intersection point of the e-ray and the rear surface of the lens relative to the origin is... Using the propagation direction of the e-ray and the intersection point of the e-ray with the front surface, the coordinates of the intersection point of the e-ray with the rear surface can be obtained.

[0093]

[0094]

[0095] Therefore, the solution can be found. The coordinates of the incident point of the e-ray on the rear surface of the convex lens are:

[0096] Having determined the incident point and direction of the e-ray on the rear surface of the lens, the orthogonal component E of the outgoing signal of the e-ray on the rear surface can be obtained using the same process as for the o-ray. oes and E oep .

[0097] The incident ray is split into o-ray and e-ray after passing through the convex lens, and then incident on the subsequent reflecting mirror. Assume the intersection of the plane reflecting mirror and the Z-axis of the coordinate system of the lens's rear surface is (0 0 l), and the angle between the plane reflecting mirror surface and the Z-axis is 45 degrees. Due to the very small film thickness, the coordinates of the exit point of the o-ray on the rear surface of the lens are... Based on the incident angle, refraction angle, incident direction, and normal to the incident surface of the o-ray on the back surface, the propagation vector of the outgoing o-ray on the back surface can be obtained. for

[0098]

[0099]

[0100] Since the surface of a plane mirror is planar, the normal direction at any point is the same, and the range of possible normals for a plane mirror is the light cone surrounding the Z-axis. Therefore, the normal to a plane mirror can be expressed as... in Assume the angle of incidence of the o-ray at the plane mirror is θ. omi ,but

[0101]

[0102] The plane mirror is made of isotropic material, and its refractive index for incident light is assumed to be n. m The incident plane can be determined by the incident ray and the normal to the mirror, and the direction of propagation of the reflected ray within the incident plane can be obtained.

[0103]

[0104]

[0105] The orthogonal components of the o-ray after reflection by the plane mirror are respectively

[0106]

[0107] Where, θ omt Let n be the angle of refraction of the o-ray within the plane mirror, satisfying n m sinθ omt =sinθ omi E oms and E omp Let S and P be the s-component and p-component of the o-ray incident on the mirror, respectively.

[0108] E oms =E oop sinφ ooi +E oos cosφ ooi

[0109] Eomp =E oop cosφ ooi +E oos sinφ ooi

[0110] Where φ ooi Let be the angle between the incident planes of the o-ray on the rear surface of the lens and the surface of the mirror.

[0111]

[0112] Where, θ' oop and satisfy

[0113]

[0114]

[0115] Using the same method, the magnitudes of the s-component and p-component of the e-ray after reflection by the plane mirror can be obtained, thus yielding the polarization information of the final signal. Since linearly polarized light can be used as the initial coherent state signal in both the analysis and practical system design, the deviation of the outgoing signal from the incident linearly polarized light can be used as the magnitude of its polarization aberration. Assuming the Jones vector of the outgoing signal is...

[0116]

[0117] The trajectory of the optical signal vector within the cross-section along the propagation direction is then...

[0118]

[0119] The trajectory equation above is an ellipse. By changing parameters such as the optical axis orientation, film thickness, film refractive index, and mirror normal vector of the optical system components, the component of the ellipse equation in the polarization direction of the incident signal is maximized, thereby optimizing the polarization aberration of the optical system. For example, when the incident signal is x-polarized light, it is required that... To obtain the maximum value.

[0120] In the above technical solution, the device coordinate system is established based on the surface of the component, and the calculation of the signal transmission process on the surface of each component is performed in the corresponding device coordinate system.

[0121] In the above technical solutions, depending on the material of the film layer, the refractive index of the film layer can be a real number or a complex number.

[0122] In the above technical solution, the gradient descent method is used to optimize the system parameters.

[0123] This invention fully considers the effects of large-angle incident light, material birefringence, and the surface curvature of optical components. By establishing a model of polarization signal propagation on the component surface, it rigorously calculates the influence of the optical system on the polarization state of the incident signal. Furthermore, it reduces the influence of the optical system on the signal polarization state by optimizing system parameters. This invention can guide optical system designers in optimizing polarization aberrations, avoiding the need for polarization detection systems and compensation devices, thus offering better economic benefits.

[0124] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Within the technical scope disclosed in the present invention, any modifications or substitutions that can be easily conceived by those skilled in the art should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing polarization aberration in a quantum signal transceiver optical system, characterized in that, Includes the following steps: (1) Establish device coordinate systems for all transmission and reflection elements in the optical system in sequence. For reflection elements, establish a device coordinate system with the center of curvature of the front surface of the element as the origin. For transmission elements, establish a device coordinate system with the center of curvature of the front surface of the element and the center of curvature of the rear surface of the element as the origin respectively. In the device coordinate system, the Z-axis makes an acute angle with the incident direction of the light. When the element is an isotropic material, the X-axis and Y-axis are established according to the right-hand Cartesian coordinate system. When the element is an anisotropic material, select the X-axis or Y-axis to coincide with the optical axis of the element. (2) Define the device coordinate system as the system coordinate system, which is established with the curvature center of the first element of the optical system as the origin. (3) Starting from the first element in the optical system, the polarization components of the incident signal on the surface of each element are represented in the device coordinate system of the corresponding element surface in turn, and the orthogonal polarization components of the outgoing signal on the surface of the element are calculated. (4) Represent the orthogonal polarization component of the signal emitted from the surface of the last element of the optical system in the system coordinate system, and calculate the integral sum of the orthogonal polarization components of the emitted signal to obtain the signal depolarization degree of the emitted signal of the entire optical system relative to the incident signal. (5) Using the polarization state of the incident quantum signal, the optical axis orientation of the optical system components, and the refractive index of the film as independent variables, the optimization algorithm is used to minimize the signal depolarization of the entire optical system, thereby optimizing the polarization aberration of the optical system.

2. The polarization aberration optimization method for a quantum signal transceiver optical system as described in claim 1, characterized in that, The front surface of the component is the signal incident surface of the entire component, and the rear surface of the component is the signal exit surface of the entire component.

3. The polarization aberration optimization method for a quantum signal transceiver optical system as described in claim 1, characterized in that, Signal depolarization = 1 - the proportion of the outgoing signal component in the polarization direction of the incident signal.

4. The polarization aberration optimization method for a quantum signal transceiver optical system as described in claim 1, characterized in that, The optimization algorithm is the gradient descent algorithm.

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