CN116699857A - Vortex light beam sorting method based on Fermat spiral transformation and optical diffraction device - Google Patents
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Abstract
The invention discloses a vortex beam sorting method based on Fermat spiral transformation and an optical diffraction device, and belongs to the field of optical communication. The incident vortex light field is decomposed along the path of the Fermat spiral line in the phase conversion plate and mapped to the correction phase plate, so that the phase distribution of the incident vortex light field is converted from the angular spiral phase to the transverse inclined plane phase, and the incident vortex light field is focused to different positions of a back focal plane through a convex lens, thereby realizing spatial separation. According to the invention, the transformation phase and the correction phase of vortex beam high-resolution separation are realized by utilizing the Fermat spiral transformation, and the coaxial separation of a plurality of vortex beams can be realized by only using two phases, wherein the number of Fermat spiral lines is far greater than that of logarithmic spiral lines, so that the resolution of the vortex beam separator is greatly improved.
Description
Technical Field
The invention relates to the field of optical communication, in particular to a vortex beam sorting method based on Fermat spiral transformation and an optical diffraction device.
Background
Vortex is a natural phenomenon which is widely found in life, and in the optical field, a vortex-carrying spiral phase structuree ilθ Is also referred to as a vortex beam due to its particular phase (wherein,lcalled topological charge number, there is no upper limit in theory,θazimuth as transverse plane). In 1992, allen et al pointed out that such light fields have orbital angular momentum of magnitude per photon in the direction of propagation, and are differentThe vortex beams with topological charges are mutually orthogonal, and the special properties enable the light field to have wide application prospects in various fields. For example, in the micro-particle manipulation, compared with the spin angular momentum sigma ℏ of the circular polarized light (sigma= -1 corresponds to the left-hand circular polarized light and sigma = 1 corresponds to the right-hand circular polarized light), the orbital angular momentum of the vortex beam is far greater than the spin angular momentum provided by the circular polarized light, so that the efficient momentum transfer of the micro-particles can be realized.
As the research of vortex beams has begun to become a hotspot in recent years, the application potential of the vortex beams in the communication field has also begun to be gradually explored. For vortex beams with different topological charges, the vortex beams are orthogonal to each other, so that the vortex beams have the possibility of being applied to the communication field, and meanwhile, due to the topological charges of the vortex beamslThere is no limit in theory, so that the channel capacity of the communication system can be greatly increased, the transmission rate of the communication system can be improved, and the communication system has excellent confidentiality in the field of quantum communication. However, it has been a core and difficulty in the orbital angular momentum multiplexing communication system to study how to efficiently separate and detect the vortex beam carrying the orbital angular momentum.
In general, vortex beam detection can be achieved by recovering a vortex beam into a normal gaussian beam using holograms with a particular phase distribution, but each hologram is only effective for a particular topological number of vortex beams, making such methods extremely inefficient. In order to further expand the detection efficiency of vortex beams, it has been proposed to realize the separation of two coaxial vortex beams by using an M-Z interferometer, and by adding Dove prisms with different rotation angles into two arms of the interferometer, the vortex beams transmitted coaxially can be separated at the end, but the method can only separate two types of vortex beams with different topologies at the same time, once the vortex beams with different topologies of N types are incident, effective separation can be realized only by cascading N-1 interferometers, and the volume of the whole device is greatly increased. In 2010 Berkhout et al proposed efficient sorting of vortex beams using a conformal optical transformation, by implementing a simple logarithmic polar transformation between the two faces, they achieved efficient sorting of vortex beams of a variety of different topologies using only two phase elements, but limited the problem of the transformation itself, the vortex beams of adjacent topological charges were not well separated, limiting the application of the method. Therefore, in 2018, wen Yuanhui et al of the university of Zhongshan proposed to widen the angular definition of the original plane by using a spiral line, and proposed a logarithmic spiral transformation to achieve effective separation of adjacent topological charge vortex beams, but this method is only applicable to logarithmic spirals, limited by the spiral properties, and there is still room for improvement.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a vortex beam sorting method and an optical diffraction device based on the Fermat spiral transformation, which construct the required transformation phase and correction phase based on the Fermat spiral transformation by utilizing the characteristics of the Fermat spiral, thereby realizing the efficient sorting of vortex beams, aiming at further improving the resolution of the current sorting scheme and solving the problem of low resolution of the current sorting scheme.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the invention provides a vortex beam sorting method based on Fermat spiral transformation, which is divided into two parts of phase transformation and phase correction, and comprises the following steps:
s1, vertically incidence of vortex light beams to be separated to thex,y) In the planar transformation phase plate, the center of the spiral light beam to be measured is aligned with the center of the transformation phase plate, wherein the wave front of the vortex light beam is distributed in an angular spiral phase;
s2, at the level ofx,y) Loading a preset first phase modulation on a planar conversion phase plateQ(x,y) The incident vortex light field is decomposed along the path of the Fermat spiral line after being modulated by the transformation phase plate and mapped to the followingu,v) A planar correction phase plate;
s3, at the level ofu,v) Correction phase of planeLoading a predetermined second phase modulation on boardP(u,v) So that the phase distribution of the incident vortex light field is converted from the angular spiral phase to the transverse inclined plane phase, the second phase modulation is adoptedP(u,v) The incident vortex light field of the lens is focused on the back focal plane through the convex lens, and vortex light beams with different topological charges are positioned at different focuses on the focal plane, so that space separation is realized.
In a first aspect, the present invention is based on the idea of conformal optical transformation to construct an optical map as follows:
wherein ,aandbthe control parameters of the size of the light spot after transformation are as followsr,θ) To change polar coordinates of phase planeu,v) To correct the cartesian coordinates of the phase plane,is a broad angle extended by the use of the fermat spiral.
Further, based on the above-described optical mapping and the expression of the fermat spiral, the mathematical expression of the transformation phase is:
wherein ,(x,y) To transform the cartesian coordinates of the phase plane,dfor the distance between the two phase surfaces,kfor the wavenumber of the light beam in vacuum,mshowing the number of turns of the spiral at which a point on the plane is located,, wherein r 0 Representing the starting position of the spiral line,a 1 for controlling the parameters of the stepping distance of each turn of the spiral, < > for each turn of the spiral>Representing rounding. The transformation phase can lead the incident vortex beam to follow the Fermat spiralThe lines are decomposed to become strip-shaped light spots distributed along the transverse direction, so that spiral phases of vortex light beams distributed along the angular direction are changed into inclined plane wave phases distributed along the transverse direction, and vortex light beams with different topological charges correspond to different inclined phase gradients.
Further, the mathematical expression of the corrected phase is:
wherein ,(u,v) To correct the cartesian coordinates of the phase plane. The phase is used for correcting the extra phase caused by the transformation phase and the optical path in the propagation, so that the corrected long-strip light spot only carries the inclined phase corresponding to the topological charge number, and finally, the corrected long-strip light spot is focused on a back focal plane by a lens, and thus, vortex light beams with different topological charge numbers are positioned at different focuses on the focal plane to realize space separation.
The invention also provides an optical diffraction device for vortex beam sorting, which comprises a phase conversion plate and a phase correction plate, wherein the phase conversion plate and the phase correction plate are the front side and the back side of a substrate and are respectively defined asx,y) Plane sum%u,v) Plane, substrate thickness ofd。
The invention also provides a vortex beam sorting system which comprises an optical diffraction device and a convex lens for vortex beam sorting, and a correction phase plateu,v) The plane corresponds to the back focal plane of the convex lens.
In general, by the above technical solutions conceived by the present invention, compared with the prior art, the following beneficial effects can be obtained:
(1) The invention provides an optical angle-keeping mapping which can be used for the Fermat spiral based on the idea of angle-keeping optical transformation, and breaks through the limitation of the optical mapping to the spiral type in the work of the former;
(2) The invention constructs the transformation phase and the correction phase which can realize the high-resolution sorting of vortex beams by utilizing the Fermat spiral transformation, and can realize the coaxial sorting of a plurality of vortex beams by only using two phases, thereby greatly reducing the volume of a sorting system;
(3) According to the invention, the Fermat spiral transformation is adopted, and under the condition of the incident light field with the same width, the number of the Fermat spiral lines is far greater than that of the logarithmic spiral lines, so that the resolution of the vortex beam classifier is greatly improved;
(4) The optical mapping method adopted by the invention can realize simultaneous sorting of vortex beams with different topologies, and greatly improves the working efficiency of the sorter.
Drawings
Fig. 1 is a graph comparing logarithmic spiral (a) and fermat spiral (b) for the same incident spot width.
Fig. 2 is a diagram of the transformation phase (a) and the correction phase (b) required for the fermat spiral transformation.
Fig. 3 is a graph comparing simulation results of logarithmic spiral transformation (a) and fermat spiral transformation (b) applied to vortex beam sorting.
Fig. 4 is a one-dimensional light intensity distribution diagram of the broken line in the fermat spiral transform (a) and the logarithmic spiral transform (b) of fig. 3.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not interfere with each other.
The invention provides a vortex beam sorting method based on Fermat spiral transformation, which is divided into two parts of phase transformation and phase correction, and comprises the following steps:
s1, vertically incidence of vortex light beams to be separated to thex,y) In the planar transformation phase plate, the center of the spiral light beam to be measured is aligned with the center of the transformation phase plate, wherein the wave front of the vortex light beam is distributed in an angular spiral phase;
s2, at the level ofx,y) Loading a preset first phase modulation on a planar conversion phase plateQ(x,y) The incident vortex light field is decomposed along the path of the Fermat spiral line after being modulated by the transformation phase plate and mapped to the followingu,v) A planar correction phase plate;
s3, at the level ofu,v) Loading a predetermined second phase modulation on a planar correction phase plateP(u,v) So that the phase distribution of the incident vortex light field is converted from the angular spiral phase to the transverse inclined plane phase, the second phase modulation is adoptedP(u,v) The incident vortex light field is focused to the back focal plane through the convex lens, and vortex light beams with different topological charges are positioned at different focuses on the focal plane, so that space separation is realized.
In a first aspect, the present invention is based on the idea of conformal optical transformation to construct an optical map as follows:
wherein ,aandbthe control parameters of the size of the light spot after transformation are as followsr,θ) To change polar coordinates of phase planeu,v) To correct the cartesian coordinates of the phase plane,is a broad angle extended by the use of the fermat spiral. As shown in fig. 1, the number of turns of the logarithmic spiral (fig. 1 (a)) and the fermat spiral (fig. 1 (b)) at the same incident width are compared, and it can be seen that the fermat spiral gradually decreases with increasing number of turns due to the step value of each turn of the spiral, so that the number of turns of the fermat spiral can be significantly larger than that of the logarithmic spiral in the same width, therefore, the azimuth angle of the transverse plane extended by the fermat spiral can obtain a larger angle range, thereby transforming to obtain longer light spots, and finally realizing higher resolution.
Further, based on the above-described optical mapping and the expression of the fermat spiral, the mathematical expression of the transformation phase is:
wherein ,(x,y) To transform the cartesian coordinates of the phase plane,dfor the distance between the two phase surfaces,kfor the wavenumber of the light beam in vacuum,mshowing the number of turns of the spiral at which a point on the plane is located,, wherein r 0 Representing the starting position of the spiral line,a 1 for controlling the parameters of the stepping distance of each turn of the spiral, < > for each turn of the spiral>Representing rounding. As shown in fig. 2 (a), the corresponding transformation phase diagram is utilized to decompose the incident vortex beam in the angular direction along the fischer spiral line, and the vortex beam propagates to the correction phase plane and is transformed into a strip-shaped light spot distributed along the transverse direction, so that the spiral phase of the vortex beam distributed along the angular direction is changed into the inclined plane wave phase distributed along the transverse direction, and vortex beams with different topological charges correspond to different inclined phase gradients.
Further, the correction phase plate is used for expressing the required correction phase, and the mathematical expression is as follows:
as shown in fig. 2 (b), the corresponding corrected phase diagram is used to correct the extra phase caused by the transformation phase and the optical path in propagation, so that the corrected elongated light spot will only carry the oblique phase corresponding to the topological charge number, and finally be focused onto the back focal plane by the lens, thus, vortex beams with different topological charge numbers will be located at different focuses on the focal plane to realize spatial separation.
FIG. 3 shows the use of different topological charges (-2 +.lLess than or equal to 2) simulation results of logarithmic spiral transformation (fig. 3 (a)) and fermat spiral transformation (fig. 3 (b)) after incidence of vortex beam. FIG. 4 is a one-dimensional intensity distribution graph taken along the dashed line in FIG. 3. As can be seen from fig. 3, the width of the focused light spot after applying the fischer spiral transformation is significantly lower than that of the focused light spot after logarithmic spiral transformation, and the difference between the two can be seen more clearly in fig. 4, it is not difficult to see that the crosstalk between adjacent light spots after decomposing by using the fischer spiral is significantly reduced compared with the logarithmic spiral, and the width of the light spot in the transverse direction is significantly reduced. Meanwhile, the definition of the optical finesse is that the vortex beam distance between adjacent topological charges is divided by the full width half maximum of a focusing light spot, so that the final resolution effect is quantized, the calculated optical finesse of the Fermat spiral is 7.65, the calculated optical finesse of the logarithmic spiral is 3.88, and the effect of double can be improved by using the Fermat spiral. Therefore, compared with a logarithmic spiral-based vortex beam classifier, the result comparison can prove that the fermat spiral-based vortex beam classifier provided by us not only breaks through the limitation of spiral types in the former work and expands the application range of the classifier, but also improves the final classifying effect by two times, effectively reduces crosstalk between adjacent topological focusing light spots and improves the final resolving effect.
The invention also provides an optical diffraction device for vortex beam sorting, which comprises a phase conversion plate and a phase correction plate, wherein the phase conversion plate and the phase correction plate are the front side and the back side of a substrate and are respectively defined asx,y) Plane sum%u,v) Plane, substrate thickness ofd。
The invention also provides a vortex beam sorting system which comprises an optical diffraction device and a convex lens for vortex beam sorting, and a correction phase plateu,v) The plane corresponds to the back focal plane of the convex lens.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. The vortex beam sorting method based on the Fermat spiral transformation is characterized by comprising the following steps of:
s1, vertically incidence of vortex light beams to be separated to thex, y) In the planar transformation phase plate, the center of the spiral light beam to be measured is aligned with the center of the transformation phase plate, wherein the wave front of the vortex light beam is distributed in an angular spiral phase;
s2, at the level ofx, y) Loading a preset first phase modulation on a planar conversion phase plateQ(x, y) The incident vortex light field is decomposed along the path of the Fermat spiral line after being modulated by the transformation phase plate and mapped to the followingu, v) A planar correction phase plate;
s3, at the level ofu, v) Loading a predetermined second phase modulation on a planar correction phase plateP(u, v) So that the phase distribution of the incident vortex light field is converted from the angular spiral phase to the transverse inclined plane phase, the second phase modulation is adoptedP(u, v) The incident vortex light field is focused to the back focal plane through the convex lens, and vortex light beams with different topological charges are positioned at different focuses on the focal plane, so that space separation is realized.
2. The vortex beam sorting method according to claim 1, wherein @ in S2x, y) The light field on the plane is decomposed along the path of the Fermat spiral and mapped tou, v) On a plane, the corresponding coordinate mapping relationship is expressed by the following formula:
wherein ,aandbthe control parameters of the size of the light spot after transformation are as followsr,θ) To change polar coordinates of phase planex, y) To change Cartesian coordinates of a phase planeu, v) To correct the cartesian coordinates of the phase plane,is a generalized angle of expansion by using Fermat screw，mShowing the number of turns of the spiral at which a point on the plane is located, < >>, wherein r 0 Representing the starting position of the spiral line,a 1 for controlling the parameters of the stepping distance of each turn of the spiral, < > for each turn of the spiral>Representing rounding.
3. The vortex beam sorting method of claim 2 wherein the first phase modulationQ(x, y) The expression is carried out by the following formula:
wherein ,dfor the distance between the two phase surfaces,kis the wavenumber of the beam in vacuum.
4. The vortex beam sorting method of claim 2 wherein the second phase modulationP(u, v) The expression is carried out by the following formula:
wherein ,dfor the distance between the two phase surfaces,kis the wavenumber of the beam in vacuum.
5. An optical diffraction device for vortex beam sorting is characterized by comprising a phase conversion plate and a phase correction plate, wherein the phase conversion plate and the phase correction plate are the front side and the back side of a substrate and are respectively defined asx, y) Plane sum%u, v) Plane, substrate thickness ofd。
6. The optical diffraction device for vortex beam sorting as claimed in claim 5, wherein the%x, y) The light field on the plane is decomposed along the path of the Fermat spiral and mapped tou, v) On a plane, the corresponding coordinate mapping relationship is expressed by the following formula:
wherein ,aandbthe control parameters of the size of the light spot after transformation are as followsr,θ) To change polar coordinates of phase planex, y) To change Cartesian coordinates of a phase planeu, v) To correct the cartesian coordinates of the phase plane,is a generalized angle expanded by using a Fermat screw,mshowing the number of turns of the spiral at which a point on the plane is located, < >>, wherein r 0 Representing the starting position of the spiral line,a 1 for controlling the parameters of the stepping distance of each turn of the spiral, < > for each turn of the spiral>Representing rounding.
7. The optical diffraction device for vortex beam sorting of claim 6 wherein the transformation phase plate is expressed by:
wherein ,dfor the distance between the two phase surfaces,kis the wavenumber of the beam in vacuum.
8. The optical diffraction device for vortex beam sorting of claim 6 wherein the modified phase plate is expressed by:
wherein ,dfor the distance between the two phase surfaces,kis the wavenumber of the beam in vacuum.
9. A vortex beam sorting system comprising an optical diffraction device for vortex beam sorting as claimed in any one of claims 5 to 8 and a convex lens, a correction phase plateu, v) The plane corresponds to the back focal plane of the convex lens.
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| CN108923880A (en) * | 2018-04-23 | 2018-11-30 | 中山大学 | A kind of photon trajectory angular momentum mode measurement method and system based on Screw transformation |
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| CN115308914A (en) * | 2022-07-31 | 2022-11-08 | 苏州大学 | System and method for generating vortex light beam based on gradual change Fermat spiral seam |
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| CN108923880A (en) * | 2018-04-23 | 2018-11-30 | 中山大学 | A kind of photon trajectory angular momentum mode measurement method and system based on Screw transformation |
| WO2022029616A1 (en) * | 2020-08-05 | 2022-02-10 | Università Degli Studi Di Padova | Device for multipole phase division demultiplexing/multiplexing and spatial division telecommunications system thereof |
| CN114488549A (en) * | 2022-01-07 | 2022-05-13 | 上海理工大学 | Universal vortex optical rotation multiplexing system and method based on spiral transformation |
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| Title |
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| ZENG ZS 等: "Multiplication and division of orbital angular momentum beams by Fermat\'s spiral transformation", PHOTONICS RESEARCH, vol. 11, no. 2, pages 165 - 172 * |
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