CN117192786A - Method for generating self-focusing light beam with adjustable focusing times and focal length - Google Patents
Method for generating self-focusing light beam with adjustable focusing times and focal length Download PDFInfo
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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
Technical Field
The invention belongs to the field of light field regulation and control, and particularly relates to a method for generating self-focusing light beams with adjustable focusing times and focal lengths.
Background
Abrupt Autofocus (AAF) field is a special beam that can suddenly release all the energy in front of the target, which has received much attention from scientific researchers due to its ability to achieve focus without lenses. In recent years, various types of autofocus beams have been found, with a circular Pi Erxi beam having increased peak intensity contrast, a shorter autofocus length, and elimination of post-focus ringing. In another study, durnin in 1987 proposed non-diffracted beams as solutions to scalar wave equations that maintain the intensity pattern unchanged during free space propagation. Among them, a circular bessel beam is a well-known non-diffracted beam, known for its unique non-diffracting power and self-healing properties. These beams open up new possibilities for optical manipulation applications with great potential in various research areas.
To make comprehensive use of the properties of a circular Pi Erxi beam and a circular Bessel beam, we have introduced a new type of beam, called a circular Pi Erxi Bessel beam. By mixing the two beams we achieve a beam that is tunable and has a stronger autofocus effect. The circular Pi Erxi Bessel beam has both the auto-focusing properties of the circular Pi Erxi beam and the non-diffracting properties of the circular Bessel beam. By precisely controlling the order and spatial offset of the Bessel function, we can produce a self-focusing beam with adjustable focusing times and focal length. This new light beam offers more possibilities and flexibility for optical research and application fields.
Chinese patent publication No.: CN 110824716A discloses a method for adjusting the self-focusing focal length of a round Airy beam. The method can realize the adjustment of the focal length of the round Airy light beam through proper parameter setting. However, this method does not realize the regulation of the number of times of focusing of the self-focusing light beam.
Disclosure of Invention
The invention provides a method for generating self-focusing light beams with adjustable focusing times and focal lengths, which is characterized in that a source plane wave function of a circular Pi Erxi Bessel light beam is formed by superposing a circular Pi Erxi function and a circular Bessel function, a corresponding phase hologram is generated by utilizing a computer holographic technology and is loaded on a spatial light modulator, and an expanded quasi-plane Gaussian beam is loaded on the wave front of the light beam to effectively encode the required complex phase distribution, so that the circular Pi Erxi Bessel light beam with specific parameters is generated.
The invention adopts the technical scheme that: a generation method of self-focusing light beam with adjustable focal length and focusing times is provided, wherein the basic theory of the generation method is as follows:
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 bezier function of the first class expands in taylor series at the point x=0:
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 an index for limiting the power and area of the beam, r 0 Representing the spatial offset of the bessel beam.
1. Setting the light field parameter ω=100 μm, r 0 =220 μm, changing the order of the bessel beam, and realizing the regulation of the number of times of focusing the self-focusing beam. A holographic phase map is generated by a computer, and a propagation side view is simulated by numerical simulation of a step Fourier method. 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.
2. Setting the light field parameter omega=100 μm, at different spatial offsets r 0 The focal length of the circular Pi Erxi bessel beam will vary with the order a. a varies from 0 to 5,r 0 Ranging from 0 to 1000 μm.
The beneficial effects of the invention are as follows: the invention provides a round Pi Erxi Bessel beam, which combines the advantages of a round Pi Erxi beam and a round Bessel beam, realizes tuning and has stronger automatic focusing effect. The propagation behavior of the circular Pi Erxi Bessel beam can be customized by adjusting the order and the spatial offset of the Bessel function, single-time, multiple-time self-focusing and diffraction-free propagation-like can be realized, and the position of a focus can be flexibly controlled. The control mode is simple and convenient to operate, and the generated light beam has excellent propagation characteristics and customizable self-focusing characteristics, so that the control mode is expected to be applied to various applications requiring precise control of light propagation, intensity and capturing force.
The foregoing is a brief summary of the technical solutions of the present invention, and may be implemented according to the detailed description of the present invention in order to more clearly understand the technical means of the present invention. Meanwhile, in order to more clearly show the objects, features and advantages of the present invention, preferred embodiments will be described in detail below by way of example with reference to the accompanying drawings.
Drawings
Fig. 1 is ω=100 μm, r 0 Circular Pi Erxi bessel beam phase diagram and propagation side view for a=220 μm, a=0.
Fig. 2 is ω=100 μm, r 0 Circular Pi Erxi bessel beam phase diagram and propagation side view for =220 μm, a=2.
Fig. 3 is ω=100 μm, r 0 Circular Pi Erxi bessel beam phase diagram and propagation side view for a=220 μm, a=4.
Fig. 4 is ω=100 μm, r 0 Circular Pi Erxi bessel beam phase diagram and propagation side view of =220 μm, a=40.
Fig. 5 is ω=100 μm, r 0 And a simultaneously changing, a changing graph of the focal length size of the circular Pi Erxi Bessel beam, wherein a ranges from 0 to 5,r 0 Ranging from 0 to 1000 μm.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
The invention aims to provide a method for generating self-focusing light beams with adjustable focusing times and focal lengths, which adopts the following technical scheme to realize the purposes of the invention:
(1) Setting omega and related parameters according to plane wave function of circular Pi Erxi Bessel beam source by changing a and r 0 The phase hologram is generated by utilizing the computer-generated hologram technology and irradiated by laser beams which are expanded and collimated, and a spatial light modulator with the phase hologram is loaded to generate a circular Pi Erxi Bessel light beam light field under the required specific parameters.
(2) The focusing times can be flexibly adjusted by changing a, the wavelength of a laser is experimentally set to be 532nm, the resolution of a spatial light modulator is 1920 multiplied by 1080 pixels, and the light field parameter omega =100μm，r 0 As shown in fig. 1-4, the left is a circular Pi Erxi bessel beam phase diagram under set parameters, the right is a numerical simulation propagation side view obtained by a step fourier method under corresponding parameters, and the propagation distance is 400 μm.
(3) As shown in fig. 1, when a=0, the optical field appears 3 times self-focusing, forming a beam trap; as shown in fig. 2, when a=2, the light field appears 2 times self-focusing, the first focusing intensity is larger than the second focusing intensity; as shown in fig. 3, when a=4, the light field appears 1 times stronger self-focusing, and the optical trap is deeper; as shown in fig. 4, when a=40, the optical field exhibits non-diffraction-like transmission, and the beam trap is very deep.
(4) Further, the focal length f of the circular Pi Erxi Bessel beam z Can be achieved by adjusting the spatial offset r 0 And the order a of the bessel function, keeping ω=100 μm, a varying in the range of 0 to 5,r 0 Ranging from 0 to 1000 μm, at different spatial offsets r 0 Where the order a is changed.
(5) As shown in fig. 5, the autofocus focal length f of a circular Pi Erxi bessel beam z The variation was irregular, with a majority of values between 175-225 mm. The focal length is recently f z ＝93mm(a＝0.5,r 0 =280 μm), at most f z ＝318mm(a＝0.6,r 0 ＝350μm)。
The foregoing is merely a preferred embodiment of the present invention, and it will be apparent to those skilled in the art from this disclosure that any simple modification, equivalent variation or modification of the above-described embodiment without departing from the scope of the present invention will still fall within the scope 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.
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| CN202311203057.7A CN117192786A (en) | 2023-09-18 | 2023-09-18 | Method for generating self-focusing light beam with adjustable focusing times and focal length |
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