Pure phase optical element

Abstract

The utility model provides a pure-phase optical element, which comprises a binary-phase optical element and a lens, and the binary-phase optical element and the lens or the lens and the binary-phase optical element are sequentially arranged along the incident direction of plane waves. The phase of the pure-phase optical element is superposed by the phase of the binary-phase optical element and the phase of the lens; the phase distribution of the binary phase optical element meets the following conditions: rho and theta respectively represent the radial distance and azimuth angle of the incident plane; the half of the arc angle with the transmission phase being 0, namely a semi-arc angle; n represents an angular order and is a positive integer; m is a parameter. The pure phase optical element formed by superposing the binary phase optical element and the lens is used for replacing an optical system composed of an amplitude type optical element and the lens, the interference effect in the optical field transmission process is regulated and controlled, and meanwhile the advantages of simplifying an optical path, avoiding alignment errors and saving cost are achieved.

Description

Technical Field

[0001] This utility model relates to the field of optical technology, and in particular to a pure phase optical element. Background Technology

[0002] Due to the limitations of optical diffraction, the minimum focusing size of an optical system, i.e., the diameter of the focused spot, is given by the Rayleigh criterion as 0.61λ / NA (where λ is the wavelength of the incident light wave and NA is the numerical aperture of the optical system). Breaking this diffraction limit and obtaining a focused spot exceeding the diffraction limit in the optical band has profound implications for multiple application fields such as laser processing, microscopic imaging, and optical storage. Achieving super-resolution focusing typically relies on controlling the interference effect during light field transmission, which can be accomplished by designing special optical structures. Related technologies typically employ pure amplitude, pure phase, or a combination of amplitude and phase methods to achieve super-resolution focusing.

[0003] Pure amplitude-based optical elements are often implemented using spatial light modulators (SLMs) or grayscale masks. However, these technologies face several challenges in practical applications. First, the transmission coefficient of a SLM is difficult to precisely match the theoretical design value; any error in the transmission coefficient of a pixel will lead to a cumulative deviation between the actual light field distribution and the expected result. Second, to accurately obtain the target light intensity distribution, SLMs typically need to balance two key indicators: large area and high spatial resolution, but these two are difficult to achieve simultaneously. Compared to amplitude modulation, pure phase-based optical elements have significant advantages in terms of process maturity, cost control, and zero energy loss. Pure phase-based optical elements can be manufactured using mature microlithography technology, avoiding the size and resolution limitations of SLMs. However, the design of phase-based optical elements in related technologies usually relies on complex iterative algorithms, which increases the difficulty of design and optimization. While an optical system composed of amplitude-based and phase-based optical elements can achieve more flexible light field manipulation, its optical system is complex, prone to alignment errors, and increases system cost and maintenance difficulty. Utility Model Content

[0004] In view of this, the purpose of this utility model is to provide a pure phase optical element that overcomes or at least partially solves the above problems.

[0005] To achieve the above objectives, this utility model provides a pure phase optical element for realizing super-resolution focusing of plane waves. It is characterized by comprising a binary phase optical element and a lens, wherein the binary phase optical element and the lens, or the lens and the binary phase optical element, are sequentially arranged along the plane wave incident direction; and the phase of the pure phase optical element is the superposition of the phase of the binary phase optical element and the phase of the lens; the phase distribution of the binary phase optical element satisfies:

[0006]

[0007] Where ρ and θ represent the radial distance and azimuth angle of the incident surface, respectively; This represents half the arc angle where the transmission phase is 0, i.e., the half-arc angle; N represents the angular order, which is a positive integer; m is a parameter. This represents the phase modulation function of a binary phase optical element with an angular order of N.

[0008] In some embodiments, the relationship between the half-arc angle of the binary phase optical element and the amplitude transmission coefficient of the amplitude-type optical element satisfies:

[0009]

[0010] Where T(ρ) is the amplitude transmission coefficient of the amplitude-type optical element.

[0011] In some embodiments, the equivalent modulation coefficients of the binary phase optical element on the circumference at a radial distance ρ satisfy:

[0012]

[0013] in, It represents the imaginary unit.

[0014] In some embodiments, the amplitude transmission coefficient distribution of the amplitude-type optical element satisfies:

[0015]

[0016] The half-arc angle distribution of the binary phase optical element satisfies:

[0017]

[0018] Where R represents the radius of the amplitude-type optical element, and R1 represents the radius of the circle smaller than R within the amplitude-type optical element.

[0019] In some embodiments, after the plane wave transmits through the pure-phase optical element, the light field distribution in the observation plane satisfies:

[0020]

[0021] In this context, the plane wave propagates along the z-axis, the xy-plane is the incident plane, and (x', y', z') represents the coordinates of the observation point within the observation plane. Let E0(ρ) represent the light field at the observation point (x', y', z'), E0(ρ) = 1 represent the amplitude of the incident plane wave, k = 2π / λ represent the wavenumber of the incident plane wave, and λ represent the wavelength of the incident plane wave. The imaginary unit, ψ represents the phase modulation function of a binary phase optical element of order N in the angular direction. Lens (ρ) represents the phase modulation function of the lens. This represents the distance between the source point (x,y,z=0) in the incident plane and the observation point (x',y',z') in the observation plane.

[0022] In some embodiments, after the plane wave transmits through the pure-phase optical element, the light intensity distribution in the observation plane satisfies:

[0023]

[0024] Here, ||...|| represents finding the modulus of a complex number.

[0025] In some implementations, for an observation point at any position z' on the z-axis, the light field distribution satisfies:

[0026]

[0027] Where (0,0,z') represents the coordinates of the observation point on the z-axis. This represents the light field at the observation point (0,0,z').

[0028] In some embodiments, the axial light intensity after the plane wave passes through the pure phase optical element satisfies:

[0029]

[0030] Here, ||...|| represents finding the modulus of a complex number.

[0031] In some embodiments, the lens is a diffractive lens.

[0032] As can be seen from the above, the pure phase optical element provided by this utility model utilizes the transformation of an amplitude-type optical element into a binary phase optical element, and then superimposes the phase of the binary phase optical element with the phase of the lens to form a pure phase optical element. This achieves control over the interference effect during light field transmission while avoiding the difficulty of accurately matching the transmission coefficient of a spatial light modulator to the theoretical design value in pure amplitude-type optical elements, thus avoiding the difficulty in achieving a balance between large area and high spatial resolution. It also avoids the difficulty of designing phase-type optical elements that relies on complex iterative algorithms, offering the advantages of simple, fast, and high-precision design. Furthermore, compared to optical systems composed of amplitude-type and phase-type optical elements, the pure phase optical element has advantages such as simple structure, avoidance of alignment errors, and cost savings. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in this utility model or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only embodiments of this utility model. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the structure of the amplitude-type optical element according to an embodiment of the present invention;

[0035] Figure 2 This is a schematic diagram of the structure of a binary phase optical element according to an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of the axial light intensity distribution of a single lens for plane wave transmission according to an embodiment of the present invention.

[0037] Figure 4 This is a schematic diagram of the lateral light intensity distribution in the actual focusing plane after a plane wave is transmitted through a single lens, according to an embodiment of the present invention.

[0038] Figure 5 The amplitude distribution of the amplitude-type optical element in this embodiment of the present invention;

[0039] Figure 6 This is a schematic diagram of the axial light intensity distribution after a plane wave is transmitted through an optical system composed of an amplitude-type optical element and a lens, according to an embodiment of the present invention.

[0040] Figure 7 This is a schematic diagram of the lateral light intensity distribution in the actual focusing plane after a plane wave is transmitted through an optical system composed of an amplitude-type optical element and a lens, according to an embodiment of the present invention.

[0041] Figure 8This is a schematic diagram of the phase distribution of a binary phase optical element with an angular order of 1 according to an embodiment of the present invention;

[0042] Figure 9 This is a schematic diagram of the phase distribution of a binary phase optical element with an angular order of 8 according to an embodiment of the present invention;

[0043] Figure 10 This is a schematic diagram of the phase distribution of a binary phase optical element with an angular order of 16 according to an embodiment of the present invention;

[0044] Figure 11 This is a schematic diagram of the phase distribution of a pure phase optical element formed by superimposing a binary phase optical element with an angular order of 1 and a lens according to an embodiment of the present invention.

[0045] Figure 12 This is a schematic diagram of the phase distribution of a pure phase optical element formed by superimposing a binary phase optical element with an angular order of 8 and a lens according to an embodiment of the present invention.

[0046] Figure 13 This is a schematic diagram of the phase distribution of a pure phase optical element formed by superimposing a binary phase optical element with an angular order of 16 and a lens, according to an embodiment of the present invention.

[0047] Figure 14 The diagram shows the axial light intensity distribution after plane wave transmission of the present invention, which is a pure phase optical element composed of binary phase optical elements and lenses of different angular orders superimposed on a lens, and an optical system composed of amplitude-type optical elements and lenses.

[0048] Figure 15 This is a diagram showing the lateral light intensity distribution in the actual focusing plane after a plane wave is transmitted through a pure phase optical element formed by superimposing a binary phase optical element with an angular order of 16 and a lens, according to an embodiment of this utility model.

[0049] Figure 16 This is a diagram showing the relative deviation of lateral light intensity in the actual focusing plane after a plane wave is transmitted through a pure phase optical element formed by superimposing a binary phase optical element with an angular order of 16 and a lens, according to an embodiment of this utility model. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this utility model clearer, the present utility model will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0051] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this utility model should have the ordinary meaning understood by one of ordinary skill in the art to which this utility model pertains. The terms "first," "second," and similar words used in the embodiments of this utility model do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are only used to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0052] As described in the background section, pure amplitude-based optical elements are mostly implemented using spatial light modulators (SLMs) or grayscale masks. However, these technologies face several challenges in practical applications. First, the transmission coefficient of a SLM is difficult to precisely match the theoretical design value; any error in the transmission coefficient of a pixel will lead to a cumulative deviation between the actual light field distribution and the expected result. Second, to accurately obtain the target light intensity distribution, SLMs typically need to strike a balance between large area and high spatial resolution, but these two are difficult to achieve simultaneously. Compared to amplitude modulation, phase-based optical elements can be manufactured using mature microlithography technology, avoiding the limitations of SLMs in terms of overall size and spatial resolution, and offering significant advantages in terms of process maturity, cost control, and zero energy loss. However, the design of phase-based optical elements in related technologies usually relies on complex iterative algorithms, which increases the difficulty of design and optimization. Although an optical system composed of amplitude-based and phase-based optical elements can achieve more flexible light field manipulation, its system structure is complex, has alignment errors, and is costly to manufacture and difficult to maintain.

[0053] Based on this, the purpose of this invention is to utilize the mature microlithography technology of phase-type optical elements to avoid the limitations of spatial light modulators in simultaneously achieving both overall size and spatial resolution. Furthermore, it eliminates the need for complex iterative algorithms typically relied upon in the design process of phase-type optical elements in related technologies. Specifically, it transforms amplitude-type optical elements into binary phase-type optical elements, thereby converting the optical system composed of both amplitude-type and phase-type optical elements into a single pure phase-type optical element, simplifying the optical system and eliminating alignment errors.

[0054] This utility model embodiment provides a pure phase optical element, including a binary phase optical element and a lens, wherein the binary phase optical element and the lens, or the lens and the binary phase optical element, are arranged sequentially along the plane wave incident direction; and the phase of the pure phase optical element is the superposition of the phase of the binary phase optical element and the phase of the lens; the phase distribution of the binary phase optical element satisfies:

[0055]

[0056] Where ρ and θ represent the radial distance and azimuth angle of the incident surface, respectively; This represents half the arc angle where the transmission phase is 0, i.e., the half-arc angle; N represents the angular order, which is a positive integer; m is a parameter. This represents the phase modulation function of a binary phase optical element with an angular order of N.

[0057] In this embodiment of the invention, the pure phase optical element is formed by superimposing a binary phase optical element and a lens. The binary phase optical element is transformed from an amplitude-type optical element. Both the binary phase optical element and the lens are phase-type optical elements. The phase of the binary phase optical element and the phase of the lens are superimposed to form the phase of the pure phase optical element.

[0058] It should be noted that after the binary phase optical element and the lens are superimposed to form a pure phase optical element, the incident direction of the plane wave can be towards the side of the binary phase optical element or towards the side of the lens. Both can achieve the super-resolution focusing function of the plane wave of this utility model. No specific limitation is made here.

[0059] Regarding the incident surface, if a plane wave is incident from one side of the binary phase optical element, the incident surface is the side of the binary phase optical element away from the lens, and the exit surface is the side of the lens away from the binary phase optical element. If a plane wave is incident from one side of the lens, the incident surface is the side of the lens away from the binary phase optical element, and the exit surface is the side of the binary phase optical element away from the lens. The observation surface refers to the plane within the transmission region used to receive the focused light field. No specific limitations are made here.

[0060] The purpose of this invention is to design an amplitude-type optical element into a binary phase optical element. The phase design process of the binary phase optical element will be described first. As shown in formula (1), the key to converting an amplitude-type optical element into a binary phase optical element is determining the half-arc angle of the binary phase optical element. The relationship between the transmission coefficient T(ρ) of the amplitude-type optical element and the amplitude-type optical element.

[0061] The relationship between the half-circle angle of a binary phase optical element and the amplitude transmission coefficient of an amplitude-type optical element satisfies:

[0062]

[0063] Where T(ρ) is the amplitude transmission coefficient of the amplitude-type optical element, as follows: Figure 1 As shown, the amplitude transmission coefficient is related to the radial distance ρ and remains constant over a circle with a radial distance of ρ. The half-arc angle is calculated by formula (2). The radian values ​​corresponding to the arcs with phases of 0 and π in the transformed binary phase optical element can be further obtained. and Since the amplitude transmission coefficient of an amplitude-type optical element is 0 ≤ T(ρ) ≤ 1, we can obtain and The magnitude of is related to the radial distance ρ of the incident surface and is uniquely determined by the amplitude transmission coefficient T(ρ) of the amplitude-type optical element.

[0064] Next, the equivalent modulation coefficient of the binary phase optical element on a circle with a radial distance of ρ is determined. Specifically, the angle corresponding to the arc with a phase of 0 on the circle with a radial distance of ρ is... Then the angle corresponding to the arc with phase π on the circumference is . Corresponding to Figure 2 The region is filled with black and white rings. Since exp(j0) = 1 and exp(jπ) = -1, for the observation point on the optical axis, the equivalent modulation coefficient of this binary phase optical element on the circumference at a radial distance ρ satisfies:

[0065]

[0066] in, The imaginary unit is represented by exp(...), which represents the natural exponential function.

[0067] Because amplitude-type optical elements have rotational symmetry, when the equivalent modulation coefficient T BPOE When (ρ) is equal to the amplitude transmission coefficient T(ρ) of the amplitude-type optical element, then theoretically the converted binary phase optical element and the amplitude-type optical element will produce completely identical axial light field distributions. The relationship between the half-circle angle of the binary phase optical element and the amplitude transmission coefficient of the amplitude-type optical element further satisfies:

[0068]

[0069] In some alternative embodiments, the amplitude transmission coefficient distribution of the amplitude-type optical element satisfies:

[0070]

[0071] Where R represents the radius of the amplitude-type optical element, and R1 represents the radius of the circle smaller than R within the amplitude-type optical element. That is, within the circle of radius R1 (ρ < R1), the amplitude transmission coefficient of the incident light (plane wave) is 0; within the annular region between radii R1 and R (R1 ≤ ρ ≤ R), the amplitude transmission coefficient of the incident light is 1.

[0072] Substituting formula (5) into formula (2), we can determine that the half-arc angle distribution of the binary phase optical element satisfies:

[0073]

[0074] Therefore, in the region where the radial distance ρ is less than R1, the arc angle with a transmission phase of 0 is π; in the region where the radial distance ρ is greater than or equal to R1 and less than or equal to R, the arc angle with a transmission phase of 0 is 2π. Thus, the phase of the incident light (plane wave) does not change after passing through this annular region.

[0075] Finally, substituting formula (6) into formula (1), the amplitude-type optical element can be converted into a binary phase optical element. The phase distribution of the converted binary phase optical element satisfies:

[0076]

[0077] Since both the converted binary phase optical element and the lens are phase-type optical elements, they can be superimposed to form a single pure phase optical element. This can replace the optical system composed of amplitude-type optical elements and lenses in related technologies, achieving the goals of simplifying the optical structure, improving experimental accuracy, and saving costs. Next, simulation calculations will demonstrate that the pure phase optical element formed by superimposing the converted binary phase optical element and the lens can achieve super-resolution focusing.

[0078] First, determine the focused spot of the optical system, which consists of amplitude-type optical elements and lenses.

[0079] The optical field after a plane wave passes through this optical system can be calculated using the complete Rayleigh-Sommerfeld method, as shown in the following formula:

[0080]

[0081] In this embodiment, the propagation direction of the plane wave is the z-axis, and the xy-plane is the incident plane, which is the plane from which the plane wave exits after passing through the pure phase optical element. The incident plane is perpendicular to the optical axis and z = 0; (x',y',z') represents the coordinates of the observation point within the observation plane, U(x',y',z') represents the light field at the observation point (x',y',z'), k = 2π / λ represents the wavenumber of the incident plane wave, and λ represents the wavelength of the incident plane wave. The imaginary unit is used; (x,y,z=0) represents the position coordinates of the source point within the incident plane, and U0(x,y,z=0) represents the light field at the source point (x,y,z=0) within the incident plane. This represents the distance between the source point (x,y,z=0) in the incident plane and the observation point (x',y',z') in the observation plane.

[0082] Taking an optical system consisting of an amplitude-type optical element and a lens as an example, the light field at the source point inside the incident plane satisfies:

[0083] U0(x,y,z=0)=E0(ρ)×exp[jψ Lens (ρ)]×T(ρ), (9)

[0084] Where E0(ρ)=1 represents the amplitude of the incident plane wave. This represents the radial distance from the source point within the incident plane. Let f represent the phase modulation function of the lens, and let T(ρ) represent the focal length of the lens; T(ρ) represents the amplitude transmission coefficient of the amplitude-type optical element, given by formula (5).

[0085] Substituting equation (9) into equation (8), we obtain the optical field of the optical system composed of a plane wave transmission amplitude optical element and a lens, which satisfies the following:

[0086]

[0087] Based on the light field after a plane wave passes through an optical system composed of an amplitude-type optical element and a lens, the light intensity after the plane wave passes through the optical system composed of the amplitude-type optical element and the lens can be calculated using the following formula:

[0088] I ALMS (x',y',z')=||U ALMS (x',y',z')|| 2 (11)

[0089] Where ||...|| represents finding the modulus of a complex number.

[0090] Because both amplitude-type optical elements and lenses have rotational symmetry, for observation points on the z-axis, equation (10) can be expressed in polar coordinates as follows:

[0091]

[0092] Where θ is the azimuth angle of the source point within the incident plane.

[0093] Therefore, the axial light intensity after passing through the optical system composed of a plane wave transmission amplitude-type optical element and a lens is:

[0094] IALMS (0,0,z')=||U ALMS (0,0,z')|| 2 (13)

[0095] Specifically, when the amplitude transmission coefficient of the amplitude-type optical element is set to T(ρ) = 1, the axial light intensity of the plane wave transmission lens can be obtained, denoted as I. Lens (0,0,z').

[0096] A set of parameters was selected to simulate and calculate the light intensity distribution of a plane wave transmission lens. The selected parameters were: the wavelength of the incident light wave was λ = 532 nm, the focal length of the lens was f = 600 μm, and the radius of the lens was R = 30 μm.

[0097] Figure 3 and Figure 4 The axial light intensity distribution after a plane wave passes through a single lens and the light intensity distribution in the transverse plane at the actual focusing position z1′=529.95μm are shown respectively when the above parameters are used. The axial focal depth is 296.72μm (axial focal depth is defined as the half-width at half maximum of the peak light intensity), the focused spot size is 11.48μm (focused spot size is defined as the distance between the lowest points on both sides of the central spot), and the focusing efficiency is 77.91% (focusing efficiency is defined as the percentage of the energy of the central spot to the incident energy).

[0098] Similarly, substituting formula (5) into formula (12) and then using formula (13), the axial light intensity after the plane wave transmits through the optical system composed of the amplitude-type optical element and the lens can be obtained. A set of parameters is selected to simulate and calculate the light intensity distribution after the plane wave transmits through the optical system composed of the amplitude-type optical element and the lens. The parameters are selected as follows: the wavelength of the incident light (plane wave) is λ = 532 nm, and the focal length of the lens is f = 600 μm. According to formula (5), the amplitude distribution of the amplitude-type optical element can be obtained, such as... Figure 5 As shown, the radius of the portion of the amplitude-type optical element with a transmission coefficient of 0 is R1 = 24 μm, that is... Figure 5 The radius of the circle filled with black in the middle is R = 30 μm for the amplitude-type optical element. Figure 6 and Figure 7 The diagram shows the axial light intensity distribution and the transverse light intensity distribution at the actual focusing position z2′=361.56μm of the optical system composed of a plane wave transmission amplitude-type optical element and a lens when using the above parameters. The axial focal depth is 360.54μm, the focused spot size is 5.45μm, and the focusing efficiency is 4.23%. These are compared with... Figure 3 and Figure 4 A comparison of the results after a plane wave is transmitted through a lens clearly shows that by adding an amplitude-type optical element, a longer axial depth of focus and a smaller focused spot are obtained.

[0099] In some embodiments, based on the complete Rayleigh-Sommerfeld method, after a plane wave is transmitted through a pure phase optical element composed of a binary phase optical element and a lens, the light field distribution in the observation plane satisfies:

[0100]

[0101] Similarly, the plane wave propagates along the z-axis, the xy plane is the incident plane, and (x', y', z') represents the coordinates of the observation point within the observation plane. Let E0(ρ) represent the light field at the observation point (x', y', z'), E0(ρ) = 1 represent the amplitude of the incident plane wave, k = 2π / λ represent the wavenumber of the incident plane wave, and λ represent the wavelength of the incident plane wave. The imaginary unit, ψ represents the phase modulation function of a binary phase optical element of order N in the angular direction. Lens (ρ) represents the phase modulation function of the lens. This represents the distance between the source point (x,y,z=0) in the incident plane and the observation point (x',y',z') in the observation plane.

[0102] In some embodiments, after a plane wave is transmitted through a pure phase optical element formed by the superposition of a binary phase optical element and a lens, the light intensity distribution within the observation plane satisfies:

[0103]

[0104] Here, ||...|| represents finding the modulus of a complex number.

[0105] In this embodiment, after completing the optical field modulation of the optical system composed of amplitude-type optical elements and lenses, it is further demonstrated that the pure phase optical element formed by the superposition of binary phase optical elements and lenses has an equivalent axial optical field modulation effect with the optical system composed of the above-mentioned amplitude-type optical elements and lenses.

[0106] In some embodiments, when a plane wave is transmitted through the pure phase optical element of this invention, the light field distribution at any observation point z' on the z-axis satisfies:

[0107]

[0108] Where (0,0,z') represents the coordinates of the observation point on the z-axis. This represents the light field at the observation point (0,0,z'). The phase modulation function of a binary phase optical element of order N in the angular direction is given by equation (7), ψ Lens(ρ) represents the phase modulation function of the lens, therefore the two can be superimposed into a single pure phase optical element. The phase distribution of the pure phase optical element can be expressed as: This is the optical field at the on-axis observation point (0,0,z') after a plane wave passes through a pure phase optical element composed of a binary phase optical element and a lens.

[0109] Furthermore, for a binary phase optical element, the integral term within the curly braces in equation (16) can be expanded and simplified as follows:

[0110]

[0111] Substituting equations (17) and (4) into equation (16) proves that equations (16) and (12) are completely equivalent. Therefore, binary phase optical elements of any angular order after transformation have the same axial optical field modulation effect as amplitude-type optical elements.

[0112] Based on the light field after a plane wave passes through a pure phase optical element formed by the superposition of a binary phase optical element and a lens, the light intensity after the plane wave passes through the pure phase optical element formed by the superposition of a binary phase optical element and a lens can be calculated.

[0113] In some embodiments, the axial light intensity after a plane wave is transmitted through a pure-phase optical element satisfies:

[0114]

[0115] Here, ||...|| represents finding the modulus of a complex number.

[0116] Using the same parameters as the amplitude-type optical elements and lenses described above, the intensity distribution of light transmitted through a plane wave through a pure phase optical element composed of binary phase optical elements and lenses of different angular orders is simulated and calculated. The parameters can be selected as follows: the wavelength of the incident light (plane wave) is λ = 532 nm, and the focal length of the lens is f = 600 μm. The radii of both the binary phase optical elements and lenses are R = 30 μm, and the angular orders are selected as N1 = 1, N2 = 8, and N3 = 16, respectively.

[0117] According to formula (7), the phase distribution of a binary phase optical element with an angular order of N can be designed. Figure 8 , 9 Figure 10 illustrates the cases where the angular orders are N1 = 1, N2 = 8, and N3 = 16. The two dashed lines represent two circles with radii R1 and R, respectively. When the radial distance satisfies R1 ≤ ρ ≤ R, we can obtain... This indicates that all source points within the ring have the same phase, resulting in the most ideal interference enhancement effect, which corresponds exactly to the case where the amplitude transmission coefficient T(ρ) = 1. From Figure 8For the case where the azimuthal order N1 = 1, it can be seen that in the annular region of R1 ≤ ρ ≤ R, the phase of the binary phase optical element is constantly 0, so the filled color is black; however, within the circle with a radial distance of ρ < R1, since the transmission coefficient T(ρ) = 0, the binary phase optical element has phase distributions of both 0 and π simultaneously. Therefore, within this circle, a black-and-white filled effect is presented, and the arc angles occupied by the parts with phases of 0 and π are equal, having the most ideal interference cancellation effect. After equally dividing the black-filled region in Figure 8 into N parts, and then evenly arranging each part at an angular interval of 2π / N along the azimuthal direction, a binary phase optical element with an azimuthal order of N can be designed. The designed binary phase optical element exhibits N-fold symmetry along the azimuthal direction, as shown in Figure 9 and Figure 10 , showing 8-fold and 16-fold symmetries respectively. Figure 11 , Figure 12 and Figure 13 are respectively the phase distributions of the pure phase optical elements formed by superimposing the binary phase optical elements and lenses in Figure 8 , Figure 9 and Figure 10 . It can be seen that the pure phase optical element has a similar azimuthal symmetry to the binary phase optical element.

[0118] Figure 14 shows the axial light intensity distributions after a plane wave passes through the pure phase optical elements formed by superimposing binary phase optical elements with different azimuthal orders and lenses. As can be seen from Figure 14 , the axial light intensity distributions after a plane wave passes through the pure phase optical elements formed by superimposing binary phase optical elements with different azimuthal orders and lenses completely coincide with the axial light intensity distributions after a plane wave passes through the optical system composed of an amplitude-type optical element and a lens. This also simultaneously proves that the transformed binary phase optical elements with different azimuthal orders have the same axial light field modulation function as the amplitude-type optical elements.

[0119] Since the binary phase optical element does not have rotational symmetry, while the lens has rotational symmetry, the pure phase optical element formed by superimposing the binary phase optical element and the lens also does not have rotational symmetry. Then, for off-axis observation points, the transverse light intensity distributions generated by the pure phase optical element formed by superimposing the binary phase optical element and the lens and the optical system composed of an amplitude-type optical element and a lens will no longer be the same. The binary phase optical element with an azimuthal order of N has N-fold symmetry along the azimuthal direction. Therefore, by increasing the azimuthal order N, the symmetry of the transverse light intensity after a plane wave passes through the pure phase optical element formed by superimposing the binary phase optical element and the lens can be improved. Figure 15The diagram shows the light intensity distribution in the cross-section at the actual focusing position z3′ = 361.56 μm after a plane wave passes through a pure phase optical element composed of a binary phase optical element with an angular order of N3 = 16 and a lens. It can be seen that the focused spot is circular, with almost no noticeable asymmetry. Numerical simulation results show that after a plane wave passes through this pure phase optical element, the actual spot size in the focusing plane is 5.45 μm, and the focusing efficiency is 4.23%, which is consistent with... Figure 7 The results are completely consistent.

[0120] To more clearly demonstrate the asymmetry of lateral light intensity, the relative deviation of lateral light intensity is defined as follows:

[0121]

[0122] in and I ALMS (x',y',z') represent the light intensity in the observation plane after a plane wave is transmitted through a pure phase optical element composed of a binary phase optical element and a lens, and an optical system composed of an amplitude optical element and a lens, respectively. max[...] represents finding the maximum value of a function.

[0123] According to formula (19), the relative deviation of lateral light intensity in the actual focusing plane was simulated and calculated. Figure 16 The diagram illustrates the relative lateral intensity deviation in the actual focusing plane after a plane wave is transmitted through a pure phase optical element composed of a binary phase optical element with an angular order of N3 = 16 and a lens. When the angular order is N3 = 16, the relative lateral intensity deviation is less than 0.03%. Therefore, the asymmetry of lateral intensity has a negligible impact on practical applications. In summary, by utilizing a pure phase optical element composed of a binary phase optical element and a lens, a super-resolution focusing function nearly equivalent to that of an optical system composed of an amplitude-type optical element and a lens is achieved.

[0124] In some embodiments, the lens is a diffractive lens. A further objective of this invention is to overcome the diffraction limit and obtain a focused light spot exceeding the diffraction limit in the optical band. To obtain a smaller focused light spot, a pure phase optical element formed by superimposing a diffractive lens and a binary phase optical element is utilized.

[0125] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the present invention (including the claims) is limited to these examples; within the framework of the present invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of the present invention as described above, which are not provided in the details for the sake of brevity.

[0126] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of the present invention, the well-known power / ground connections to the integrated circuit (IC) chip and other components may or may not be shown in the provided drawings. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of the present invention, and this also takes into account the fact that the details of the implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of the present invention will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuits) have been set forth to describe exemplary embodiments of the present invention, it will be apparent to those skilled in the art that the embodiments of the present invention can be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0127] Although the present invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0128] The embodiments of this utility model are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of this utility model should be included within the protection scope of this utility model.

Claims

1. A pure phase optical element characterized in that, The optical system includes a binary phase optical element and a lens, wherein the binary phase optical element and the lens, or the lens and the binary phase optical element, are arranged sequentially along the plane wave incident direction; and the phase of the pure phase optical element is the superposition of the phase of the binary phase optical element and the phase of the lens; the phase distribution of the binary phase optical element satisfies: where p and q represent the radial distance and azimuth angle of the incident plane, respectively; represents half of the circular arc angle of the transmission phase, i.e., half of the arc angle; N represents the angular order, which is a positive integer; m is a parameter, represents the phase modulation function of a binary phase optical element with an angular order of N.

2. The pure phase optical element according to claim 1, characterized in that, The relationship between the half-arc angle of the binary phase optical element and the amplitude transmission coefficient of the amplitude-type optical element satisfies: Where T(ρ) is the amplitude transmission coefficient of the amplitude-type optical element.

3. The pure phase optical element according to claim 1, characterized in that, The equivalent modulation coefficient of the binary phase optical element on the circumference at a radial distance ρ satisfies: in, The imaginary unit is represented by exp(...), which represents the natural exponential function.

4. The pure phase optical element according to claim 2, characterized in that, The amplitude transmission coefficient distribution of the amplitude-type optical element satisfies: The half-arc angle distribution of the binary phase optical element satisfies: Where R represents the radius of the amplitude-type optical element, and R1 represents the radius of the circle smaller than R within the amplitude-type optical element.

5. The pure phase optical element according to claim 1, characterized in that, After the plane wave is transmitted through the pure-phase optical element, the light field distribution in the observation plane satisfies: In this context, the plane wave propagates along the z-axis, the xy-plane is the incident plane, and (x', y', z') represents the coordinates of the observation point within the observation plane. Let E0(ρ) represent the light field at the observation point (x', y', z'), E0(ρ) = 1 represent the amplitude of the incident plane wave, k = 2π / λ represent the wavenumber of the incident plane wave, and λ represent the wavelength of the incident plane wave. The imaginary unit, ψ represents the phase modulation function of a binary phase optical element of order N in the angular direction. Lens (ρ) represents the phase function of the lens. This represents the distance between the source point (x,y,z=0) in the incident plane and the observation point (x',y',z') in the observation plane.

6. The pure phase optical element according to claim 5, characterized in that, After the plane wave is transmitted through the pure-phase optical element, the light intensity distribution in the observation plane satisfies: Here, ||...|| represents finding the modulus of a complex number.

7. The pure phase optical element according to claim 5, characterized in that, For any observation point z' on the z-axis, the light field distribution satisfies: Where (0,0,z') represents the coordinates of the observation point on the z-axis. This represents the light field at the observation point (0,0,z').

8. The pure phase optical element according to claim 7, characterized in that, The axial light intensity after a plane wave passes through the pure phase optical element satisfies: Here, ||...|| represents finding the modulus of a complex number.

9. The pure phase optical element according to claim 1, characterized in that, The lens is a diffractive lens.

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