Method and system for demultiplexing and demodulating signals multiplexed in variable orbital angular momentum

Abstract

Describes a method for demultiplexing and demodulating (in particular, "local" demultiplexing and demodulating) an amplitude-modulated signal that is grouped by means of orbital angular momentum multiplexing. The method involves demultiplexing and demodulating the information a(t), b(t) modulated on each of a first modulated beam Fm1 and at least one second modulated beam Fm2 based on the phase differences ΔP ab and ΔR detected by a beam detector located downstream of the interferometric structure 40. Two portions of the electromagnetic beam carrying the modulation channels are provided to the interferometric structure as inputs multiplexed in the orbital angular momentum variable. Also described is a corresponding system 100 for demultiplexing and demodulating an amplitude-modulated signal and capable of implementing the above-described method.

Description

Technical Field

[0001] The present invention generally relates to the technical field of the emission and reception of electromagnetic beams (in particular optical / laser beams and microwave beams) with detection of the orbital angular momentum of the beam, and to the field of telecommunication based on electromagnetic beams (in particular optical / laser beams and microwave beams), orbital angular momentum modulation and / or orbital angular momentum multiplexing.

[0002] The present invention particularly relates to the demultiplexing and demodulation of signals multiplexed in orbital angular momentum variables (i.e., signals multiplexed by orbital angular momentum). Background Art

[0003] The propagation theory of electromagnetic beams (in particular laser beams and microwave beams) has recently demonstrated the existence of orbital angular momentum.

[0004] From a traditional perspective, orbital angular momentum is a concept related to different transverse modes of beam propagation.

[0005] This can also be considered as an illustration of the fact that the propagation front of an orbital angular momentum (OAM) wave is not a simple plane, but has an evolution that can be represented by a helical surface.

[0006] In other words, the Poynting vector and the wave vector are no longer simply parallel to the propagation direction, but are twisted around the propagation direction.

[0007] From a quantum perspective, orbital angular momentum is treated by another quantum number different from spin.

[0008] Recently, beams with non-zero orbital angular momentum and capable of taking different values have also been experimentally demonstrated.

[0009] When the detector is irradiated only by a finite portion of the radiation beam, even if the singularity is very distant, the "orbital angular momentum" variable is particularly difficult to detect and characterize due to its above-mentioned characteristics. In fact, there is no reliable system and method that allows the detection of the orbital angular momentum of an electromagnetic beam. For example, by means of local measurements of the received laser, even if the singularity is very distant, only a finite portion of the beam is incident on the detector.

[0010] On the other hand, due to various reasons including, for example, the characterization of the beam and the utilization of the angular momentum variable for telecommunication purposes, there is a felt need to detect the orbital angular momentum of the received beam.

[0011] This need cannot currently be met by known technical solutions through local measurements.

[0012] The applicant also realizes the possibility of exploiting the orbital angular momentum variable as an additional degree of freedom, which is advantageous for both modulating and multiplexing signals.

[0013] However, the background art in the considered technical field does not provide a reliable solution for long-distance communication based on orbital angular momentum multiplexing and / or modulation. Therefore, there is a particular need for such a solution.

[0014] In addition, in an important field of long-distance communication applications, there is a need for methods and systems capable of effectively demodulating and demultiplexing multiple signals transmitted on two or more amplitude-modulated and angular momentum multiplexed electromagnetic beams. Summary of the Invention

[0015] In view of the above, an object of the present invention is to provide a method for demultiplexing and demodulating an amplitude-modulated signal, which is grouped by multiplexing in an orbital angular momentum variable, for example, to at least partially eliminate the disadvantages of the prior art referred to above and to meet the above-mentioned needs particularly felt in the considered technical field.

[0016] This object is achieved by a method for demultiplexing and demodulating an amplitude-modulated signal according to a first aspect of the present invention, which is grouped by multiplexing in an orbital angular momentum variable.

[0017] In the method, the signal to be demultiplexed and demodulated includes a composite electromagnetic radiation beam, which comprises a superposition of a reference beam and a main beam, and further comprises a superposition of a first modulated beam and at least one second modulated beam;

[0018] wherein the first modulated beam is obtained by modulating a first piece of information on a first electromagnetic radiation beam by means of any amplitude modulation technique, and the first piece of information is represented by a first modulation function a(t), and wherein the at least one second modulated beam is obtained by modulating at least one second piece of information on at least one corresponding second electromagnetic radiation beam by means of any amplitude modulation technique, and the second piece of information is represented by a second modulation function b(t);

[0019] wherein the first electromagnetic radiation beam is characterized by a first orbital angular momentum, and the at least one second electromagnetic radiation beam is characterized by at least one corresponding second orbital angular momentum, wherein the first electromagnetic radiation beam and the at least one second electromagnetic radiation beam both have corresponding spectra in the same first frequency band and also have corresponding curvature radii that are substantially consistent with a first beam curvature radius value,

[0020] And wherein, the reference beam is characterized by a third orbital angular momentum, a second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature having a value substantially consistent with the value of the first beam radius of curvature;

[0021] Wherein, the method comprises the following steps:

[0022] - Passing the composite electromagnetic radiation beam through two openings so as to obtain a first composite beam portion downstream of the first opening and a second composite beam portion downstream of the second opening;

[0023] - Emitting the first composite beam portion along a first branch of the interferometer and emitting the second composite beam portion along a second branch of the interferometer;

[0024] - By means of a beam splitter of the interferometer, superimposing the first composite beam portion and the second composite beam portion along a third branch of the interferometer to obtain a corresponding third electromagnetic beam, and superimposing the first composite beam portion and the second composite beam portion along a fourth branch of the interferometer to obtain a corresponding fourth electromagnetic beam;

[0025] - Performing frequency discrimination of the third electromagnetic beam around the first frequency band so as to obtain a third filtered electromagnetic beam, wherein the contributions of the reference beam from the first composite beam portion and the reference beam from the second composite beam portion have been cancelled, and wherein, the components from the corresponding first modulation beam and at least one second modulation beam are retained;

[0026] - Performing frequency discrimination of the fourth electromagnetic beam around the second frequency band of the reference beam so as to obtain a fourth filtered electromagnetic beam, the fourth filtered electromagnetic beam comprising the superposition of two reference beams respectively belonging to the first composite beam portion and the second composite beam portion;

[0027] - Detecting the third filtered electromagnetic beam by means of a first beam detector to generate a first electrical signal, the first electrical signal representing the intensity of the electromagnetic radiation of the third filtered electromagnetic beam;

[0028] - At the first beam detector, based on the first electrical signal, determining a first phase difference between the component of the third filtered electromagnetic beam from the filtered portion of the first composite beam and the component of the third electromagnetic beam from the filtered portion of the second composite beam, wherein, the first phase difference depends on the values taken by the first modulation function a(t) and the second modulation function b(t);

[0029] - Detecting the fourth filtered electromagnetic beam by means of a second beam detector to generate a second electrical signal, the second electrical signal representing the intensity of the electromagnetic radiation of the fourth filtered electromagnetic beam;

[0030] - At the second beam detector, based on the second electrical signal, determine a second phase difference between two reference beams belonging to the first composite beam portion and the second composite beam portion;

[0031] - Based on the first phase difference and the second phase difference, demultiplex and demodulate the modulated information on each of the first modulated beam and the at least one second modulated beam.

[0032] The present invention also relates to a system for demultiplexing and demodulating an amplitude - modulated signal, which amplitude - modulated signal is grouped by multiplexing in an orbital angular momentum variable, and the system is capable of performing the above - mentioned method.

[0033] In a second aspect of the present invention, a system for demultiplexing and demodulating an amplitude - modulated signal, the amplitude - modulated signal being grouped by multiplexing in an orbital angular momentum variable,

[0034] wherein the signal to be demultiplexed and demodulated includes a composite electromagnetic radiation beam, the composite electromagnetic radiation beam comprising a superposition of a reference beam and a main beam, and thus comprising a superposition of a first modulated beam and at least one second modulated beam;

[0035] wherein the first modulated beam is obtained by modulating a first piece of information on a first electromagnetic radiation beam by means of any amplitude - modulation technique, the first piece of information being represented by a first modulation function a(t), and wherein the at least one second modulated beam is obtained by modulating at least one second piece of information on at least one corresponding second electromagnetic radiation beam by means of any amplitude - modulation technique, the second piece of information being represented by a second modulation function b(t);

[0036] wherein the first electromagnetic radiation beam is characterized by a first orbital angular momentum, and the at least one second electromagnetic radiation beam is characterized by at least one corresponding second orbital angular momentum, wherein the first electromagnetic radiation beam and the at least one second electromagnetic radiation beam both have corresponding spectra in the same first frequency band and also have corresponding curvature radii that are substantially consistent with a first beam curvature radius value,

[0037] and wherein the reference beam is characterized by a third orbital angular momentum, a second spectrum in a second frequency band different from the first frequency band, and a second beam curvature radius having a value that is substantially consistent with the first beam curvature radius value;

[0038] wherein the system comprises:

[0039] - A screen equipped with two openings, the screen being configured to allow the composite electromagnetic radiation beam to pass through the two openings so as to obtain a first composite beam portion downstream of the first opening and a second composite beam portion downstream of the second opening;

[0040] - An interferometer arranged downstream relative to the two openings, the interferometer comprising:

[0041] - A first branch configured to be passed through by the first composite beam portion;

[0042] - A second branch configured to be passed through by the second composite beam portion;

[0043] - A beam splitter configured to superimpose the first composite beam portion and the second composite beam portion along a third branch of the interferometer to obtain a corresponding third electromagnetic beam, and to superimpose the first composite beam portion and the second composite beam portion along a fourth branch of the interferometer to obtain a corresponding fourth electromagnetic beam;

[0044] - A first frequency discrimination device configured to discriminate the frequency of the third electromagnetic beam around the first frequency band so as to obtain a third filtered electromagnetic beam, in which the contributions of the reference beam from the first composite beam portion and the reference beam from the second composite beam portion have been cancelled, and in which the components from the corresponding first modulated beam and the at least one second modulated beam are retained;

[0045] - A second frequency discrimination device configured to discriminate the frequency of the fourth electromagnetic beam around the second frequency band of the reference beam so as to obtain a fourth filtered electromagnetic beam, the fourth filtered electromagnetic beam comprising the superposition of two reference beams respectively belonging to the first composite beam portion and the second composite beam portion;

[0046] - A first beam detector configured to detect the third filtered electromagnetic beam to generate a first electrical signal, the first electrical signal representing the intensity of the electromagnetic radiation of the third filtered electromagnetic beam;

[0047] - A second beam detector configured to detect the fourth filtered electromagnetic beam to generate a second electrical signal, the second electrical signal representing the intensity of the electromagnetic radiation of the fourth filtered electromagnetic beam;

[0048] - A processing device configured to:

[0049] - At the first beam detector, based on the first electrical signal, determine a first phase difference between a component of the third filtered electromagnetic beam from the first composite beam filtering section and a component of the third electromagnetic beam from the second composite beam filtering section, where the first phase difference depends on values taken by the first modulation function a(t) and the second modulation function b(t);

[0050] - At the second beam detector, based on the second electrical signal, determine a second phase difference between two reference beams belonging to the first composite beam section and the second composite beam section;

[0051] - Based on the first phase difference and the second phase difference, demultiplex and demodulate the information modulated on each of the first modulated beam and the at least one second modulated beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Further features and advantages of the above - described method and system according to the present invention will become apparent from the following description of preferred embodiments, which are given by way of indicative and non - limiting examples with reference to the accompanying drawings, in which:

[0053] - Figure 1 shows a simplified diagram of the transmitting part of an embodiment of a system for transmitting and receiving electromagnetic radiation beams according to the present invention; and Figure 1 certain steps of the corresponding method are shown simultaneously;

[0054] - Figure 2 shows a simplified diagram of the receiving part of an embodiment of a system for transmitting and receiving electromagnetic radiation beams according to the present invention; and Figure 2 certain other steps of the corresponding method are shown simultaneously;

[0055] - Figure 3 shows a simplified diagram of the transmitting part of an embodiment of a telecommunication system according to the present invention; and Figure 3 certain steps of the corresponding method are shown simultaneously;

[0056] - Figure 4 shows a simplified diagram of the receiving part of an embodiment of a telecommunication system according to the present invention; and Figure 4 certain other steps of the corresponding method are shown simultaneously;

[0057] - Figure 5 shows an embodiment of a system according to the present invention, including a correlator;

[0058] - Figure 6 describes certain geometric quantities used in the system diagrams;

[0059] -Figure 7 depicts a system for demultiplexing and demodulating signals according to an embodiment of the present invention;

[0060] - Figure 8 and Figure 9 depicts systems for demultiplexing and demodulating signals according to two respective further embodiments of the present invention. DETAILED DESCRIPTION

[0061] Reference Figures 1 to 6 describes a method for transmitting and receiving a beam of electromagnetic radiation, the method being suitable for determining the orbital angular momentum of the received beam of electromagnetic radiation.

[0062] The method first includes the step of generating at least one main electromagnetic radiation beam F1, and the step of generating a reference beam F0, the main electromagnetic radiation beam being characterized by a first orbital angular momentum L1, a first spectrum in a first frequency band, and a first beam curvature radius, the reference electromagnetic radiation beam F0 being characterized by a third orbital angular momentum L0, a second spectrum in a second frequency band different from the above-mentioned first frequency band, and a second beam curvature radius substantially consistent with the above-mentioned first beam curvature radius.

[0063] It should be noted that the above-mentioned characterizations based on the first orbital angular momentum L1 and the third orbital angular momentum L0 can also be correspondingly described in terms of topological charges (l1, l0), since the angular momentum L and the topological charge l are related by the following relationship:

[0064] L = (l * h) / 2π (where h is Planck's constant).

[0065] Therefore, the method includes generating a composite electromagnetic radiation beam Q1, the composite electromagnetic radiation beam comprising a superposition of the above-mentioned at least one main beam F1 and the reference beam F0, and transmitting the resulting composite electromagnetic radiation beam Q1.

[0066] The method further includes the step of receiving the above-mentioned composite electromagnetic radiation beam Q1 by means of a first beam detector 1 located at a first position to generate a first composite beam electrical signal D1, the first composite beam electrical signal D1 representing the electric field, and / or magnetic field, and / or intensity of the electromagnetic radiation of the composite beam at such a first position; and the step of receiving the above-mentioned composite electromagnetic radiation beam Q1 by means of a second beam detector 2 located at a second different position relative to the above-mentioned first position to generate a second composite beam electrical signal D2, the second composite beam electrical signal D2 representing the electric field, and / or magnetic field, and / or intensity of the received electromagnetic radiation of the composite beam at such a second position.

[0067] The method further includes the following steps: performing frequency discrimination on a first composite beam electrical signal D1 to obtain a first main beam electrical signal P1 and a first reference beam electrical signal R1, where the first main beam electrical signal P1 represents the electric field, and / or magnetic field, and / or intensity attributed to the main beam at the first position, and the first reference beam electrical signal R1 represents the electric field, and / or magnetic field, and / or intensity attributed to the reference beam at the first position; and performing frequency discrimination on a second composite beam electrical signal D2 to obtain a second main beam electrical signal P2 and a second reference beam electrical signal R2, where the second main beam electrical signal P2 represents the electric field, and / or magnetic field, and / or intensity attributed to the main beam at the second position, and the second reference beam electrical signal R2 is the electric field, and / or magnetic field, and / or intensity attributed to the reference beam at the second position.

[0068] Finally, the method includes determining the orbital angular momentum L1 of the main electromagnetic radiation beam and / or the spatial phase variable of the main electromagnetic radiation beam attributed to the orbital angular momentum L1 of the main beam based on the above first main beam electrical signal P1, second main beam electrical signal P2, first reference beam electrical signal R1, and second reference beam electrical signal R2.

[0069] According to an embodiment of the method, the determining step includes: determining a first phase difference ΔP, where the first phase difference ΔP corresponds 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 ΔR, where the second phase difference ΔR 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, subtracting the second phase difference ΔR divided by the second wave number k' from the first phase difference ΔP divided by the first wave number k to obtain a difference (Q2 = ΔP / k - ΔR / k'), the above difference is independent of the positional inclination condition between the first beam detector and the second beam detector, but is derived from the relative positions of the two detectors with respect to the beam propagation, and the difference is independent of the phase variable caused by the interference suffered by the transmitted composite beam before reception; and then determining the orbital angular momentum of the main electromagnetic radiation beam based on the obtained difference (Q2 = ΔP / k – ΔR / k').

[0070] The first wave number k is the wave number corresponding to the main beam, defined as k = 2π / λ, where λ is the wavelength of the main beam belonging to the above first frequency band. The second wave number k' is the wave number corresponding to the reference beam, defined as k' = 2π / λ', where λ' is the wavelength of the reference beam belonging to the above second frequency band.

[0071] The "positional inclination" (or "positional tilt") is defined as the angle formed between the straight line connecting two detectors and the (orthogonal) projection of this straight line on a plane orthogonal to the beam propagation axis.

[0072] According to a specific implementation example, the steps of determining the orbital angular momentum of the main electromagnetic radiation beam include determining the orbital angular momentum of the main electromagnetic radiation beam based on the following formula:

[0073] ΔP / k–ΔR / k'∝(L1 / k-L0 / k')(θ2-θ1)

[0074] Where θ1 is the angular position of the first beam detector measured in a plane orthogonal to the composite beam propagation vector including the first beam detector; θ2 is the angular position of the second beam detector measured in a plane orthogonal to the composite beam propagation vector including the second beam detector; ∝ indicates proportional.

[0075] According to an implementation option, the step of determining the first phase difference ΔP includes 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 ΔR includes 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.

[0076] According to another implementation option, the step of determining the first phase difference ΔP includes 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 ΔR includes performing a correlation operation between the first reference beam electrical signal R1 and the second reference beam electrical signal R2.

[0077] According to an implementation of this method, the orbital angular momentum of the reference beam is always known.

[0078] According to an implementation option, the orbital angular momentum of the reference beam takes a constant value L0 = 0.

[0079] According to an implementation of this method, the first position of the first beam detector 1 and the second position of the second beam detector 2 are fixed and constant, and are different from the position of the singularity point of the beam.

[0080] According to another implementation of this method, the first position of the first beam detector 1 and / or the second position of the second beam detector 2 are movable, and the reciprocal relationship between the above first position and the second position is always known.

[0081] According to an implementation option, the second frequency band is substantially monochromatic.

[0082] According to a specific implementation option, the second frequency band is adjacent to the first frequency band.

[0083] According to a possible implementation of the method, the step of performing frequency discrimination on the first composite beam electrical signal or the second composite beam electrical signal includes performing frequency filtering, or performing frequency separation by means of heterodyne technology or other frequency separation methods.

[0084] According to an implementation of the method, at least one main electromagnetic radiation beam is unmodulated.

[0085] According to other implementations of the method, at least one main electromagnetic radiation beam is amplitude-modulated, and / or phase-modulated, and / or frequency-modulated, and / or orbital angular momentum-modulated.

[0086] According to an implementation of the method, all the emitted and received electromagnetic beams mentioned above are light beams and / or laser beams.

[0087] Hereinafter, specific implementation examples of the method are given by using relevant physical and mathematical analyses.

[0088] In the following description and in Figure 1 and Figure 2 for simplicity, the points where different signals are located (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, the second reference beam electrical signal) are designated by the same names as their respective signals.

[0089] As has been observed, the composite beam Q1 is generated by superimposing at least one beam having an orbital angular momentum L = L1 (except 0) (defined herein as the main beam F1) on a beam having an angular momentum L = L0 (defined herein as the reference beam F0).

[0090] The main beam can 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 substantially has the same curvature and the same propagation vector as the main beam. The reference beam preferably has a topological charge l0 = 0, which also means an orbital angular momentum L0 = 0.

[0091] The identification of the spatial phase difference generated by the main beam having an orbital angular momentum L1 is obtained by using two detectors at any position in space except at the points of the singularities of the vortex.

[0092] As is well known, the expression "singularity of vortex" refers to the point in the vortex where the result of the electromagnetic field is reduced to zero and the phase of the field cannot be determined at that point.

[0093] In the case where the main beam is unmodulated, the electric field E1 or the related signal on the first beam detector 1 (in Figure 2The one indicated as D1 in [ ] can be represented by the following analytical formula:

[0094]

[0095] where t is time, A1 and B1 are non-zero arbitrary amplitudes, l1 is the topological charge of the main beam, l0 is the topological charge of the reference beam, θ1 is the angular position of the detector measured in a plane orthogonal to the propagation vector of the composite beam containing the first beam detector 1, and is an arbitrary phase attributable to the positional tilt, and α(x → 1) and α′(x → 1) are arbitrary phases attributable to the interference of the propagation wavefront.

[0096] Similarly, the electric field E2 or the related signal ( Figure 2 indicated as D2 in [ ]) on the second beam detector 2 can be represented by the following analytical formula:

[0097]

[0098] where t is time, A2 and B2 are non-zero arbitrary amplitudes, l1 is the topological charge of the main beam, l0 is the topological charge of the reference beam, θ2 is the angular position of detector 2 measured in a plane orthogonal to the propagation vector of the composite beam containing detector 2, and are arbitrary phases attributable to the positional tilt, and α(x → 2) and α′(x → 2) are arbitrary phases attributable to the interference of the propagation wavefront.

[0099] As a further illustration of the geometric quantities defined above, Figure 6 the propagation axis z of the composite beam Q1 generated by the composite beam generation system (indicated by reference numeral 30 in Figure 6 ) described previously is shown by a dotted line. Figure 6 The plane xy orthogonal to the propagation axis z is also indicated, as well as the position vectors x → 1 and x → 2 of the two detectors 1 and 2 respectively, and the above-mentioned angular positions θ1 and θ2 of the two detectors respectively.

[0100] The field or related signal is frequency-separated by means of various possible techniques (which are known per se) so as to have only the field or related signal in the frequency band of the reference beam in R1 and R2, while having only the field or related signal in the frequency band of the main beam in P1 and P2.

[0101] Thus, the following analytical expressions can be obtained:

[0102] In R1:

[0103] In R2:

[0104] In P1:

[0105] In P2:

[0106] The second phase comparator 4 provides a quantity proportional to the phase difference between the field and the correlation signal between R1 and R2:

[0107]

[0108] The first phase comparator 3 provides a quantity proportional to the phase difference between the field and the correlation signal between P1 and P2:

[0109]

[0110] Since the main beam has a curvature substantially equal to that of the reference beam and a propagation direction substantially consistent with that of the reference beam, the phase difference related to the tilt (inclination) has an excellent approximation:

[0111]

[0112] Since the distortion phenomena due to propagation are very similar for the main beam and the reference beam (emitted superposed in the composite beam), the phase difference related to the distortion has an excellent approximation:

[0113]

[0114] In addition, the proportionality constants of the two phase comparators can be selected to make the phase differences consistent.

[0115]

[0116] Based on the above, the signal Q2 provides a quantity proportional to the difference:

[0117]

[0118] As desired, such a quantity is independent of the positional tilt and the interference due to propagation.

[0119] Once the value of Q2 is measured (i.e., ΔP / k – ΔR / k'), and the values of θ1, θ2, k, k', and l0 (the topological charge of the reference beam, which can be initially set) are known, the topological charge value l1 of the main beam can be easily obtained from the above formula, and thus the orbital angular momentum L1 of the main beam can also be obtained. Remember:

[0120] L = (l * h) / 2π。

[0121] If the main beam is phase - modulated, the equations at points R1, R2, P1, and P2 become:

[0122] At R1:

[0123] At R2:

[0124] At P1:

[0125] At P2:

[0126] where δ(t) is a time - varying phase term attributable to the phase modulation detected equally on the first - beam detector and the second - beam detector. Since the phase term δ(t) is compensated at the output of the second phase comparator 4, the following results are also obtained:

[0127]

[0128] If the main beam is frequency - modulated, the equations at points R1, R2, P1, and P2 become:

[0129] At R1:

[0130] At R2:

[0131] At P1:

[0132] At P2:

[0133] where m(τ) is a time - varying modulation signal, and k f is a constant. Since this term is compensated at the output of the second phase comparator, the following results will still be obtained:

[0134]

[0135] Now a method will be described, which is also included in the present invention, for performing long - distance communication of signals modulated according to any known modulation technique and grouped by means of orbital - angular - momentum variable multiplexing.

[0136] This method includes: the step of generating a first electromagnetic radiation beam F1 characterized by a first orbital angular momentum L1, and the step of generating at least one second electromagnetic radiation beam F2 characterized by at least one corresponding second orbital angular momentum L2. The first electromagnetic radiation beam F1 and the at least one second electromagnetic radiation beam F2 have respective spectra in the same first frequency band, and also have respective curvature radii that are substantially consistent with the first beam curvature radius value.

[0137] Then, the method includes: modulating a first piece of information to be transmitted (represented by a first modulation function a(t)) on the first electromagnetic radiation beam F1 by means of any modulation technique to obtain a first modulated beam Fm1; further, modulating at least one second piece of information to be transmitted (represented by a second modulation function b(t)) on the at least one second electromagnetic radiation beam F2 by means of any modulation technique to obtain a second modulated beam Fm2; then, generating a reference beam F0, which is characterized by a third orbital angular momentum L0, a second spectrum in a second frequency band different from the above-mentioned first frequency band, and a second beam curvature radius, and the second beam curvature radius has a value that is substantially consistent with the above-mentioned first beam curvature radius value.

[0138] Then, the method includes: the step of superimposing and / or combining the above-mentioned reference beam F0, the first modulated beam Fm1, and the second modulated beam Fm2 to generate a composite electromagnetic radiation beam Q1, which includes the superposition of the reference beam F0 and the main beam, and further includes the superposition of the above-mentioned first modulated beam Fm1 and the at least one second modulated beam Fm2.

[0139] Then, the method includes the step of transmitting the generated composite electromagnetic radiation beam Q1.

[0140] Then, the method includes: receiving the above-mentioned composite electromagnetic radiation beam by means of a first beam detector 1 located at a first position to generate a first composite beam electrical signal D1, which represents the electric field, and / or magnetic field, and / or intensity of the electromagnetic radiation of the composite beam at the above-mentioned first position; and receiving the above-mentioned composite electromagnetic radiation beam by means of a second beam detector located at a second different position relative to the first position to generate a second composite beam electrical signal D2, which represents the electric field, and / or magnetic field, and / or intensity of the received electromagnetic radiation of the composite beam at the second position.

[0141] The method further includes: performing frequency discrimination on a first composite beam electrical signal D1 to obtain a first main beam electrical signal P1 and a first reference beam electrical signal R1, where the first main beam electrical signal P1 represents the electric field, and / or magnetic field, and / or intensity attributed to the main beam at a first position, and the first reference beam electrical signal R1 represents the electric field, and / or magnetic field, and / or intensity attributed to the reference beam at the first position; and performing frequency discrimination on a second composite beam electrical signal D2 to obtain a second main beam electrical signal P2 and a second reference beam electrical signal R2, where the second main beam electrical signal P2 represents the electric field, and / or magnetic field, and / or intensity attributed to the main beam at a second position, and the second reference beam electrical signal R2 represents the electric field, and / or magnetic field, and / or intensity attributed to the reference beam at the second position.

[0142] The method further includes: determining the phase of the first main beam electrical signal P1 and the 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, determining a first phase difference ΔP ab , the first phase difference ΔP ab 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, where such a first phase difference ΔP ab depends on the values of a first modulation function a(t) and a second modulation function b(t); further, determining a second phase difference ΔR, where the second phase difference ΔR 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.

[0143] Then, the method includes: subtracting the second phase difference ΔR divided by a second wave number k' from the first phase difference ΔP ab divided by a first wave number k to obtain a difference (Q2 = ΔP ab / k – ΔR / k'). The first wave number k is the wave number corresponding to the main beam, defined as k = 2π / λ, where λ is the wavelength of the main beam belonging to the above-mentioned first frequency band. The second wave number k' is the wave number corresponding to the reference beam, defined as k' = 2π / λ', where λ' is the wavelength of the reference beam belonging to the above-mentioned second frequency band.

[0144] The above difference Q2 represents a combination of the values of the first modulation function a(t) and the second modulation function b(t), independent of the positional inclination condition between the first beam detector 1 and the second beam detector 2 and independent of the phase variables caused by the interference suffered by the transmitted composite light beam before reception.

[0145] Finally, the method includes: based on the above-determined difference (Q2 = ΔP abDemultiplex and demodulate the information modulated on each of the first modulation beam Fm1 and at least one modulation beam Fm2 by ( / k - ΔR / k').

[0146] According to an embodiment of this method, the number of modulation beams multiplexed with orbital angular momentum is greater than 2.

[0147] According to an embodiment of this method, the first electromagnetic radiation beam F1 and at least one second electromagnetic radiation beam F2 are digitally amplitude modulated according to the amplitudes of the first modulation function a(t) and at least one second modulation function b(t).

[0148] In this case, the difference (Q2 = ΔP ab / k - ΔR / k') can take multiple expected values, each expected value representing a corresponding combination of the digital amplitude values taken by the first modulation function a(t) and at least one second modulation function b(t).

[0149] According to an implementation option, the first electromagnetic radiation beam F1 and at least the second electromagnetic radiation beam F2 are digitally amplitude modulated in a binary manner, and the amplitudes of the first modulation function a(t) and at least one second modulation function b(t) can take logical values 0 or 1.

[0150] In this case, the method further includes the step of detecting the received power or intensity Q3 (by means of detector 16) 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.

[0151] The determined difference (Q2 = ΔP ab / k - ΔR / k') can take a first expected value (ΔP 10 / k - ΔR / k'), or a second expected value (ΔP 01 / k - ΔR / k'), or a third expected value (ΔP 11 / k - ΔR / k'), where the first expected value depends on the first angular momentum (L1), the second expected value depends on the second angular momentum (L2), and the third expected value depends on the combination of the first angular momentum and the second angular momentum.

[0152] The steps of demodulating, demultiplexing, and demodulating the modulation information include: if the determined difference (ΔP ab / k - ΔR / k') takes the above-mentioned first expected value (ΔP 10 / k - ΔR / k'), then identify that the first modulation beam Fm1 carries the information corresponding to 1, and the second modulation beam Fm2 carries the information corresponding to 0; if the determined difference (ΔP ab / k - ΔR / k') takes the above-mentioned second expected value (ΔP 01 / k - ΔR / k'), then it is recognized 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 (ΔP ab / k - ΔR / k') takes the above third expected value (ΔP 11 / k - ΔR / k’), then it is recognized 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 minimum threshold, then it is recognized that the first modulation beam Fm1 carries information corresponding to 0, and the second modulation beam Fm2 carries information corresponding to 0.

[0153] According to another embodiment of this method, the first electromagnetic radiation beam F1 and at least one second electromagnetic radiation beam F2 are digitally modulated based on angular momentum. In this case, the angular momentum of the first beam F1 can take two different discrete values based on the first modulation function a(t), and the angular momentum of at least one second beam F2 can take two different discrete values based on their respective at least one second modulation function b(t).

[0154] The difference (Q2 = ΔP ab / k - ΔR / k') can take multiple expected values, and each expected value represents a corresponding combination of the digital amplitude values taken by the first modulation function a(t) and the at least second modulation function b(t).

[0155] According to an implementation option, the amplitudes of the first modulation function a(t) and the at least second modulation function b(t) can take logical values 0 or 1.

[0156] The determined difference (ΔP ab / k - ΔR / k') can: when the first modulation function a(t) takes the value 1 and the second modulation function takes the value 0, take the first expected value (ΔP 10 / k - ΔR / k'); or, when the first modulation function a(t) takes the value 0 and the second modulation function takes the value 1, take the second expected value (ΔP 01 / k - ΔR / k'); or, when the first modulation function a(t) takes the value 1 and the second modulation function takes the value 1, take the third expected value (ΔP 11 / k - ΔR / k'); or, when the first modulation function a(t) takes the value 0 and the second modulation function takes the value 0, take the fourth expected value (ΔP 00 / k - ΔR / k').

[0157] In this case, the steps of demodulating, demultiplexing, and demodulating the modulated information include: if the determined difference (ΔP ab / k - ΔR / k') takes the first expected value (ΔP 10 / k - ΔR / k'), the first modulation beam Fm1 is recognized as carrying information corresponding to 1, and the second modulation beam Fm2 is recognized as carrying information corresponding to 0; if the determined difference (ΔP ab / k - ΔR / k') takes a second expected value (ΔP 01 / k - ΔR / k’), the first modulation beam Fm1 is recognized as carrying information corresponding to 0, and the second modulation beam Fm2 is recognized as carrying information corresponding to 1; if the determined difference (ΔP ab / k - ΔR / k') takes a third expected value (ΔP 11 / k - ΔR / k’), the first modulation beam Fm1 is recognized as carrying information corresponding to 1, and the second modulation beam Fm2 is recognized as carrying information corresponding to 1; if the determined difference (ΔP ab / k - ΔR / k') takes a fourth expected value (ΔP 00 / k - ΔR / k’), the first modulation beam Fm1 is recognized as carrying information corresponding to 0, and the second modulation beam Fm2 is recognized as carrying information corresponding to 0.

[0158] According to an embodiment of this method, the transmitted and received electromagnetic beams mentioned above are light beams and / or laser beams.

[0159] Specific implementation examples of the above-mentioned remote communication method using relevant physical - mathematical analysis are given below.

[0160] In the following description and Figures 3 to 5 for simplicity, the points where 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 P2f, the second reference beam electrical signal R2) are located are indicated by the same names as their respective signals.

[0161] A first beam with angular momentum L1 (here defined as the first main beam F1) and a second beam with angular momentum L2 (here defined as the second main beam F2) are superimposed on a reference beam with angular momentum L0, as Figure 3 shown. The two main beams have coincident and / or overlapping frequency bands and (in the examples detailed herein) are digitally amplitude - modulated. In addition, the two main beams have substantially the same curvature.

[0162] The electric field at the electrical signal D1 can be described by the following analytical formula:

[0163]

[0164] where t is time, A1(t) and C1(t) are the amplitudes of the main beams varying with time, B1 is an arbitrary non-zero amplitude of the reference beam, l1 is the topological charge of the first main beam, l2 is the topological charge of the second main beam, l0 is the topological charge of the reference beam, θ1 is the angular position of the first beam detector measured in a plane orthogonal to the composite beam propagation vector containing the first beam detector 1, and is an arbitrary phase attributable to the positional tilt, and α(x → 1), α′(x → 1) and α″(x → 1) are arbitrary phases attributable to the propagation wavefront interference.

[0165] The electric field at the electrical signal D2 can be described by the following analytical expression:

[0166]

[0167] where t is time, A2(t) and C2(t) are the main beam amplitudes varying with time, B2 is an arbitrary non-zero amplitude of the reference beam, l1 is the topological charge of the first main beam, l2 is the topological charge of the second main beam, l0 is the topological charge of the reference beam, θ2 is the angular position of the second beam detector measured in a plane orthogonal to the composite beam propagation vector containing the second beam detector 2, and is an arbitrary phase attributable to the positional tilt, and α(x → 2), α′(x → 2) and α″(x → 2) are arbitrary phases attributable to the propagation wavefront interference.

[0168] As previously observed, the signals D1 and D2 are measured with the aid of two detectors, and the reference beam is distinguished from the main beam in terms of frequency. Therefore, the signals in R1, R2, P1, and P2 are obtained using the following equations:

[0169] - In R1:

[0170] - In R2:

[0171] - In P1:

[0172]

[0173] - In P2:

[0174]

[0175] Only the reference beam is present in R1 and R2, and the superimposed main beams are present in P1 and P2.

[0176] The second phase comparator 4 provides a quantity proportional to the phase difference:

[0177]

[0178] In digital modulation, the amplitudes can be written as A1 = A 1max a(t), A2 = A 2max a(t), C1 = C 1max b(t), C2 = C 2max b(t), where the functions a(t) and b(t) take the values 0 or 1, depending on the information digitally modulated in the first and second modulators respectively.

[0179] A 1max 、C 1max represent the maximum amplitudes of the fields or signals of the main beams (first and second respectively) received by the first beam detector; A 2max 、C 2max represent the maximum amplitudes of the fields or signals of the main beams (first and second respectively) received by the second beam detector. In the transmitter, it is possible to set the amplitudes of the main beams to be equal, i.e.:

[0180] A 1max = C 1max , A 2max = C 2max .

[0181] The first phase comparator 3 provides a quantity proportional to the phase difference between the fields or signals in P1 and P2, which depends on the digital coding of the modulation functions a(t), b(t).

[0182] Now all possible combinations will be considered.

[0183] When a(t) = 0 and b(t) = 0, the amplitudes of the main beams cancel each other out, so the phase difference is indeterminate.

[0184] When a(t) = 1 and b(t) = 0, only the first main beam with angular momentum L1 is present, so a relationship similar to the one already described above in the case of a single main beam applies:

[0185]

[0186] When a(t) = 0 and b(t) = 1, only the second main beam with angular momentum L2 is present, so a relationship similar to the one already described above in the case of a single main beam applies:

[0187]

[0188] When a(t) = 1 and b(t) = 1, there is a main beam in both cases, so the following relationship holds:

[0189]

[0190] Based on the above relationship, it is possible to calculate all possible combinations of the modulation signals in order to eliminate the phase arbitrariness attributed to the position tilt and the wavefront distortion related to propagation, similar to that described in the case of a single main beam.

[0191] In summary, the following relationship is thus obtained.

[0192] When a(t) = 0 and b(t) = 0, the amplitudes of the main beams cancel each other out, so the phase difference is indeterminate.

[0193] When a(t) = 1 and b(t) = 0, the following results are obtained:

[0194]

[0195] When a(t) = 0 and b(t) = 1, the following results are obtained:

[0196]

[0197] When a(t) = 1 and b(t) = 1, considering that the main beams also have substantially consistent curvatures, the following results are obtained:

[0198]

[0199] These quantities (ΔP 10 / k – ΔR / k'), (ΔP 01 / k - ΔR / k'), (ΔP 11 / k - Δr / k') can be easily distinguished simply by appropriately selecting the reference beam and the topological charges l0, l1, l2 of the two main beams (i.e., the respective orbital angular momenta), that is, setting them to three different predefined known values. Therefore, these quantities measured at reception are recognizable and are an indication of the modulation values 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 recognized.

[0200] Furthermore, advantageously, these quantities are made independent of the phase difference attributed to the position tilt and independent of the distortion of the propagation wavefront, which can be eliminated due to the presence of the reference beam (as already noted above).

[0201] Possible examples of the choice of topological charge values are:

[0202] l0 = 0, l1 = 0, l2 = 2.

[0203] Other combinations are clearly detectable.

[0204] There still exists the state a(t)=0, b(t)=0 to be recognized, and the phase of this state is undetermined (as shown above). This state is easily recognizable because it is the only combination in which the amplitudes of the fields or signals received by the two main beams are eliminated. Therefore, when the intensity or power of the signal detected at point Q3 (by means of Figure 4 the detector 16 shown in

[0205] Below are specific implementation examples of the above-mentioned method of long-distance communication based on orbital angular momentum modulation and using relevant physical-mathematical analysis.

[0206] Angular momentum modulation can be described using parameters similar to those developed for the case of digital amplitude modulation.

[0207] The modulation functions a(t) and b(t) take values of 0 or 1, which depend on the information digitally modulated in the first modulator and the second modulator respectively. Such modulation functions determine the discrete variables of the angular momentum of the first electromagnetic radiation beam and at least one second electromagnetic radiation beam respectively according to the binary values taken, that is, depending on the functions L1 and L2 taken by a(t) and b(t):

[0208] L1 = L1(a(t)), L2 = L2(b(t))

[0209] That is, equivalently referring to the topological charge: l1 = l1(a(t)), l2 = l2(b(t)).

[0210] Therefore, the signals existing in R1, R2, P1, and P2 can be expressed as:

[0211] - In R1:

[0212] - In R2:

[0213] - In P1:

[0214]

[0215] - In P2:

[0216]

[0217] Only the reference beams exist in R1 and R2; the superimposed main beams exist in P1 and P2.

[0218] The second phase comparator 4 provides a quantity proportional to the phase difference (as in the general case):

[0219]

[0220] The first phase comparator 3 provides a quantity proportional to the phase difference between the fields or signals in P1 and P2, which depends on the digital encoding of the modulation functions a(t) and b(t).

[0221] Considering all possible combinations, the following results are obtained:

[0222]

[0223] Among them, the combinations are determined by the indices a, b and the corresponding values taken by the functions a(t) and b(t).

[0224] Then, the difference ΔP ab / k - ΔR / k' is calculated for all possible combinations of the modulation signals by means of the following formula in order to eliminate the phase arbitrariness attributable to the position tilt and the wavefront distortion related to propagation:

[0225]

[0226] The topological charge values l0, l1(0), l1(1), l2(0), l2(1) or the respective orbital angular momenta can be selected such that the corresponding quantities (ΔP 00 / k - ΔR / k'), (ΔP 01 / k - ΔR / k'), (ΔP 10 / k - ΔR / k'), (ΔP 11 / k - ΔR / k') are different from each other and thus distinguishable to allow decoding (demodulation) of the encoded (modulated) information.

[0227] In addition, the above-mentioned quantities are independent of the phase difference attributable to the position tilt and distortion of the propagation wavefront, which can be eliminated due to the presence of the reference beam.

[0228] An example of the selection of the topological charge values is l0 = 0, l1(0) = 0, l1(1) = 1, l2(0) = 0, l2(1) = 2, from which it follows that:

[0229]

[0230] As can be seen, the above four quantities are different and thus distinguishable.

[0231] Similar to the examples reported above, other value assignments are clearly possible.

[0232] It should be noted that angular momentum modulation is in many respects similar to amplitude modulation, Figure 3 and Figure 4 the block diagrams shown in are also suitable for angular momentum modulation, the only obvious difference being that the modulator modulates angular momentum rather than amplitude. Additionally, in this case, Figure 4 and Figure 5 the threshold detectors of are not necessary.

[0233] Referring to Figure 1 and Figure 2 a system for transmitting and receiving a beam of electromagnetic radiation is now described, which is suitable for determining the orbital angular momentum of the received beam of electromagnetic radiation.

[0234] Such a system includes means 5 for generating a primary electromagnetic radiation beam F1, means 6 for generating a reference beam F0, means 7 for generating a composite electromagnetic radiation beam Q1 (as shown in Figure 1 ) and means 14 for transmitting the composite electromagnetic radiation beam Q1 (as shown in Figure 1 ), means for receiving the composite electromagnetic radiation beam, first beam detection means 1, second beam detection means 2, first frequency discrimination means 8, second frequency discrimination means 9 and means 10 for determining the orbital angular momentum (as shown in Figure 2 ).

[0235] The means 5 for generating the primary electromagnetic radiation beam is configured to generate a primary electromagnetic radiation beam F1, which is characterized by a first orbital angular momentum L1, a first spectrum in a first frequency band and a first beam radius of curvature.

[0236] The means 6 for generating the reference beam is configured to generate a reference beam F0, which is characterized by a third orbital angular momentum L0, a second spectrum in a second frequency band different from the first frequency band, and a second beam radius of curvature that is substantially consistent with the first beam radius of curvature.

[0237] The means 7 for generating the composite electromagnetic radiation beam and the means 14 for transmitting the composite electromagnetic radiation beam are configured to generate a composite electromagnetic radiation beam Q1 that contains the superposition of the above-mentioned primary beam F1 and reference beam F0 and to transmit such a generated composite electromagnetic radiation beam Q1.

[0238] The device for receiving a composite electromagnetic radiation beam includes: a first beam detection device 1 located at a first position, which is configured to generate a first composite beam electrical signal D1 representing the electric field, and / or magnetic field, and / or intensity of the electromagnetic radiation of the composite beam at the first position; and a second beam detection device 2 located at a second position, which is configured to generate a second composite beam electrical signal D2, the second position being different from the above-mentioned first position, and the second composite beam electrical signal representing the electric field, and / or magnetic field, and / or intensity of the composite beam at the second position.

[0239] The first frequency discrimination device 8 is configured to perform frequency discrimination on 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 representing the electric field, and / or magnetic field, and / or intensity attributable to the main beam at the first position, and the first reference beam electrical signal R1 representing the electric field, and / or magnetic field, and / or intensity attributable to the reference beam at the first position.

[0240] The second frequency discrimination device 9 is configured to perform frequency discrimination on 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 representing the electric field, and / or magnetic field, and / or intensity attributable to the main beam at the second position, and the second reference beam electrical signal R2 representing the electric field, and / or magnetic field, and / or intensity attributable to the reference beam at the second position.

[0241] The device 10 for determining the orbital angular momentum is configured to determine the orbital angular momentum L1 of the main electromagnetic radiation beam and / or the spatial phase variable of the main electromagnetic radiation beam attributable to the orbital angular momentum L1 of the main beam based on the above-mentioned first main beam electrical signal P1, second main beam electrical signal P2, first reference beam electrical signal R1, and second reference beam electrical signal R2.

[0242] According to different implementation options, the system is configured to perform the method for transmitting and receiving an electromagnetic radiation beam according to any one of the above-mentioned embodiments.

[0243] According to an embodiment of the system, the device 5 for generating the main electromagnetic radiation beam and the device 6 for generating the reference beam include one or more electromagnetic beam sources or emitters known per se (for example, in the implementation option, a laser).

[0244] According to an implementation option, the device 5 for generating the main electromagnetic radiation beam further includes an amplitude, and / or frequency, and / or phase modulator 50, and / or one or more angular momentum modulators 50 (for example, such an angular momentum modulator 50 can be a spatial light modulator).

[0245] According to an embodiment of the system, the device 7 for generating a combined electromagnetic radiation beam includes an electromagnetic beam combiner (e.g., a beam combiner) having two or more inputs and outputs known per se.

[0246] According to an embodiment of the system, the first beam detection device 1 includes one or more diaphragms (optical apertures), or antennas, or a set of antennas, or any other electromagnetic beam receiver known per se suitable for operating at the frequencies of the first beam and the second beam. For example, the device 14 for emitting an electromagnetic beam includes one or more transmitting antennas.

[0247] According to an embodiment of the system, the second beam detection device 2 includes one or more diaphragms (optical apertures), or antennas, or a set of antennas, or any other electromagnetic beam receiver known per se suitable for operating at the frequencies of the first beam and the second beam.

[0248] According to different embodiments, the first frequency discrimination device 8 and the second frequency discrimination device 9 may include frequency filters known per se.

[0249] According to an embodiment of the system, the device 10 for determining the orbital angular momentum includes at least two phase comparators 3, 4 and at least one processor 15, and the device for determining the orbital angular momentum is configured to derive the orbital angular momentum by means of processing (e.g., according to the formula shown above) based on the output signals from the phase comparators.

[0250] According to an embodiment of the system, the device 10 for determining the orbital angular momentum includes at least two correlators 11, 12 and at least one processor 15, and the device for determining the orbital angular momentum is configured to derive the orbital angular momentum by means of processing (e.g., according to the formula shown above) based on the output signals from the correlators.

[0251] Reference Figure 5 , further details regarding implementation options involving the use of correlators are provided herein.

[0252] In this case, instead of using a phase comparator that provides a value proportional to the phase difference ΔP or ΔR, a correlator that provides a value proportional to the cosine of the phase difference cos(ΔP) or cos(ΔR) is used. Then, the phase difference is determined by the inverse function:

[0253] ΔP = arccos[cos(ΔP)]

[0254] ΔR = arccos[cos(ΔR)]

[0255] 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.

[0256] Alternatively, it is possible by means of measuring the interference average intensity between fields having intensities I P1 and I P2 respectively at P1 and P2, or between fields having intensities I R1 and I R2 respectively at R1 and R2 to determine the correlation by interference, it is known that:

[0257] cos(ΔP) = ( -I P1 -I P2 ) / (2(I P1 I P2 ) 1 / 2 )

[0258] cos(ΔR) = ( -I R1 -I R2 ) / (2(I R1 I R2 ) 1 / 2 )

[0259] According to an embodiment of the above system, the electromagnetic beams transmitted and received as mentioned above are light beams and / or laser beams.

[0260] Reference Figure 3 and Figure 4 , a system for the long-distance communication of signals that are modulated according to any known modulation technique and grouped by means of orbital angular momentum variable multiplexing will now be described.

[0261] Such a system includes means 5, 6 for generating electromagnetic beams, a modulation means 50, a beam combining and / or superposition means 7, a transmitting means 14, beam receiving means 1, 2, 8, 9, a phase determination means 20, and a processing means 15.

[0262] The means 5, 6 for generating electromagnetic beams are configured to generate a first electromagnetic radiation beam F1 characterized by a first orbital angular momentum L1, and at least one second electromagnetic radiation beam F2 characterized by at least one corresponding second orbital angular momentum L2.

[0263] The first electromagnetic radiation beam F1 and the at least one second electromagnetic radiation beam F2 each have a spectrum in the same first frequency band, and also each have a curvature radius that is substantially consistent with the first beam curvature radius value.

[0264] The means 5, 6 for generating electromagnetic beams are further configured to generate a reference beam F0, which is characterized by a third orbital angular momentum L0, a second spectrum in a second frequency band different from the above-mentioned first frequency band, and a second beam curvature radius having a value that is substantially consistent with the above-mentioned first beam curvature radius value.

[0265] The modulation means 50 is configured to modulate the first piece of information to be transmitted, represented by a first modulation function a(t), on the first electromagnetic radiation beam F1 by means of any amplitude, and / or phase, and / or frequency modulation technique to obtain a first modulated beam Fm1; and to modulate the at least one second piece of information to be transmitted, represented by a second modulation function b(t), on the at least one second electromagnetic radiation beam F2 by means of any amplitude, and / or phase, and / or frequency modulation technique to obtain a second modulated beam Fm2.

[0266] The beam combining and / or superposing device 7 is configured to superpose and / or combine the above-mentioned reference beam F0, the first modulated beam Fm1, and the second modulated beam Fm2 to generate a composite electromagnetic radiation beam Q1, which includes the superposition of the reference beam and the main beam, and thus includes the superposition of the above-mentioned first modulated beam Fm1 and at least one second modulated beam Fm2.

[0267] The transmitting device 14 is configured to transmit the generated composite electromagnetic radiation beam.

[0268] The device for receiving the composite electromagnetic radiation beam includes a first beam detection device 1, a second beam detection device 2, a first frequency discrimination device 8, and a second frequency discrimination device 9.

[0269] The first beam detection device 1 is located at a first position and is configured to generate a first composite beam electrical signal D1, which represents the electric field, and / or magnetic field, and / or intensity of the electromagnetic radiation of the composite beam at the first position.

[0270] The second beam detection device 2 is located at a second position different from the first position and is configured to generate a second composite beam electrical signal D2, which represents the electric field, and / or magnetic field, and / or intensity of the electromagnetic radiation of the composite beam at the second position.

[0271] The first frequency discrimination device 8 is configured to perform frequency discrimination on the first composite beam electrical signal D1 to obtain a first main beam electrical signal P1 and a first reference beam electrical signal R1, where the first main beam electrical signal represents the electric field, and / or magnetic field, and / or intensity attributed to the main beam at the first position, and the first reference beam electrical signal represents the electric field, and / or magnetic field, and / or intensity attributed to the reference beam at the first position.

[0272] The second frequency discrimination device 9 is configured to perform frequency discrimination on the second composite beam electrical signal to obtain a second main beam electrical signal P2 and a second reference beam electrical signal R2, where the second main beam electrical signal represents the electric field, and / or magnetic field, and / or intensity attributed to the main beam at the second position, and the second reference beam electrical signal represents the electric field, and / or magnetic field, and / or intensity attributed to the reference beam at the second position.

[0273] The phase determination 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 also configured to determine the phase of the first reference beam electrical signal R1 and the phase of the second reference beam electrical signal R2.

[0274] The phase determination device 20 is further configured to determine a first phase difference ΔP 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 where such a first phase difference ΔP ab Depending on the values of the first modulation function a(t) and the second modulation function b(t), a second phase difference value ΔR 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 is determined; further, from the first phase difference value ΔP ab Divide by the wave number k minus the second phase difference ΔR divided by the wave number k' to obtain the difference Q2 = ΔP ab / k–ΔR / k'. The first wave number k is the wave number corresponding to the main beam and is defined as k = 2π / λ, where λ is the wavelength of the main beam belonging to the first frequency band. The second wave number k' is the wave number corresponding to the reference beam and is defined as k' = 2π / λ', where λ' is the wavelength of the reference beam belonging to the second frequency band.

[0275] The above difference Q2 = ΔP ab / k-ΔR / k' represents the combination of the values taken by the first modulation function a(t) and the second modulation function b(t), and is independent of the positional inclination condition between the first beam detector 1 and the second beam detector 2, and is independent of the phase variable caused by the interference to which the transmitted composite beam is subjected before reception.

[0276] The processing device 15 is configured to determine the difference Q2 = ΔP based on the above determination. ab / k-ΔR / k′ to demultiplex and demodulate the modulation information on each of the first modulation beam Fm1 and the at least one second modulation beam Fm2.

[0277] According to various embodiments, the system is configured to perform the method for electromagnetic radiation beam telecommunication according to any of the above embodiments.

[0278] 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 known per se (for example, in an implementation option, lasers).

[0279] According to one embodiment of the system, the modulation means 50 comprise amplitude, and / or frequency, and / or phase, and / or angular momentum modulators known per se.

[0280] According to one 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 an antenna, or a group of antennas, or any other electromagnetic beam receiver known per se, each adapted to operate at the frequency of the first beam and the second beam.

[0281] According to one embodiment of the system, the first frequency discrimination means 8 and the second frequency discrimination means 9 comprise frequency filters known per se.

[0282] According to an embodiment of the system, the phase determination device 20 includes at least two phase comparators 3, 4 known per se.

[0283] According to an embodiment of the system, the first frequency discrimination device and the second frequency discrimination device include correlators 11, 12 known per se. The same considerations apply to such correlators as those of the system for transmitting and receiving electromagnetic beams referred to above.

[0284] According to an embodiment of the system, the processing device 15 includes one or more processors known per se, and associated software.

[0285] According to an embodiment of the above system, the electromagnetic beams transmitted and received as mentioned above are light beams and / or laser beams.

[0286] Reference Figures 7 to 9 , a method for demultiplexing and demodulating an amplitude-modulated signal will be described below, the amplitude-modulated signal being grouped by means of multiplexing in the orbital angular momentum variable.

[0287] The method is applicable to the case where the signal to be demultiplexed and demodulated includes a composite electromagnetic radiation beam Q1, the composite electromagnetic radiation beam Q, including a superposition of a reference beam F0 and a main beam, and further including a superposition of a first modulated beam Fm1 and at least one second modulated beam Fm2.

[0288] The first modulated beam Fm1 is obtained by modulating a first piece of information on a first electromagnetic radiation beam by means of any amplitude modulation technique, the first piece of information being represented by a first modulation function a(t).

[0289] The above-mentioned at least one second modulated beam Fm2 is obtained by modulating at least one second piece of information on at least one corresponding second electromagnetic radiation beam (F2) by means of any amplitude modulation technique, the second piece of information being represented by a second modulation function b(t).

[0290] The above-mentioned first electromagnetic radiation beam F1 is characterized by a first orbital angular momentum L1; the aforementioned at least one second electromagnetic radiation beam F2 is characterized by a corresponding at least one second orbital angular momentum L2, wherein the first electromagnetic radiation beam F1 and the at least one second electromagnetic radiation beam F2 both have corresponding spectra in the same first frequency band, and also have corresponding curvature radii that are substantially consistent with the value of the first beam curvature radius.

[0291] The above-mentioned reference beam F0 is characterized by a third orbital angular momentum L0, a second spectrum in a second frequency band different from the first frequency band, and a second beam curvature radius, the second beam curvature radius having a value that is substantially consistent with the value of the first beam curvature radius.

[0292] First, the method includes the step of passing the above-mentioned composite electromagnetic radiation beam Q1 through two openings Z1, Z2 so as to obtain a first composite beam portion Q1(x1) downstream of the first opening Z1 and a second composite beam portion Q1(x2) downstream of the second opening Z2.

[0293] The method further includes emitting the first composite beam portion Q1(x1) along a first branch A of the interferometer 40 and emitting the second composite beam portion Q1(x2) along a second branch B of the interferometer 40.

[0294] Then, the method includes superimposing the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2) along a third branch D of the interferometer by means of a beam splitter 41 of the interferometer to obtain a corresponding third electromagnetic beam D, and superimposing the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2) along a fourth branch of the interferometer C to obtain a corresponding fourth electromagnetic beam C.

[0295] The method further includes the step of performing frequency discrimination on the third electromagnetic beam D around a first frequency band so as to obtain a third filtered electromagnetic beam F, wherein the contributions of the reference beams from the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2) have been cancelled, and wherein the components from the corresponding first modulated beams Fm1(x1), Fm1(x2) and at least one second modulated beam Fm2(x1), Fm2(x2) are retained.

[0296] Then, frequency discrimination is performed on the fourth electromagnetic beam C around a second frequency band of the reference beam so as to obtain a fourth filtered electromagnetic beam E including the superposition of two reference beams F0(x1), F0(x2) that respectively belong to the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2).

[0297] The method further includes: detecting the third filtered electromagnetic beam F by means of a first beam detector 1 to generate a first electrical signal V1, the first electrical signal V1 representing the intensity of the electromagnetic radiation of the third filtered electromagnetic beam F; and at the first beam detector 1, based on the first electrical signal V1, determining a first phase difference ΔP between the components of the third filtered electromagnetic beam from the first composite beam filtered portion Fm1(x1), Fm2(x1) and the components of the third electromagnetic beam from the second composite beam filtered portion Fm1(x2), Fm2(x2) ab , wherein the above-mentioned first phase difference ΔP ab depends on the values taken by the first modulation function a(t) and the second modulation function b(t).

[0298] The method further includes: detecting the fourth filtered electromagnetic beam E by means of the second beam detector 2 to generate a second electrical signal V2, which represents the intensity of the electromagnetic radiation of the fourth filtered electromagnetic beam E; and at the second beam detector 2, based on the second electrical signal V2, determining a second phase difference ΔR between two reference beams F0(x1) and F0(x2) belonging to the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2).

[0299] Finally, the method provides for demultiplexing and demodulating the information a(t), b(t) modulated on each of the first modulated beam Fm1 and at least one second modulated beam Fm2 based on the first phase difference ΔP ab and the second phase difference ΔR.

[0300] It should be noted that the demodulation and modulation performed in this method are advantageously "local" modulation and demultiplexing, in the sense that they are based on detecting even only a limited, i.e., "local", portion of the electromagnetic beam, without the need to detect the entire wavefront of the beam.

[0301] According to an embodiment of the method, the steps of demultiplexing and demodulating include: dividing the first phase difference ΔP ab by the first wave number k minus the second phase difference ΔR divided by the second wave number k' to obtain a difference Q2 = ΔP ab / k – ΔR / k'; then, based on the difference Q2 = ΔP ab / k – ΔR / k' thus determined, demultiplexing and demodulating the modulation information on each of the first modulated beam Fm1 and at least one second modulated beam Fm2.

[0302] The first wave number k is the wave number corresponding to the main beam, defined as k = 2π / λ, where λ is the wavelength of the main beam, and the second wave number k' is the wave number corresponding to the reference beam, defined as k' = 2π / λ', where λ' is the wavelength of the reference beam.

[0303] The difference Q2 = ΔP ab / k - ΔR / k' represents a combination of the values taken by the first modulation function a(t) and the second modulation function b(t), independent of the positional tilt condition between the first beam detector and the second beam detector and independent of the phase variables caused by the interference suffered by the transmitted composite beam before reception.

[0304] According to an implementation option of the method, the first electromagnetic radiation beam F1 and at least one second electromagnetic radiation beam F2 are digitally amplitude modulated according to the amplitudes of the first modulation function a(t) and at least one second modulation function b(t).

[0305] The difference Q2 = ΔP ab / k - ΔR / k' can take multiple expected values, each of which represents a respective combination of digital amplitude values taken by the first modulation function a(t) and at least one second modulation function b(t).

[0306] According to an implementation option of the method, the first electromagnetic radiation beam F1 and at least one second electromagnetic radiation beam F2 are digitally amplitude - modulated in a binary manner, and the amplitudes of the first modulation function a(t) and at least one second modulation function b(t) can take logical values 0 or 1.

[0307] In this case, the method further includes the steps of detecting the received power or intensity of the third filtered electromagnetic beam F and comparing the received power or intensity with a minimum threshold, where the received power or intensity corresponds to the first electrical signal V1 detected by the first beam detector 1.

[0308] The determined difference (Q2 = ΔP ab / k - ΔR / k') can take a first expected value (ΔP 10 / k - ΔR / k'), or a second expected value (ΔP 01 / k - ΔR / k'), or a third expected value (ΔP 11 / k - ΔR / k'), where the first expected value depends on the first orbital angular momentum (L1), the second expected value depends on the second orbital angular momentum (L2), and the third expected value depends on the combination of the first and second angular momenta.

[0309] In this case, the steps of demultiplexing and demodulating the modulation information include:

[0310] - If the determined difference (ΔP ab / k – ΔR / k') takes the above - mentioned first expected value (ΔP 10 / k – ΔR / k'), then identify that the first modulated beam Fm1 carries information corresponding to 1 and the second modulated beam Fm2 carries information corresponding to 0;

[0311] - If the determined difference (ΔP ab / k – ΔR / k') takes the above - mentioned second expected value (ΔP 01 / k – ΔR / k'), then identify that the first modulated beam Fm1 carries information corresponding to 0 and the second modulated beam Fm2 carries information corresponding to 1;

[0312] - If the determined difference (ΔP ab / k – ΔR / k') takes the above - mentioned third expected value (ΔP 11 / k – ΔR / k'), then identify that the first modulated beam Fm1 carries information corresponding to 1 and the second modulated beam Fm2 carries information corresponding to 1;

[0313] - If the received power or intensity of the third filtered electromagnetic beam is below the above-mentioned minimum threshold, identify that the first modulated beam Fm1 carries information corresponding to 0 and the second modulated beam Fm2 carries information corresponding to 0.

[0314] According to another embodiment of the method, the first phase difference ΔP ab depends on the average intensity Im1 of the third filtered electromagnetic beam F associated with the corresponding interference pattern, and the above-mentioned first electrical signal V1 represents such an average intensity of the third filtered electromagnetic beam F detected by the first beam detector 1; the second phase difference ΔR depends on the average intensity Im2 of the fourth filtered electromagnetic beam E associated with the corresponding interference pattern, and the above-mentioned second electrical signal V2 represents the average intensity Im2 of the fourth filtered electromagnetic beam E detected by the second beam detector 2.

[0315] In this case, the method further includes the step of maintaining the average intensity Im2 of the fourth filtered electromagnetic beam E as constant at a predefined intensity value by means of a feedback control loop controlled by the second electrical signal V2 and acting on the first composite beam portion Q1(x1), such that the second phase difference ΔR is maintained constant and set to a predefined value.

[0316] According to an implementation option, the first electromagnetic radiation beam F1 and at least one second electromagnetic radiation beam F2 are digitally amplitude modulated according to the amplitudes of the first modulation function a(t) and at least one second modulation function b(t).

[0317] In this case, the first phase difference = ΔP ab can take multiple expected values, each expected value representing a corresponding combination of the digital amplitude values taken by the first modulation function a(t) and at least one second modulation function b(t).

[0318] According to an implementation option, the first electromagnetic radiation beam F1 and at least one second electromagnetic radiation beam F2 are digitally amplitude modulated in a binary manner (for example, by means of ON - OFF - KEYING – OOK – modulation, or other modulation methods known per se), and the amplitudes of the first modulation function a(t) and at least one second modulation function b(t) can take logical values 0 or 1.

[0319] In this case, the method further includes the steps of detecting the received power or intensity of the third filtered electromagnetic beam F and comparing the received power or intensity with a minimum threshold, where the received power or intensity corresponds to the first electrical signal V1 detected by the first beam detector 1.

[0320] The determined first phase difference ΔP ab can take a first expected value ΔP 10 or a second expected value ΔP 01 or a third expected value ΔP 11 wherein the first expected value depends on the first orbital angular momentum L1, the second expected value depends on the second orbital angular momentum L2, and the third expected value depends on a combination of the first and second orbital angular momenta.

[0321] The steps of demultiplexing and demodulating the modulated information include:

[0322] - If the determined first phase difference ΔP ab takes the above first expected value ΔP 10 , then it is recognized that the first modulated beam Fm1 carries information corresponding to 1 and the second modulated beam Fm2 carries information corresponding to 0;

[0323] - If the determined first phase difference ΔP ab takes the above second expected value ΔP 01 , then it is recognized that the first modulated beam Fm1 carries information corresponding to 0 and the second modulated beam Fm2 carries information corresponding to 1;

[0324] - If the determined first phase difference ΔP ab takes the above third expected value ΔP 11 , then it is recognized that the first modulated beam Fm1 carries information corresponding to 1 and the second modulated beam Fm2 carries information corresponding to 1;

[0325] - If the received power or intensity of the third filtered electromagnetic beam F is lower than the minimum threshold, then it is recognized that the first modulated beam Fm1 carries information corresponding to 0 and the second modulated beam Fm2 carries information corresponding to 0.

[0326] According to an embodiment of the method, the number of modulated beams for orbital angular momentum multiplexing is equal to N, where N is greater than 2.

[0327] Each modulated beam is characterized by its respective orbital angular momentum Li and amplitude modulated by its respective modulation function, and each of the possible value combinations of the modulation functions on the N modulated beams corresponds to a corresponding value of the first phase difference ΔP a1..aN and / or corresponds to a corresponding difference (Q2 = ΔP a1..aNb / k – ΔR / k').

[0328] According to an embodiment of the method, as shown, the method further includes the following steps: Before the superposition of the first composite beam portion and the second composite beam portion, in the interferometer, arranging a first additional optical path (along the Figure 8 branches indicated as A and G in Figure 8 branches indicated as B, B', and G therein, where B' passes through twice).

[0329] The aforementioned first additional optical path and second additional optical path are predefined and dimensioned so as to eliminate the phase difference caused between the phase of the second composite beam portion Q1(x2) and the phase of the first composite beam portion Q1(x1) due to the total optical path difference between the corresponding entrance opening and the first beam detector 1 and so as to eliminate the phase difference caused between the phase of the second composite beam portion Q1(x2) and the phase of the first composite beam portion Q1(x1) due to the total optical path difference between the corresponding entrance opening and the second beam detector 2

[0330] According to another embodiment of the method, the step of keeping the average intensity Im2 of the fourth filtered electromagnetic beam E constant includes: by means of a control unit 61 that receives the second electrical signal V2 and the setting signal SP as inputs, controlling the first mirror 42 hit by the first composite beam portion Q1(x1), thereby changing in a controlled manner the length of the optical path A passed through by the first composite beam portion (Q1(x1)), and thus respectively changing the phase shifts of the first electromagnetic beam portion Q1(x1) and the second electromagnetic beam portion Q2(x2), so as to alter the average intensity Im2 detected by the second beam detector 2 in a controlled manner depending on the second electrical signal V2 and the setting signal SP, so as to keep the second phase difference ΔR and the average intensity Im2 of the fourth filtered electromagnetic beam E constant and set at corresponding predefined values that depend on the setting signal SP.

[0331] According to an implementation option, the change in the optical path A is obtained by a controlled translation of the first mirror 42 by an actuator 43 controlled by the control unit 61 (for example, the control unit can be configured to perform "PID (Proportional-Integral-Derivative) control").

[0332] According to another embodiment of the method, as Figure 8 shown, the step of keeping the average intensity Im2 of the fourth filtered electromagnetic beam E constant includes: at the second beam detector 2, compensating for the change in the intensity I of the reference beam associated with the first composite beam portion R1 and, at the second beam detector 2, compensating for the change in the intensity I of the reference beam associated with the second composite beam portion R2 of.

[0333] The above-mentioned compensation steps include:

[0334] - deflecting a portion of the beam corresponding to the first composite beam portion Q1(x1) at the first branch A of the interferometer;

[0335] - Detecting, by means of a third beam detector 63, the intensity of the deflected portion of the beam corresponding to the first composite beam portion Q1(x1) and generating a first compensation electrical signal GI R1 , the first compensation electrical signal GI R1 representing the intensity of the first composite beam portion;

[0336] - Deflecting, at a second branch B of the interferometer, a portion of the beam corresponding to the second composite beam portion Q1(x2);

[0337] - Detecting, by means of a fourth beam detector 64, the intensity of the second composite beam portion and generating a second compensation electrical signal GI R2 , the second compensation electrical signal GI R2 representing the intensity of the second composite beam portion;

[0338] - Modifying, by means of a processing unit 65, the setting signal SP based on the first compensation electrical signal GI R1 and the second compensation electrical signal GI R2 .

[0339] According to an implementation option of the method, all of the above electromagnetic beams are light beams and / or laser beams.

[0340] According to an implementation of the method, the orbital angular momentum of the reference beam is always known.

[0341] According to a specific implementation option, the orbital angular momentum of the reference beam takes a constant value L0 = 0.

[0342] According to an implementation of the method, the second frequency band is substantially single-frequency.

[0343] According to a specific implementation option, the second frequency band is adjacent to the first frequency band.

[0344] According to an implementation option, the step of performing frequency discrimination on the first electrical signal or the second electrical signal of the composite beam includes performing frequency filtering.

[0345] Reference Figure 9 , a system 100 for demultiplexing and demodulating an amplitude-modulated signal will be described below, the amplitude-modulated signal being grouped by means of multiplexing in the orbital angular momentum variable.

[0346] According to what has been previously described with reference to the method according to the present invention, the types of signals to be demultiplexed and demodulated include: a composite electromagnetic radiation beam Q1, which comprises a superposition of a reference beam F0 and a main beam, and thus comprises a superposition of a first modulated beam Fm1 and at least one second modulated beam Fm2.

[0347] System 100 includes a screen equipped with two openings Z1, Z2, and the screen is configured to allow a composite electromagnetic radiation beam Q1 to pass through the two openings Z1, Z2, so as to obtain a first composite beam portion Q1(x1) downstream of the first opening Z1 and a second composite beam portion Q1(x2) downstream of the second opening Z2.

[0348] System 100 further includes an interferometer 40, which is arranged downstream with respect to the two openings Z1, Z2 and further includes: a first branch A configured to be traversed by the first composite beam portion Q1(x1); a second branch B configured to be traversed by the second composite beam portion Q1(x2); a beam splitter 41 configured to superimpose the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2) along a third branch D of the interferometer to obtain a corresponding third electromagnetic beam D, and superimpose the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2) along a fourth branch C of the interferometer C to obtain a corresponding fourth electromagnetic beam C.

[0349] The interferometer 40 further includes a first frequency discrimination device 45 and a second frequency discrimination device 44.

[0350] The first frequency discrimination device 45 is configured to discriminate the frequency of the third electromagnetic beam D around a first frequency band to obtain a third filtered electromagnetic beam F, in which the contributions of the reference beams from the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2) have been canceled, and in which the components from the corresponding first modulation beams Fm1(x1), Fm1(x2) and at least one second modulation beam Fm2(x1), Fm2(x2) are retained.

[0351] The second frequency discrimination device 44 is configured to discriminate the frequency of the fourth electromagnetic beam C around a second frequency band of the reference beam to obtain a fourth filtered electromagnetic beam E, which contains the superposition of two reference beams F0(x1), F0(x2) belonging to the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2) respectively.

[0352] System 100 further includes a first beam detector 1 configured to detect the above-mentioned third filtered electromagnetic beam F to generate a first electrical signal V1, which represents the intensity of the electromagnetic radiation of the third filtered electromagnetic beam F.

[0353] System 100 further includes a second beam detector 2 configured to detect the above-mentioned fourth filtered electromagnetic beam E to generate a second electrical signal V2, which represents the intensity of the electromagnetic radiation of the fourth filtered electromagnetic beam E.

[0354] Finally, system 100 includes a processing device 65 configured to:

[0355] - At the first beam detector 1, based on the first electrical signal V1, determine a first phase difference ΔP between the components of the third filtered electromagnetic beam originating from the first composite beam filtering sections Fm1(x1), Fm2(x1) and the components of the third electromagnetic beam originating from the second composite beam filtering sections Fm1(x2), Fm2(x2). ab ; such a first phase difference ΔP ab depends on the values taken by the first modulation function a(t) and the second modulation function b(t);

[0356] - At the second beam detector 2, based on the above-mentioned second electrical signal V2, determine a second phase difference ΔR between the two reference beams F0(x1), F0(x2) belonging to the first composite beam section Q1(x1) and the second composite beam section Q1(x2);

[0357] - Based on the above-mentioned first phase difference ΔP ab and the second phase difference ΔR, demultiplex and demodulate the modulation information a(t), b(t) on each of the first modulated beam Fm1 and at least one second modulated beam Fm2.

[0358] According to an implementation option of the system, the first frequency discrimination device 45 includes an optical band-pass filter, where the passband corresponds to the first band frequency.

[0359] According to an implementation option of the system, the second frequency discrimination device 44 includes a narrow-band optical band-pass filter (laser line), where the passband corresponds to the second band frequency of the reference beam.

[0360] According to an implementation option of the system, the first beam detector 1 and the second beam detector 2 respectively include a first photodiode and a second photodiode.

[0361] According to an implementation option of the system, the processing device 65 includes one or more electronic processors 65.

[0362] According to an implementation manner, the system 100 further includes a control unit 61, which is adapted to receive the second electrical signal V2 and the setting signal SP as inputs, and further includes an actuator 43 controlled by the control unit 61, and a first mirror controlled by the actuator 43, and the first mirror is arranged such that the first composite beam section Q1(x1) hits the first mirror.

[0363] The control unit 61 is configured to change, in a controlled manner, the length of the optical path A traversed by the first composite beam portion Q1(x1), thereby changing the phase shifts of the first electromagnetic beam portion Q1(x1) and the second electromagnetic beam portion Q2(x2), so as to vary the average intensity Im2 detected by the second beam detector 2 in a controlled manner depending on the second electrical signal V2 and the setting signal SP, so as to keep the second phase difference ΔR and the average intensity Im2 of the fourth filtered electromagnetic beam E constant and set at corresponding predefined values that depend on the setting signal SP.

[0364] According to one embodiment, the system 100 further includes means 46, 47, 48, 49 for balancing the optical path, which are configured to: before the superposition of the first composite beam portion and the second composite beam portion, in the interferometer, arrange a first additional optical path (A, G) for the first composite beam portion Q1(x1), and arrange a second additional optical path (B, B', B', G) for the second composite beam portion Q1(x2).

[0365] Such an arrangement step includes arranging the first additional optical path (A, G) and the second additional optical path (B, B’, B’, G) so as to eliminate the phase difference caused between the phase of the second composite beam portion Q1(x2) and the phase of the first composite beam portion Q1(x1) due to the total optical path difference between the corresponding inlet openings and the first beam detector 1 and so as to eliminate the phase difference caused between the phase of the second composite beam portion Q1(x2) and the phase of the first composite beam portion Q1(x1) due to the total optical path difference between the corresponding inlet openings and the second beam detector 2

[0366] According to one implementation option, the above-mentioned means for balancing the optical path includes a second mirror 48, a compensation plate 47, a semi-reflective plate 46 and a third mirror 49 arranged along the second branch B of the interferometer and along the path of the second composite beam portion Q1(x2) so as to form the second additional optical path (B, B', B', G).

[0367] The above-mentioned semi-reflective plate 46 is also arranged along the path of the first composite beam portion Q1(x2) and is configured to emit the first composite beam portion Q1(x1) and the second composite beam portion Q1(x2) to the beam splitter 41.

[0368] According to one embodiment, the system 100 further includes beam intensity compensation means configured to compensate, at the second beam detector 2, for changes in the intensity (I R1 ) of the reference beam associated with the first composite beam portion, and to compensate, at the second beam detector 2, for changes in the intensity (I R2 ) of the reference beam associated with the second composite beam portion.

[0369] The beam intensity compensation device includes: a first half-reflecting plate 66, a first narrow-band optical band-pass filter 68, a third beam detector 63, a second half-reflecting plate 67, a second optical band-pass filter 69, a fourth beam detector 64, and a processing unit 65.

[0370] The first half-reflecting plate 66 is configured to deflect a part of the beam corresponding to the first composite beam portion Q1(x1) at the first branch A of the interferometer.

[0371] The first narrow-band optical band-pass filter 68 is configured to filter the deflected portion of the beam corresponding to the first composite beam portion Q1(x1) around the second frequency band of the reference beam.

[0372] The third beam detector 63 is configured to detect the intensity of the deflected portion of the beam corresponding to the first composite beam portion Q1(x1) and generate a first compensation electrical signal GI R1 which first compensation electrical signal GI R1 represents the intensity of the first composite beam portion.

[0373] The second half-reflecting plate 67 is configured to deflect a part of the beam corresponding to the second composite beam portion Q1(x2) at the second branch B of the interferometer.

[0374] The second optical band-pass filter 69 is configured to filter the deflected portion of the beam corresponding to the second composite beam portion Q1(x2) around the second frequency band of the reference beam.

[0375] The fourth beam detector 64 is configured to detect the intensity of the deflected portion of the beam corresponding to the second composite beam portion Q1(x2) and generate a second compensation electrical signal GI R2 which second compensation electrical signal GI R2 represents the intensity of the second composite beam portion.

[0376] The processing unit 65 is configured to modify the setting signal SP based on the first compensation electrical signal GI R1 and the second compensation electrical signal GI R2 to modify the setting signal SP.

[0377] According to an implementation option of the system, the above electrical signals generated by different beam detectors are appropriately amplified in an obvious and well-known manner by corresponding electronic amplifiers (denoted by reference numerals 71, 72, 73, 74 in Figures 7 to 9 ).

[0378] According to a possible implementation, the above system 100 is configured to execute the method according to any one of the above method implementations.

[0379] By way of non-limiting example, a detailed description of embodiments of the method and system according to the present invention will be provided below, wherein interferometry techniques and several variants thereof allow for the long-distance communication of signals that are OOK (ON-OFF-KEYING) amplitude modulated and orbital angular momentum multiplexed using a composite beam.

[0380] In this example, an optical beam is considered and the beam detector is a photodiode.

[0381] As Figures 7 to 9 shown, the composite beam Q1 generated, modulated, and multiplexed as described above (e.g., see Figure 7 ) enters the two branches A and B of the interferometer through two openings Z1 and Z2.

[0382] The beam in branch A is split into two beams by a beam splitter 41 along branches C and D.

[0383] The beam in branch B is also split into two beams by a beam splitter 41 along branches C and D.

[0384] The beam propagating along branch C is filtered by a laser line bandpass filter 44 that can only emit a reference beam (frequency discrimination).

[0385] The central band wavelength of the laser line filter 44 must be equal to the wavelength of the laser used as the reference beam in the emission.

[0386] In part E, on the plane containing the photodiode 2 and along the optical axis, the fields of the reference beams from branches A and B alone can be respectively expressed as

[0387]

[0388] wherein, is the phase term attributed to the radiation propagation from to the photodiode 2, is the phase term attributed to the radiation propagation from to the photodiode 2.

[0389] It should be noted that the phase terms are both attributed to the optical paths in the two arms of the interferometer. In an unbalanced configuration, such as the configuration in Figure 3 , there is no limitation as long as ΔL < c / Δu, where ΔL is the optical path difference between the arms of the interferometer and Δu is the information bandwidth, and c is the speed of light in a vacuum.

[0390] For example, if limitations arise from this perspective, for high information bandwidths (GHz or dozens of GHz) or when the distance between the two openings Z1 and Z2 is wide, an embodiment with a balanced interferometer can be used, which will be described below with reference to Figure 7 .

[0391] In any case, unbalanced interferometers are still of great interest due to their simpler construction and can still be used in practice when the relation ΔL < c / Δu is well verified.

[0392] field is defined as:

[0393]

[0394] wherein the various quantities have the meanings described above.

[0395] field interfere with each other to produce an interference pattern, the average intensity Im2 of the interference pattern (also denoted here by the symbol is associated with the cosine of the phase difference ΔR of the field itself according to the following relation [1], and the average intensity Im2 of this interference pattern is measured at the center (along the optical axis) of the interference pattern in the plane containing the photodiode 2:

[0396] cos(ΔR) = ( -I R1 -I R2 ) / (2(I R1 I R2 ) 1 / 2 )

[0397] where I R1 and I R2 are the intensities of the fields respectively.

[0398] The intensity of the interference pattern It is converted into an electrical signal by the photodiode 2. The electrical signal is appropriately amplified, conditioned and applied to the input of the control unit 61.

[0399] According to an implementation option, such a control unit 61 performs a control of the well-known PID type (Proportional-Integral-Derivative). The PID control acts on the actuator 43 of the first mirror 42, such that the intensity measured and amplified on the photodiode 2 Is substantially equal to the value of the setting signal SP.

[0400] According to various possible implementation variants, the aforementioned actuator of the first mirror 42 is piezoelectric, or magnetic, or capacitive, or of another type known per se.

[0401] When the position tilt of the wavefront irradiating the interferometer changes, the intensity is further maintained by PID control It is mainly constant. The tilt may be caused by the relative displacement between the wavefront and the interferometer, or by the vibration or perturbation of the propagating wavefront.

[0402] Since the intensities I R1 and I R2 are also substantially constant during the measurement, the quantity ΔR is also substantially constant, as shown in relation [1].

[0403] If the intensities I R1 and I R2 are not constant, an embodiment with a compensation setting signal is used, which will be described below with reference to Figure 8 This will be described.

[0404] Interestingly, it is noted that this feedback solution for the interferometer (also called "locked interferometer") is rejected here in a novel and special way, because the "locking" of the interferometer is carried out by the reference beam of the composite beam (by means of frequency discrimination), while the main beam of the composite beam is frequency discriminated along another branch of the interferometer.

[0405] The beam along branch D is filtered only by the band-pass filter 45 capable of emitting the main beam.

[0406] The central band wavelength of the band-pass filter 45 must be equal to the laser wavelength used to generate the main beam in the emission, and the band of the filter must be equal to or greater than the information band to be transmitted.

[0407] In part F, on the plane containing the photodiode 1 and along the optical axis, the fields of the main beams from branches A and B can be respectively expressed as:

[0408]

[0409] where is the phase term attributed to the radiation propagation from to the photodiode 1, is attributed to the radiation propagation from to the photodiode 1.

[0410] The field is expressed by means of the following equation

[0411]

[0412] The field interfere with each other, generating an interference pattern, and the average intensity Im1 of the interference pattern (also denoted here by the symbol is associated with the cosine of the phase difference ΔR of the field itself according to the following relationship [2], and the average intensity Im1 of this interference pattern is measured at the center (along the optical axis) of the interference pattern in the plane containing the photodiode 1:

[0413] cos(ΔP) = ( -I R1 -I R2 ) / (2(I R1 I R2 ) 1 / 2 )

[0414] where I P1 and I P2 are respectively the intensities of the fields.

[0415] The phase difference ΔR of the field of the portion E of the interferometer on the photodiode 2 is expressed by means of the following formula:

[0416]

[0417] For the various combinations of the digital modulation functions a(t), b(t), the phase difference ΔP of the field in the portion F of the interferometer on the photodiode 1 is:

[0418] Case a(t) = 0, b(t) = 0

[0419] The amplitude of the main beam is cancelled, so the phase difference is indeterminate.

[0420] Case a(t) = 1, b(t) = 0

[0421] Only the first main beam with angular momentum L1 exists:

[0422]

[0423] Case a(t) = 0, b(t) = 1

[0424] Only the second main beam with angular momentum L2 exists:

[0425]

[0426] Case a(t) = 1, b(t) = 1

[0427] Both main beams exist, and the following result is obtained:

[0428]

[0429] By calculating the phase difference Δ / k - Δ / k' for all possible combinations of the modulation signals, the following result is obtained:

[0430] Case a(t) = 0, b(t) = 0

[0431] The amplitude of the main beam is cancelled, so the phase difference is indeterminate.

[0432] Case a(t) = 1, b(t) = 0

[0433] The following equation [3] holds:

[0434]

[0435] For the case a(t) = 0, b(t) = 1

[0436] The following equation [4] holds:

[0437]

[0438] For the case a(t) = 1, b(t) = 1

[0439] The following equation [5] holds:

[0440]

[0441] As described above, advantageously, these relationships are independent of the phase differences attributable to the positional tilt and distortion of the propagating wavefront, which can be eliminated by virtue of the presence of the reference beam.

[0442] Now, from equations [3], [4] and [5], the values of the phase difference ΔP for various combinations of the modulation functions a(t), b(t) are obtained.

[0443] For the case a(t) = 0, b(t) = 0

[0444] The amplitude of the main beam is cancelled, so the phase difference is indeterminate;

[0445] For the case a(t) = 1, b(t) = 0

[0446] The following equation holds:

[0447]

[0448] For the case a(t) = 0, b(t) = 1

[0449] The following equation holds:

[0450]

[0451] For the case a(t) = 1, b(t) = 1

[0452] The following equation holds:

[0453]

[0454] where, "cost" is a constant represented by the following equation:

[0455]

[0456] In various combinations, the quantity ΔR is a constant quantity that can be selected by varying the value of the setpoint signal SP of the PID control.

[0457] As the position tilts, the phase difference due to the tilt of the position and the distortion of the propagation wavefront varies by virtue of the negative feedback of the PID control, and such a quantity ΔR also remains constant.

[0458] In addition, there are quantities and that are constant because they depend on the optical paths along the branches of the interferometer and thus depend solely on geometric and construction parameters.

[0459] As a result, the quantity ΔP 10 、ΔP 01 、ΔP 11 can be set to three different values simply by appropriately selecting the topological charges l0, l1, l2 of the reference beam and the two main beams (i.e., the respective orbital angular momenta L0, L1, L2).

[0460] The values of ΔP 10 、ΔP 01 、ΔP 11 must also be selected so that they produce the average intensity detected on the photodiode 1, which has many different, known, and predefined non - zero values. 10 、 01 、 11 , as indicated by equation [2].

[0461] Thus, the corresponding average intensity measured upon reception is recognizable and is indicative of the modulation value 0 or 1 applied to each of the two main beams. The information encoded on these quantities can thus be decoded, i.e., demodulated and recognized.

[0462] In fact, it is possible to demodulate the transmitted information by measuring the intensity on photodiode 1 after a preliminary calibration operation.

[0463] Calibration requires associating with each combination a(t), b(t) of the corresponding average intensity values detected on photodiode 1, and consists of transmitting a known sequence of all combinations and recording, with the aid of a processing unit, the corresponding average intensity measured on photodiode 1.

[0464] Demodulation consists of associating the respective combinations with each intensity measured on photodiode 1, as defined by the previous calibration. This association can be performed by the same processing unit used during the calibration step.

[0465] Obviously, the system is designed such that the quantities I P1 , I P2 and ΔP create a one-to-one correlation between the combinations of the modulation function a(t)b(t) and the average intensity measured on photodiode 1 under various usage conditions.

[0466] For a fixed application, calibration can be performed only once or periodically to compensate for any drift. For a non-fixed application, calibration must also be performed periodically using a specific telecommunication protocol.

[0467] There still remains the state a(t) = 0, b(t) = 0 to be recognized, the phase of which is undetermined (as shown above). This combination is deterministically recognized when the intensity on photodiode 1 is canceled. 00 = 0.

[0468] Note that, in the description of this example, two main beams with two modulation functions are used.

[0469] However, in other possible embodiments, there may be more main beams and respective modulation functions.

[0470] In fact, by appropriately selecting the orbital angular momentum of the main beam, it is possible to ensure that the phase difference ΔP in various combinations of the modulation functions is different.

[0471] In the case of an interferometer, it is also necessary to ensure the relative average intensity calculated by replacing each ΔP in Equation [2] They are different from each other and thus recognizable.

[0472] According to another embodiment ( Figure 9 as shown), a balanced interferometer is employed.

[0473] In terms of what happens after the beam splitter, the function of the balanced interferometer corresponds to that of the unbalanced interferometer ( Figure 8 ).

[0474] In this configuration, the beam of branch A is reflected by the semi-reflecting plate 46 and travels along part G before being split into two beams along branches C and D (as in the configuration with an unbalanced interferometer), while the beam B hits the second mirror 48, passes through the compensation plate 47, is reflected by the semi-reflecting plate 46 towards the third mirror 49, is reflected by the mirror 49 towards the semi-reflecting plate 46 and travels along part G before being split into two beams along branches C and D (as in the configuration with an unbalanced interferometer).

[0475] The advantage of this configuration is that by properly positioning the mirrors 42, 48, 49, it is possible to ensure that the optical path from to G is equal to the sum between the optical path from to G and twice the optical path of part B'.

[0476] This means that the phase differences and cancel each other out advantageously, so there is no longer a need to satisfy the previously disclosed relation: ΔL < c / Δu.

[0477] The compensation plate 47 is used to compensate for the optical path inside the semi-reflecting plate 46 (for example, as done in other types of interferometers, such as the Michelson interferometer).

[0478] According to another embodiment ( Figure 7 as shown), compensation for the set signal SP is employed.

[0479] According to relation [1], the constant average intensity corresponds to a constant phase ΔR, but this only occurs when the two quantities I R1 and I R2 are substantially constant.

[0480] However, in non-stable applications, these quantities may vary significantly and must be compensated to keep the phase difference ΔR of the reference beam constant.

[0481] To achieve this, the setpoint signal SP of the PID control can be operated on.

[0482] As Figure 9 shown, using two half-reflecting plates 66, 67, laser line filters 68, 69 with wavelengths consistent with the wavelength of the reference beam used in transmission, two photodiodes 63, 64, and two amplifiers 73, 74 is sufficient to cause the partial beams to hit the openings Z1 and Z2.

[0483] The voltage value of the setpoint signal SP to be applied to the PID controller for compensation is determined by the following relationship:

[0484]

[0485] GI R1 and GI R2 are the voltage values of the signals at the output of the amplifiers, proportional to the intensities I R1 and I R2 respectively, where G is the proportionality constant.

[0486] G is measured at the output of amplifier 71 (see Figure 9 Figure 7 ), and is related to the first electrical signal V1 and intensity Proportional (or corresponding) voltage values, where G is a proportionality constant and ΔR is a value of the phase difference that remains constant. The calculation can be carried out by means of a processing unit 65 (which can correspond to a processing unit configured to obtain the demodulation functions a(t) and b(t), or it can use an additional processor to execute).

[0487] It can be noted that the object of the present invention is fully achieved by the systems and methods shown above, by virtue of the functional and structural characteristics of the above-mentioned systems and methods.

[0488] In fact, the systems and methods for transmitting and receiving electromagnetic beams described above are capable of precisely and reliably detecting the orbital angular momentum of the received beam in a manner independent of the tilt of the receiver's position and independent of the distortions suffered by the beam during propagation.

[0489] This is achieved by means of a double spatial detection of the composite beam at two different points, which composite beam includes, in addition to the beam to be studied, another reference beam.

[0490] The possibility of precisely and reliably detecting the orbital angular momentum of the received beam is in turn advantageously applicable to a variety of different applications, including, for example, the characterization of the beam and the exploitation of the angular momentum variable for telecommunication purposes.

[0491] Referring to the application of telecommunication, the method and system of the present invention allow the exploitation of the angular momentum variable as an additional degree of freedom, which is useful for both modulating signals and multiplexing signals.

[0492] In particular, the orbital angular momentum provides an additional multiplexing level (with the consequent obvious advantages), allowing signals that are the same from the perspective of other multiplexing variables (such as time or frequency) to be grouped, and these signals can be distinguished based on different orbital angular momenta.

[0493] Furthermore, the present invention provides an effective method for locally demultiplexing and demodulating amplitude modulation signals grouped by means of multiplexing in the orbital angular momentum variable.

[0494] Advantageously, this demultiplexing and demodulation is local, since it can be carried out by means of local detection, detecting even a small part of the wavefront of the beam.

[0495] By means of this method of demultiplexing and demodulation and the associated system, it is possible to implement the aforementioned telecommunication methods and systems based on orbital angular momentum multiplexing, thus managing the simultaneous transmission of multiple information (with orbital angular momentum multiplexing) on a single transmission channel.

[0496] Those skilled in the art may make modifications and adjustments to the embodiments of the above systems and methods and replace them with other functionally equivalent elements without departing from the scope of the appended claims to meet possible needs. Each feature described as belonging to a possible embodiment may be implemented without regard to the other described embodiments.

Claims

1. A method for demultiplexing and demodulating an amplitude - modulated signal, the amplitude - modulated signal being grouped by means of multiplexing in orbital - angular - momentum variables, Among them, The signal to be demultiplexed and demodulated comprises a composite electromagnetic radiation beam (Q1), the composite electromagnetic radiation beam comprising a superposition of a reference beam (F0) and a main beam, and thus comprising a superposition of a first modulated beam (Fm1) and at least one second modulated beam (Fm2); wherein the first modulated beam (Fm1) is obtained by modulating a first electromagnetic radiation beam (F1) with a first piece of information by means of any amplitude - modulation technique, the first piece of information being represented by a first modulation function a(t), and wherein the at least one second modulated beam (Fm2) is obtained by modulating at least one corresponding second electromagnetic radiation beam (F2) with at least one second piece of information by means of any amplitude - modulation technique, the second piece of information being represented by a second modulation function b(t); wherein the first electromagnetic radiation beam (F1) is characterized by a first orbital angular momentum (L1), and the at least one second electromagnetic radiation beam (F2) is characterized by at least one corresponding second orbital angular momentum (L2), wherein the first electromagnetic radiation beam (F1) and the at least one second electromagnetic radiation beam (F2) both have corresponding spectra in the same first frequency band and also have corresponding curvature radii that are substantially consistent with a first beam - curvature - radius value, and wherein the reference beam (F0) is characterized by a third orbital angular momentum (L0), a second spectrum in a second frequency band different from the first frequency band, and a second beam - curvature - radius having a value that is substantially consistent with the first beam - curvature - radius value; wherein the method comprises the following steps: - passing the composite electromagnetic radiation beam (Q1) through two apertures (Z1, Z2) so as to obtain a first composite - beam portion (Q1(x1)) downstream of the first aperture (Z1) and a second composite - beam portion (Q1(x2)) downstream of the second aperture (Z2); - emitting the first composite - beam portion (Q1(x1)) along a first branch (A) of an interferometer (40) and emitting the second composite - beam portion (Q1(x2)) along a second branch (B) of the interferometer; - superimposing the first composite - beam portion (Q1(x1)) and the second composite - beam portion (Q1(x2)) along a third branch (D) of the interferometer by means of a beam splitter (41) of the interferometer to obtain a corresponding third electromagnetic beam (D), and superimposing the first composite - beam portion (Q1(x1)) and the second composite - beam portion (Q1(x2)) along a fourth branch (C) of the interferometer to obtain a corresponding fourth electromagnetic beam (C); - Perform frequency discrimination of the third electromagnetic beam (D) around the first frequency band to obtain a third filtered electromagnetic beam (F), in which the contributions of the reference beam from the first composite beam portion (Q1(x1)) and the reference beam from the second composite beam portion (Q1(x2)) have been cancelled, and in which the components from the respective first modulated beams (Fm1(x1), Fm1(x2)) and at least one second modulated beam (Fm2(x1), Fm2(x2)) are retained; - Perform frequency discrimination of the fourth electromagnetic beam (C) around the second frequency band of the reference beam to obtain a fourth filtered electromagnetic beam (E), the fourth filtered electromagnetic beam (E) comprising the superposition of two reference beams (F0(x1), F0(x2)) belonging to the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)) respectively; - Detect the third filtered electromagnetic beam (F) by means of a first beam detector (1) to generate a first electrical signal (V1), the first electrical signal (V1) representing the intensity of the electromagnetic radiation of the third filtered electromagnetic beam (F); - determining, at the first beam detector (1), a first phase difference (ΔP) between a component of the third filtered electromagnetic beam originating from the first composite beam filtering portion (Fm1(x1), Fm2(x1)) and a component of the third electromagnetic beam originating from the second composite beam filtering portion (Fm1(x2), Fm2(x2)), based on the first electrical signal (V1); ab ), wherein the first phase difference (ΔP ab ) depends on the values taken by the first modulation function a(t) and the second modulation function b(t); - Detect the fourth filtered electromagnetic beam (E) by means of a second beam detector (2) to generate a second electrical signal (V2), the second electrical signal (V2) representing the intensity of the electromagnetic radiation of the fourth filtered electromagnetic beam (E); - At the second beam detector (2), based on the second electrical signal (V2), determine a second phase difference (ΔR) between the two reference beams (F0(x1), F0(x2)) belonging to the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)); - Based on the first phase difference (ΔP ab ), and the second phase difference (ΔR), demultiplex and demodulate the information (a(t), b(t)) modulated on each of the first modulation beam (Fm1) and the at least one second modulation beam (Fm2).

2. The method according to claim 1, wherein, The steps of demultiplexing and demodulating include: - Subtract the division of the second phase difference (ΔR) by the second wave number k' from the division of the first phase difference (ΔP ab ) by the first wave number k to obtain a difference Q2, wherein the first wave number k is the wave number corresponding to the main beam, defined as k = 2π / λ, λ being the wavelength of the main beam, and wherein the second wave number k' is the wave number corresponding to the reference beam, defined as k' = 2π / λ', λ' being the wavelength of the reference beam; The difference Q2 represents the combination of the values taken by the first modulation function a(t) and the second modulation function b(t), independent of the positional inclination condition between the first beam detector and the second beam detector and independent of the phase variables caused by the interference suffered by the transmitted composite beam before reception; - Based on the determined difference Q2, demultiplex and demodulate the modulation information on each of the first modulated beam (Fm1) and the at least one second modulated beam (Fm2).

3. The method according to any one of claims 1 or 2, wherein, Digitally amplitude-modulate the first electromagnetic radiation beam (F1) and the at least one second electromagnetic radiation beam (F2) according to the amplitudes of the first modulation function a(t) and the at least one second modulation function b(t), And wherein, the difference Q2 can take a plurality of expected values, each expected value representing a corresponding combination of digital amplitude values taken by the first modulation function a(t) and the at least one second modulation function b(t), wherein the difference Q2 is obtained by subtracting the second phase difference (ΔR) divided by the second wave number k' from the first phase difference (ΔP ab ) divided by the first wave number k.

4. The method according to claim 3, wherein: - The first electromagnetic radiation beam (F1) and the at least one second electromagnetic radiation beam (F2) are digitally amplitude modulated in a binary manner, and the amplitudes of the first modulation function a(t) and the at least one second modulation function b(t) can take on the logical values 0 or 1; - The method further comprises the step of: detecting the received power or intensity of the third filtered electromagnetic beam (F) and comparing the received power or intensity with a minimum threshold, the received power or intensity corresponding to the first electrical signal (V1) detected by the first beam detector (1); - The determined difference Q2 can take a first expected value EX1, or a second expected value EX2, or a third expected value EX3, where EX1 = ΔP 10 / k - ΔR / k', ΔP 10 is the first expected value of the first phase difference (ΔP ab ); EX2 = ΔP 01 / k - ΔR / k', ΔP 01 is the second expected value of the first phase difference (ΔP ab ); EX3 = ΔP 11 / k - ΔR / k', ΔP 11 is the third expected value of the first phase difference (ΔP ab ); the first expected value EX1 depends on the first orbital angular momentum (L1), the second expected value EX2 depends on the second orbital angular momentum (L2), and the third expected value EX3 depends on the combination of the first orbital angular momentum and the second orbital angular momentum; - The steps of demultiplexing and demodulating the modulation information include: - If the determined difference Q2 takes the first expected value EX1, identifying that the first modulated beam (Fm1) carries information corresponding to 1 and the second modulated beam (Fm2) carries information corresponding to 0; - If the determined difference Q2 takes the second expected value EX2, identifying that the first modulated beam (Fm1) carries information corresponding to 0 and the second modulated beam (Fm2) carries information corresponding to 1; - If the determined difference Q2 takes the third expected value EX3, identifying that the first modulated beam (Fm1) carries information corresponding to 1 and the second modulated beam (Fm2) carries information corresponding to 1; - If the received power or intensity of the third filtered electromagnetic beam F is below the minimum threshold, identifying that the first modulated beam (Fm1) carries information corresponding to 0 and the second modulated beam (Fm2) carries information corresponding to 0.

5. The method according to any one of claims 1 or 2, wherein: - The first phase difference (ΔP ab ) depends on the average intensity (Im1) of the third filtered electromagnetic beam (F) associated with the corresponding interference pattern, and the first electrical signal (V1) represents the average intensity of the third filtered electromagnetic beam (F) detected by the first beam detector (1); - The second phase difference (ΔR) depends on the average intensity (Im2) of the fourth filtered electromagnetic beam (E) associated with the corresponding interference pattern, and the second electrical signal (V2) represents the average intensity (Im2) of the fourth filtered electromagnetic beam (E) detected by the second beam detector (2); And wherein the method further comprises the step of: - By means of a feedback control loop controlled by the second electrical signal (V2) and acting on the first composite beam portion (Q1(x1)), keeping the average intensity (Im2) of the fourth filtered electromagnetic beam (E) constant at a predefined intensity value, such that the second phase difference (ΔR) remains constant and is set at a predefined value.

6. The method according to claim 5, wherein, Digitally amplitude modulate the first electromagnetic radiation beam (F1) and the at least one second electromagnetic radiation beam (F2) according to the amplitudes of the first modulation function a(t) and the at least one second modulation function b(t), and wherein, the first phase difference ΔP ab is able to take a plurality of expected values, each expected 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).

7. The method according to claim 6, wherein: - The first electromagnetic radiation beam (F1) and the at least one second electromagnetic radiation beam (F2) are digitally amplitude modulated in a binary manner, and the amplitudes of the first modulation function a(t) and the at least one second modulation function b(t) can take on the logical values 0 or 1; - The method further comprises the following additional step: detecting the received power or intensity of the third filtered electromagnetic beam (F) and comparing the received power or intensity with a minimum threshold, the received power or intensity corresponding to the first electrical signal (V1) detected by the first beam detector (1); - The determined first phase difference (ΔP ab ) can take a first expected value (ΔP 10 ), or a second expected value (ΔP 01 ), or a third expected value (ΔP 11 ), where the first expected value depends on the first orbital angular momentum (L1), the second expected value depends on the second orbital angular momentum (L2), and the third expected value depends on the combination of the first orbital angular momentum and the second orbital angular momentum; - The steps of demultiplexing and demodulating the modulated information include: - If the determined first phase difference (ΔP ab ) takes the first expected value (ΔP 10 ), then it is recognized 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 first phase difference (ΔP ab ) takes the second expected value (ΔP 01 ), then it is recognized 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 first phase difference (ΔP ab ) takes the third expected value (ΔP 11 ), then it is recognized 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 of the third filtered electromagnetic beam F is below the minimum threshold, identifying that the first modulated beam (Fm1) carries information corresponding to 0 and the second modulated beam (Fm2) carries information corresponding to 0.

8. The method according to any one of claims 1 or 2, wherein The number of the modulated beams multiplexed by orbital angular momentum is equal to N, where N is greater than 2. Each modulation beam is characterized by its respective orbital angular momentum (L i ), and is amplitude-modulated by the corresponding modulation function, and wherein each of the possible value combinations of the modulation functions on the N modulation beams corresponds to a respective first phase difference (ΔP a1…aN ) and / or a respective difference Q2, where Q2 = ΔP a1…aN / k – ΔR / k'.

9. The method according to any one of claims 1 or 2, the method further comprising the following steps: - Before the superposition of the first composite beam portion and the second composite beam portion, arranging a first additional optical path (A, G) for the first composite beam portion (Q1(x1)) and a second additional optical path (B, B', B', G) for the second composite beam portion (Q1(x2)) in the interferometer; Wherein, the first additional optical path (A, G) and the second additional optical path (B, B', B', G) are predefined and dimensioned so as to eliminate a phase difference caused between a phase of the second composite beam portion (Q1(x2)) and a phase of the first composite beam portion (Q1(x1)) due to an overall optical path difference between a respective entrance aperture and the first beam detector (1). and in order to eliminate a phase difference caused between the phase of the second composite beam portion (Q1(x2)) and the phase of the first composite beam portion (Q1(x1)) due to an overall optical path difference between the corresponding entrance opening and the second bundle detector (2) 10. The method according to claim 5, wherein, The step of keeping the average intensity (Im2) of the fourth filtered electromagnetic beam (E) constant includes: - By means of a control unit (61) receiving the second electrical signal (V2) and a setting signal (SP) as inputs, controlling the first mirror (42) hit by the first composite beam portion (Q1(x1)), thereby changing in a controlled manner the length of the optical path (A) passed through by the first composite beam portion ((Q1(x1)) and thus changing the phase shift between the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)), so as to change the average intensity (Im2) detected by the second beam detector (2) in a controlled manner depending on the second electrical signal (V2) and the setting signal (SP), so as to keep the second phase difference (ΔR) and the average intensity (Im2) of the fourth filtered electromagnetic beam (E) constant at corresponding predefined values, the predefined values depending on the setting signal (SP).

11. The method according to claim 10, wherein, The step of keeping the average intensity (Im2) of the fourth filtered electromagnetic beam (E) constant includes: at the second beam detector (2), compensating for the change in the intensity (I R1 ) of the reference beam associated with the first composite beam portion, and at the second beam detector (2), compensating for the change in the intensity (I R2 ) of the reference beam associated with the second composite beam portion, Wherein, the step of compensation includes: - Deflecting a part of the beam corresponding to the first composite beam portion (Q1(x1)) at the first branch (A) of the interferometer; - Detecting, by means of a third beam detector (63), the intensity of the deflected portion of the beam corresponding to the first composite beam portion (Q1(x1)) and generating a first compensation electrical signal (GI R1 ), the first compensation electrical signal representing the intensity of the first composite beam portion; - Deflecting a part of the beam corresponding to the second composite beam portion (Q1(x2)) at the second branch (B) of the interferometer; - Detecting the intensity of the second composite beam portion by means of a fourth beam detector (64) and generating a second compensation electrical signal (GI R2 ), the second compensation electrical signal representing the intensity of the second composite beam portion; - Based on the first compensation electrical signal (GI R1 ), and the second compensation electrical signal (GI R2 ), the processing unit (65) modifies the setting signal (SP).

12. The method according to any one of claims 1 or 2, wherein All electromagnetic beams are light beams and / or laser beams.

13. The method according to any one of claims 1 or 2, wherein The orbital angular momentum of the reference beam is always known.

14. The method according to claim 13, wherein, The orbital angular momentum of the reference beam takes a constant value L0 = 0.

15. The method according to any one of claims 1 or 2, wherein The second frequency band is substantially single-frequency.

16. The method according to claim 15, wherein, The second frequency band is adjacent to the first frequency band.

17. The method according to any one of claims 1 or 2, wherein The step of performing frequency discrimination on the first electrical signal or the second electrical signal of the composite beam includes performing frequency filtering.

18. A system (100) for demultiplexing and demodulating an amplitude-modulated signal, the amplitude-modulated signal being grouped by multiplexing in an orbital angular momentum variable. Among them, The signal to be demultiplexed and demodulated includes a composite electromagnetic radiation beam (Q1), which comprises a superposition of a reference beam (F0) and a main beam, and thus a superposition of a first modulated beam (Fm1) and at least one second modulated beam (Fm2); wherein the first modulated beam (Fm1) is obtained by modulating a first electromagnetic radiation beam (F1) with a first piece of information by means of any amplitude modulation technique, the first piece of information being represented by a first modulation function a(t), and wherein the at least one second modulated beam (Fm2) is obtained by modulating at least one corresponding second electromagnetic radiation beam (F2) with at least one second piece of information by means of any amplitude modulation technique, the second piece of information being represented by a second modulation function b(t); wherein the first electromagnetic radiation beam (F1) is characterized by a first orbital angular momentum (L1), and the at least one second electromagnetic radiation beam (F2) is characterized by at least one corresponding second orbital angular momentum (L2), wherein the first electromagnetic radiation beam (F1) and the at least one second electromagnetic radiation beam (F2) both have corresponding spectra in the same first frequency band and also have corresponding curvature radii that are substantially consistent with a first beam curvature radius value; and wherein the reference beam (F0) is characterized by a third orbital angular momentum (L0), a second spectrum in a second frequency band different from the first frequency band, and a second beam curvature radius having a value that is substantially consistent with the first beam curvature radius value; wherein the system (100) comprises: - a screen equipped with two openings (Z1, Z2), the screen being configured to let the composite electromagnetic radiation beam (Q1) pass through the two openings (Z1, Z2) so as to obtain a first composite beam portion (Q1(x1)) downstream of the first opening (Z1) and a second composite beam portion (Q1(x2)) downstream of the second opening (Z2); - an interferometer (40) arranged downstream with respect to the two openings (Z1, Z2), the interferometer comprising: - a first branch (A) configured to be passed through by the first composite beam portion (Q1(x1)); - a second branch (B) configured to be passed through by the second composite beam portion (Q1(x2)); - a beam splitter (41) configured to superimpose the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)) along a third branch (D) of the interferometer to obtain a corresponding third electromagnetic beam (D), and to superimpose the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)) along a fourth branch (C) of the interferometer to obtain a corresponding fourth electromagnetic beam (C); - A first frequency discrimination device (45) configured to discriminate the frequency of the third electromagnetic beam (D) around the first frequency band to obtain a third filtered electromagnetic beam (F), wherein the contributions of the reference beams from the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)) have been cancelled, and wherein the components from the respective first modulated beams (Fm1(x1), Fm1(x2)) and the at least one second modulated beam (Fm2(x1), Fm2(x2)) are retained; - A second frequency discrimination device (44) configured to discriminate the frequency of the fourth electromagnetic beam (C) around the second frequency band of the reference beam to obtain a fourth filtered electromagnetic beam (E), the fourth filtered electromagnetic beam (E) comprising the superposition of two reference beams (F0(x1), F0(x2)) belonging to the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)) respectively; - A first beam detector (1) configured to detect the third filtered electromagnetic beam (F) to generate a first electrical signal (V1), the first electrical signal representing the intensity of the electromagnetic radiation of the third filtered electromagnetic beam (F); - A second beam detector (2) configured to detect the fourth filtered electromagnetic beam (E) to generate a second electrical signal (V2), the second electrical signal representing the intensity of the electromagnetic radiation of the fourth filtered electromagnetic beam (E); - A processing device (65) configured to: - At the first beam detector (1), based on the first electrical signal (V1), determine a first phase difference (ΔP ab ) between the component of the third filtered electromagnetic beam originating from the first composite beam filtering section (Fm1(x1), Fm2(x1)) and the component of the third electromagnetic beam originating from the second composite beam filtering section ((Fm1(x2), Fm2(x2))), where the first phase difference (ΔP ab ) depends on the values taken by the first modulation function a(t) and the second modulation function b(t); - At the second beam detector (2), based on the second electrical signal (V2), determine a second phase difference (ΔR) between the two reference beams (F0(x1), F0(x2)) belonging to the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)); -Based on the first phase difference (ΔP ab ), and the second phase difference (ΔR), demultiplex and demodulate the information (a(t), b(t)) modulated on each of the first modulation beam (Fm1) and the at least one second modulation beam (Fm2).

19. The system (100) according to claim 18, the system further comprising: - A control unit (61) adapted to receive the second electrical signal (V2) and a setting signal (SP) as inputs, - An actuator (43) controlled by the control unit (61), - A first mirror (42) controlled by the actuator (43) and arranged such that the first composite beam portion (Q1(x1)) hits the first mirror; Wherein, the control unit (61) is configured to change, in a controlled manner, the length of the optical path (A) traversed by the first composite beam portion (Q1(x1)), thereby changing the phase shift of the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)), so as to vary the average intensity (Im2) detected by the second beam detector (2) in a controlled manner depending on the second electrical signal (V2) and the setting signal (SP), so as to keep the second phase difference (ΔR) and the average intensity (Im2) of the fourth filtered electromagnetic beam (E) constant and set at corresponding predefined values, the predefined values depending on the setting signal (SP).

20. The system (100) according to claim 19, the system further comprising means (46, 47, 48, 49) for balancing the optical path, the means for balancing the optical path being configured to: - Before the superposition of the first composite beam portion and the second composite beam portion, arrange a first additional optical path (A, G) for the first composite beam portion (Q1(x1)) and a second additional optical path (B, B', B', G) for the second composite beam portion (Q1(x2)) in the interferometer; Among them, The steps of said arrangement include: arranging said first additional optical path (A, G) and said second additional optical path (B, B', B', G) so as to eliminate the phase difference caused between the phase of said second composite beam portion (Q1(x2)) and the phase of said first composite beam portion (Q1(x1)) due to the total optical path difference between the respective inlet openings and said first bundle of detectors (1) and in order to eliminate the phase difference between the phase of the second composite beam portion (Q1(x2)) and the phase of the first composite beam portion (Q1(x1)) due to the total optical path difference between the corresponding inlet opening and the second bundle detector (2) 21. The system (100) according to claim 20, wherein, The means for balancing the optical path comprises: - Along the second branch (B) of the interferometer, a second mirror (48), a compensation plate (47), a semi-reflective plate (46) and a third mirror (49) arranged along the path of the second composite beam portion (Q1(x2)) to form the second additional optical path (B, B', B', G); Wherein, the semi-reflective plate (46) is also arranged along the path of the first composite beam portion (Q1(x2)) and is configured to emit the first composite beam portion (Q1(x1)) and the second composite beam portion (Q1(x2)) to the beam splitter (41).

22. The system according to any one of claims 18 - 21, the system further comprising a beam intensity compensation device configured to compensate for changes in the intensity (I R1 ) of the reference beam associated with the first composite beam portion at the second beam detector (2), and to compensate for changes in the intensity (I R2 ) of the reference beam associated with the second composite beam portion at the second beam detector (2), Among them, The beam intensity compensation means comprises: - A first semi-reflective plate (66) configured to deflect a part of the beam corresponding to the first composite beam portion (Q1(x1)) at the first branch (A) of the interferometer; - A first narrowband optical band-pass filter (68) configured to filter the deflected part of the beam corresponding to the first composite beam portion (Q1(x1)) around the second frequency band of the reference beam; - A third beam detector (63), the third beam detector being configured to detect the intensity of the deflected portion of the beam corresponding to the first composite beam portion (Q1(x1)) and to generate a first compensation electrical signal (GI R1 ), the first compensation electrical signal representing the intensity of the first composite beam portion; - A second semi-reflective plate (67) configured to deflect a part of the beam corresponding to the second composite beam portion (Q1(x2)) at the second branch (B) of the interferometer; - A second optical band-pass filter (69) configured to filter the deflected part of the beam corresponding to the second composite beam portion (Q1(x2)) around the second frequency band of the reference beam; - The fourth beam detector (64), which detects the intensity of the deflected portion of the beam corresponding to the second composite beam portion (Q1(x2)) and generates a second compensation electrical signal (GI R2 ), where the second compensation electrical signal represents the intensity of the second composite beam portion; - A processing unit (65), the processing unit being configured to change a setting signal (SP) based on the first compensation electrical signal (GI R1 ) and the second compensation electrical signal (GI R2 ).

23. The system according to any one of claims 18-21, wherein, The system (100) is configured to perform the method according to any one of claims 1 to 17.

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