Abstract:
Photonic signals are tagged with a pre-selected modification, such as a polarization signature to carry data across an obstructed path between sender and receiver. Communication authentication through polarization variation allows for Yuen-Kumar or entangled photon quantum communication protocols to propagate through environmental scattering media such as air, smoke, fog, rain, and water. While ultraviolet light photons are well suited as a carrier for quantum communication signals scattered in air, it is appreciated that visible wavelengths have longer propagation paths in water to convey non-line-of-sight data. A secure signal is scattered by the media and simultaneously communicated to a single recipient or multiple recipients exposed to scattered signal portions. A process of solving the scattering processes through a random scattering media is provided to reconstruct a quantum keyed message at a receiver. The scattering of the signal is utilized herein to provide non-line-of-sight and intentional short-range communication.

Description:
RELATED APPLICATION 
       [0001]    This application claims priority of U.S. Provisional Patent Application Ser. No. 60/663,143 filed Mar. 18, 2005, which is incorporated herein by reference. 
     
    
     GOVERNMENT INTEREST 
       [0002]    The invention described herein may be manufactured, used, and licensed by or for the United States Government. 
     
    
     FIELD OF THE INVENTION 
       [0003]    This invention relates in general to methods and apparatus for non-line-of-sight quantum communication and in particular to a short-range, secure optical communication scheme using the properties of solar blind photon propagation in the scattering media. 
       BACKGROUND OF THE INVENTION 
       [0004]    Currently, short-range communication of up to one kilometer is largely dependent on infrastructure-intensive cellular networks, direct radio frequency or optical signaling. However, in regions lacking such infrastructure and points of communication are separated by obstructions, these traditional methods of communication are inadequate. Additionally, traditional optical and radio frequency communication are prone to interference associated with conditions such as environmental scatter and other signals. In situations where confidential information is to be communicated, existing methods of information transmission rely on data encryption since the transmitted signals are subject to eavesdropping. These problems have previously been so intractable in the area of secure communication that business, governmental, and military units often resort to couriers for the short-range transport of such messages. The use of a courier is an incomplete solution that is cumbersome and slow, especially when a geographic or manmade obstacle is involved. 
         [0005]    In an effort to address these limitations, others have looked to optical communication. There have been reports of U.S. Navy research on intentionally short-range optical communications [5]. Many solar-blind UV systems were reported on, including an ultraviolet (UV) laser system that showed 500 m non-line-of-sight (NLOS) digital data transmission in field tests. Unfortunately, the reported transmissions were not of a secure nature. 
         [0006]    Thus, there exists a need for a short range, secure communication that is not dependent on line-of-sight. An additional need exists for a communication system that is tolerant of environmental scattering as the signal propagates there through. 
       SUMMARY OF THE INVENTION 
       [0007]    Photonic signals are tagged with a pre-selected modification, such as a polarization signature to carry data across an obstructed path between sender and receiver. Communication authentication through polarization variation allows for Yuen-Kumar or entangled photon quantum communication protocols to propagate through environmental scattering media such as air, smoke, fog, rain, and water. While ultraviolet light photons are well suited as a carrier for quantum communication signals scattered in air, it is appreciated that visible wavelengths have longer propagation paths in water to convey non-line-of-sight data. A secure signal is scattered by the media and simultaneously communicated to a single recipient or multiple recipients exposed to scattered signal portions. A process of solving the scattering processes through a random scattering media is provided to reconstruct a quantum encoded message at a receiver. The scattering of the signal is utilized herein to provide non-line-of-sight and intentional short-range communication. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]      FIG. 1  is a prior art scheme depicting a key encryption technique based on coherent state qumodes; 
           [0009]      FIG. 2  is a schematic of an inventive non-line-of-sight quantum communication scheme operating with a Yuen-Kumar protocol, multiple receivers are depicted to illustrate the multi-cast aspect of the present invention; and 
           [0010]      FIG. 3  is a schematic of an inventive non-line-of-sight quantum communication scheme operating with an entangled photon protocol. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0011]    The present invention has utility as a secure short range quantum communication scheme that is operative independent of a direct line of sight between a sender and receiver. The scatter caused by the environment to a light beam is the basis of non-line-of-sight communication. The manipulation of photons as a carrier for quantum communication data is provided by a polarization signature as the basis for the inventive non-line of sight secure, short range communication. The present invention has applications for communication within mobile small networks that optionally have a need for simultaneous multicasting to multiple recipients. 
         [0012]    As used herein “short-range” communication is defined as the ability to send a signal between a sender and receiver separated by up to several kilometers, within an outside range of ten kilometers. 
         [0013]    It is appreciated that ultraviolet (UV) radiation is well suited for non-line-of-sight quantum communication in air; specific wavelengths will have different scattering characteristics under a given set of environmental conditions illustratively including humidity, particulate and turbulence. In a preferred embodiment, a UV light source, such as UV laser is provided with multiple laser lines is used with the ability to change carrier wave wavelength to achieve a desired range of signal propagation through the scattering medium. The present invention is also operative with water as the scattering media with the recognition that longer wavelengths of visible blue-green light have greater propagation distances in water relative to ultraviolet wavelengths. As such, a water based intentionally short-range non-line-of-sight quantum communication system uses a blue-green carrier wavelength of between 440 and 560 nanometers for maximal range. It is appreciated that the present invention is also operative in transmission through solid substance such as ice, soil, and rock with resort to a propagation wavelength that is scattered by the solid media, yet transmissive through the volume of solid to be traverse by the message. Communication through a solid typically involves infrared and longer wavelengths of more than 800 nanometers. 
         [0014]    Radiation is subject to absorption and scattering in media. The media is characterized by absorption and scattering parameters. A light ray scattering can be characterized by Mueller matrices which also handle partial absorption. On the other, hand scattering of discrete photons results in absorption, or a form of scattering depending on the state of the photon and atoms. 
         [0015]    To understand light propagation through a random medium, resort is made to Maxwell&#39;s equation. Environmental media such as air, water, smoke and fog are well approximated as random media. Maxwell&#39;s equations can be put in the following form typically suitable for scattering considerations [1]. 
         [0000]    
       
         
           
             
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         [0016]    For scattering purposes the version of the equations that are uses assume no sources and currents. The material properties are provided by the relations 
         [0000]        D ( r,t )=ε( r ) E ( r,t ) 
         [0000]        B ( r,t )=μ( r ) H ( r,t ) 
         [0000]    where ε(r) and μ(r) are in the form of scalars for isotropic media and otherwise are in the form of tensors. Substituting the isotopic media scalar forms of these equations into Maxwell&#39;s Equations yields 
         [0000]    
       
         
           
             
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         [0000]    These equations can be combined to obtain 
         [0000]    
       
         
           
             
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         [0000]    If time harmonic solutions are assumed as 
         [0000]        E ( r,t )=exp(− iwt ) E ( r,t ) 
         [0000]    then the vector Helmholtz equation is obtained 
         [0000]    
       
         
           
             
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         [0000]    Using a vector identity produces a simpler Helmholtz equation, 
         [0000]      [∇ 2   +k   2 ( r )] E ( r )=0 
         [0000]      and 
         [0000]      [∇ 2   +k   2 ( r )] H ( r )=0 
         [0000]    where 
         [0000]    
       
         
           
             
               
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         [0000]    The equation needs to be solved subject to boundary conditions and a radiation condition [1]. Usually these equations apply scattering to single particles. However a T Matrix method can be used to average over the orientations of ensembles of particles [1]. However, other solutions are possible. The equation subject to random parameters is subjected to the Decomposition Method to model the information reconstruction as a receiver subsequent to scatter. 
         [0017]    The Decomposition Method is applied to the random Helmholtz equation 
         [0000]      [∇ 2   +k   2 ( r )] E ( r )= g ( r ) 
         [0000]    in Cartesian coordinates. Here k 2 (r) is considered to be a random variable with outcomes prescribed by a probability density function. The equation is solved as 
         [0000]        L   x   E+L   y   E+L   z   E+k   2 ( x,y,z ) E=g ( x,y,z ) 
         [0000]      where 
         [0000]      ∇ 2   =L   x   +L   y   +L   z    
         [0000]    and 
         [0000]    
       
         
           
             
               
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         [0000]    The inverse operators are defined as 
         [0000]        L   x   −1 (·)=∫ 0   x ∫ 0   x (·) dxdx    
         [0000]        L   y   −1 (·)=∫ 0   x ∫ 0   x (·) dxdx    
         [0000]        L   z   −1 (·)=∫ 0   x ∫ 0   x (·) dxdx.    
         [0000]    Now the system of equations is put into the triplicate form by shifting the operators 
         [0000]        L   x   E=−L   y   E−L   z   E−k   2 ( x,y,z ) E+g ( x,y,z ) 
         [0000]        L   y   E=−L   x   E−L   z   E−k   2 ( x,y,z ) +g ( x,y,z ) 
         [0000]        L   z   E=−L   x   E−L   y   E−k   2 ( x,y,z ) +g ( x,y,z ). 
         [0000]    Each equation is capable of a separate solution given suitable boundary conditions. However in this form it is possible to average the solutions at each step and obtain a different approximation or convergence rate. 
         [0018]    Operating on the first equation yields 
         [0000]        L   x   −1   L   x   E=−L   x   −1   L   y   E−L   x   −1   L   z   E−L   x   −1   k   2 ( x,y,z ) E+L   x   −1   g ( x,y,z ) 
         [0000]    The result is 
         [0000]        E ( x,y,z )= E (0, y,z )+ xE   x (0, y,z )− L   x   −1   L   y   E−L   x   −1   L   z   E−L   x   −1   k   2 ( x,y,z ) E+L   x   −1   g ( x,y,z ) 
         [0000]        E ( x,y,z )= E ( x, 0, z )+ yE   y ( x, 0, z )− L   y   −1   L   y   E−L   y   −1   L   z   E−L   y   −1   k   2 ( x,y,z ) E+L   y   −1   g ( x,y,z ) 
         [0000]        E ( x,y,z )= E ( x,y, 0)+ zE   z ( x,y, 0)− L   z   −1   L   y   E−L   z   −1   L   z   E−L   z   −1   k   2 ( x,y,z ) E+L   z   −1   g ( x,y,z ) 
         [0000]    The terms E are expanded in a series 
         [0000]    
       
         
           
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         [0000]    The zeroth terms are 
         [0000]        E   0 ( x,y,z )= E (0, y,z )+ xE   x (0, y,z )+ L   x   −1   g ( x,y,z ) 
         [0000]        E   0 ( x,y,z )= E ( x, 0, z )+ yE   y ( x, 0, z )+ L   y   −1   g ( x,y,z ) 
         [0000]        E   0 ( x,y,z )= E ( x,y, 0)+ zE   z ( x,y, 0)+ L   z   −1   g ( x,y,z ) 
         [0000]    At the next step the partial solutions are averaged or integrated separately to find E 1 (x,y,z). 
         [0019]    A recursion yields 
         [0000]    
       
         
           
             
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         [0020]    Resulting from the scattered collection of photons is a beam that spreads because of scattering in turbid media, which is analogous to a diffusion or Markov process [6]. The dispersion in the atmosphere depends on the wavelength [7]. While many of the photons of the beam change polarization, some of the photons do not have polarization changes, and some have only small polarization changes. Over small distances the polarization of most photons does not change very much, although some photons will have significant changes in polarization. Experimental results on beam breakdown caused by aerosols at 266 nm have also been presented [8]. These types of data can be compared against longer wavelength energy loss. Atmospheric propagation losses at the longer wavelength of 523 nm are known [9]. 
         [0021]    In the atmosphere, ozone and oxygen are the major absorbers [10, 11]. Radiation is scattered by molecules, according to the Rayleigh scattering process [12], and by aerosols, according to general Mie scattering principles [13]. In the case of the atmosphere or any fluid, the density and corresponding index of refraction time-space variability create beam spreading called optical turbulence [14, 15]. In the atmosphere there is far more scattering for UV than for visible light. 
         [0022]    Because atmospheric density decreases quickly with height, in the ideal atmosphere there is less turbulence-induced scattering for UV vertical beams than for horizontal beams. In non-storm conditions the turbulence near the ground tends to have more thermal, moisture, and terrain forcing. The atmosphere has temperature and density inversions as a function of height. These inversions create channeling; ducting, and reflecting of signals due to density patterns. The inversions often signal pollution layers. These concentrations have their own scattering and absorption properties [16-18]. In addition meteorological clouds may be present. These clouds provide extra scattering properties. The density of the atmosphere decreases rapidly with height, and under ideal conditions UV for light detection and ranging (lidar) can propagate many kilometers in the vertical [19]. Results of a UV 351 nm guidestar system working out to 20 km from the ground have been documented [20]. Stand-off remote Raman lidar using 266 nm light for ranges up to 60 m [21] have been documented. A study predicts the character of 200 m pulse propagation for 220-440 nm laser pulses [22]. 
         [0023]    Non-Poisson quantum fluctuations in an invariance regime can propagate farther than coherent laser speckle. In such situations the non-Poissonian statistics survive over long distances [23]. Lodhal shows that the spatial correlations of quantum light have “infinite” range and remain intact after moving through random media. The non-Poisson aspects of a quantum system in having a long linear extent relative to classical beam coherence is invoked in the present invention to for authentication and increased transmission range beyond the extent of laser speckle or other coherence associated with the light source. 
         [0024]    A variation of the polarization amplitude or timing allows Yuen-Kumar [3] quantum communication (QC) as an authentication of the signal. QC in the presence of scattering has implications in quantum microdevices, such as quantum dots used for quantum computing and QC as well as in the macro environment. 
         [0025]    Free-space UV QC is more stealthy than many other forms of visible light optical communication. If the UV is in the solar blind region then there are far fewer competing external noise photons from the sun. The source beam is absorbed by the atmosphere after a propagation distance and will thus be shielded from long-distance surveillance. Also, because of the small natural background of UV solar blind noise photons, a smaller source strength can be used and hence lower power. The quantum encoding presents secure encryption capability. 
         [0026]    Tagging a photon modeled by scatter from a random media with a polarization or an entanglement with another photon signature provides a method of communicating information by way of a scattered photon. 
         [0027]    A quantum key encryption technique according to the present invention preferably invokes Yuen-Kumar coherent states of different amplitudes that are linearly independent and span infinite dimensional space denoted as qumodes. In a single-mode realization, M possible coherent states |α t            are represented by 
         [0000]    
       
         
           
             
               
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         [0000]    where α 0   2  is the observable probability as to the occurrence of the state and the angle between two neighboring states is 2π/M [2]. In a two-mode realization, for example, the prior art Yuen-Kumar free-space scheme is presented in  FIG. 1 , where the states are a product of two different coherent states as defined by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
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         [0028]    The qumodes are optionally associated with polarization, time, or frequency. As depicted in prior art  FIG. 1  (Left), M points uniformly distributed on a fixed great circle on the Poincaré sphere are used for M/2 possible bases. The opposite points on a diameter correspond to two orthogonal states of a basis, representing the 0 and 1 bit value for that basis. The two neighbors of each point on the circle are taken to represent a different bit value. A secret key is used to select a specific basis for each qumode between users A and B, as well as a polarity bit that is added to the data bit for randomizing the polarity of the basis. A long running key K′ for such selection is obtained as the output from a standard encryption mechanism operating on a basic shorter key K, as depicted in  FIG. 1  (Right). For each data bit, a total of 1+log 2 (M/2) bits from K′ is used to determine the polarity bit and the selection of M/2 possible bases. Yuen [3, 4] has shown that, granting an eavesdropper E a perfect copy of the ciphered bit but without knowing the secret key, the probability of error is P e ˜½, when M&gt;&gt;α 0 , while P e ˜e −α     0       2    for B, since the secret key is known to B. Thus even with perfect eavesdropping, that is, getting a perfect copy of the ciphered bit, E&#39;s probability of making correct decisions is the same as pure guessing. 
         [0000]    In application a secret key is used to synchronize the qumode variable. Preferably, the qumode variable is polarization of a light source even though, through the use of a frequency modulating crystal or a chopper, frequency or pulse time qumode variables, respective are used. It is appreciated in the case of polarization that a large number of polarization keys are available as defined by the Poincaré sphere. A light source as used herein is appreciated to include both coherent sources and non-Poisson statistical sources. A light source is considered a coherent (or Poisson) light source when it satisfies at least criterion of: constant intensity, intensity fluctuation but only a small fraction of the output is used to transmit data, intensity fluctuations are rapid (temporal incoherence), perfect monochromaticity (spatially and temporally coherent), and quantum mechanically coherent state. A light source is considered an incoherent (or non-Poisson) light source when it satisfies at least criterion of: slow intensity fluctuations, is quasi-thermal, or the light produced is from an ensemble of light source elements. 
         [0029]    A properly functioning laser operating as a Poissonian light source is appreciated to be a convenient, high flux source of photons is preferred for the practice of the present invention. However, as detailed above, non-Poissonian sources do afford advantages over Poissonian sources in terms of longer transmission distances and signal authenitication. 
         [0030]    A communication system according to the present invention is shown in  FIG. 2  and uses an ultraviolet laser as a light source  12  in an air medium as a photonic source. A polarizer  14  receives a light source output  13  and is set to a preselected modifcation key value relative to a receiver shown generally at  20 . It is appreciated that the effective communication range is decreased by insertion of a filter into the optical intermediate between the light source  12  and a receiver  20 . An optical amplitude or phase modulator  16  receives the polarized quantum communication photonic signal  18  and creates an arbitrarily modulated quantum communication photonic signal  22  that proceeds to scatter through a light scattering medium denoted A. Exemplary polarization phase modulators illustratively include liquid crystals, Kerr cells, and Pockel cells. Preferably, a series of two liquid crystal devices and a quarter wave plate are used to achieve arbitrary polarization. A scattered portion  23  of the arbitrarily modulated quantum communication photonic signal  22  has scattered around an obstacle denoted at B. It is appreciated that the scatter that affords the non-line-of-sight capability of the present invention also limits the distance at which the arbitrarily modulated quantum communication photonic signal  22  is detectable. 
         [0031]    A receiver  20  includes an optical phase or amplitude modulator  24  of the same type as that in place in the transmitter modulator  14 , with the modulator  24  configured as a demodulator. A polarizer  26  is set to the same Poincaré sphere setting as polarizer  16  and represents the shared key. The resulting signal  28  then contacts a polarization beam splitter  32 . Preferably beam splitter  32  is a 50/50 splitter. The orthogonal signals  34  and  34 ′ are incident on photon detectors  36  and  36 ′ that count incident photon receipt and report a counting event to temporal coincidence electronics  40  as a series of zeroes and ones. Photon detectors operative herein illustratively include single photon counting modules and conventional photon-intensity detectors such as charge coupled devices and gated photon counters. Optionally, lenses  42  are interposed within the receiver  20  to collimate optical signals to subsequent components. It is appreciated that beam on additional splitters or filters along an optical path further facilitates signal attenuation in the event of a signal of excessive intensity. A second receiver  20 ′ is also depicted in  FIG. 2  with like components relative to receiver  20  and modulator  24 ′ and polarizer  26 ′ to illustrate the multi-cast nature of the present invention. 
         [0032]    It is appreciated that short range, non-line-of-sight quantum communication is also performed with a dual photon entangled pair carrier. As shown in  FIG. 3 , where like numerals correspond to those detailed with respect to  FIG. 2 , a Type-I nonlinear crystal  60  receives an optical output  13  from light source  12 . The crystal  60  generates entangled photon pairs with near collinearity  61 . The entangled photon pairs with near collinearity  61  is scattered by medium A to generate a scattered signal  63  that scatters around an obstacle B and to a receiver, shown collectively at  80 . Preferably, the crystal  60  is tuned for non-degenerative down conversion with regard to dichroic mirrors  62  and  62 ′. Narrow band filters  64  and  64 ′ are used to provide shared quantum keys after optical signals are transmitted through optional lenses  42  to photon detectors  36 ,  36 ′,  37  and  37 ′ before a signal is fed to electronics  40 . Although the stochastic-energy-based entanglement technique is not theoretically resistant to eavesdropping on shared quantum keys, because of the possibility of cloning, in practice it is difficult to eavesdrop on because of timing constraints. This method can be used as a research model system and can be used to generate shared random keys in an environment where eavesdropping is not a threat. Optionally, the insertion of Poincaré sphere aligned polarizers  16  and  26  afford a secure communication system. 
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       [0000]    
       
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         [0056]    Patent documents and publications mentioned in the specification are indicative of the levels of those skilled in the art to which the invention pertains. These documents and publications are incorporated herein by reference to the same extent as if each individual document or publication was specifically and individually incorporated herein by reference. 
         [0057]    The foregoing description is illustrative of particular embodiments of the invention, but is not meant to be a limitation upon the practice thereof. The following claims, including all equivalents thereof, are intended to define the scope of the invention.