Patent ID: 12235162

DESCRIPTION OF EMBODIMENTS

In order to make the above objects, features and advantages of the present disclosure more obvious and understandable, the following detailed description of the specific embodiments of the present disclosure will be made with reference to the drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, the present disclosure can be implemented in many other ways different from those described here, and those skilled in the art can make similar improvements without violating the connotation of the present disclosure, so the present disclosure is not limited by the specific implementation disclosed below.

Unless otherwise defined, all technical and scientific terms used herein have the same meanings as commonly understood by those skilled in the technical field of the present disclosure. The terminology used in this specification of the present disclosure is only for the purpose of describing specific embodiments, and is not intended to limit the present disclosure. The technical features of the above embodiments can be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction between the combinations of these technical features, they should be considered within the scope of the specification.

Embodiment 1

Referring toFIG.1, the comparison of polarization state distribution between uniformly polarized beams and non-uniformly polarized beams is given. It can be seen fromFIG.1(a)that for uniformly polarized beams, all points on the beam cross section show the same polarization state at any moment, and the polarization state only evolves with time; for non-uniformly polarized beams, as shown inFIG.1(b), the polarization states are different at different positions of the beam cross section. Spirally polarized beams (SPBs) as a kind of common non-uniformly polarized beams, the polarization states on the cross section are linearly polarized beams, and the angle of linearly polarized beams changes with the radial angle of the beam cross section. The Jones matrix of the SPBs of this embodiment is as follows:

ES⁢P⁢B⁢s(r)=r·exp⁡(-r2w02)·(cos⁢(θ+γ)sin⁢(θ+γ))(1)where (r,θ) is the polar coordinate axis of the beam cross section, ω0is the beam waist radius of the spot, and γ is a fixed angle, which determines the evolution angle of the linear polarization state of SPBs. When γ=0, the linear polarization distribution of the cross section of the SPBs grows along the radial direction, while when γ=π/2, the linear polarization distribution of the cross section of the SPBs grows along the tangential direction.FIG.4(a)shows the light intensity and Stokes parameter distribution of SPBs in formula (1), in which the S3parameter of SPBs is zero. Using the Stokes parameter of the beam cross section inFIG.4(a), the distribution of its polarization state on the Poincare sphere is obtained. As shown inFIG.4(b), the polarization states on the cross section of the SPBs are all at the equator of the Poincare sphere, indicating that the polarization states are composed of linearly polarized beams at various angles.

The polarization uniformity of the SPBs is calculated.FIG.2gives a flow chart. An embodiment of the present disclosure provides a method for measuring the polarization uniformity of non-uniformly totally polarized beams, which includes the following steps:

S101, a Stokes parameter distribution of the cross section of non-uniformly totally polarized beams is input.

In an embodiment, in practical application, the Stokes parameter distribution can be measured by a CCD camera. As the polarization states on the cross section of SPBs are linearly polarized, they are all distributed on the equator of the Poincare sphere, so S3in the Stokes parameters is always zero, as shown inFIG.4(a).

S102, the Stokes parameter distribution is calculated to correspond to the Poincare sphere.

In an embodiment, the normalized Stokes parameters can be calculated through the obtained Stokes parameter distribution, and the polarization state distribution of the beam cross section corresponds to the Poincare sphere, i.e.FIG.4(b).

S103, surface fitting is performed on the polarization state distribution on the Poincare sphere through a spatial triangle surface fitting algorithm (that is, an improved Delaunay triangulation algorithm), which, referring toFIG.3, specifically includes:

S1031, inputting polarization data points and setting a threshold value K.

S1032, separating the polarization data points according to the eight octants of the spatial rectangular coordinate system; dividing the data points on the Poincare sphere into eight octants for Delaunay fitting respectively, which can reduce the computational cost of the algorithm, that is, the number of fitted Delaunay triangles.

S1033, performing Delaunay triangulation algorithm fitting on the polarization state data point in each octant.

S1034, judging whether at least two sides of fitted Delaunay triangle are longer than the set threshold value K, if so, deleting the corresponding Delaunay triangle; by deleting, screening and eliminating Delaunay triangles whose side length is greater than the threshold value K, the polarization state mutation data caused by errors in Stokes parameter distribution measurement can be avoided, and the fitting error can be reduced.

S1035, describing the remaining Delaunay triangles after the above deletion on the Poincare sphere.

S104, calculating the sum SDof the areas of the fitted triangular surfaces; specifically, the sum SDof the areas of the fitted triangular surfaces is calculated by a Heron's formula, which specifically includes:

Calculating the area Siof the corresponding Delaunay triangle according to the lengths of three sides of the fitted triangle:

Si=pi(pi-ai)⁢(pi-bi)⁢(pi-ci)(2)where i is the serial number of the Delaunay triangle, and pi, ai, biand ciare respectively the half circumference and lengths of the three sides of the Delaunay triangle, so the total area of surface fitting is

SD=∑iSi.

S105, the SDis divided by the total area S0S of the unit Poincare sphere to obtain the polarization uniformity Ū of non-uniformly totally polarized beams.

In an embodiment,FIG.5(a)andFIG.5(b)respectively show the polarization uniformity measurement of spirally polarized beams within the eight octants of the Poincare sphere and the total fitting result. It can be seen fromFIG.5(a)that the polarization states of SPBs are all distributed near the equator of the upper hemisphere of the Poincare sphere, that is, the first to fourth octants. The Delaunay triangle fitting area SD=0.021, so the polarization uniformity of SPBs is:

US_=SDS0=0.0⁢2⁢14π=0.17%(3)

The polarization uniformity of SPBs is close to zero, which indicates that there are few types of polarization states on its cross section, only linearly polarized beams.

Further, the method also includes: performing mathematical statistics on the polarization state data points of non-uniformly totally polarized beams on the Poincare sphere to obtain the types and proportions of polarized beams existing on the beam cross section.

In an embodiment, the mathematical statistics of the polarization points on the Poincare sphere show that the proportion of linearly polarized beams is 100%, the proportion of right-handed elliptically polarized beams is 0, the proportion of left-handed elliptically polarized beams is 0, the proportion of right-handed circularly polarized beams is 0, and the proportion of left-handed circularly polarized beams is 0.

The embodiment of the present disclosure provides a use of a method for measuring the polarization uniformity of non-uniformly totally polarized beams for measuring the characteristics of non-uniformly totally polarized beams, and the method for measuring the polarization uniformity of non-uniformly totally polarized beams is the method described in the first aspect. The types and proportions of polarization states on the cross section can be obtained intuitively, which provides effective guidance for the use of SPBs.

Embodiment 2

In the present embodiment, the non-uniformly polarized beams LGBs superimposed by Laguerre and Gaussian mode fields is taken as an embodiment, and its Jones matrix is:

ELGBs(r)=E0·exp⁡(-r2w02)·(cos⁢(ϕ)2⁢rω0⁢ei⁢θ⁢sin⁡(ϕ))(4)where E0is a light field intensity and ϕ is a scale factor, which determines the proportions of the two modes in the beams. Refer toFIG.6(a)for the light intensity and Stokes parameter distribution diagram of LGBs when the beam waist of the spot of LGBs is ω0=1 mm, andFIG.6(b)for the polarization states distribution of the crosssection of LGBs on the Poincare sphere; refer toFIG.8(a)for the light intensity and Stokes parameter distribution of LGBs when the beam waist of the spot of LGBs is ω0=2 mm, andFIG.8(b)for the polarization states distribution of the cross section of LGBs on the Poincare sphere. By comparison, it can be seen that the polarization states of LGBs has no distribution near S1=−1 on the Poincare sphere, and there is a circular arc gap. With the increase of the beam waist of the spot, the gap range of the polarization states on the Poincare sphere also increases, that is, the types of the polarization states on the cross section of LGBs decrease.

This characteristic of LGBs can be quantitatively analyzed by using the polarization uniformity algorithm proposed in the present disclosure.FIGS.7(a) and9(a)show the fitting results within eight octants of the polarization uniformity algorithm under the radius of the above two beam waists of the spot, whileFIGS.7(b) and9(b)show the fitting total output and the calculation results of polarization uniformity under two conditions:

ULG_(ω0=1⁢mm)=SDS0=11.344⁢π=90.24%(5)ULG_(ω0=2⁢mm)=SDS0=9.924⁢π=78.96%(6)

The proportion of linearly polarized beams, right-handed elliptically polarized beams, left-handed elliptically polarized beams, right-handed circularly polarized beams and left-handed circularly polarized beams are 3.94%, 48.01%, 0.02% and 0.02%, respectively, when the beam waist of the spot of the LGBs is ω0=1 mm. The proportion of linearly polarized beams, right-handed elliptically polarized beams, left-handed elliptically polarized beams, right-handed circularly polarized beams and left-handed circularly polarized beams are 3.92%, 48.00%, 0.04% and 0.04%, respectively, when the beam waist of the spot of the LGBs is ω0=2 mm.

The fitting results show that with increasing the radius of the beam waist of LGBs, the corresponding polarization uniformity decreases, that is, the types of polarization states on the beam cross section decrease, but the content of each main polarization state does not change much. This embodiment provides a quantitative analysis method for measuring and distinguishing LGBs, non-uniformly polarized beams, with different radiuses of the beam waist, which can help better understand and apply Laguerre-Gaussian non-uniformly polarized beams.

Embodiment 3

The present embodiment takes the non-uniformly polarized beams, FPBs, whose polarization state covers the whole Poincare sphere as an embodiment. Different from the LGBs in Embodiment 2, FPBs are generated by superposition of Laguerre and Gaussian mode fields with orthogonal polarization states, and its Jones matrix is expressed as:

EFPBs(r)=E0·exp⁡(-r2w02)·(rω0⁢ei⁢θ⁢cos⁡(ϕ)(1-2⁢r2ω02)⁢sin⁡(ϕ))(7)

Referring toFIG.10(a)for the light intensity and Stokes parameter distribution of FPBs, andFIG.10(b)for the polarization state distribution of the cross section of FPBs on the Poincare sphere, it can be seen that polarization states of the cross section of FPBs are distributed on the whole Poincare sphere, that is, all polarization states are included.

The FPBs can be quantitatively analyzed by using the polarization uniformity algorithm proposed in the present disclosure.FIGS.11(a) and11(b)respectively show the fitting total output and the fitting results within eight octants of the polarization uniformity algorithm, and at the same time give the calculation results of polarization uniformity:

U¯F⁢P⁢B⁢s=SDS0=1⁢2.5⁢14π=9⁢9.5⁢5⁢%(8)

The calculation results show that for FPBs, the cross section thereof contains all polarization states, and on the Poincare sphere, the polarization points cover the whole sphere, so the polarization uniformity thereof is 100%, and the fitting output result is 99.55%. Therefore, the present embodiment can prove that the polarization uniformity and its algorithm proposed by the present disclosure are reasonable and correct.

Embodiment 4

The present embodiment provides a device for measuring the polarization uniformity of non-uniformly totally polarized beams. Referring toFIG.12, the device according to the present embodiment corresponds to Embodiment 1, and includes at least one processors and a memory configured to store programmable instructions executable by at least one processors, and the instructions are programmed as the following modules:

An input module10configured for inputting a Stokes parameter distribution of a cross section of non-uniformly totally polarized beams.

A first calculation module20configured for calculating the stoke parameter distribution to correspond to a Poincare sphere.

A fitting module30configured for performing surface fitting on a polarization state distribution on the Poincare sphere through a spatial triangle surface fitting algorithm.

A second calculation module40configured for calculating a sum SDof the areas of the fitted triangular surfaces.

A third calculation module50configured for dividing SDby a total area S0of the unit Poincare sphere to obtain the polarization uniformity Ū of non-uniformly totally polarized beams.

Further, the device also includes:

A statistic module configured for performing mathematically statistics on the polarization state data points of non-uniformly totally polarized beams on the Poincare sphere to obtain the types and proportions of polarized beams existing on the beam cross section.

Embodiment 5

The present embodiment provides an electronic equipment, including:

One or more processors;

A memory for storing one or more programs;

When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in Embodiment 1.

Embodiment 6

The present embodiment provides a computer readable storage medium on which a computer program is stored, when the program executed by a processor, implements the method according to Embodiment 1.

The above serial numbers of the embodiments of the present disclosure are for description only, and do not represent the advantages and disadvantages of the embodiments.

In the above embodiments of the present disclosure, the description of each embodiment has its own emphasis. For the parts not detailed in one embodiment, please refer to the related descriptions of other embodiments.

In the several embodiments provided in this application, it should be understood that the disclosed technical content can be realized by other ways. Among them, the above device embodiment is only schematic, for example, the division of the units may be a logical function division, and there may be other division modes in actual implementation, for example, multiple units or combinations may be combined or integrated into another system, or some features may be ignored or not executed. On the other hand, the shown or discussed mutual coupling or direct coupling or communication connection may be indirect coupling or communication connection through some interfaces, units or modules, which may be in electrical or other forms.

The units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place or distributed over multiple units. Some or all of the units can be selected according to the actual needs to achieve the purpose of the present embodiment.

In addition, each functional unit in each embodiment of the present disclosure may be integrated in one processing unit, each unit may exist physically alone, or two or more units may be integrated in one unit. The above-mentioned integrated units may be realized in the form of hardware or software functional units.

If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer readable storage medium. Based on this understanding, the technical solution of the present disclosure, which essentially contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions to make a computer device (such as a personal computer, a server or a network device, etc.) perform all or part of the steps of the methods described in various embodiments of the present disclosure. The aforementioned storage media include: U disk, Read-Only Memory (ROM), Random Access Memory (RAM), removable hard disk, magnetic disk or optical disk and other media that can store program codes.

The above are only the preferred embodiments of the present disclosure, and it should be pointed out that for those of ordinary skill in the technical field, without departing from the principle of the present disclosure, several improvements and embellishments can be made, and these improvements and embellishments should also be regarded as the protection scope of the present disclosure.