CN113064284A - Polygonal perfect vortex optical rotation preparation and control method based on high-order cross phase - Google Patents
Polygonal perfect vortex optical rotation preparation and control method based on high-order cross phase Download PDFInfo
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Abstract
The invention relates to a polygonal perfect vortex optical rotation preparation and control method based on a high-order cross phase. The perfect vortex light is a vortex light field with the beam radius irrelevant to the topological charge number, the cross phase is a special light field phase structure, the perfect vortex rotation can be regulated and controlled into a polygon, and 3-order and above are called high-order cross phases. Firstly, a holographic pattern carrying perfect vortex light information and a cross phase is prepared by utilizing a multi-parameter joint regulation and control technology and loaded to a spatial light modulator, a beam of linearly polarized Gaussian light irradiates the spatial light modulator to perform complex amplitude modulation, emergent light passes through a convex lens, a polygonal perfect vortex optical rotation can be obtained on a back focal plane of the lens, and the shape and the light intensity distribution of the perfect vortex optical rotation can be controlled by regulating a high-order cross phase parameter. The method has the advantages of simple light path and strong flexibility, belongs to the field of vortex light control, and can be applied to polygonal perfect vortex optical rotation preparation and control and optical control of microscopic particles.
Description
Technical Field
The invention relates to a polygonal perfect vortex optical rotation preparation and control method based on a high-order cross phase. The perfect vortex light is a vortex light field with the beam radius irrelevant to the topological charge number, the cross phase is a special light field phase structure, the 3 rd order and above is called as a high-order cross phase, and the high-order cross phase can regulate and control the light spot of the perfect vortex rotation to be a polygon. Firstly, a holographic pattern carrying perfect vortex light information and a cross phase is prepared by utilizing a multi-parameter joint regulation and control technology and is loaded to a spatial light modulator, a beam of linearly polarized Gaussian light irradiates the spatial light modulator to perform complex amplitude modulation, emergent light passes through a convex lens, polygonal perfect vortex optical rotation can be obtained on a back focal plane of the convex lens, and a high-order cross phase can be used for preparing perfect vortex optical rotation through the spatial light modulator and controlling the shape and light intensity distribution of the perfect vortex optical rotation. The method has the advantages of simple light path and strong flexibility, belongs to the field of vortex light control, can be applied to preparation and control of polygonal perfect vortex optical rotation, and has wide application prospect in the field of optical control of microscopic particles.
Technical Field
The vortex light is an optical field with a spiral wave front and special light intensity distribution, and the perfect vortex light is a vortex optical field with the beam radius and the topological charge number being irrelevant, namely the beam radius does not change along with the change of the topological charge number, and the perfect vortex optical rotation with small radius can carry the large topological charge number. The characteristic can compensate the defect that the radiuses of the Laguerre-Gaussian beam and the Bessel-Gaussian beam increase along with the increase of the topological charge number. In recent years, perfect vortex optical rotation has attracted much attention in the fields of optical manipulation, optical communication, optical micro-measurement and the like because of its special properties and wide application value.
The phase of the perfect vortex rotation contains an angular phase factor exp (il theta), wherein l is the orbital angular momentum topological charge number, and theta is an azimuth angle; each photon carries
The orbital angular momentum of (a) is,
in order to approximate Planck constant, the angular phase factor indicates that in the process of propagation of perfect vortex rotation, if the perfect vortex rotation is propagated for a period around the optical axis, the wave front just rotates for a circle around the optical axis, and the phase is correspondingly changed by 2 pi l; the center of the helical phase is a phase singularity where the phase is uncertain and the optical field amplitude is zero, thus forming a hollow dark kernel in the center of the optical field. The common perfect vortex rotation is usually obtained by Fourier transformation of a Bessel-Gaussian beam through a convex lens, and the light spot and the fundamental mode Gaussian beam are both circular. The traditional preparation method of perfect vortex rotation puts high requirements on the optical path because of the need of precise alignment.
Cross-phasing is a special optical field phase structure, with 2 nd order cross-phasing referred to as low order cross-phasing and 3 rd and above as high order cross-phasing. At present, the cross phase as a new phase structure is already used for preparation and mode detection of structured light beams such as a Laguerre-Gaussian beam and a round Airy beam, and a brand new approach is provided for control of vortex light. The high-order cross phase can realize the control of any vortex light field under the far field condition, however, the perfect vortex light can only be obtained on the focal plane of the lens, so the Bessel-Gaussian beam is combined with the high-order cross phase, the convex lens is used for Fourier transformation, and the preparation and the control of the polygonal perfect vortex optical rotation can be realized on the back focal plane of the convex lens.
The preparation and control of the polygonal perfect vortex rotation have important significance for expanding the application of the perfect vortex rotation. The polygonal perfect vortex rotation has the characteristics that the beam radius is irrelevant to the topological charge number, has special energy and phase distribution, and has extremely high application value in the aspects of complex motion control of particles, optical communication and the like. Under the laboratory environment, the cross phase and the spatial light modulator are combined to realize the preparation and control of the polygonal perfect vortex optical rotation, the spatial light modulator has the advantages of small volume and convenience in use, a holographic pattern carrying perfect vortex optical information and a high-order cross phase is loaded to the spatial light modulator, emergent light passes through a convex lens, and the preparation and control of the polygonal perfect vortex optical rotation can be realized on the back focal plane of the convex lens. The high-order cross phase can realize the shaping of the polygonal perfect vortex optical rotation, the number of edges is equal to the order of the high-order cross phase, the number is irrelevant to the topological charge number of the perfect vortex optical rotation, and the size of the light spot is irrelevant to the topological charge number. Meanwhile, the order of the high-order cross phase is equal to the sum of two positive integer indexes, the symmetry of the polygonal perfect vortex rotation is influenced by the difference of the two positive integer indexes, and the smaller the difference is, the stronger the symmetry is. The intensity factor of the high-order cross phase is adjusted to control the light intensity distribution and the mode purity of the polygonal perfect vortex rotation without changing the shape of the light spot, and the greater the intensity factor is, the more concentrated and uniformly distributed the light intensity distribution at each vertex of the polygon, and the greater the mode purity is.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problems that the existing perfect vortex optical rotation preparation and control method is single and has high requirement on the precision degree of an optical path, the polygonal perfect vortex optical rotation preparation and control method based on the high-order cross phase is provided.
The technical solution of the invention is as follows:
the invention relates to a polygonal perfect vortex optical rotation preparation and control method based on a high-order cross phase, which mainly comprises the following steps:
(1) and multiplying the phase and the cross phase of the conical lens on the basis of the phase of the common vortex optical rotation by using a multi-parameter combined regulation and control technology, then superposing a blazed grating to obtain a holographic pattern carrying perfect vortex optical information and cross phase, and loading the holographic pattern to a spatial light modulator.
(2) Circularly polarized Gaussian light emitted by a laser is converted into linearly polarized Gaussian light through a polarizer, the linearly polarized Gaussian light is irradiated onto a spatial light modulator after being adjusted by a light beam collimation system for complex amplitude modulation, polygonal perfect vortex optical rotation can be obtained on a back focal plane of a convex lens after emergent light passes through the convex lens, perfect vortex light beams in different shapes can be prepared by controlling the order and the intensity of a high-order cross phase, and the symmetry, the light intensity distribution and the orbital angular momentum purity of the polygonal perfect vortex optical rotation are controlled, as shown in figure 1.
The principle of the invention is as follows:
the perfect vortex light is a vortex light field with the beam radius and the topological charge number being irrelevant, and the preparation and the control of the polygonal perfect vortex optical rotation can be realized on the back focal plane of the convex lens by applying the high-order cross phase.
In a cylindrical coordinate system, when the propagation distance z is 0, the wave function of ideal perfect vortex rotation can be expressed as:
E1(r,φ)≡δ(r-R)exp(imφ) (1)
wherein E1For the wave vector of the perfect vortex rotation, (R, phi) is a cylindrical coordinate, R is a polar diameter, phi is a polar angle, delta (R-R) is a Dirac equation, R is the spot radius of the perfect vortex rotation, and m is a topological charge number. Theoretical analysis shows that the ideal perfect vortex optical ring width tends to zero, and the power on the ring tends to infinity, so that the ideal perfect vortex optical rotation does not exist in reality. Research shows that the fourier transform of the bessel beam is a perfect vortex beam, and the bessel beam has an infinitely extended optical field distribution and does not exist in reality. A bessel-gaussian beam is used as an approximation of the bessel beam, which can be expressed in cylindrical coordinates as:
E2(r,φ)≡Jn(krr)exp(-r2/ω0 2)exp(imφ) (2)
wherein E2Is the wave vector of Bessel-Gaussian light, (r, phi) is the cylindrical coordinate, r is the polar diameter, phi is the polar angle, JnIs an n-th order Bessel polynomial of the first kind, krIs a radial wave vector, ω0Is the beam waist radius of the fundamental mode Gaussian beam, and m is the rubbingNumber of plop charges. After Fourier transformation is carried out on the Bessel-Gaussian beam through the lens, an approximate perfect vortex light field can be obtained, and the approximate perfect vortex light field can be expressed as follows under cylindrical coordinates:
wherein E3For the wave vector of perfect vortex rotation, (r, phi) is the cylindrical coordinate, r is the polar diameter, phi is the polar angle, i is the imaginary unit, omega is the radius of the Gaussian beam at the back focal plane of the lens, omega0Beam waist radius of fundamental mode Gaussian light, InThe optical fiber is an n-order first-class modified Bessel polynomial, R is the radius of a perfect vortex light, and m is the topological charge number.
The preparation and control of perfect vortex rotation can be realized by combining a high-order cross phase with a spatial light modulator. The cross phase is a special phase structure, and provides a brand new method for preparation and control of polygonal perfect vortex optical rotation, and the expression of the cross phase in a Cartesian coordinate system is as follows:
wherein psi0Indicating the cross-phase, (x, y) is Cartesian coordinates, x is the abscissa, y is the ordinate, μ is the intensity factor of the cross-phase, the azimuth angle
An azimuth factor representing the angle of rotation of the beam in a plane, m and n being positive integer indices, the sum of which is the order of the cross-phase. When in use
When (1) can be simplified as follows:
ψ0(x,y)＝μxmyn (5)
when m is 1 and n is 1, the order of 2 is the cross phase; the high-order cross phase refers to a cross phase of 3 orders or more, such as 3 orders, 4 orders, 5 orders, etc., as shown in fig. 2, fig. 2(a), (b), and (c) are respectively 2 orders, 3 orders, and 4 orders.
When the high-order cross phase is used for realizing the preparation and the control of the polygonal perfect vortex optical rotation, firstly, the phase and the cross phase of the conical lens are multiplied on the basis of the phase of the common vortex optical rotation by utilizing a multi-parameter joint regulation and control technology, and then, a blazed grating is superposed to obtain a holographic pattern carrying perfect vortex optical information and the high-order cross phase, and the holographic pattern is loaded to a spatial light modulator, as shown in figure 3. Fig. 3(a), (b), (c), and (d) show a axicon phase, a vortex phase, a cross phase, and a blazed grating, respectively, and fig. 3(e) shows the obtained hologram.
Secondly, a beam of linearly polarized Gaussian light is incident to the spatial light modulator, and the expression before incidence is as follows:
wherein E represents a linearly polarized Gaussian light wave function, E0Is the intensity coefficient, ω0The beam waist radius of the fundamental mode, z the beam propagation distance, ω (z) the beam waist radius, and r the radius of the beam as it propagates z, the intensity distribution is shown in FIG. 4. The reflected light of the spatial light modulator passes through a convex lens, and then the preparation and control of the polygonal perfect vortex rotation can be realized on the back focal plane of the convex lens.
Compared with the prior art, the scheme of the invention has the main advantages that:
(1) the light path is concise, the requirement on the precision degree of the light path is reduced, and the applicability is strong;
(2) the cost is reduced, the space is saved, and the preparation and control of the polygonal perfect vortex optical rotation can be realized by using the preparation light path of the common vortex optical rotation.
(3) The flexibility is strong, the parameters of the high-order cross phase can be flexibly adjusted according to the requirements, and the preparation and the control of the polygonal perfect vortex rotation can be realized. The light spots can be regulated into polygons by regulating the order of the high-order cross phase, and the number of edges is equal to the order of the cross phase; and adjusting two positive integer indexes of the high-order cross phase, wherein the difference of the two positive integer indexes can influence the symmetry of the polygonal perfect vortex rotation, and the smaller the difference is, the stronger the symmetry is. The intensity factor of the high-order cross phase is adjusted to control the light intensity distribution and the mode purity of the polygonal perfect vortex optical rotation under the condition of not changing the shape of the light spot, the greater the intensity factor is, the more the light intensity is concentrated on each vertex of the polygon, the more the distribution of each vertex is uniform, and the greater the mode purity is.
Drawings
FIG. 1 is a flow chart of polygonal perfect vortex rotation preparation and manipulation;
FIG. 2 is a cross-phase distribution plot;
FIG. 3 is a schematic diagram of a hologram preparation process;
FIG. 4 is a linearly polarized Gaussian light intensity profile;
FIG. 5 is a schematic diagram of a polygonal perfect vortex rotation preparation and manipulation scheme;
FIG. 6 is a graph of the result of a polygonal perfect vortex light preparation with high order cross-phasing applied;
FIG. 7 is a diagram of the result of polygonal perfect vortex optical symmetry manipulation;
FIG. 8 is a graph of the control results of the intensity distribution of polygonal perfect vortex light.
Detailed description of the preferred embodiments
The implementation object of the invention is a spatial light modulator, and the specific implementation steps are as follows:
(1) polygonal perfect vortex optical rotation preparation scheme
A hologram of perfect vortex optical rotation is multiplied by a high-order cross phase by utilizing a multi-parameter joint regulation and control technology, then a blazed grating is superposed to obtain a holographic pattern which can be accurately regulated and controlled, the holographic pattern is loaded to a spatial light modulator (6), a laser generator (1) generates stable Gaussian light, the stable Gaussian light sequentially penetrates through a linear polaroid (2) and a half-wave plate (3), the spatial light modulator (6) is irradiated through a light beam collimation system formed by a lens (4) and a lens (5), emergent light after complex amplitude modulation is subjected to Fourier transformation through a lens (7) and then is incident to a CCD camera (9) through a diaphragm (8), the CCD camera (9) is placed on a back focal plane of the lens, the shape of a light spot is observed, namely, the preparation of the polygonal perfect vortex optical rotation is realized, and.
For example, the vortex optical rotation with the topological charge number of 3 is multiplied by the cross phase of 0 order, 3 order, 4 order and 5 order to obtain a holographic pattern which can be accurately regulated and controlled, and the holographic pattern is loaded to a spatial light modulator (6); then, linear polarized gaussian light described in formula (6) is irradiated to the spatial light modulator, and after fourier transform is performed on the emergent light by the convex lens, the shape of a light spot is observed on the back focal plane of the lens, as shown in fig. 6. Fig. 6(a) is a graph of a simulation result of polygonal perfect vortex light intensity distribution, fig. 6(b) is a graph of a simulation result of polygonal perfect vortex light phase distribution, and fig. 6(c) is a graph of an experimental result of polygonal perfect vortex light intensity distribution on a back focal plane of a lens. As can be seen from fig. 6(c), the shapes of the light spots from left to right are respectively circular, triangular, quadrilateral and pentagonal, and the corresponding cross phases are respectively 0 order, 3 order, 4 order and 5 order, which are consistent with the preset conditions of the experiment.
(2) Polygonal perfect vortex optical symmetry control scheme
The optical path of the polygonal perfect vortex optical symmetry manipulation scheme is the same as the polygonal perfect vortex optical preparation scheme, as shown in fig. 4. For example, a vortex optical hologram with a topological charge number of 3 is multiplied by a cross phase of 6 orders, and two positive integer index combinations of the cross phase are respectively: (m-3, n-3), (m-2, n-4), (m-1, n-5), obtaining a hologram pattern which can be precisely controlled, and loading the hologram pattern to a spatial light modulator (6); the spatial light modulator is irradiated with linearly polarized gaussian light described in formula (6), and the exit light is fourier-transformed by a convex lens, and then the shape of a light spot is observed on the back focal plane of the lens, as shown in fig. 7. Fig. 7(a) is a graph of simulation results of intensity distribution of polygonal perfect vortex optical symmetry manipulation, and fig. 7(b) is a graph of simulation results of phase distribution of polygonal perfect vortex optical symmetry manipulation. As can be seen from fig. 7(a), the light spots are all 6-sided polygons, and when m is 3 and n is 3, the light spots are regular hexagons, and the symmetry of the light spots gradually decreases as the difference between the two positive integer indices increases.
(3) Polygonal perfect vortex light intensity distribution control scheme
The optical path of the polygonal perfect vortex light intensity distribution manipulation scheme is the same as the polygonal perfect vortex light preparation scheme, as shown in fig. 4. For example, perfect vortex optical holograms with a topological charge number of 3The intensity factor u is 1 × 106、u＝1.4×106、u＝1.8×106、u＝2.2×106Multiplying the 4-order cross phase to obtain a holographic pattern which can be accurately regulated and controlled, and loading the holographic pattern to a spatial light modulator (6); then, the spatial light modulator is irradiated with the linearly polarized gaussian light described in the formula (6), and after fourier transform is performed on the outgoing light by the convex lens, the shape and intensity distribution of the light spot are observed on the back focal plane of the lens, as shown in fig. 8. Fig. 8(a) is a simulation result diagram of polygonal perfect vortex light intensity distribution manipulation, and fig. 8(b) is a simulation result diagram of polygonal perfect vortex light phase distribution manipulation, which is an experimental result diagram of polygonal perfect vortex light intensity distribution manipulation. As can be seen from fig. 8, when the intensity factors are all greater than 0, the shape of the perfect vortex light spot is quadrilateral; the spot shape remains the same as the intensity factor increases, but the more the intensity distribution is concentrated on each vertex of the polygon and the more uniform the distribution is between the vertices, the greater the mode purity of the light field.
In addition, the spatial light modulator limits the incident angle and power of the light beam, so the specific light path design is performed according to the actual conditions of a laboratory.
Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.
Claims (5)
1. A polygonal perfect vortex optical rotation preparation and control method based on high-order cross phase is characterized in that: the polygonal perfect vortex light is a vortex light field with the beam radius and the topological charge number being irrelevant, the light spot is a polygon, the cross phase is a special light field phase structure, and the order of 3 and above is called as a high-order cross phase; a holographic pattern carrying perfect vortex optical information and a cross phase is prepared by utilizing a multi-parameter joint regulation and control technology and is loaded to a spatial light modulator, one beam of linear polarization Gaussian beam irradiates the spatial light modulator to carry out complex amplitude modulation, and after emergent light penetrates through one convex lens, preparation and control of polygonal perfect vortex optical rotation can be realized on a back focal plane of the convex lens.
2. The method for polygonal perfect vortex rotation preparation and manipulation based on high order cross-phase as claimed in claim 1, wherein: when a hologram carrying perfect vortex optical information and a cross phase is prepared, the phase of a conical lens is multiplied on the basis of the phase of common vortex optical rotation, then the phase is multiplied by the cross phase, and then a blazed grating is superposed to generate a hologram carrying perfect vortex optical information and the cross phase.
3. The method for polygonal perfect vortex rotation preparation and manipulation based on high order cross-phase according to claims 1 and 2, characterized in that: the high-order cross phase can control the shape of the perfect vortex optical rotation, the emergent light of the spatial light modulator passes through a convex lens, the shape of a light spot is collected on the back focal plane of the convex lens, the shape of the perfect vortex optical rotation is regulated into a polygon, the number of sides of the polygon is equal to the order of the high-order cross phase, the polygon is irrelevant to the self topological charge number of the perfect vortex optical rotation, and the size of the light spot is irrelevant to the topological charge number.
4. The method for polygonal perfect vortex rotation preparation and manipulation based on high order cross-phase according to claims 1, 2, 3, wherein: the order of the high-order cross phase is equal to the sum of two positive integer indexes, the two positive integers are respectively the indexes of the abscissa and the ordinate, the difference of the two positive integer indexes can influence the symmetry of the perfect vortex rotation of the polygon, and the smaller the difference is, the stronger the symmetry is, and the closer the light beam is to the regular polygon.
5. The method for polygonal perfect vortex rotation preparation and manipulation based on high order cross-phase according to claims 1, 2, 3, 4, wherein: the intensity factor of the high-order cross phase is adjusted to control the light intensity distribution and the mode purity of the polygonal perfect vortex rotation without changing the shape of the light spot, and the greater the intensity factor is, the more the light intensity distribution is concentrated on each vertex of the polygon, and the greater the mode purity is.
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| CN115037377B (en) * | 2022-05-25 | 2024-04-19 | 中国科学院光电技术研究所 | High-dimension digital signal coding and decoding method and system based on multi-ring perfect vortex beam |
| CN115032790A (en) * | 2022-06-07 | 2022-09-09 | 之江实验室 | Laguerre-Gaussian vortex beam generation and detection method based on cross phase and lens phase combined diffraction device |
| CN115032790B (en) * | 2022-06-07 | 2023-12-12 | 之江实验室 | Laguerre-Gaussian vortex beam generation and detection method based on cross phase and lens phase combined diffraction device |
| CN115453752A (en) * | 2022-09-19 | 2022-12-09 | 苏州大学 | Design method of vortex beam mask plate with abnormal radius |
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