CN117192786A - A method for generating a self-focusing beam with adjustable focusing times and focal length - Google Patents

Abstract

The invention provides a method for generating a self-focusing light beam with adjustable focusing times and focal length, which is characterized in that a circular Pi Erxi light beam and a circular Bessel light beam are overlapped to generate the self-focusing light beam with adjustable focusing times and focal length, which is called a circular Pi Erxi Bessel light beam. By adjusting the order of the Bessel function, the self-focusing times of the circular Pi Erxi Bessel beam can be flexibly adjusted, and single-time, multiple-time self-focusing and diffraction-free propagation can be realized. Meanwhile, the order and the space offset of the Bessel function are adjusted, so that the self-focusing focal length of the circular Pi Erxi Bessel beam can be adjusted. Experimentally, a phase hologram with specific parameters is generated by a computer and loaded onto a spatial light modulator, and the parameters of the bessel function are changed to control the number of times of focusing and the self-focusing focal length of the circular Pi Erxi bessel beam. The control mode is simple and convenient to operate, and the generated light beam has excellent propagation characteristics and customizable automatic focusing characteristics.

Description

A method for generating a self-focusing beam with adjustable focusing times and focal length

Technical field

The invention belongs to the field of light field control, and specifically relates to a method for generating a self-focusing light beam with adjustable focusing times and focal length.

Background technique

The sudden autofocus (AAF) field is a special beam that can suddenly release all its energy in front of the target. This beam has been receiving widespread attention from scientific researchers due to its ability to focus without a lens. In recent years, various types of autofocus beams have been discovered, among which the circular Piercy beam has attracted much attention due to its enhanced peak intensity contrast, short autofocus length, and elimination of oscillation effects after focus. In another study, Durnin in 1987 proposed non-diffracted beams as solutions to the scalar wave equation. These beams maintain the intensity pattern unchanged during propagation in free space. Among them, the circular Bessel beam is a famous non-diffraction beam, famous for its unique non-diffraction ability and self-healing properties. These beams open up new possibilities for optical manipulation applications and have great potential in various research fields.

In order to comprehensively utilize the characteristics of circular Piercy beams and circular Bessel beams, we introduce a new type of beam called circular Piercy-Bessel beam. By mixing these two beams, we achieved a tunable beam with stronger autofocus. The circular Piercy-Bessel beam has both the auto-focusing characteristics of the circular Piercy beam and the non-diffraction characteristics of the circular Bessel beam. By precisely controlling the order and spatial offset of the Bessel function, we can generate a self-focusing beam with adjustable focusing times and focal length. This new type of beam offers more possibilities and flexibility for optical research and applications.

Chinese patent publication number: CN 110824716 A, discloses a method for adjusting the self-focusing focal length of a circular Airy beam. This method can adjust the focal length of the circular Airy beam through appropriate parameter settings. However, this method cannot control the number of focusing times of the self-focusing beam.

Contents of the invention

The present invention proposes a method for generating a self-focusing beam with adjustable focusing times and focal lengths. The source plane wave function of the circular Piercy-Bessel beam is formed by superposing the circular Piercy function and the circular Bessel function, and utilizes computer holography. The technology generates a corresponding phase hologram and loads it onto a spatial light modulator, which loads an extended quasi-planar Gaussian beam onto the wavefront of the beam, effectively encoding the desired complex phase distribution, resulting in a circular shape with specific parameters. Shaped Piercy-Bessel beam.

The technical solution adopted by the present invention is: a method for generating a self-focusing beam with adjustable focal length and focusing times. The basic theory of the generation method is as follows:

The concept of "diffraction-free beam" was proposed by Durnin. It is an accurate solution to the aligned sub-Helmholtz equation in restricted cylindrical coordinates, and the transverse distribution of the beam can be described by the Bessel function: a-order The Taylor series expansion of the Bessel function of the first kind at the point x=0:

Among them, k! is the factorial of k, Γ(z) is the Γ function, which can be regarded as the generalization of the factorial function to non-integer independent variables, and a represents the order of the Bessel function;

The integral expression of Piercy function is:

Among them, parameters u and v are transverse coordinates, satisfying 0 ≤ (function’s) independent variable (u) ≤ π and v is a real number, and t is an integral variable;

The superimposed circular Piercy-Bessel beam source light field wave function is expressed as:

Among them, A ₀ is the amplitude, the second term is the finite energy circular Bessel beam, the last two terms are the circular Piercy beam, ω is the transverse scale factor that adjusts the initial intensity distribution of the circular Piercy beam, is the radial coordinate, where x and y are the transverse coordinates,/> is an index used to limit the power and area of the beam, r ₀ represents the spatial offset of the Bessel beam.

1. Set the light field parameters ω = 100 μm, r ₀ = 220 μm, change the order of the Bessel beam, and control the number of focusing times of the self-focusing beam. Side view of propagation from a numerical simulation using the stepwise Fourier method using a computer-generated holographic phase map. When a=0, the light field self-focuses three times; when a=2, the light field self-focusses twice; when a=4, the light field self-focusses once; when a=40, the light field self-focuses Diffraction-like transmission.

2. Set the light field parameter ω = 100 μm, and change the order a at different spatial offsets r _0. The focusing focal length of the circular Piercy Bessel beam will change accordingly. The variation range of a is 0 to 5, and the variation range of r ₀ is 0 to 1000μm.

The beneficial effects of the present invention are: the present invention proposes a circular Piercy Bessel beam, which combines the advantages of the circular Piercy beam and the circular Bessel beam, is tunable and has stronger automatic Focus effect. By adjusting the order and spatial offset of the Bessel function, the propagation behavior of the circular Piercy Bessel beam can be customized to achieve single, multiple self-focusing and quasi-diffraction-free propagation, and flexibly control the position of the focus. This control method is easy to operate, and the generated beam has excellent propagation characteristics and customizable self-focusing characteristics. It is expected to be used in various applications that require precise control of light propagation, intensity and capture force.

The above content is a brief summary of the technical solution of the present invention. In order to understand the technical means of the present invention more clearly, it can be implemented according to the detailed content of the description. At the same time, in order to more clearly demonstrate the purpose, features and advantages of the present invention, the preferred embodiments will be described in detail below with reference to the accompanying drawings.

Description of the drawings

Figure 1 shows the phase diagram and propagation side view of a circular Piercy Bessel beam with ω = 100 μm, r ₀ = 220 μm, and a = 0.

Figure 2 shows the phase diagram and propagation side view of a circular Piercy Bessel beam with ω = 100 μm, r ₀ = 220 μm, and a = 2.

Figure 3 shows the phase diagram and propagation side view of a circular Piercy Bessel beam with ω = 100 μm, r ₀ = 220 μm, and a = 4.

Figure 4 is a phase diagram and propagation side view of a circular Piercy Bessel beam with ω = 100 μm, r ₀ = 220 μm, and a = 40.

Figure 5 shows the changes in the focal length of the circular Piercy Bessel beam when r ₀ and a change simultaneously when ω = 100 μm. The change range of a is from 0 to 5, and the change range of r ₀ is from 0 to 1000 μm. .

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

The purpose of the present invention is to provide a method for generating a self-focusing beam with adjustable focusing times and focal length. To achieve the above-mentioned purpose of the present invention, the technical solutions adopted are as follows:

(1) According to the plane wave function of the circular Piercy Bessel beam source, set ω and related parameters, by changing the values of a and r ₀ , use computer holography technology to generate a phase hologram and undergo beam expansion and collimation laser irradiation , a spatial light modulator loaded with a phase hologram, produces a circular Piercy-Bessel beam light field under the specific parameters required.

(2) The number of focusing times can be flexibly adjusted by changing a. The experiment set the laser wavelength to 532nm, the resolution of the spatial light modulator to 1920×1080 pixels, the light field parameters ω = 100μm, r ₀ = 220μm, as shown in Figure 1- As shown in Figure 4, the left side is the phase diagram of the circular Piercy Bessel beam under the set parameters, and the right side is the numerical simulation propagation side view obtained by the step Fourier method under the corresponding parameters. The propagation distance is 400 μm.

(3) As shown in Figure 1, when a=0, the light field self-focuses three times, forming a beam trap; as shown in Figure 2, when a=2, the light field self-focuses twice, and the first time it focuses The intensity is greater than the second focusing intensity; as shown in Figure 3, when a=4, the light field appears a strong self-focusing, and the light trap is deeper; as shown in Figure 4, when a=40, the light field appears Diffraction-like transmission, the beam trap is very deep.

(4) In addition, the focusing focal length f _z of the circular Piercy Bessel beam can be fine-tuned by adjusting the spatial offset r ₀ and the order a of the Bessel function, maintaining ω = 100 μm, and the range of a is 0 to 5. The variation range of r ₀ is from 0 to 1000 μm, and the order a is changed at different spatial offsets r ₀ .

(5) As shown in Figure 5, the autofocus focal length f _z of the circular Piercy Bessel beam changes irregularly, with most values between 175-225mm. The closest focal length is f _z =93 mm (a = 0.5, r ₀ =280 μm), and the farthest focal length is f _z =318 mm (a = 0.6, r ₀ =350 μm).

The above are only preferred embodiments of the present invention. For those skilled in the art, any simple modifications to the above embodiments may be made according to the technical essence of the present invention without departing from the scope of the technical solution of the present invention. , equivalent changes or modifications still belong to the scope of the technical solution of the present invention.

Claims (3)

1. A method for generating self-focusing light beams with adjustable focusing times and focal lengths is characterized in that: forming a source light field wave function of a circular Pi Erxi Bessel beam by superposing a circular Pi Erxi function and a circular Bessel function, generating a specific light field phase hologram by utilizing a computer-generated hologram technology, loading the specific light field phase hologram onto a spatial light modulator, and then loading an expanded quasi-planar Gaussian beam onto the wavefront of the beam, so as to effectively encode a required complex phase distribution, thereby generating a circular Pi Erxi Bessel beam with specific parameters;

the concept of "non-diffracted beam" was proposed by Durnin, which is an exact solution to align the homogeneous helmholtz equation in a restricted cylindrical coordinate, and the lateral distribution of the beam can be described by a bessel function, the a-th order first class bessel function at the point x=0Taylor seriesAnd (3) unfolding:

wherein, k-! Being a factorial of k, Γ (z) being a function of Γ may be considered as a generalization of the factorial function to non-integer arguments, a representing the order of the Bessel function;

the integral expression of the Pi Erxi function is:

wherein, the parameter u, v is a transverse coordinate, the independent variable (u) which is more than or equal to 0 and less than or equal to pi (of a function) is satisfied, v is a real number, and t is an integral variable;

the superimposed circular Pi Erxi bessel beam source light field wave function is expressed as:

wherein A is ₀ The second term is a finite energy circular Bessel beam, the latter two are circular Pi Erxi beams, ω is the lateral scale factor that adjusts the initial intensity distribution of the circular Pi Erxi beam,is a radial coordinate, wherein x and y are transverse coordinates,/->Is used to limit the power and area of the beamIndex of domain, r ₀ Representing the spatial offset of the bessel beam.

2. The method for generating a self-focusing light beam with adjustable focusing times and focal length according to claim 1, wherein: setting the light field parameter ω=100 μm, r ₀ =220 μm, changing the order a of the bessel beam, thereby changing the number of times of focusing of the circular Pi Erxi bessel beam; when a=0, the light field appears 3 times self-focusing; when a=2, the light field appears 2 times self-focusing; when a=4, the light field appears 1 self-focusing; when a=40, the light field exhibits diffraction-like transmission.

3. The method for generating a self-focusing light beam with adjustable focusing times and focal length according to claim 1, wherein: setting the light field parameter omega=100 μm, at different spatial offsets r ₀ The focal length of the circular Pi Erxi Bessel beam changes with the change of the order a, and the change of a ranges from 0 to 5,r ₀ Ranging from 0 to 1000 μm.