A method for generating partially coherent full Poincare beams

Abstract

The present invention discloses a method for generating a partially coherent full Poincare beam. By introducing a twisted phase and regulating the initial parameters on the beam source plane, when the twist factor is under certain conditions, the full Poincare beam can be expanded to a more general partially coherent field, so that the beam always maintains complete polarization during transmission along the optical axis, and all polarization states of the beam are retained and cover the entire surface of the Poincare sphere, that is, all possible polarization states are included in the beam cross section. The present invention introduces relevant parameters such as coherence parameters and twisted phase, which can be used to modulate the rigid rotation speed and far-field spot size of the Poincare sphere, and has important applications in polarization detection, Mueller matrix polarization measurement, flat-top beam shaping, etc.

Description

Technical Field

[0001] The invention relates to a light field control technology, in particular to a method for generating a partially coherent full Poincare light beam. Background Art

[0002] In recent years, beams with spatially non-uniform polarization states have received particular attention, such as cylindrical vector beams (e.g., radially or azimuthally polarized beams). Typically, the polarization state of a fully polarized beam can be intuitively described on the Poincare sphere. For example, the polarization state of a spatially uniformly polarized beam can be uniquely visualized as a point on the Poincare sphere. As a high-order solution of Maxwell's vector wave equations, the polarization state of a cylindrical vector beam spans the equator of the Poincare sphere surface. Recently, Brown et al. theoretically and experimentally introduced a special class of so-called fully Poincare beams, which can be constructed by coaxial superposition of orthogonally polarized Gaussian beams and Laguerre-Gaussian beams, and whose polarization is mapped to the entire surface of the Poincare sphere, that is, the beam cross section contains all possibilities of polarization states, and the propagation corresponds to a rigid rotation of the sphere.

[0003] Full Poincare beams have many applications in light trapping, Mueller matrix polarimetry, second harmonic generation, and optical communications. Meanwhile, subsequent studies have also considered partial polarization and proposed a new class of light fields whose polarization content in any transverse plane spans a disk-like region within the Poincare sphere. However, as a more general case, the generation of full Poincare beams in the partially coherent domain remains an open challenge. For example, similar to the coherent case, the direct coaxial superposition of a partially coherent Gaussian beam and a partially coherent vortex-phase Laguerre-Gaussian beam with orthogonal polarizations will inevitably lead to correlation-induced depolarization effects during propagation, even in free space. Therefore, how to introduce a conservative full Poincare beam in the partially coherent domain without depolarization is a problem worthy of in-depth study. Summary of the invention

[0004] The object of the present invention is to provide a method for generating a partially coherent full Poincare beam, and to accurately control the polarization state and the spot of the beam at the source plane and the far field position.

[0005] The technical solution to achieve the purpose of the present invention is as follows: In the first aspect, the present invention provides a method for generating a partially coherent full Poincare beam, by introducing a twisted phase and adjusting the initial parameters on the beam source plane, so that the beam always remains fully polarized during transmission along the optical axis, and all polarization states of the beam are retained and cover the entire surface of the Poincare sphere; the correlation characteristics of such a beam on the source plane are:

[0006]

[0007] where g αβ(r1, r2) characterizes the correlation characteristics between the α and β polarization directions, r1 = (x1, y1) and r2 = (x2, y2) represent the position vectors on the source plane, δ0 represents the beam coherence parameter, k represents the beam wave number, and μ represents the twist factor; the exponential term exp[-ikμ(x1y2-y1x2)] is the introduced twist phase, and by regulating the twist factor, a fully polarized partially coherent full Poincare beam is generated during the transmission process.

[0008] The beam satisfies the constraints on the twist factor in a partially coherent twisted beam And take the minimum value of the distortion factor When the beam is partially coherent, it generates a fully Poincare beam. During the lens focusing process or free space transmission process, the beam cross section always contains all possible polarization states, and the propagation corresponds to the rigid rotation of the sphere. The size and sign of the distortion factor μ can regulate the rotation speed and direction of the beam and polarization state during the transmission process. The size of the coherence length δ0 will affect the coherence distribution and the size of the spot during the lens focusing process or free space transmission process.

[0009] The weight function required to construct the target beam and kernel function H α (r, v):

[0010]

[0011]

[0012] Where r = (x, y) represents the position vector on the source plane, v is a unitless vector without dimension restriction, and a is an arbitrarily chosen positive parameter. Indicates the electric field strength U α The square root of (r), σ0 represents the beam waist width at the beam source plane, l α represents the topological charge in the α polarization direction, and ε is the antisymmetric matrix Equal to tan -1 (y / x), B αβ =|B αβ |exp(iφ αβ ) is the Cartesian component of the fluctuating electric field vector and the constant phase difference φ αβ The correlation coefficient between .

[0013] The cross spectral density matrix element expression of the modulated beam is:

[0014]

[0015] in Indicates the electric field strength U α The square root of (r), Indicates the electric field strength U β The square root of (r), l α represents the topological charge in the α polarization direction, l β represents the topological charge in the β polarization direction, Equal to tan -1 (y j / x j ), j = 1, 2, the coherence length in the correlation characteristics on the target beam source plane a is an arbitrarily chosen positive parameter, and the correlation coefficient B αβ Satisfy condition B xx =B yy =B xy =B yx =1.

[0016] In a second aspect, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method described in the first aspect when executing the program.

[0017] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0018] In a fourth aspect, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: by introducing the well-known twisted phase, the present invention successfully eliminates the correlation-induced polarization change and derives a class of partially coherent full Poincare beams that propagate unchanged under specific parameter conditions. Similar to the coherent full Poincare beam, all polarization states of the beam are retained and cover the entire surface of the Poincare sphere, and the propagation corresponds to the rigid rotation of the sphere. The beam waist width σ0 can accurately control the spot size, the size and sign of the twist factor μ can control the rotation speed and direction of the polarization state of the beam during the transmission process, and the size of the coherence length δ0 will affect the coherence distribution and spot size of the beam during the lens focusing process or free space transmission process. Controlling the topological charge l x and l y The spectral intensity and polarization state of partially coherent light beams can be controlled, which provides more means for vector light beams in laser shaping, laser manipulation, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is the normalized intensity and polarization state distribution of the partially coherent full Poincare beam at different coherence lengths δ0 during the focusing process.

[0021] Figure 2 is the difference in topological charge between the partially coherent fully Poincare beam and the beam during focusing. y Normalized intensity and polarization state distribution under .

[0022] Figure 3 The partially coherent full Poincare beam changes its topological charge during the focusing process. x and l y Normalized intensity and polarization state distribution under . DETAILED DESCRIPTION

[0023] The present invention proposes a method for generating a partially coherent full Poincare beam, which utilizes the characteristics of the introduced twisted phase to resist depolarization and the sufficient conditions for synthesizing the cross-spectral density matrix of the partially coherent vector beam to generate a polarization state covering the entire surface of the Poincare sphere that will never degenerate during the lens focusing process or the free space transmission process, and the propagation corresponds to the rigid rotation of the sphere.

[0024] In the actual process of synthesizing such partially coherent full Poincare beams, different types of full Poincare beams can be generated by coaxially superposing two orthogonally polarized Laguerre-Gaussian beams of different orders, and then the phase modulation is performed by loading the correlation structure onto a spatial light modulator, and then a partially coherent full Poincare beam with a twisted phase can be obtained through a filtering system. In the embodiment, the sufficient conditions for partially coherent vector beams that are physically realizable are:

[0025]

[0026] where p αβ (v) is the weighting matrix The non-negative elements of need to satisfy the non-negative condition p αβ (v)≥0, H α (r2, v) and is H β (r2, v) are arbitrary square integrable kernel functions in the α and β polarization directions respectively.

[0027] First, the non-negative weight function of the partially coherent full Poincare beam is constructed, and its expression can be expressed as:

[0028]

[0029] Where v = (v x , v y ), is a unitless vector with no dimension restriction, and a is a positive parameter.

[0030] The kernel function of the partially coherent full Poincare beam is set as:

[0031]

[0032] where ε is an antisymmetric matrix.

[0033] The expression of the cross-spectral density matrix element of the partially coherent vector light field generated by the weight and the transmission kernel function on the source plane is:

[0034]

[0035] where r i =(x i ,y i ), and The electric field strength U x (r) and U y The square root of (r). αβ =|B αβ |exp(iφ αβ ) is the Cartesian component of the fluctuating electric field vector and the constant phase difference φ αβ The correlation coefficient between them. σ0 and δ0 represent the lateral beam width and lateral coherence parameter, respectively. The exponential term represents the vortex phase, where l α represents the topological charge in the α polarization direction, Equal to tan -1 (y i / x i ), μ represents the scalar real distortion factor, k = 2π / λ and λ is the wavelength. a is an arbitrarily chosen positive parameter.

[0036] The study of the spectral intensity transmission characteristics of partially coherent vector light fields mainly relies on the generalized Collins formula. The cross-spectral density matrix element can be given by the following integral expression after being transmitted through the ABCD optical system:

[0037]

[0038] Where W αβ (r1, r2) represents the cross-spectral density matrix element at the source plane, A, B, C, D are the corresponding elements of the optical system transmission matrix, ρ1, ρ2 represent the two position vectors on the plane after transmission through the ABCD optical system. The intensity distribution of the light beam during the transmission process of the ABCD optical system can be numerically calculated by equation (5).

[0039] The polarization state of partially coherent vector light fields can be characterized by polarization ellipse, which mainly includes four basic parameters, namely the major semi-axis A1, the minor semi-axis A2, the ellipticity ε and the orientation angle θ of the polarization ellipse:

[0040]

[0041]

[0042]

[0043] In formula (6), "+" indicates the major semi-axis A1, and "-" indicates the minor semi-axis A2. The polarization state distribution of the light beam during the transmission process of the ABCD optical system can be numerically calculated by formulas (6)-(8).

[0044] The core of the present invention is to propose a class of partially coherent full Poincare beams, which successfully eliminate the correlation-induced polarization changes by introducing twisted phases. During the propagation process, all polarization states of the beam are retained and cover the entire surface of the Poincare sphere, and the propagation corresponds to the rigid rotation of the sphere. In addition, the introduction of relevant parameters such as coherence parameters and twisted phases can be used to modulate the rigid rotation speed and far-field spot size of the Poincare sphere.

[0045] The present invention is described in detail below with reference to the embodiments.

[0046] Example

[0047] In this embodiment, the parameters are: k = 2π / λ, λ = 632.8 nm, σ0 = 1 mm, f = 400 mm, |B xy |=1,φ xy =0,

[0048] Figure 1 The normalized intensity and polarization state distribution of the partially coherent full Poincare beam at different focusing positions under the coherence length δ0→∞ and δ0=0.5mm. It can be seen that the polarization state of the beam always covers the entire surface of the Poincare sphere, and the rotation speed of the polarization state is different for different coherence lengths. The white (black) ellipsoid represents left-handed elliptical polarization (right-handed elliptical polarization). Figure 2 is the topological charge y =2, l y =3The normalized intensity and polarization state distribution of the partially coherent full Poincare beam at different focusing positions in the two cases. It can be seen that the topological charge l y The polarization state distribution can be precisely controlled. y =n, the polarization state distribution of the beam cross section will pass through the Poincare sphere surface n times. Figure 3 The partially coherent full Poincare beam changes its topological charge during the focusing process. x and l y The normalized intensity and polarization state distribution under the condition of light intensity distribution and polarization state can be controlled by changing the topological charge in two directions.

[0049] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field of the present invention, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the scope of protection of the present invention.

Claims

1. A method for generating a partially coherent full Poincare beam, characterized in that: By introducing a twisted phase and adjusting the initial parameters on the beam source plane, the beam is always fully polarized during transmission along the optical axis. All polarization states of the beam are retained and cover the entire surface of the Poincare sphere. The correlation characteristics of such a beam on the source plane are: where g αβ (r1, r2) represents the correlation between the α and β polarization directions, r1 = (x1, y1) and r2 = (x2, y2) represent the position vectors on the source plane, δ0 represents the coherence length, k represents the beam wave number, and μ represents the distortion factor; the exponential term exp[-ikμ(x1y2-y1x2)] is the introduced distortion phase. By regulating the distortion factor, a fully polarized partially coherent full Poincaré beam is generated during the transmission process; The beam satisfies the constraints on the twist factor in a partially coherent twisted beam And take the minimum value of the distortion factor A partially coherent full Poincare beam is generated. During the lens focusing process or free space transmission process, the beam cross section always contains all possible polarization states, and the propagation corresponds to the rigid rotation of the sphere. The size and sign of the distortion factor μ can regulate the rotation speed and direction of the beam and polarization state during the transmission process.

2. The method for generating a partially coherent full Poincare beam according to claim 1, characterized in that: The weight function required to construct the target beam and kernel function H α (r,v): Where r = (x, y) represents the position vector on the source plane, v is a unitless vector without dimension restriction, and a is an arbitrarily chosen positive parameter. Indicates the electric field strength U α The square root of (r), σ0 represents the beam waist width at the beam source plane, l α represents the topological charge in the α polarization direction, and ε is the antisymmetric matrix Equal to tan -1 (y / x), B αβ =|B αβ |exp(iφ αβ ) is the Cartesian component of the fluctuating electric field vector and the constant phase difference φ αβ The correlation coefficient between .

3. The method for generating a partially coherent full Poincare beam according to claim 2, characterized in that: The cross spectral density matrix element expression of the modulated beam is: in Indicates the electric field strength U α The square root of (r), Indicates the electric field strength U β The square root of (r), l α represents the topological charge in the α polarization direction, l β represents the topological charge in the β polarization direction, Equal to tan -1 (y j / x j ),j=1,2, the coherence length in the correlation characteristics on the target beam source plane Correlation coefficient B αβ Satisfy condition B xx =B yy =B xy =B yx =1.

4. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method according to any one of claims 1 to 3 are implemented.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

6. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method described in any one of claims 1 to 3 are realized.

Images