Phase optical element and method for obtaining stable transmission intensity of non-diffracting beam

Abstract

The application provides a phase optical element and a method for obtaining stable transmission of light intensity of non-diffraction light beams. The phase optical element having an equivalent light field modulation function to the amplitude optical element is used to replace the amplitude optical element, so that the light intensity distribution of the non-diffraction light beams is obtained. Compared with the amplitude optical element, the phase optical element has the advantages of small energy loss, low cost, easy processing and the like, and is suitable for more extensive practical applications.

Description

Technical Field

[0001] This application relates to the field of optical technology, and in particular to phase-type optical elements and methods for obtaining stable transmission of light intensity in diffraction-free beams. Background Technology

[0002] When a non-diffractive light beam (such as a Bessel beam or a plane wave) passes through a circular aperture of finite size, the axial light intensity exhibits a significant oscillating effect. In related technologies, an amplitude-type optical element (such as a graded amplitude stop or a binary amplitude stop) is placed on the plane of the circular aperture to obtain a stable axial light intensity distribution for the transmission of the non-diffractive light beam.

[0003] However, amplitude-type optical elements have drawbacks such as large energy loss, high cost, and difficult processing, which limit their widespread application in practical optical systems. Summary of the Invention

[0004] In view of this, the purpose of this application is to propose a phase-type optical element and a method for obtaining stable transmission of light intensity in a diffraction-free beam.

[0005] To achieve the above objectives, this application provides a phase-type optical element for obtaining a light intensity distribution for stable transmission of a diffraction-free beam, comprising a first part and a second part; the phase of the beam does not change after passing through the first part, but the phase of the beam changes after passing through the second part.

[0006] The first part is a circular area, and the second part is an annular area surrounding the first part. The center of the first part coincides with the center of the second part.

[0007] The phase change of the non-diffractive beam after passing through the second part satisfies the following equation:

[0008]

[0009] Where ρ is the radial distance, which is the distance between a point in the second part and the center of the circle in the first part. For phase transformation, the phase transformation is determined based on the radial distance, θ is the azimuth angle of the point within the second part, N is the angular order (a positive integer), and m is a parameter. This represents the phase change of a non-diffractive beam after it passes through a point within the second part.

[0010] As can be seen from the above, the phase-type optical element and the method for obtaining stable light intensity transmission of a diffraction-free beam provided in this application achieve a stable light intensity distribution for diffraction-free beam transmission by replacing the amplitude-type optical element with a phase-type optical element that has an equivalent light field modulation function. Furthermore, compared to amplitude-type optical elements, phase-type optical elements have advantages such as lower energy loss, lower cost, and easier fabrication, making them more suitable for practical applications. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a schematic diagram of the structure of a phase-type optical element according to an embodiment of this application.

[0013] Figure 2 This is a diagram showing the axial light intensity distribution of a Bessel beam after it passes through a circular aperture.

[0014] Figure 3 This is a diagram showing the axial intensity distribution of a Bessel beam after it passes through an amplitude-type optical element.

[0015] Figure 4 The phase distribution of the basic phase-type optical element in the embodiments of this application is shown.

[0016] Figure 5 This is a diagram showing the axial intensity distribution of a Bessel beam after it has passed through a basic phase-type optical element and an amplitude-type optical element.

[0017] Figure 6 The phase distribution of a phase-type optical element with an angular order of 8 in this embodiment of the application is shown.

[0018] Figure 7 The phase distribution of a phase-type optical element with an angular order of 16 in this embodiment of the application is shown.

[0019] Figure 8 This is a diagram showing the axial intensity distribution of a Bessel beam after it has passed through phase-type and amplitude-type optical elements of different angular orders.

[0020] Figure 9 This is a diagram showing the transverse light intensity distribution of a Bessel beam after it has passed through a phase-type optical element with an angular order of 1.

[0021] Figure 10 This is a diagram showing the transverse light intensity distribution of a Bessel beam after it has passed through a phase-type optical element with an angular order of 8.

[0022] Figure 11 This is a diagram showing the transverse light intensity distribution of a Bessel beam after it passes through a phase-type optical element with an angular order of 16.

[0023] Figure 12 This is a diagram showing the relative deviation of the transverse light intensity after a Bessel beam passes through a phase-type optical element with an angular order of 1.

[0024] Figure 13 This is a diagram showing the relative deviation of the transverse light intensity after a Bessel beam passes through a phase-type optical element with an angular order of 8.

[0025] Figure 14 This is a diagram showing the relative deviation of the transverse light intensity after a Bessel beam passes through a phase-type optical element with an angular order of 16.

[0026] The reference numerals in the figure include: Part 1, Part 2. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0028] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this application should have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their 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.

[0029] The transverse optical field distribution of a non-diffractive beam remains unchanged during propagation, thus holding broad application prospects in laser processing, interferometry, optical trapping, and optical microscopy. Previous literature indicates that the axial intensity of a non-diffractive beam exhibits a significant oscillation effect when transmitted through a circular aperture of finite size. To suppress this axial intensity oscillation, related technologies employ the placement of a gradually varying amplitude stop or a binary amplitude stop on the plane of the circular aperture.

[0030] However, amplitude stops have drawbacks such as large energy loss, high cost, and difficult processing, which limit their widespread application in practical optical systems.

[0031] In view of the above-mentioned drawbacks of amplitude stops, embodiments of this application provide phase-type optical elements and methods for obtaining stable transmission of light intensity in diffraction-free beams.

[0032] The phase-type optical element and method for obtaining stable light intensity transmission of a diffraction-free beam provided in this application convert an amplitude-type optical element with rotational symmetry into a phase-type optical element through calculation. Numerical simulation results show that the converted phase-type optical element has equivalent light field modulation function to the amplitude-type optical element, thus achieving a stable light intensity distribution by using the phase-type optical element instead of the amplitude-type optical element. Furthermore, compared with the amplitude-type optical element, the phase-type optical element has advantages such as lower energy loss, lower cost, and easier fabrication, making it more suitable for practical applications.

[0033] Figure 1 The structure of a phase-type optical element according to an embodiment of this application is shown.

[0034] like Figure 1 As shown, this application provides a phase-type optical element for stabilizing the intensity distribution of a non-diffractive light beam after passing through a circular aperture. It may include a first part 1 and a second part 2. The phase of the light beam does not change after passing through the first part 1, but the phase changes after passing through the second part 2.

[0035] The first part 1 can be a circular area, and the second part 2 can be an annular area surrounding the first part 1, with the center of the first part 1 coinciding with the center of the second part 2.

[0036] The phase change of the non-diffractive beam after passing through part 2 satisfies the following equation:

[0037]

[0038] Where ρ is the radial distance, that is, the distance between a point in the second part 2 and the center of the circle in the first part 1. To perform phase transformation, the phase transformation is determined based on the radial distance. θ is the azimuth angle of the point within section 2, N is the angular order (a positive integer), and m is a parameter. The phase change is the result of a non-diffractive beam passing through a point in the second part 2.

[0039] In this embodiment, the phase-type optical element is obtained by transforming the amplitude-type optical element, which has rotational symmetry. The transformed phase of the phase-type optical element and the amplitude transmission coefficient of the amplitude-type optical element satisfy the following correspondence:

[0040]

[0041] Where T(ρ) is the amplitude transmission coefficient of the amplitude-type optical element, which is determined according to the radial distance ρ, arccos(...) is the inverse function of the cosine function, and cos(...) is the cosine function.

[0042] As an optional embodiment, the amplitude transmission coefficient of the amplitude-type optical element satisfies the following formula:

[0043]

[0044] Corresponding to the phase-type optical element, the amplitude-type optical element also includes two parts: the first part 1 is a circular region, and the second part 2 is an annular region surrounding the first part 1. In equation (3), R1 is the radius of the first part 1 of the amplitude-type optical element, and R2 is the radius of the amplitude-type optical element.

[0045] Substituting equation (3) into equation (2), the conversion phase of the phase-type optical element can be calculated to satisfy the following equation:

[0046]

[0047] At this time, the phase conversion of the phase-type optical element It has the following characteristics: In the region where the radial distance ρ is less than R1, that is, the conversion phase of the first part 1 is 0, and the phase does not change after the beam passes through the first part 1; In the region where the radial distance ρ is greater than or equal to R1 and less than or equal to R2, the conversion phase increases monotonically with the increase of the radial distance, and the value range of the conversion phase is from 0 to π / 2.

[0048] Substituting equation (4) into equation (1) will transform the amplitude-type optical element into a phase-type optical element. The resulting phase-type optical element has the same light field modulation effect as the amplitude-type optical element, and can stabilize the light intensity distribution of the non-diffractive beam during transmission.

[0049] The following calculations and simulations demonstrate that the aforementioned phase-type optical element can effectively stabilize the intensity distribution of the non-diffraction beam transmitted through the circular aperture.

[0050] First, it is demonstrated that amplitude-type optical elements have a modulating effect on the stable axial optical field.

[0051] The optical field after a non-diffractive beam passes through an optical element can be calculated using the complete Rayleigh-Sommerfeld method, as shown in the following formula:

[0052]

[0053] In this diagram, the propagation direction of the non-diffractive beam is the z-axis, the xy plane is the input plane (the plane where the optical element first contacts the non-diffractive beam), (x′,y′,z′) are the coordinates of the observation point in the output plane, U(x′,y′,z′) is the light field at the observation point (x′,y′,z′), k=2π / λ is the wave vector of the incident light wave, and λ is the wavelength of the incident light wave. The unit is the imaginary unit, (x,y,z=0) represents the coordinates of the source point in the input plane, and U0(x,y,z=0) represents the light field at the source point (x,y,z=0) in the input plane. This represents the distance between the observation point and the source point.

[0054] Taking a Bessel beam as an example to calculate the transmission characteristics of a non-diffraction beam, after the Bessel beam passes through an amplitude-type optical element with rotational symmetry, the light field at the source point in the input plane can be calculated using the following formula:

[0055] U0(x,y,z=0)=U0(ρ,z=0)=E0(ρ)×T(ρ)(6)

[0056] Where E0(ρ)=J0(βρ) is the optical field when the Bessel beam propagates to the amplitude-type optical element, J0 is the zeroth-order Bessel function of the first kind, and β is the transverse wave vector of the Bessel beam. This is the radial distance of the source point in the input plane.

[0057] Substituting equation (6) into equation (5) yields the light field of the Bessel beam after it has passed through the amplitude-type optical element, as follows:

[0058]

[0059] Wherein, U1(x′,y′,z′) is the light field at the observation point (x′,y′,z′) after the Bessel beam passes through the amplitude-type optical element.

[0060] Because amplitude-type optical elements have rotational symmetry, for observation points on the z-axis, equation (7) can be expressed in polar coordinates as follows:

[0061]

[0062] Where θ is the azimuth angle of the source point in the input plane.

[0063] The intensity of the Bessel beam after it passes through an amplitude-type optical element can be calculated from the light field of the beam. The calculation formula is as follows:

[0064] I1(x′,y′,z′)=‖U1(x′,y′,z′)‖ 2 (9)

[0065] Where, ‖…‖ represents finding the modulus of a complex number, and I1(x′,y′,z′) is the light intensity at the observation point (x′,y′,z′) after the Bessel beam passes through the amplitude-type optical element.

[0066] Specifically, when the amplitude transmission coefficient of the amplitude-type optical element is set to...

[0067]

[0068] At this time, the amplitude-type optical element is a circular hole with a radius of R2. By replacing T(ρ) in equation (8) with T0(ρ) in equation (10), and then using equation (9), the axial light intensity of the Bessel beam after passing through the circular hole can be obtained, denoted as I0(0,0,z′).

[0069] A set of parameters is selected to simulate and calculate the intensity distribution of the Bessel beam after it passes through a circular aperture. The parameters can be chosen as follows: the transverse wave vector of the incident Bessel beam is β = 10. 4 m -1 The wavelength of the incident light wave is λ = 0.6328 μm; the radius of the transmission aperture is R2 = 30 mm.

[0070] Figure 2 The diagram shows the axial intensity distribution of the Bessel beam after passing through the circular aperture when the above parameters are used. Figure 2 It can be clearly seen that the axial light intensity exhibits a violent oscillation effect, with a relative deviation of approximately ±10%.

[0071] Substituting equation (3) into equation (8), and then using equation (9), the axial intensity of the Bessel beam after passing through the amplitude-type optical element can be obtained. Using the same parameters as when passing through the circular aperture, the intensity distribution of the Bessel beam after passing through the amplitude-type optical element is simulated and calculated. The parameters can be selected as follows: the transverse wave vector of the incident Bessel beam is β = 10. 4 m -1 The wavelength of the incident light wave is λ = 0.6328 μm; the radius of the first part 1 of the amplitude-type optical element is R1 = 15 mm, and the radius of the amplitude-type optical element is R2 = 30 mm. Figure 3 The diagram shows the axial intensity distribution of the Bessel beam after passing through an amplitude-type optical element when the above parameters are used. Figure 3 It can be clearly seen that by setting amplitude-type optical elements, a stable axial light intensity distribution for Bessel beam transmission was obtained.

[0072] Subsequently, it was demonstrated that phase-type optical elements have an axial optical field modulation effect equivalent to that of amplitude-type optical elements.

[0073] For phase-type optical elements, we first discuss the basic phase-type optical element that satisfies equation (1). The angular order of the basic phase-type optical element is N1 = 1, and the phase change of the beam after passing through part 2 satisfies the following equation:

[0074]

[0075] Figure 4The phase distribution of a basic phase-type optical element is shown. This is illustrated by equation (11) and... Figure 4 It can be concluded that the basic phase-type optical element has the following three characteristics: First, on a circle with a given radial distance ρ, its phase distribution consists of two semicircles with opposite phases; second, when the azimuth angle is 0 or π, this phase-type optical element exists along the azimuth direction. The phase abrupt change; third, along the radial direction, the aforementioned phase abrupt change It is not a constant value; it is related to the radial distance ρ.

[0076] According to equation (2), when the amplitude transmission coefficient T(ρ) of the amplitude-type optical element is 1, we can obtain... At this point, for a basic phase-type optical element, all source points on a circle with a radial distance of ρ have the same phase. This provides the most ideal interference enhancement effect for the observation points on the axis; when the amplitude transmission coefficient T(ρ) = 0, it can be obtained from equation (2) At this point, the source points of the upper and lower semicircles produce diffraction field distributions with opposite phases at the observation point on the axis, and the real parts of the two diffraction fields are both 0. That is, the diffraction fields of all source points on the circumference of the radial distance in the input plane are superimposed on the observation point to be 0, thus obtaining a perfectly destructive interference result at the observation point on the axis.

[0077] When a Bessel beam passes through a phase-type optical element, the optical field at any observation point (x′, y′, z′) can be calculated using the complete Rayleigh-Somerfi method as follows:

[0078]

[0079] Specifically, after the Bessel beam passes through the phase-type optical element, the light field at the observation point on the z-axis is represented as follows:

[0080]

[0081] in, Let be the phase distribution function of the phase-type optical element, given by equation (1). This is the optical field at the on-axis observation point (0,0,z′) after the Bessel beam passes through the phase-type optical element.

[0082] For a basic phase-type optical element, the integral term within the curly braces in equation (13) can be expanded and simplified as follows:

[0083]

[0084] Substituting equations (14) and (2) into equation (13), it can be proven that equation (13) is completely equivalent to equation (8). Therefore, the transformed basic phase-type optical element and amplitude-type optical element have the same axial optical field modulation function.

[0085] By analogy, it can also be proven that phase-type optical elements of any angular order have the same axial optical field modulation effect as amplitude-type optical elements.

[0086] The intensity of the Bessel beam after it passes through a phase-type optical element can be calculated from the light field of the beam. The calculation formula is as follows:

[0087]

[0088] in, This represents the light intensity at the observation point (x′, y′, z′) after the Bessel beam has passed through a phase-type optical element.

[0089] Using the same parameters as when transmitting through an amplitude-type optical element, simulate and calculate the intensity distribution of the Bessel beam after it passes through a basic phase-type optical element. The parameters can be selected as follows: the transverse wave vector of the incident Bessel beam is β = 10. 4 m -1 The wavelength of the incident light wave is λ = 0.6328 μm; the radius of the basic phase-type optical element is R2 = 30 mm, and the radius of the first part 1 is R1 = 15 mm.

[0090] Figure 5 The diagram shows the axial intensity distribution of the Bessel beam after passing through the basic phase-type optical element and amplitude-type optical element when the above parameters are used. Figure 5 It can be seen that the axial light intensity distribution of the Bessel beam after passing through the basic phase-type optical element is completely consistent with the axial light intensity distribution of the Bessel beam after passing through the amplitude-type optical element. This also proves that the converted basic phase-type optical element and the amplitude-type optical element have the same axial light field modulation function.

[0091] However, the basic phase-type optical element does not have rotational symmetry, while the amplitude-type optical element does, resulting in different transverse light field distributions for off-axis observation points. Therefore, in order to reduce the asymmetry of the transverse light field distribution after a non-diffractive beam passes through the phase-type optical element, a parameter along the azimuth direction, namely the angular order N, is introduced. The phase distribution in equation (11) is first compressed by a factor of N along the azimuth direction, and then repeated N times along the azimuth direction to obtain the phase distribution function of the phase-type optical element with an angular order of N, which is equation (1).

[0092] Figure 6 and Figure 7 The phase distributions of phase-type optical elements with angular orders N2 = 8 and N3 = 16 are shown respectively. Using the same parameters as when transmitting through amplitude-type optical elements, the intensity distributions of the Bessel beam after transmission through phase-type optical elements with angular orders N2 = 8 and N3 = 16 are simulated and calculated. The parameters are selected as follows: the transverse wave vector of the incident Bessel beam is β = 10. 4 m -1 The wavelength of the incident light wave is λ = 0.6328 μm; the radius of the phase-type optical element is R2 = 30 mm, and the radius of the first part 1 is R1 = 15 mm.

[0093] Figure 8 This diagram illustrates the axial intensity distribution of a Bessel beam after passing through phase-type and amplitude-type optical elements of different angular orders, using the aforementioned parameters. Figure 8 It can be seen that the axial light intensity distribution of the Bessel beam after passing through the phase-type optical element is completely consistent with the axial light intensity distribution of the Bessel beam after passing through the amplitude-type optical element. Therefore, regardless of the angular order of the phase-type optical element, it has the same axial light field modulation function as the amplitude-type optical element.

[0094] The introduction of the angular order N gives the phase-type optical element N-fold symmetry along the azimuth direction. As the angular order of the phase-type optical element increases, the asymmetry of the transverse optical field gradually weakens. When the angular order of the phase-type optical element approaches infinity, the asymmetry of the transverse optical field will disappear completely.

[0095] To quantitatively characterize the asymmetry of the transverse optical field after a Bessel beam passes through a phase-type optical element. Figures 9 to 11 The light intensity distribution of a Bessel beam transmitted through phase-type optical elements with angular orders N1=1, N2=8, and N3=16 is shown on a cross section with a transmission distance of z′=10m. Figures 9 to 11 All exhibit concentric ring light intensity patterns, with almost no discernible asymmetry in lateral light intensity. This indicates that the lateral light intensity distribution is not strongly dependent on the azimuth direction.

[0096] To more clearly demonstrate the asymmetry of lateral light intensity, the relative deviation of lateral light intensity is defined as follows:

[0097]

[0098] Here, |…| represents finding the absolute value of a function, and max(…) represents finding the maximum value of a function.

[0099] According to equation (16), the relative deviation of transverse light intensity was simulated and calculated. Figures 12 to 14The relative lateral intensity deviations of a Bessel beam transmitted through phase-type optical elements with angular orders N1 = 1, N2 = 8, and N3 = 16 are shown at a transmission distance z′ = 10 m. It can be seen that the relative lateral intensity deviation decreases rapidly with increasing angular order. When the angular order is N3 = 16, the relative lateral intensity deviation is less than 0.4%. Considering that practical applications primarily focus on the intensity distribution within the central main lobe, numerical simulation results show that when the angular order is N3 = 16, the relative lateral intensity deviation within the central main lobe is only 0.0069%. Therefore, the asymmetry of lateral intensity has a negligible impact on practical applications. In summary, a phase-type optical element has been used to achieve a lateral optical field modulation function equivalent to that of an amplitude-type optical element.

[0100] As an alternative embodiment, the phase-type optical element can be one of a diffractive optical element, a phase plate, a spatial light modulator, and a variable phase delayer; diffractive optical elements and phase plates are inexpensive and easy to manufacture; spatial light modulators and variable phase delayers can be used in laboratories or in applications with high beam requirements, and the desired phase can be obtained by adjustment.

[0101] Based on the same inventive concept, corresponding to the phase-type optical element of any of the above embodiments, this disclosure also provides a method for obtaining stable transmission intensity of a diffraction-free beam, the method comprising transmitting the diffraction-free beam through the phase-type optical element of any of the above embodiments.

[0102] 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 this application (including the claims) is limited to these examples; within the framework of this application, 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 this application as described above, which are not provided in the details for the sake of brevity.

[0103] Although this application 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.

[0104] The embodiments of this 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 this application should be included within the protection scope of this application.

Claims

1. A phase-type optical element for obtaining a light intensity distribution for stable transmission of a diffraction-free beam, characterized in that, The phase-type optical element includes a first part and a second part; the phase of the non-diffraction beam does not change after passing through the first part, and the phase of the non-diffraction beam changes after passing through the second part. The first part is a circular region, and the second part is an annular region surrounding the first part, with the center of the first part coinciding with the center of the second part; The phase change of the non-diffractive beam after passing through the second part satisfies the following equation: in, The radial distance is the distance between a point within the second part and the center of the circle in the first part. For phase conversion, the phase conversion is determined based on the radial distance. Let be the azimuth angle of the point within the second part. It is an angular order, belonging to positive integers. For parameters, The phase change of the non-diffractive beam after it passes through a point in the second part; The transition phase satisfies the following equation: in, Let be the radius of the first part. The outer radius of the second part is... It is a cosine function. It is the inverse function of the cosine function; The conversion phase increases as the radial distance increases; The transition phase is greater than or equal to 0 and less than or equal to 0. .

2. The phase-type optical element as described in claim 1, characterized in that, The phase-type optical element is a diffractive optical element.

3. The phase-type optical element as described in claim 1, characterized in that, The phase-type optical element is a phase plate.

4. The phase-type optical element as described in claim 1, characterized in that, The phase-type optical element is a spatial light modulator.

5. The phase-type optical element as described in claim 1, characterized in that, The phase-type optical element is a variable phase delayer.

6. A method for obtaining stable transmission intensity of a diffraction-free beam, characterized in that, include: The non-diffraction beam is transmitted through the phase-type optical element as described in any one of claims 1 to 5.

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