Open Access
Add to BibSonomy
Abstract
Underwater turbulence presents a myriad of challenges for underwater optical systems through wavefront distortion and beam deflection. In this work, an underwater turbulence emulator is developed and thoroughly characterized to experimentally test the proposed underwater turbulence mitigation technique. This technique applies a modified HOBBIT system introduced in atmospheric turbulence to the relatively unknown underwater turbulence domain. By varying a beam’s spatial position and relative phase gradient, a volume of turbulence is rapidly probed to determine the beam state for optimal propagation. This probe and control method is applied in multiple facets, including improved optical power transmission as well as supporting a 25-Gbps communication link through a dynamic environment.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nearly all classical communication techniques used for underwater environments utilize acoustic based systems. However, as technologies have progressed, the physical nature of these acoustic systems has been associated with many drawbacks such as high latency, high transmission losses, and limited bandwidth [1]. Due to these limitations, alternative forms of communication are attracting an increasing interest, including underwater wireless optical communication (UWOC). The UWOC market is predicted to quadruple in size by 2027, and has applications in military, environmental, and commercial fields [2]. Due to fundamental properties of light waves, these optical systems have inherent advantages over acoustic and even RF systems, including the ability to support higher data rates, lower latency, and larger bandwidths [3]. These characteristics are crucial for the advancement of this technology in underwater environments, and it is apparent from the amount of activity and resources being allocated to this area of study that the scientific community has put an emphasis on its development.
Currently, the naturally occurring phenomena of underwater turbulence presents a challenging obstacle facing UWOC systems. The environmental factors of concern that create underwater turbulence are temperature and salinity, each of which contribute to the fluctuations in the refractive index of the water [2]. These fluctuations degrade the performance of UWOC systems by introducing wavefront distortion as well as large variations in the intensity of propagated beams due to beam breakup and deflection [4–6]. The power loss due to underwater turbulence was experimentally measured in [7], while the effects of simulated oceanic turbulence on system performance parameters such as signal-to-noise ratio (SNR) and bit error rate (BER) are discussed in [8] and [9], respectively. Numerous techniques have been identified to help mitigate the effects of underwater turbulence through the use of adaptive optics, spatial diversity and aperture averaging [10–14]. In the referenced works, these techniques led to improvements in both SNR and BER, however, were demonstrated in simulation only. Additionally, each of these techniques have fundamental limitations as turbulence strengths increase. The aperture averaging technique is constrained by the size of the receiver aperture, while spatial diversity techniques drastically increase the complexity of the hardware and software components required of a system. Comparatively, adaptive optics such as deformable mirrors have mechanical constraints that limit the speed and possible phase front compensation that would be needed when encountering higher levels of turbulence, as well as having damage thresholds that render high-powered systems unattainable. A simpler, faster, more adaptable turbulence mitigation technique is crucial to unlocking the full potential of optical systems in a real-world underwater environment.
As compared to underwater turbulence, there is a far greater collection of research and knowledge on the behavior of optical turbulence in the atmosphere. This includes turbulence mitigation techniques that have been experimentally carried out through atmospheric turbulence yet have not been explored in the underwater realm. In [15], optical channels within atmospheric turbulence are sensed and coupled into, leading to an increase in power and data transmission. The referenced work is based on the knowledge that eigenmodes exist for volumes of atmospheric turbulence, and that these complex structures of light can pass through a turbulent medium relatively undisturbed [16]. It is also noted that a varying refractive index, caused by thermal gradients contained within a turbulent volume, can induce waveguide-like channels that certain modes of light may be coupled into and guided with minimal distortion through the turbulence [17,18]. Following exploitation of these channels in atmospheric turbulence, it begs the question: can these channels be experimentally exploited in underwater turbulence?
In this paper, we demonstrate the existence of optical channels and their exploitation in underwater turbulence resulting in an improved transmission of a high data-rate communication link as well as improved optical power. An underwater turbulence emulator (UTE) capable of producing stable and repeatable turbulence was constructed to allow for the propagation of beams through a turbulent underwater environment. The generated turbulence was analyzed and characterized using multiple methods to aide in the comparison of conditions with other underwater turbulence setups. The probing and control system demonstrated in [15] was setup in conjunction with the UTE. This system is based on the Higher-Order-Bessel-Beams-Integrated-in-Time (HOBBIT) architecture [19,20], and uses orbital angular momentum (OAM) and azimuthal position around a vortex envelope as a probing basis, while utilizing the uniquely advantageous capabilities such as rapid mode-switching that the HOBBIT system offers. With an acousto-optic deflector (AOD) and log-polar coordinate transform optics, the HOBBIT system has been used to probe turbulence with a continuous OAM spectrum [21], as well as generating a wavelet basis of optical fields for probing turbulence [22]. For this experiment, a modified HOBBIT system offers both the OAM and azimuthal position of a beam with a fixed size to be tuned rapidly. This real-time tuning allows for the probing of a turbulent volume of water to determine the optimal input mode that will reach the receiver. The system can then fix the desired parameters to tailor the beam for optimal propagation through the current turbulence.
2. Background
2.1 Underwater turbulence
In comparison to atmospheric turbulence, which has been researched and published on many times [23–25], little work has been conducted on optical turbulence in underwater environments. There are analytical methods that have been developed to evaluate the effects of atmospheric turbulence, yet due to the differences in functional form of the refractive index power spectrum (in air versus water, these cannot be directly applied to underwater conditions [26,27]. Underwater turbulence can be treated using the advection theory of scalar quantities in a fluid like atmospheric turbulence. The main difference in mediums significant to this work is that the thermal eddy diffusion coefficient is much smaller than the viscosity leading to slower turbulence rates unlike in the atmosphere where they are similar [28]. However, each medium can be expressed with similar models of the energy cascade where largest eddies, deemed outer scale, breakdown following a ${\mathrm{\Phi }_n}(\kappa )\sim {\kappa ^{ - 5/3}}$ power law until dissipation by heat at the smallest eddy called the inner scale. The region where the power spectrum follows the form, ${\mathrm{\Phi }_n}(\kappa )\sim {\kappa ^{ - 5/3}}$, is called the inertial subrange which contains length scales of $\mathrm{\Delta }r$ to fall within ${l_0} < \mathrm{\Delta }r < {L_0}$. The differences in the refractive index power spectrum occur due to how water diffuses the kinetic motion into heat within the viscous-diffusive region which change the power spectrum’s functional form [28]. Taking note of these differences are important to understand how the HOBBIT’s form of turbulence compensation compares with past atmospheric results.
2.2 Turbulence generation
To create the UTE a 3 m long,100 mm diameter PVC tube was customized and filled with water, as can be seen in Fig. 1(a). The tube was sealed with endcaps which included 50 mm diameter, 12 mm thick optical flats made of fused silica that act as windows to allow the beams to enter and exit the tube. A 10 m heating wire was triple passed through the bottom of the tube, while two chilled copper pipes were installed along the top of the tube. These components, seen in Fig. 1(b), allow a controlled temperature gradient to be created along the length of the tube that is transverse to the direction of the beam propagation. The output of the heated wire is constant once it is given 15 minutes to completely warm up. The copper pipes are connected to a chiller which is circulating temperature-controlled water within the pipes in a closed system.
Fig. 1. (a) UTE secured on an optical table using 3D-printed mounts. (b) View through the optical flat at the end of the UTE. The heated wire (bottom) and copper tubes (top) can be seen running the length of the tube.
By setting the temperature of the water in the copper pipes to 10°C and the heated wire to output 150W, a controlled and repeatable condition is created within the UTE. It is noted that no significant heat exchange with the environment occurs. In this work, all experiments and analysis are carried out with the UTE at this condition. However, many different conditions could be created by varying either the temperature of the water circulating within the copper pipes using the chiller or the power output of the heater wire. Through constant monitoring of the temperature of the water within the UTE, it was determined that the temperature stabilized after 1 hour of the turbulence generation components running, indicating that the heat generated from the wires is being removed by the chilled copper pipes. Once the UTE was in this condition, the turbulence created was analyzed and characterized. It is noted that while oceanic conditions include salinity, this work only considers the thermal properties of underwater turbulence.
2.3 Turbulence characterization
Various forms of turbulence characterization exist to determine the fluctuations of the medium’s refractive index that can be done using optical [5,6,27,29] or thermal [29] based methods. The method chosen to estimate the refractive index fluctuation strength is done using beam wander to overcome the differences in functional form of water’s refractive index spectrum. This is true given that the diameter of the beam is within the scale of the inertial subrange. This holds true because any turbulent cells smaller than the diameter of the beam only result in beam distortion rather than beam wander and therefore do not contribute to centroid motion [27]. The variance of the random beam wander for a collimated Gaussian beam is found in [30], and is shown below:
To measure the beam wander, a single Gaussian beamlet with a diameter of 1 mm was propagated through the UTE using a 532 nm wavelength, CW source. The beamlet was imaged by a camera at the exit of the UTE for 500s at 1 fps to ensure that the recorded data entries were statistically independent. The centroid position for each frame was determined, and the beam wander from the average centroid position was calculated and averaged for the entire dataset. The variance of this beam wander was used in Eq. (2) to calculate $C_n^2$ and characterize the turbulence. Ten datasets were taken to calculate a standard deviation for the $C_n^2$ values.
To confirm that the estimate of $C_n^2$ using this optical method provides a reasonable result, a method reliant on temperature fluctuation, as discussed in [29], was used. Measurement of the temperature fluctuations over a given length scale that falls within the inertial subrange $({l_0} < \mathrm{\Delta }r < {L_0})$ can be characterized using the temperature structure function, ${D_T}$, defined as:
$C_T^2$ is related to the index of refraction structure constant, $C_n^2$, through the following equation:
To measure the temperature fluctuations necessary to determine ${D_T}$, two NTC FP07 Fastip Probe Thermistors were positioned vertically in the UTE, with the sensors centrally located inside the tube. Custom mounts were utilized to ensure that all measurements were taken at the same central depth within the tube and that the measurement depth corresponded to the depth of the propagation path of the beam through the UTE. Temperature measurements were taken with the probes at 6 different distances apart ($\mathrm{\Delta }\hat{r}$ = 1, 2, 5, 10, 50, and 100 cm) for 10 minutes each with a 20 ms sampling time. Each dataset was divided into five 2-minute segments to analyze the standard deviation of the results. Using this data in Eq. (3), a ${D_T}$ value can be determined for each $\mathrm{\Delta }\hat{r}$. The temperature structure constant is then fitted to the values of ${D_T}$ and $\mathrm{\Delta }\hat{r}$ using Eq. (4). To determine the rate at which the refractive index of water changes as a function of temperature, $\frac{{dn}}{{dT}}$, data published in [31] was utilized. This value, along with the temperature structure constant, is used in Eq. (5) to calculate $C_n^2$.
Using the optical method to characterize the underwater turbulence, a $C_n^2$ value of (2.78 ± 1.82) × 10−10m-2/3 was obtained. Comparatively, a $C_n^2$ value of (4.67 ± 0.48) × 10−10m-2/3 as found using the temperature probe approach. The values from the two respective methods are within the measured error and can be considered to agree. This strength of underwater turbulence, with $C_n^2$ on the order of 10−10m-2/3, falls well within the range reported by [27] in another underwater turbulence setup containing a different geometry. Additionally, when fitting the temperature structure constant to the measured ${D_T}$ and $\mathrm{\Delta }r$ values using Eq. (4), the exponent defined as $2/q$ was found to be 0.275 when best fitting the data. This closely matches the value of the same $2/q$ exponent that was reported to be 0.29 when best fitting the regions of strong vertical updraft in simulation of a water tank in [27]. These results indicate reasonable and reliable conditions have been generated in the UTE.
2.4 Turbulence mitigation system implementation
Figure 2 shows a visualization of the underwater turbulence mitigation technique. The top image depicts a beam propagating through underwater turbulence. As it propagates, the beam breaks up into beamlets that each experience deflection and distortion as they continue to propagate. When trying to provide power to a specific point in space such as an optical receiver, the spatial variability of the inputted beamlets resulting from these deflections and distortions is devastating to an optical system. To address this challenge, beamlets can be guided through desired paths in the turbulence to reach a specific location by manipulating their optical phase. By correcting for the initial trajectory, set by the beamlet’s phase, the beamlet can be guided through the turbulence to maximize intensity at a specific point in space. While each of the beamlets in the top image is a transmission path through the turbulence, the pink paths indicate those beamlets that reach the desired target after the turbulence with the correct phase. Figure 3 demonstrates the visual effect that the underwater turbulence has on a beam. Figure 3(a) depicts a Gaussian beamlet scanned around a vortex envelope, which creates a ring due to the integration of the camera. Figure 3(b) depicts the same ring propagated through underwater turbulence in the UTE. The pink arrows highlight the areas of localized intensity that correspond to the pink propagation paths shown in Fig. 2. Parameters such as the optimal beam size and phase gradients are crucial to this system performing at maximum efficiency, and are discussed for work done in atmospheric turbulence in [15]. These parameters are related to the statistics of the turbulence present in the propagation environment, and analysis of beam propagation in the environment can inform the optimization of these system parameters.
Fig. 3. A Gaussian beamlet is scanned through azimuthal positions around a vortex envelope. (a) Scan in ambient conditions. (b) Scan in turbulent conditions, with arrows indicating points of maximum intensity/optimal propagation paths.
When measuring the beam wander as part of the characterization efforts of the UTE discussed previously, the initial beamlet that was propagated through the turbulence had a diameter of 3.5 mm. While extreme beam distortion and breakup was easily observable from the images captured, it was also determined through image analysis of the data that localized areas of undisturbed high intensity on the order of 1 mm featured prevalently. The size of these high-intensity regions were assumed to approximate the Fried parameter, ${r_0},$ of the turbulence generated in the UTE. The Fried parameter is defined as [30]
where k is the optical wavenumber and L is the length of the tank. This metric is used to describe the spatial features of turbulence where $D/{r_0}$ can be used to estimate the turbulence induced distortion relative to the beam diameter $D = 2{w_0}$ [21]. Equation (6) is found by assuming the refractive index fluctuations follow Kolmogorov statistics which can exist in air or water. Therefore, an estimate of ${r_0}$ can be obtained using the measured values of $C_n^2$ from Section 2.2. It is noted that a more exact form of ${r_0}$ can be found using the explicit forms of the spatial power spectrum of air or water [2,30].A beamlet that is larger than ${r_0}$ ($D/{r_0} > 1$, where D is the diameter of the beamlet) will experience beam breakup and distortion. Conversely, beamlets that are close in size to ${r_0}$ ($D/{r_0} \approx 1$) experience beam wander without significant breakup or distortion [32–34]. To utilize this consequence effectively, the size of the input beamlet was altered to have a 1 mm diameter at the entrance of the UTE to match the approximated ${r_0} = 0.8 - 1.1mm$ calculated using $C_n^2$ estimates from Section 2.2. Figure 4 displays examples of a Gaussian beamlet after being propagated through the UTE. The images in Row I depict a beamlet with the initial diameter of 3.5 mm. This beamlet size has a $D/{r_0} \cong 3.5$ which indicates the expected presence of beam breakup and distortion. This expectation matches the images in Fig. 4, as breakup and distortion are readily visible, as are the localized regions of high intensity. Row II contains images of the beamlet with the new diameter of 1 mm. This beamlet size has a $D/{r_0} \cong 1$ and these images show the beam being deflected by the turbulence, but not experiencing the same distortion and breakup as the larger beamlet, matching the expected behavior of a beam that is on the order of the Fried parameter of the turbulence.
Fig. 4. Images of a Gaussian beam after propagation through the UTE in turbulent conditions. The beam imaged in Row I has a diameter of 3.5 mm and a $D/{r_0} \cong 3.5$. The beam imaged in Row II has a diameter of 1 mm and a $D/{r_0} \cong 1$.
Since the beam size closely matched the estimated ${r_0}$, the turbulence will not cause significant beam breakup. It will instead induce a phase tilt which results in the beamlet shifting off-axis. This beam wander is a deflection angle before focusing and corresponds to a spatial shift at the aperture, which still causes optical system degradation [32–34]. The nature of this random beam wander is the driving force behind the use of a modified HOBBIT system for turbulence mitigation [15,21,22]. The HOBBIT system can realize various phase tilts along the azimuthal direction by applying an OAM phase profile across an input beamlet while also varying the spatial position of the input beamlet around a vortex envelope. Crucially, the HOBBIT system can switch between spatial positions and OAM modes on the order of MHz, resulting in the relatively much slower turbulence appearing frozen for any sensing instance. This allows the best input state to be selected per instantaneous realization of turbulence. Therefore, instantaneous correction for turbulence can be utilized for immediate power transmission or communications link in a turbulent underwater environment.
3. Methods
3.1 Probing
To address the two-part requirement of manipulating a beamlet’s spatial location and phase gradient, a modified HOBBIT system was implemented [15]. The elements of the modified HOBBIT are shown in Fig. 5, which include two AODs for control of the two desired dimensions, as well as a pair of log-polar optics which map locations across an inputted line around a ring envelope through a coordinate transform. Immediately after exiting the system, the resulting near-field for a single beamlet can be expressed as:
Fig. 5. (a) Elements of the modified HOBBIT system with beam transformations for creating OAM beamlets. The line and ring of gaussian spots show several possible locations for the beamlet, which are all cycled through during the probing sequence. (b) Hardware setup used to create the modified HOBBIT system.
The beamlet then propagates through the UTE to the receiver, maintaining the Gaussian profile throughout. Figure 6(a) depicts an individual Gaussian beamlet being scanned through discrete positions around the ring envelope, while Fig. 6(b) illustrates an OAM charge of m = 5 which is applied across the entire ring. The beamlet is then locked at the optimal azimuthal location with its corresponding phase tilt to be transmitted through a particular realization of turbulence, Fig. 6(c). The OAM charge depicted in Fig. 6 is arbitrary and is applied by the modified HOBBIT system, creating a phase gradient along the ring envelope. As can be observed from Fig. 6(a), with adequate azimuthal resolution, the Gaussian spots begin to overlap at the discrete locations. This provides a continuous probing space about the ring envelope.
Fig. 6. (a) A Gaussian beamlet rapidly scans through discrete points around a ring envelope (intensity shown). (b) A phase gradient is applied across the profile (phase shown). (c) A specific azimuthal position around the ring, with its corresponding phase tilt, is selected to be transmitted (phase shown).
After propagating through the 3 m long UTE, the beamlet is focused into the Fourier plane using a 250 mm lens. A beam splitter directs 10% of the output through another lens to image the beamlet onto a high-speed camera (Phantom T-1340), while another beam splitter steers 10% of the remaining output to a 50 MHz avalanche photodetector (APD120A2) that is used as part of the feedback loop for probing. Most of the output enters a 50$\mu \textrm{m}$ diameter multi-mode fiber connected to a 10 GHz AC-coupled photoreceiver (RXM10BF) with a responsivity of 0.2A/W at a wavelength of 532 nm and a 3 dB bandwidth of 11 GHz. To recover the signal, the photoreceiver was sampled at 25GSps by an oscilloscope (MSO71245C). This photoreceiver was interchanged with a DET10A detector with a responsivity of 0.25A/W at 532 nm when the DC power through the multimode fiber was measured. The output of the power detector was amplified by 10 dB and sampled using the same oscilloscope.
3.2 Control system
The hardware utilized to direct the modified HOBBIT system is detailed in [15], and includes a ScopeFun microcontroller as well as an arbitrary waveform generator (AWG5208). The complete probing sequence is defined by 35 azimuthal positions and 7 OAM states. The OAM states range from charge -30 to charge 30 in steps of 10 OAM. Given that the OAM spectrum of the beamlets created in Eq. (7) is defined as:
where m is the global OAM of the beam and n is the modal index, the step size of 10 OAM is less than the width of the OAM spectrum, ensuring adequate resolution. The sequence begins at a location -153° from the bottom of the ring envelope with a charge of -30 OAM. The beamlet is stepped clockwise through each position using a shift of 9° while the OAM charge is kept constant until it reaches 153° from the bottom of the ring. The beamlet is shifted back to -153° and the OAM charge is then stepped by 10 to -20 OAM. This process repeats until all OAM charges have been designated at every position. The total time for the probing sequence is 151µs, with each beam state being held for 615 ns. This switching time is limited by how long it takes the new acoustic frequency to propagate fully across the input beam and is defined by $2{w_0}/V$, where ${w_0}$ is the beam radius and V is the acoustic velocity of the TeO2 crystal in the AOD. At the beginning of a probing sequence, the APD is sampled by the microcontroller at 12.5 MHz, and the feedback is captured for the sequence. The beam state with maximal voltage is then locked by the AWG, and the data signal is triggered. This feedback data is visualized in the spectrograms in Fig. 7. The spectrograms are generated offline by normalizing the feedback voltages recovered and mapping them to the probing space. The voltages are converted to optical power for the spectrograms, where the intensity of a pixel indicates the power received for that specific beam state (azimuthal position and OAM charge.) In Fig. 7(a), it is observed that power is received across all azimuthal positions with 0 OAM charge in ambient conditions. This spectrogram does not shift while ambient conditions are constant, and the system is adequately aligned. Once the turbulence is induced inside the UTE, the beamlet is distorted and deflected and the optimal beam state varies, an example of which is shown in Fig. 7(b). The spectrograms taken with turbulence active constantly change, with each spectrogram indicating the optimal beam state for that instantaneous realization of turbulence. The beam state that is transmitted is designated with a red rectangle in Fig. 7. It is noted that the control system’s decision always corresponded to the beam state with the maximum optical power. The transmission window between scans ranged between 10-50 ms to guarantee that data is collected. Due to the relatively slow movement of the turbulence (100s of ms), this window length is arbitrary, and no difference was observed in the data when it was switched between 10 ms and 50 ms. The block diagram of the control loop is displayed in Fig. 8. The delay associated with the control algorithm itself is less than 1 ms.Fig. 7. Feedback spectrogram (a) in ambient conditions and (b) in turbulent conditions. Each pixel represents a beam state of the probing sequence, where the color of the pixel indicates how much power is received at that beam state. The red rectangle indicates the beam state that was selected and transmitted through the environment for each instantaneous realization.
Fig. 8. Control system diagram. The AWG uses the probing sequence waveform to trigger the microcontroller sampling of the feedback detector.
4. Experimental results
4.1 Improved transmission of optical power
To quantify the performance of the probe and control system through underwater turbulence, 1244 measurements of optical power were taken in 12.44s (10 ms sampling rate) with the control system actively deciding the optimal beam state. Similarly, 1244 of the same measurements were taken with the control system inactive by continually sending a beamlet at an arbitrary azimuthal position with an arbitrary phase tilt. Figure 9(a) depicts the received optical power without the use of the control system relative to the reference power level (blue line, 350$\mathrm{\mu}$W) measured through no turbulence. Figure 9(b) depicts the optical power received with the control system active, relative to the reference level. In Fig. 9, the red line indicates a -3 dB “fade threshold” from the reference power level. Of the 1244 realizations captured with the control system inactive, only 46% were above this fade threshold, compared to 94% above the fade threshold when the control system was on. Additionally, with the control system off, the average power loss across the 1244 realizations was over 5 dB, whereas when the control system was active the average power loss was less than 1.45 dB.
Fig. 9. Received optical power through turbulence relative to reference power taken without turbulence, (a) with control system off and (b) with control system on.
4.2 Improved recovery of high-speed communication link
To analyze the performance of this probe and control turbulence mitigation technique when transmitting and receiving a data link, a PAM2 signal was modulated on the beam with a data rate of 5Gbit/s. The methodology behind the modulation scheme of this signal is detailed in [15]. Each experiment lasted 12.44s and consisted of transmitting a signal through 1244 realizations of turbulence with a 10 ms sampling rate. In total, 8 experiments were conducted, and the results were analyzed. On average, the 5Gbit/s signal was recovered in 79% of the realizations while the probe and control system was active, compared to just 28% of the realizations having a recoverable signal when the system was inactive. This demonstrates a recoverability increase of over 50% in underwater turbulence, very closely matching the increase of optical power transmission discussed earlier. Figure 10 depicts the differences in the feedback scalograms and corresponding recovered signal when the probe and control system is active and inactive. Figure 10(a) depicts a realization where the control system is on and has identified a channel. This eye diagram (Fig. 10(b)) clearly shows the two voltage levels, and the SNR measured resembles that at the reference power level. In this realization, the 5 Gbit/s signal is recovered clearly. Comparatively, Fig. 10(c) illustrates a realization when the control system is inactive, with the beamlet position and phase gradient set arbitrarily. In this case, the stationary beamlet missed a channel, as the corresponding eye diagram (Fig. 10(d)) indicates nearly no separation between voltage levels. In this case, the SNR is not discernible from the noise floor of the oscilloscope. When the control system is on, the system will always pick the optimal beam state, however, due to a restricted scanning space, there is not a guarantee that a strong channel exists for every realization of turbulence. This limited scanning space is the reason why the signal recovery rate when the control system is active is not higher.
Fig. 10. (a) Controlled beamlet in a channel. (b) PAM2 eye diagram, hit channel. (c) Fixed beamlet (no control), missed channel. (d) Eye diagram, missed channel.
To further test the capabilities of this underwater turbulence mitigation scheme, a 32QAM 25 Gbit/s signal (methodology of signal creation detailed in [15]) is transmitted through the turbulence. Figure 10 displays multiple constellations from various realizations. The reference constellation through no turbulence (Fig. 11(a)) shows 32 separate constellations and has a BER of $1.28 \times {10^{ - 4}}$. Through turbulence, the constellations are reduced to an undiscernible conglomeration (Fig. 11(b)) with a BER of $0.073$, and no signal is present at the receiver side while the control system is inactive. Once the control system is active, the signal can be recovered through the turbulence and the constellations (Fig. 11(c)) return to a similar image as the reference constellation with a BER of $2.12 \times {10^{ - 5}}$. The constellations shown in Fig. 10(c) has a lower BER than that of the constellations from the no turbulence case (Fig. 11(a)). This is due to the focusing effects of the channels within the turbulence compared to the divergence of the beamlets when no turbulence is present because of the small beam size and short Rayleigh range.
Fig. 11. Constellations of 25 Gbit/s 32QAM signal (a) through no turbulence, (b) through turbulence, with control system inactive and (c) through turbulence with control system active.
5. Conclusions
This work details the application of a turbulence mitigation technique previously tested in atmospheric turbulence on the phenomena of underwater turbulence. A UTE was constructed and characterized using methods consistent with comparable underwater research tanks [27,35]. The characterization results indicate that a stable, repeatable turbulence level was generated. This setup provides the unique opportunity to experimentally test and analyze beam propagation through real-world underwater turbulence levels, as well as the ability to further explore varying turbulence conditions by adjusting the strength of the temperature gradient in the UTE. Specifically in this work, the UTE was utilized to test the validity of the turbulence mitigation technique, which involves rapidly scanning a Gaussian beamlet through discrete azimuthal positions about a vortex envelope, while also changing the OAM across the entire envelope. A modified HOBBIT system, reliant on two AODs, can switch beam states more rapidly than mechanical components of other adaptive optic systems, as well as more rapidly than the turbulence itself. This allows the optimal combination of position and phase to be determined for a single instance of turbulence, and the beam state is transmitted through the turbulence. By coupling into waveguide like channels within the turbulence, this mitigation technique allows for underwater optical systems to increase power efficiency and was also demonstrated to support a high data rate communication link. To extend the capabilities of this system, simultaneous beamlets that can be generated using the HOBBIT to aid in the exploitation of multiple channels will be implemented into the control system, using a customized FPGA. Multi-channel utilization will vastly improve data rates while also allowing for the transmission of encoded data through multiple paths. Additionally, preliminary results show that this system continues to perform well through a turbid and turbulent environment, indicating promising possibilities for optical system performance in a real-world underwater environment.
Funding
Multidisciplinary University Research Initiative (N00014-20-1-2558).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. G. Schirripa Spagnolo, L. Cozzella, and F. Leccese, “Underwater Optical Wireless Communications: Overview,” Sensors 20(8), 2261 (2020). [CrossRef]
2. Y. Baykal, Y. Ata, and M. C. Gökçe, “Underwater turbulence, its effects on optical wireless communication and imaging: A review,” Opt. Laser Technol. 156, 108624 (2022). [CrossRef]
3. H. Kaushal and G. Kaddoum, “Underwater Optical Wireless Communication,” IEEE Access 4, 1518–1547 (2016). [CrossRef]
4. M. Yousefi, F. Dabbagh Kashani, A. Aghajani, and M. R. Hedayati Rad, “Experimental study of the effects of thermally induced optical turbulence on underwater wireless optical communication link parameters,” J. Opt. 22(2), 025702 (2020). [CrossRef]
5. H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, M. Abdallah, T. K. Ng, M. Hamdi, M.-S. Alouini, and B. S. Ooi, “Simple statistical channel model for weak temperature-induced turbulence in underwater wireless optical communication systems,” Opt. Lett. 42(13), 2455 (2017). [CrossRef]
6. E. Zedini, H. M. Oubei, A. Kammoun, M. Hamdi, B. S. Ooi, and M.-S. Alouini, “Unified Statistical Channel Model for Turbulence-Induced Fading in Underwater Wireless Optical Communication Systems,” IEEE Trans. Commun. 67(4), 2893–2907 (2019). [CrossRef]
7. Z. Vali, A. Gholami, Z. Ghassemlooy, M. Omoomi, and D. G. Michelson, “Experimental study of the turbulence effect on underwater optical wireless communications,” Appl. Opt. 57(28), 8314 (2018). [CrossRef]
8. Y. Baykal, “Signal-to-noise ratio reduction due to oceanic turbulence in oceanic wireless optical communication links,” Opt. Commun. 427, 44–47 (2018). [CrossRef]
9. H. Gerçekcioğlu, “Bit error rate of focused Gaussian beams in weak oceanic turbulence,” J. Opt. Soc. Am. A 31(9), 1963 (2014). [CrossRef]
10. Y. Fu, Q. Duan, C. Huang, Y. Du, and L. Zhou, “Average BER performance of rectangular QAM-UWOC over strong oceanic turbulence channels with pointing error,” Opt. Commun. 476, 126362 (2020). [CrossRef]
11. M. C. Gökçe, Y. Baykal, and Y. Ata, “Effects of adaptive optics on bit error rate of M-ary PPM oceanic optical wireless communication systems with aperture averaging in strong turbulence,” Laser Phys. 31(11), 115204 (2021). [CrossRef]
12. W. Liu, Z. Xu, and L. Yang, “SIMO detection schemes for underwater optical wireless communication under turbulence,” Photonics Res. 3(3), 48 (2015). [CrossRef]
13. L. Zhu, H. Yao, H. Chang, Q. Tian, Q. Zhang, X. Xin, and F. R. Yu, “Adaptive Optics for Orbital Angular Momentum-Based Internet of Underwater Things Applications,” IEEE Internet Things J. 9(23), 24281–24299 (2022). [CrossRef]
14. L. Zhu, H. Yao, J. Wang, Q. Tian, Q. Zhang, and L. Hanzo, “Channel Modeling for Orbital Angular Momentum Based Underwater Wireless Optical Systems,” IEEE Trans. Veh. Technol. 71(6), 5880–5895 (2022). [CrossRef]
15. M. Lemon, E. Robertson, J. Free, K. Dai, J. K. Miller, L. Vanderschaaf, M. Cox, R. J. Watkins, and E. G. Johnson, “Sensing and coupling of optical channels in dynamic atmospheric turbulence using OAM beamlets for improved power and data transmission,” Opt. Express 30(26), 47598 (2022). [CrossRef]
16. A. Klug, C. Peters, and A. Forbes, “Robust structured light in atmospheric turbulence,” Adv. Photonics 5(01), (2023).
17. C. A. Friehe, J. C. La Rue, F. H. Champagne, C. H. Gibson, and G. F. Dreyer, “Effects of temperature and humidity fluctuations on the optical refractive index in the marine boundary layer,” J. Opt. Soc. Am. 65(12), 1502 (1975). [CrossRef]
18. P. M. Lushnikov and N. Vladimirova, “Toward Defeating Diffraction and Randomness for Laser Beam Propagation in Turbulent Atmosphere,” JETP Lett. 108(9), 571–576 (2018). [CrossRef]
19. E. G. Johnson, J. K. Miller, R. J. Watkins, K. Morgan, W. Li, K. Dai, C. O’Donnell, and G. White, “Higher-order Bessel beams integrated with time (HOBBIT) for dynamic structured light control,” in Complex Light and Optical Forces XIV, D. L. Andrews, E. J. Galvez, and H. Rubinsztein-Dunlop, eds. (SPIE, 2020), p. 29.
20. W. Li, K. S. Morgan, Y. Li, J. K. Miller, G. White, R. J. Watkins, and E. G. Johnson, “Rapidly tunable orbital angular momentum (OAM) system for higher order Bessel beams integrated in time (HOBBIT),” Opt. Express 27(4), 3920 (2019). [CrossRef]
21. R. J. Watkins, K. Dai, G. White, W. Li, J. K. Miller, K. S. Morgan, and E. G. Johnson, “Experimental probing of turbulence using a continuous spectrum of asymmetric OAM beams,” Opt. Express 28(2), 924 (2020). [CrossRef]
22. J. Free, K. Dai, L. Vanderschaaf, M. Cox, J. K. Miller, R. J. Watkins, and E. G. Johnson, “OAM-based optical wavelet using a single pixel detection system for probing dynamic environments with application to real-time measurements of strong atmospheric turbulence,” Opt. Express 30(23), 42564 (2022). [CrossRef]
23. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
24. M. C. Roggemann and B. Welsh, Imaging through Turbulence, The CRC Press Laser and Optical Science and Technology Series (CRC Press, 1996).
25. S. Avramov-Zamurovic, K. P. Judd, S. Matt, R. A. Handler, A. T. Watnik, J. R. Lindle, J. M. Esposito, and W. A. Jarrett, “Propagating beams carrying orbital angular momentum through simulated optical turbulence generated by Rayleigh–Bénard natural convection,” Waves in Random and Complex Media 1–21 (2023).
26. V. V. Nikishov and V. I. Nikishov, “Spectrum of Turbulent Fluctuations of the Sea-Water Refraction Index,” Int. J. Fluid Mech. Res. 27(1), 82–98 (2000). [CrossRef]
27. G. Nootz, S. Matt, A. Kanaev, K. P. Judd, and W. Hou, “Experimental and numerical study of underwater beam propagation in a Rayleigh–Bénard turbulence tank,” Appl. Opt. 56(22), 6065 (2017). [CrossRef]
28. O. Korotkova, “Light Propagation in a Turbulent Ocean,” in Progress in Optics (Elsevier, 2019), 64, pp. 1–43.
29. G. Nootz, E. Jarosz, F. R. Dalgleish, and W. Hou, “Quantification of optical turbulence in the ocean and its effects on beam propagation,” Appl. Opt. 55(31), 8813 (2016). [CrossRef]
30. L. C. Andrews, Laser Beam Propagation through Random Media (SPIE Press, 2005).
31. I. Thormählen, J. Straub, and U. Grigull, “Refractive Index of Water and Its Dependence on Wavelength, Temperature, and Density,” J. Phys. Chem. Ref. Data 14(4), 933–945 (1985). [CrossRef]
32. M. Beason, S. Gladysz, and L. Andrews, “Comparison of probability density functions for aperture-averaged irradiance fluctuations of a Gaussian beam with beam wander,” Appl. Opt. 59(20), 6102 (2020). [CrossRef]
33. H. Kaushal, V. Kumar, A. Dutta, H. Aennam, V. K. Jain, S. Kar, and J. Joseph, “Experimental Study on Beam Wander Under Varying Atmospheric Turbulence Conditions,” IEEE Photon. Technol. Lett. 23(22), 1691–1693 (2011). [CrossRef]
34. R. L. Phillips, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng 45(7), 076001 (2006). [CrossRef]
35. S. Matt, W. Hou, W. Goode, and S. Hellman, “Introducing SiTTE: A controlled laboratory setting to study the impact of turbulent fluctuations on light propagation in the underwater environment,” Opt. Express 25(5), 5662 (2017). [CrossRef]
