An ultra-thin planar geometric phase polymer liquid crystal wave plate for generating arbitrary vector light field and a light field complex amplitude modulation method

Abstract

The present invention discloses an ultra-thin planar geometric phase polymer liquid crystal wave plate and a light field complex amplitude modulation method for generating arbitrary vector light fields, and relates to the technical fields of optics and micro-nano photonics. The technical points of the present invention include: constructing an intensity mask and a phase mask as the front and back surfaces of the polymer liquid crystal wave plate, respectively, and performing intensity modulation and phase modulation functions on the front and back surfaces respectively: calculating the blazed grating phase depth distribution function according to the target light field amplitude distribution function, and superimposing this function on the blazed grating to obtain the intensity mask; extracting the target phase distribution from the target light field spatial complex amplitude, translating it into the optical axis orientation distribution of the polymer liquid crystal, and obtaining the phase mask. The polymer liquid crystal wave plate with spatial complex amplitude modulation capability proposed by the present invention has the characteristics of low cost, easy integration, small size, light weight, greatly shortened optical path, and can precisely control the spatial amplitude and phase of the light field to generate arbitrary vector light fields.

Description

Technical Field

[0001] The present invention relates to the technical field of optics and micro-nano photonics, and in particular to an ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field and a light field complex amplitude modulation method. Background Art

[0002] Vector light fields are paraxial light fields characterized by spatially uneven distributions of polarization, amplitude, and phase. The entanglement between the polarization and spatial mode degrees of freedom makes their in-depth study valuable for practical applications. Generally speaking, generating vector light fields requires independent modulation of the field's spatial complex amplitude—that is, its amplitude and phase.

[0003] There are two main technical approaches for generating vector light fields. The first is to utilize the spatial complex amplitude modulation function of a spatial light modulator (SLM) to modulate two orthogonally polarized beams separately, ultimately obtaining an arbitrary target vector light field at the output of the constructed interferometer. For example, the technical principle demonstrated in "Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement," published in Optics Letters, Vol. 32, No. 24, 2007. However, this approach requires an active spatial light modulator (SLM), which is expensive and cannot achieve a compact, easily integrated optical structure. Furthermore, SLMs are susceptible to external influences and are prone to fluctuations in actual optical paths. Another approach utilizes binary optical elements based on the principle of geometric phase, namely spatially variable orientation wave plates fabricated using spatially variable orientation liquid crystal (LC) or dielectric metasurface technology. These elements can impart a spatial geometric phase (i.e., optical spin-orbit coupling) that is dependent on the chirality of the optical polarization. This principle is described in the paper "Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media," published in Physical Review Letters, Vol. 96, No. 16, 2006. Although this approach implements transmissive or reflective binary optical elements, it only provides pure phase modulation and cannot achieve precise spatial complex amplitude control, significantly limiting its application. Summary of the Invention

[0004] To this end, the present invention proposes an ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field and a light field complex amplitude modulation method, in an effort to solve or at least alleviate at least one of the above problems.

[0005] According to one aspect of the present invention, an ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field is proposed. The front surface mask of the liquid crystal wave plate is designed according to the following design process:

[0006] Extracting two-dimensional distribution information of amplitude space from the spatial complex amplitude of the target light field;

[0007] Calculate and obtain the blazed grating phase depth distribution function according to the amplitude spatial two-dimensional distribution information;

[0008] The blazed grating phase depth distribution function is superimposed on the blazed grating structure to obtain the light intensity information corresponding to the target light field generated in the 0th order diffraction direction, so as to obtain a front surface intensity mask capable of achieving intensity modulation;

[0009] The rear surface mask of the liquid crystal wave plate is designed according to the following design process:

[0010] Extracting two-dimensional distribution information of phase space from the spatial complex amplitude of the target light field;

[0011] The required optical axis orientation spatial distribution function is calculated based on the two-dimensional distribution information of the phase space of the target light field, so as to obtain a rear surface phase mask that can realize phase modulation.

[0012] Furthermore, the calculation formula for the blazed grating phase depth distribution function calculated based on the amplitude spatial two-dimensional distribution information is:

[0013]

[0014] Where A(x, y) represents the amplitude distribution function of the target light field; A in (x, y) represents the spatial amplitude distribution function of the incident light field.

[0015] Furthermore, the calculation formula for obtaining the required optical axis orientation spatial distribution function is calculated based on the two-dimensional distribution information of the phase space of the target light field:

[0016]

[0017] Where β(x, y) represents the desired optical axis orientation spatial distribution function; α(x, y) represents the phase distribution function of the target light field.

[0018] Furthermore, the front and rear surface masks of the liquid crystal wave plate respectively include multiple areas corresponding to target light fields of different modes, so as to simultaneously realize complex amplitude modulation of different vector light fields when multiple beams of light simultaneously enter the liquid crystal wave plate.

[0019] Furthermore, the target light fields of different modes include: Ince-Gaussian beam, Hermite-Gaussian beam, Laguerre-Gaussian beam, Airy beam, and Bessel beam.

[0020] Furthermore, the polarization state of the incident light field incident on the liquid crystal wave plate is linear polarization.

[0021] According to another aspect of the present invention, a light field complex amplitude modulation method is proposed, wherein the method utilizes the ultra-thin planar geometric phase polymer liquid crystal wave plate described above to achieve complex amplitude modulation of light fields with different target vectors.

[0022] The beneficial technical effects of the present invention are:

[0023] Compared with the existing technology, the polymer liquid crystal wave plate with spatial complex amplitude modulation capability proposed in the present invention has the following significant advantages: low cost (no spatial light modulator is required), simple production, easy integration, small size (25.4mm in diameter), light weight (about a few grams), greatly shortened optical path, and can be easily installed on the surface of other optical components. It can precisely control the spatial amplitude and phase of the light field to produce arbitrary vector light fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily apparent by reading the following detailed description with reference to the accompanying drawings, in which several embodiments of the present invention are shown by way of example and not limitation, in which:

[0025] Figure 1 This is a schematic diagram of the design of an ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field according to an embodiment of the present invention.

[0026] Figure 2 Schematic diagram of the optical path of the polymer liquid crystal wave plate in an embodiment of the present invention.

[0027] Figure 3 This is another design schematic diagram of an ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field according to an embodiment of the present invention. DETAILED DESCRIPTION

[0028] The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are provided solely to enable those skilled in the art to better understand and implement the present invention, and are not intended to limit the scope of the present invention in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of the present disclosure to those skilled in the art.

[0029] The present invention is based on polymer liquid crystal materials and proposes a lightweight, small and inexpensive ultra-thin planar geometric phase polymer liquid crystal wave plate with complete spatial complex amplitude (i.e. phase and amplitude) precision modulation capability.

[0030] The polymer liquid crystal wave plate device, capable of complete spatial complex amplitude precision modulation, is divided into two parts: an intensity mask and a phase mask are constructed as the front and back surfaces of the polymer liquid crystal, respectively, to perform intensity modulation and phase modulation functions on the front and back surfaces, respectively. The first part calculates the blazed grating phase depth distribution function based on the target light field amplitude distribution function, superimposes this function on the blazed grating to obtain an intensity mask, and then exposes this intensity mask design to the front surface of the polymer liquid crystal to achieve intensity modulation. The second part extracts the target phase distribution from the target light field spatial complex amplitude, translates it into the optical axis orientation distribution of the polymer liquid crystal, and obtains a phase mask. This phase mask is then exposed to the back surface of the polymer liquid crystal to achieve phase modulation.

[0031] In actual operation, the polarization state of the incident light is fixed to linear polarization. When linearly polarized light is incident on the front surface of the polymer liquid crystal wave plate, the intensity distribution of the target light field will appear in the 0th order diffraction direction of the grating (±1 orders are circular polarization states, and the 0th order polarization state is the same as the incident polarization state. That is, the front surface of the polymer liquid crystal achieves intensity modulation without changing the polarization of the incident light). Then, the polarization-independent light spot passes through the back surface of the polymer liquid crystal, realizing the pure phase modulation function and obtaining the spatial phase distribution of the target light field. At this point, the entire complex amplitude modulation function is completed. Since the element is purely transmissive, the propagation direction of the target light beam will not change.

[0032] In the prior art, since the scalar light fields with orthogonal polarization states and orthogonal spatial modes generated at the ±1 levels are not vectors, a liquid crystal polarization grating must be used to combine the beams again to obtain a vector light field. However, in the present invention, the linear polarization state is incident on the 0th order diffraction direction to directly obtain an intensity modulated light spot with the same polarization as the incident polarization (linear polarization), realizing polarization-independent intensity modulation; phase modulation is then performed on the rear surface of the liquid crystal to directly obtain a vector light field, eliminating the previous complicated work of building a long optical path.

[0033] An embodiment of the present invention provides an ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field. The front surface mask of the liquid crystal wave plate is designed according to the following design process:

[0034] Extracting two-dimensional distribution information of amplitude space from the spatial complex amplitude of the target light field;

[0035] Calculate and obtain the blazed grating phase depth distribution function according to the amplitude spatial two-dimensional distribution information;

[0036] The blazed grating phase depth distribution function is superimposed on the blazed grating structure to obtain the light intensity information corresponding to the target light field generated in the 0th order diffraction direction, so as to obtain a front surface intensity mask capable of achieving intensity modulation;

[0037] The rear surface mask of the liquid crystal wave plate is designed according to the following design process:

[0038] Extracting two-dimensional distribution information of phase space from the spatial complex amplitude of the target light field;

[0039] The required optical axis orientation spatial distribution function is calculated based on the two-dimensional distribution information of the phase space of the target light field, so as to obtain a rear surface phase mask that can realize phase modulation.

[0040] The following is based on polymer liquid crystal wave plate material and uses Laguerre-Gaussian beam mode (LG 3,1 ) The cylindrical vector light field as the OAM carrier is the target light field, and the embodiments of the present invention are described in detail.

[0041] First, the spatial complex amplitude of the target light field is expressed as the product of the amplitude A(x, y) and the phase distribution φ(x, y), that is,

[0042] ψ CV (x,y)=A(x,y)exp[iφ(x,y)] (1)

[0043] According to the target light field shown in formula (1), the reverse design is performed: To achieve spatial intensity modulation, the blazed grating phase depth distribution function M(x, y)∈|0, 1] is calculated according to the target light field amplitude distribution function A(x, y), that is:

[0044]

[0045] Where A in (x, y) is the spatial amplitude distribution of the incident light field (Gaussian distribution in this example).

[0046] By superimposing the function M(x,y) on the blazed grating structure, the light intensity information required to generate the target beam in the 0th order diffraction direction can be obtained, and the intensity mask can be obtained.

[0047] Then, the phase distribution φ(x, y) of the target light field is extracted from the spatial complex amplitude information and used as the target light field geometric phase spatial distribution α(x, y). According to the geometric phase principle of polymer liquid crystal, the relationship between the required optical axis orientation spatial distribution function β(x, y) and the phase distribution function α(x, y) of the target light field is obtained:

[0048]

[0049] Figure 1(a) shows the spatial distribution of the optical axis orientation on the front surface of the designed liquid crystal polymer wave plate, and (b) shows the spatial distribution of the optical axis orientation on the back surface of the designed polymer liquid crystal. Complex amplitude modulation is performed on the front and back surfaces to achieve the modulation of the target vector light field. The optical path diagram in actual use is shown in the figure below. Figure 2 shown.

[0050] Furthermore, the front and rear surface masks of the liquid crystal wave plate respectively include multiple areas corresponding to target light fields of different modes, so as to simultaneously realize complex amplitude modulation of different vector light fields when multiple beams of light simultaneously enter the liquid crystal wave plate.

[0051] As an example, the size of the polymer liquid crystal wave plate is a circle with a diameter of 25.4 mm. Multiple modes of vector light fields can be generated simultaneously in different regions on the same polymer liquid crystal wave plate. For example, it can also realize, but not limited to, Ince-Gaussian beam (IG), Hermite-Gaussian beam (HG), Laguerre-Gaussian beam (LG), Airy beam, Bessel beam, etc. A beam splitter is added in front of the liquid crystal polymer wave plate to split the incident light into multiple beams. For example, it can be a non-polarizing beam splitter (NPBS), such as Figure 3 As shown, 9 areas are exposed on the glass substrate of the same polymer liquid crystal wave plate. Figure 3 The area within the dotted box on the right side of the center shows that 9 different vector light modes and orders can be generated.

[0052] Another embodiment of the present invention further provides a light field complex amplitude modulation method, which utilizes the ultra-thin planar geometric phase polymer liquid crystal wave plate described above to achieve complex amplitude modulation of different target vector light fields.

[0053] Although the spirit and principles of the present invention have been described with reference to several specific embodiments, it should be understood that the present invention is not limited to the specific embodiments disclosed, and the division into various aspects does not mean that the features of these aspects cannot be combined to benefit. Such division is only for the convenience of expression. The present invention is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. An ultrathin planar geometric phase polymer liquid crystal wave plate for generating arbitrary vector light fields, characterized by: The front surface mask of the liquid crystal wave plate is designed according to the following design process: Extracting two-dimensional distribution information of amplitude space from the spatial complex amplitude of the target light field; Calculate and obtain the blazed grating phase depth distribution function according to the amplitude spatial two-dimensional distribution information; The blazed grating phase depth distribution function is superimposed on the blazed grating structure to obtain the light intensity information corresponding to the target light field generated in the 0th order diffraction direction, so as to obtain a front surface intensity mask capable of achieving intensity modulation; The rear surface mask of the liquid crystal wave plate is designed according to the following design process: Extracting two-dimensional distribution information of phase space from the spatial complex amplitude of the target light field; The required optical axis orientation spatial distribution function is calculated based on the two-dimensional distribution information of the phase space of the target light field to obtain a rear surface phase mask that can realize phase modulation; Wherein, the polarization state of the incident light field incident on the liquid crystal wave plate is linear polarization.

2. The ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field according to claim 1, characterized in that: The calculation formula for the blazed grating phase depth distribution function calculated based on the amplitude spatial two-dimensional distribution information is: Where A(x, y) represents the amplitude distribution function of the target light field; A in (x, y) represents the spatial amplitude distribution function of the incident light field.

3. The ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field according to claim 1, characterized in that: The calculation formula for the required optical axis orientation spatial distribution function is calculated based on the two-dimensional distribution information of the phase space of the target light field: Where β(x,y) represents the desired spatial distribution function of the optical axis orientation; α(x,y) represents the phase distribution function of the target light field.

4. An ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field according to any one of claims 1 to 3, characterized in that: The front and rear surface masks of the liquid crystal wave plate respectively include multiple areas corresponding to target light fields of different modes, so as to simultaneously realize complex amplitude modulation of different vector light fields when multiple beams of light simultaneously enter the liquid crystal wave plate.

5. The ultra-thin planar geometric phase polymer liquid crystal wave plate for generating an arbitrary vector light field according to claim 4, characterized in that: The target light fields of different modes include: Ince-Gaussian beam, Hermite-Gaussian beam, Laguerre-Gaussian beam, Airy beam, and Bessel beam.

6. A light field complex amplitude modulation method, characterized in that: The ultra-thin planar geometric phase polymer liquid crystal wave plate according to any one of claims 1 to 5 is used to realize complex amplitude modulation of different target vector light fields.

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