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In this work we experimentally demonstrated an underwater wireless optical communications (UWOC) link over a 2.96 m distance with two 445-nm fiber-pigtailed laser diodes employing Orbital Angular Momentum (OAM) to allow for spatial multiplexing. Using an on-off keying, non-return-to-zero (OOK-NRZ) modulation scheme, a data rate of 3 Gbit/s was achieved in water with an attenuation coefficient of 0.4128 m−1 at an average bit error rate (BER) of 2.073 × 10−4, well beneath the forward error correction (FEC) threshold.
© 2016 Optical Society of America
1. Introduction
As the underwater environment has recently become the site of increased human activity, a need has arisen for reliable underwater communication mechanisms with data rates rivaling those achieved in free space. One major challenge that has stood in the way of progress in this area is the unfortunate attenuation of radio-frequency (RF) signaling schemes underwater, preventing them from serving as a viable communication technique in such environments. The classical approach to underwater communications has been the utilization of acoustic modulation schemes, but these suffer from major drawbacks in the form of limited data rates and lack of stealth [1].
An alternative approach to underwater communication that provides a solution to the problems inherent to RF and acoustic modulation methods is the utilization of a wireless optical channel with a carrier wavelength in the blue-green window of the visible spectrum. It has been shown that light with wavelengths in the range of 425 – 475 nm experiences very little attenuation as it propagates through clear water [2]. Moreover, optical channels lend themselves to an inherent degree of stealth due to their point-to-point nature and can be manipulated in many ways to achieve data rates competitive to those used in free-space communications. In previous works, data rates in excess of 1 Gbit/s at 532 nm were demonstrated in turbid water with an external modulator [3]. Additional results were also shown for an increase in data rate through the use of polarization and wavelength modulation [4]. Recent developments in GaN laser diode technology have pushed the potential bandwidth of blue laser devices in excess of 2.5 GHz with a 4 Gbit/s data rate [5]. These GaN devices have been used in On Off Keying (OOK) underwater data links at 2.3 Gbit/s [6] and a further increase in data rates to 4.8 Gbits/s with Quadrature Amplitude Modulation – Orthogonal Frequency Division Multiplexing (QAM-OFDM) [7]. These developments in GaN diodes and encoding schemes continue to increase the potential data rates for underwater applications in line-of-sight communications. However, space division multiplexing has not been leveraged for underwater communications and still remains an additional degree of freedom for increasing bandwidth capabilities.
Light can possess both Spin and Orbital Angular Momentum (OAM), where spin angular momentum is related to circular polarization and OAM is related to a helical rotation of the phasefront [8]. The angular momentum induced by a helically rotating phase front has been exploited for particle manipulation as optical tweezers [9–11]. Beams with OAM also possess self-healing properties [12], making them an interesting candidate for use in communication links. OAM has been used to multiplex data streams in a free space communication link [13–15], and a quantum entanglement of photon pairs has been demonstrated over 3 km using OAM [16]. It is only natural to take these unique communication methods into an underwater environment, where traditional high-speed communication methods fail.
In this work we investigate the potential for increasing underwater wireless optical data rates through the use of OAM. It has previously been shown that OAM serves as a viable method of spatially multiplexing optical channels in an underwater environment and that OAM channels maintain their vortex configurations as they propagate through turbid waters [17, 18]. With their feasibility thus established, we seek here to further explore the potential of parallel OAM channels by encoding them with digital data and investigating the bit error rates (BER) on the receiving end of the link. This work focuses on two parallel channels with OAM beams of charge numbers |m| = 8 and |m| = 4, with the turbidity of the water having an attenuation coefficient ranging from c = 0.0425 m−1 to c = 0.4128 m−1, for per-channel data rates ranging from 800 Mbit/s to 1.5 Gbit/s.
2. Orbital angular momentum
2.1 Background
Orbital Angular Momentum describes the momentum a beam of light possesses due to the azimuthal rotation of its phase front. A beam exhibiting orbital angular momentum is known as a vortex beam. Many methods exist to create such a beam, with the most common being the use of an azimuthal phase plate [19]. This phase plate is placed in front of the input Gaussian beam and the emerging beam takes on the azimuthal phase component with additional phase and amplitude terms due to the propagation of the composite beam. Analytic solutions can be found for a Gaussian passing through an azimuthal phase plate at different locations along the propagation path, but they are not simple modes, but a superposition of radial functions with the azimuthal rotation term preserved [20]. Therefore, if we approximate the beam with a Laguerre Gaussian beam for a specific charge number, or integer m, the field can be considered a seperable function in terms of the radial dependence and azimuthal phase part [21],
which is an expression for the beam with a beam waist . This expression will have an additional parabolic phase term as it propagates and the radius will diverge as a function of charge number m and distance z as seen by [21]In general, the resulting beam will have a ring of maximum intensity that is a function of the charge number, m, the initial beam waist and the distance it has propagated. The azimuthal phase term is preserved during the propagation and can be used in the demultiplexing as will be discussed later.The phase plate in question is designed with an azimuthally increasing thickness, which induces a circular delay of the phase front of the incident beam from 0 to 2πm radians. The charge number of the phase plate is the charge that the incident beam takes on after propagation through the plate and into the far field. To visualize this process see Fig. 1, where a Gaussian beam of unpolarized light (m = 0) is incident on a phase plate of charge number m = + 1, and another beam is incident on a phase plate of charge number m = −1. For images of the intensity and phase profiles of the resulting vortex beams, see Figs. 2(a)-2(d). Note that while the spatial intensity of each beam is identical, the polarity of the phases are preserved.
Fig. 1 Generation of OAM beams using vortex phase plates of charge numbers (a) m = + 1 and (b) m = −1.
Fig. 2 Intensity and phase profiles of vortex beams of charge numbers m = + 1 ((a) and (b), respectively) and m = −1 ((c) and (d), respectively).
2.2 Multiplexing of vortex beams
Due to the orthogonality of different charge states, vortex beams of differing charge numbers can be overlapped without fear of interference. As mentioned above, the phase plates used to induce OAM onto the beams vary in thickness in an azimuthal manner. It turns out that the value of the charge number m is the number of 2π phase intervals etched onto the phase plate as one travels around it radially. As the m value of the phase plate increases, so does the diameter of the resulting vortex beam.
It is important to note that vortex beams are differentiable in both charge number and polarity. While the intensity profile of vortex beams of charges ± m are identical, the azimuthal spin of the beam of charge + m is counter-clockwise (as seen in Fig. 1(a)), while the azimuthal spin of the beam of charge –m is clockwise (as seen in Fig. 1(b)). This allows for another degree of beam combination.
2.3 Demultiplexing of vortex beams
The combination of multiple OAM beams would be of little use for communicative purposes with no method of separating them back into their individual channels after propagation through the medium of interest. Fortunately, separation is achieved by putting each beam through a phase plate of charge number opposite that of the beam itself. However, the resulting beam will have the azimuthal phase term removed through phase conjugation or an additional azimuthal phase will be added on the existing beam, which has a ring shaped intensity based on the initial azimuthal phase state encoded with the diffractive phase plate. Given the complexity of the radial term of the beam and the new azimuthal phase term, we can consider it to be a narrow width ring of radius with a corresponding azimuthal phase as follows:
In order to estimate the impact of the phase filtering, the phase filtered beam is placed in front of a lens of focal length f and the resulting intensity in the Fourier plane of the lens can be approximated as follows:Here represents the approximation of the intensity distribution of the output beam in the Fourier plane after the input vortex beam of charge number m (given by Eq. (1)) is passed through a phase plate of charge number m0. The parameter r0 is the radius of the vortex beam at the phase plate, approximated as a ring, of charge m0, f is the focal length of the lens used to induce the Fourier transform onto the incoming beam, andis the wavelength of the beam. Figure 3(a) illustrates this description pictorially, in which a vortex beam of charge number m = + 1 is successfully demultiplexed via propagation through a phase plate of charge number m = −1. The intensity and phase profiles of the resulting demultiplexed beam may be seen in Figs. 3(b) and 3(c). The maximum on axis peak intensity occurs for the condition and has a minimum for the case where . This provides for the demultiplexing of different charge numbers based on the azimuthal phase term in the beam. The exact beams have more complex radial functions, which are convolved with this result; however, characteristic phase matching of the charge numbers still holds and provide an efficient method of demultiplexing based on using the phase conjugate term in the diffractive phase element.Fig. 3 (a) Regeneration of plane wave through inverse phase plate propagation. (b) Intensity and (c) phase profiles of resulting demultiplexed beam.
3. Orbital angular momentum phase plate fabrication
The charge |m| = 4 and |m| = 8 phase plates were fabricated for 450-nm light at Clemson University using photolithography. Both types of phase plates are 16-level devices, which means the fabrication procedure has four-layer loops. Every loop of the process started with cleaning the wafer, followed by a coating of photoresist on the surface. A stepper was used to expose special patterns of that layer onto the photoresist. The only difference between the charge 4 and charge 8 phase plates is the pattern exposure. The etching step transfers the pattern from the photoresist to the fused silica substrate.
Since the refractive index of fused silica at 450 nm is 1.466, the finest etching depth will be 60 nm. This was realized using the following recipe: Inductively Coupled Plasma (ICP) power of 800 W, bias power of 80 W, oxygen flow rate of 2 sccm, trifluoromethane flow rate of 70 sccm, chamber pressure of 10 mTorr and chamber temperature of 15 °C. The etching rate and the selectivity of the recipe were 240 nm/min and 1.8, respectively. Figures 4(a)-4(d) illustrate the phase optics for |m| = 4 and |m| = 8.
Fig. 4 Profile of (a) |m| = 4 and (b) |m| = 8 phase plates, along with a top-down view of the completed optics for (c) |m| = 4 and (d) |m| = 8.
4. Attenuation of underwater vortex beam propagation
When creating an optical communications link, it is necessary to characterize the channel in order to predict the attenuation of the propagated signal. Optical propagation is affected by absorption, a, and scattering, b, from particulates in the optical path. The combination of these two phenomena yield attenuation, c, where c = a + b. The power lost due to absorption and scattering can be predicted by Beer’s Law and is given by P1 = P0e-cz where P1 is the received power, P0 is the transmitted power, and z is the transmission length.
Beer’s Law has been verified for the attenuation of Gaussian beams through simulated ocean turbidities using liquid antacid [22,23]. Given that the receiver in section 5 was designed with a restricted field of view, only non-scattered light of the rotating vortex beam is collected and its attenuation should follow the same trend as a Gaussian beam. Figure 5 shows the attenuation of vortex beams traveling through turbid media, where the attenuation coefficient is varied from 0.06 m−1 to 2.21 m−1 using liquid antacid. Three OAM beams (of charge numbers 0 [Guassian], 8, and 16) were generated by passing a 532-nm laser beam modulated at a frequency of 1 GHz through interchangeable diffractive phase plates. The signal was collected by a photomultiplier tube and the RF power was measured using a spectrum analyzer. The optical power drop in decibels is compared to Beer’s Law. As seen in Fig. 5, all three beams experience attenuation as predicted by Beer’s Law, demonstrating that the attenuation experienced by different vortex beams underwater can be approximated using Beer’s Law regardless of charge number without increased degradation of the modulation relative to a Gaussian beam.
Fig. 5 Attenuation of OAM beams through underwater environments for beams of charge numbers m = 0, m = |8|, and m = |16|.
5. Experimental procedure
The transmitter consisted of two channels that were encoded with binary digital data. Onto each channel a 32-bit, M-series, pseudo-random, on-off-keying, non-return-to-zero (OOK-NRZ) line code was generated using a Textronix AWG7052 arbitrary waveform generator. The output of this device was then amplified using a 10 dB Picosecond Pulse Labs 5828-MP amplifier and coupled with a DC bias current via a bias-tee located inside a ThorLabs LDM9LP pigtailed laser diode mount. The amount of DC bias applied to the ThorLabs LP450-SF15 single-mode fiber-pigtailed laser diode was set by observing the optical output to allow for maximum RF swing between the threshold and maximum operating current. The DC bias applied to the laser diodes for Channel 1 and Channel 2 (formally defined below) were 60 mA and 75 mA, respectively. After the amplifier, the amplitude of the RF modulation was 50 mA peak-to-peak for both channels.
A vortex phase plate was introduced in front of the collimated emission of each laser diode to induce Orbital Angular Momentum (OAM) on each channel. The phase plates were situated in such a way as to produce OAM beams of opposite charge numbers relative to one another. The beams were then multiplexed using a 50/50 non-polarizing beam splitter so that the emission of each laser diode traveled along the same optical path. After traveling through a 5X beam expander, both channels were allowed to propagate through a water tube that was 2.96 m long. Varying concentrations of antacid were used to increase the turbidity of the de-ionized (DI) water inside the tube.
The receiver used a 50/50 non-polarizing beam splitter to separate the incoming beam into two channels, and an inverse phase plate was placed on each leg to demultiplex the incoming data. A 40-μm pinhole was used as a spatial filter to separate the mode being demultiplexed from the mode doubling in charge number after the second phase plate. The output power of each channel was held constant using neutral density filters and was incident on a Menlo Systems APD210 Si Avalanche PhotoDetector (APD) that fed directly into a Textronix TDS8200 digital sampling oscilloscope. From this device, the output of both channels could be examined simultaneously and characterized to yield the computational results shown in section 6. A complete diagram of the experimental layout is shown in Fig. 6. For ease of terminology, the signal exiting the AWG and sent left to right horizontally in Fig. 6 (i.e. A to P) will be referred to as Channel 1. Similarly, the data being multiplexed and demultiplexed at right angles to the underwater link (i.e. A to U) will be referred to as Channel 2. Photographs of the transmitter and receiver are shown in Fig. 7.
Fig. 6 Experimental Layout: A. Arbitrary Waveform Generator, B. 10 dB Amplifiers, C. Bias-tees/Fiber-pigtailed LDs, D. DC Power Supply, E. Fiber Collimator (f = 4.6 mm), F. Optical Phase Plate, G. Fiber Collimator (f = 4.6 mm), H. Optical Phase Plate, I. 50/50 Non-polarizing Beam Splitter, J. 5X Beam Expander (f = 30 mm and f = 150 mm pair), K. 50/50 Non-polarizing Beam Splitter, L. Optical Phase Plate, M. Focusing lens (f = 125 mm), N. Pinhole (40 μm), O. Focusing lens (f = 50 mm), P. Avalanche Photodetector, Q. Optical Phase Plate, R. Focusing lens (f = 125 mm), S. Pinhole (40 m), T. Focusing lens (f = 50 mm), U. Avalanche Photodetector.
6. Results and discussion
6.1 Orbital angular momentum charge number: |m| = 8
Before examining the digital data sent via the underwater link, it is helpful to image the intensity distributions of the beams to ensure proper alignment. Shown in Fig. 8 are such images, taken of beams of charge numbers m = ± 8 after propagation through a phase plate of charge number m = −8. After the phase plate, the beam with charge number m = −8 becomes m = −16, seen in Fig. 8(a), and the beam with charge number m = + 8 becomes m = 0, as seen in Fig. 8(b). These modes are then easily demultiplexed using a pinhole as a spatial filter.
Fig. 8 Demultiplexed image distributions of (a) m = −8 beam; (b) m = + 8 beam; (c) m = ± 8 beams, all after propagation through an m = −8 phase plate.
After examination of the demultiplexed beams, the cameras were replaced with avalanche photodetectors to analyze the incoming digital data. After conversion from optical to electrical energy through the APDs, this data was displayed on the oscilloscope in the form of an eye diagram. Shown below are eye diagrams for Channel 1 and Channel 2 operating in parallel at 1 Gbit/s and 1.5 Gbit/s per channel (Figs. 9(a) and 9(b), respectively). This data was captured after optical transmission through the underwater link with an attenuation coefficient of c = 0.4128 m−1.
Fig. 9 Eye diagrams for |m| = 8 showing Channel 1 (top) and Channel 2 (bottom) transmitting in parallel at (a) 1 Gbit/s and (b) 1.5 Gbit/s, all through water with an attenuation coefficient of c = 0.4128 m−1.
From the eye diagrams, the mean and standard deviation values of the “1” and “0” signals can be found through use of a histogram measuring a cross section of each rail in the 40-60% window of the bit period. From this information the bit error rate (BER) of the transmitted data can be computed according to the formula
where μi and σi are the mean and standard deviation, respectively, of signal i, i = 0 or 1, erfc(⋅) is the complementary error function defined byand Vth is the threshold voltage, given byArmed with these equations, the BERs of each channel were computed across a range of attenuation environments for data rates ranging from 800 Mbit/s to 1.5 Gbit/s in 100 Mbit/s intervals. The results for Channel 1 and Channel 2 can be seen in Fig. 10 and Fig. 11, respectively.6.2 Orbital angular momentum charge number: |m| = 4
Having examined in detail the behavior of the communication link enabled with beams of charge number |m| = 8, attention was turned to similar investigation of beams of charge |m| = 4. Shown below are images taken of beams of charge numbers m = ± 4 after propagation through a phase plate of charge number m = −4. After the phase plate, the beam with charge number m = −4 becomes m = −8, seen in Fig. 12(a), and the beam with charge number m = + 4 becomes m = 0, seen in Fig. 12(b). As before, these modes are now easily demultiplexed using a pinhole as a spatial filter.
Fig. 12 Demultiplexed image distributions of (a) m = −4 beam; (b) m = + 4 beam; (c) m = ± 4 beams, all after propagation through an m = −4 phase plate.
As illustrated above for the |m| = 8 beams, the BERs were calculated using Eqs. (5)-(7). This procedure was repeated with the |m| = 4 beams at 1.25 Gbit/s across a range of attenuation environments, c = 0.0425 m−1 to c = 0.3853 m−1, resulting in a BER of 3.6 to 3.9 × 10−4 for Channel 1 and a BER of 5.3 to 6 × 10−5 for Channel 2. Therefore, the impact of the turbidity on the data rate was similar compared to the higher charge number.
It is important to realize that even though this experiment was conducted with beams of charges m = ± 4 and m = ± 8, the potential exists for combinations of multiple beams of multiple differing charge states. The limit lies only in the capability of spatially separating the multiplexed beams at the receiver. Recall that orthogonality is achieved by demultiplexing, or phase-cancelling, only one of the input beams at any branch of the receiver via propagation through a matched receiving phase element. The distribution of the beam experiencing phase cancellation can be described in terms of a Bessel function of the first kind of order 0 (obtained by setting m = -m0 in Eq. (4)), which has a peak on axis. The other beams, however, will retain their ring intensity distributions and will have nulls on axis. The radius of a vortex beam can be approximated by setting m ≠ -m0 in Eq. (4). Given the parameters for the experimental configuration (λ = 450 nm, f = 125 mm, and r0 = 3 mm), the beam shown in Fig. 12(a) has an approximated radius of 27 µm (54 µm diameter). To block this unwanted mode, a 40 μm pinhole was chosen so that this spatial filter was smaller than the beam size. With this restriction, the lower limit for spatial separation is a vortex beam of charge m = 4 incident on the demultiplexing phase element. To demultiplex modes smaller than m = 4, a smaller pinhole would be needed to spatially filter the unwanted modes.
7. Conclusion
In this work a high-speed underwater optical communications link was demonstrated using Orbital Angular Momentum to enable dual-channel parallelism in the transmission of digital data at rates up to 3 Gbit/s. Utilizing the m = |8| optical vortex beams, the two channels carried RF signals that were modulated independently of one another at speeds varying from 800 Mbit/s to 1.5 Gbit/s while the attenuation of the water was increased from c = 0.0857 m−1 (roughly that of pure sea water) to c = 0.4128 m−1 (about that of a coastal ocean environment). The corresponding BERs of each channel were then computed from the eye diagrams generated at the receiving end of the link, with an average BER of 2.073 × 10−4 achieved at c = 0.4128 m−1 at a collective data rate of 3 Gbit/s (1.5 Gbit/s/channel). Note that this value is well below the FEC threshold, even under these relatively strenuous conditions.
An additional finding as a result of this effort lies in the fact that increasing the turbidity of the water does not jeopardize the quality of data transmission via Orbital Angular Momentum. This discovery demonstrates the versatility of these vortex beams and solidifies their practicality in the underwater realm. Moreover, this imples that scaling the data rate can be achieved by including additional OAM channels of increasing charge numbers and no mixing is observed in the beams as a result of the turbidity.
Although this research was done using only two superimposed vortex beams, it should be clear that the potential exists for scaling this method of data transmission to multiple channels of differing OAM charge numbers for added degrees of freedom, resulting in a multiplicative effect on the overall data rate. This is not to mention a host of encoding schemes that enable data rates well in excess of the simple 1 Hz:1 bit/s modulation-to-data rate scheme employed in this work, such as QAM, M-PAM, and OFDM. Additional scaling can also be achieved with spectral beam combining and/or polarization multiplexing [24], which could easily lead to data rates on the order of 100s of Gbit/s.
Acknowledgments
Funding for this research was provided by ONR N00014-141-0264, HEL-JTO/AFOSR FA9550-10-1-0543 and ONR STTR N13A-023-0367.
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