A method and system for improving the intensity of first-order Airy derivative beam interference enhancement effect

Abstract

The present invention discloses a method and system for improving the intensity of the interference enhancement effect of a first-order Airy derivative light beam, belonging to the field of optical research technology. A second-order chirp factor is introduced into the electric field expression on the initial plane of the first-order Airy derivative light beam; an analytical expression of the electric field of the chirped first-order Airy derivative light beam when it is transmitted in free space is derived; based on the obtained analytical expression of the electric field, the interference enhancement effect is characterized by using the maximum light intensity, the observation plane position where the maximum light intensity appears, and the range of the interference enhancement effect; a relationship curve diagram of the maximum light intensity, the observation plane position where the maximum light intensity appears, and the range of the interference enhancement effect relative to the second-order chirp factor is drawn; based on the drawn relationship curve diagram, the value range of the second-order chirp factor is determined, and the second-order chirp factor is reasonably selected according to actual conditions to improve the intensity of the interference enhancement effect.

Description

Technical Field

[0001] The present invention relates to the field of optical research technology, and in particular to a method and system for improving the intensity of a first-order Airy derivative light beam interference enhancement effect by utilizing a second-order chirp factor. Background Art

[0002] Airy beams have attracted significant research interest due to their unique properties of non-diffraction, self-acceleration, and self-healing. Airy beams are widely used in free-space optical communications, all-optical routing, photonic interconnects, optical cleaning, optical trapping, optical manipulation, space-time photon bullets, optical micromachining, optical super-resolution imaging, optical tomography, and light-sheet microscopy. The unique properties of Airy beams make new beams derived from Airy functions unique and possess distinctive properties. Consequently, researchers are actively exploring the development of Airy beams and exploring a wide range of avenues to discover new beams based on Airy functions.

[0003] Using the first-order derivative of the Airy function, researchers have attempted to construct first-order Airy derivative beams. Although initial attempts did not provide a true first-order Airy derivative beam, such attempts paved the way for subsequent researchers. Recently, a first-order Airy derivative beam, formally similar to an Airy beam, was successfully introduced. By performing an Airy transformation after superposing four specific graceful Hermite-Gaussian modes, a pure first-order Airy derivative beam was generated. The first-order Airy derivative beam not only retains the three main characteristics of the Airy beam but also adds a new characteristic: the interference enhancement effect. The so-called interference enhancement effect refers to the phenomenon that the peak light intensity on a non-initial plane is greater than the peak light intensity on the initial plane. For simplicity, the peak light intensity on the initial plane is set to 1, and the intensity of the interference enhancement effect is described by the maximum light intensity during free-space transmission. How to further improve the intensity of the interference enhancement effect of the first-order Airy derivative beam without changing the existing beam parameters is a question of great concern to researchers. Summary of the Invention

[0004] The purpose of the present invention is to provide a method and system for improving the intensity of the first-order Airy derivative beam interference enhancement effect, which can further improve the intensity of the first-order Airy derivative beam interference enhancement effect.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] The present invention provides a method for increasing the intensity of the first-order Airy derivative beam interference enhancement effect, comprising:

[0007] Introducing a second-order chirp factor into the electric field expression of the first-order Airy derivative beam on the initial plane to obtain a target electric field expression; the target electric field expression is the electric field expression of the chirped first-order Airy derivative beam on the initial plane;

[0008] According to the target electric field expression, the Collins integral formula is used to derive the electric field analytical expression of the chirped first-order Airy derivative beam when it propagates in free space;

[0009] Determining, based on the electric field analytical expression, correlation factors describing the intensity of the interference enhancement effect; the correlation factors include the maximum light intensity, the position of the observation plane where the maximum light intensity occurs, and the range of the interference enhancement effect; the range of the interference enhancement effect refers to the distance from the observation plane where the first peak light intensity is greater than 1 to the observation plane where the last peak light intensity is greater than 1;

[0010] Determining a relationship curve of a correlation factor with respect to a second-order chirp factor based on parameters of the first-order Airy derivative beam;

[0011] Determine the value range of the second-order chirp factor based on a relationship curve of the correlation factors relative to the second-order chirp factor;

[0012] According to target requirements, the value of the second-order chirp factor of the first-order Airy derivative beam is determined; the value of the second-order chirp factor of the first-order Airy derivative beam is used to improve the intensity of the interference enhancement effect of the first-order Airy derivative beam.

[0013] Optionally, the target electric field expression is:

[0014]

[0015] Where E(x,y,0) is the electric field expression of the chirped first-order Airy derivative beam on the initial plane z = 0, x is the coordinate value on the x-axis in the rectangular coordinate system; y is the coordinate value on the y-axis in the rectangular coordinate system; z is the coordinate value on the z-axis in the rectangular coordinate system, and the z-axis is the propagation direction of the chirped first-order Airy derivative beam; the constant A is the intensity control parameter, which makes the peak intensity on the initial plane z = 0 equal to 1; a is the exponential decay factor; w0 is the scale factor; c is the second-order chirp factor; Ai'(.) is the first-order derivative of the Airy function, and i is the dotted unit.

[0016] Optionally, the electric field distribution of the chirped first-order Airy derivative beam during free space transmission is characterized by the Collins integral formula:

[0017]

[0018] Where k = 2π / λ is the wave number, λ is the wavelength of the first-order Airy derivative beam; x' is the integral variable on the x-axis; y' is the integral variable on the y-axis;

[0019] After a series of integrations, the analytical expression for the electric field of a chirped first-order Airy derivative beam propagating in free space is expressed as E(x,y,z)=E(x,z)E(y,z).

[0020] When z = -z0 / (2c), E(x,z) and E(y,z) are:

[0021]

[0022]

[0023] When z≠-z0 / (2c), E(x,z) and E(y,z) are:

[0024] E(x,z)=E Ap (x,z)+E Ar (x,z);

[0025] E(y,z)=E Ap (y,z)+E Ar (y,z);

[0026]

[0027]

[0028]

[0029]

[0030] Where, is the Rayleigh distance; β(z) = 1 + 2cz / z0; Ai(·) is the Airy function; the subscript Ap represents the chirp first-order Airy derivative mode; the subscript Ar represents the chirp Airy correlation mode.

[0031] Therefore, the electric field in any transverse direction on the observation plane with z≠-z0 / (2c) when a chirped first-order Airy derivative beam propagates in free space is the coherent superposition of the chirped first-order Airy derivative mode and the chirped Airy related mode.

[0032] Optionally, determining a relationship curve diagram of the correlation factor relative to the second-order chirp factor based on the first-order Airy derivative beam parameter specifically includes:

[0033] Under the conditions of the first-order Airy derivative beam parameters, the value of the second-order chirp factor c is changed, the light intensity I(x,y,z) distribution on different observation planes z is calculated, and the maximum light intensity I is searched. max (x,y,z), maximum light intensity I max (x,y,z) The viewing plane position z m , the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1;

[0034] Draw the maximum light intensity I maxA first variation graph of (x, y, z) relative to the second-order chirp factor c;

[0035] Draw the viewing plane position z m A second variation curve diagram relative to the second-order chirp factor c;

[0036] According to the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1, the interference enhancement effect range Δz=z2-z1 is calculated, and a third variation curve of the interference enhancement effect range Δz relative to the second-order chirp factor c is plotted.

[0037] Optionally, the maximum value in the value range of the second-order chirp factor is 0, and the minimum value in the value range of the second-order chirp factor is a critical second-order chirp factor; the critical second-order chirp factor is the second-order chirp factor corresponding to 1 / 2 of the observation plane position where the maximum light intensity appears when there is no chirp.

[0038] Optionally, when the target requirement is that the intensity of the first-order Airy derivative beam interference enhancement effect is the maximum light intensity, the second-order chirp factor of the first-order Airy derivative beam is the critical second-order chirp factor, and the observation plane position where the maximum light intensity occurs is nearly 50% of that when there is no chirp.

[0039] Optionally, when the target requirement is that the observation plane position where the maximum light intensity appears is closer than when there is no chirp, the second-order chirp factor of the first-order Airy derivative beam is between zero and a critical second-order chirp factor.

[0040] The present invention also provides a system for enhancing the intensity of the first-order Airy derivative beam interference enhancement effect, comprising:

[0041] a target electric field expression determination module, configured to introduce a second-order chirp factor into the electric field expression of the first-order Airy derivative beam on the initial plane to obtain a target electric field expression; the target electric field expression is the electric field expression of the chirped first-order Airy derivative beam on the initial plane;

[0042] An electric field analytical expression determination module is used to derive an electric field analytical expression of a chirped first-order Airy derivative beam when propagating in free space using the Collins integral formula based on the target electric field expression;

[0043] a correlation factor calculation module, configured to determine, based on the electric field analytical expression, correlation factors describing the intensity of the interference enhancement effect; the correlation factors comprising the maximum light intensity, the position of the observation plane where the maximum light intensity occurs, and the range of the interference enhancement effect; the range of the interference enhancement effect being the distance from the observation plane where the first peak light intensity is greater than 1 to the observation plane where the last peak light intensity is greater than 1;

[0044] a relationship curve graph calculation module, configured to determine a relationship curve graph of a correlation factor relative to a second-order chirp factor based on parameters of the first-order Airy derivative beam;

[0045] A module for determining a value range of the second-order chirp factor, configured to determine a value range of the second-order chirp factor based on a relationship curve diagram of correlation factors relative to the second-order chirp factor;

[0046] The second-order chirp factor numerical determination module is used to determine the value of the second-order chirp factor of the first-order Airy derivative beam according to target requirements; the value of the second-order chirp factor of the first-order Airy derivative beam is used to improve the intensity of the interference enhancement effect of the first-order Airy derivative beam.

[0047] Optionally, the relationship curve graph calculation module specifically includes:

[0048] The search unit is used to change the value of the second-order chirp factor c under the first-order Airy derivative beam parameter conditions, calculate the light intensity I(x,y,z) distribution on different observation planes z, and search for the maximum light intensity I max (x,y,z), maximum light intensity I max (x,y,z) The viewing plane position z m , the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1;

[0049] The first change curve drawing unit is used to draw the maximum light intensity I max A first variation graph of (x, y, z) relative to the second-order chirp factor c;

[0050] The second change curve drawing unit is used to draw the observation plane position z m A second variation curve diagram relative to the second-order chirp factor c;

[0051] The third change curve drawing unit is used to calculate the interference enhancement effect range Δz=z2-z1 based on the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1, and to draw a third change curve diagram of the interference enhancement effect range Δz relative to the second-order chirp factor c.

[0052] Optionally, the maximum value in the value range of the second-order chirp factor is 0, and the minimum value in the value range of the second-order chirp factor is a critical second-order chirp factor; the critical second-order chirp factor is the second-order chirp factor corresponding to 1 / 2 of the observation plane position where the maximum light intensity appears when there is no chirp;

[0053] The second-order chirp factor value determination module is used to:

[0054] When the target requirement is that the intensity of the interference enhancement effect of the first-order Airy derivative beam is the maximum light intensity, the second-order chirp factor of the first-order Airy derivative beam is the critical second-order chirp factor, and the observation plane position where the maximum light intensity occurs is nearly 50% of that when there is no chirp;

[0055] When the target requirement is that the observation plane position where the maximum light intensity appears is closer than when there is no chirp, the second-order chirp factor of the first-order Airy derivative beam is between zero and the critical second-order chirp factor.

[0056] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0057] The present invention provides a method and system for improving the intensity of the interference enhancement effect of a first-order Airy derivative beam using a second-order chirp factor, comprising: introducing the second-order chirp factor into the expression of the electric field on the initial plane of the first-order Airy derivative beam; deriving an analytical expression for the electric field of the chirped first-order Airy derivative beam during free-space transmission; based on the obtained analytical expression of the electric field, characterizing the interference enhancement effect using the maximum light intensity, the observation plane position where the maximum light intensity occurs, and the range of the interference enhancement effect; plotting a relationship curve of the maximum light intensity, the observation plane position where the maximum light intensity occurs, and the range of the interference enhancement effect relative to the second-order chirp factor; determining the value range of the second-order chirp factor based on the plotted relationship curve, and reasonably selecting the second-order chirp factor to improve the intensity of the interference enhancement effect according to actual conditions. The method provided by the present invention is clear and very effective. As long as the value of the second-order chirp factor is between zero and the critical second-order chirp factor, the intensity of the interference enhancement effect can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0059] Figure 1 A schematic flow chart of a method for increasing the intensity of the first-order Airy derivative beam interference enhancement effect provided by an embodiment of the present invention;

[0060] Figure 2 A diagram showing the influence of the second-order chirp factor on the interference enhancement effect of the chirped first-order Airy derivative beam in the method provided by an embodiment of the present invention;

[0061] Figure 3 Spot patterns of a first-order Airy derivative light beam with c=0 in a method provided by an embodiment of the present invention when transmitting in free space on different observation planes;

[0062] Figure 4 Spot patterns of a chirped first-order Airy derivative beam with c=-0.114 on different observation planes during free-space transmission in the method provided in an embodiment of the present invention;

[0063] Figure 5 Spot patterns of a chirped first-order Airy derivative beam with c=-0.05 in the method provided in an embodiment of the present invention during free-space transmission on different observation planes;

[0064] Figure 6 A schematic structural diagram of a system for enhancing the intensity of the first-order Airy derivative beam interference enhancement effect provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0066] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] Example 1

[0068] This embodiment provides a method for increasing the intensity of the interference enhancement effect of a first-order Airy derivative beam by utilizing a second-order chirp factor. By introducing the second-order chirp factor and using the maximum light intensity to describe the intensity of the interference enhancement effect, the second-order chirp factor required to increase the intensity of the interference enhancement effect is determined by analyzing the effect of the second-order chirp factor on the maximum light intensity of a chirped first-order Airy derivative beam during free-space transmission, the position of the observation plane where the maximum light intensity occurs, and the range of the interference enhancement effect.

[0069] like Figure 1 As shown, the method includes the following steps:

[0070] Step 100: Introducing a second-order chirp factor into the electric field expression of the first-order Airy derivative beam on the initial plane to obtain a target electric field expression; the target electric field expression is the electric field expression of the chirped first-order Airy derivative beam on the initial plane.

[0071] Among them, the target electric field expression is:

[0072]

[0073] where E(x,y,0) is the electric field expression of the chirped first-order Airy derivative beam on the initial plane z = 0, x is the coordinate value on the x-axis in the rectangular coordinate system; y is the coordinate value on the y-axis in the rectangular coordinate system; z is the coordinate value on the z-axis in the rectangular coordinate system, and the z-axis is the propagation direction of the chirped first-order Airy derivative beam; the constant A is the intensity control parameter, which makes the peak intensity on the initial plane z = 0 equal to 1; a is the exponential decay factor; w0 is the scale factor; c is the second-order chirp factor; Ai′(·) is the first-order derivative of the Airy function, and i is the dotted unit.

[0074] The introduction of the second-order chirp factor c does not change the intensity distribution of the first-order Airy derivative beam on the initial plane I(x,y,0)=|E(x,y,0)| 2 When there is no chirp, that is, c = 0, it corresponds to a first-order Airy derivative beam.

[0075] Step 200: Based on the target electric field expression, the Collins integral formula is used to derive an analytical expression for the electric field of the chirped first-order Airy derivative beam when it is transmitted in free space.

[0076] When a chirped first-order Airy derivative beam propagates in free space, its electric field distribution is characterized by the Collins integral formula:

[0077]

[0078] Wherein, k = 2π / λ is the wave number, λ is the wavelength of the first-order Airy derivative beam; i is the imaginary unit; x' is the integral variable on the x-axis; and y' is the integral variable on the y-axis.

[0079] After a series of integrations, the analytical expression of the electric field of a chirped first-order Airy derivative beam propagating in free space is expressed as E(x,y,z)=E(x,z)E(y,z);

[0080] When z = -z0 / (2c), E(x,z) and E(y,z) are:

[0081]

[0082]

[0083] When z≠-z0 / (2c), E(x,z) and E(y,z) are:

[0084] E(x,z)=E Ap (x,z)+E Ar (x,z);

[0085] E(y,z)=E Ap (y,z)+E Ar (y,z);

[0086] And E Ap (x,z),E Ar (x,z),E Ap (y,z) and E Ar (y,z) are determined by the following formulas:

[0087]

[0088]

[0089]

[0090]

[0091] Where, is the Rayleigh distance; β(z) = 1 + 2cz / z0; β(z) is introduced for simplicity; Ai(·) is the Airy function; the subscript Ap denotes a chirped first-order Airy derivative mode; and the subscript Ar denotes a chirped Airy-related mode. The chirped Airy-related mode is the product of the weight coefficient z / [2z0β(z)] and a chirped Airy mode with a phase shift of π / 2. When a chirped first-order Airy derivative beam propagates in free space, the electric field in any transverse direction on the observation plane where z ≠ -z0 / (2c) is the coherent superposition of the chirped first-order Airy derivative mode and the chirped Airy-related mode.

[0092] Step 300: Determine the associated factors describing the intensity of the interference enhancement effect based on the electric field analytical expression; the associated factors include the maximum light intensity, the position of the observation plane where the maximum light intensity occurs, and the range of the interference enhancement effect; the range of the interference enhancement effect refers to the distance from the observation plane where the first peak light intensity is greater than 1 to the observation plane where the last peak light intensity is greater than 1.

[0093] When a chirped first-order Airy derivative beam propagates in free space, the light intensity at any observation plane z is I(x,y,z)=I(x,z)I(y,z)=|E(x,z)| 2 |E(y,z)| 2 When a chirped first-order Airy derivative beam propagates in free space, the peak intensity on some observation planes will exceed 1. This is due to the interference between the chirped first-order Airy derivative mode and the chirped Airy related mode. This phenomenon of the peak intensity on non-initial planes being greater than 1 is called the interference enhancement effect. The intensity of the interference enhancement effect is expressed as the maximum intensity I max (x,y,z) to describe the maximum light intensity I max The larger (x,y,z) is, the stronger the interference enhancement effect is. max The position of the observation plane where (x,y,z) appears is represented by z mThe interference enhancement effect range Δz refers to the distance from the observation plane where the first peak light intensity is greater than 1 to the observation plane where the last peak light intensity is greater than 1. In summary, the interference enhancement effect is expressed by I max (x,y,z),z m and Δz are used to characterize it.

[0094] Step 400: Determine a relationship curve of the correlation factor with respect to the second-order chirp factor based on the parameters of the first-order Airy derivative beam, specifically:

[0095] (1) Given the existing first-order Airy derivative beam parameters, change the value of the second-order chirp factor c, calculate the light intensity I(x,y,z) distribution on different observation planes z, and search for the maximum light intensity I max (x,y,z), maximum light intensity I max (x,y,z) The viewing plane position z m , the observation plane position z1 where the first peak light intensity is greater than 1, and the observation plane position z2 where the last peak light intensity is greater than 1.

[0096] (2) Draw the maximum light intensity I max First variation graph of (x, y, z) versus the second-order chirp factor c.

[0097] (3) Draw the observation plane position z m Second variation graph relative to the second-order chirp factor c.

[0098] (4) Based on the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1, the interference enhancement effect range Δz = z2 - z1 is calculated, and a third variation curve of the interference enhancement effect range Δz relative to the second-order chirp factor c is plotted.

[0099] Step 500: Determine a value range of the second-order chirp factor based on a curve diagram showing the relationship between the correlation factor and the second-order chirp factor. The maximum value in the value range of the second-order chirp factor is 0, and the minimum value in the value range of the second-order chirp factor is a critical second-order chirp factor. The critical second-order chirp factor is the second-order chirp factor corresponding to a position on the observation plane halfway between the maximum light intensity and the position without chirp.

[0100] When the second-order chirp factor takes a positive value, it has a negative effect on the interference enhancement effect, that is, the intensity of the interference enhancement effect is reduced; when the second-order chirp factor takes a negative value, the intensity of the interference enhancement effect of the chirped first-order Airy derivative beam is stronger than that of the first-order Airy derivative beam, that is, the intensity of the interference enhancement effect is improved. When the second-order chirp factor decreases from zero, the maximum light intensity I max (x,y,z) always increases, and the observation plane position zm The interference enhancement effect range Δz always decreases, while the range of the interference enhancement effect Δz first increases rapidly and then decreases, and the increase in the interference enhancement effect range Δz is very brief. The increase in the intensity of the interference enhancement effect caused by the negative second-order chirp factor comes at the expense of shortening the observation plane position where the maximum light intensity occurs and the interference enhancement effect range. Therefore, the second-order chirp factor corresponding to the observation plane position where the maximum light intensity occurs when there is no chirp is determined to be the critical second-order chirp factor.

[0101] Step 600: Determine the value of the second-order chirp factor of the first-order Airy derivative beam according to target requirements; the value of the second-order chirp factor of the first-order Airy derivative beam is used to increase the intensity of the interference enhancement effect of the first-order Airy derivative beam.

[0102] There are two options for the second-order chirp factor required to increase the intensity of the interference enhancement effect. The first option is to directly take the critical second-order chirp factor as the second-order chirp factor. At this time, the intensity of the interference enhancement effect reaches its maximum, but the position of the observation plane where the maximum light intensity appears is 50% closer than when there is no chirp. The second option is to determine a range for the second-order chirp factor, that is, as long as the value of the second-order chirp factor is between zero and the critical second-order chirp factor, the intensity of the interference enhancement effect is greater than when there is no chirp, but the position of the observation plane where the maximum light intensity appears is closer than when there is no chirp.

[0103] In summary, when the target requirement is that the intensity of the first-order Airy derivative beam interference enhancement effect is the maximum light intensity, the second-order chirp factor of the first-order Airy derivative beam is the critical second-order chirp factor, and the observation plane position where the maximum light intensity occurs is nearly 50% of that when there is no chirp.

[0104] When the target requirement is that the observation plane position where the maximum light intensity appears is closer than when there is no chirp, the second-order chirp factor of the first-order Airy derivative beam is between zero and the critical second-order chirp factor.

[0105] The method provided in this embodiment is clear and very effective. As long as the value of the second-order chirp factor is between zero and the critical second-order chirp factor, the intensity of the interference enhancement effect can be improved. If the second-order chirp factor is directly set to the critical second-order chirp factor, the intensity of the interference enhancement effect reaches the maximum.

[0106] The following is a specific example to illustrate the method provided by the present invention for improving the intensity of the first-order Airy derivative beam interference enhancement effect by using the second-order chirp factor:

[0107] In a rectangular coordinate system, x is the coordinate value on the x-axis, y is the coordinate value on the y-axis, and z is the coordinate value on the z-axis. The z-axis is also the direction of beam propagation, and the plane z = 0 is the initial plane. The electric field expression of a chirped first-order Airy derivative beam on the initial plane z = 0 has the following form:

[0108]

[0109] Where constant A is the intensity control parameter, ensuring that the peak intensity on the initial plane is 1; a is the exponential decay factor; w0 is the scale factor; c is the introduced second-order chirp factor; Ai′(·) is the first-order derivative of the Airy function; and i is the imaginary unit. The introduction of the second-order chirp factor c does not change the intensity distribution of the first-order Airy derivative beam on the initial plane: I(x,y,0) = |E(x,y,0)| 2 c = 0 corresponds to a first-order Airy derivative beam.

[0110] When a chirped first-order Airy derivative beam propagates in free space, the electric field on the observation plane z is described by the Collins integral formula:

[0111]

[0112] Among them, E(x,z) and E(y,z) are

[0113]

[0114]

[0115] Where k = 2π / λ is the wave number, λ is the wavelength of the first-order Airy derivative beam; x' is the integral variable on the x-axis; y' is the integral variable on the y-axis. First, derive the analytical expression of E(x,z). First, rewrite E(x,z) as

[0116]

[0117] Where, is the Rayleigh distance; β(z) = 1 + 2cz / z0. β(z) is introduced only for simplicity. The analytical expression of the above equation is derived for two cases.

[0118] In the first case, β(z)≠0, that is, z≠-z0 / (2c). When z≠-z0 / (2c), the integral definition of the first-order derivative of the Airy function is used

[0119]

[0120] Where u is the integral variable. E(x,z) can be rewritten as

[0121]

[0122] t=x' / w0 is the integral variable. Use the following mathematical integral formula

[0123]

[0124] Where p and q are constants, and t is the integral variable. E(x,z) can be expressed as

[0125]

[0126] Then use the following mathematical integral formula

[0127]

[0128] Where p and q are constants, u is the integral variable, and Ai(·) is the Airy function. E(x,z) can be expressed analytically as E(x,z)=E Ap (x,z)+E Ar (x,z);

[0129]

[0130]

[0131] Where the subscript Ap denotes the chirped first-order Airy derivative mode, and the subscript Ai denotes the chirped Airy correlation mode. The chirped Airy correlation mode is the product of the weight coefficient z / [2z0β(z)] and a chirped Airy mode with a phase shift of π / 2.

[0132] In the second case, β(z) = 0, i.e. z = -z0 / (2c). When z = -z0 / (2c), E(x,z) is simplified to

[0133]

[0134] The above formula is a Fourier transform.

[0135] Similarly, we can get the analytical expression of E(y,z). When z≠-z0 / (2c), E(y,z)=E Ap (y,z)+E Ar (y,z). Among them, E Ap (y,z) and E Ar (y,z) are

[0136]

[0137]

[0138] When z = -z0 / (2c), E(y,z) can be concisely expressed as

[0139]

[0140] When a chirped first-order Airy derivative beam propagates in free space, the electric field in any transverse direction on the observation plane with z≠-z0 / (2c) is the coherent superposition of the chirped first-order Airy derivative mode and the chirped Airy related mode.

[0141] When a chirped first-order Airy derivative beam propagates in free space, the light intensity at any observation plane z is defined as I(x,y,z)=I(x,z)I(y,z)=|E(x,z)| 2 |E(y,z)| 2 When a chirped first-order Airy derivative beam propagates in free space, the peak intensity on some observation planes will exceed 1. This is due to the interference between the chirped first-order Airy derivative mode and the chirped Airy related mode. This phenomenon of the peak intensity on non-initial planes being greater than 1 is called the interference enhancement effect. The intensity of the interference enhancement effect is expressed as the maximum intensity I max (x,y,z) to describe the maximum light intensity I max The larger (x,y,z) is, the stronger the interference enhancement effect is. Maximum light intensity I max The position of the observation plane where (x,y,z) appears is represented by z m The interference enhancement effect range Δz refers to the distance from the observation plane where the first peak light intensity is greater than 1 to the observation plane where the last peak light intensity is greater than 1. In summary, the interference enhancement effect is expressed by I max (x,y,z),z m and Δz are used to characterize it.

[0142] In the following calculations, a = 0.1, w0 = 0.1mm, and λ = 532nm. The three beam parameters are fixed and remain unchanged. In this case, z0 = 0.118m. Now change the value of the second-order chirp factor c and calculate the distribution of I(x, y, z) on different z planes to find the maximum light intensity, that is, I max (x, y, z) and the observation plane position z where the maximum light intensity occurs m , draw I max (x,y,z) and z m A curve diagram of the change relative to the second-order chirp factor c; search for the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1, calculate the interference enhancement effect range Δz = z2 - z1, and draw a curve diagram of the change of Δz relative to the second-order chirp factor c.

[0143] Figure 2 The influence of the second-order chirp factor on the interference enhancement effect of the chirped first-order Airy derivative beam is given. Figure 2 Part (a) is Imax Curve relationship of (x, y, z) with respect to the second-order chirp factor c; Figure 2 Part (b) is the observation plane position z where the maximum light intensity appears m Curve relationship with respect to the second-order chirp factor c; Figure 2 Part (c) is a curve diagram showing the variation of the interference enhancement effect range Δz with respect to the second-order chirp factor c. Figure 2 Part (b) and Figure 2 The dotted lines in part (c) are added for the convenience of connection. max When (x, y, z) equals 1, the interference enhancement effect disappears, and the maximum light intensity value 1 appears on the initial plane z = 0, and the corresponding Δz = 0. Figure 2 It shows that the positive second-order chirp factor has a negative effect on the interference enhancement effect, that is, the intensity of the interference enhancement effect decreases. When c = 0, the maximum light intensity value of the first-order Airy derivative beam interference enhancement effect is equal to 1.424, which appears at the observation plane z m =0.579m; the interference enhancement effect range Δz is equal to 0.351m, specifically 0.411m≤z≤0.762m. When c = 0.016, the maximum light intensity is equal to 1.022, which is 28.2% lower than that without chirp; the maximum light intensity occurs at the observation plane z m =0.648m, which is 11.9% farther than when there is no chirp; the interference enhancement effect range Δz is equal to 0.117m, and the specific range is 0.591m≤z≤0.708m; the interference enhancement effect range is shortened by 66.7% compared with when there is no chirp. When c>0.016, the interference enhancement effect disappears. When the second-order chirp factor is negative, the interference enhancement effect intensity of the chirped first-order Airy derivative beam must be stronger than that of the first-order Airy derivative beam, that is, the interference enhancement effect intensity is improved. When the second-order chirp factor decreases from zero, I max (x,y,z) always increases, z m It always decreases. When the second-order chirp factor decreases from zero to -0.008, Δz first increases rapidly, and this increase process is very short; when the second-order chirp factor decreases from -0.008, Δz always decreases. The increase in the intensity of the interference enhancement effect caused by the negative second-order chirp factor comes at the expense of shortening the observation plane position where the maximum light intensity appears and the range of the interference enhancement effect. Therefore, the second-order chirp factor corresponding to 1 / 2 of the observation plane position where the maximum light intensity appears when there is no chirp is determined as the critical second-order chirp factor, that is, z m =0.289m, the second-order chirp factor c = -0.114 is determined to be the critical second-order chirp factor. Figure 2 As shown by the gray dotted line in (b). Figure 2 (a) and Figure 2As shown by the gray dotted line in (c), when c = -0.114, the maximum light intensity is equal to 6.852, which is 381.2% higher than that without chirp. The interference enhancement effect range Δz is equal to 0.171m, and the specific range is 0.182m≤z≤0.352m. The interference enhancement effect range is shortened by 51.3% compared with the case without chirp.

[0144] In order to facilitate comparison and verification, Figure 3 The spot image of the first-order Airy derivative beam with c=0 propagating in free space is given. Figure 3 Parts (a) to (d) correspond to the intensity distribution of the first-order Airy derivative beam with c = 0 at the free space observation plane z = 0, observation plane z = 0.3m, observation plane z = 0.579m and observation plane z = 0.8m, respectively. Figure 3 、 Figure 4 and Figure 5 In the equation, the light intensity distribution is given by I(x,y,z)=E(x,z)E(y,z), and the three fixed observation planes are observation plane z=0, observation plane z=0.3m, and observation plane z=0.8m. The other observation plane is the observation plane position where the maximum light intensity appears. Figure 5 The values ​​on the color bar in (d) are rounded to two decimal places, which will make them indistinguishable, so Figure 5 The values ​​on the intensity bars in (d) are rounded to three decimal places. The values ​​on the intensity bars in other sub-graphs are rounded to two decimal places. When c = 0, when the first-order Airy derivative beam propagates in free space, the peak intensity first decreases. Figure 3 The peak light intensity is 0.50 at the observation plane z = 0.3m shown in part (b), and then the peak light intensity increases again. Figure 3 The peak light intensity reaches a maximum value of 1.42 on the observation plane z = 0.579m shown in part (c), and then gradually decreases. Figure 3 The peak light intensity at the observation plane z=0.8m shown in part (d) is 0.86.

[0145] Figure 4 The spot image of a chirped first-order Airy derivative beam propagating in free space is given when the second-order chirp factor takes the critical second-order chirp factor. Figure 4 Parts (a) to (d) correspond to the intensity distribution of the chirped first-order Airy derivative beam with c = -0.114 at the observation plane z = 0, observation plane z = 0.289m, observation plane z = 0.3m, and observation plane z = 0.8m in free space, respectively. When c = -0.114, the peak light intensity of the chirped first-order Airy derivative beam decreases rapidly when it propagates in free space (the peak light intensity decreases very quickly, Figure 4 Not shown in Figure 3), then the peak light intensity increases again, as shown in Figure 3. Figure 4 The peak light intensity at the observation plane z = 0.289m shown in part (b) has reached a maximum value of 6.85. Figure 4 The peak light intensity at the observation plane z = 0.3m shown in part (c) is still 6.62, and the peak light intensity decreases rapidly. Figure 4 Part (d) shows a peak light intensity of only 0.05 at the observation plane z = 0.8 m. When the second-order chirp factor is at the critical second-order chirp factor, the maximum light intensity is about five times the maximum light intensity in the absence of chirp, but the maximum light intensity occurs 50% closer to the observation plane than in the absence of chirp.

[0146] Figure 5 The spot images of a chirped first-order Airy derivative beam propagating in free space are given when the second-order chirp factor takes a value between zero and the critical second-order chirp factor. Figure 5 Parts (a) to (d) correspond to the intensity distribution of the chirped first-order Airy derivative beam with c = -0.05 at the observation plane z = 0, observation plane z = 0.3m, observation plane z = 0.410m and observation plane z = 0.8m in free space, respectively. When c = -0.05, when the chirped first-order Airy derivative beam is transmitted in free space, the peak light intensity first decreases rapidly, and then the peak light intensity increases again. Figure 5 The peak light intensity at the observation plane z = 0.3m shown in part (b) has reached 1.72. Figure 5 The peak light intensity reaches a maximum value of 3.25 on the observation plane z = 0.410m shown in part (c), and then decreases rapidly. Figure 5 The peak light intensity at the observation plane z = 0.8 m shown in part (d) is only 0.03. When c = -0.05, the maximum light intensity increases by 128.9% compared to the maximum light intensity without chirp, and the observation plane position where the maximum light intensity value appears is 29.2% closer than the non-chirp state. Figure 3 Part (a) Figure 4 Part (a) and Figure 5 Part (a) shows that the introduction of the second-order chirp factor does not change the intensity distribution of the first-order Airy derivative beam at the initial plane z = 0.

[0147] Under three conditions, namely, the second-order chirp factor is zero, the critical second-order chirp factor, and a value between the two, the spot images of the chirp-free and chirped first-order Airy derivative beams during free-space transmission are given to verify the improvement of the interference enhancement effect.

[0148] In summary, after determining the critical second-order chirp factor, there are two options for increasing the second-order chirp factor required to enhance the intensity of the first-order Airy derivative beam interference enhancement effect. The first option is to directly use the critical second-order chirp factor as the second-order chirp factor. At this time, the intensity of the chirped first-order Airy derivative beam interference enhancement effect reaches its maximum, but the observation plane position where the maximum light intensity occurs is 50% closer than when there is no chirp. The second option is to define a range for the second-order chirp factor. That is, as long as the value of the second-order chirp factor is between zero and the critical second-order chirp factor, the intensity of the chirped first-order Airy derivative beam interference enhancement effect is greater than when there is no chirp, but the observation plane position where the maximum light intensity occurs is closer than when there is no chirp.

[0149] In practical applications, the method for increasing the intensity of the interference enhancement effect of a first-order Airy derivative light beam given in the above embodiment can improve the quality of atmospheric optical communications. A chirped first-order Airy derivative light beam is used to replace the first-order Airy derivative light beam as a light source, and the modulation of the light source by information is completed. Due to the influence of the diffraction of the light beam itself and the atmospheric turbulence, the light intensity of the chirped first-order Airy derivative light beam will decrease when it is transmitted in the atmosphere. However, the interference enhancement effect of the chirped first-order Airy derivative light beam makes the peak light intensity of the chirped first-order Airy derivative light beam transmitted to the desired distance not only not decrease but increase, which can resist the light intensity loss caused by atmospheric interference, so that a strong optical signal is received at the receiving end, and then the photoelectric converter performs efficient and high-quality photoelectric conversion, ultimately improving the quality of atmospheric optical communications.

[0150] Example 2

[0151] In order to execute the corresponding method of the above-mentioned embodiment 1 and achieve the corresponding functions and technical effects, a system for improving the intensity of the first-order Airy derivative beam interference enhancement effect is provided below.

[0152] like Figure 6 As shown, the first-order Airy derivative beam interference enhancement effect intensity improvement system comprises:

[0153] The target electric field expression determination module 1 is used to introduce a second-order chirp factor into the electric field expression of the first-order Airy derivative beam on the initial plane to obtain the target electric field expression; the target electric field expression is the electric field expression of the chirped first-order Airy derivative beam on the initial plane.

[0154] The electric field analytical expression determination module 2 is used to derive the electric field analytical expression of the chirped first-order Airy derivative beam when it is transmitted in free space based on the target electric field expression using the Collins integral formula.

[0155] The correlation factor calculation module 3 is used to determine the correlation factors describing the intensity of the interference enhancement effect based on the electric field analytical expression; the correlation factors include the maximum light intensity, the observation plane position where the maximum light intensity occurs, and the interference enhancement effect range; the interference enhancement effect range refers to the distance from the observation plane where the first peak light intensity is greater than 1 to the observation plane where the last peak light intensity is greater than 1.

[0156] The relationship curve diagram calculation module 4 is used to determine the relationship curve diagram of the correlation factor relative to the second-order chirp factor according to the parameters of the first-order Airy derivative beam.

[0157] The module 5 for determining the value range of the second-order chirp factor is configured to determine the value range of the second-order chirp factor according to a relationship curve diagram of the correlation factor relative to the second-order chirp factor.

[0158] The second-order chirp factor value determination module 6 is used to determine the value of the second-order chirp factor of the first-order Airy derivative beam according to target requirements; the value of the second-order chirp factor of the first-order Airy derivative beam is used to improve the intensity of the interference enhancement effect of the first-order Airy derivative beam.

[0159] The relationship curve diagram calculation module 4 specifically includes:

[0160] The search unit is used to change the value of the second-order chirp factor c under the first-order Airy derivative beam parameter conditions, calculate the light intensity I(x,y,z) distribution on different observation planes z, and search for the maximum light intensity I max (x,y,z), maximum light intensity I max (x,y,z) The viewing plane position z m , the observation plane position z1 where the first peak light intensity is greater than 1, and the observation plane position z2 where the last peak light intensity is greater than 1.

[0161] The first change curve drawing unit is used to draw the maximum light intensity I max First variation graph of (x, y, z) versus the second-order chirp factor c.

[0162] The second change curve drawing unit is used to draw the observation plane position z m Second variation graph relative to the second-order chirp factor c.

[0163] The third change curve drawing unit is used to calculate the interference enhancement effect range Δz=z2-z1 based on the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1, and to draw a third change curve diagram of the interference enhancement effect range Δz relative to the second-order chirp factor c.

[0164] The maximum value in the value range of the second-order chirp factor is 0, and the minimum value in the value range of the second-order chirp factor is the critical second-order chirp factor; the critical second-order chirp factor is the second-order chirp factor corresponding to 1 / 2 of the observation plane position where the maximum light intensity appears when there is no chirp;

[0165] The second-order chirp factor value determination module 6 is used to:

[0166] When the target requirement is that the intensity of the first-order Airy derivative beam interference enhancement effect is the maximum light intensity, the second-order chirp factor of the first-order Airy derivative beam is the critical second-order chirp factor, and the observation plane position where the maximum light intensity occurs is nearly 50% of that when there is no chirp.

[0167] When the target requirement is that the observation plane position where the maximum light intensity appears is closer than when there is no chirp, the second-order chirp factor of the first-order Airy derivative beam is between zero and the critical second-order chirp factor.

[0168] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0169] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A method for increasing the intensity of the first-order Airy derivative beam interference enhancement effect, characterized in that: include: The second-order chirp factor is introduced into the electric field expression of the first-order Airy derivative beam on the initial plane to obtain the target electric field expression; The target electric field expression is the electric field expression of the chirped first-order Airy derivative beam on the initial plane; According to the target electric field expression, the Collins integral formula is used to derive the electric field analytical expression of the chirped first-order Airy derivative beam when it propagates in free space; Determining, based on the electric field analytical expression, correlation factors describing the intensity of the interference enhancement effect; the correlation factors include the maximum light intensity, the position of the observation plane where the maximum light intensity occurs, and the range of the interference enhancement effect; the range of the interference enhancement effect refers to the distance from the observation plane where the first peak light intensity is greater than 1 to the observation plane where the last peak light intensity is greater than 1; Determining a relationship curve of a correlation factor with respect to a second-order chirp factor based on parameters of the first-order Airy derivative beam; Determine the value range of the second-order chirp factor based on a relationship curve of the correlation factors relative to the second-order chirp factor; According to target requirements, the value of the second-order chirp factor of the first-order Airy derivative beam is determined; the value of the second-order chirp factor of the first-order Airy derivative beam is used to improve the intensity of the interference enhancement effect of the first-order Airy derivative beam.

2. The method for improving the intensity of the first-order Airy derivative beam interference enhancement effect according to claim 1, characterized in that: The target electric field expression is: Where E(x,y,0) is the electric field expression of the chirped first-order Airy derivative beam on the initial plane z = 0, x is the coordinate value on the x-axis in the rectangular coordinate system; y is the coordinate value on the y-axis in the rectangular coordinate system; z is the coordinate value on the z-axis in the rectangular coordinate system, and the z-axis is the propagation direction of the chirped first-order Airy derivative beam; the constant A is the intensity control parameter, which makes the peak intensity on the initial plane z = 0 equal to 1; a is the exponential decay factor; w0 is the scale factor; c is the second-order chirp factor; Ai'(.) is the first-order derivative of the Airy function, and i is the dotted unit.

3. The method for improving the intensity of the first-order Airy derivative beam interference enhancement effect according to claim 2, characterized in that: The electric field distribution of the chirped first-order Airy derivative beam during free space transmission is characterized by the Collins integral formula: Where k = 2π / λ is the wave number, λ is the wavelength of the first-order Airy derivative beam; x' is the integral variable on the x-axis; y' is the integral variable on the y-axis; After a series of integrations, the analytical expression of the electric field of a chirped first-order Airy derivative beam propagating in free space is expressed as E(x,y,z)=E(x,z)E(y,z); When z = -z0 / (2c), E(x,z) and E(y,z) are: When z≠-z0 / (2c), E(x,z) and E(y,z) are: E(x,z)=E Ap (x,z)+E Ar (x,z); E(y,z)=E Ap (y,z)+E Ar (y,z); Where, is the Rayleigh distance; β(z) = 1 + 2cz / z0; Ai(·) is the Airy function; the subscript Ap represents the chirp first-order Airy derivative mode; the subscript Ar represents the chirp Airy correlation mode; Therefore, the electric field in any transverse direction on the observation plane with z≠-z0 / (2c) when a chirped first-order Airy derivative beam propagates in free space is the coherent superposition of the chirped first-order Airy derivative mode and the chirped Airy related mode.

4. The method for improving the intensity of the first-order Airy derivative beam interference enhancement effect according to claim 2, characterized in that: Determining a relationship curve diagram of the correlation factor relative to the second-order chirp factor based on the first-order Airy derivative beam parameters specifically includes: Under the conditions of the first-order Airy derivative beam parameters, the value of the second-order chirp factor c is changed, the light intensity I(x,y,z) distribution on different observation planes z is calculated, and the maximum light intensity I is searched. max (x,y,z), maximum light intensity I max (x,y,z) The viewing plane position z m , the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1; Draw the maximum light intensity I max A first variation graph of (x, y, z) relative to the second-order chirp factor c; Draw the viewing plane position z m A second variation curve diagram relative to the second-order chirp factor c; According to the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1, the interference enhancement effect range Δz=z2-z1 is calculated, and a third variation curve of the interference enhancement effect range Δz relative to the second-order chirp factor c is plotted.

5. The method for improving the intensity of the first-order Airy derivative beam interference enhancement effect according to claim 2, characterized in that: The maximum value in the value range of the second-order chirp factor is 0, and the minimum value in the value range of the second-order chirp factor is a critical second-order chirp factor; The critical second-order chirp factor is the second-order chirp factor corresponding to a position on the observation plane half where the maximum light intensity appears when there is no chirp.

6. The method for improving the intensity of the first-order Airy derivative beam interference enhancement effect according to claim 5, characterized in that: When the target requirement is that the intensity of the first-order Airy derivative beam interference enhancement effect is the maximum light intensity, the second-order chirp factor of the first-order Airy derivative beam is the critical second-order chirp factor, and the observation plane position where the maximum light intensity occurs is nearly 50% of that when there is no chirp.

7. The method for improving the intensity of the first-order Airy derivative beam interference enhancement effect according to claim 5, characterized in that: When the target requirement is that the observation plane position where the maximum light intensity appears is closer than when there is no chirp, the second-order chirp factor of the first-order Airy derivative beam is between zero and the critical second-order chirp factor.

8. A system for enhancing the intensity of the first-order Airy derivative beam interference enhancement effect, characterized in that: include: A target electric field expression determination module is used to introduce a second-order chirp factor into the electric field expression of the first-order Airy derivative beam on the initial plane to obtain the target electric field expression; The target electric field expression is the electric field expression of the chirped first-order Airy derivative beam on the initial plane; An electric field analytical expression determination module is used to derive an electric field analytical expression of a chirped first-order Airy derivative beam when propagating in free space using the Collins integral formula based on the target electric field expression; a correlation factor calculation module, configured to determine, based on the electric field analytical expression, correlation factors describing the intensity of the interference enhancement effect; the correlation factors comprising the maximum light intensity, the position of the observation plane where the maximum light intensity occurs, and the range of the interference enhancement effect; the range of the interference enhancement effect being the distance from the observation plane where the first peak light intensity is greater than 1 to the observation plane where the last peak light intensity is greater than 1; a relationship curve graph calculation module, configured to determine a relationship curve graph of a correlation factor relative to a second-order chirp factor based on parameters of the first-order Airy derivative beam; A module for determining a value range of the second-order chirp factor, configured to determine a value range of the second-order chirp factor based on a relationship curve diagram of correlation factors relative to the second-order chirp factor; The second-order chirp factor numerical determination module is used to determine the value of the second-order chirp factor of the first-order Airy derivative beam according to target requirements; the value of the second-order chirp factor of the first-order Airy derivative beam is used to improve the intensity of the interference enhancement effect of the first-order Airy derivative beam.

9. The system for enhancing the intensity of the first-order Airy derivative beam interference enhancement effect according to claim 8, characterized in that: The relationship curve graph calculation module specifically includes: The search unit is used to change the value of the second-order chirp factor c under the first-order Airy derivative beam parameter conditions, calculate the light intensity I(x,y,z) distribution on different observation planes z, and search for the maximum light intensity I max (x,y,z), maximum light intensity I max (x,y,z) The viewing plane position z m , the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1; The first change curve drawing unit is used to draw the maximum light intensity I max A first variation graph of (x, y, z) relative to the second-order chirp factor c; The second change curve drawing unit is used to draw the observation plane position z m A second variation curve diagram relative to the second-order chirp factor c; The third change curve drawing unit is used to calculate the interference enhancement effect range Δz=z2-z1 based on the observation plane position z1 where the first peak light intensity is greater than 1 and the observation plane position z2 where the last peak light intensity is greater than 1, and to draw a third change curve diagram of the interference enhancement effect range Δz relative to the second-order chirp factor c.

10. The system for enhancing the intensity of the first-order Airy derivative beam interference enhancement effect according to claim 8, characterized in that: The maximum value in the value range of the second-order chirp factor is 0, and the minimum value in the value range of the second-order chirp factor is a critical second-order chirp factor; The critical second-order chirp factor is the second-order chirp factor corresponding to half the observation plane position where the maximum light intensity appears when there is no chirp; The second-order chirp factor value determination module is used to: When the target requirement is that the intensity of the interference enhancement effect of the first-order Airy derivative beam is the maximum light intensity, the second-order chirp factor of the first-order Airy derivative beam is the critical second-order chirp factor, and the observation plane position where the maximum light intensity occurs is nearly 50% of that when there is no chirp; When the target requirement is that the observation plane position where the maximum light intensity appears is closer than when there is no chirp, the second-order chirp factor of the first-order Airy derivative beam is between zero and the critical second-order chirp factor.

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