Phase-type optical element and method for suppressing light intensity oscillation of non-diffracting beam

Abstract

The present application provides a phase-type optical element and a method for suppressing the light intensity oscillation of a non-diffracting beam. By using a phase-type optical element with an equivalent light field modulation function to an amplitude-type optical element to replace the amplitude-type optical element, the purpose of suppressing the light intensity oscillation of the non-diffracting beam is achieved. Moreover, compared with the amplitude-type optical element, the phase-type optical element has advantages such as small energy loss, low cost, and easy processing, and is suitable for a wider range of practical applications.

Description

Technical Field

[0001] This application relates to the field of optical technologies, and particularly to a phase-type optical element and a method for suppressing the light intensity oscillation of a non-diffracting beam. Background Art

[0002] When a non-diffracting beam (such as a Bessel beam, a plane wave) passes through a circular hole with a finite size, the axial light intensity exhibits a significant oscillation effect. In related technologies, an amplitude-type optical element (such as a gradient amplitude aperture, a binary amplitude aperture) is arranged on the plane of the circular hole to suppress the axial light intensity oscillation of the non-diffracting beam.

[0003] However, the amplitude-type optical element has disadvantages such as large energy loss, high cost, and difficult processing, which limit its wide application in actual optical systems. Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a phase-type optical element and a method for suppressing the light intensity oscillation of a non-diffracting beam.

[0005] Based on the above purpose, this application provides a phase-type optical element for suppressing the light intensity oscillation of a non-diffracting beam, including a first part and a second part; the phase of the beam does not change after passing through the first part, and the phase of the beam changes after passing through the second part;

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

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

[0008]

[0009] where ρ is the radial distance, the radial distance is the distance between a point in the second part and the center of the first part, is the conversion phase, the conversion phase is determined according to the radial distance, θ is the azimuth angle of a point in the second part, N is the angular order, belonging to a positive integer, m is a parameter, is the phase change of the non-diffracting beam after passing through a point in the second part.

[0010] As can be seen from the above, the phase-type optical element and the method for suppressing the light intensity oscillation of a non-diffracting beam provided by this application use a phase-type optical element with an equivalent light field modulation function instead of the amplitude-type optical element to achieve the effect of suppressing the light intensity oscillation of the non-diffracting beam. And compared with the amplitude-type optical element, the phase-type optical element has advantages such as small energy loss, low cost, and easy processing, and is more suitable for practical applications. Brief Description of the Drawings

[0011] To more clearly illustrate the technical solutions in this application, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only the embodiments of this application. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

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

[0013] Figure 2 It is the axial light intensity distribution diagram after the Bessel beam passes through the circular hole.

[0014] Figure 3 It is the axial light intensity distribution diagram after the Bessel beam passes through the amplitude-type optical element.

[0015] Figure 4 It is the phase distribution of the basic phase-type optical element according to the embodiment of this application.

[0016] Figure 5 It is the axial light intensity distribution diagram after the Bessel beam passes through the basic phase-type optical element and the amplitude-type optical element.

[0017] Figure 6 It is the phase distribution of the phase-type optical element with an angular order of 4 according to the embodiment of this application.

[0018] Figure 7 It is the phase distribution of the phase-type optical element with an angular order of 8 according to the embodiment of this application.

[0019] Figure 8 It is the axial light intensity distribution diagram after the Bessel beam passes through the phase-type optical elements with different angular orders.

[0020] Figure 9 It is the transverse light intensity distribution diagram after the Bessel beam passes through the phase-type optical element with an angular order of 1.

[0021] Figure 10 It is the transverse light intensity distribution diagram after the Bessel beam passes through the phase-type optical element with an angular order of 4.

[0022] Figure 11 It is the transverse light intensity distribution diagram after the Bessel beam passes through the phase-type optical element with an angular order of 8.

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

[0024] Figure 13It is a diagram of the relative deviation of the transverse light intensity after a Bessel beam passes through a phase-type optical element with an angular order of 4.

[0025] Figure 14 It is a diagram of 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.

[0026] The reference numerals in the figure include: the first part 1, the second part 2. Specific embodiments

[0027] To make the objectives, technical solutions, and advantages of the present application clearer and more understandable, the following further elaborates on the present application in detail with reference to specific embodiments and the accompanying drawings.

[0028] 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 pertains. Words such as "including" or "comprising" and the like mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. Words such as "connected" or "coupled" and the like are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0029] The transverse light field distribution of a non-diffracting beam does not change during propagation. Therefore, it has broad application prospects in laser processing, interference metrology, optical trapping, optical microscopy, etc. Previous literature has shown that when a non-diffracting beam passes through a circular hole with a finite size, significant oscillation effects occur in the axial intensity. To suppress the axial light intensity oscillation of the non-diffracting beam, the solution in related technologies is to set a gradient amplitude aperture or a binary amplitude aperture on the plane of the circular hole.

[0030] However, amplitude apertures have disadvantages such as large energy loss, high cost, and difficult processing, which limit their wide application in actual optical systems.

[0031] In view of the above disadvantages of the amplitude aperture, the embodiments of the present application provide a phase-type optical element and a method for suppressing the light intensity oscillation of a non-diffracting beam.

[0032] The phase-type optical element and the method for suppressing the light intensity oscillation of a non-diffracting beam provided by the present application convert an amplitude-type optical element with rotational symmetry into a phase-type optical element through calculation. The numerical simulation results show that the converted phase-type optical element has an equivalent light field modulation function to the amplitude-type optical element. Thus, by using the phase-type optical element instead of the amplitude-type optical element, the effect of suppressing the light intensity oscillation of the non-diffracting beam is achieved. Moreover, compared with the amplitude-type optical element, the phase-type optical element has advantages such as small energy loss, low cost, and easy processing, and is more suitable for practical applications.

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

[0034] As Figure 1 shown, an embodiment of the present application provides a phase-type optical element for suppressing the light intensity oscillation of a non-diffracting beam transmitted through a circular hole, which may include a first part 1 and a second part 2. The phase of the beam does not change after passing through the first part 1, and the phase of the beam changes after passing through the second part 2.

[0035] The first part 1 may be a circular region, and the second part 2 may be an annular region surrounding the first part 1. The centers of the first part 1 and the second part 2 coincide.

[0036] The phase change of the non-diffracting beam after passing through the second part 2 satisfies the following formula:

[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 first part 1, is the conversion phase, the conversion phase is determined according to the radial distance, θ is the azimuth angle of a point in the second part 2, N is the angular order, which belongs to a positive integer, and m is a parameter, is the phase change of the non-diffracting beam after passing through a point in the second part 2.

[0039] In this embodiment, the phase-type optical element is obtained by transforming an amplitude-type optical element with rotational symmetry. The following correspondence relationship is satisfied between the conversion phase of the phase-type optical element and the amplitude transmission coefficient of the amplitude-type optical element:

[0040]

[0041] where T(ρ) is the amplitude transmission coefficient of the amplitude-type optical element, the amplitude transmission coefficient is determined according to the radial distance, arcsinc(…) is the inverse function of the sinc function, and the calculation method of the sinc function is sin(…) is the sine 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. 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 conversion phase of the phase-type optical element 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 of the light beam does not change after passing through the first part 1; in the region where the radial distance 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 ρ; the value range of the conversion phase is from 0 to π.

[0048] Substituting Equation (4) into Equation (1), the amplitude-type optical element can be converted into a phase-type optical element, and the obtained phase-type optical element has an equivalent light field modulation effect to the amplitude-type optical element, which can effectively suppress the light intensity oscillation of the non-diffracting beam.

[0049] Next, it is proved by calculation and simulation that the above-mentioned phase-type optical element can effectively suppress the light intensity oscillation of the non-diffracting beam transmitted through the circular hole.

[0050] First, it is proved that the amplitude-type optical element has the effect of suppressing the axial light intensity oscillation of the non-diffracting beam.

[0051] The light field after the non-diffracting beam passes through the optical element can be calculated by using the complete Rayleigh-Sommerfeld method, and the calculation formula is as follows:

[0052]

[0053] Among them, the propagation direction of the non-diffracting beam is the z-axis, the xy plane is the input plane, that is, the plane where the optical element first contacts the 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, λ is the wavelength of the incident light wave, is the imaginary unit, (x, y, z = 0) are the coordinates of the source point in the input plane, U0(x, y, z = 0) is the light field at the source point (x, y, z = 0) in the input plane, is the distance between the observation point and the source point.

[0054] Taking the Bessel beam as an example to calculate the propagation characteristics of non-diffracting beams, after the Bessel beam passes through an amplitude-type optical element with rotational symmetry, the optical field at the origin in the input plane can be calculated by 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 zero-order Bessel function of the first kind, β is the transverse wave vector of the Bessel beam, and ρ is the radial distance of the origin in the input plane.

[0057] Substituting Equation (6) into Equation (5), the optical field after the Bessel beam passes through the amplitude-type optical element can be obtained as follows:

[0058]

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

[0060] Because the amplitude-type optical element has rotational symmetry, for the 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 origin in the input plane.

[0063] According to the optical field after the Bessel beam passes through the amplitude-type optical element, the optical intensity after the Bessel beam passes through the amplitude-type optical element can be calculated. The calculation formula is as follows:

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

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

[0066] In particular, when the amplitude transmittance 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. Substituting T0(ρ) in Equation (10) for T(ρ) in Equation (8) and using Equation (9), the axial light intensity after the Bessel beam passes 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 light intensity distribution after the Bessel beam passes through the circular hole. 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 = 500 nm; the radius of the transmitted circular hole is R2 = 50 mm.

[0070] Figure 2 shows the axial light intensity distribution after the Bessel beam passes through the circular hole when the above parameters are adopted. It can be clearly seen from Figure 2 that there is a severe oscillation effect in the axial light intensity, and the relative deviation of the axial light intensity is about ±10%.

[0071] Substituting Equation (3) into Equation (8) and then using Equation (9), the axial light intensity after the Bessel beam passes through the amplitude-type optical element can be obtained. Selecting the same parameters as when passing through the circular hole, the light intensity distribution after the Bessel beam passes 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 = 500 nm; the radius of the first part 1 of the amplitude-type optical element is R1 = 40 mm; the radius of the amplitude-type optical element is R2 = 50 mm. Figure 3 shows the axial light intensity distribution after the Bessel beam passes through the amplitude-type optical element when the above parameters are adopted. It can be clearly seen from Figure 3 that by setting the amplitude-type optical element, the axial light intensity oscillation of the Bessel beam is perfectly suppressed.

[0072] Subsequently, it is proved that the phase-type optical element has an axial light field modulation effect equivalent to that of the amplitude-type optical element.

[0073] For the phase-type optical element, first, the basic phase-type optical element satisfying Equation (1) is explored. The angular order of the basic phase-type optical element takes the value of N1 = 1. The phase change after the Bessel beam passes through the second part 2 satisfies the following equation:

[0074]

[0075] Figure 4 shows the phase distribution of the basic phase-type optical element. Through Equation (11) and Figure 4It can be concluded that the basic phase-type optical element has the following three characteristics: First, on the circumference at a given radial distance ρ, when the azimuth angle θ increases from 0 to 2π, its phase distribution changes from linearly increasing to Therefore, this element is a vortex-phase optical element; Second, when the azimuth angle is 0, there is a phase mutation along the azimuth direction for this phase-type optical element; Third, along the radial direction, the above-mentioned phase mutation is not a constant value and is related to the radial distance ρ.

[0076] For the basic phase-type optical element, when the radial distance ρ is less than R1, from Equation (4), we can obtain This indicates that the phases of all source points within the circle with a radius of R1 are the same, having the most ideal interference enhancement effect, exactly corresponding to the case where the amplitude transmission coefficient T(ρ) of the amplitude-type optical element is 1; within the circular ring where the radial distance ρ is greater than or equal to R1 and less than or equal to R2, from Figure 4 it can be seen that this element exhibits a vortex-phase distribution along the azimuth direction, there is a phase mutation when the azimuth angle θ = 0, and the value of the phase mutation gradually increases with the increase of the radial distance, corresponding to the case where the amplitude transmission coefficient gradually decreases from 1 to 0.

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

[0078]

[0079] In particular, after the Bessel beam passes through the phase-type optical element, for the observation point on the z-axis, the optical field is expressed as follows:

[0080]

[0081] where, is the phase distribution function of the phase-type optical element, given by Equation (1), 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 the basic phase-type optical element, the integral term inside the curly brackets in Equation (13) can be expanded and simplified as follows:

[0083]

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

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

[0086] Based on the light field of a Bessel beam transmitted through a phase-type optical element, the light intensity of the Bessel beam transmitted through the phase-type optical element can be calculated. The calculation formula is as follows:

[0087]

[0088] where, is the light intensity at the observation point (x′, y′, z′) after the Bessel beam is transmitted through the phase-type optical element.

[0089] Selecting the same parameters as when transmitting through the amplitude-type optical element, the axial light intensity distribution of the Bessel beam transmitted through the basic phase-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 = 500 nm; the radius of the basic phase-type optical element is R2 = 50 mm, and the radius of the first part 1 is R1 = 40 mm.

[0090] Figure 5 shows the axial light intensity distributions of the Bessel beam transmitted through the basic phase-type optical element and the amplitude-type optical element when the above parameters are used. It can be seen from Figure 5 that the axial light intensity distribution of the Bessel beam transmitted through the basic phase-type optical element completely coincides with the axial light intensity distribution of the Bessel beam transmitted through the amplitude-type optical element, which also proves that the transformed basic phase-type optical element has the same axial light field modulation function as the amplitude-type optical element.

[0091] However, the basic phase-type optical element does not have rotational symmetry, while the amplitude-type optical element has rotational symmetry, resulting in different transverse light field distributions for the basic phase-type optical element and the amplitude-type optical element at off-axis observation points. Therefore, in order to weaken the asymmetry of the transverse light field distribution of the Bessel beam transmitted through the phase-type optical element, a parameter in the azimuthal direction, i.e., the angular order N, is introduced. First, the phase distribution in Equation (11) is compressed N times in the azimuthal direction, and then repeated N times in the azimuthal direction to obtain the phase distribution function of the phase-type optical element with angular order N, which is Equation (1).

[0092] Figure 6 and Figure 7 respectively show the phase distributions of the phase-type optical elements with angular orders N2 = 4 and N3 = 8. As the angular order increases, the number of phase mutation points in the azimuthal direction gradually increases, as shown inFigure 6 and 7 As shown, the phase distribution exhibits angular multiple symmetry.

[0093] Select the same parameters as when transmitting through the amplitude-type optical element, and simulate and calculate the intensity distribution of the Bessel beam after transmitting through the phase-type optical elements with angular orders N2 = 4 and N3 = 8. 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 = 500 nm; the radius of the phase-type optical element is R2 = 50 mm, and the radius of the first part 1 is R1 = 40 mm.

[0094] Figure 8 Shows the axial intensity distribution of the Bessel beam after transmitting through the phase-type optical elements with different angular orders when using the above parameters. It can be seen from Figure 8 that the axial intensity distributions of the Bessel beam after transmitting through the phase-type optical elements with different angular orders completely coincide. Therefore, regardless of the value of the angular order, the phase-type optical element has the same axial light field modulation function as the amplitude-type optical element.

[0095] The introduction of the angular order N makes the phase-type optical element have N-fold symmetry along the azimuthal direction, and as the angular order of the phase-type optical element increases, the asymmetry of the transverse light field gradually weakens. When the angular order of the phase-type optical element approaches infinity, the asymmetry of the transverse light field will completely disappear.

[0096] To quantitatively characterize the asymmetry of the transverse light field of the Bessel beam after transmitting through the phase-type optical element, Figures 9 to 11 respectively show the intensity distributions on the cross-section at a transmission distance of z' = 20 m after the Bessel beam transmits through the phase-type optical elements with angular orders N1 = 1, N2 = 4, and N3 = 8. Figures 9 to 11 All show an intensity pattern of concentric rings, and it is almost impossible to see the asymmetry of the transverse intensity, indicating that the dependence of the transverse intensity distribution on the azimuthal direction is not strong.

[0097] To more clearly show the asymmetry of the transverse intensity, define the relative deviation of the transverse intensity as follows:

[0098]

[0099] where |…| represents taking the absolute value of a function, and max(…) represents taking the maximum value of a function.

[0100] According to Equation (16), the relative deviation of the transverse intensity was simulated and calculated. Figures 12 to 14The relative transverse light intensity deviations on the cross-section at a propagation distance of z' = 20 m are respectively shown after a Bessel beam passes through phase-type optical elements with azimuthal orders N1 = 1, N2 = 4, and N3 = 8. It can be seen that as the azimuthal order increases, the relative transverse light intensity deviation decreases rapidly. When the azimuthal order is N3 = 8, the relative transverse light intensity deviation is less than 0.8%. Considering the light intensity distribution mainly concerned in practical applications within the central main lobe, the numerical simulation results show that when the azimuthal order is N3 = 8, the relative transverse light intensity deviation within the central main lobe is only 0.12%. Therefore, the asymmetry of the transverse light intensity has almost negligible influence on practical applications. In summary, using the phase-type optical element, the equivalent transverse light field modulation function of the amplitude-type optical element is achieved.

[0101] As an optional 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 retarder; the diffractive optical element and the phase plate are low-cost and easy to process; the spatial light modulator and the variable phase retarder can be used in laboratories or occasions with high beam requirements, and the required phase can be obtained by adjustment.

[0102] Based on the same inventive concept, corresponding to the phase-type optical element of any of the above embodiments, the present disclosure also provides a method for suppressing the light intensity oscillation of a non-diffracting beam, the method including making the non-diffracting beam pass through the phase-type optical element of any of the above embodiments.

[0103] 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 between 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.

[0104] Although the present application has been described in conjunction with specific embodiments of the present application, many substitutions, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description.

[0105] The 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 omission, modification, equivalent substitution, improvement, etc. made within the spirit and principle of the embodiments of the present application shall be included within the protection scope of the present application.

Claims

1. A phase-type optical element for suppressing the intensity oscillation of a non-diffracting beam, characterized in that, The phase-type optical element includes a first part and a second part; the non-diffracting beam does not change its phase after passing through the first part, and the non-diffracting beam changes its phase after passing through the second part; The first part is a circular region, the second part is an annular region surrounding the first part, and the center of the first part coincides with the center of the second part; The phase change of the non-diffracting beam after passing through the second part satisfies the following formula: where ρ is the radial distance, which is the distance between a point in the second part and the center of the circle of the first part. is the conversion phase, which is determined according to the radial distance, θ is the azimuth angle of a point in the second part, N is the angular order, which belongs to positive integers, and m is a parameter. is the phase change after the non-diffracting beam passes through a point in the second part. The conversion phase increases as the radial distance increases; The conversion phase satisfies the following formula: Wherein, R1 is the radius of the first part, R2 is the outer ring radius of the second part, cos(…) is the cosine function, arcsinc(…) is the inverse function of the sinc function, and the calculation method of the sinc function is sin(…) is the sine function.

2. The phase type optical element according to claim 1, wherein The conversion phase is greater than or equal to 0 and less than or equal to π.

3. The phase-type optical element according to claim 1, wherein The phase-type optical element is a diffractive optical element.

4. The phase type optical element according to claim 1, characterized in that, The phase-type optical element is a phase plate.

5. The phase-type optical element according to claim 1, wherein, The phase-type optical element is a spatial light modulator.

6. The phase-type optical element according to claim 1, wherein The phase-type optical element is a variable phase retarder.

7. A method for suppressing the intensity oscillation of a non-diffracting beam, characterized in that, Comprising: Passing the non-diffracting beam through the phase-type optical element according to any one of claims 1 to 6.

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