Pure phase optical element and super-resolution focusing method

Abstract

The invention provides a pure-phase optical element and a super-resolution focusing method, the pure-phase optical element 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 a plane wave; 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 # imgabs0 #, wherein rho and theta respectively represent the radial distance and azimuth angle of the incident plane; # imgabs 1 # represents half of an 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] The present application relates to the field of optical technologies, and particularly to a pure-phase optical element and a super-resolution focusing method. Background Art

[0002] Due to the limitation of optical diffraction effect, the ultimate focusing size of an optical system, that is, the minimum value of the diameter of the focused spot, is given as 0.61λ / NA (λ is the wavelength of the incident light wave, and NA is the numerical aperture of the optical system) according to the Rayleigh criterion. Breaking through this diffraction limit and obtaining a focused spot beyond the diffraction limit in the optical band has far-reaching implications for multiple application fields such as laser processing, microscopy imaging, and optical storage. Achieving super-resolution focusing usually relies on regulating the interference effect during the light field transmission process, which can be accomplished by designing special optical structures. In related technologies, super-resolution focusing is usually achieved by using pure amplitude, pure phase, or a combination of amplitude and phase.

[0003] Pure-amplitude optical elements are mostly realized through a spatial light modulator (SLM) or a gray-scale mask. However, such technologies face some challenges in practical applications. First, it is difficult to accurately match the transmission coefficient of the spatial light modulator with the theoretical design value, and any error in the transmission coefficient of a pixel will cause a certain cumulative deviation between the actual light field distribution and the expected result. Second, in order to accurately obtain the target light intensity distribution, the SLM usually needs to balance two key indicators: large area and high spatial resolution, but it is difficult to achieve both simultaneously. Compared with amplitude modulation, pure-phase optical elements have significant advantages in terms of process maturity, cost control, and no energy loss. Pure-phase optical elements can be manufactured through mature micro-lithography technology, avoiding the limitations of the spatial light modulator in terms of size and resolution. However, in related technologies, the design of phase-type optical elements usually relies on complex iterative algorithms, which increases the difficulty of design and optimization. Although an optical system composed of an amplitude-type optical element and a phase-type optical element can achieve more flexible light field regulation, its optical system is complex, prone to alignment errors, and increases the system cost and maintenance difficulty. Summary of the Invention

[0004] In view of this, the purpose of the present application is to propose a pure-phase optical element and a super-resolution focusing method that overcome the above problems or at least partially solve the above problems.

[0005] For the above purposes, in the first aspect of the present application, a pure-phase optical element is provided for achieving the super-resolution focusing function of a plane wave. It is characterized in that it includes 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 arranged in sequence along the incident direction of the plane wave; 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 respectively represent the radial distance and azimuth angle of the incident plane; represents half of the arc angle with a transmission phase of 0, that is, the half-arc angle; N represents the angular order and is a positive integer; m is a parameter, represents the phase modulation function of the 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 coefficient of the binary phase optical element on the circumference with a radial distance of ρ satisfies:

[0012]

[0013] where, 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 R 1 represents the radius of a circle smaller than R within the amplitude-type optical element.

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

[0020]

[0021] Among them, the propagation direction of the plane wave is along the z-axis direction, the xy plane is the incident plane, and (x', y', z') represents the coordinates of the observation point in the observation plane. represents the optical field at the observation point (x', y', z'), E 0 (ρ) = 1 represents the amplitude of the incident plane wave, k = 2π / λ represents the wave number of the incident plane wave, and λ represents the wavelength of the incident plane wave. is the imaginary unit. represents the phase modulation function of the binary phase optical element with the angular order of N, ψ Lens (ρ) represents the phase modulation function of the lens. 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] Among them, ||...|| represents taking the modulus of a complex number.

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

[0026]

[0027] Among them, (0, 0, z') represents the coordinates of the observation point on the z-axis. represents the optical field at the observation point (0, 0, z').

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

[0029]

[0030] Among them, ||...|| represents taking the modulus of a complex number.

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

[0032] In the second aspect of the present application, a super-resolution focusing method is provided, including:

[0033] Using a plane wave to transmit through the pure phase optical element as described in the first aspect.

[0034] As can be seen from the above, the pure-phase optical element and the super-resolution focusing method provided by the present application convert an amplitude-type optical element into a binary-phase optical element, and then superimpose the phase of the binary-phase optical element and the phase of the lens to form a pure-phase optical element. While realizing the regulation of the interference effect during the light field transmission process, it avoids the difficulty that it is difficult to accurately match the theoretical design value of the transmission coefficient of the spatial light modulator with the pure amplitude-type optical element, and it is difficult to achieve a balance between large area and high spatial resolution. At the same time, it avoids the difficulty that the design of the phase-type optical element in the related technology depends on complex iterative algorithms, and has the characteristics of simple, fast and high-precision design. At the same time, compared with the optical system composed of an amplitude-type optical element and a phase-type optical element, the pure-phase optical element has the advantages of simple structure, avoiding alignment errors and saving costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions in the present application or related technologies, the following will briefly introduce the drawings required for use in the description of the embodiments or related technologies. Obviously, the drawings in the following description are only the embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0036] Figure 1 Structural schematic diagram of the amplitude-type optical element in the embodiment of the present application;

[0037] Figure 2 Structural schematic diagram of the binary-phase optical element in the embodiment of the present application;

[0038] Figure 3 Axial light intensity distribution schematic diagram of a plane wave transmitted through a single lens in the embodiment of the present application;

[0039] Figure 4 Transverse light intensity distribution schematic diagram in the actual focal plane after a plane wave is transmitted through a single lens in the embodiment of the present application;

[0040] Figure 5 Amplitude distribution of the amplitude-type optical element in the embodiment of the present application;

[0041] Figure 6 Axial light intensity distribution schematic diagram after a plane wave is transmitted through the optical system composed of an amplitude-type optical element and a lens in the embodiment of the present application;

[0042] Figure 7 Transverse light intensity distribution schematic diagram in the actual focal plane after a plane wave is transmitted through the optical system composed of an amplitude-type optical element and a lens in the embodiment of the present application;

[0043] Figure 8Schematic diagram of the phase distribution of the binary phase optical element with an angular order of 1 according to the embodiment of the present application;

[0044] Figure 9 Schematic diagram of the phase distribution of the binary phase optical element with an angular order of 8 according to the embodiment of the present application;

[0045] Figure 10 Schematic diagram of the phase distribution of the binary phase optical element with an angular order of 16 according to the embodiment of the present application;

[0046] Figure 11 Schematic diagram of the phase distribution of the pure phase optical element formed by superimposing the binary phase optical element with an angular order of 1 and a lens according to the embodiment of the present application;

[0047] Figure 12 Schematic diagram of the phase distribution of the pure phase optical element formed by superimposing the binary phase optical element with an angular order of 8 and a lens according to the embodiment of the present application;

[0048] Figure 13 Schematic diagram of the phase distribution of the pure phase optical element formed by superimposing the binary phase optical element with an angular order of 16 and a lens according to the embodiment of the present application;

[0049] Figure 14 Axial light intensity distribution diagram after the plane wave transmits through the pure phase optical element formed by superimposing the binary phase optical element with different angular orders and a lens and the optical system composed of the amplitude type optical element and a lens according to the embodiment of the present application;

[0050] Figure 15 Transverse light intensity distribution diagram in the actual focal plane after the plane wave transmits through the pure phase optical element formed by superimposing the binary phase optical element with an angular order of 16 and a lens according to the embodiment of the present application;

[0051] Figure 16 Transverse light intensity relative deviation diagram in the actual focal plane after the plane wave transmits through the pure phase optical element formed by superimposing the binary phase optical element with an angular order of 16 and a lens according to the embodiment of the present application. Detailed implementation manners

[0052] To make the objectives, technical solutions and advantages of the present application clearer and more understandable, the present application will be further described in detail below with reference to specific embodiments and the accompanying drawings.

[0053] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should have the ordinary meanings understood by those of ordinary skill in the field to which the present application belongs. The "first", "second" and similar terms used in the embodiments of the present application do not denote any order, quantity or importance, but are only used to distinguish different components. Words such as "including" or "comprising" mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Upper", "lower", "left", "right", etc. are only used to represent relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0054] As described in the above background art, pure amplitude optical elements are mostly realized by a spatial light modulator (SLM) or a gray-scale mask. However, such technologies face some challenges in practical applications. First, it is difficult to accurately match the transmittance coefficient of the spatial light modulator to the theoretical design value, and any error in the transmittance coefficient of a pixel will cause a certain cumulative deviation between the actual light field distribution and the expected result. Second, in order to accurately obtain the target light intensity distribution, the SLM usually needs to balance between a large area and a high spatial resolution, but it is difficult to achieve both at the same time. Compared with amplitude modulation, phase optical elements can be fabricated by mature micro-lithography techniques, avoiding the limitations of the spatial light modulator in terms of overall size and spatial resolution, and having significant advantages in terms of process maturity, cost control, and no energy loss. However, the design of phase 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 optical elements and phase optical elements can achieve more flexible light field control, its system structure is complex, there are alignment errors, and the preparation cost and maintenance difficulty are high.

[0055] Based on this, the purpose of the present application is to utilize the mature micro-lithography technology of phase optical elements to avoid the limitation that it is difficult to simultaneously take into account the overall size and spatial resolution of the spatial light modulator. At the same time, it is not necessary to rely on complex iterative algorithms in the design process of phase optical elements in related technologies. That is, the amplitude optical element is transformed into a binary phase optical element, and then the optical system composed of the amplitude optical element and the phase optical element can be converted into a single pure phase optical element, simplifying the optical system and eliminating alignment errors.

[0056] A pure-phase optical element includes a binary phase optical element and a lens. The binary phase optical element and the lens, or the lens and the binary phase optical element, are arranged in sequence along the incident direction of a plane wave. 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:

[0057]

[0058] where ρ and θ respectively represent the radial distance and azimuth angle of the incident surface; represents half of the arc angle with a transmission phase of 0, that is, the half-arc angle; N represents the angular order, which is a positive integer; m is a parameter, represents the phase modulation function of the binary phase optical element with an angular order of N.

[0059] In the pure-phase optical element in the embodiment of the present application, it is formed by the superposition of 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 superposed to form the phase of the pure-phase optical element.

[0060] It should be noted that after the binary phase optical element and the lens are superposed 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, and both can achieve the super-resolution focusing function of the plane wave in the present application, which is not specifically limited here.

[0061] For the incident surface, if the plane wave is incident from the 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 the plane wave is incident from the 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 in the transmission region for receiving the focused light field. This is not specifically limited here.

[0062] The purpose of the present application is to design an amplitude-type optical element as a binary phase optical element. Next, the phase design process of the binary phase optical element will be elaborated first. It can be seen from formula (1) that when transforming an amplitude-type optical element into a binary phase optical element, the key is to determine the relationship between the half-arc angle of the binary phase optical element and the transmission coefficient T(ρ) of the amplitude-type optical element.

[0063] 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:

[0064]

[0065] Among them, 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 unchanged on the circumference with the radial distance of ρ. The half-arc angle calculated by formula (2) can further obtain that the radian values corresponding to the arcs with phases of 0 and π in the converted binary phase optical element are respectively and Since the amplitude transmission coefficient 0 ≤ T(ρ) ≤ 1 of the amplitude-type optical element, it can be obtained that 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.

[0066] Next, determine the equivalent modulation coefficient of the binary phase optical element on the circumference with the radial distance of ρ. Specifically, when the angle corresponding to the arc with a phase of 0 on the circumference with the radial distance of ρ is then the angle corresponding to the arc with a phase of π on this circumference is corresponding to Figure 2 the filled areas of the black and white circular rings in respectively. Since exp(j0) = 1 and exp(jπ) = -1, therefore, for the observation point on the optical axis, the equivalent modulation coefficient of this binary phase optical element on the circumference with the radial distance of ρ satisfies:[[]]END]]

[0067]

[0068] Among them, represents the imaginary unit, and exp(...) represents the natural exponential function.

[0069] Since the amplitude-type optical element has rotational symmetry, when the equivalent modulation coefficient T BPOE (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 exactly the same axial light field distribution, and the relationship between the half-arc angle of the binary phase optical element and the amplitude transmission coefficient of the amplitude-type optical element further satisfies:[[]]END]]

[0070]

[0071] In some alternative embodiments, the amplitude transmission coefficient distribution of the amplitude-type optical element satisfies:[[]]END]]

[0072]

[0073] where R represents the radius of the amplitude-type optical element, and R 1 represents the radius of the circle smaller than R within the amplitude-type optical element. That is, within the radius of R1 inside the circle (ρ < R 1 ), the amplitude transmission coefficient of the incident light (plane wave) is 0; in the annular region between the radius of R 1 and R (R 1 ≤ ρ ≤ R), the amplitude transmission coefficient of the incident light is 1.

[0074] Substitute formula (5) into formula (2) to determine that the half-arc angle distribution of the binary phase optical element satisfies:

[0075]

[0076] From this, it can be obtained that in the region where the radial distance ρ is less than R 1 , 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 R 1 and less than or equal to R, the arc angle with a transmission phase of 0 is 2π. Therefore, the phase of the incident light (plane wave) does not change after passing through this annular region.

[0077] Finally, substitute formula (6) into formula (1), and 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:

[0078]

[0079] Since the converted binary phase optical element and the lens are both phase-type optical elements, they can be superimposed to form a single pure phase optical element, which can replace the optical system composed of the amplitude-type optical element and the lens in the related technology, achieving the purpose of simplifying the optical structure, improving the experimental accuracy, and saving costs. Next, through simulation calculations, it will be proved that the pure phase optical element formed by superimposing the converted binary phase optical element and the lens can achieve the function of super-resolution focusing.

[0080] First, determine the focused spot of the optical system composed of the amplitude-type optical element and the lens.

[0081] The light field after the plane wave passes through this optical system can be calculated by using the complete Rayleigh - Sommerfeld method, and the calculation formula is as follows:

[0082]

[0083] where the propagation direction of the plane wave is the z-axis, the xy plane is the incident plane, that is, the plane where the plane wave of the embodiment of the present application 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 observation point coordinates in the observation plane, U(x', y', z') represents the light field at the observation point (x', y', z'), k = 2π / λ represents the wave number of the incident plane wave, and λ represents the wavelength of the incident plane wave. is the imaginary unit; (x, y, z = 0) represents the position coordinates of the source point in the incident plane, and U 0 (x, y, z = 0) represents the optical field at the source point (x, y, z = 0) in the incident plane, 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.

[0084] Taking the optical system composed of an amplitude-type optical element and a lens through which a plane wave is transmitted as an example, the optical field at the source point in the incident plane satisfies:

[0085] U 0 (x, y, z = 0) = E 0 (ρ) × exp[jψ Lens (ρ)] × T(ρ), (9)

[0086] where, E 0 (ρ) = 1 represents the amplitude of the incident plane wave, represents the radial distance of the source point in the incident plane, represents the phase modulation function of the lens, f represents the focal length of the lens; T(ρ) represents the amplitude transmittance coefficient of the amplitude-type optical element, which is given by formula (5).

[0087] Substituting formula (9) into formula (8), the optical field after the plane wave is transmitted through the optical system composed of the amplitude-type optical element and the lens satisfies:

[0088]

[0089] According to the optical field after the plane wave is transmitted through the optical system composed of the amplitude-type optical element and the lens, the light intensity after the plane wave is transmitted through the optical system composed of the amplitude-type optical element and the lens can be calculated, and the calculation formula is as follows:

[0090] I ALMS (x', y', z') = ||U ALMS (x', y', z')|| 2 , (11)

[0091] where ||...|| represents finding the modulus of a complex number.

[0092] Because both the amplitude-type optical element and the lens have rotational symmetry, for the observation point on the z-axis, formula (10) can be represented in polar coordinates as follows:

[0093]

[0094] where θ is the azimuth angle of the source point in the incident plane.

[0095] Therefore, the axial light intensity after the optical system composed of a plane-wave transmissive amplitude-type optical element and a lens is:

[0096] I ALMS (0, 0, z') = ||U ALMS (0, 0, z')|| 2 , (13)

[0097] In particular, when the amplitude transmittance coefficient of the amplitude-type optical element is set to T(ρ) = 1, the axial light intensity of the plane-wave transmissive lens can be obtained, denoted as I Lens (0, 0, z').

[0098] A set of parameters is selected to simulate and calculate the light intensity distribution of the plane-wave transmissive lens. The selected parameters are: the wavelength of the incident light wave is λ = 532 nm, the focal length of the lens is f = 600 μm, and the radius of the lens is R = 30 μm.

[0099] Figure 3 and Figure 4 respectively show the axial light intensity distribution after the plane wave transmits through a single lens and the light intensity distribution in the transverse plane at the actual focal position z 1 ′ = 529.95 μm. Its axial focal depth is 296.72 μm (the axial focal depth is defined as the full width at half maximum of the peak light intensity), the focused spot size is 11.48 μm (the 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% (the focusing efficiency is defined as the percentage of the energy of the central spot in the incident energy).

[0100] Similarly, substituting Equation (5) into Equation (12) and then using Equation (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 parameter selection is 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 Equation (5), the amplitude distribution of the amplitude-type optical element can be obtained, as shown in Figure 5 shown, the radius of the part with a transmittance coefficient of 0 of the amplitude-type optical element is R 1 = 24 μm, that is, Figure 5 the radius of the circle in the black-filled area in Figure 6 and Figure 7 show the axial light intensity distribution after the plane wave transmits through the optical system composed of the amplitude-type optical element and the lens and the actual focal position z 2The light intensity distribution in the transverse plane at ′ = 361.56 μm is obtained, and its axial focal depth is 360.54 μm, the focused spot size is 5.45 μm, and the focusing efficiency is 4.23%. Respectively compared with Figure 3 and Figure 4 the results after the plane wave passes through the lens in the middle plane, it can be clearly seen that by adding the amplitude-type optical element, a longer axial focal depth and a smaller focused spot are obtained.

[0101] In some embodiments, based on the complete Rayleigh - Sommerfeld method, after the plane wave passes through the pure phase optical element composed of the binary phase optical element and the lens superimposed, the light field distribution in the observation plane satisfies:

[0102]

[0103] Similarly, the propagation direction of the plane wave is along the z-axis direction, the xy plane is the incident plane, and (x', y', z') represents the coordinates of the observation point in the observation plane. represents the light field at the observation point (x', y', z'), E 0 (ρ) = 1 represents the amplitude of the incident plane wave, k = 2π / λ represents the wave number of the incident plane wave, λ represents the wavelength of the incident plane wave. is the imaginary unit. represents the phase modulation function of the binary phase optical element with the angular order of N, ψ Lens (ρ) represents the phase modulation function of the lens. 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.

[0104] In some embodiments, after the plane wave passes through the pure phase optical element composed of the binary phase optical element and the lens superimposed, the light intensity distribution in the observation plane satisfies:

[0105]

[0106] Among them, ||...|| represents finding the modulus of a complex number.

[0107] In this embodiment, after completing the light field modulation of the optical system composed of the amplitude-type optical element and the lens, it is further proved that the pure phase optical element composed of the binary phase optical element and the lens superimposed has an equivalent axial light field modulation effect with the optical system composed of the above-mentioned amplitude-type optical element and the lens.

[0108] In some embodiments, when the plane wave passes through the pure phase optical element of the embodiment of the present application, for the observation point at any position z' on the z-axis, the light field distribution satisfies:

[0109]

[0110] Among them, (0, 0, z') represents the coordinates of the observation point on the z-axis, represents the optical field at the observation point (0, 0, z').

[0111] represents the phase modulation function of the binary phase optical element with an angular order of N, which 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, and the phase distribution of the pure-phase optical element can be expressed as is the optical field at the on-axis observation point (0, 0, z') after the plane wave passes through the pure-phase optical element formed by the superposition of the binary phase optical element and the lens.

[0112] Furthermore, for the binary phase optical element, the integral term in the curly brackets in Equation (16) can be expanded and simplified as follows:

[0113]

[0114] Substituting Equation (17) and Equation (4) into Equation (16), it can be proved that Equation (16) and Equation (12) are completely equivalent. Therefore, any binary phase optical element with a converted angular order has the same axial optical field modulation effect as the amplitude-type optical element.

[0115] According to the optical field after the plane wave passes through the pure-phase optical element formed by the superposition of the binary phase optical element and the lens, the light intensity after the plane wave passes through the pure-phase optical element formed by the superposition of the binary phase optical element and the lens can be calculated.

[0116] In some embodiments, the axial light intensity after the plane wave passes through the pure-phase optical element satisfies:

[0117]

[0118] Among them, ||...|| represents finding the modulus of a complex number.

[0119] Select the same parameters as the above amplitude-type optical element and the lens, and simulate and calculate the light intensity distribution after the plane wave passes through the pure-phase optical element formed by the superposition of binary phase optical elements with different angular orders and the lens. 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 element and the lens are R = 30 μm, and the angular orders are respectively selected as N 1 = 1, N 2 = 8 and N 3 = 16.

[0120] 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 Figures 9 and 10 show the cases where the angular orders are N 1 = 1, N 2 = 8, and N 3 = 16. The two dashed lines respectively represent two circles with radii of R 1 and R. When the radial distance satisfies R 1 ≤ ρ ≤ R, it can be obtained that This indicates that the phases of all source points within this circular ring are the same, with the most ideal interference enhancement effect, exactly corresponding to the case where the amplitude transmission coefficient T(ρ) = 1. From Figure 8 for the case where the angular order N 1 = 1, it can be seen that within the circular ring region where R 1 ≤ ρ ≤ R, the phase of the binary phase optical element is constantly 0, so the filled color is black; however, within the circle where the radial distance is ρ < R 1 , since the transmission coefficient T(ρ) = 0, the binary phase optical element has phase distributions of both 0 and π at the same time. Therefore, within this circle, a black-and-white alternating filling effect is presented, and the arc angles occupied by the parts with phases of 0 and π are equal, with 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 along the azimuthal angle direction at an angular interval of 2π / N, a binary phase optical element with an angular order of N can be designed. The designed binary phase optical element exhibits N-fold symmetry along the azimuthal angle direction, as shown in Figure 9 and Figure 10 , showing 8-fold and 16-fold symmetries respectively. Figure 11 , Figure 12 and Figure 13 respectively show 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 an angular symmetry similar to that of the binary phase optical element.

[0121] Figure 14 shows the axial light intensity distribution after a plane wave is transmitted through the pure phase optical elements formed by superimposing binary phase optical elements with different angular orders and lenses using the above parameters. From Figure 14It can be seen that the axial intensity distribution of a plane wave transmitted through a pure-phase optical element formed by superimposing a binary phase optical element with different azimuthal orders and a lens is exactly the same as that of a plane wave transmitted through an optical system composed of an amplitude-type optical element and a lens. This also 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.

[0122] Since the binary phase optical element does not have rotational symmetry while the lens does, 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 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 the amplitude-type optical element and the lens will no longer be the same. The binary phase optical element with azimuthal order N has N-fold symmetry along the azimuthal direction. Therefore, by increasing the azimuthal order N, the symmetry of the transverse intensity of the plane wave transmitted through the pure-phase optical element formed by superimposing the binary phase optical element and the lens can be improved. Figure 15 shows the cross-sectional intensity distribution at the actual focal position z 3 ′ = 361.56 μm after a plane wave is transmitted through a pure-phase optical element formed by superimposing a binary phase optical element with azimuthal order N 3 = 16 and a lens. It can be seen that the focused spot is circular and its asymmetry is hardly noticeable. The numerical simulation results show that after the plane wave is transmitted through this pure-phase optical element, the spot size in the actual focal plane is 5.45 μm and the focusing efficiency is 4.23%, which is exactly the same as the results in Figure 7 .

[0123] To more clearly show the asymmetry of the transverse intensity, the relative deviation of the transverse intensity is defined as follows:

[0124]

[0125] where and I ALMS (x', y', z') represent the light intensities in the observation plane after a plane wave is transmitted through the pure-phase optical element formed by superimposing the binary phase optical element and the lens and the optical system composed of the amplitude-type optical element and the lens, respectively, and max[...] represents finding the maximum value of a function.

[0126] According to formula (19), the relative deviation of the transverse intensity in the actual focal plane was simulated and calculated. Figure 16 shows the relative deviation of the transverse intensity in the actual focal plane after a plane wave is transmitted through a pure-phase optical element formed by superimposing a binary phase optical element with azimuthal order N 3 = 16 and a lens. When the azimuthal order is N3 When = 16, the relative deviation of the transverse light intensity is less than 0.03%. Therefore, the asymmetry of the transverse light intensity has almost negligible influence on practical applications. In summary, by using a pure-phase optical element formed by superimposing a binary phase optical element and a lens, a super-resolution focusing function that is nearly equivalent to an optical system composed of an amplitude-type optical element and a lens is achieved.

[0127] In some embodiments, the lens is a diffractive lens. The purpose of the embodiments of the present application is also to break through the diffraction limit and obtain a focused spot that exceeds the diffraction limit in the optical band. To obtain a smaller focused spot, a pure-phase optical element formed by superimposing a diffractive lens and a binary phase optical element is used.

[0128] Based on the same inventive concept, the embodiments of the present application provide a super-resolution focusing method, including: transmitting a plane wave through the pure-phase optical element of any of the above embodiments.

[0129] Those of ordinary skill in the art should understand that the discussion of any of the above embodiments is only exemplary and is not intended to imply that the scope of the present application (including the claims) is limited to these examples; under the concept of the present application, the technical features in the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations in different aspects of the embodiments of the present application as described above, which are not provided in detail for the sake of brevity.

[0130] In addition, to simplify the description and discussion and to avoid making the embodiments of the present application difficult to understand, the known power / ground connections to integrated circuit (IC) chips and other components may or may not be shown in the provided drawings. In addition, the device may be shown in block diagram form to avoid making the embodiments of the present application difficult to understand, and this also takes into account the fact that the details of the implementation of these block diagram devices are highly dependent on the platform on which the embodiments of the present application will be implemented (i.e., these details should be completely within the understanding of those skilled in the art). In the case where specific details (such as circuits) are set forth to describe the exemplary embodiments of the present application, it will be apparent to those skilled in the art that the embodiments of the present application can be implemented without these specific details or with variations of these specific details. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0131] Although the present application has been described in connection with specific embodiments of the present application, many alternatives, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other memory architectures (such as dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0132] Embodiments of the present application 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 the present application shall be included within the protection scope of the present application.

Claims

1. A pure phase optical element, characterized in that: The invention comprises 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 in sequence along the incident direction of a plane wave; 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; and the phase distribution of the binary phase optical element satisfies: Where ρ and θ represent the radial distance and azimuth angle of the incident surface, respectively; It represents half of the arc angle with a transmission phase of 0, i.e., the half-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 angular order N.

2. The pure phase optical element according to claim 1, characterized in that: The relationship between the semi-arc angle of the binary phase optical element and the amplitude transmission coefficient of the amplitude type optical element satisfies: Here, 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 of the radial distance ρ satisfies: in, represents the imaginary unit and exp(...) 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 semi-arc angle distribution of the binary phase optical element satisfies: Here, R represents the radius of the amplitude type optical element, and R1 represents the radius of a 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 transmits the pure phase optical element, the light field distribution in the observation plane satisfies: Among them, the propagation direction of the plane wave is along the z-axis, the xy plane is the incident plane, and (x', y', z') represents the coordinates of the observation point in the observation plane. represents the light field at the observation point (x', y', z'), E0(ρ) = 1 represents the amplitude of the incident plane wave, k = 2π / λ represents the wave number of the incident plane wave, λ represents the wavelength of the incident plane wave, is an imaginary unit, represents the phase modulation function of a binary phase optical element with angular order N, ψ Lens (ρ) represents the phase function of the lens, It 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 transmits the pure phase optical element, the light intensity distribution in the observation plane satisfies: Among them, ||...|| means finding the modulus of a complex number.

7. The pure phase optical element according to claim 5, characterized in that: For an observation point at any position z' on the z-axis, the light field distribution satisfies: Among them, (0,0,z') represents the coordinates of the observation point on the z-axis, 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 of the plane wave after transmitting through the pure phase optical element satisfies: Among them, ||...|| means 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.

10. A super-resolution focusing method, characterized in that: include: A plane wave is transmitted through the pure phase optical element as claimed in any one of claims 1 to 9.

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