Tapping underwater wireless optical communication in pure water and natural Dead-Sea ultra-high-salinity water by diffraction grating

Dor Shaboy; Dror Rockban; Amir Handelman

doi:10.1364/OE.26.029700

1. Introduction

Although water is known to be a poor media for propagation of light beams due to significant scattering and absorption properties, Underwater Wireless Optical Communication (UWOC) has attracted a lot of attention recently [1-4]. UWOC systems may be used for oceanographic studies, such as sea-floor survey and pollution control [5] and for military applications, such as aircraft-submarines communication [6], and could be deployed in underwater imaging systems, such as light detection and ranging (LIDAR) [7].

Current research activities in UWOC have mainly focused on increasing data rates and transmission distance, [5,8-11] improving performance [12,13], developing better transmitters and receivers [14-16], establishing networking protocols [17,18], using advanced modulation formats [8–11,14], and transmitting video [19]. All of these developments use the cumulative knowledge of channel models in different water types [20,21] to customize their solutions to such harsh aqueous environment.

With the increase interest in high-speed long-range UWOC systems, security issues become important [22,23]. And yet, little research has been done so far on security weaknesses (such as channel tapping) of UWOC. In the work [23], a mirror placed between the transmitter and a receiver was used to deflect the direct line-of-sight (LOS) beam towards the eavesdropping receiver module. This method requires fine-tuning of the mirror if the eavesdropper does not want to be identified.

In this paper, we show how one could tap an optical communication channel between a sender and an addressee without their awareness by using a diffraction grating in two extreme water types: (1) sweet, pure, municipal water, and (2) natural ultra-salty water taken directly from the Dead-Sea, a unique place in the world. Since it is well known today that a variety of instruments, such as smart televisions, and Internet-of-Things (IoT) devices can “spy” on users using electronic components that the users are not aware of, we hypothetically relate to a reasonable hacking scenario of adding a secret optical element (such as a diffraction grating) to an UWOC system by an enemy diver or unmanned underwater vehicles (UUV).

We also investigated how far from the addressee a message can be tapped, and discuss the different possibilities to tap the channel – one from the air and one underwater. We believe that by flooding this problem, countermeasures to better secure UWOC will be developed and implemented.

2. Experimental setup

Our aim is to show that eavesdropping is possible from a distance without the awareness of the sender and the addressee by using an amplitude diffraction grating. In order to prove this concept, two setups were designed. Setup A included a grating outside a water tank. This setup simulates eavesdropping off-water, i.e., a case in which an eavesdropper attempts to hack the free-space optical communication (FSOC) channel before light enters the water. Setup B included a grating inside the water tank. It simulates hacking scenarios such as eavesdropping to a fixed underwater optical communication system at a harbour or lake by divers or UUVs.

The experimental setups that demonstrate our principle of tapping an UWOC channel are illustrated in Fig. 1. In both setups the transmission module included a waveform generator (Tektronix 33500B), and a laser diode (LD) operated at 520 nm (PL520, Thorlabs) and mounted on a temperature-controller (TCLDM9, Thorlabs) that was connected to a LD controller (LDC205, Thorlabs). An arbitrary 7-sec voice signal, presented as inset graph in Fig. 1, was recorded offline and fed to the waveform generator (WG). The voice signal (represents the message) sampled at a sampling rate of 8kSa/sec modulated the LD emitted light with a sampling rate of 40 kSa/sec. The input voltage peak-to-peak (Vpp) of the voice signal remained constant at 340 mV, and the DC current for the LD controller was set to 70 mA for both experimental setups, which attributed to P_opt ~27 mW optical output power. The modulated light from the LD passed through a lens having a focal length of 5 cm and positioned so that the LD was at the focal point of the lens. The light exiting from the lens then passed through a diaphragm positioned at a distance of 10 cm from the lens.

Fig. 1 Sketch that demonstrates experimental model of underwater channel tapping by diffraction grating. A 7-sec voice signal modulates a 520 nm green laser beam that impinges on the grating, and is divided into several diffraction orders. A detector is placed at a position along the Line-of-Sight of the 0-order light beam, while the other beams continue to propagate in different directions. In Setup A, the grating is outside the water tank, and in Setup B the grating is inside the water tank.

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In setup A, a diffraction grating presented as inset in Fig. 1, with a pitch of 30 µm, and a fill factor of a = 1/7 was placed between the diaphragm and the water tank at a distance of 26 cm from the diaphragm and at a distance of 20 cm from the water tank. In setup B the diffraction grating was placed inside the water tank. The diffraction grating diffracts beams impinging thereon. In setup A, all diffraction orders pass through the air in the space between the diffraction grating and the water tank and then through the water tank (with volume of 98x29x50 cm³). In setup B, all diffraction orders pass through the water tank.

In both setups, a receiver module that included a Si photodiode detector (SM05PD1A, Thorlabs) connected to a Digital Storage Oscilloscope (DSO7012A, Agilent Tech.) was used. The detector was positioned in different locations to detect the beam of the 0-order and the beam of the 1-order, as shown in Figs. 4(a) and 4(c).

The 0-order beam simulates the direct communication of the voice signal (the message) from the sender to the addressee because it is along the direct LOS between the sender and the addressee. The 1-order beam (as well as higher order beams) is deflected from the direct LOS and can therefore be detected by a detector placed to detect it away from the direct LOS. Thus, if an eavesdropper places a diffraction grating as mentioned above along the direct LOS between the sender and the addressee and places a detector (connected to a receiver module) in a position suitable for detecting higher order beam, the eavesdropper can listen to the message received over the high order beam when the addressee listens to the message received over the 0-order beam. In our experiment we used the same detector (and receiver module) to detect the 0-order beam and the 1-order beam by placing the detector at the appropriate different locations outside the water tank. Although in a real case scenario of UWOC the detectors of the addressee and the eavesdropper are both expected to be in the water, use of the detector outside the water tank is still appropriate because the walls of the water tank do not change the basic concept of the deflection of the 1-order beam.

The experiment was first performed with an empty tank. We then filled the water tank with municipal fresh water, and afterwards with ultra-salty water taken directly from the Dead-Sea in Israel in 6 bottles of 2 litters each. Figure 2(b) shows how the light beam propagates in setup A. The green laser beam impinges the grating and then diffracts, and all diffraction orders beams enter the tank filled with water. Each beam propagates in a different direction, spreads [24,25], and then exits the water tank. In Fig. 2(b), the detector covers the 0-order, and the rest of the beams continue to propagate in the air until they reach a screen behind the detector, where all the diffraction orders (besides the 0-order) are seen. The same procedure was done for the 1-order, and for setup B.

Fig. 2 (a) Simulation of the propagation of the Gaussian laser beam in Setup A. A green-color Gaussian beam impinges upon a binary amplitude diffraction grating, and splits into different orders with intensity coefficients of ${| sinc (a m) |}^{2}$ . The beams enter the water tank and propagate in the water for a distance of 1-m. Each beam diverges, spreads and experiences intensity loss due to absorption and scattering in water. A detector is placed to collect the 0-order beam. (b) A photo of the outputs of setup A. The green laser beam impinges upon the grating, and splits into several diffraction orders. Multiple beams are now propagating ins the water. A detector is placed in a position that is in the direction of the 0-order light beams, while the other beams continue to propagate in different directions.

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3. Concept of channel tapping and eavesdropping using a diffraction grating

When laser light impinges normally upon the diffraction grating, it diffracts according to the well-known diffraction grating law [24]:

\frac{m λ}{Λ} = n_{i} \sin (θ_{i}) + n_{m e d} \sin (θ_{m e d})

where m is the diffraction order (m = 0, ± 1, ± 2,…), Λ is the distance between the slits (in our grating it equals 30μm), λ is the wavelength (for our green laser illumination, λ = 0.52μm), $n_{i}$ and $θ_{i}$ are the media's refractive index and angle of the incident beam, respectively, and $n_{m e d}$ and $θ_{m e d}$ are the media's refractive index and angle of the diffracted beam, respectively. In Setup A [Fig. 1(a)], the grating was positioned in the air and the beams diffracted also in air so $n_{i} = n_{m e d} = 1$ . As such, the diffraction angle was 0.9932° for every order and for normal illumination of the grating. Setup A models channel tapping outside the water, for example, by placing the grating before the laser beam enters the water. In setup B [Fig. 1(b)], the grating was positioned inside the water tank. As such, the diffraction angle was ~0.767° for every order in pure water having a refractive index of $n_{i} = n_{m e d} = 1.33$ [1]. Setup B models channel tapping in the water, for example putting a hacking device next to a submarine or an UUV.

The 0-order (m = 0) beam continues in a straight line without deviation from the direct LOS between the receiver and the transmitter, whereas other orders deviate from the LOS in accordance with their diffraction angles. If we place a binary amplitude diffraction grating in a random location along the LOS, neither the addressee nor the sender will be aware that such a device was added because the 0-order beam, which has also the maximum intensity [24,25], will still reach the receiver in the same direction and angle as the beam without the grating. In order to tap the communication, an attacker could detect the weaker high-orders beams that propagate far-away from the 0-order light beam. Unlike using a mirror for eavesdropping [23], with a diffraction grating an attacker could hack the channel far-away from the receiver, without the awareness of both the sender and the addressee.

We are now in a position to ask how far from the receiver an attacker can hack the communication channel without being exposed. The answer to this question is divided into two regimes: an attacker can eavesdrop far away from the receiver in the x-axis (on the left or right side of the addressee) or in the z-axis (behind the addressee), as presented in Fig. 2.

3.1 Diffraction of a Gaussian beam

Let us follow the laser light beam in our setups [Fig. 2], where we used binary diffraction grating with the pitch of $Λ =$ 30 μm. Suppose that the incident field amplitude in our setup is a Gaussian beam of the form [25]:

u_{i} (x, y, 0) = \exp (- π \frac{x^{2} + y^{2}}{ω_{0}^{2}})

where

w_{0}

is the radius of the Gaussian beam waist, which is half the spot size.

The amplitude transmission function, $t (x, y)$ of a binary amplitude grating has the following form:

t (x, y, 0) = (r e c t (\frac{x}{a Λ}) r e c t (\frac{y}{d}) \otimes \sum_{m = - \infty}^{\infty} δ (x - m Λ)) r e c t (\frac{x}{B}) r e c t (\frac{y}{B})

where

\otimes

denotes convolution,

δ

is the Dirac delta function,

Λ

is the pitch, a is the fill factor,

m = 0, \pm 1, \pm 2, ..

, B is the width of the square aperture bounding the grating, and d is the longitudinal distance which is much larger than

a

, i.e., (

d > > a Λ

)[24]. If the grating is normally illuminated by the Gaussian laser beam, then at the exit of the grating the field amplitude will be:

u_{t} (x, y, 0) = \exp (- π \frac{x^{2} + y^{2}}{ω_{0}^{2}}) t (x, y, 0)

In our setups, we can infer to the far-field Fraunhofer distribution, since the distance z from the grating to the water tank (20 cm in setup A) or to the exit plane from the water tank (50 cm in setup B) is much larger than

\frac{2 Λ^{2}}{λ} = 0.35

cm. As such, we can estimate the amplitude of the field at a distance z from the grating from the Fourier transform (marked as

ℑ {•}

) of

u_{t} (x, y, 0)

which is [25]:

U_{t} (f_{x}, f_{y}) = ℑ {u_{t} (x, y, 0)} = \int \int_{- \infty}^{\infty} u_{t} (x, y, 0) \exp [- j 2 π (x f_{x} + y f_{y})] d x d y = U_{i} (f_{x}, f_{y}) \otimes T (f_{x}, f_{y})

where

f_{x} = \frac{x}{λ z}

and

f_{y} = \frac{y}{λ z}

are the spatial frequencies, and

U_{i} (f_{x}, f_{y}), T (f_{x}, f_{y})

are the Fourier transforms of

u_{i} (x, y, 0)

and

t (x, y, 0)

, respectively. We can disregard the y component and use the separability property, since the product

r e c t (\frac{y}{d})

r e c t (\frac{y}{B})

does not depend on the diffraction orders m. The Fourier transform of the amplitude transmission function of the grating in the x-axis only is [24]:

T (f_{x}) = (\sum_{m = - \infty}^{\infty} a \sin c (a m) δ (f_{x} - \frac{m}{Λ})) \otimes B \sin c (B f_{x})

where we used the property of multiplication of delta function and the definitions for comb:

\frac{1}{Λ} c o m b (\frac{x}{Λ}) = \sum_{m = - \infty}^{\infty} δ (x - m Λ)

ℑ {\frac{1}{Λ} c o m b (\frac{x}{Λ})} = c o m b (Λ f_{x}) = \frac{1}{Λ} \sum_{m = - \infty}^{\infty} δ (f_{x} - \frac{m}{Λ})

The field at the exit of the binary grating is (for the x-axis only):

\begin{array}{l} U_{t} (f_{x}) = ω_{0}^{2} \exp (- π ω_{0}^{2} f_{x}^{2}) \otimes (\sum_{m = - \infty}^{\infty} a \sin c (a m) δ (f_{x} - \frac{m}{Λ})) \otimes B \sin c (B f_{x}) = \\ a ω_{0}^{2} (\sum_{m = - \infty}^{\infty} \sin c (a m) \exp (- π ω_{0}^{2} {(f_{x} - \frac{m}{Λ})}^{2}) \otimes B \sin c (B f_{x}) \end{array}

The analytic solution to this convolution [26,27] is (Appendix):

U_{t} (f_{x}) = a ω_{0}^{3} \sum_{m = - \infty}^{\infty} \sin c (a m) \exp (- π ω_{0}^{2} {(f_{x} - \frac{m}{Λ})}^{2}) [Re {e r f (\frac{B \sqrt{π}}{2 ω_{0}} + j \sqrt{π} ω_{0} (f_{x} - \frac{m}{Λ}))})]

Equation (10) shows that we will get m Gaussian functions, separated by

Δ x = \frac{λ z}{Λ}

from each other. Thus, at spatial coordinates the intensity of each shifted Gaussian beam that depends on diffraction order m is [24]:

I_{m} = {| U_{m} |}^{2} \propto {| \sin c (a m) |}^{2}

These diffraction orders are seen at

x_{m} = \frac{λ z}{Λ} m

. Now that we obtained the intensity of every diffraction order at the entrance plane of the water tank we can follow the propagation of each order in the water.

3.2 Propagation of diffracted Gaussian beams in water

As light travels in water, it suffers from power degradation and beam spreading [28] in the spatial domain (as well as in the angular, polarization and temporal domains) due to effects of absorption and scattering that depend on water type [1]. For a LOS communication link as in our setups, where the receiver and transmitter are aligned, the received power at the detector that travels underwater can be written as [28]:

P_{z} = P_{0} η_{T} η_{R} \frac{A}{π {(z \tan (θ_{d}))}^{2}} \exp (- c z) = {\tilde{P}}_{0} \exp (- c z)

where

η_{T}

and

η_{R}

are the transmitter and receiver efficiencies, respectively,

P_{0}

is the incident power,

\exp (- c z)

is the loss due to propagation at a distance z in the water with extinction ratio c, A is the receiver aperture area, and

ϑ_{d}

is the laser beam divergence angle, which in our case is very narrow and much smaller than

π / 20

[28]. As clearly seen from Eq. (11), the received power depends on different water types through the extinction coefficient, c.

The spreading of each Gaussian beam is mainly due to the scattering effect in water [1]. This is usually modelled by a Monte-Carlo algorithm (MCA), where the position of the photons is constantly updated by the random path lengths and scattering angles [29]. A simulation of the diffraction-orders Gaussian beams widening for z = 1 m can be viewed in Fig. 2(a). The simulation procedure is mainly based on [30], and was designed for clear ocean water and for simple isotropic scattering. As can be noticed from Fig. 2(a), photons appear outside the original Gaussian beams' radiuses. For a large number of photons or a longer distance, scattering can severely affect the beam's spot size.

4. Experimental results and discussion

In order to check if our UWOC system is feasible for various water types and to examine the cases of eavesdropping in free-space and underwater (a scenario that simulates tapping communication to submarines or UUV), we designed Setup A and Setup B, which their sketch is presented in Fig. 1. For reference, we first detected the voice signal when the tank was empty, as shown in Fig. 3. The diffracted pattern can be viewed in Fig. 3, where the detector was positioned to receive the 0-order [Fig. 3(a)] and 1-order [Fig. 3(c)]. As can be seen in Fig. 3, the voice signal can be deduced also from 1-order beam.

Fig. 3 Eavesdropping in free-space (Setup A). (a) Image of all diffraction orders on a screen behind the detector, which is positioned directly to detect the 0-order beam. (b) Part of the input voice signal (green), and detected voice signal from the 0-order beam (yellow). (c) Image of all diffraction orders on a screen behind the detector, which is positioned directly to detect the 1-order beam. (d) Part of the input voice signal (green), and detected voice signal from the 1-order beam (yellow). The SNR is ~52 dB (for 0-order beam) and ~41 dB (for 1-order beam).

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It is to be noted that we kept the input root-mean-square (RMS) voltage constant (1.35 V) throughout all the experiments and hence we can estimate intensity degradation between the 1-order and 0-order. Furthermore, the detector's noise (expressed in RMS voltage) in ambient conditions of our measurements was 800 μV, which allows us to calculate the signal-to-noise (SNR) ratio for each m-order beam. It is apparent that the light intensity of the 1-order beam is ~3.5 smaller than the light intensity of the 0-order beam. This degradation is mainly due to differences in the transmission coefficients since air attenuation, laser wavelength, responsivity of the detector ( $ℜ$ ), load resistance, and distance remain unchanged.

In order to prove that underwater eavesdropping is possible from a distance without the awareness of the sender and the addressee, we performed the experiment again, but this time with the tank filled with municipal pure water. Figure 4 shows that eavesdropping is possible even when the grating is positioned inside the water, as indicated in Figs. 4(b) and 4(d). In both setups, the voice signal is detected at the 0-order and the 1-order. In Setup A, the intensity of the 1-order is ~2.3 smaller than the intensity of the 0-order, and the intensity of the 0-order in water is ~3.2 smaller than the intensity of the 0-order in free-space. In Setup B, where the grating is inside the water tank, the intensity of the 1-order is ~2.7 smaller than the intensity of the 0-order as indicated in Figs. 4(b) and 4(d). We should also note that the intensities of the 0-order and the 1-order in Setup B are ~2 smaller than the corresponding ones in Setup A.

Fig. 4 Eavesdropping in pure water. (a) Part of the input voice signal (green), and detected voice signal from the 0-order beam (yellow) in Setup A. The SNR is ~42 dB. (b) Part of the input voice signal (green), and detected voice signal from the 0-order beam (yellow) in Setup B. The SNR is ~37 dB. (c) Part of the input voice signal (green), and detected voice signal from the 1-order beam (yellow) in Setup A. The SNR is ~35 dB. (d) Part of the input voice signal (green), and detected voice signal from the 1-order beam (yellow) in Setup B. The SNR is ~29 dB.

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Motivated by the feasibility of our setups in pure water, we were intrigue to examine if channel tapping can also be done in high-salinity water. We collected 12 liters of water directly from the Dead-Sea located in Israel [Fig. 5], and checked if we can tap the channel in this water type. So far, little research has been conducted to study the optical properties of Dead-Sea water at visible wavelengths and to the best of our knowledge, in this work we show for the first time the possibility of UWOC in such high-salinity water. This is the place to note that the Dead-Sea is a hypersaline lake located in the rift valley between Israel and Jordan, and is known as the lowest water body on Earth [31]. It has a salinity of ~270 g/kg, which is almost ~7 times higher than the salinity of sea water [32]. The absorption coefficient, [31] around 520 nm is approximately ~0.15 m⁻¹. The scattering coefficient, b, of the Dead-Sea water around 520 nm is absent in the literature, but we can estimate it from linear extrapolation of scattering as a function of salinity, which appears in [32], and get that its value is around ~0.0042 m⁻¹. These values are higher than the absorption and scattering coefficients of pure sea water (0.0405 m⁻¹ and 0.0025 m⁻¹, respectively [23]) and thus it is not surprising that the attenuation of Dead-Sea water is larger than that of pure water.

Fig. 5 Eavesdropping in natural water from the Dead-Sea. (a) Collection of natural water from the Dead-Sea. (b) Part of the input voice signal (green), and detected voice signal from the 0-order beam (yellow) in Setup A. The SNR is ~37 dB. (c) Part of the input voice signal (green), and detected voice signal from the 1-order beam (yellow) in Setup A. The SNR is ~33 dB.

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Figure 5 depicts detection of the voice signal from the 0-order and 1-order beams that propagate in the natural Dead-Sea water [Fig. 5(a)]. As can be seen, the intensity of the 1-order beam is ~1.55 smaller than the intensity of the 0-order beam. Note that the 0-order of natural Dead-Sea water has lower intensity than that of pure water due to the larger extinction coefficient, c, of high-salinity water.

We can now evaluate how far from the addressee one can tap the message. In principle, eavesdropping can be performed at any order m of the laser beam other than the 0-order beam [Fig. 2(a)] (the detector is placed to detect the 0-order beam which does not deflect from the LOS [Eq. (1)]). This is the advantage of using a diffraction grating and not, for example, a beam splitter. The highest detectable order of the laser beam determines the farthest distance from the addressee (in the x-axis in the plane of the detector) at which the message can still be tapped, and for a given minimum detectable intensity of the detector the highest detectable order of the laser beam depends on the distance in the z-axis. Thus, by knowing the minimum detectable intensity at the detector, we can find the number of the most far away detectable order beam, m, for a given distance d in the z-axis from the source and calculate the distance in the x-axis from the 0-order (detector) to the m order. The detectable signal's power $P_{z m}$ that depends on m at distance d and for a fill factor $α$ is given by the product of Eq. (11) and Eq. (12):

P_{z m} = P_{i n} \exp (- c d) {| \sin c (a m) |}^{2}

where

P_{i n} = {\tilde{P}}_{0} \cos ϕ = {\tilde{P}}_{0} \frac{z}{d}

[28], and each m-order beam travels a distance of

d = \sqrt{z^{2} + x_{m}^{2}}

. The voltage obtained from the detector that corresponds to

P_{z m}

is

V_{z m} = ℜ P_{z m}

, where

ℜ

is the responsivity of the detector.

The results of such simulations are shown in Fig. 6 for various distances d in the z-axis and for clear ocean water (c = 0.151 1/m). We substituted the minimum detectable detector’s signal power $P_{m i n}$ (40 nW) for $P_{z m}$ in Eq. (12) to obtain the highest detectable order $m_{\max}$ , and deduced $x_{m a x}$ (according to $\frac{λ z}{Λ} m_{\max}$ ), where $x_{m a x}$ is the maximum distance from the original detector in the x-axis at which an eavesdropper may place a secret detector for tapping the message.

Fig. 6 The relation between the location of the diffraction grating in the z-axis and the maximum displacement in the x-axis at which an attacker can place a secret detector for eavesdropping. The simulation was performed for an input power of 5 mW, a minimum detectable dark power of 40 nW, and for clear ocean water (c = 0.151 1/m).

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The results in Fig. 6 show that the maximum displacement $x_{m a x}$ increases with the increase of the distance d (the position of the grating from the sender) in the z-axis for values of d up to ~20 m although signal power decreases as $m_{\max}$ (and accordingly $x_{m a x}$ ) increases. This is because of the phenomenon that separation between the orders increases with the increase in z as mentioned above (see the discussion regarding Eq. (9)). However, for values of d beyond ~20 m, such phenomenon does not dominate any more, and the decrease in signal power as $m_{\max}$ (and accordingly $x_{m}$ ) increases dominates instead.

Another point that can be concluded from Fig. 6 is that use of a grating with a small fill factor increases the maximum distance in the x-axis at which the eavesdropper can place the secret detector.

Eavesdropping can also be performed by detecting the signal behind the addressee's original detector [Fig. 2(a)] with some deviation (in the x-axis) from the LOS. Since orders ± 1 have the second strongest intensity after the 0-order beam [24], the secret detector can be placed along the path of these orders behind the addressee's original detector. The maximum excess distance, $z_{\max}$ , in the z-axis for detection of the 1-order (m = 1) behind the addressee's original detector can be deduced from:

P_{\min} = P_{d} \exp (- c z_{\max}) {| \sin c (a) |}^{2}

where

P_{d}

is the power of the 1-order beam at some point along the z-axis in water. We can easily deduce the distance at which one can tap the signal for a fill factor of a = 1/7:

z_{\max} = \frac{1}{c} [\ln (\frac{P_{d}}{P_{\min}}) - 0.0676]

As an example, suppose that the power obtained at some distance along the z-axis in pure water ( $c = 0.043$ m⁻¹ [23]) from a Gaussian laser 1-order beam (m = 1) is $P_{d} = 1$ μW at λ = 520 nm. For a minimum detectable power assumed as before ( $P_{\min} = 40$ nW), we get $z_{\max} ~ 73$ m behind the addressee's original detector. If the power obtained at some distance along the z-axis in Dead-Sea water having an approximate extinction coefficient of $c = 0.1542$ m⁻¹, then we get $z_{\max} ~ 20$ m behind the addressee's original detector. Of course that these values depend on the water type, minimum detectable power and input power. Knowing the upper limit of the distances at which one can tap the received signal allows better protection against eavesdroppers at an underwater area where UWOC is used.

5. Conclusions

In this paper, we showed that hacking UWOC is feasible for different types of water by using a diffraction grating. Such channel tapping can be done in the portion of the channel that is in the water or in the portion that is in the air. We analyzed the propagation of diffracted Gaussian beams in water and calculated the distances for which one can still tap UWOC. We also demonstrated for the first time transmission of information through ultra-high salinity Dead-Sea water. This means that UWOC is possible even in high salty water. The aim of this work is to flood the security issues of UWOC, and to shed light on different ways to tap a channel having at least an underwater portion, besides the natural scattering effect. We stress that in designing secure UWOC, one should be able to prevent the possibility of inserting optical elements that may be used for tapping the system, and not only to deploy advanced encryption methods.

6 Appendix

The convolution in Eq. (9) can be written explicitly as:

U_{t} (f_{x}) = a ω_{0}^{2} \sum_{m = - \infty}^{\infty} \sin c (a m) \int_{- \infty}^{\infty} \exp (- π ω_{0}^{2} {(f_{x} - f_{x}^{'} - \frac{m}{Λ})}^{2}) B \sin c (B f_{x}^{'}) d f_{x}^{'}

By noting the following:

\begin{array}{l} f_{0} = f_{x} - \frac{m}{Λ} \\ s = π ω_{0}^{2} \\ \frac{1}{π} \int_{0}^{B π} \cos (β f_{x}) d β = B \sin c (B f_{x}) \end{array}

and substituting these notations, we get:

U_{t} (f_{x}) = \frac{a ω_{0}^{2}}{π} \sum_{m = - \infty}^{\infty} \sin c (a m) \int_{- \infty}^{\infty} \exp (- s {(f_{0} - f_{x}^{'})}^{2}) d f_{x}^{'} \int_{0}^{B π} \cos (β f_{x}^{'}) d β

Now let us change variables

u = f_{x}^{'} - f_{0}

so the integration is:

\begin{array}{l} U_{t} (f_{x}) = \frac{a ω_{0}^{2}}{π} \sum_{m = - \infty}^{\infty} \sin c (a m) \int_{- \infty}^{\infty} \exp (- s u^{2}) \cos (β u + β f_{0}) d u \int_{0}^{B π} d β = \\ \frac{a ω_{0}^{2}}{π} \sum_{m = - \infty}^{\infty} \sin c (a m) \int_{- \infty}^{\infty} \exp (- s u^{2}) [\cos (β u) \cos (β f_{0}) - \sin (β u) \sin (β f_{0})] d u \int_{0}^{B π} d β \end{array}

Since the integrand with

\sin (β u)

is odd, and integration over a symmetrical range gives 0, and so we can write using Eq. (9) in [26] –

\begin{array}{l} U_{t} (f_{x}) = \frac{a ω_{0}^{2}}{π} \sum_{m = - \infty}^{\infty} \sin c (a m) \int_{- \infty}^{\infty} \exp (- s u^{2}) \cos (β u) d u \int_{0}^{B π} \cos (β f_{0}) d β = \\ = \frac{a ω_{0}^{2}}{π} \sum_{m = - \infty}^{\infty} \sin c (a m) \int_{0}^{B π} \exp (- \frac{β^{2}}{4 s}) \cos (β f_{0}) d β \end{array}

And the last integral equals to (using

v = \frac{β}{2 \sqrt{s}} - j \sqrt{s} f_{0}

and

t = \frac{β}{2 \sqrt{s}} + j \sqrt{s} f_{0}

) –

\begin{array}{l} U_{t} (f_{x}) = \frac{a ω_{0}^{2}}{π} \sum_{m = - \infty}^{\infty} \sin c (a m) \int_{0}^{B π} \exp (- \frac{β^{2}}{4 s}) \frac{[\exp (j β f_{0}) + \exp (- j β f_{0})]}{2} d β = \\ \frac{a ω_{0}^{2}}{2 π} \sum_{m = - \infty}^{\infty} sinc (a m) \int_{0}^{B π} [\exp (- {(\frac{β}{2 \sqrt{s}} - j \sqrt{s} f_{0})}^{2} - s f_{0}^{2}) + \exp (- {(\frac{β}{2 \sqrt{s}} + j \sqrt{s} f_{0})}^{2} - s f_{0}^{2})] d β = \\ = \frac{a ω_{0}^{2}}{2 π} \sum_{m = - \infty}^{\infty} sinc (a m) [2 \sqrt{s} \exp (- s f_{0}^{2}) \int_{- j \sqrt{s} f_{0}}^{\frac{B π}{2 \sqrt{s}} - j \sqrt{s} f_{0}} \exp (- v^{2}) d v + 2 \sqrt{s} \exp (- s f_{0}^{2}) \int_{j \sqrt{s} f_{0}}^{\frac{B π}{2 \sqrt{s}} + j \sqrt{s} f_{0}} \exp (- t^{2}) d t] = \\ \frac{a ω_{0}^{3}}{2} \sum_{m = - \infty}^{\infty} sinc (a m) \exp (- s f_{0}^{2}) [e r f (\frac{B π}{2 \sqrt{s}} - j \sqrt{s} f_{0}) - e r f (- j \sqrt{s} f_{0}) + e r f (\frac{B π}{2 \sqrt{s}} j \sqrt{s} f_{0}) - e r f (j \sqrt{s} f_{0})] = \\ a ω_{0}^{3} \sum_{m = - \infty}^{\infty} sinc (a m) \exp (- s f_{0}^{2}) [Re {e r f (\frac{B π}{2 \sqrt{s}} + j \sqrt{s} f_{0})})] \end{array}

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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Tapping underwater wireless optical communication in pure water and natural Dead-Sea ultra-high-salinity water by diffraction grating

Abstract

1. Introduction

2. Experimental setup

3. Concept of channel tapping and eavesdropping using a diffraction grating

3.1 Diffraction of a Gaussian beam

3.2 Propagation of diffracted Gaussian beams in water

4. Experimental results and discussion

5. Conclusions

6 Appendix

Disclosures

References

Cited By

Figures (6)

Equations (21)

Optics Express