Free-space optical communications using holographic conjugation

A beacon beam is transmitted from a receiver to a transmitter. The transmitter generates and transmits a conjugate beacon beam back to the receiver, where it is interfered with a local oscillator beam to form a hologram. The hologram is used to configure a spatial light modulator as a diffraction grating. A conjugate communications laser beam containing information is subsequently transmitted to the receiver. The diffraction grating deflects the conjugate communications beam to a fixed and known direction, whereupon it is directed through a spatial filter.Since the direction of the conjugate communications beam is fixed and known, the diameter of the filter aperture can be minimized to accept the communications beam while rejecting almost all of the background light. A high-speed detector directly detects the filtered conjugate communications beam. The detector output is transmitted to a demodulator that extracts the information carried by the communications beam.

FIELD OF THE INVENTION

The present invention relates to adaptive optics and, more particularly, to reducing receiver noise in free-space laser communications by using holographic conjugation.

BACKGROUND OF THE INVENTION

Lasers comprise a preferred means of communication through free-space because they can transmit substantially more information over long distances in comparison to radio waves or microwaves, due to their much higher frequency and therefore significantly smaller beam divergence and greater bandwidth. However, laser communications traversing earth's atmosphere are degraded by ubiquitous turbulence. Lasers are affected more than lower frequency electromagnetic waves because atmospheric turbulence causes rapid changes in the density, and thus the index of refraction, across the path of the laser beam.

Due to the heterogeneous nature of turbulence, the rays composing the beam will encounter differing densities. This will cause their respective path lengths to the receiver to become unequal, resulting in differing phases and thus a distorted wavefront at the receiver. Furthermore, the received laser beam will no longer have the uniform amplitude that it had when emitted. The turbulence-induced distortion also increases the divergence of the beam, which reduces the signal-to-noise ratio (“SNR”) because it increases the portion of the laser beam that will fall outside of the receiver aperture.

Under operating conditions where the receiver noise is dominated by background light, the SNR is given by S2/n, where S and n are the number of photoelectrons per bit due to the signal and background, respectively. Background light, especially solar, represents a significant source of communications receiver noise. Reducing the receiver field-of-view lowers the background light, but it increases the difficulty of closing the communications link between the receiver and the transmitter, especially when the two are separated by a long distance or are translating relative to one another. One approach is to use a mechanical servo system to vary the direction of the receiver's field-of-view. However, such servo systems are expensive, bulky, heavy and mechanically complex. While certainly a consideration for even a terrestrial receiver, the size and weight become particularly critical when the receiver is to be placed in earth orbit or airborne.

Receiver noise sources other than background light, in particular detector thermal (Johnson) noise, further decrease the SNR of optical communications receivers. Heterodyne detection can overcome the noise introduced by receiver noise as well as background light, and provide quantum-limited detection, but its use in free-space communications has been rendered impossible or impractical due to pointing jitter and wavefront distortions of the received communications beam.

As encryption has become an increasingly important aspect of communications, the additional demands it places on laser communications have been brought to the forefront. Quantum encryption, which provides the ultimate encryption technique, requires distribution of a quantum key (“QKD”). QKD requires the receiver to detect and differentiate between individual photons. This, in turn, makes it necessary to eliminate or at least mitigate the adverse effects of atmospheric refraction and background light, while at the same time maximizing the field-of-view of the receiver to facilitate closure of the communications link.

One solution to the problem of atmospheric turbulence is described in U.S. Pat. No. 5,378,888, “Holographic System for Interactive Target Acquisition and Tracking,” issued to the present inventor. The foregoing reference uses real-time holography to generate a phase-conjugate laser beam that, after twice traversing the intervening turbulence, impinges the receiver aperture having the lateral cross section, the phase across its wavefront, and the angle of incidence that it would have had in the absence of turbulence. However, neither this reference nor any other prior art resolves the technical difficulties attendant to optical communications posed by receiver background light, detector noise, atmospheric turbulence, and the relative translation between the receiver and a transmitter; as well as provides the capability to detect and differentiate single photons for QKD under the foregoing conditions. The present invention fulfills these needs in the art.

SUMMARY OF THE INVENTION

Briefly, a spatial light modulator in a receiver is configured with a quadratic phase pattern corresponding to a diverging lens so that, when a laser beam is applied, a diverging beacon beam is transmitted from the receiver in the direction of the transmitter. Although the location of the transmitter may not be precisely known, the divergence is sufficient to ensure intersection of the beacon beam with an optical aperture on the transmitter. The atmosphere in between the receiver and the transmitter typically distorts the beacon beam. Holographic apparatus on the transmitter determines the distortion of the received beacon beam and uses this information to configure a spatial light modulator. A laser beacon beam is applied to the configured spatial light modulator to generate a phase-conjugated or field-conjugated beacon beam that travels along the same path, in the opposite direction, as the diverging beacon beam.

The conjugate beacon beam intersects an optical aperture on the receiver and is subsequently interfered with a local oscillator beam to form a hologram. The hologram is used to configure a spatial light modulator as a diffraction grating. A communications laser beam containing information is subsequently applied to the previously configured spatial light modulator on the transmitter to form a conjugate communications beam that is transmitted to the receiver along the same path as the conjugate beacon beam. The conjugate communications beam is deflected by the diffraction grating written on the receiver spatial light modulator to a fixed and known direction, whereupon it is passed through a spatial filter comprised of a lens and an optical aperture.

Since the direction of the conjugate communications beam is fixed and known, the diameter of the aperture can be minimized to accept the communications beam while rejecting almost all of the background light. A high-speed detector then detects the filtered conjugate communications beam. The output of the high-speed detector is transmitted to a demodulator that extracts the information carried by the communications beam.

In an alternative embodiment, the conjugate communications beam is composed of single photons for QKD, in which case a single-photon detector is used for detection of the spatially filtered photons. Another alternative uses a heterodyne detection apparatus in conjunction with the fixed, known direction of the conjugate communications beam.

In a further alternative embodiment, a random phase pattern is initially written on the spatial light modulator of the receiver. As a result, the returning conjugate beacon beam impinges the entire receiver aperture, in comparison to impinging only a portion of the receiver aperture when a quadratic phase pattern is used. The resultant hologram has a noisy, irregular grating pattern, but one of enhanced accuracy with respect to the direction of the incident beacon beam because the beam fills the entire aperture. Additional processing is required to extract the periodicity and orientation of the grating pattern from the hologram, and obtain the approximate direction of the transmitter.

The spatial light modulator of the receiver is then written with a numerically-generated pattern derived from the hologram and a superimposed quadratic pattern so that it emits a secondary beacon beam having a divergence angle less than that of the first beacon beam. The divergence angle can be decreased because the centerline of secondary beacon beam will pass closer to the transmitter than that of the first beacon beam. A secondary conjugate beam returned from the transmitter is used to write a diffraction grating on the spatial light modulator of the receiver.

A communications beam is then applied to the spatial light modulator of the transmitter using a secondary conjugate pattern written thereon. The resultant conjugate communications beam is transmitted to the receiver and the information carried therein is extracted as previously discussed in conjunction with the first embodiment. The additional, secondary steps of the foregoing alternative embodiment are typically used only for the initial closure of the communications link between the receiver and the transmitter.

DETAILED DESCRIPTION OF THE INVENTION

Turning to the drawings,FIGS. 1A,1B and1C present the sequence of steps used by the present invention to establish optical communication between receiver11and transmitter13.FIG. 2is a schematic drawing showing the elements comprising receiver11and transmitter13. Receiver11includes optical aperture14, beacon laser15, beamsplitter16, mirrors17and18, spatial light modulator (“SLM”)19, beamsplitter21, local oscillator (“LO”)23, integrating detector array (“IDA”)25, processor26, field-imaging telescope27, spatial filter31, high-speed detector33, and demodulator34. Beacon laser15emits pulsed beacon laser beam35, which is reflected off of beamsplitter16and mirror17, and onto SLM19.

Beam35is near diffraction-limited, i. e., it has nearly uniform phase across its wavefront. SLM19is configured with a quadratic phase pattern causing SLM19to act as a diverging optic with respect to beam35. The application of beam35to SLM19generates diverging beacon laser beam39, having a spherical wavefront and a conical axial cross section. SLM19is cleared of the foregoing phase pattern immediately after the transmission of beacon beam39.

Since the location of transmitter13relative to receiver11is usually not precisely known, and to simplify beacon beam pointing, SLM19provides beam39with sufficient divergence to ensure that a portion of beam39intersects transmitter13.FIG. 1Aschematically shows the interception of transmitter13by diverging beacon beam39. Beam39is typically distorted by turbulence as it passes through atmosphere41in traveling from receiver11to transmitter13.

Transmitter13includes optical aperture42, beamsplitter43, LO45, IDA47, SLM49, communications laser50, beacon laser51, beamsplitter52, mirrors53and54, and processor55. LO45emits near diffraction-limited LO beam56. A portion of distorted beacon beam39is reflected off of beamsplitter43and interfered with LO beam56to form a hologram on IDA47. The hologram is processed by processor55using methodology well known to knowledgeable practitioners of adaptive optics, to derive a conjugate wavefront pattern. SLM49is configured with the foregoing conjugate wavefront pattern.

As shown inFIG. 3, pulsed beacon laser beam57is emitted by beacon laser51and, after reflecting off of beamsplitter52and mirror53, is applied to SLM49, resulting in the emission of conjugate beacon beam59from transmitter13towards receiver11. As also shown inFIG. 1B, conjugate beacon beam59retraces the path of beacon beam39due to its phase conjugate property, and subsequently intersects receiver11. Since beacon beam59has a conjugate wavefront derived from distorted beacon beam39, and as it again passes through distorting atmosphere41along the same path and in the opposite direction as beacon beam39, the wavefront of conjugate beacon beam59is near diffraction-limited upon impinging aperture14.

Field-imaging telescope27includes two lenses separated by the sum of their respective focal lengths. As schematically shown inFIG. 4, beacon beam59passes through aperture14and enters telescope27at angle of incidence α with respect to telescope optical axis28, which lies colinear with the optical axis for aperture14. Telescope27increases the angle of incidence of beacon beam59on IDA25by the factor M, i.e., to Mα, where M is the ratio of the respective focal lengths of its two lenses, and is at least one. Concomitantly, telescope27reduces the diameter of beacon beam59by a factor of M.

After being modified by telescope27, a portion of impinging beacon beam59is reflected off of beamsplitter21and onto IDA25. LO23emits near diffraction-limited LO beam61and it is directed onto IDA25, where it interferes with beacon beam59. The resulting hologram consists of a simple grating-like pattern with a fringe orientation and a period that are both a function of the magnified angle of incidence, Mα, of conjugate beacon beam59on IDA25. The angle between beacon beam59and LO beam61is also Mα. The hologram is transferred to processor26. The resulting processed hologram is written on SLM19, which thereby forms a diffraction grating.

As shown inFIG. 5, communications laser50then emits communications laser beam65carrying information to be transmitted from transmitter13to receiver11. After reflecting off of mirrors54and53, beam65is applied to SLM49while SLM49is still configured with the conjugate phase pattern previously written thereon and applied to beacon beam59. As also shown inFIG. 1C, this results in the transmission of conjugate communications beam67from transmitter13along the same path through distorting atmosphere41as previously traveled by conjugate beacon beam59.

Conjugate communications beam67has a near diffraction-limited wavefront upon impinging aperture14and telescope27at an angle of incidence α. As shown inFIG. 6, beam67is emitted from telescope27at an angle of Mα with respect to optical axis28and LO beam61. As shown inFIG. 4, the diffraction grating written on SLM19was derived from interfering beacon beam59and LO beam61, with the angle Mα between them. Therefore, the diffraction grating of SLM19will deflect an incident beam the same angle Mα from its original, incident course. For communications beam67incident on SLM19at the angle Mα with respect to the known, fixed direction of LO beam61, the diffraction grating of SLM19will deflect communications beam67from its original, incident course by the angle Mα. Plane geometry indicates that the deflected communications beam67will lie parallel to LO beam61. In summary, regardless of the angle of incidence, α, of communications beam67onto aperture14, the diffraction grating written on SLM19will deflect communications beam67to a fixed, known direction, i.e., parallel to fixed LO beam61.

The period of the interference fringes of the hologram formed on IDA25is equal toλα*M(1)
where λ is the wavelength of conjugate beacon beam59.

Thus, the period of the interference fringes decreases as α increases. A periodicity that is too small for the spatial sampling rate of IDA25will adversely affect the accuracy of the reconstructed hologram written on SLM19and ultimately result in communications beam67not being deflected precisely parallel to LO beam61.

Spatial filter31includes lens69and optical aperture71, with aperture71being located in the focal plane of lens69. Aperture71is sized according to the quality of communications beam67, and is aligned with the predicted course of communications beam67after it has been deflected by the grating of SLM19. Thus, an inaccurate or imprecise grating will cause communications beam67to wander from a course parallel to LO beam61and cause a part of communications beam67to fall outside of and be rejected by aperture71. This will lower the SNR. To avoid the foregoing outcome, and in accordance with the Nyquist criteria, the hologram must be sampled by IDA25at the rate of at least two samples per cycle.

The receiver field-of-view at aperture14within which transmitter13can be acquired is proportional to the number of pixels on IDA25. This relationship is expressed as follows:FOV=N*λD(2)
where: FOV is the two-dimensional field-of-view at aperture14;

N is the number of pixels in each row and column of IDA25(assuming an equal number of rows and columns, i.e., IDA25is a square);

D is the diameter of aperture14; and

λ is the wavelength of the beam being emitted, i.e., beacon beam39. (The respective wavelengths of all of the beams referred to herein are identical and equal to λ).

For a prior art communication apparatus having a receiver aperture diameter and a field-of-view equal to those of the present in invention, and where the wavelength of the laser beams used therein is identical to λ of the present invention:
FOVp=FOV  (3)
and;np~FOV⁢2=(N*λD)2(4)
where;

FOVpis the field-of-view for a receiver aperture of the prior art; and

npis the background light impinging the detector of the prior art.

FOV and its equivalent are squared in equation (4) because FOV is defined as a two-dimensional angle, whereas npis incident in three dimensions.

With the present invention, the grating of SLM19deflects communications beam67to a known and fixed direction, whereupon it passes through spatial filter31. The diameter of aperture71is sized no smaller than the diffraction limit of communications beam67:λ*fd(5)
where: d is the diameter of communications beam67incident upon lens69; and

f is the focal length of lens69.

Virtually all of communications beam67will thus pass through spatial filter31and impinge high-speed detector32.

The background rejection factor, BRF, is defined as the ratio of the background light accepted by the communications apparatus of the prior art, to the background light accepted by the present invention, and is given by the square of the ratio of the spot diameter of the background light in the focal plane of the prior art equivalent of lens69, f*FOV*D/d, to the diameter of aperture71of the present invention, λf/d. Since M=D/d, BRF may be expressed as:BRF=(f*FOV*M)2(λ*fd)2=(f*N*λd)2(λ*fd)2=N⁢2(6)
For a typical N=128, BRF=1.6*104, which indicates that the present invention obtains a reduction in the accepted background light up to 4 orders of magnitude relative to the prior art. This reduction can be advantageously used in several ways.

Assuming the same SNR for a communications device of the prior art as that for the present invention, and with the identical range between the respective transmitters and receivers:
SNRi=SNRp(8)
orSi⁢2ni=Sp⁢2np(9)
where: SNRiis the signal-to-noise ratio and Siis the required signal strength for the present invention; and

‘SNRpis the signal-to-noise ratio and Spis the required signal strength for a communications device of the prior art.
Rearranging the terms and taking the square root:Si=Sp⁡(ninp).5(10)
Since:(npni)=N2(11)
it follows thatSi=SpN(12)

Equation (12) indicates that, keeping the same SNR and maintaining the same range, the signal strength required using the present invention, Si, is reduced from the signal strength required using the prior art, Sp, by a factor of N. Thus, for N=128, Siwould be less than Spby up to 2 orders of magnitude.

Alternatively, for the same SNR and communications laser power, the decreased background light accepted by the present invention allows for an increase in the range, “R”, over the prior art. Generally,S~1R2(13)
Where Riis the maximum range provided by the present invention, and Rpis the maximum range provided by the prior art:RiRp=(SpSi).5=N.5(14)

The equation 14 shows that, for the same SNR, Riis increased over Rpby a factor of N5. For N=128 and for the same signal strength, S, the present invention will thus increase the range by up to a factor of 11.3, or approximately an order of magnitude, over the prior art.

After passing through spatial filter31, filtered communications beam67impinges high-speed detector32, which detects the intensity of communication beam67and translates the foregoing into electronic output33. Output33is conveyed to demodulator75, which extracts the information carried by communications beam67using means and methods well known to those skilled in the communication arts.

Alternatively, communications beam67is composed of a burst of single photons. This alternative is feasible because the increase in the SNR obtained by the present invention allows single photons to be detected in the midst of background light. As shown inFIG. 7, single-photon detector77(instead of high-speed detector32) detects the photons passing through spatial filter31. Output78of single-photon detector77is conveyed to photon demodulator79, which extracts the information carried by the photons composing communications beam67using means and methods well known to those skilled in the communication arts, including a decoding device for QKD. This allows quantum encryption of the information carried by communications beam67.

As the present invention provides a near diffraction-limited communications beam having a fixed and known direction, heterodyne detection may also be used in conjunction with the present invention. In such an alternative embodiment, spatial filter31is not a part of receiver11. As shown inFIG. 8, receiver11instead includes heterodyning apparatus81, including high-speed detector83, lens84, LO85and beamsplitter86.

LO beam87is emitted by LO85. Beamsplitter86transmits communications beam67and reflects LO beam87onto a course collinear with communications beam67. The combined beams pass through lens84and interfere on high-speed detector83. The interference causes detector83to generate output signal88. Demodulator89then demodulates output signal88to extract the information carried by communications beam67. Heterodyne detection eliminates both background light noise and detector noise, and thereby provides quantum-limited sensitivity having a SNR of 2S. This is typically an improvement of two to three orders of magnitude over the SNR for direct detection using a semiconductor detector.

Although the previously described embodiment of the present invention provides an improvement in the SNR over that of the prior art, error sources such as strong turbulence in atmosphere41or a high rate of transverse motion between receiver11and transmitter13, may change the path between receiver11and transmitter13at a rate that degrades the accuracy of the grating formed by SLM19. This would, in turn, cause the direction of communications beam67to wander outside of aperture71and decrease the SNR to a value lower than it would be under more sanguine operating conditions. Although the size of aperture71could be enlarged to ensure transmission of the communications beam through the aperture, this solution would also decrease the SNR because it would increase the amount of background light transmitted by the spatial filter.

Additional processing of the hologram on IDA25to enhance the accuracy of the grating formed by SLM19would avoid an adverse effect on the SNR otherwise occasioned by the aforementioned difficult operating conditions. The foregoing entails processor26using means and methods well known to those skilled in the field of adaptive optics, e.g., a Fourier transform, to extract the periodicity and orientation of the fringes. A digital, numerically generated grating pattern having the periodicity and orientation of the hologram created on IDA25by interfering conjugate beacon beam59and LO beam61, is then written on SLM19. The additional processing adds time to the processing step.

As illustrated inFIG. 9, diverging beacon beam39results from applying a quadratic phase profile to SLM19. This causes beacon beam39to have virtual focal point94behind aperture14and a spherical diverging wavefront. Only a portion of the spherical wavefront intercepts transmitter aperture42. Due to the intrinsic properties of phase conjugation, the area on aperture14illuminated by conjugated beacon beam59is only a fraction of the aperture size.

A reduction in the illuminated area of aperture14proportionally decreases the area of IDA25being illuminated and, therefore, the size of the hologram. This reduced size, in turn, adversely affects the accuracy of the grating formed by SLM19. This effect aggravates the degradation in accuracy caused by a reduction in the number of samples per period of the hologram that is concurrently occasioned by increasing the angle of incidence, α. As previously discussed, such a grating inaccuracy causes aperture71to reject a portion of communications beam67, thereby decreasing the SNR.

However, the present invention can be modified from the previously described embodiment to improve the SNR. More particularly,FIGS. 10 and 11Ashow beacon beam91being emitted upon beam35being applied to SLM19written with a spatially random pattern of 0 and π phase values. Each pixel of SLM19independently transmits a beamlet having no phase relationship with the other beamlets. Beacon beam91is composed of the foregoing beamlets, each having a spherical wavefront that diverges at the diffraction-limit, φ, according to the following expression:φ=λp*M(15)
where p=the size of each of the uniform pixels composing the face of SLM19. Since the number of pixels in each row and column of SLM19is the same as the number, N, for IDA25:p*M=DN(16)
Substituting equation (16) into equation (15):φ=N*λD(17)
or
φ=FOV  (18)

Therefore, the divergence angle, φ, for beacon beam91when the pixels of SLM19are written with random 0 and π phase values is the same as the receiver FOV at aperture14, and the same as the maximum divergence angle possible using a quadratic phase profile simulating a diverging lens. However, unlike uniform intensity across beacon beam39, the intensity across beam91randomly varies and its wavefront is not spherical.

Instead, each of the pixels of SLM19transmits a beamlet with an optical axis orthogonal to aperture14and with a far-field spherical wavefront. If the range is sufficiently large, the wavefront of beacon beam91at aperture42is nearly flat as it impinges across aperture42.

Aperture42intercepts part of each beamlet composing beacon beam91. Conjugate beacon beam93is formed responsive to beacon beam91by the components comprising transmitter13in the manner previously discussed herein.FIGS. 10 and 11Bshow conjugate beacon beam93being transmitted from transmitter13to receiver11. Each of the conjugate beamlets composing conjugate beacon beam93returns to its originating pixel on SLM19; however, since only a small fraction of beacon beam91is intercepted by aperture42, the cross section for each conjugate beamlet at aperture14is larger than the pixel size, with the exact size depending on the range. The electric field at aperture14is the sum of all the conjugate beamlets, and conjugate beam93thus impinges the entire aperture14. Consequently, the hologram created by interfering beam93and LO beam61covers the entire area of IDA25.

Since each of the beamlets composing beacon beam91has a random phase, each of the beamlets composing conjugate beacon beam93also has a random phase. When interfered with LO beam61, the resulting hologram is not a pure sinusoidal waveform, but has some distortion. Even so, the periodicity and direction of the grating pattern can be extracted by using the additional processing previously discussed in conjunction with processor63to generate a digital hologram.

To compensate for error in determining the direction of transmitter13relative to the receiver optical axis at aperture14, processor63superimposes a quadratic phase profile simulating a diverging lens onto the directional tilt phase profile extracted from the hologram formed on IDA25. This combined pattern is written on SLM19so that secondary beacon beam98is pointed at transmitter13, but with some divergence to compensate for remaining errors. Since the position of transmitter is approximately known from the directional information provided by the hologram on IDA25, this divergence angle is significantly less than the divergence angle, φ, of first beacon beam91.

As shown inFIG. 11C, a portion of secondary beacon beam98intercepts transmitter13. In the manner previously discussed in reference to beacon beams39and91, a secondary conjugate beacon beam99is generated by transmitter13and, as shown inFIG. 11D, transmitted towards and intercepted by receiver11. Beam99is then interfered with LO beam61to create a hologram on IDA25and, after processing by processor63, writes a grating on SLM19.

As shown inFIG. 11E, conjugate communications beam67is then generated and transmitted from transmitter13to receiver11. The grating written on SLM19that results from interfering secondary conjugate beacon beam99and LO beam61, deflects communications beam67to a known, fixed direction. Beam67is subsequently filtered and demodulated as previously described.

The additional intermediate steps described in the latter embodiment, i.e., the steps shown inFIGS. 11C and 11D, enhance the accuracy of the deflection grating of SLM19. They are particularly useful in the presence of strong turbulence in atmosphere41or in the event of a high rate of transverse motion between receiver11and transmitter13. However, even under the aforementioned extreme operating conditions, these steps are typically required only for the initial closure of the communications link between receiver11and transmitter13, i.e., the first reception of communications beam67by receiver11. Subsequent updates of the grating pattern on SLM19can typically be carried out without the aforementioned intermediate loop closure employing a random phase pattern on SLM19because the direction of transmitter13will remain known with sufficient precision.

The random phase pattern may also be initially written on SLM19without subsequently emitting secondary beacon beam98and secondary conjugate beacon beam99. In this alternative embodiment, only beacon beam91and conjugate beacon beam93are used to close the communications link between receiver11and transmitter13, and subsequently update the grating pattern on SLM19, i.e., beacon beam91and conjugate beacon beam93are used in conjunction with the steps shown inFIGS. 1A and 1B.

It is to be understood that the foregoing description relates to several embodiments of the invention, and that modifications may be made thereto without departing from the spirit and scope of the invention as set forth in the following claims.