Patent Publication Number: US-2023163853-A1

Title: Electromagnetic Communication with a Vortex Beam Concurrently Conveying Multiple Topological Charges

Description:
FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT 
     The United States Government has ownership rights in this invention. Licensing and technical inquiries may be directed to the Office of Research and Technical Applications, Naval Information Warfare Center Pacific, Code 72120, San Diego, Calif., 92152; voice (619) 553-5118; ssc_pac_t2@navy.mil. Reference Navy Case Number 107438. 
    
    
     BACKGROUND OF THE INVENTION 
     Data communication typically encodes data into symbols serially transmitted one bit at a time. Data throughput can be increased by simultaneously transmitting multiple bits, such as simultaneously sending a bit over each of multiple parallel wires. There is a general need to increase data throughput over communication interfaces. There is also a general need for data communications with encodings that are unique to increase the security of the data communication. 
     SUMMARY 
     A system for electromagnetic communication with a vortex beam concurrently conveys multiple topological charges of orbital angular momentum. The system includes a source, at least one vortex-sensing diffraction grating, and an array of photodetectors. The source generates the vortex beam concurrently conveying a respective number of selected topological charges during each of the time intervals. The selected topological charges for each time interval are selected from a set of available topological charges. The selected topological charges for each time interval encode a symbol of data. The vortex-sensing diffraction grating combines a vortex phase pattern and a linear phase pattern. The vortex sensing diffraction grating produces a diffraction pattern from diffracting the vortex beam received from the source. The array of photodetectors detects portions of the diffraction pattern and from the detected portions recovers the selected topological charges encoding the symbol of each time interval. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Throughout the several views, like elements are referenced using like references. The elements in the figures are not drawn to scale and some dimensions are exaggerated for clarity. 
         FIG.  1    is a block diagram of a system for electromagnetic communication with a vortex beam concurrently conveying multiple topological charges of orbital angular momentum in accordance with an embodiment of the invention. 
         FIG.  2    is an example cross section through a vortex beam in accordance with an embodiment of the invention. 
         FIG.  3    is an example cross section through a vortex beam in accordance with an embodiment of the invention. 
         FIG.  4 A  is an example diffraction pattern that a vortex-sensing diffraction grating is simulated to produce from the vortex beam having the example cross section shown in  FIG.  2   . 
         FIG.  4 B  shows the portions of the diffraction pattern of  FIG.  4 A  from which the array of photodetectors recovers the selected topological charges included in the example cross section shown in  FIG.  2   . 
         FIG.  5    is a block diagram of a system for electromagnetic communication with a vortex beam concurrently conveying multiple topological charges of orbital angular momentum in accordance with an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     The disclosed systems below may be described generally, as well as in terms of specific examples and/or specific embodiments. For instances where references are made to detailed examples and/or embodiments, it should be appreciated that any of the underlying principles described are not to be limited to a single embodiment, but may be expanded for use with any of the other methods and systems described herein as will be understood by one of ordinary skill in the art unless otherwise stated specifically. 
     Embodiments of the invention encode data symbols that include many binary bits of information transmitted concurrently in a beam of electromagnetic energy, such as a light beam or a radiofrequency beam. The concurrent transmission of a symbol including multiple binary bits increases the throughput of the electromagnetic communication. Each symbol is encoded in multiple topological charges of orbital angular momentum conveyed concurrently in the electromagnetic communication. This encoding in multiple topological charges of orbital angular momentum is also unique, which increases the security of the electromagnetic communication even when the electromagnetic communication is intercepted during eavesdropping. 
       FIG.  1    is a block diagram of a system  100  for electromagnetic communication with a vortex beam concurrently conveying multiple topological charges of orbital angular momentum in accordance with an embodiment of the invention. During successive time intervals, a symbol of data is encoded in the multiple topological charges of orbital angular momentum that the vortex beam conveys in each time interval. The particular topological charges conveyed during a particular time interval collectively specify an encoding of the symbol of data. Because many combinations of topological charges are possible, multiple binary bits of data can be concurrently encoded in the topological charges selected for each time interval. 
     A source  110  generates the vortex beam conveyed through free space or through an optional multimode optical fiber  112  from the source  110  to the vortex-sensing diffraction grating  120 . Typically, the vortex-sensing diffraction grating  120  is disposed at a distance from the source  110  to form a segment of a telecommunications network. During each time interval within a sequence of time intervals, the vortex beam concurrently conveys multiple topological charges selected from a set of available topological charges. In one embodiment, the source  110  includes a spatial light modulator  114  having regions that each provide one of the available topological charges during each of the time intervals, and hence the number S of selected topological charges for each of the time intervals is fixed at a number of the regions of the spatial light modulator  114 . More generally, the number of the topological charges selected for each time interval is dynamically variable, but includes at least two selected topological charges for at least one of the time intervals. 
       FIG.  2    is an example cross section  200  through a vortex beam in accordance with an embodiment of the invention. When optional multimode optical fiber  112  is omitted, the vortex beam is collimated through free space and has the circular cross section  200  at section  1 - 1  of  FIG.  1   . Alternatively or additionally, the vortex beam has the circular cross section  200  at the spatial light modulator  114  of  FIG.  1   . 
     The example circular cross section  200  is partitioned into two regions, a central circular region  210  and a concentric annular region  220  surrounding the central circular region  210 . Within each of the regions  210  and  220 , the relative phase of the vortex beam is shown with the white shade corresponding to a phase delay of zero and the darkest shade corresponding to a phase delay of nearly 2π radians. The inner region  210  has three complete helical cycles  211 ,  212 , and  213  of phase increasing clockwise, and the outer region  220  has four complete helical cycles  221 ,  222 ,  223 , and  224  of phase increasing counterclockwise. The three complete helical cycles  211 ,  212 , and  213  of phase increasing clockwise of inner region  210  is denoted a topological charge of −3 with the minus sign denoting clockwise increasing phase, and the four complete helical cycles  221 ,  222 ,  223 , and  224  of phase increasing counterclockwise of the outer region  220  is denoted a topological charge of +4 with the plus sign denoting counterclockwise increasing phase. Thus, the example circular cross section  200  is partitioned into the central circular region  210  with topological charge −3 and the concentric annular region  220  with topological charge +4. 
       FIG.  2    shows the example topological charges of −3 and +4 for two regions  210  and  220 , respectively. There are more than two regions in other embodiments. Typically, the topological charge of each of the regions  210  and  220  is an integer value with an absolute value ranging between 0 and a maximum allowed topological charge M; however, non-integer topological charges are possible, but correspond to incomplete cycles of phase increasing clockwise or counterclockwise. A topological charge of zero in a region  210  or  220  corresponds to an electromagnetic beam with the same phase across that region of the cross section  200 , such as the unmodulated plane wave emitted from a typical laser. 
     In  FIG.  2   , the central region  210  has a radius that is about half the outer radius of the annular region  220 . Thus, the annular region  220  has twice the area of the central region  210 . This is appropriate for an electromagnetic beam having decreased intensity in the outer annular region  220 , such as a light beam with a Gaussian profile. 
       FIG.  3    is an example cross section  300  through a vortex beam in accordance with an embodiment of the invention. Like  FIG.  2   ,  FIG.  3    shows two regions  310  and  320 , but each spread over two subregions. Region  310  includes subregions  311  and  312  together having three complete helical cycles  313 ,  314 , and  315  of phase increasing clockwise. Region  320  includes subregions  321  and  322  together having four complete helical cycles  323 ,  324 ,  325 , and  326  of phase increasing counterclockwise. 
     In  FIG.  3   , each of the subregions  311 ,  312 ,  321 , and  322  have equal area. This is appropriate for a light beam having the same intensity across the cross section  300 . Because the outermost subregion  322  most efficiently conveys angular orbital momentum and the innermost subregion  321  least efficiently conveys angular orbital momentum, these two subregions  321  and  322  are allocated to the same region  320 . In an embodiment with more than two regions, there are at least twice as many subregions as regions, with the innermost and outermost subregions allocated to the same region, the next innermost and next outermost subregions allocated to the same region, and so on to equalize the angular orbital momentum conveyed in each of the regions. 
     Returning to  FIG.  1   , the spatial light modulator  114  of an embodiment of the invention imparts the helical cycles of phase onto an electromagnetic beam with uniform phase, such as the unmodulated plane wave emitted from a typical laser. The spatial light modulator  114  is either transmitting or reflecting in embodiments of the invention. For example, a transmitting spatial light modulator  114  adjusts the phase with the tilt angle of a liquid crystal have rod-like molecules with different refractive indices along the length and across the length of the rod-like molecules, and a reflecting spatial light modulator  114  adjusts the phase with an array of piston-displaceable mirrors. Such a transmitting or reflecting spatial light modulator  114  with an array of 540×480 pixels has sufficient resolution to impart, in each of S regions, one of the 2M+1 available topological charges in the set −M, −M+1, . . . −1, 0, +1, . . . +M−1, +M for the maximum allowed topological charge of M≈60. Note that a pixelated spatial light modulator  114  can impart either of the example cross sections  200  and  300  of  FIGS.  2  and  3    onto a light beam or other electromagnetic beam. 
     The vortex beam is conveyed through free space or through the optional multimode optical fiber  112  from the source  110  to the vortex-sensing diffraction grating  120 . By diffracting the vortex beam received from the source  110 , the vortex-sensing diffraction grating  120  produces at section  2 - 2  an example diffraction pattern  400  of  FIG.  4 A . The example diffraction pattern  400  of  FIG.  4 A  is a negative image with darker shading indicating higher light intensity that the vortex-sensing diffraction grating  120  is simulated to produce from the vortex beam having the example cross section  200  shown in  FIG.  2   . 
     As discussed below, the vortex-sensing diffraction grating  120  combines a vortex phase pattern and a linear phase pattern. Roughly, the vortex phase pattern of the vortex-sensing diffraction grating  120  produces focal spots each corresponding to a particular topological charge, and the linear phase pattern of the vortex-sensing diffraction grating  120  laterally separates these focal spots. The array  130  of photodetectors detects portions of the diffraction pattern and from the detected portions recovers the S selected topological charges included in the vortex beam. 
       FIG.  4 B  shows the focal portions  401  through  409  of the example diffraction pattern  400  of  FIG.  4 A  from which the array  410  of photodetectors  411  through  419  recovers the S=2 selected topological charges included in the vortex beam with the example cross section  200  shown in  FIG.  2   . The array  410  of  FIG.  4 B  corresponds to the array  130  of  FIG.  1   . The array  410  of photodetectors includes a respective photodetector  411  through  419  for each portion  401  through  409 . For example, the array  410  includes photodetector  411  for portion  401  that corresponds, in this example, to the topological charge −4 at diffraction order −4. 
     Recall that the example cross section  200  shown in  FIG.  2    is partitioned into the central circular region  210  conveying topological charge −3 and the concentric annular region  220  conveying topological charge +4. For topological charge −3, the photodetector  412  examines the portion  402  of the example diffraction pattern  400  and detects the topological charge −3 is included in the selected topological charges for the example cross section  200  because photodetector  412  detects presence of the electromagnetic energy at the central spot of the portion  402 . Portion  402  includes the central spot (dark shade indicating high light intensity in the negative image of  FIG.  4 A-B ) surrounded by a ring of lower intensity. Similarly, for topological charge +4, the photodetector  419  detects the topological charge +4 is included in the selected topological charges for the example cross section  200  because photodetector  419  detects presence of the electromagnetic energy at the central spot of the portion  409  relative to the surrounding ring. In summary, photodetectors  412  and  419  are highlighted in  FIG.  4 B  to indicate that these photodetectors respectively detect topological charges −3 and +4 are included in the vortex beam having the example cross section  200  of  FIG.  2   . 
     In contrast, photodetectors  411 ,  414 ,  415 ,  416 ,  417 , and  418  detect absence of electromagnetic energy at the central null surrounded by a ring of higher intensity of portions  401 ,  404 ,  405 ,  406 ,  407 , and  408 , respectively. The remaining photodetector  413  detects apparent ambiguity in  FIG.  4 B  because the central spot and surrounding ring of portion  403  have similar intensities at the gray scale shown. However, this apparent ambiguity is resolved either with similar intensities between the central spot and the surrounding ring indicating the corresponding topological charge is not present, or through picking the best two portions  402  and  409  using the knowledge that the example cross section  200  includes exactly S=2 different selected topological charges. 
     Because the example cross section  300  of  FIG.  3    includes the same selected topological charges −3 and +4 as the example cross section  200  of  FIG.  2   , the resulting diffraction pattern (not shown) would closely resemble the diffraction pattern  400  shown in  FIG.  4 A , even though the example cross section  300  of  FIG.  3    has rearranged regions and subregions presenting these same selected topological charges. Generally, the detected topological charges indicate the presence, but not the actual placement, of these topological charges within the cross section of the vortex beam. 
     The S selected topological charges, which are selected from the available topological charges, typically change for each time interval. Thus, the array  410  of photodetectors  411  through  419  recovers the selected topological charges from the central spot or central null of the portions  401  through  409  of the diffraction pattern for the vortex beam during each time interval of the sequence of the time intervals. The source  100  encodes a symbol of data with the topological charges selected for each of the time intervals. The array  130  or  410  of the photodetectors recovers the symbol for each time interval from the selected topological charges recovered from the detected portions. 
     As mention above, the vortex-sensing diffraction grating  120  combines a vortex phase pattern and a linear phase pattern. In one embodiment, the vortex-sensing diffraction grating  120  combines the vortex phase pattern and the linear phase pattern in a product that multiplies the vortex phase pattern and the linear phase pattern. For example, the vortex-sensing diffraction grating  120  has a binary phase pattern having a phase delay of zero when the product is below a threshold and π radians when the product is above the threshold. The threshold is selected so that 70% of the binary phase pattern has a phase delay of zero and 30% of the binary phase pattern has a phase delay of π radians. The product equals the vortex phase pattern of exp(iLφ) times the linear phase pattern of exp(iγX), where i is an imaginary number basis, L is a topological charge of the vortex phase pattern, φ is a polar angle coordinate of the vortex phase pattern, γ is a period of the linear phase pattern, and X is a Cartesian coordinate of the linear phase pattern. 
     In  FIG.  4 B , diffraction orders ranging between −4 to +4 are shown, and these correspond one-to-one with topological charges ranging between −4 to +4 as shown. However, this is due to the characteristics of the vortex-sensing diffraction grating  120  of  FIG.  1   . The vortex-sensing diffraction grating  120  shown in  FIG.  1    has L=0.5, and this produces the one-to-one correspondence between the numerical values of the diffraction orders and the topological charges. However, parameter L is not restricted to the value L=0.5. Varying L shifts which topological charges correspond to the diffraction orders of the diffraction pattern. 
     As shown in  FIG.  4 A , the diffraction orders get weaker the farther away a particular diffraction order is from the zeroth diffraction order in the center of  FIG.  4 A . The previously mentioned 70%/30% ratio between the areas with a phase delay of zero and the areas with phase delay of π radians within the vortex-sensing diffraction grating  120  helps equalize the weaker outer diffraction orders as compared with a 50%/50% ratio, but still diffraction orders below about −4 and above about +4 become too weak for reliable detection. However, this hindrance is overcome by using multiple vortex-sensing diffraction gratings as discussed next. 
       FIG.  5    is a block diagram of a system  500  for electromagnetic communication with a vortex beam concurrently conveying multiple topological charges of orbital angular momentum in accordance with an embodiment of the invention. Because system  500  enables robust detection of more topological charges than system  100  of  FIG.  1   , many more combinations of topological charges are possible, and hence the symbol of data transmitted during each time interval concurrently encodes more binary bits of data into the S topological charges selected for each time interval. 
     A source  510  includes a spatial light modulator  514  that generates the vortex beam conveyed to an arrangement of beam splitters  541 ,  542 , and  543 . Typically, the beam splitters  541 ,  542 , and  543  are disposed at a distance from the source  510  to form a segment of a telecommunications network. The beam splitters  541 ,  542 , and  543  divide the vortex beam into fractions conveyed to the vortex-sensing diffraction gratings  521 ,  522 , and  523 . 
     The vortex-sensing diffraction gratings  521 ,  522 , and  523  each combine a vortex phase pattern and a linear phase pattern in a product that multiplies the vortex phase pattern and the linear phase pattern. Collectively, the vortex-sensing diffraction gratings  521 ,  522 , and  523  accumulate a total diffraction pattern at section  3 - 3  from diffracting the vortex beam received from the source  510 . The arrays  531 ,  532 , and  533  of photodetectors recover the selected topological charges in each time interval from the total diffraction pattern at section  3 - 3 . It will be appreciated that the separate arrays  531 ,  532 , and  533  of photodetectors can be considered a single array of photodetectors. 
     The operation of the middle vortex-sensing diffraction grating  522  and the middle array  532  of photodetectors is identical to the vortex-sensing diffraction grating  120  and the array  130  of  FIG.  1   . The array  532  of photodetectors detects presence of the topological charges −4, −3, −2, −1, 0, +1, +2, +3, and +4 in correspondingly numbered diffraction orders of the diffraction pattern from the vortex-sensing diffraction grating  522 . 
     The operation of the vortex-sensing diffraction grating  521  and the array  531  of photodetectors is similar to the vortex-sensing diffraction grating  120  and the array  130  of  FIG.  1   , but the vortex-sensing diffraction grating  521  differs from the vortex-sensing diffraction grating  120 . As shown in  FIG.  5   , the vortex-sensing diffraction grating  521  diffracts the vortex beam so the photodetector  511  at the diffractive order −4 detects the topological charge +5. Similarly, the remaining vortex-sensing diffraction grating  523  diffracts the vortex beam so the photodetector  513  at the diffractive order +4 detects the topological charge −5. 
     A parameter n scales the vortex-sensing diffraction gratings  521  and  523  relative to the vortex-sensing diffraction grating  522 . Recall each vortex-sensing diffraction grating combines a vortex phase pattern and a linear phase pattern in a product that multiplies the vortex phase pattern and the linear phase pattern. To scale both the vortex phase pattern and the linear phase pattern in coordination, the product is the vortex phase pattern of exp(inLφ) times the linear phase pattern of exp(iγnX), where i is an imaginary number basis, n is the scaling factor, nL is a topological charge of the vortex phase pattern, φ is a polar angle coordinate of the vortex phase pattern, γn is a period of the linear phase pattern, and X is a Cartesian coordinate of the linear phase pattern. Benefits of coordinated scaling with scaling faction n include having the same pitch between the photodetectors in each of arrays  531 ,  532 , and  533 . Each of the vortex-sensing diffraction gratings  521 ,  522 , and  523  has a binary phase pattern with a phase delay of zero when the product is below a threshold and π radians when the product is above the threshold. 
     An equation relating the scaling factor with the diffraction orders and the topological charge detected at that diffraction order is: 
         j= 2* n*L+m −1
 
     where j a particular diffraction order, n is the scaling factor, L is an unscaled topological charge of the vortex phase pattern, and m is a particular topological charge detected at the diffraction order j. Because the middle vortex-sensing diffraction grating 522 has n=1 and L=0.5, the above equation simplifies to j=m and this indicates the diffraction orders and detected topological charges are identically numbered as shown at the array  532  of photodetectors. 
     As shown in  FIG.  5   , the vortex-sensing diffraction grating  521  diffracts the vortex beam so the photodetector  511  at diffractive order j=−4 detects the topological charge m=+5. Solving for scaling factor n in the above equation yields n=−8. Thus, the scaled topological charge nL of the vortex phase pattern of the vortex-sensing diffraction grating  521  is nL=−4. Similarly, the vortex-sensing diffraction grating  523  diffracts the vortex beam so the photodetector  513  at diffractive order j=+4 detects the topological charge m=−5, yielding a scaling factor n=10 and a scaled topological charge nL=5 for the vortex-sensing diffraction grating  523 . 
     Thus, when the set of available topological charges is fixed at J=2M+1 utilized topological charges, where M is the maximum absolute value of the allowed topological charges, then a number of the photodetectors in the array is J photodetectors, including a respective one of the J photodetectors for detecting each of the J utilized topological charges. When the number of available topological charges is variable, the number of photodetectors required equals the maximum value of the variable number of available topological charges. In one example, when the utilized topological charges range from −13 to M=13 shown in  FIG.  5   , there are fixed J=27 utilized topological charges and J=27 photodetectors. Given a number of the vortex-sensing diffraction gratings is N vortex-sensing diffraction gratings, then the array of photodetectors includes K photodetectors for each of the N vortex-sensing diffraction gratings, with these NK total photodetectors each detecting presence or absence of a respective one of the J=NK utilized topological charges. For example, when the number of the vortex-sensing diffraction gratings is N=3 as shown in  FIG.  5   , there are K=9 photodetectors for each vortex-sensing diffraction grating. 
     It will be appreciated that  FIG.  5    is extended in another embodiment to include more vortex-sensing diffraction gratings and more photodetectors, and thereby utilize and detect more available topological charges. For example, the a vortex-sensing diffraction grating with corresponding photodetectors could be added above and below the vortex-sensing diffraction gratings  521 ,  522 , and  523  and the arrays  531 ,  532 , and  533  of photodetectors, thereby increasing the utilized topological charges to J=45 utilized topological charges. Appropriate beam spitting is also needed and could include a balanced binary tree of half-silvered mirrors. 
     A modified embodiment compensates for the weakness of the wider diffractive orders from each vortex-sensing diffraction grating. Referring to  FIG.  5   , array  532  is expanded to include photodetector  550 . Thus, topological charge +5 is detected by both photodetector  550  and photodetector  511 . Further extension includes photodetector  551 . Not shown is extension of array  531  toward array  532  and extensions between arrays  532  and  533 . The double detection compensates for the weakness of the wider diffractive orders. With careful alignment of system  500 , such double detection does not require additional photodetectors when the electromagnetic energy of the +5 diffraction order from vortex-sensing diffraction grating  522  overlaps at photodetector  511  with the electromagnetic energy from the −4 diffraction order from vortex-sensing diffraction grating  521 . 
     The unique combinations possible in each time interval is C=J!/[S!(J−S)!] unique combinations possible throughout the time interval, where the set of available topological charges is fixed at J utilized topological charges and the respective number of the selected topological charges in each time interval is fixed at S distinct topological charges selected from the J utilized topological charges. Thus, the vortex beam conveys a symbol for each time interval and the symbol contains and concurrently conveys log 2  C binary bits of information. For example, when the J utilized topological charges are twenty-seven utilized topological charges as shown in  FIG.  5    and the S distinct topological charges in each time interval are five distinct topological charges (not shown) selected from the twenty-seven utilized topological charges, then the unique combinations possible in each time interval are C=80,730 unique combinations and the vortex beam concurrently conveys more than sixteen binary bits of information in each time interval. 
     From the above description of Electromagnetic Communication with a Vortex Beam Concurrently Conveying Multiple Topological Charges, it is manifest that various techniques may be used for implementing the concepts of systems  100  and  500  without departing from the scope of the claims. The described embodiments are to be considered in all respects as illustrative and not restrictive. The systems disclosed herein may be practiced in the absence of any element that is not specifically claimed and/or disclosed herein. It should also be understood that system  100  or  500  is not limited to the particular embodiments described herein, but is capable of many embodiments without departing from the scope of the claims.