CN114488546A - Method for generating multifocal self-focusing light beam with adjustable focal point characteristic - Google Patents
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Abstract
The invention discloses a method for generating a multifocal self-focusing light beam with adjustable focal point characteristics, which comprises the following steps: constructing a self-focusing light beam by a caustic method; superposing wave fronts corresponding to the multiple groups of self-focusing light beams; encoding the complex amplitude distribution of the wavefront into a pure phase form; loading the obtained phase distribution on a spatial light modulator to modulate an incident light field; and Fourier transform is carried out on the modulated light field by using the lens. The invention has the advantages that the optical field can be converged to a plurality of focuses along different tracks after being modulated once, and the number, the position and the relative strength among the focuses of the focuses can be regulated and controlled simultaneously, thereby realizing more flexible control on the energy of the optical field. The invention provides a method for encoding the complex wavefront required by generating the multi-focus self-focusing light beam into a pure phase form by using a biphase method, thereby reducing the requirements on optical field regulation and control equipment.
Description
Technical Field
The invention belongs to the technical field of light beam regulation and control, and particularly relates to a method for generating a multifocal self-focusing light beam with adjustable focal point characteristics.
Background
Since the Airy beam was experimentally generated and observed in 2007, the beam has received much attention from researchers due to its unique lateral self-accelerating, diffraction-free, self-healing properties. In order to break through the limitation that airy beams can only propagate along a parabolic trajectory, researchers have proposed an optical caustic method that allows the construction of self-accelerating beams that propagate along arbitrary convex trajectories in real space or fourier space.
The study of self-accelerating beams has led to another class of beams with novel characteristics: a sharply self-focused beam. It was first proposed in 2010 and experimentally verified in 2011. By constructing a circular airy beam, the energy of such a beam is distributed in the initial phase at a position far from the center, converges towards the center in an accelerated manner as the light field propagates, and can suddenly increase by several orders of magnitude when reaching the focus. The sharp self-focusing light beam is applied to the fields needing the sudden change of the light field energy, such as micro-processing, particle control, medical laser treatment and the like. Since then, many methods have been proposed to further improve the intensity contrast of the focus, or to introduce other new features for sharp self-focusing beams, such as changing the phase chirp, introducing vortex phase, constructing self-focusing beams of other trajectories, generalizing from the paraxial case to the non-paraxial case, etc.
To address the problem of how to generate a multifocal autofocus beam, chinese patent publication No.: CN111522140A, application publication date: in 2021, 03 and 19, a method for constructing a symmetrical multicycle cosine self-accelerating light beam is disclosed, which can generate a plurality of focuses on the central axis, but the method constructs a two-dimensional light beam, the generated focus has low contrast, and the intensity and position of the focus cannot be effectively controlled.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for generating a multifocal self-focusing beam with adjustable focal point characteristics, the degree of freedom of the design of the self-focusing beam is improved, the more flexible control on the energy of an optical field is realized, further, the method can simultaneously realize the regulation and control on the number, the position and the relative intensity between focal points, and the beam can be generated only by using a pure phase device.
In order to achieve the purpose, the invention adopts the following technical scheme,
a method of producing a multifocal self-focusing beam having adjustable focal properties, said method comprising the steps of:
s1 constructing a self-focusing light beam by a caustic method;
s2 superposing wave fronts corresponding to the multiple groups of self-focusing light beams;
s3 encoding the complex amplitude distribution of the wavefront into a pure phase form;
s4, the phase distribution obtained by loading on the spatial light modulator is used for modulating the incident light field;
s5 fourier-transforms the modulated light field using a lens.
It should be noted that the step S1 includes constructing the self-accelerated light beam with a circular parabolic trajectory in the spatial frequency domain, wherein the equation of the focal-dispersion trajectory can be expressed as:
r is the radial coordinate in polar coordinates, r0Is the radius of the central dark space, z is the light field propagation direction, zcIs the intersection of the caustic and the central axis and can be approximated as the location of the focal point.
It should be noted that, the step S2 includes that for the case that the focal points are all on the central axis, the complex amplitude distribution of the wavefront of the multi-focal self-focusing beam can be expressed as:
where n is the number of tracks/focal points, the index j indicates the parameters of the jth group of self-focusing beams, cjRepresenting the additional phase of the jth group of traces, the term 1/M being to ensure that the amplitude a (r) is not greater than 1, M can be expressed as:
by choosing appropriate additional phases for each set of trajectories, the relative intensity between the foci after superposition of the light fields can be kept constant.
Further, assuming that a lens with a focal length f is used for fourier transform, the phase distribution of the tracking self-focusing beam in the phase plane (the front focal plane of the lens) in step S1 is:
where k is the wave number of the light wave. To maximize the energy of the light field, the amplitude distribution of the wavefront, a (r), is set to: the amplitude is 1 in a circle with a radius R and 0 outside the circle. By utilizing an angular spectrum diffraction formula under paraxial approximation, the complex amplitude of the light field on the central axis can be obtained as follows:
to produce a sharp self-focusing effect, the selected light field range needs to be satisfied
Calculation of the above formula shows that the focal intensity increases with increasing R within a certain range, and the intensity of the generated focal spot can be controlled by changing the value of R.
It should be noted that, for the case where the focal point is off-axis, the complex amplitude distribution of the wavefront of the multifocal self-focusing beam can be represented as:
wherein (x'j,y′j) Is the offset of the jth group of tracks and is also the coordinate on the focal plane.
It should be noted that the step S3 includes decomposing the complex amplitude distribution of the wavefront of the multifocal self-focusing beam into two phase components by using a biphase method, which can be expressed as:
meanwhile, 2 × 2 pixel units of the spatial light modulator form a giant pixel unit, the complex amplitude of the wavefront at the center position of the giant pixel is decomposed into two phase components, and the two phase components are respectively arranged on two diagonal lines of the giant pixel.
It should be noted that the step S4 includes assuming that the spatial light modulator pixel unit side is p, the light field reconstructed in real space must satisfy the nyquist bandwidth limitation, that is, the light field reconstructed in real space must satisfy the nyquist bandwidth limitation
It should be noted that the light fields at the front focal plane and the back focal plane of the lens satisfy the relationship of fourier transform, and the front focal plane of the lens coincides with the spatial light modulator.
The invention has the beneficial effects that:
1. the invention can make the light field converge to a plurality of focuses along different tracks after once modulation, and can simultaneously realize the regulation and control of the number, the position and the relative intensity between the focuses, thereby realizing more flexible control of the light field energy.
2. The invention provides a method for encoding the complex wavefront required by generating the multi-focus self-focusing light beam into a pure phase form by using a biphase method, thereby reducing the requirements on optical field regulation and control equipment.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a schematic diagram of an optical path system for implementing a multi-focus self-focusing beam according to an embodiment of the present invention.
FIG. 3 is a simulated intensity profile of a multifocal autofocus beam produced by an embodiment of the invention; wherein the left image is a multifocal autofocus beam having three uniform intensity foci on the central axis, and the right image is a multifocal autofocus beam having three uniform intensity foci on the focal plane.
Fig. 4 is an amplitude and phase diagram of a complex wavefront and a phase diagram loaded on a spatial light modulator after encoding according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, wherein the following examples are provided to explain the detailed embodiments and specific operations on the premise of the technical solutions, but the scope of the present invention is not limited to the examples.
The invention relates to a method for generating a multifocal self-focusing light beam with adjustable focal characteristics, which comprises the following steps:
s1 constructing a self-focusing light beam by a caustic method;
s2 superposing wave fronts corresponding to the multiple groups of self-focusing light beams;
s3 encoding the complex amplitude distribution of the wavefront into a pure phase form;
s4, the phase distribution obtained by loading on the spatial light modulator is used for modulating the incident light field;
s5 fourier-transforms the modulated light field using a lens.
Further, step S1 of the present invention includes constructing the self-accelerated light beam with a circular parabolic trajectory in the spatial frequency domain, wherein the equation of the focal-dispersion trajectory can be expressed as:
r is the radial coordinate in polar coordinates, r0Is the radius of the central dark space, z is the light field propagation direction, zcIs the intersection of the caustic and the central axis and can be approximated as the location of the focal point.
Further, step S2 according to the present invention includes that for the case that the focal points are all on the central axis, the complex amplitude distribution of the wavefront of the multifocal self-focusing beam can be expressed as:
where n is the number of tracks/focal points, the index j indicates the parameters of the jth group of self-focusing beams, cjRepresenting the additional phase of the jth group of traces, the term 1/M being to ensure that the amplitude a (r) is not greater than 1, M can be expressed as:
by choosing appropriate additional phases for each set of trajectories, the relative intensity between the foci after superposition of the light fields can be kept constant.
Further, assuming that fourier transform is performed using a lens with a focal length f, the phase distribution of the tracking autofocus light beam in the phase plane (the lens front focal plane) in step S1 is:
where k is the wave number of the light wave. To maximize the energy of the light field, the amplitude distribution of the wavefront, a (r), is set to: the amplitude is 1 in a circle with a radius R and 0 outside the circle. By utilizing an angular spectrum diffraction formula under paraxial approximation, the complex amplitude of the light field on the central axis can be obtained as follows:
to produce a sharp self-focusing effect, the selected light field range needs to be satisfied
Calculation of the above formula shows that the focal intensity increases with increasing R within a certain range, and the intensity of the generated focal spot can be controlled by changing the value of R.
Further, the present invention also includes that for the case of off-axis focal point, the complex amplitude distribution of the wavefront of the multifocal self-focusing beam can be expressed as:
wherein (x'j,y′j) Is the offset of the jth group of tracks and is also the coordinate on the focal plane.
Further, step S3 according to the present invention includes decomposing the complex amplitude distribution of the wavefront of the multifocal self-focusing beam into two phase components by using the biphase method, which can be expressed as:
meanwhile, 2 × 2 pixel units of the spatial light modulator form a giant pixel unit, the complex amplitude of the wavefront at the center position of the giant pixel is decomposed into two phase components, and the two phase components are respectively arranged on two diagonal lines of the giant pixel.
Further, step S4 of the present invention includes assuming that the spatial light modulator has a pixel unit side length of p, the light field reconstructed in real space must satisfy the constraints of nyquist bandwidth, i.e. the method is applied to a pixel unit with a pixel unit side length of p
Furthermore, the light field at the front focal plane and the rear focal plane of the lens of the invention satisfies the relationship of Fourier transform, and the front focal plane of the lens is superposed with the spatial light modulator.
Examples
In one specific embodiment, to obtain a multi-focal autofocus beam having three uniform focal points of intensity along the central axis, three sets of autofocus beam parameters are selected: r is01＝0.6mm，zc1＝60mm，R1＝2.15mm，c1＝0；r02＝0.9mm，zc2＝90mm，R2＝2.19mm，c2＝0.6π；r03＝1.2mm，zc3＝120mm，R3＝2.25mm，c3The resulting wavefront amplitude, phase profile and encoded phase profile is shown in the first row of fig. 4, resulting in a multifocal self-accelerating beam as shown in the left panel of fig. 3. To obtain a multifocal self-focusing beam with three foci of uniform intensity in the focal plane, self-focusing is chosenFocal beam parameter r0＝0.8mm，zc80mm, R2.25 mm and superimposed with the track shifted by + -4 mm along the Y-axis, the resulting wavefront amplitude, phase profile and encoded phase profile are shown in the second row of fig. 4, resulting in a multifocal self-accelerating beam as shown in the right hand graph of fig. 3.
Various corresponding changes and modifications can be made by those skilled in the art based on the above technical solutions and concepts, and all such changes and modifications should be included in the protection scope of the present invention.
Claims (7)
1. A method of producing a multifocal self-focusing beam having adjustable focal properties, said method comprising the steps of:
s1 constructing a self-focusing light beam by a caustic method;
s2 superposing wave fronts corresponding to the multiple groups of self-focusing light beams;
s3 encoding the complex amplitude distribution of the wavefront into a pure phase form;
s4, the phase distribution obtained by loading on the spatial light modulator is used for modulating the incident light field;
s5 fourier-transforms the modulated light field using a lens.
2. A method for generating a multifocal self-focusing beam with adjustable focal characteristics according to claim 1, wherein said step S1 comprises constructing a self-accelerating beam with a circular parabolic trajectory in a spatial frequency domain, wherein a caustic trajectory equation can be expressed as:
r is the radial coordinate in polar coordinates, r0Is the radius of the central dark space, z is the light field propagation direction, zcIs the intersection of the caustic and the central axis and can be approximated as the location of the focal point.
3. A method for generating a multifocal self-focusing beam with adjustable focal characteristics as claimed in claim 1, wherein said step S2 includes that for the case where the focal points are all on the central axis, the complex amplitude distribution of the wavefront of the multifocal self-focusing beam can be expressed as:
where n is the number of tracks/focal points, the index j indicates the parameters of the jth group of self-focusing beams, cjRepresenting the additional phase of the jth group of traces, the term 1/M being to ensure that the amplitude a (r) is not greater than 1, M can be expressed as:
by choosing appropriate additional phases for each set of trajectories, the relative intensity between the foci after superposition of the light fields can be kept constant.
4. A method of producing a multifocal self-focusing beam having adjustable focal properties according to claim 3 and further comprising, for the case of off-axis focal points, the complex amplitude profile of the wavefront of the multifocal self-focusing beam is expressed as:
wherein (x'j,y′j) Is the offset of the jth group of tracks and is also the coordinate on the focal plane.
5. A method for generating a multifocal self-focusing beam with adjustable focal characteristics as claimed in claim 1, wherein said step S3 includes decomposing the complex amplitude distribution of the wavefront of the multifocal self-focusing beam into two phase components by a bi-phase method, which can be expressed as:
meanwhile, 2 × 2 pixel units of the spatial light modulator form a giant pixel unit, the complex amplitude of the wavefront at the center position of the giant pixel is decomposed into two phase components, and the two phase components are respectively arranged on two diagonal lines of the giant pixel.
6. A method for generating a multi-focal self-focusing light beam with adjustable focal characteristics as claimed in claim 1, wherein the step S4 comprises assuming that the spatial light modulator pixel unit side length is p, the light field reconstructed in real space must satisfy the nyquist bandwidth limitation, i.e. the nyquist bandwidth limitation is satisfied
7. The method of claim 1, wherein the optical field at the front focal plane and the back focal plane of the lens satisfy a fourier transform relationship, and the front focal plane of the lens coincides with the spatial light modulator.
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Cited By (1)
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Cited By (2)
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| CN115166971A (en) * | 2022-08-04 | 2022-10-11 | 浙江农林大学 | Method and system for improving sudden self-focusing capability of first-order circular Airy derivative light beam |
| CN115166971B (en) * | 2022-08-04 | 2023-09-01 | 浙江农林大学 | Method and system for improving abrupt self-focusing capability of first-order round Airy derivative light beam |
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