阅读说明：本技术 用于发射和接收具有轨道角动量检测的电磁辐射束的方法和系统以及相关的远程通讯的方法和系统 (Method and system for transmitting and receiving electromagnetic radiation beam with orbital angular momentum detection and related telecommunication method and system ) 是由 马可·波坦察 布鲁诺·帕罗利 米尔科·思亚诺 于 2020-04-02 设计创作，主要内容包括：描述了一种用于发射和接收电磁辐射束的方法,该方法适合于确定接收到的电磁辐射束的轨道角动量。进一步描述了一种用于发射和接收电磁辐射束的系统,该系统能够执行上述方法。进一步描述了一种用于执行根据任何调制技术调制的、并借助于轨道角动量复用进行分组的信号的远程通讯的方法。进一步描述了一种能够执行用于执行调制信号的远程通讯的上述方法的远程通讯的系统。(A method for emitting and receiving a beam of electromagnetic radiation is described, which method is adapted to determine the orbital angular momentum of the received beam of electromagnetic radiation. Further described is a system for emitting and receiving a beam of electromagnetic radiation, which system is capable of performing the above-mentioned method. Further described is a method for performing telecommunication of signals modulated according to any modulation technique and grouped by means of orbital angular momentum multiplexing. A telecommunication system capable of performing the above method for performing telecommunication of modulated signals is further described.)

1. A method for emitting and receiving a beam of electromagnetic radiation, the method being adapted for determining an orbital angular momentum of the received beam of electromagnetic radiation, the method comprising the steps of:

-generating at least one main beam of electromagnetic radiation (F1) consisting of a first orbital angular momentum (L)₁) A first spectrum in a first frequency band, and a first beam radius of curvature characterization;

-generating a reference beam of electromagnetic radiation (F0) consisting of a second orbital angular momentum (L)₀) A second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature characterization substantially coincident with the first beam radius of curvature;

-generating a composite beam of electromagnetic radiation (Q1) comprising a superposition of the at least one main beam (F1) and the reference beam (F0);

-emitting said generated composite beam of electromagnetic radiation (Q1);

-receiving said composite beam of electromagnetic radiation by means of a first beam detector (1) located in a first position, to produce a first composite beam electrical signal (D1) representative of the electric and/or magnetic field and/or intensity of electromagnetic radiation of said composite beam in said first position;

-receiving said composite beam of electromagnetic radiation by means of a second beam detector (2) located in a second different position with respect to said first position, to produce a second composite beam electrical signal (D2) representative of the electric and/or magnetic field of said composite beam and/or the intensity of the received electromagnetic radiation in said second position;

-performing a frequency discrimination of the first composite beam electrical signal (D1) to obtain a first main beam electrical signal (P1) representative of an electric field, and/or a magnetic field, and/or an intensity, attributed to the main beam in the first position, and a first reference beam electrical signal (R1 representative of an electric field, and/or a magnetic field, and/or an intensity, attributed to the reference beam in the first position;

-performing a frequency discrimination of the second composite beam electrical signal (D2) to obtain a second main beam electrical signal (P2) representative of an electric field, and/or a magnetic field, and/or an intensity, attributed to the main beam in the second position, and a second reference beam electrical signal (R2 representative of an electric field, and/or a magnetic field, and/or an intensity, attributed to the reference beam in the second position;

-determining the orbital angular momentum (L) of the main beam of electromagnetic radiation based on the first main beam electrical signal (P1), the second main beam electrical signal (P2), the first reference beam electrical signal (R1) and the second reference beam electrical signal (R2)₁) And/or due to the main beam orbital angular momentum (L)₁) Of the main beam of electromagnetic radiation.

2. The method of claim 1, wherein the determining step comprises:

-determining a first phase difference value (Δ P) corresponding to a difference between the phase of the first main beam electrical signal (P1) and the phase of the second main beam electrical signal (P2),

-determining a second phase difference value (AR) corresponding to a difference between the phase of the first reference beam electrical signal (R1) and the phase of a second reference beam electrical signal (R2),

-subtracting said second phase difference value (AR) divided by the second wave number (k ') from said first phase difference value (Δ P) divided by the first wave number (k) to obtain a difference value (Q2 ═ Δ P/k- Δ R/k'), said difference value being independent of the condition of the inclination of the position between said first detector and said second detector, but being derived from the relative position of these two detectors with respect to the propagation of the beam, and said difference value being independent of the phase variation due to the interference to which the transmitted composite beam is subjected before reception,

wherein the first wavenumber (k) is a wavenumber corresponding to the main beam defined as k 2 pi/λ, λ being a wavelength of the main beam, and wherein the second wavenumber (k ') is a wavenumber corresponding to the reference beam defined as k ' 2 pi/λ, λ ' being a wavelength of the reference beam;

-determining said orbital angular momentum of said main beam of electromagnetic radiation on the basis of said obtained difference (Q2 ═ Δ P/k- Δ R/k').

3. The method according to claim 2, wherein the step of determining the orbital angular momentum of the primary beam of electromagnetic radiation comprises:

-determining the orbital angular momentum of the primary beam of electromagnetic radiation according to

ΔP/k–ΔR/k'∝(L₁/k-L₀/k')(θ₂-θ₁)

Wherein, theta₁Is the angular position of the first detector measured on a plane orthogonal to the composite beam propagation vector containing the first detector, and θ₂Is the angular position of the second detector measured on a plane orthogonal to the composite beam propagation vector containing the second detector.

4. The method of claim 2, wherein:

-the step of determining the first phase difference value (Δ Ρ) comprises: comparing the phase of the first main beam electrical signal (P1) with the phase of the second main beam electrical signal (P2) by means of a first phase comparator (3);

-the step of determining the second phase difference value (ar) comprises: comparing the phase of the first reference beam electrical signal (R1) with the phase of the second reference beam electrical signal (R2) by means of a second phase comparator (4).

5. The method of claim 2, wherein:

-the step of determining the first phase difference value (Δ Ρ) comprises: performing a correlation operation between the first main beam electrical signal (P1) and the second main beam electrical signal (P2);

-the step of determining the second phase difference value (ar) comprises: performing a correlation operation between the first reference beam electrical signal (R1) and the second reference beam electrical signal (R2).

6. The method according to any of the preceding claims, wherein the orbital angular momentum of the reference beam is always known.

7. The method of claim 6, wherein the orbital angular momentum of the reference beam takes a constant value L₀＝0。

8. The method according to any of the preceding claims, wherein the first position of the first detector (1) and the second position of the second detector (2) are fixed and constant and different from the position of the singularity of the vortex of the beam.

9. The method according to any of the preceding claims, wherein the first position of the first detector (1) and/or the second position of the second detector (2) is movable and the correlation between the first position and the second position is known at all times.

10. The method of any preceding claim, wherein the second frequency band is substantially single frequency.

11. The method of claim 10, wherein the second frequency band is adjacent to the first frequency band.

12. The method according to any one of the preceding claims, wherein the step of performing frequency discrimination of the first or second composite beam electrical signal comprises:

-performing frequency filtering; or

Frequency separation is performed by means of heterodyne techniques or other frequency separation methods.

13. The method according to any of claims 1-12, wherein said at least one main beam of electromagnetic radiation is unmodulated.

14. Method according to any one of claims 1-12, wherein said at least one main beam of electromagnetic radiation is amplitude modulated, and/or phase modulated, and/or frequency modulated, and/or orbital angular momentum modulated.

15. The method according to any of the preceding claims, wherein the transmitted and received electromagnetic beams are light beams and/or laser beams.

16. A method for performing telecommunication of modulated signals according to any known modulation technique, said modulated signals being grouped by means of multiplexing in orbital angular momentum variables, said method comprising the steps of:

-generating a first orbital angular momentum (L)₁) A first beam of electromagnetic radiation (F1) characterized and generating a first angular momentum (L) consisting of at least one corresponding second orbital momentum (L)₂) Characterized by at least one second beam of electromagnetic radiation (F2),

wherein the first beam of electromagnetic radiation (F1) and the at least one second beam of electromagnetic radiation (F2) have respective spectra in a same first frequency band and further have respective radii of curvature substantially coincident with a first beam radius of curvature value;

-modulating a first piece of information to be emitted, represented by a first modulation function a (t), on said first beam of electromagnetic radiation (F1) by means of any modulation technique, so as to obtain a first modulated beam (Fm 1);

-modulating at least one second piece of information to be emitted, represented by a second modulation function b (t), on said at least one second beam of electromagnetic radiation (F2) by means of any modulation technique, so as to obtain a second modulated beam (Fm 2);

-generating a reference beam of electromagnetic radiation (F0) consisting of a second orbital angular momentum (L)₀) A second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature characterization, the second beam radius of curvature having a value substantially coincident with the first beam radius of curvature value;

-superimposing and/or combining said reference beam (F0), said first modulated beam (Fm1) and said second modulated beam (Fm2) to produce a composite beam of electromagnetic radiation (Q1) comprising a superposition of said reference beam (F0) and a main beam, in turn comprising a superposition of said first modulated beam (Fm1) and of at least one second modulated beam (Fm 2);

-emitting said generated composite beam of electromagnetic radiation (Q1);

-receiving said composite beam of electromagnetic radiation by means of a first beam detector (1) located in a first position, to produce a first composite beam electrical signal (D1) representative of the electric and/or magnetic field and/or intensity of electromagnetic radiation of said composite beam in said first position;

-receiving said composite beam of electromagnetic radiation by means of a second beam detector (2) located at a second different position with respect to said first position, to produce a second composite beam electrical signal (D2) representative of the electric and/or magnetic field of said composite beam and/or the intensity of the received electromagnetic radiation in said second position;

-performing a frequency discrimination of the first composite beam electrical signal (D1) to obtain a first main beam electrical signal (P1) representative of an electric field, and/or a magnetic field, and/or an intensity, attributed to the main beam in the first position, and a first reference beam electrical signal (R1 representative of an electric field, and/or a magnetic field, and/or an intensity, attributed to the reference beam in the first position;

-performing a frequency discrimination of the second composite beam electrical signal (D2) to obtain a second main beam electrical signal (P2) representative of an electric field, and/or a magnetic field, and/or an intensity, attributed to the main beam in the second position, and a second reference beam electrical signal (R2 representative of an electric field, and/or a magnetic field, and/or an intensity, attributed to the reference beam in the second position;

-determining the phase of the first main beam electrical signal (P1) and the phase of the second main beam electrical signal (P2);

-determining the phase of the first reference beam electrical signal (R1) and the phase of the second reference beam electrical signal (R2);

-determining a first phase difference value (Δ Ρ)_ab) A first phase difference value corresponding to a difference between a phase of the first main beam electrical signal (P1) and a phase of the second main beam electrical signal (P2), the first phase difference value (Δ P)_ab) A value taken in dependence on the first modulation function a (t) and the second modulation function b (t);

-determining a second phase difference value (ar) corresponding to a difference between the phase of the first reference beam electrical signal (R1) and the phase of the second reference beam electrical signal (R2);

-deriving from said first phase difference value (Δ Ρ)_ab) Dividing by the first wave number k minus the second phase difference (Δ R) divided by the second wave number k' to obtain a difference (Q2 ═ Δ P)_ab/k–ΔR/k')，

Wherein the first wavenumber (k) is a wavenumber corresponding to the main beam defined as k 2 pi/λ and λ is a wavelength of the main beam, and wherein the second wavenumber (k ') is a wavenumber corresponding to the reference beam defined as k' 2 pi/λ 'and λ' is a wavelength of the reference beam,

the difference (Q2 ═ Δ P_abK- Δ R/k') represents the values taken by the first modulation function a (t) and the second modulation function b (t)Combining independent of a position tilt condition between the first detector and the second detector, and independent of a phase variation due to interference experienced by the transmitted composite beam prior to reception;

-based on said determined difference (Q2 ═ Δ P_ab-ar/k'), demultiplexing and demodulating the information modulated on each of said first modulation beam (Fm1) and said at least one second modulation beam (Fm 2).

17. The method of claim 16, wherein the number of modulated beams for orbital angular momentum multiplexing is greater than 2.

18. The method according to any one of claims 16 or 17, wherein said first beam of electromagnetic radiation (F1) and said at least one second beam of electromagnetic radiation (F2) are digitally amplitude modulated according to the amplitude of said first modulation function a (t) and the amplitude of said at least one second modulation function b (t),

and wherein the difference (Q2 ═ Δ P_abK-ar/k') can take a plurality of desired values, each representing a respective combination of digital amplitude values taken by said first modulation function a (t) and said at least one second modulation function b (t).

19. The method of claim 18, wherein:

-said first beam of electromagnetic radiation (F1) and said at least one second beam of electromagnetic radiation (F2) are digitally amplitude modulated in a binary manner, and said amplitude of said first modulation function a (t) and said amplitude of said at least one second modulation function b (t) can take a logical value 0 or 1;

-the method comprises the further step of detecting the received power or intensity (Q3) corresponding to the first main beam electrical signal (P1) or the second main beam electrical signal (P2), and comparing the received power or intensity with a minimum threshold;

-determined difference (Q2 ═ Δ P_abK- Δ R/k') can assume a first desired value (Δ P)₁₀K- Δ R/k'), or second stageAbsolute value (Δ P)₀₁K- Δ R/k'), or a third desired value (Δ P)₁₁K- Δ R/k'), the first desired value depending on the first angular momentum (L)₁) The second desired value depending on a second angular momentum (L)₂) The third desired value depends on a combination of the first angular momentum and the second angular momentum;

-the steps of demodulating, demultiplexing and demodulating the modulated information comprise:

-if said determined difference (Δ Ρ)_abK- Δ R/k') takes the first desired value (Δ P)₁₀- Δ R/k'), identifying that the first modulation beam (Fm1) carries information corresponding to 1 and the second modulation beam (Fm2) carries information corresponding to 0;

-if said determined difference (Δ Ρ)_abK- Δ R/k') taking the second desired value (Δ P)₀₁- Δ R/k'), identifying that the first modulation beam (Fm1) carries information corresponding to 0 and the second modulation beam (Fm2) carries information corresponding to 1;

-if said determined difference (Δ Ρ)_abK- Δ R/k') takes the third desired value (Δ P)₁₁- Δ R/k'), identifying that the first modulation beam (Fm1) carries information corresponding to 1 and the second modulation beam (Fm2) carries information corresponding to 1;

-identifying that the first modulation beam (Fm1) carries information corresponding to 0 and the second modulation beam (Fm2) carries information corresponding to 0 if the received power or intensity (Q3) is below the minimum threshold.

20. Method according to any one of claims 16 or 17, wherein said first beam of electromagnetic radiation (F1) and said at least one second beam of electromagnetic radiation (F2) are digitally modulated with angular momentum, wherein the angular momentum of said first beam (F1) takes two different discrete values based on a first modulation function a (t) and the angular momentum of said at least one second beam (F2) takes two different discrete values based on at least one corresponding second modulation function b (t),

and wherein the difference (Q2 ═ Δ P_abK- Δ R/k') can take a plurality of desired values, eachThe expected values represent respective combinations of digital amplitude values taken by said first modulation function a (t) and said at least one second modulation function b (t).

21. The method of claim 20, wherein:

the amplitudes of the first modulation function a (t) and of the at least one second modulation function b (t) can take the logical value 0 or 1;

-the determined difference (Δ P)_abK- Δ R/k') is capable of:

taking a first desired value (Δ P) when the first modulation function a (t) takes a value of 1 and the second modulation function takes a value of 0₁₀K- Δ R/k'); or, when the first modulation function a (t) takes a value of 0 and the second modulation function takes a value of 1, a second expected value (Δ P) is taken₀₁K- Δ R/k'); or, when the first modulation function a (t) takes a value of 1 and the second modulation function takes a value of 1, a third expected value (Δ P) is taken₁₁K- Δ R/k'); or, when the first modulation function a (t) takes a value of 0 and the second modulation function takes a value of 0, a fourth expected value (Δ P) is taken₀₀/k–ΔR/k')；

-the steps of demodulating, demultiplexing and demodulating the modulated information comprise:

-if said determined difference (Δ Ρ)_abK- Δ R/k') takes the first desired value (Δ P)₁₀- Δ R/k'), identifying that the first modulation beam (Fm1) carries information corresponding to 1 and the second modulation beam (Fm2) carries information corresponding to 0;

-if said determined difference (Δ Ρ)_abK- Δ R/k') taking the second desired value (Δ P)₀₁- Δ R/k'), identifying that the first modulation beam (Fm1) carries information corresponding to 0 and the second modulation beam (Fm2) carries information corresponding to 1;

-if said determined difference (Δ Ρ)_abK- Δ R/k') takes the third desired value (Δ P)₁₁- Δ R/k'), identifying that the first modulation beam (Fm1) carries information corresponding to 1 and the second modulation beam (Fm2) carries information corresponding to 1;

-if said determined difference (Δ Ρ)_abK- Δ R/k') takes the fourth desired value (Δ P)₀₀-ar/k'), identifying that the first modulation beam (Fm1) carries information corresponding to 0 and the second modulation beam (Fm2) carries information corresponding to 0.

22. The method according to any of the preceding claims, wherein the transmitted and received electromagnetic beams are light beams and/or laser beams.

23. A system for emitting and receiving a beam of electromagnetic radiation, the system being adapted to determine an orbital angular momentum of the received beam of electromagnetic radiation, the system comprising:

-means (5) for generating a main beam of electromagnetic radiation, said means for generating a main beam of electromagnetic radiation being configured to generate a main beam of electromagnetic radiation (F1), said main beam of electromagnetic radiation being composed of a first orbital angular momentum (L1)₁) A first spectrum in a first frequency band, and a first beam radius of curvature characterization;

-means (6) for generating a reference beam of electromagnetic radiation, said means for generating a reference beam of electromagnetic radiation being configured to generate a reference beam of electromagnetic radiation (F0), said reference beam of electromagnetic radiation being composed of a second orbital angular momentum (L0)₀) A second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature characterization substantially coincident with the first beam radius of curvature;

-means (7) for generating a composite beam of electromagnetic radiation configured to generate a composite beam of electromagnetic radiation (Q1) comprising a superposition of said main beam (F1) and a reference beam (F2), and means (14) for emitting composite electromagnetic radiation configured to emit said generated composite beam of electromagnetic radiation (Q1);

-means for receiving said composite beam of electromagnetic radiation, comprising:

-a first beam detection device (1) located in a first position configured to generate a first composite beam electrical signal (D1) representative of the electric and/or magnetic field and/or intensity of electromagnetic radiation of the composite beam in said first position;

-a second beam detection device (2) located in a second position different with respect to the first position, configured to generate a second composite beam electrical signal (D2) representative of the electric and/or magnetic field and/or intensity of electromagnetic radiation of the composite beam in the second position;

-a first frequency discrimination device (8) configured to perform a frequency discrimination of the first composite beam electrical signal (D1) to obtain a first electrical main beam signal (P1) representative of an electric field, and/or a magnetic field, and/or an intensity attributed to the main beam in the first position, and a first reference beam electrical signal (R1 representative of an electric field, and/or a magnetic field, and/or an intensity attributed to the reference beam in the first position;

-a second frequency discrimination device (9) configured to perform frequency discrimination of the second composite beam electrical signal to obtain a second main beam electrical signal (P2) representative of an electric field, and/or a magnetic field, and/or a strength, attributed to the main beam in the second position, and a second reference beam electrical signal (R2 representative of an electric field, and/or a magnetic field, and/or a strength, attributed to the reference beam in the second position;

-means (10) for determining an orbital angular momentum, configured to determine the orbital angular momentum (L) of the main beam of electromagnetic radiation based on the first main beam electrical signal (P1), the second main beam electrical signal (P2), the first reference beam electrical signal (R1) and the second reference beam electrical signal (R2)₁) And/or an orbital angular momentum (L) due to said main beam₁) Of the main beam of electromagnetic radiation.

24. The system of claim 23, wherein the system is configured to perform the method of any of claims 1-15.

25. A system for performing telecommunication of modulated signals according to any known modulation technique, said modulated signals being grouped by means of orbital angular momentum multiplexing, said system comprising:

-means (5, 6) for generating an electromagnetic beam configured to:

-generating a first orbital angular momentum (L)₁) A first beam of electromagnetic radiation (F1) characterized and generating a first angular momentum (L) consisting of at least one corresponding second orbital momentum (L)₂) At least one second beam of electromagnetic radiation (F2) characterized, wherein the first beam of electromagnetic radiation (F1) and the at least one second beam of electromagnetic radiation (F2) both have respective spectra in a same first frequency band and further have respective radii of curvature substantially coincident with the first beam radius of curvature value;

-generating a reference beam of electromagnetic radiation (F0) consisting of a second orbital angular momentum (L)₀) A second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature characterization, the second beam radius of curvature having a value substantially coincident with the first beam radius of curvature value;

-a modulation device (50) configured to:

-modulating a first piece of information to be emitted on said first beam of electromagnetic radiation (F1) by means of any amplitude, and/or phase, and/or frequency modulation technique, so as to obtain a first modulated beam (Fm1), said first piece of information to be emitted being represented by a first modulation function a (t);

-modulating at least one second piece of information to be emitted, represented by a second modulation function b (t), on said at least one second beam of electromagnetic radiation (F2) by means of any amplitude and/or phase and/or frequency modulation technique, so as to obtain a second modulated beam (Fm 2);

-a beam combining and/or superimposing device (7) configured to superimpose and/or combine said reference beam (F0), first modulated beam (Fm1) and second modulated beam (Fm2) so as to produce a composite beam of electromagnetic radiation (Q1) comprising the superposition of said reference beam (F0) and of a main beam, in turn comprising the superposition of said first modulated beam (Fm1) and of at least one second modulated beam (Fm 2);

-an emitting device (14) configured to emit the generated composite beam of electromagnetic radiation (Q1);

-means for receiving said composite beam of electromagnetic radiation, said means for receiving said composite beam of electromagnetic radiation comprising:

-a first beam detection device (1) located in a first position configured to generate a first composite beam electrical signal (D1) representative of the electric and/or magnetic field and/or intensity of electromagnetic radiation of the composite beam in said first position;

-a second beam detection device (2) located in a second position different with respect to the first position, configured to generate a second composite beam electrical signal (D2) representative of the electric and/or magnetic field and/or intensity of electromagnetic radiation of the composite beam in the second position;

-a first frequency discrimination device (8) configured to perform a frequency discrimination of the first composite beam electrical signal (D1) to obtain a first main beam electrical signal (P1) representative of an electric field, and/or a magnetic field, and/or an intensity attributed to the main beam in the first position, and a first reference beam electrical signal (R1 representative of an electric field, and/or a magnetic field, and/or an intensity attributed to the reference beam in the first position;

-a second frequency discrimination device (9) configured to perform frequency discrimination of the second composite beam electrical signal to obtain a second main beam electrical signal (P2) representative of an electric field, and/or a magnetic field, and/or a strength, attributed to the main beam in the second position, and a second reference beam electrical signal (R2 representative of an electric field, and/or a magnetic field, and/or a strength, attributed to the reference beam in the second position;

-a phase determination device (20) configured to:

-determining the phase of the first main beam electrical signal (P1) and the phase of the second main beam electrical signal (P2);

-determining the phase of the first reference beam electrical signal (R1) and the phase of the second reference beam electrical signal (R2);

-determining a first phase difference value (Δ Ρ) corresponding to the difference between the phase of the first main beam electrical signal (P1) and the phase of the second main beam electrical signal (P2)_ab) Said first phase difference value (Δ P)_ab) A value taken in dependence on the first modulation function a (t) and the second modulation function b (t);

-determining a second phase difference value (ar) corresponding to the difference between the phase of the first reference beam electrical signal (R1) and the phase of the second reference beam electrical signal (R2);

-deriving from said first phase difference value (Δ Ρ)_ab) Subtracting the second phase difference (Δ R) by the wavenumber k' to obtain a difference (Q2 ═ Δ P)_ab- Δ R/k'), said difference (Q2 ═ Δ P_ab-ar/k') represents the combination of the values taken by said first modulation function a (t) and said second modulation function b (t), independently of the condition of position inclination between said first detector (1) and said second detector (2), and independently of the phase variation due to the interference to which the transmitted composite beam is subjected before reception;

wherein the first wavenumber (k) is a wavenumber corresponding to the main beam defined as k 2 pi/λ and λ is a wavelength of the main beam belonging to the first frequency band, and wherein the second wavenumber k 'is a wavenumber corresponding to the reference beam defined as k' 2 pi/λ 'and λ' is a wavelength of the reference beam belonging to the second frequency band;

-processing means (15) configured to determine a difference (Q2 ═ Δ P) based on said difference_ab-ar/k') demultiplexing and demodulating the information modulated on each of the first modulated beam (Fm1) and the at least one second modulated beam (Fm 2).

26. The system of claim 25, wherein the system is configured to perform the method of any of claims 16-22.

Technical Field

The present invention relates generally to the technical field of transmission and reception of electromagnetic beams (in particular light/laser and microwave beams) with detection of orbital angular momentum of the beams, and to the field of telecommunications based on electromagnetic beams (in particular light/laser and microwave beams), modulation of orbital angular momentum and/or multiplexing of orbital angular momentum.

Background

The theory of propagation of electromagnetic beams, in particular laser beams and microwave beams, has recently demonstrated the presence of Orbital Angular Momentum (Orbital Angular Momentum).

From a conventional perspective, orbital angular momentum is a concept related to the different transverse modes of beam propagation.

This can also be considered to be illustrative of the fact that the propagation front of Orbital Angular Momentum (OAM) waves is not a simple plane, but has an evolution that can be represented by a helicoid.

In other words, Poynting vectors (Poynting vectors) and wave vectors (wave vectors) are no longer simply parallel to the direction of propagation, but are twisted around the direction of propagation.

From a quantum point of view, orbital angular momentum is handled by another quantum number different from the spin.

Recently, beams with orbital angular momentum different from 0 and capable of taking different values have also been experimentally demonstrated.

When the detector is illuminated by only a limited portion of the radiation beam, the "orbital angular momentum" variations are particularly difficult to detect and characterize due to their above-mentioned characteristics, even if they are far away from the singularity. In fact, there are no reliable systems and methods that allow to detect the orbital angular momentum of an electromagnetic beam, for example by means of local measurements of the received laser light, with only a limited part of the beam incident on the detector, even if far away from the singularity.

On the other hand, the need to detect the orbital angular momentum of the received beam is felt for various reasons including, for example, the characterization of the beam and the exploitation of the angular momentum variables for telecommunication purposes.

This need cannot currently be met by known solutions by local measurements.

The applicant has also realised that there is a possibility to hopefully exploit the orbital angular momentum variation as an additional degree of freedom, which is advantageous for both modulated and multiplexed signals.

However, the background art in the field of considered technology does not provide a reliable telecommunications solution based on orbital angular momentum multiplexing and/or modulation. Thus, a particular need is felt for such a solution.

Disclosure of Invention

In view of the above-mentioned circumstances, it is an object of the present invention to provide a method for emitting and receiving a beam of electromagnetic radiation, which is suitable for determining the orbital angular momentum of the received beam of electromagnetic radiation, for example to allow eliminating at least partially the drawbacks cited above with reference to the prior art, and to satisfy the above-mentioned needs particularly felt in the technical field considered.

This object is achieved by a method according to claim 1.

Further embodiments of this method are defined by claims 2-15.

The invention also relates to a system for emitting and receiving a beam of electromagnetic radiation, which system is capable of performing the above-mentioned method. Such a system is defined in claims 23 and 24.

The invention also relates to a method for performing telecommunication of signals modulated according to any modulation technique and grouped by means of orbital angular momentum multiplexing. Such a method is defined in claim 16.

Further embodiments of this method are defined by claims 17-22.

The invention also relates to a telecommunication system capable of implementing the above-mentioned method for performing telecommunication of modulated signals. Such a system is defined in claims 25 and 26.

Drawings

Further characteristics and advantages of the above-described method and system according to the invention will become apparent from the following description of a preferred embodiment, given by way of indicative and non-limiting example with reference to the accompanying drawings, in which:

figure 1 shows a simplified diagram of an emitting portion of an embodiment of a system for emitting and receiving a beam of electromagnetic radiation according to the invention; such fig. 1 shows at the same time some steps of the corresponding method;

figure 2 shows a simplified diagram of a receiving portion of an embodiment of a system for emitting and receiving a beam of electromagnetic radiation according to the invention; such fig. 2 also shows some other steps of the corresponding method;

fig. 3 shows a simplified diagram of the transmitting part of an embodiment of the system for telecommunication according to the invention; such FIG. 3 illustrates simultaneously certain steps of a corresponding method;

fig. 4 shows a simplified diagram of the receiving part of an embodiment of the system for telecommunication according to the invention; such fig. 4 also shows some other steps of the corresponding method;

figure 5 shows an embodiment of the system according to the invention, comprising a correlator;

fig. 6 depicts some of the geometric quantities used in the system diagram.

Detailed Description

With reference to fig. 1 to 6, a method for emitting and receiving a beam of electromagnetic radiation is described, which method is suitable for determining the orbital angular momentum of the received beam of electromagnetic radiation.

The method first comprises a step of generating at least one main beam of electromagnetic radiation F1 consisting of a first orbital angular momentum L, and a step of generating a reference beam of electromagnetic radiation F0₁Characterized by a first spectrum in a first frequency band and a first beam radius of curvature, the reference beam of electromagnetic radiation F0 being characterized by a second orbital angular momentum L₀A second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature substantially coincident with the first beam radius of curvature.

Need to make sure thatNote that the above is based on the first orbital angular momentum L₁And a second orbital angular momentum L₀Can also be correspondingly topologically charged (l)₁，l₀) Described because the angular momentum L and the topological charge L are related by the following relationship:

l ═ h)/2 pi (where h is planck constant).

Accordingly, the method includes generating a composite beam of electromagnetic radiation Q1 containing the superposition of the at least one main beam F1 and the reference beam F0, and emitting a composite beam of electromagnetic radiation Q1 generated thereby.

The method further comprises the step of receiving said composite beam of electromagnetic radiation Q1 by means of a first beam detector 1 located in a first position to produce a first composite beam electrical signal D1, the first composite beam electrical signal D1 being representative of the electric and/or magnetic field and/or intensity of electromagnetic radiation of the composite beam in such first position; and a step of receiving said composite beam of electromagnetic radiation Q1 by means of a second beam detector 2 located in a second different position with respect to said first position, to generate a second composite beam electrical signal D2, the second composite beam electrical signal D2 being representative of the electric and/or magnetic field of the composite beam and/or the intensity of the electromagnetic radiation received in such second position.

The method further comprises the following steps: performing frequency discrimination of the first composite beam electrical signal D1 to derive a first main beam electrical signal P1 and a first reference beam electrical signal R1, the first main beam electrical signal P1 representing an electric field, and/or a magnetic field, and/or an intensity attributed to the main beam in said first position, the first reference beam electrical signal R1 representing an electric field, and/or a magnetic field, and/or an intensity attributed to the reference beam in the first position; and performing frequency discrimination of the second composite beam electrical signal D2 to derive a second main beam electrical signal P2 and a second reference beam electrical signal R2, the second main beam electrical signal P2 being representative of the electric field, and/or magnetic field, and/or intensity attributed to the main beam in the second position, and the second reference beam electrical signal R2 being the electric field, and/or magnetic field, and/or intensity attributed to the reference beam in the second position.

Finally, the method comprises a first step of generating a first main beam electrical signal P1 based on the first main beam electrical signal P1Determining the orbital angular momentum L of the primary beam of electromagnetic radiation from the two main beam electrical signals P2, the first reference beam electrical signal R1, and the second reference beam electrical signal R2₁And/or due to the main beam orbital angular momentum L₁The spatial phase variation of the main beam of electromagnetic radiation.

According to one embodiment of the method, the determining step comprises: determining a first phase difference value Δ Ρ corresponding to the difference between the phase of the first main beam electrical signal P1 and the phase of the second main beam electrical signal P2; further, determining a second phase difference value Δ R corresponding to a difference between the phase of the first reference beam electrical signal R1 and the phase of the second reference beam electrical signal R2; then, the second phase difference value Δ R divided by the second wave number k 'is subtracted from the first phase difference value Δ P divided by the first wave number k to obtain a difference value (Q2 ═ Δ P/k- Δ R/k') which is independent of the condition of the position inclination between the first and second detectors and is derived from the relative position of the two detectors with respect to the propagation of the beam, said difference value being independent of the phase variation due to the interference to which the transmitted composite beam is subjected before reception; and then determining the orbital angular momentum of the primary beam of electromagnetic radiation based on the difference (Q2 ═ Δ P/k- Δ R/k') obtained above.

The first wave number k is a wave number corresponding to a main beam, defined as k 2 pi/λ, λ being a wavelength of the above-mentioned main beam belonging to the above-mentioned first frequency band. The second wave number k 'is a wave number corresponding to the reference beam, defined as k' 2 pi/λ ', and λ' is a wavelength of the above-mentioned reference beam belonging to the above-mentioned second frequency band.

The definition of "positional inclination" (or positional tilt ") is indicative of the angle formed between a straight line connecting the two detectors and the (orthogonal) projection of this straight line on a plane orthogonal to the beam propagation axis.

According to a specific implementation example, the step of determining the orbital angular momentum of the main beam of electromagnetic radiation comprises determining the orbital angular momentum of the main beam of electromagnetic radiation based on:

ΔP/k–ΔP/k'∝(L₁/k-L₀/k')(θ₂-θ₁)

wherein, theta₁Is at the same timeAn angular position of the first detector measured on a plane orthogonal to a composite beam propagation vector containing the first detector; theta₂Is the angular position of the second detector measured in a plane orthogonal to the composite beam propagation vector containing the second detector; oc indicates proportional.

According to an implementation option, the step of determining the first phase difference value Δ P comprises comparing the phase of the first main beam electrical signal P1 with the phase of the second main beam electrical signal P2 by means of the first phase comparator 3; the step of determining the second phase difference value ar comprises comparing the phase of the first reference beam electrical signal R1 with the phase of the second reference beam electrical signal R2 by means of the second phase comparator 4.

According to another implementation option, the step of determining the first phase difference value Δ P comprises performing a correlation operation between the first main beam electrical signal P1 and the second main beam electrical signal P2; and the step of determining the second phase difference value ar comprises performing a correlation operation between the first reference beam electrical signal R1 and the second reference beam electrical signal R2.

According to an embodiment of the method, the orbital angular momentum of the reference beam is always known.

According to an implementation option, the orbital angular momentum of the reference beam is taken to a constant value L₀＝0。

According to an embodiment of the method, the first position of the first detector 1 and the second position of the second detector 2 are fixed and constant and different from the position of the singular point (singular point) of the beam.

According to another embodiment of the method, the first position of the first detector 1 and/or the second position of the second detector 2 are movable, and the mutual relationship (correlation) between the first position and the second position is always known.

According to an implementation option, the second frequency band is substantially single frequency (monochromatic).

According to a particular implementation option, the second frequency band is adjacent to the first frequency band.

According to a possible embodiment of the method, the step of performing a frequency discrimination of the first composite beam electrical signal or the second composite beam electrical signal comprises performing a frequency filtering, or performing a frequency separation by means of a heterodyne technique or other frequency separation method.

According to an embodiment of the method, at least one of the primary beams of electromagnetic radiation is unmodulated.

According to other embodiments of the method, the at least one main beam of electromagnetic radiation is amplitude-modulated, and/or phase-modulated, and/or frequency-modulated, and/or orbital angular momentum-modulated.

According to one embodiment of the method, all of the aforementioned emitted and received electromagnetic beams are light beams and/or laser beams.

In the following, a specific implementation example of the method is given using a related physical mathematical analysis.

In the following description and in fig. 1 and 2, for simplicity, the points at which the different signals are located (first composite beam electrical signal D1, second composite beam electrical signal D2, first main beam electrical signal P1, first reference beam electrical signal R1, second main beam electrical signal P2, second reference beam electrical signal) are referred to by the same names as the respective signals.

As has been observed, the composite beam Q1 is composed of at least one beam having an orbital angular momentum L ═ L₁Beams (other than 0) (defined herein as the main beam F1) are superimposed on an angular momentum L ═ L₀Is generated on the beam (defined herein as reference beam F0).

The main beam may be modulated or unmodulated. The reference beam has a frequency band that does not overlap with the frequency band of the main beam. The frequency band of the reference beam is preferably quasi-monochromatic and adjacent to the frequency band of the main beam. The reference beam has substantially the same curvature and the same propagation vector as the main beam. The reference beam preferably has a topological charge l₀0, this also means the orbital angular momentum L₀＝0。

By having orbital angular momentum L₁The identification of the spatial phase difference generated by the main beam is obtained by using two detectors at any position in space except the point of the singularity of the vortex.

It is well known that the expression "singular point of vortex" refers to a point in the vortex at which the result of the electromagnetic field is reduced to zero and at which the phase of the field cannot be determined.

The electric field E on the first detector 1 without modulation of the main beam₁Or the correlation signal (indicated as D1 in fig. 2) may be represented by the following analytical formula:

wherein t is time, A₁And B₁Is a non-zero arbitrary amplitude, /)₁Topological charge of the main beam, /)₀To reference the topological charge of the beam, θ₁As measured in the angular position of the detector in a plane orthogonal to the composite beam propagation vector containing the first detector 1,andis an arbitrary phase due to a position gradient, anAndis an arbitrary phase due to interference of the propagating wavefront.

Likewise, the electric field E2 or related signal (indicated as D2 in fig. 2) on the second detector 2 can be represented by the following analytical formula:

wherein t is time, A₂And B₂Is a non-zero arbitrary amplitude, /)₁Topological charge of the main beam, /)₀To reference the topological charge of the beam, θ₂Is in a plane orthogonal to the composite beam propagation vector containing the detector 2The angular position of the detector 2 measured on the face,andis an arbitrary phase due to a position gradient, anAndis an arbitrary phase due to interference of the propagating wavefront.

As a further illustration of the geometric quantities defined above, fig. 6 shows, by means of a dash-dot line, the propagation axis z of a composite beam Q1 generated by the composite beam generating system (indicated with reference numeral 30 in fig. 6) already described above. Figure 6 also indicates the plane xy orthogonal to the propagation axis z, the respective position vectors of the two detectors 1 and 2Andand the angular position theta of each of the two detectors₁And theta₂。

The field or related signals are separated in frequency by means of various possible techniques (these techniques are known per se) so as to have in R1 and R2 only the field or related signal in the frequency band of the reference beam, and in P1 and P2 only the field or related signal in the frequency band of the main beam.

The following analytical expressions can thus be obtained:

in R1:

in R2:

in P1:

in P2:

the second phase comparator 4 provides an amount proportional to the phase difference of the field and the correlated signal between R1 and R2:

the first phase comparator 3 provides an amount proportional to the phase difference of the field and the correlated signal between P1 and P2:

because the main beam has a curvature substantially equal to the reference beam curvature and a propagation direction substantially coinciding with the reference beam propagation direction, the phase difference related to the inclination (tilt) has an excellent approximation:

since the distortion phenomena due to propagation are very similar for the main and reference beams (emitted superimposed in the composite beam), the phase difference associated with the distortion has an excellent approximation:

further, the proportionality constants of the two phase comparators may be selected so that the phase differences coincide.

Based on the above, the signal Q2 provides a quantity proportional to the difference:

as desired, such an amount is independent of the position inclination and the disturbance due to propagation.

Once the value of Q2 (i.e., Δ P/k- Δ R/k') is measured, at θ₁、θ₂K, k' and l₀(reference beam topology charge, can be initially set) is known, then the main beam topology charge value l₁Since the above formula is easily obtained, the orbital angular momentum L of the main beam can be obtained₁Please remember:

L＝(l*h)/2π。

if the main beam is phase modulated, the equations at the points R1, R2, P1, P2 become:

in R1:

in R2:

in P1:

in P2:

where δ (t) is a time-varying phase term due to phase modulation detected identically on the first and second detectors. Since the phase term δ (t) is compensated at the output of the second phase comparator 2, the following result is also obtained:

if the main beam is frequency-modulated, the equations at the points R1, R2, P1, P2 become:

in R1:

in R2:

in P1:

in P2:

where m (τ) is the time-varying modulation signal, and k_fIs a constant. Due to the itemCompensation at the output of the second phase comparator will still result in:

a method will now be described, also included in the present invention, for performing telecommunication of signals modulated according to any known modulation technique and grouped by means of orbital angular momentum multiplex.

Such a method comprises: generating a first orbital angular momentum L₁A step of characterizing the first beam of electromagnetic radiation F1, and generating a second beam of electromagnetic radiation characterized by at least one corresponding second orbital angular momentum L₂Step of characterizing at least one second beam of electromagnetic radiation F2. The first beam of electromagnetic radiation F1 and the at least one second beam of electromagnetic radiation F2 have respective spectrums in the same first frequency band and also have respective radii of curvature that substantially coincide with a value of the first beam radius of curvature.

Then, the method comprises: modulating a first piece of information to be emitted (represented by a first modulation function a (t)) on a first beam of electromagnetic radiation F1 by means of any modulation technique, to obtain a first modulated beam Fm 1; furthermore, at least one second information to be emitted (represented by a second modulation function b (t)) is modulated on at least one second beam of electromagnetic radiation F2 by means of any modulation technique, so as to obtain a second modulated beam Fm 2; then, a reference beam of electromagnetic radiation F0 is generated, which is dominated by the second orbital angular momentum L₀A second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature having a value substantially coincident with the first beam radius of curvature value.

Then, the method comprises: the step of superimposing and/or combining said reference beam F0, first modulated beam Fm1 and second modulated beam Fm2 to produce a composite beam of electromagnetic radiation Q1, said composite beam of electromagnetic radiation Q1 comprising the superposition of the reference beam F0 and of the main beam, and further comprising the superposition of said first modulated beam Fm1 and of at least one second modulated beam Fm 2.

The method then includes the step of emitting the resulting composite beam of electromagnetic radiation Q1.

Then, the method comprises: receiving said composite beam of electromagnetic radiation by means of a first beam detector 1 located at a first position to produce a first composite beam electrical signal D1 representing the electric and/or magnetic field and/or intensity of the electromagnetic radiation of the composite beam in said first position; and receiving the composite beam of electromagnetic radiation by means of a second beam detector located at a second different position relative to the first position to produce a second composite beam electrical signal D2, the second composite beam electrical signal D2 being representative of the electric and/or magnetic field of the composite beam and/or the intensity of the received electromagnetic radiation in said second position.

The method further comprises the following steps: a step of performing a frequency discrimination of the first composite beam electrical signal D1 to obtain a first main beam electrical signal P1 and a first reference beam electrical signal R1, the first main beam electrical signal P1 being representative of an electric field, and/or a magnetic field, and/or an intensity attributed to the main beam in the first position, the first reference beam electrical signal R1 being representative of an electric field, and/or a magnetic field, and/or an intensity attributed to the reference beam in the first position; and a step of performing a frequency discrimination of the second composite beam electrical signal D2 to derive a second main beam electrical signal P2 and a second reference beam electrical signal R2, the second main beam electrical signal P2 being representative of the electric field, and/or magnetic field, and/or intensity attributed to the main beam in the second position, and the second reference beam electrical signal R2 being representative of the electric field, and/or magnetic field, and/or intensity attributed to the reference beam in the second position.

The method further comprises the following steps: determining a phase of the first main beam electrical signal P1 and a phase of the second main beam electrical signal P2; further, determining the phase of the first reference beam electrical signal R1 and the phase of the second reference beam electrical signal R2; then, a first phase difference value Δ P is determined_abThe first phase difference value Δ P_abCorresponding to the difference between the phase of the first main beam electrical signal P1 and the phase of the second main beam electrical signal P2, wherein such first phase difference value Δ P_abDepending on the values of the first modulation function a (t) and the second modulation function b (t); still further, a second phase difference value Δ R is determined, which corresponds to the difference between the phase of the first reference beam electrical signal R1 and the phase of the second reference beam electrical signal R2.

Then, the method comprises: from the first phase difference Δ P_abDivide by the first wave number k minus the second phase difference Δ R divided by the second wave number k' to yield the difference (Q2 ═ Δ P_abK- Δ R/k'). The first wave number k is a wave number corresponding to a main beam, defined as k 2 pi/λ, λ being a wavelength of the above-mentioned main beam belonging to the above-mentioned first frequency band. The second wave number k 'is a wave number corresponding to the reference beam, defined as k' 2 pi/λ ', and λ' is a wavelength of the above-mentioned reference beam belonging to the above-mentioned second frequency band.

The above-mentioned difference Q2 represents the combination of the values of the first modulation function a (t) and the second modulation function b (t) irrespective of the condition of the position inclination between the first detector 1 and the second detector 2 and irrespective of the phase variation due to the disturbance to which the emitted composite beam is subjected before reception.

Finally, the method comprises: difference (Q2 ═ Δ P) based on the above determination_ab/k- Δ R/k') demultiplexes and demodulates information modulated on each of the first modulation beam Fm1 and the at least one modulation beam Fm 2.

According to an embodiment of this method, the number of modulated beams for orbital angular momentum multiplexing is greater than 2.

According to one embodiment of such a method, first beam of electromagnetic radiation F1 and at least one second beam of electromagnetic radiation F2 are digitally amplitude modulated in accordance with the amplitudes of a first modulation function a (t) and at least one second modulation function b (t).

In this case, the difference (Q2 ═ Δ P)_abK- Δ R/k') may take a plurality of desired values, each desired value representing a respective combination of digital amplitude values taken by the first modulation function a (t) and the at least one second modulation function b (t).

According to an implementation option, first beam of electromagnetic radiation F1 and at least second beam of electromagnetic radiation F2 are digitally amplitude modulated in a binary manner, and the amplitudes of first modulation function a (t) and at least one second modulation function b (t) may take on a logical value of 0 or 1.

In this case, the method further comprises the step of detecting the power or intensity Q3 (by means of the detector 16) received in correspondence of the first main beam electrical signal P1 or of the second main beam electrical signal P2, and comparing the received power or intensity with a minimum threshold value.

Determined difference (Q2 ═ Δ P)_abThe first desired value (Δ P) can be taken as/k- Δ R/k₁₀K- Δ R/k'), or a second desired value (Δ P)₀₁K- Δ R/k'), or a third desired value (Δ P)₁₁K- Δ R/k'), the first desired value being dependent on the first angular momentum (L)₁) The second desired value being dependent on the second angular momentum (L)₂) The third desired value depends on a combination of the first angular momentum and the second angular momentum.

The steps of demodulating, demultiplexing, and demodulating the modulated information include: if the determined difference (Δ P)_abK- Δ R/k') takes the first periodAbsolute value (Δ P)₁₀K- Δ R/k'), identifying that the first modulation beam Fm1 carries information corresponding to 1 and the second modulation beam Fm2 carries information corresponding to 0; if the determined difference (Δ P)_abK- Δ R/k') takes the second desired value (Δ P)₀₁K- Δ R/k'), identifying that the first modulation beam Fm1 carries information corresponding to 0 and the second modulation beam Fm2 carries information corresponding to 1; if the determined difference (Δ P)_abK- Δ R/k') takes the third expected value (Δ P)₁₁K- Δ R/k'), identifying that the first modulation beam Fm1 carries information corresponding to 1 and the second modulation beam Fm2 carries information corresponding to 1; if the received power or intensity Q3 is less than the above-mentioned minimum threshold, it is identified that the first modulation beam Fm1 carries information corresponding to 0 and the second modulation beam Fm2 carries information corresponding to 0.

According to another embodiment of such a method, first beam of electromagnetic radiation F1 and at least one second beam of electromagnetic radiation F2 are digitally modulated based on angular momentum. In this case, the angular momentum of the first beam F1 may take two different discrete values based on the first modulation function a (t), and the angular momentum of the at least one second beam F2 may take two different discrete values based on the respective at least one second modulation function b (t).

Difference (Q2 ═ Δ P)_abK- Δ R/k') may take a plurality of desired values, each desired value representing a respective combination of digital amplitude values taken by the first modulation function a (t) and the at least second modulation function b (t).

According to an implementation option, the amplitudes of the first modulation function a (t) and of the at least second modulation function b (t) may take logic values 0 or 1.

Determined difference (. DELTA.P)_abK- Δ R/k') may be: when the first modulation function a (t) takes a value of 1 and the second modulation function takes a value of 0, the first expected value (Δ P) is taken₁₀K- Δ R/k'); or, when the first modulation function a (t) takes a value of 0 and the second modulation function takes a value of 1, the second expected value (Δ P) is taken₀₁K- Δ R/k'); or, when the first modulation function a (t) takes a value of 1 and the second modulation function takes a value of 1, the third expected value (Δ P) is taken₁₁K- Δ R/k'); or, when the first modulation function a (t) takes a value of 0 and the second modulation function takes a value of 0, the fourth expected value (Δ P) is taken₀₀/k-ΔR/k')。

In this case, the steps of demodulating, demultiplexing, and demodulating the modulation information include: if the determined difference (Δ P)_abK- Δ R/k') takes a first desired value (Δ P)₁₀K- Δ R/k'), identifying that the first modulation beam Fm1 carries information corresponding to 1 and the second modulation beam Fm2 carries information corresponding to 0; if the determined difference (Δ P)_abK- Δ R/k') takes the second desired value (Δ P)₀₁K- Δ R/k'), identifying that the first modulation beam Fm1 carries information corresponding to 0 and the second modulation beam Fm2 carries information corresponding to 1; if the determined difference (Δ P)_abTaking a third expected value (Δ P) (/ k- Δ R/k)₁₁K- Δ R/k'), identifying that the first modulation beam Fm1 carries information corresponding to 1 and the second modulation beam Fm2 carries information corresponding to 1; if the determined difference (Δ P)_abK- Δ R/k') takes the fourth desired value (Δ P)₀₀K- Δ R/k'), it is identified that the first modulation beam Fm1 carries information corresponding to 0 and the second modulation beam Fm2 carries information corresponding to 0.

According to an embodiment of the method, the above-mentioned transmitted and received electromagnetic beams are light beams and/or laser beams.

A specific implementation example of the above telecommunication method with the associated physico-mathematical analysis is given below.

In the following description and in fig. 3 to 5, for simplicity, the points where the different signals (the first composite beam electrical signal D1, the second composite beam electrical signal D2, the first main beam electrical signal P1, the first reference beam electrical signal R1, the second main beam electrical signal P2 f, the second reference beam electrical signal R2) are located are indicated by the same names as the respective signals.

Having an angular momentum L₁And has an angular momentum L (defined herein as the first main beam F1)₂Is superimposed on the second beam (here defined as the second main beam F2) with an angular momentum L₀As shown in fig. 3. The two main beams have coincident and/or overlapping frequency bands and (in the examples detailed herein) are digitally amplitude-modulated. Furthermore, the two main beams have substantially uniform curvature.

The electric field at the electrical signal D1 can be described by the following analytical formula:

wherein t is time, A₁(t) and C₁(t) amplitude of the time-varying main beam, B₁Is a non-zero arbitrary amplitude of the reference beam,/₁Is the topological charge of the first main beam,/₂Is the topological charge of the second main beam, /)₀To reference the topological charge of the beam, θ₁As measured in the angular position of the first detector in a plane orthogonal to the composite beam propagation vector containing the first detector 1,andis an arbitrary phase due to a position gradient, andandis an arbitrary phase due to propagating wavefront disturbances.

The electric field at the electrical signal D2 can be described by the following analytical formula:

wherein t is time, A₂(t) and C₂(t) is the amplitude of the time-varying main beam, B₂Is a non-zero arbitrary amplitude of the reference beam,/₁Is the topological charge of the first main beam,/₂Is the topological charge of the second main beam, /)₀To reference the topological charge of the beam, θ₂As measured in the angular position of the second detector in a plane orthogonal to the composite beam propagation vector containing the second detector 2,andis an arbitrary phase due to a position gradient, andandis an arbitrary phase due to propagating wavefront disturbances.

As already observed previously, the signals D1 and D2 are measured by means of two detectors, the reference beam being distinguished in frequency from the main beam, and the signals in R1, R2, P1, P2 are therefore obtained using the following formula:

-in R1:

-in R2:

-in P1:

-in P2:

there is only a reference beam in R1 and R2, and there are superimposed main beams in P1 and P2.

The second phase comparator 4 provides a quantity proportional to the phase difference:

in digital modulation, the amplitude can be written as a₁＝A_1maxa(t)、A₂＝A_2maxa(t)、C₁＝C_1maxb(t)、C₂＝C_2maxb (t), wherein the functions a (t) and b (t) take the values 0 or 1, depending on the information digitally modulated in the first modulator and the second modulator, respectively.

A_1max、C_1maxIs the maximum amplitude of the field or signal representing the main beam (first and second, respectively) received by the first detector; a. the_2max、C_2maxIs the maximum amplitude of the field or signal representing the main beam (first and second, respectively) received by the second detector. In the transmitter, it is possible to set the amplitudes of the main beams such that they are equal, i.e.:

A_1max＝C_1max，A_2max＝C_2max。

the first phase comparator 3 provides a quantity proportional to the phase difference between the fields or signals in P1 and P2, which phase difference depends on the digital coding of the modulation functions a (t), b (t).

All possible combinations will now be considered.

When a (t) is 0 and b (t) is 0, the amplitudes of the main beams cancel each other, and thus the phase difference is uncertain.

When a (t) is 1 and b (t) is 0, only the angular momentum L exists₁Thus a relationship similar to that already described above in the case of a single main bundle applies:

when a (t) is 0 and b (t) is 1, only the angular momentum L exists₂Of the second main bundle, thus applyingA relationship similar to that already described above in the case of a single main bundle:

when a (t) is 1 and b (t) is 1, the main bundle exists, and therefore the following relationship holds:

based on the above-mentioned relations, it is possible to calculate all possible combinations of modulation signals in order to eliminate the phase arbitrariness due to position tilt and propagation-related wavefront distortion, similar to what is described in the case of a single main beam.

In summary, the following relationship is thus obtained.

When a (t) is 0 and b (t) is 0, the amplitudes of the main beams cancel each other, and thus the phase difference is uncertain.

When a (t) is 1 and b (t) is 0, the following results are obtained:

when a (t) is 0 and b (t) is 1, the following results are obtained:

when a (t) is 1 and b (t) is 1, the following results are obtained considering that the main bundle also has a substantially uniform curvature:

can be simply determined by appropriately selecting the topological charges l of the reference beam and the two main beams₀、l₁、l₂(i.e., the respective orbital angular momenta) to easily distinguish the above quantities (Δ P)₁₀/k–ΔR/k')、(ΔP₀₁/k-ΔR/k')、(ΔP₁₁K- Δ r/k'), i.e., set to three different predefined known values. These quantities measured at reception are therefore identifiable and are a description of the modulation value 0 or 1 applied to each of the two main beams. The information encoded in these quantities can thus be decoded, i.e. demodulated and identified.

Furthermore, it is advantageous to make these quantities independent of the phase difference due to the position inclination and independent of the distortions of the propagating wavefront, which can be eliminated due to the presence of the reference beam (as already noted above).

Possible examples of the choice of topological charge values are:

l₀＝0，l₁＝0，l₂＝2。

other combinations are clearly detectable.

There are still states to be identified, a (t) 0 and b (t) 0, the phase of which is not determined (as indicated above). This state is easily identified because it is the only combination in which the amplitude of the field or signal received by the two main beams is cancelled. Thus, when the intensity or power of the signal detected at point Q3 (by means of detector 16 shown in fig. 4) is below a predefined threshold, states a (t) 0, b (t) 0 are identified deterministically. Alternatively, both the first and second composite beam electrical signals D1 and D2 may be monitored to identify a condition in which both signals are below respective predefined thresholds.

A specific implementation example of the above-described method of telecommunication based on orbital angular momentum modulation with associated physico-mathematical analysis is given below.

The angular momentum modulation can be described using parameters similar to those already developed for the case of digital amplitude modulation.

The modulation functions a (t), b (t) take the values 0 or 1, depending on the information digitally modulated in the first modulator and the second modulator, respectively. Such a modulation function depends on the binary value taken, i.e. on the function L taken by a (t) and b (t)₁And L₂Determining discrete variables of angular momentum of the first beam of electromagnetic radiation and the at least one second beam of electromagnetic radiation, respectively:

L₁＝L₁(a(t))，L₂＝L₂(b(t))

that is, the topological charge is equivalently referenced: l₁＝l₁(a(t))，l₂＝l₂(b(t))。

Thus, the signals present in R1, R2, P1, P2 can be expressed as:

-in R1:

-in R2:

-in P1:

-in P2:

there is only a reference beam in R1 and R2; there are superimposed main beams in P1 and P2.

The second phase comparator 4 provides a quantity proportional to the phase difference (as in the general case):

the first phase comparator 3 provides a quantity proportional to the phase difference between the fields or signals in P1 and P2, which phase difference depends on the digital coding of the modulation functions a (t), b (t).

Considering all possible combinations, the following results were obtained:

wherein the combination is determined by the indices a, b and the corresponding values taken by the functions a (t), b (t).

Then, the difference Δ P_abThe/k- Δ R/k' is calculated for all possible combinations of modulation signals by means of the following formula in order to eliminate the phase arbitrariness due to position inclination and propagation-related wavefront distortion:

the topological charge value l can be selected₀、l₁(0)、l₁(1)、l₂(0)、l₂(1) Or respectively corresponding orbital angular momentum, such that the corresponding amount (Δ P)₀₀/k-ΔR/k')、(ΔP₀₁/k-ΔR/k')、(ΔP₁₀/k-ΔR/k')、(ΔP₁₁K-ar/k') are different from each other and therefore identifiable, to allow decoding (demodulation) of the encoded (modulated) information.

Furthermore, the above quantities are independent of the phase difference due to the position inclination and distortion of the propagating wavefront, which can be eliminated due to the presence of the reference beam.

An example of a topological charge value selection is/₀＝0、l₁(0)＝0、l₁(1)＝1、l₂(0)＝0、l₂(1) 2, from this it follows:

as can be seen, the four quantities are different and can therefore be identified.

Other value assignments are obviously possible, similar to the examples reported above.

It should be noted that angular momentum modulation is similar in many respects to amplitude modulation, and the block diagrams shown in fig. 3 and 4 are also suitable for angular momentum modulation, the only obvious difference being that the modulator modulates angular momentum rather than amplitude. Also in this case, the threshold detector of fig. 4 and 5 is not necessary.

With reference to fig. 1 and 2, a system for emitting and receiving a beam of electromagnetic radiation is now described, which is adapted to determine the orbital angular momentum of the received beam of electromagnetic radiation.

Such a system comprises means 5 for generating a main beam of electromagnetic radiation F1, means 6 for generating a reference beam of electromagnetic radiation F0, means 7 for generating a composite beam of electromagnetic radiation Q1 (as shown in fig. 1) and means 14 for emitting a composite beam of electromagnetic radiation Q1 (as shown in fig. 1), means for receiving the composite beam of electromagnetic radiation, first beam detecting means 1, second beam detecting means 2, first frequency discriminating means 8, second frequency discriminating means 9 and means 10 for determining orbital angular momentum (as shown in fig. 2).

The means 5 for generating a main beam of electromagnetic radiation are configured to generate a main beam of electromagnetic radiation F1, the main beam of electromagnetic radiation F1 having a first orbital angular momentum L₁A first spectrum in a first frequency band, and a first beam radius of curvature.

The means 6 for generating a reference beam of electromagnetic radiation are configured to generate a reference beam of electromagnetic radiation F0, the reference beam of electromagnetic radiation F0 being represented by a second beam of electromagnetic radiation F0Orbital angular momentum L₀A second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature substantially coincident with the first beam radius of curvature.

The means 7 for generating a composite beam of electromagnetic radiation and the means 14 for emitting a composite beam of electromagnetic radiation are configured to generate a composite beam of electromagnetic radiation Q1 comprising the superposition of the aforementioned main beam F1 and the reference beam F0 and to emit such a generated composite beam of electromagnetic radiation Q1.

Apparatus for receiving a composite beam of electromagnetic radiation comprising: a first beam detection device 1 located in a first position, the first beam detection device being configured to generate a first composite beam electrical signal D1 representative of the intensity of the electric and/or magnetic field and/or electromagnetic radiation of the composite beam in the first position; and a second beam detection device 2 located in a second position, the second beam detection device being configured to generate a second composite beam electrical signal D2, the second position being different with respect to the first position, the second composite beam electrical signal being representative of the electric and/or magnetic field and/or intensity of the electromagnetic radiation of the composite beam in the second position.

The first frequency discrimination means 8 are configured to perform a frequency discrimination of the first composite beam electrical signal D1 to derive a first main beam electrical signal P1, which first main beam electrical signal P1 represents the electric field, and/or the magnetic field, and/or the intensity attributed to the main beam in the first position, and a first reference beam electrical signal R1, which first reference beam electrical signal R1 represents the electric field, and/or the magnetic field, and/or the intensity attributed to the reference beam in the first position.

The second frequency discrimination means 9 is configured to perform frequency discrimination of the second composite beam electrical signal to obtain a second main beam electrical signal P2 and a second reference beam electrical signal R2, the second main beam electrical signal P2 being representative of the electric field, and/or the magnetic field, and/or the strength, attributed to the main beam in the second position, and the second reference beam electrical signal R2 being representative of the electric field, and/or the magnetic field, and/or the strength, attributed to the reference beam in the second position.

The device 10 for determining orbital angular momentum is configured to determine the first electrical signal P1, the second main beam, based on the above-mentioned main beamsThe electrical signal P2, the first reference beam electrical signal R1 and the second reference beam electrical signal R2 determine the orbital angular momentum L of the primary beam of electromagnetic radiation₁And/or due to the main beam orbital angular momentum L₁The spatial phase variation of the main beam of electromagnetic radiation.

According to different implementation options, the system is configured to perform the method for emitting and receiving a beam of electromagnetic radiation according to any of the above embodiments.

According to an embodiment of the system, the means 5 for generating the main beam of electromagnetic radiation and the means 6 for generating the reference beam of electromagnetic radiation comprise one or more sources or emitters of electromagnetic radiation (for example, in an implementation option, lasers) known per se.

According to an implementation option, the means 5 for generating a main beam of electromagnetic radiation further comprise an amplitude, and/or frequency, and/or phase modulator 50, and/or one or more angular momentum modulators 50 (such angular momentum modulators 50 may be spatial light modulators, for example).

According to an embodiment of the system, the means 7 for generating a composite beam of electromagnetic radiation comprise an electromagnetic beam combiner (e.g. a beam combiner) having two or more inputs and outputs known per se.

According to an embodiment of the system, the first beam detection means 1 comprises one or more diaphragms (optical openings), or an antenna, or a set of antennas, or any other per se known electromagnetic beam receiver, adapted to operate at the frequencies of the first and second beams. The means 14 for transmitting the electromagnetic beam comprise, for example, one or more transmitting antennas.

According to an embodiment of the system, the second beam detection means 2 comprise one or more diaphragms (optical openings), or antennas, or a set of antennas, or any other per se known electromagnetic beam receiver, suitable for operating at the frequencies of the first and second beams.

According to different embodiments, the first frequency discrimination means 8 and the second frequency discrimination means 9 may comprise frequency filters known per se.

According to an embodiment of the system, the means 10 for determining orbital angular momentum comprise: at least two phase comparators 3, 4 and at least one processor 15, the means for determining orbital angular momentum being configured to derive orbital angular momentum by means of processing (e.g. according to the formula shown above) based on output signals from the phase comparators.

According to one embodiment of the system, the apparatus 10 for determining orbital angular momentum comprises: at least two correlators 11, 12 and at least one processor 15, the means for determining the orbital angular momentum being configured to derive the orbital angular momentum based on output signals from the correlators by means of processing (e.g. according to the formula shown above).

Further details regarding implementation options involving the use of correlators are provided further herein with reference to fig. 5.

In this case, instead of using a phase comparator that provides a value proportional to the phase difference Δ P or Δ R, a correlator that provides a value proportional to the cosine of the phase difference cos (Δ P) or cos (Δ R) is used. The phase difference is then determined by the inverse function:

ΔP＝arccos[cos(ΔP)]

ΔR＝arccos[cos(ΔR)]

the correlation can be determined by means of the direct product of the fields or signals represented by P1 and P2 or R1 and R2.

Alternatively, it is possible to have the intensity I at P1 and P2, respectively, by means of passing measurements_P1And I_P2Or have an intensity I at R1 and R2, respectively_R1And I_R2Average intensity of interference between fields of<I>To determine the correlation, knowing:

cos(ΔP)＝(<I>-I_P1-I_P2)/(2(I_P1I_P2)^1/2)

cos(ΔR)＝(<I>-I_R1-I_R2)/(2(I_R1I_R2)^1/2)

according to an embodiment of the above system, the above mentioned emitted and received electromagnetic beam is a light beam and/or a laser beam.

With reference to fig. 3 and 4, a system will now be described for the telecommunication of signals modulated according to any known modulation technique and grouped by means of orbital angular momentum variate multiplexing.

Such a system comprises means 5, 6 for generating an electromagnetic beam, modulation means 50, beam combining and/or superimposing means 7, transmitting means 14, beam receiving means 1, 2, 8, 9, phase determining means 20 and processing means 15.

The means 5, 6 for generating an electromagnetic beam are configured to generate a first orbital angular momentum L₁Characterised by a first beam of electromagnetic radiation F1, and generating a second orbital angular momentum L consisting of at least one corresponding second orbital angular momentum L₂Characterized by at least one second beam of electromagnetic radiation F2.

The first beam of electromagnetic radiation F1 and the at least one second beam of electromagnetic radiation F2 have respective spectrums in the same first frequency band and also have respective radii of curvature that substantially coincide with a value of the first beam radius of curvature.

The means 5, 6 for generating an electromagnetic beam are further configured to generate a reference beam of electromagnetic radiation F0, the reference beam of electromagnetic radiation F0 being comprised of a second orbital angular momentum L₀A second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature having a value substantially coincident with the first beam radius of curvature value.

Modulating means 50 are configured to modulate a first piece of information to be emitted, represented by a first modulation function a (t), on a first beam of electromagnetic radiation F1, by means of any amplitude, and/or phase, and/or frequency modulation technique, so as to obtain a first modulated beam Fm 1; at least one second piece of information to be emitted, represented by a second modulation function b (t), is modulated on at least one second beam of electromagnetic radiation F2 by means of any amplitude, and/or phase, and/or frequency modulation technique, so as to obtain a second modulated beam Fm 2.

The beam combining and/or superimposing means 7 are configured to superimpose and/or combine the aforementioned reference beam F0, first modulated beam Fm1 and second modulated beam Fm2 so as to produce a composite beam of electromagnetic radiation Q1, this composite beam of electromagnetic radiation Q1 comprising the superimposition of the reference beam and the main beam, and in turn of the aforementioned first modulated beam Fm1 and at least one second modulated beam Fm 2.

The emitting device 14 is configured to emit the generated composite beam of electromagnetic radiation described above.

The means for receiving the composite beam of electromagnetic radiation comprise a first beam detecting means 1, a second beam detecting means 2, a first frequency discriminating means 8, a second frequency discriminating means 9.

The first beam detection device 1 is located in a first position and is configured to generate a first composite beam electrical signal D1 representative of the electric and/or magnetic field and/or the intensity of the electromagnetic radiation of the composite beam in the first position.

The second beam detection device 2 is located in a second position different with respect to the first position and is configured to generate a second composite beam electrical signal D2 representative of the electric and/or magnetic field and/or intensity of the electromagnetic radiation of the composite beam in the second position.

The first frequency discrimination device 8 is configured to perform frequency discrimination of the first composite beam electrical signal D1 to derive a first main beam electrical signal P1 representing an electric field, and/or a magnetic field, and/or an intensity attributed to the main beam in the first position, and a first reference beam electrical signal R1 representing an electric field, and/or a magnetic field, and/or an intensity attributed to the reference beam in the first position.

The second frequency discrimination means 9 is configured to perform frequency discrimination of the second composite beam electrical signal to obtain a second main beam electrical signal P2 representing the electric and/or magnetic field and/or strength attributed to the main beam in the second position and a second reference beam electrical signal R2 representing the electric and/or magnetic field and/or strength attributed to the reference beam in the second position.

The phase determining device 20 is configured to determine the phase of the first main beam electrical signal P1 and the phase of the second main beam electrical signal P2, and is further configured to determine the phase of the first reference beam electrical signal R1 and the phase of the second reference beam electrical signal R2.

The phase determining device 20 is further configured to determine a phase difference between the phase corresponding to the first main beam electrical signal P1 and the phase corresponding to the second main beam electrical signal P2A first phase difference value delta P_abWherein such first phase difference value Δ P_abA value taken in dependence on the first modulation function a (t) and the second modulation function b (t); still further, a second phase difference value Δ R is determined corresponding to the difference between the phase of the first reference beam electrical signal R1 and the phase of the second reference beam electrical signal R2; further, from the first phase difference Δ P_abDivide by wave number k minus the second phase difference Δ R divided by wave number k' to yield the difference Q2 ═ Δ P_abK- Δ R/k'. The first wave number k is a wave number corresponding to a main beam, defined as k 2 pi/λ, λ being a wavelength of the above-mentioned main beam belonging to the above-mentioned first frequency band. The second wave number k 'is a wave number corresponding to the reference beam, defined as k' 2 pi/λ ', and λ' is a wavelength of the above-mentioned reference beam belonging to the above-mentioned second frequency band.

The difference Q2 ═ Δ P_abThe/k-ar/k' represents the combination of the values taken by the first modulation function a (t) and the second modulation function b (t), independently of the condition of the position inclination between the first detector 1 and the second detector 2 and independently of the phase variation due to the interference to which the transmitted composite beam is subjected before reception.

The processing means 15 are configured to determine the difference Q2 ═ Δ P based on the preceding description_abK- Δ R/k' to demultiplex and demodulate the modulation information on each of the first modulation beam Fm1 and the at least one second modulation beam Fm 2.

According to various embodiments, the system is configured to perform a method of remote communication of a beam of electromagnetic radiation according to any one of the above embodiments.

According to an embodiment of the system, the means 5, 6 for generating an electromagnetic beam comprise one or more electromagnetic beam sources or emitters (for example, in the implementation option, lasers) known per se.

According to an embodiment of the system, the modulation means 50 comprise amplitude, and/or frequency, and/or phase, and/or angular momentum modulators, known per se.

According to an embodiment of the system, the first beam detection device 1 and the second beam detection device 2 comprise one or more diaphragms (optical openings), or antennas, or a set of antennas, or any other per se known electromagnetic beam receiver, each adapted to operate at the frequency of the first beam and the second beam.

According to an embodiment of the system, the first frequency discrimination means 8 and the second frequency discrimination means 9 comprise frequency filters known per se.

According to an embodiment of the system, the phase determination means 20 comprise at least two phase comparators 3, 4 known per se.

According to an embodiment of the system, the first and second frequency discrimination means comprise correlators 11, 12 known per se. With respect to such a correlator, the same considerations apply to the above referenced system for transmitting and receiving electromagnetic beams.

According to an embodiment of the system, the processing means 15 comprise one or more processors known per se, and associated software.

According to an embodiment of the above system, the above mentioned emitted and received electromagnetic beam is a light beam and/or a laser beam.

It is noted that the objects of the present invention are achieved entirely by the above-described systems and methods, by virtue of their functional and structural features.

In fact, the system and method for transmitting and receiving electromagnetic beams described above are able to detect accurately and reliably the orbital angular momentum of the received beam, in a manner independent of the inclination of the position of the receiver and independent of the distortions to which the beam is subjected during propagation.

This is achieved by means of a dual spatial detection of the composite beam at two different points, which composite beam comprises, in addition to the beam to be studied, another reference beam.

The possibility of accurately and reliably detecting the orbital angular momentum of a received beam is in turn advantageously suitable for a number of different applications, including for example the characterization of beams and the utilization of angular momentum variables for telecommunication purposes.

With reference to telecommunications applications, the method and system of the present invention allow the use of orbital angular momentum variables as additional degrees of freedom, which is advantageous for both signal modulation and signal multiplexing.

In particular, orbital angular momentum provides an additional level of multiplexing (with consequent obvious advantages) allowing to group the same signals from the point of view of other multiplexing variables (for example time or frequency), and these signals can be differentiated on the basis of different orbital angular momenta.

Modifications and adaptations of the above-described system and method embodiments, as well as replacement of functionally equivalent elements, may be made by those skilled in the art to meet contingent needs without departing from the scope of the appended claims. Each feature described as belonging to a possible embodiment may be implemented irrespective of the other embodiments described.