CN115755417A - Regulation and imaging system of symmetrical butterfly light beam - Google Patents
Regulation and imaging system of symmetrical butterfly light beam Download PDFInfo
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Abstract
The application relates to a regulating and imaging system of a symmetrical butterfly beam, which is used for theoretically deducing the diffraction characteristic of the symmetrical Gaussian butterfly beam and carrying out numerical study on the diffraction characteristic in order to study the diffraction of the symmetrical Gaussian butterfly beam of the beam. Wherein the symmetric gaussian butterfly beam is generated by the product of a gaussian term and two butterfly integrals. Obtaining a hologram of the symmetric butterfly light beam after the two-dimensional light field of the symmetric butterfly light beam obtained by calculation interferes with the parallel light; after the laser beam illuminates the image, it is incident on the spatial light modulator loaded with the hologram, carrying the image information. In the fourier plane, the image can be modulated onto a symmetric butterfly beam. After a certain distance, image information can be recovered from the butterfly beam through Fourier transformation, and dynamic imaging is realized. The present application generates symmetric butterfly beams by utilizing holographic techniques. The symmetric butterfly light beam is used for transmitting image signals, and the adjustment, control and application of the symmetric butterfly light beam are achieved through the application.
Description
Technical Field
The invention belongs to the technical field of optics, and particularly relates to a symmetrical butterfly beam regulating and imaging system.
Background
In the field of optics, some laser beams with an abrupt function have attracted great interest both theoretically and in applications. The mutation function can be described generally with 7 basic mutations, namely fold, cusp, dovetail, butterfly, hyperbolic umbilical cord, elliptic umbilical cord and parabolic umbilical cord. Among these different types of beams, the control of their symmetrical intensity distribution has been a research focus in recent years. In the current research, most of the research relates to Airy beams and Pierce beams, and in 2010 and 2013, symmetric circular Airy beams and two-dimensional symmetric Airy beams are realized in a cylindrical coordinate system and a Cartesian coordinate system respectively. In 2021, researchers looked at relatively higher order mutant beams, i.e., the pierce gaussian beam and the dovetail gaussian beam, and conducted intensive studies on their symmetrical structures to obtain symmetrical pierce and dovetail beams. With the increase of the order of the mutation function, the difficulty of regulating and controlling the light field distribution of the light beam is gradually increased, and the complexity is improved.
Researchers are dedicated to obtain more high-dimensional diffraction mutation light beams with adjustability and stable light field structures, and adjust and control the focusing distance, the focusing intensity and the like of the light beams, so that the application of the method in various optical fields such as optical communication, particle capture, optical imaging and the like is realized. In past research, it is proposed to modulate information on airy light by inverse fourier transform based on information superimposed on the spectrum of an airy beam and an airy array, thereby realizing information transmission. The high-order diffraction mutation light beam has high dimensionality, can be regulated and controlled by controlling the state variable load control variable parameters thereof and is expressed as various different light field structures. As the order of the symmetric diffraction break beam increases, it appears as a more abundant and diverse light field structure. The difficulty of experimentally generating the corresponding beam also increases. Therefore, an effective method is provided for realizing high-dimensional rectangular symmetrical diffraction abrupt light beams with distribution functions of 6 orders or above, and the method has great significance in the aspects of information transmission and dynamic imaging by utilizing the unique symmetrical intensity light field distribution and propagation characteristics, and an effective solution is not provided for the method.
Disclosure of Invention
In order to solve the above problems, the present invention discloses a system for regulating and imaging a symmetric butterfly beam, comprising:
a laser for generating a gaussian beam;
the beam expanding collimating lens is used for collimating and expanding the Gaussian beam;
an image for verifying the validity of the system for image signal transmission;
and the beam splitter prism is positioned between the collimation beam expander and the spatial light modulator and is used for splitting the Gaussian beam after collimation beam expansion, and part of light is transmitted to the spatial light modulator.
And the spatial light modulator is used for loading a phase hologram generated by interference of the loading plane wave and the butterfly beam and carrying out phase modulation on the Gaussian beam.
In the 4f optical system, the light beam reflected after being modulated by the spatial light modulator is subjected to Fourier transform through the first lens to obtain a frequency spectrum surface, and information is superposed on the frequency spectrum of the symmetrical butterfly light beam. The diaphragm is used for filtering to obtain a positive first-order interference fringe, and the second lens is used for carrying out inverse Fourier transform on the obtained interference fringe, so that image information is modulated on the symmetrical butterfly light. An initial light field is obtained.
And the charge coupling device is used for receiving the initial light field, light field information obtained after diffraction at different distances and transmitted image information.
Further, the laser generates a Gaussian beam with a wavelength of 532 nm.
Furthermore, the beam expanding collimator lens comprises a microscope objective lens and a lens, and the size of a light spot incident on the spatial light modulator is adjusted according to requirements by using a diaphragm.
Further, a reflective spatial light modulator is used to generate the symmetric butterfly beam based on the hologram.
Further, the 4f optical system comprises two lenses and a diaphragm, and the reflected light beam modulated by the reflective spatial light modulator is subjected to Fourier transform through the first lens to obtain a frequency spectrum plane; the diaphragm is placed on the frequency spectrum surface, the positive first-order interference fringes of the frequency spectrum surface are obtained, the distance between the second lens and the diaphragm is the focal length of the second lens, and inverse Fourier transform is carried out on the obtained interference fringes.
Further, the CCD is used for receiving the generated symmetrical butterfly beams which diffract different distances and the image information transmitted by the system, and the resolution of the CCD is 2048 x 2048.
Further, the hologram is obtained by the interference of two-dimensional field distribution of symmetric butterfly beams with the light field distribution function of
u(x,y,0,0)＝BBu(x,p,0,0)BBu(y,p,0,0)，
Wherein BBu (-) is a variant of butterfly integral:
x,y,a 1 ,a 2 are dimensionless coordinates in space.
The working principle of the invention is as follows:
according to the system for regulating and imaging the symmetric butterfly beam, the phase modulation pattern obtained by interference between the symmetric butterfly beam obtained by simulation and the plane wave is generated on the spatial light modulator, and the Gaussian beam is subjected to phase modulation by using the phase modulation pattern, so that the symmetric butterfly beam is obtained. Through numerical calculation, the light intensity distribution of the butterfly light beam on different cross sections in the transmission process is given, and the butterfly light beam can generate a self-focusing phenomenon when being transmitted to a specific distance and becomes a bright line with the most concentrated energy. Due to the remarkable automatic focusing and transverse self-accelerating propagation characteristics, the light beam is deformed in the propagation process, the distribution of the cross-section light field of the light beam is reversed along with the increase of the transmission distance, and the light field is gradually split into four independent main lobes from a bright spot.
The invention has the beneficial effects that: the beneficial effects of the regulating and imaging system of the symmetric butterfly light beam are as follows:
first, the butterfly beam can auto-focus in the near field, and its longitudinal auto-focus area is longer compared to the conventional symmetric airy beam.
Secondly, the butterfly light beam is diverged in a rectangular symmetrical distribution mode after being focused, and transmitted information changes, so that the opportunity of information conversion in the propagation process is provided for people. The distribution and the focal length of the rectangular light field can be changed by adjusting the dimensionless distribution factor in the adjustment mode, and the method has the potential in the aspect of dynamic imaging and the aspect of optical encryption.
Thirdly, the butterfly light beam can also introduce vortex on the main lobe of the rectangular light intensity, and the topological kernel characteristic can be reflected along the track in the propagation process. This new symmetrical beam opens up another possibility for particle trapping and plasma applications.
Drawings
Fig. 1 is a schematic flow chart of a symmetric butterfly beam modulation system according to embodiments 1, 2 and 3 of the present invention;
FIG. 2 is a hologram loaded on a spatial light modulator according to one embodiment of the present invention 1;
FIG. 3 is a side view profile and intensity profile and energy flow variation during propagation of a symmetric butterfly beam according to an embodiment 1 of the present invention;
FIG. 4 is a graph of the propagation intensity of a symmetric butterfly beam according to one embodiment of the present invention 1;
FIG. 5 is a graph of symmetric butterfly beam propagation intensities for different p-values regulated in accordance with an embodiment 2 of the present invention;
FIG. 6 (a) shows an intensity plot of symmetric butterfly vortex beams with topological loads of 2,4,6,8, -2, -4, -6, -8, with corresponding phases indicated in the inset; FIG. 6 (b) is a graph showing the diffracted intensity of the astigmatic butterfly vortex beam after diffraction for 40cm
Fig. 7 is a schematic diagram of an imaging system of a symmetric butterfly beam and dynamic imaging of a letter "T" by the symmetric butterfly beam at different distances according to an embodiment 3 of the present invention.
Fig. 8 is a system diagram of the present invention.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and detailed description, which will be understood as being illustrative only and not limiting in scope. It should be noted that the terms "front," "back," "left," "right," "upper" and "lower" used in the following description refer to directions in the drawings, and the terms "inner" and "outer" refer to directions toward and away from, respectively, the geometric center of a particular component.
As shown in fig. 1, the present application discloses a system for generating and regulating a symmetric butterfly beam, which includes a semiconductor solid laser, a beam expanding collimator, a spatial light modulator, and a beam splitting prism. The 4f optical system and the electric coupling device regulate and control the phase of the incident beam to generate a symmetrical butterfly beam.
The derivation process of the light field expression of the symmetric butterfly beam at different diffraction distances described in the present application is:
the butterfly score is defined as
According to a Fourier transform, has an angular spectral distribution of
k x ，k y Is variable in X and Y directions of the frequency spectrum, and p is a constant factor and is used for regulating and controlling the symmetric butterfly beam. And performing inverse Fourier transform on the angular spectrum components and multiplying by Gaussian terms to obtain the initial field distribution of the symmetric butterfly light beam with limited energy:
through a Fresnel diffraction integral formula, a light field analytical expression of symmetric butterfly light at different diffraction distances can be obtained, namely:
where z is the diffraction distance, i is the imaginary unit,
is the wave number, lambda is the wavelength,by derivation, it is further obtained
Wherein q (z) = iz + z R ，
In this embodiment, w is set by the simulation parameter 0 ＝1.5mm，b 1 ＝b 2 ＝0.07,p 1 ＝p 2 And (3) acquiring a phase hologram, namely a graph 2, according to the interference condition of the initial light field of the symmetric butterfly light beam and the plane wave of the symmetric butterfly light beam of =0, and loading the phase hologram to the spatial light modulator, wherein an emergent light beam is the symmetric butterfly light beam. A side view profile of a symmetric butterfly beam is further simulated in fig. 3 (a) and the intensity profile during propagation, fig. 3 (b 1-b 4). The diffraction distance was set as: z =0, z =0.03z R ,z＝0.04z R ,z＝0.045z R . The light field is gradually split from a bright spot into four independent main lobes. Furthermore, according to the principles of the poynting vector
S is energy flux, magnetic field distribution H, E is electric field distribution, c is light speed in vacuum, and energy flow of symmetric butterfly beams under different diffraction distances is calculated. It is also clear from the energy flow diagram that as the diffraction distance changes, the main lobe energy gradually splits and shifts to the side lobes, and finally the energy is concentrated on the four main lobes, i.e. fig. 3 (c 1-c 4). The light intensity distribution and the energy flow diagram clearly show the symmetry of the butterfly symmetrical light beam. In addition, the propagation intensity graph of the symmetrical butterfly light beam is simulated by the ratio of the light intensity at any point to the light intensity of the initial plane of the symmetrical butterfly light beam. The ratio of the autofocus intensity to the initial focus intensity is several times.
Example 2
Referring to fig. 4, in this embodiment, on the basis of the system of embodiment 1, the spatial light modulator modulates the phase hologram, so as to regulate the focusing intensity of the symmetric butterfly beam.
The method for regulating and controlling the focusing intensity of the symmetric butterfly beam comprises the following steps:
the constant factor p is changed, the rest parameters are set in the same way as in the embodiment 1, a new set parameter phase hologram is obtained, and the spatial light modulator is irradiated by Gaussian light, so that a new symmetrical butterfly beam can be obtained. FIG. 5 is a graph of the propagation intensity of a symmetric butterfly beam at different diffraction distances for different p values. From the graph analysis, it can be concluded that: the adjustment of the p-value can realize the change of the focusing intensity, the focusing intensity is increased along with the increase of the p-value, and the focusing distance is longer. Thereby demonstrating the tunability of the symmetric butterfly beam.
Introducing vortex phase on the main lobe of a symmetric butterfly beam
Wherein
Is azimuth angle, generates a symmetric butterfly vortex beam, and secondly introduces astigmatic phase ψ = a [ (x) 2 +y 2 )cos(2α)+2xysin(2α)]Thereby generating an astigmatic butterfly vortex beam with parameters set with an astigmatism constant a =1.1 × 10 6 m -2 Angle of astigmatism
The topological charge characteristic of the symmetrical butterfly vortex light beam can be embodied along the track in the propagation process. FIG. 6 (a) shows a graph of intensity for symmetric butterfly vortex beams with topological holsters of 2,4,6,8, -2, -4, -6, -8, with insets showing the corresponding phase. FIG. 6 (b) shows the diffraction intensity chart after the butterfly vortex beam is diffracted for 40cm, the sign and size of the topological charge can be determined according to the black and white stripes in the diffraction pattern, the number of the dark stripes is equal to the mode of the topological charge, the positions of the dark stripes are marked by white lines, the dark stripes are numbered by (1) and (2), and the inclination of the stripes shows the topological chargeThe symbol of (2). The diffraction pattern is tilted clockwise 45 degrees relative to the y-axis when the topological charge of the astigmatic butterfly vortex beam is positive, and is tilted counterclockwise 45 degrees relative to the y-axis when the topological charge is negative.
Example 3
On the basis of the embodiment 1 and the embodiment 2, an image is placed in front of the spatial light modulator, gaussian light carrying image information is transmitted to the spatial light modulator, the image information is superposed on the frequency spectrum of the symmetric butterfly light beam through Fourier transformation of a lens, and then the image information is modulated on the symmetric butterfly light beam through inverse Fourier transformation. Due to the diffraction characteristic of the symmetric butterfly beam, dynamic imaging is realized. As shown in fig. 7, the letter T, at which the imaging information is converted at different diffraction distances, is at z =0, z =0.03z R ,z＝0.04z R The images are 'T', 'plus', 'on', respectively. Therefore, the system designed by the application has the capability of transmitting information and dynamically imaging, and has great potential in applications such as optical encryption and the like.
The system is adopted to realize the regulation and the imaging of the symmetric butterfly light beam, can well regulate and control the focusing intensity and the distance of the light beam and realize dynamic imaging. The system has simple structure and easy operation.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (7)
1. A symmetric butterfly beam steering and imaging system, comprising:
a solid state laser for generating a gaussian beam;
the collimation beam expander is used for connecting the Gaussian beam and performing collimation beam expansion processing on the Gaussian beam;
an image for verifying the validity of the system for image signal transmission;
the beam splitting prism splits the Gaussian beam, and a part of light enters the spatial light modulator and is received and transmitted by the light reflected by the spatial light modulator;
a reflective spatial light modulator for loading a hologram; generating a symmetric butterfly beam based on the hologram;
a 4f optical system for filtering zero-order diffraction information of the light beam reflected by the spatial light modulator; obtaining an initial light field;
and the charge coupling device is used for receiving the initial light field and the light field information after diffracting different distances.
2. The system of claim 1, wherein the butterfly beam is symmetric about the optical axis,
the method is characterized in that: the laser produces a gaussian beam of wavelength 532 nm.
3. The system of claim 1, wherein the butterfly beam is symmetric about the optical axis,
the method is characterized in that: the beam expanding collimating lens comprises a microscope objective and a lens, and the size of a light spot incident on the spatial light modulator is adjusted according to needs by using a diaphragm.
4. The system of claim 1, wherein the butterfly beam is symmetric about the optical axis,
the method is characterized in that: a reflective spatial light modulator is used to generate the symmetric butterfly beam based on the hologram.
5. The system of claim 1, wherein the butterfly beam is symmetric about the optical axis,
the method is characterized in that: the 4f optical system comprises two lenses and a diaphragm, and the reflected light beam modulated by the reflective spatial light modulator realizes Fourier transform through the first lens to obtain a frequency spectrum surface; the diaphragm is placed on the frequency spectrum surface, the positive first-order interference fringes of the frequency spectrum surface are obtained, the distance between the second lens and the diaphragm is the focal length of the second lens, and inverse Fourier transform is carried out on the obtained interference fringes.
6. The system of claim 1, wherein the system further comprises: the CCD is used for receiving the generated symmetric butterfly beams which diffract different distances and image information transmitted by the system, and the resolution of the CCD is 2048 x 2048.
7. The system of claim 4, wherein the butterfly beam modulator and imager system further comprises: the hologram is obtained by the interference of two-dimensional field distribution of symmetric butterfly beams in plane waves, and the light field distribution function of the butterfly beams is
u(x,y,0,0)＝BBu(x,p,0,0)BBu(y,p,0,0)，
Wherein BBu (-) is a variant of butterfly integral:
x,y,a 1 ,a 2 are dimensionless coordinates in space.
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| CN202211115946.3A CN115755417A (en) | 2022-09-14 | 2022-09-14 | Regulation and imaging system of symmetrical butterfly light beam |
| CN202310185574.XA CN116338944A (en) | 2022-09-14 | 2023-03-01 | Symmetrical butterfly beam generation and application method thereof in imaging |
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