CN112505935A

CN112505935A - Hermite-Gaussian mode beam splitter based on single polarization modulation device

Info

Publication number: CN112505935A
Application number: CN202011264449.0A
Authority: CN
Inventors: 张沛; 刘青; 贾俊亮
Original assignee: Xian Jiaotong University
Current assignee: Xian Jiaotong University
Priority date: 2020-11-12
Filing date: 2020-11-12
Publication date: 2021-03-16

Abstract

The invention discloses a Hermite-Gaussian mode beam splitter based on a single polarization modulator, which comprises a single polarization phase converter and a common-path polarization interference system, wherein the common-path polarization interference system comprises the following components: the single polarization phase converter consists of two single polarization cylindrical lenses, which phase modulate only one of the orthogonal polarization states. The two single-polarization cylindrical lenses are opposite in plane and coaxially arranged, the state of the curved surface of the lens can be divided into a horizontal arrangement mode and a vertical arrangement mode, and the distance between the lenses meets the requirement that d is 2sin (theta/2) f; the common-path polarization interference system uses two orthogonal polarization substrates to replace two paths of a traditional interferometer, and uses polarization projection to replace path beam combination at an outlet. The phase value and the arrangement mode of the single-polarization phase converter are changed, so that a phase difference directly related to horizontal or vertical parameters of a Hermite-Gaussian mode is generated between the two polarization components, different input modes finally appear from different channels by means of a common-path polarization interference system, and the purpose of distinguishing the HG modes is achieved.

Description

Hermite-Gaussian mode beam splitter based on single polarization modulation device

Technical Field

The invention belongs to the technical field of optics, and particularly relates to a Hermite-Gaussian mode beam splitter based on a single polarization modulator.

Background

The Hermite-Gaussian (HG) mode and the Laguerre-Gaussian (LG) mode are two laser transverse modes which are widely applied in the field of optical technology, but in practice, in order to use the Hermite-Gaussian (HG) mode and the Laguerre-Gaussian (LG) mode for research, the Hermite-Gaussian (HG) mode and the Laguerre-Gaussian (LG) mode have to have the capability of effectively distinguishing different modes of. To achieve this, researchers have begun to construct a wide variety of such devices, i.e., mode splitters. At present, the technology of the LG mode beam splitter is mature, but research results of the HG mode beam splitter are still few.

The existing distinction work of the HG modes is mainly of two types, the first type is a scheme based on a path interferometer such as a Mach-Zehnder interferometer, and the practicability and stability of the interferometer in the method greatly limit the number of the HG modes which can be distinguished and the experimental quality. The other scheme is still not mature, the basic principle is to convert the HG light into the LG light, and then the purpose of splitting the light is achieved by combining the LG mode distinguishing method, so that the HG mode beam splitter is complex and complicated in structure and not practical. To date, there is no beam splitter that is directly perfectly suited for HG mode. Therefore, it is very interesting to establish a highly efficient and stable splitter, and a low cross talk split HG mode.

Disclosure of Invention

The invention aims to provide a Hermite-Gaussian mode beam splitter based on a single polarization modulation device.

The invention is realized by adopting the following technical scheme:

a Hermite-Gaussian mode beam splitter based on a single polarization modulation device comprises a single polarization phase converter and a common-path polarization interference system; the single-polarization phase converter consists of two single-polarization cylindrical lenses, has the phase modulation effect of the cylindrical lenses on one of two orthogonal polarization states, has no effect on the other, and is divided into a horizontal placing mode and a vertical placing mode according to the state of a lens curved surface; the two single-polarization cylindrical lenses are opposite in plane and coaxially arranged, and the distance d between the two single-polarization cylindrical lenses meets the condition that d is 2sin (theta/2) f, wherein theta is a phase value introduced by the phase converter between the two polarization components, the value range is [0, pi ], and f is the focal length of the single-polarization cylindrical lens;

the common-path polarization interference system utilizes two orthogonal polarization substrates of horizontal polarization and vertical polarization or left-hand circular polarization and right-hand circular polarization to replace two paths of a traditional interferometer, and polarization projection is used for replacing an inherent path to combine beams at an outlet, so that a compact and robust interferometer is built.

A further improvement of the invention is that the two orthogonal polarization states are horizontally and vertically polarized.

A further improvement of the invention is that the two orthogonal polarization states are left-hand circular polarization and right-hand circular polarization.

A further improvement of the present invention is that the basic principle of the HG mode splitter is: making incident HG light comprise two orthogonal polarization substrates, wherein one polarization component is modulated by a phase converter, and the other polarization component is recombined into a new polarization state at the outlet of the common-path polarization interference system without passing through the phase converter; when the phase converter is in a horizontal arrangement mode, the introduced phase value is (m +1/2) theta after the HG modes with different horizontal mode parameter m values pass, namely, the phase difference related to the horizontal parameter m is introduced between the two polarization components; when theta is equal to pi, the geometric phase difference between the two polarization components is adjusted, so that the mode parameter m is an even or odd HG mode, the total phase difference between the two polarizations is respectively changed into pi or 2 pi, and finally the two polarizations are separated into different channels, so that the Hermite-Gaussian mode beam splitting effect with different level parameter m values is realized; similarly, when the phase converter is changed into a vertical arrangement mode, the HG modes with different vertical parameter n values are distinguished.

The invention is further improved in that different phase differences directly related to the horizontal parameter m or the vertical parameter n of the Hermite-Gaussian mode are correspondingly generated between the two polarization components by changing the phase value introduced by the phase converter and the arrangement mode of the two cylindrical lenses, and then the input mode finally appears in different channels by virtue of the common-path polarization interference system, so that the purpose of distinguishing the HG modes is realized.

The invention is further improved in that a relative phase difference Delta theta of pi is introduced between two modes to be distinguished, and then the two modes are separated into different outlets based on a common-path polarization interference system, wherein

Δθ＝(m₂+1/2)θ-(m₁+1/2)θ＝Δm·θ。

In addition, the cascade multi-stage beam splitter can achieve the purpose of distinguishing any HG modes by reasonably designing the arrangement mode of the single-polarization phase converters in each stage and the numerical value of the phase difference theta.

Compared with the prior art, the invention has at least the following beneficial technical effects:

the hermitian-gaussian mode has two characteristic parameters m and n, corresponding to two orthogonal directions (horizontal for m, vertical for n), respectively. In the intensity distribution, the number of the bright spots in each row in the horizontal direction is equal to m +1, and the number of the bright spots in each column in the vertical direction is equal to n + 1. Correspondingly, by studying the mathematical expression form of the HG mode, it is found that mode splitting can be achieved by the correlation of its mode parameters with the Gouy phase. The HG mode beam splitter provided by the invention can be summarized as follows: two orthogonal polarization substrates of incident light are taken to replace two propagation paths in a traditional interferometer, and the core of the scheme is to use a proper single-polarization modulation device to introduce a Gouy phase in a single polarization, which is similar to the single-path modulation of the interferometer. When HG modes with different mode parameters pass, different phase differences related to the parameters are introduced between two arms of the interferometer, and polarization projection is used for replacing path beam combination at an outlet, so that the polarization beam combination appears in different channels, and a novel common-path polarization interference system independent of the path beam combination and the path beam combination is realized, thereby realizing mode differentiation. In summary, the present invention has the following advantages:

1. the method is used for distinguishing the HG modes, and no mode conversion process occurs in the whole process;

2. the method is based on parameters m and n in the HG mode orthogonal direction in principle, is suitable for all HG modes, and has the theoretical distinguishing efficiency of 100 percent;

3. the common-path polarization interference system used by the invention gets rid of the limitations of the stability and the accuracy of the traditional path-splitting interferometer, so that the efficiency of the beam splitter is higher, and the cascade of the multi-stage beam splitter can be better completed;

4. the mode beam splitter designed by the invention can work under the single photon level and is reversible, namely, the device can realize mode demultiplexing and mode multiplexing.

Drawings

FIG. 1 is a schematic diagram of the modulation effect of the single polarization phase converter on two orthogonal polarization substrates in a horizontal arrangement.

Fig. 2 is a schematic diagram of the modulation effect of the single polarization phase converter on two orthogonal polarization substrates when the single polarization phase converter is vertically disposed.

Fig. 3 is a schematic view of embodiment 1 of the present invention.

Fig. 4 is a raster pattern corresponding to the horizontal arrangement of the lenticular lenses loaded on the spatial light modulator in embodiment 1 of the present invention.

Fig. 5 is a grating pattern with corresponding lenticular lens upright arrangement loaded on the spatial light modulator in example 1 of the present invention.

Fig. 6 is a schematic view of embodiment 2 of the present invention.

Fig. 7 is a schematic diagram of a three stage beam splitter cascade process of the present invention.

Description of reference numerals:

BS is a beam splitter, M is a reflector, CL is a single polarization cylindrical lens, PBS is a polarization beam splitter, HWP is a half-wave plate, QWP is a quarter-wave plate, and SLM is a spatial light modulator.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

The invention designs an HG mode beam splitter based on a single-polarization modulator, which mainly comprises a single-polarization phase converter and a common-path polarization interference system. The design scheme of the whole HG mode beam splitter is as follows: making incident HG light comprise two orthogonal polarization substrates, but only one polarization component is modulated by a single polarization phase converter, and the other polarization component is recombined into a new polarization state at the outlet of the interference system without passing through the single polarization phase converter; when the single-polarization phase converter is in a horizontal arrangement mode, the introduced phase value is (m +1/2) theta after the HG modes with different horizontal mode parameter m values pass, namely, the phase difference related to the horizontal parameter m is introduced between the two polarization components; when theta is equal to pi, the geometric phase difference between the two polarization components is adjusted, the length of two optical paths of the interferometer is similarly adjusted, so that the mode parameter m is an even or odd HG mode, the total phase difference between the two polarizations is respectively changed into pi or 2 pi, and the two polarizations are finally separated into different channels, so that the effect of splitting Hermite-Gaussian modes with different horizontal parameter m values is achieved; correspondingly, when the phase converter is changed into a vertical arrangement mode, the HG modes with different vertical parameter n values can be distinguished.

To sum up, the simple summary of the beam splitting process is: by changing the phase value introduced by the single-polarization phase converter and the arrangement mode of the two cylindrical lenses, different phase differences directly related to the horizontal parameter m or the vertical parameter n of the Hermite-Gaussian mode are correspondingly generated between the two polarization components, and then the input mode finally appears in different channels by means of an interference system, so that the purpose of distinguishing the HG modes is achieved. The simple summary is that: as long as a relative phase difference Δ θ of magnitude pi is introduced between the two modes that it is desired to distinguish, it can be split to different outlets based on the interferometric system. While

Δθ＝(m₂+1/2)θ-(m₁+1/2)θ＝Δm·θ

Therefore, assuming that it is desired to distinguish HG modes where m is 3 and m is 7, the distinction condition of Δ θ being 4 · pi/4 being pi can be satisfied by simply placing the phase converter in the beam splitter horizontally and introducing the phase value θ being pi/4 according to the above equation.

Because the single-polarization phase converter used in the invention has two implementation modes, namely simulation and physical construction, two better implementation schemes of the HG mode beam splitter are designed. Hereinafter, the structures and operations of the two exemplary embodiments will be described in detail with reference to the accompanying drawings.

Example 1

As shown in fig. 3, the function of implementing a single polarization phaser is simulated with a spatial light modulator.

First, keeping the incident HG mode horizontally polarized, with an ultrafast axis angle of 22.5 HWP, becoming linearly polarized in the 45 direction, and illuminating the SLM vertically with the loaded grating as shown in fig. 4 and 5; the beam splitter, the reflector and the reflective spatial light modulator are used for reflecting back and forth, so that incident light passes through the SLM twice and irradiates two different areas on the left and the right respectively, and the light path collimation is kept equivalent to passing through two cylindrical lenses which are arranged coaxially and are opposite in plane. In addition, the conventional reflective phase type spatial light modulator has a characteristic of modulating only a single polarization (e.g. Holoeye Pluto VIS-016 modulates only a horizontal polarization), so that it is equivalent to that a horizontal polarization component in incident light passes through the phase converter, and a vertical polarization component does not pass through the phase converter, so that a single polarization phase converter is formed, and as shown in fig. 1 and fig. 2, a phase value of (m +1/2) θ or (n +1/2) θ is introduced between two polarization components, which is related to the HG mode parameter. The different theta values introduced by the single-polarization phase converter can be realized by changing the focal length parameters of the Fresnel phase plate loaded on the SLM by a control program or changing the distances between the SLM and the BS and M in the optical path. Two ways of arranging the phase converter are realized by rotating the phase plate loaded on the SLM.

And then, the emergent light sequentially passes through a geometric phase shifter, a 22.5-degree HWP and a PBS to complete the construction of the common-path interference system. The geometric phase shifter is composed of two QWPs and one HWP and is used for compensating the condition that the phase difference added between the horizontal polarization component and the vertical polarization component is less than integral multiple of pi. The fast axis directions of the two QWPs are both 45 degrees, and the HWP is arranged between the two QWPs

The jones matrix of the geometric phase shifter can be written as:

after passing through this geometric phase shifter, the horizontal polarization component changes:

after passing through this geometric phase shifter, the vertical component changes:

by rotating the HWP by an angle, an arbitrary phase offset can be introduced between the horizontally and vertically polarized components, which in a common path interferometer is equivalent to adding a path compensation.

The overall mode discrimination process of the beam splitter is illustrated: when the SLM is loaded with the graph 4 and the distance between the SLM and the BS is equal to the focal length of the loaded cylindrical lens, the phase converter theta is equal to pi and horizontally arranged, and after an HG mode with m being

odd numbers

1, 3 and 5 passes through the single-polarization phase converter, the phase values introduced between the horizontal polarization component and the vertical polarization component are 3 pi/2, 7 pi/2 and 11 pi/2 in sequence; after the HG modes with m being even numbers of 0, 2 and 4 pass, the generated phase differences are pi/2, 5 pi/2 and 9 pi/2 in sequence; and introducing a pi/2 fixed phase difference between the two polarization components by using a subsequent geometric phase shifter, wherein the phase difference introduced by the HG mode with the parameter m being odd number and the HG mode with the parameter m being even number is respectively changed into 2 pi and pi, and the phase difference is finally changed into horizontal polarization and vertical polarization through a HWP with the parameter m being 22.5 degrees, so that the phase difference is successfully separated to different outlets at the final PBS. Similarly, when FIG. 5 is loaded on the SLM under otherwise unchanged conditions, HG modes with different n-value parity can be distinguished.

Example 2

As shown in fig. 6, the single polarization cylindrical lens CL is used to complete the construction of the phase converter, and due to the polarization response characteristic of the single polarization cylindrical lens, the phase converter performs phase modulation on the left-hand circularly polarized part, but does not perform any action on the right-hand circularly polarized part, thereby implementing the function of performing phase operation on the single polarization substrate.

Firstly, an incident HG mode is kept to be horizontal polarization, left-hand circular polarization and right-hand circular polarization are used for replacing two propagation paths of a traditional path interferometer, then two phase converters which are opposite in plane and formed by single polarization cylindrical lenses arranged in parallel are used for introducing a discrete phase difference (m +1/2) theta or (n +1/2) theta related to mode parameters between left-hand circular polarization components and right-hand circular polarization components in incident light, and the split is carried out through PBS after compensation of a geometric phase shifter, so that the beam splitter with good robustness and strong practicability is completed. The principle is the same as that of embodiment 1, and the specific structural differences are mainly the following 3 points:

1. the phase converter is directly built by a single-polarization cylindrical lens and only modulates a single polarization substrate;

2. changing to operate with left-handed circular polarization and right-handed circular polarization as orthogonal basis, using the properties of a single-polarized lenticular lens;

3. the construction of the geometric phase shifter is modified by adding a geometric phase shifter consisting of two HWPs before the PBS at the exit of the beam splitter to compensate for the phase difference added by the phase converter between the two polarization components in the interferometer being less than an integer multiple of pi. Two HWPs with a first fast axis direction set at 45 DEG and a second fast axis direction set at

The jones matrix of the geometric phase shifter is then:

after the incident left-hand circular polarization component and the incident right-hand circular polarization component pass through the geometric phase shifter, the changes are respectively as follows:

thus, by rotating the second HWP, an arbitrary phase offset can be introduced between the left-hand and right-hand circular polarization components, which in a common path interferometer amounts to adding a path compensation.

Cascading of beam splitters: when the multistage beam splitter is cascaded, the purpose of distinguishing any HG modes can be achieved by reasonably designing the arrangement mode of the phase converters in each stage and the numerical value of the phase difference theta.

In the following, taking an HG mode in which the horizontal parameter m is different and the vertical parameter n remains the same as an example, a design principle of a three-stage cascade splitting process is specifically described, as shown in fig. 7. Let HG light with two orthogonal polarization substrates, m-0, 1,2,3,4,5,6,7, enter the tertiary beam splitter:

1. setting the phase converter in the first stage beam splitter to θ ═ and lying horizontally, then: when the mode with m being

odd numbers

1, 3 and 5 passes through the phase converter, the phase values introduced between the two polarization substrates are 3 pi/2, 7 pi/2 and 11 pi/2 in sequence; when the HG modes with m being

even numbers

0, 2 and 4 pass through, the generated phase difference is pi/2, 5 pi/2 and 9 pi/2 in sequence, at the moment, the mode parameter m is the relative phase difference delta theta between the HG modes with odd numbers and even numbers pi, and then the modes with different parity numbers can be successfully separated to the first outlet and the second outlet by means of an interference system;

2. the phase converter of the second stage beam splitter is set to be theta pi/2 and horizontally arranged, and cascaded after the two outlets of the first stage beam splitter, the mode distinguishing situation is as follows:

(1) after the mode with m being 1 and 5 passes through the second-stage beam splitter, the phase values introduced by the phase converter are 3 pi/4 and 11 pi/4 in sequence; the mode with m being 3 and 7 passes through a phase converter, and the introduced phase values are 7 pi/4 and 15 pi/4 in sequence; when the relative phase difference delta theta between the HG modes with the mode parameters m being 1 and 5 and m being 3 and 7 is pi, successfully separating to an outlet three and an outlet four by means of an interference system;

(2) in a similar way, after the mode with m being 0 and 4 passes through the secondary beam splitter, phase values introduced by the phase converter are pi/4 and 9 pi/4 in sequence; after the mode with m being 2 and 6 passes through the beam splitter, the phase values introduced by the phase converter are 5 pi/4 and 13 pi/4 in sequence; at this time, the relative phase difference between the HG modes with the mode parameters m of 0 and 4 and m of 2 and 6 is Δ θ ═ pi, and the HG mode is successfully separated into the outlet five and the outlet six by means of the interference system;

3. setting the phase converters of the four third-stage beam splitters as theta pi/4 and horizontally placing, and respectively cascading after the four outlets of the second-stage beam splitter, wherein the mode distinguishing conditions are respectively as follows:

(1) after the mode with m being 1 passes through the third-stage beam splitter, the phase value introduced by the phase converter is 3 pi/8; after the mode with m being 5 passes through the three-stage beam splitter, the phase value introduced by the phase converter is 11 pi/8; at the moment, the relative phase difference delta theta between the HG modes with the mode parameters m being 1 and m being 5 is pi, and the HG modes are successfully separated into an outlet seven and an outlet eight by virtue of an interference system;

(2) after the mode with m being 3 passes through the third-stage beam splitter, the phase value introduced by the phase converter is 7 pi/8; after the mode with m being 7 passes through the third-stage beam splitter, the phase value introduced by the phase converter is 15 pi/8; at the moment, the relative phase difference delta theta between the HG modes with the mode parameters m being 3 and m being 7 is pi, and the HG modes are successfully separated to an outlet nine and an outlet ten by virtue of an interference system;

(3) after the mode with m being 0 passes through the third-stage beam splitter, the phase value introduced by the phase converter is pi/8; after the mode with m being 4 passes through the third-stage beam splitter, the phase value introduced by the phase converter is 9 pi/8; at the moment, the relative phase difference delta theta between the HG modes with the mode parameters m being 0 and m being 4 is pi, and the HG modes are successfully separated into an outlet eleven and an outlet twelve by virtue of an interference system;

(4) after the mode with m being 2 passes through the third-stage beam splitter, the phase value introduced by the phase converter is 5 pi/8; after the mode with m being 6 passes through the three-stage beam splitter, the phase value introduced by the phase converter is 13 pi/8; the relative phase difference Δ θ between the HG modes with mode parameters m 2 and m 6 is pi, which by means of the interferometric system, successfully splits to outlet thirteen and outlet fourteen.

In addition, in an actual experiment, due to manual operation or insufficient accuracy of a device, a certain error exists between a phase value and a theoretical value, which are introduced by a single-polarization phase converter in an optical path and are related to a mode parameter, and at the moment, the geometric phase shifter can perfectly compensate the error, so that an experimental result is more consistent with a theoretical result.

The above description is only exemplary of the preferred embodiments of the present invention, and is not intended to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims

1. The Hermite-Gaussian mode beam splitter based on the single polarization modulation device is characterized by comprising a single polarization phase converter and a common-path polarization interference system;

the single-polarization phase converter consists of two single-polarization cylindrical lenses, has the phase modulation effect of the cylindrical lenses on one of two orthogonal polarization states, has no effect on the other, and is divided into a horizontal placing mode and a vertical placing mode according to the state of a lens curved surface; the two single-polarization cylindrical lenses are opposite in plane and coaxially arranged, and the distance d between the two single-polarization cylindrical lenses meets the condition that d is 2sin (theta/2) f, wherein theta is a phase value introduced by the phase converter between the two polarization components, the value range is [0, pi ], and f is the focal length of the single-polarization cylindrical lens;

2. The hermitian-gaussian mode beam splitter based on a single polarization modulation device according to claim 1, wherein the two orthogonal polarization states are horizontal polarization and vertical polarization.

3. The hermitian-gaussian mode beam splitter based on a single polarization modulation device according to claim 1, wherein the two orthogonal polarization states are left-handed circular polarization and right-handed circular polarization.

4. The hermitian-gaussian mode beam splitter based on the single polarization modulation device as recited in claim 1, wherein the basic principle of the HG mode beam splitter is as follows: making incident HG light comprise two orthogonal polarization substrates, wherein one polarization component is modulated by a phase converter, and the other polarization component is recombined into a new polarization state at the outlet of the common-path polarization interference system without passing through the phase converter; when the phase converter is in a horizontal arrangement mode, the introduced phase value is (m +1/2) theta after the HG modes with different horizontal mode parameter m values pass, namely, the phase difference related to the horizontal parameter m is introduced between the two polarization components; when theta is equal to pi, the geometric phase difference between the two polarization components is adjusted, so that the mode parameter m is an even or odd HG mode, the total phase difference between the two polarizations is respectively changed into pi or 2 pi, and finally the two polarizations are separated into different channels, so that the effect of splitting the Hermite-Gaussian modes with different level parameter m values is achieved; correspondingly, when the phase converter is changed into a vertical arrangement mode, the HG modes with different vertical parameter n values are distinguished.

5. The hermitian-gaussian mode beam splitter based on the single-polarization modulation device as claimed in claim 4, wherein the phase value introduced by the phase converter and the arrangement of the two cylindrical lenses are changed, so that different phase differences directly related to the horizontal parameter m or the vertical parameter n of the hermitian-gaussian mode are correspondingly generated between the two polarization components, and then the input mode finally appears in different channels by means of a common-path polarization interference system, thereby realizing the purpose of distinguishing HG modes.

6. Hermite-Gaussian mode beam splitter based on single polarization modulation device according to claim 5, characterized in that a relative phase difference Δ θ of pi is introduced between two modes to be distinguished, and then the two modes are separated to different outlets based on a common path polarization interference system, wherein

Δθ＝(m₂+1/2)θ-(m₁+1/2)θ＝Δm·θ。