rus
Issue #3/2019
V. V. Grishachev
Traffic Interception in Optical Network: Informative Parasitic Electromagnetic Radiation
Traffic Interception in Optical Network: Informative Parasitic Electromagnetic Radiation
The paper presents an analysis of the possibility of forming an informative radio band signal in optical networks on the basis of non-linear optical generation of difference frequencies. On the basis of a simplified physical model of traffic interception in optical networks with amplitude modulation, power estimates of the informative parasitic electromagnetic radiation are obtained. The model and estimates show the reality of remote traffic interception in optical networks. The most dangerous parts of the optical network and some methods of increasing the efficiency of interception are discussed. Also, methods of traffic protection by technical means are offered.
DOI: 10.22184/1993-7296.FRos.2019.13.3.280.294
DOI: 10.22184/1993-7296.FRos.2019.13.3.280.294
Теги: informative parasitic electromagnetic radiation technical means of traffic protection traffic intercept in optical network информативные паразитные электромагнитные излучения перехват трафика в оптических сетях технические средства защиты трафика
The transition in cable communication systems from copper (electrical) to optical (dielectric) cable has led to an increase in all information transmission characteristics: throughput, range, reliability, durability and protection [1–4]. The latter advantage is associated with the absence of side electromagnetic radiation (SEMR) during the passage of light through the dielectric channel (optical fibre), the absence of which does not exclude the possibility of interception of the transmitted information [4].
Traffic interception in optical networks [4–10]. The main methods of interception are connected with the formation of optical informative signals by outputting a part of the optical information signal, e. g., by removing a part of the radiation when the fibre is bent; registration of side optical radiation on the basis of leaky modes in the initial part of the optical fibre or scattered radiation in other parts of the optical network. Features of the propagation of light in the fibre, the design of the optical cable limit the possibilities of interception based on optical informative signals by the difficulties of registering fast processes with limited optical power output; the development of optical network monitoring technology using reflectometric and other methods.
Theoretical analysis of the physical features of the propagation of light in the fibre and the practical search for technical implementations of existing fibre-optic technologies allows us to offer new ways to intercept traffic, including on the basis of parasitic electromagnetic radiation generated as a result of non-linear-optical transformations in the fibre. The essence of this interception comes down to the fact that information is encoded in optical networks at speeds up to C = 100 Gbit / s and corresponding modulation frequencies of the order of f = 100 GHz of optical carrier at wavelengths λ = 800–1600 nm. Detection of optical radiation by non-linear optics can lead to the formation of parasitic electromagnetic radiation (PEMR) at modulation frequencies that can be informative signals for traffic interception systems. The paper presents a physical analysis of this interception type.
FIBRE CHANNEL AND INFORMATION OPTICAL SIGNAL MODEL
The advantages of optical cable networks over electrical ones are associated with an increased frequency of the carrier and with the medium of the information transmission channel [3–5]. The basis of a fibre-optic communication channel is an optical fibre made of an optically transparent dielectric. In telecommunications, it is purified amorphous quartz (silicon dioxide, SiO2) in the form of a thin flexible cylindrical filament with a diameter of 125 μm (shell) with a cylinder selected inside the axis (core) with a diameter less than 10 μm for single-mode fibre and 62.5 or 50 μm for multimode fibre. The geometrical and optical parameters of the shell and core are chosen so that the light propagating inside the shell experiences total internal reflection from the shell, for which the core refractive index (nc is about 1.46) is chosen more than that of the shell (ns) in order of magnitude by Δn = nc– ns = 0.01. The refractive index is controlled by introducing a small amount of additives to increase nc – Ge and P, and to reduce ns – B and F.
The loss in quartz fibres is influenced by impurities of Fe, Cu, Cr and OH- with a typical concentration of about 10–1000 mln–1. For optical amplification in the wavelength range of 1060–1300 nm, the core is doped with Yb, and in the region of 1500 nm – with Er. The low content of impurities determines the optical properties of the fibre, such as low loss, elastic and inelastic scattering, non-linear transformations.
Linear and non-linear optical phenomena in a fibre-optic channel [2–4, 11–13]. The propagation of light in the dielectric fibre is accompanied by losses, the absorption spectrum of which is characterized by a decrease in losses with increasing wavelength from optical to infrared wavelengths of the order of 1600 nm with characteristic bursts of absorption on individual types of impurities and areas between them with a slight change in the absorption coefficient (transparency region) on the wavelengths of 850 nm, 1310 nm, 1550 nm. The smallest attenuation of about 0.22 dB / km is observed over the lengths of 1550 nm. A further increase in wavelength causes an increase in absorption associated with vibrations of the atoms of the crystal lattice. In the field of transparency, the main contribution to the attenuation of the light flux is made by Rayleigh scattering by optical inhomogeneities much smaller than the wavelength of light, which is characterized by the dependence on the wavelength ~λ–4.
Additional losses are caused by structural inhomogeneities of the fibre comparable to wavelengths (Mie scattering), flat chipped fractures, cracks, etc. (Fresnel reflection). These and other types of losses form side optical radiation (SOR) having a characteristic scattering indicatrix (Fig. 1) with the direction of maximum scattering along the fibre axis and a quadratic dependence on the scattering angle θ.
Fused silica SiO2, which forms the basis of the optical fibre, has an amorphous structure with a small fraction of impurities and optical inhomogeneities; therefore, non-linear optical transformation of radiation can be observed in the fibre with low efficiency, which is associated with a small channel size, high input radiation power, and the influence of external factors. In particular, inelastic Raman scattering is observed (on lattice vibrations), Brillouin scattering (on acoustic phonons), which lead to the appearance of characteristic maxima and broadening of the spectrum of optical radiation. In practice, these effects are used for distributed fibre-optic measurements of temperature, mechanical stresses.
Another type of non-linear optical transformations in optical fibre is associated with a change in the refractive index, the generation of harmonics, the total and difference frequencies. These include phase self-modulation, four-wave bias, modulation instability, the formation of solitons, phase cross-modulation, which have a significant impact on the transmission of information in optical lines. For example, four-wave mixing is observed when signals are distributed in the fibre at three (ωi, ωj, ωk) or more frequencies, and a signal is generated at the mixed frequency (ωijk = ωi + ωj – ωk) close to the operating frequency of the channels, which affects transmission. For effective non-linear optical transformation of optical radiation, it is necessary to achieve critical intensities, which is quite possible due to the small cross section of the fibre and high radiation power. The efficiency of non-linear optical transformations can significantly increase when phase (wave) synchronism is achieved, as well as when external influences increase the non-linearity of the medium.
Non-linear optical transformations occurring during the propagation of optical radiation in an optical fibre are determined by the non-linear susceptibility tensor of amorphous silicon with impurities. The non-linear polarization of the fibre material induced by radiation occurs at mixed frequencies and is equal to
,
where is the electric constant, is the electric intensity of the interacting waves at frequencies ω1, ω2, while the non-linear susceptibility may depend on both the electric fields of the same and other waves in the optical fibre, and it also depends on external influences of an electric or other nature, e. g., from mechanical stresses existing or arising when twisting the optical fibre. In ideal crystals, the components of the non-linear susceptibility tensor are determined by symmetry, as in materials with an amorphous structure, the quadratic non-linearity is zero and third-order and higher-order non-linearities appear. In actual materials, there are structural inhomogeneities, external influences, which lead to the fact that the effective non-linear susceptibility may differ from the ideal one. Therefore, the effective quadratic non-linearity of amorphous SiO2 differs from the zero value, and when exposed to external fields it can take values sufficient to observe a second-order non-linear-optical transformation.
In addition to the above phenomena, other processes can take place in the fibre that are not taken into account when operating optical networks, since they do not have a significant impact on the transmission of information, but can be used as sources of informative signals for intercepting traffic.
Information signal [2–4,12]. Information is transmitted in optical networks by modulating an optical carrier, which uses radiation at wavelengths from transparency areas at frequencies ν = ω / 2π · 1014 Hz (λ = 850 nm), 2.3 ∙ 1014 Hz (1310 nm) and 1.9 ∙ 1014 Hz (1550 nm). When encoding information, amplitude and phase modulation is used at frequencies f = Ω / 2π = 108 Hz and above. The main way to increase the bandwidth of the communication line is associated with wave multiplexing of 40 or more wavelengths. The power of the information signal is determined by the optical budget of the line (without intermediate amplification) expressed in dB, i. e. total losses in the passive elements, which must be less than the difference in power source and the sensitivity of the receiver.
INFORMATIVE PARASITIC ELECTROMAGNETIC RADIATION
Based on the description of the information signal, line and communication channel in optical networks, it is possible to propose a simplified physical model of a fibre-optic information transmission system. The information transmission medium is a single-mode optical fibre with a stepped refractive index profile of n = 1.46 and a diameter of d = 125 / 10 μm with an absorption coefficient of α = 0.22 dB / km (5.1 ∙ 10–5 m–1). Information signal in the form of a monochrome optical carrier at a wavelength of λ = 1 550 nm (ν = 1,9 · 1014 Hz) with a source power of P0 = 1 mW modulated by a sinusoidal signal with a frequency of f = 1 GHz in amplitude with a modulation factor of m ≤ 1. The optical channel contains side optical radiation, generated mainly due to Rayleigh scattering, coherent carrier and having a power of about P1 = α λ P0 / 2, where Λ = c / f is the wavelengths of the modulating signal and c is the speed of light in vacuum, i. e. of the order of the spatial length of the bit.
In accordance with this approximation, the propagating optical radiation in the optical fibre consists in the forward direction of the flux of photons with energy and of photons of each type with energies and . The number of carrier photons in the stream decreases with the x distance travelled, so that
,
and modulated photons for each energy
.
In addition to direct photons that form the information optical signal, back-scattered photons are present in the optical fibre, which form side optical radiation with energies , and . Their number is determined by the Rayleigh and Mie scattering, the Fresnel reflection, and is equal to the carrier at the · distance from the source
.
The number of modulated photons for each energy
,
where the additional decrease is two times due to the symmetry of the scattering indicatrix.
The photons scattered from other distant parts of the optical fibre are not coherent with the information optical signal; therefore, their contribution to non-linear processes is insignificant and is not taken into account. The coherence length of the information optical signal with a spectrum width of 2Ω is equal to
,
i.e., the coherence length lc of the signal is slightly less than the bit length Λ / 2, therefore almost all photons of the information bit can participate in coherent processes.
Non-linear optical demodulation of the information signal can occur for any mutual direction of the wave vectors of photons [11–13] – collinear, anti-collinear and non-collinear (Fig. 2). In this case, the laws of conservation of energy and momentum , which are transformed into relations for the frequencies
for collinear interaction
and ,
hence the frequency of the generated radiation
;
for anti-collinear interaction
and ,
where ω is the polarization energy of the substance at zero frequency, hence the frequency of the generated radiation
;
for non-collinear interaction with an angle θ between the wave vectors
and ,
and for the frequency of the generated radiation
.
With collinear interaction, demodulation is possible only with three-wave mixing of photons, the probability of which is lower than two-wave interaction. With anti-collinear and noncollinear interactions, in the approximation of the proximity of frequencies , since , , and the smallness of the angle θ, we obtain
.
The differential frequency of the generated radiation is determined by the types of photons involved in the interaction, it can take values
,
where the first frequency is generated by the interaction of photons by the carrier frequency and one of the modulated waves , and doubled by the interaction of the modulated waves and with the opposite direction of the wave vectors. Demodulation leads to the generation of radiation at a frequency that belongs to the radio band and where the dielectric fibre is not a waveguide. This radiation propagates in all directions from the cable, forming an informative parasitic electromagnetic signal.
Let us estimate the radiation power at the frequency . Based on the present model of PEMR generation, the maximum value of its power is determined by the condition of non-linear optical transformation of all scattered waves of both carrier and modulated waves, i. e., it includes interaction processes carrier in the forward direction ( photons) and backscattered modulated wave ( photons);
backscattered carrier ( photons) and forward modulated wave ( photons)
Thus, determined by the smaller number of photons participating in the interaction, the total maximum possible number of demodulation photons is
or for the power of the informative signal at the frequency Ω
.
The power of the informative signal at the input (x = 0) for 100% modulation depth is equal to
= 7.3∙10–9 W,
which occurs at a frequency f = 1 GHz from a section of fibre with a length of Λ / 2 = 0.1 m.
In the case of registration of informative parasitic electromagnetic radiation from optical inhomogeneity such as a detachable connection with return losses of the order of β = –40 dB, their power can reach
,
and make at the input of
= 3∙10–7 W.
Received power of informative signals can be reliably received and decoded by public microwave receivers.
Let us estimate the optimal value of the effective non-linear susceptibility for type transformation . Since non-linear polarization at frequency
,
it can be represented as a connection between the incident , and generated photon fluxes in the form of
,
where the coefficient τ, having the dimension of time, is defined as
,
where is the cross-sectional area of the core.
The physical meaning of the coefficient τ is associated with the time of complete transformation of photons, limited by the limiting number of photons in the flux. Let the condition be satisfied in the photon flux, i. e. the flux of photons with energy exceeds the flux of photons with energy , where the flux of generated photons with energy cannot exceed a numerically smaller flux of photons, i. e. . The most effective transformation occurs when , i. e. when all photons from a smaller existing flux are converted to a forming flux . In this case, it is required that a greater photon flux
.
From here you can find the optimal value of the effective non-linear susceptibility
for full transformation of all photons. Thus, for 100% non-linear optical transformation, it is required that the value of the effective non-linear susceptibility exceed a certain critical value, which depends on the intensity of the larger flux and the frequency ratio of the generated and incident photons. The dependence on the ratio of frequencies leads to the fact that the process of generating the difference frequency occurs when the non-linearities are smaller by several orders of magnitude than to generate the second harmonic.
Estimation of the optimal value of the effective non-linear susceptibility for the generation of difference frequencies in optical fibre gives the value
10–8 м / В,
where it is assumed that the frequencies of the interacting waves are approximately equal to the carrier frequency = 3,8 π · 1014 rad / s, as well as the refractive indices = 1,46; the frequency of the generated wave is equal to the modulation frequency = 2 π · 109 rad / s, and the refractive index = 1; the intensity of the wave at a frequency is equal to the intensity of the carrier in the optical fibre = 1,27 · 107 W / m2.
The resulting value is quite achievable. In fused quartz, the linear susceptibility has a magnitude of the order of 1, the quadratic susceptibility is 10–11–10–13 m / V, and the cubic susceptibility is 10–21–10–23 m2 / V2 [11–13]. Since the magnitude of the non-linear susceptibility in the material of the defect-free fibre is 3 orders of magnitude less than that required for 100% transformation, hence the coefficient is 6 orders of magnitude less than the critical value, i. e. only 10–6 of the maximum possible number of photons will be converted. The power of informative parasitic electromagnetic radiation will take values less than 10–13 W, which is recorded in close proximity to the sources. In this case, to increase the transformation efficiency, an external effect can be used to increase the non-linearity of the medium.
FEATURES OF INTERCEPTION AND PROTECTION IN OPTICAL NETWORKS
The implementation of traffic interception in optical networks is associated with the choice of technical reconnaissance equipment, its optimal location. The main element is a receiving antenna, the design of which depends on the type of cable system installation (underground, underwater, air), cable design (dielectric or metal protective / carrying elements), the number of optical fibres. For a cylindrical informative parasitic electromagnetic wave radiating from a cable, the antenna can be in the form of a conductive film or wire screw cylinder around a fibre of the order of the Λ / 2 bit length, the signal from which is transmitted to the amplifier and receiver (Fig.3).
Metallic protective and supporting cable elements can weaken the informative electromagnetic signal, so they perform the functions of the first protective echelon. At modulation Ω = 2 π · 109 rad / s, the penetration depth of electromagnetic radiation is about 2.5 μm for iron with a specific conductivity of 107 Ohm / m, which is much less than the thickness of protective shells. To overcome it, the intruder must destroy the protective steel cable sheaths and gain access to the internal surfaces of the metal protective sheaths, in which case the internal surfaces themselves can act as antennas.
The power of the informative signal is influenced by the power of the information optical signal (carrier); therefore, the most dangerous are sections of the optical network near active elements, such as a transmitter / amplifier / repeater, and less dangerous – sections at the input in front of the receiver / amplifier / repeater. Of these considerations, the most dangerous are the parts of the optical network with optical inhomogeneities, such as couplings, where welded fibres are placed; distribution cabinets where fibre detachable joints are placed; as well as any other fibre areas with increased local losses.
The power of the informative signal can be increased by increasing the optical non-linearity in the fibre by external influence by constant electric, magnetic fields, or mechanical action. The magnitude of the impact can be determined experimentally or theoretically by the physical characteristics of the optical fibre, but in any case, the additional effect increases the power of informative parasitic electromagnetic radiation, as it increases not only the optical non-linearity, but also increases the local loss in the optical fibre.
Countering threats of interception can be accomplished in many ways. For example, by feeding a coherent noise signal into the shell at frequencies other than the information one, but with a bandwidth close to the bandwidth of the information signal, the same can be applied when multiplexing the information and noise signals directly in the core. In this case, the informative parasitic electromagnetic signal generated from the information signal will be noised by the parasitic electromagnetic radiation from the noise signals.
CONCLUSION
A theoretical analysis of non-linear optical processes with an information optical signal in optical fibres of communication networks shows the possibility of generating information parasitic electromagnetic signals that can be used for remote (i. e., without destroying the protective shells of an optical cable) to intercept traffic in optical networks. The effectiveness of interception is determined by the location of technical intelligence relative to the active elements, the proximity of the receiving antenna to the optical fibre, external influence on the optical fibre to increase its non-linear susceptibility. The revealed features of interception allow us to formulate requirements for means of technical protection of traffic, such as the use of a noise signal, etc.
Traffic interception in optical networks [4–10]. The main methods of interception are connected with the formation of optical informative signals by outputting a part of the optical information signal, e. g., by removing a part of the radiation when the fibre is bent; registration of side optical radiation on the basis of leaky modes in the initial part of the optical fibre or scattered radiation in other parts of the optical network. Features of the propagation of light in the fibre, the design of the optical cable limit the possibilities of interception based on optical informative signals by the difficulties of registering fast processes with limited optical power output; the development of optical network monitoring technology using reflectometric and other methods.
Theoretical analysis of the physical features of the propagation of light in the fibre and the practical search for technical implementations of existing fibre-optic technologies allows us to offer new ways to intercept traffic, including on the basis of parasitic electromagnetic radiation generated as a result of non-linear-optical transformations in the fibre. The essence of this interception comes down to the fact that information is encoded in optical networks at speeds up to C = 100 Gbit / s and corresponding modulation frequencies of the order of f = 100 GHz of optical carrier at wavelengths λ = 800–1600 nm. Detection of optical radiation by non-linear optics can lead to the formation of parasitic electromagnetic radiation (PEMR) at modulation frequencies that can be informative signals for traffic interception systems. The paper presents a physical analysis of this interception type.
FIBRE CHANNEL AND INFORMATION OPTICAL SIGNAL MODEL
The advantages of optical cable networks over electrical ones are associated with an increased frequency of the carrier and with the medium of the information transmission channel [3–5]. The basis of a fibre-optic communication channel is an optical fibre made of an optically transparent dielectric. In telecommunications, it is purified amorphous quartz (silicon dioxide, SiO2) in the form of a thin flexible cylindrical filament with a diameter of 125 μm (shell) with a cylinder selected inside the axis (core) with a diameter less than 10 μm for single-mode fibre and 62.5 or 50 μm for multimode fibre. The geometrical and optical parameters of the shell and core are chosen so that the light propagating inside the shell experiences total internal reflection from the shell, for which the core refractive index (nc is about 1.46) is chosen more than that of the shell (ns) in order of magnitude by Δn = nc– ns = 0.01. The refractive index is controlled by introducing a small amount of additives to increase nc – Ge and P, and to reduce ns – B and F.
The loss in quartz fibres is influenced by impurities of Fe, Cu, Cr and OH- with a typical concentration of about 10–1000 mln–1. For optical amplification in the wavelength range of 1060–1300 nm, the core is doped with Yb, and in the region of 1500 nm – with Er. The low content of impurities determines the optical properties of the fibre, such as low loss, elastic and inelastic scattering, non-linear transformations.
Linear and non-linear optical phenomena in a fibre-optic channel [2–4, 11–13]. The propagation of light in the dielectric fibre is accompanied by losses, the absorption spectrum of which is characterized by a decrease in losses with increasing wavelength from optical to infrared wavelengths of the order of 1600 nm with characteristic bursts of absorption on individual types of impurities and areas between them with a slight change in the absorption coefficient (transparency region) on the wavelengths of 850 nm, 1310 nm, 1550 nm. The smallest attenuation of about 0.22 dB / km is observed over the lengths of 1550 nm. A further increase in wavelength causes an increase in absorption associated with vibrations of the atoms of the crystal lattice. In the field of transparency, the main contribution to the attenuation of the light flux is made by Rayleigh scattering by optical inhomogeneities much smaller than the wavelength of light, which is characterized by the dependence on the wavelength ~λ–4.
Additional losses are caused by structural inhomogeneities of the fibre comparable to wavelengths (Mie scattering), flat chipped fractures, cracks, etc. (Fresnel reflection). These and other types of losses form side optical radiation (SOR) having a characteristic scattering indicatrix (Fig. 1) with the direction of maximum scattering along the fibre axis and a quadratic dependence on the scattering angle θ.
Fused silica SiO2, which forms the basis of the optical fibre, has an amorphous structure with a small fraction of impurities and optical inhomogeneities; therefore, non-linear optical transformation of radiation can be observed in the fibre with low efficiency, which is associated with a small channel size, high input radiation power, and the influence of external factors. In particular, inelastic Raman scattering is observed (on lattice vibrations), Brillouin scattering (on acoustic phonons), which lead to the appearance of characteristic maxima and broadening of the spectrum of optical radiation. In practice, these effects are used for distributed fibre-optic measurements of temperature, mechanical stresses.
Another type of non-linear optical transformations in optical fibre is associated with a change in the refractive index, the generation of harmonics, the total and difference frequencies. These include phase self-modulation, four-wave bias, modulation instability, the formation of solitons, phase cross-modulation, which have a significant impact on the transmission of information in optical lines. For example, four-wave mixing is observed when signals are distributed in the fibre at three (ωi, ωj, ωk) or more frequencies, and a signal is generated at the mixed frequency (ωijk = ωi + ωj – ωk) close to the operating frequency of the channels, which affects transmission. For effective non-linear optical transformation of optical radiation, it is necessary to achieve critical intensities, which is quite possible due to the small cross section of the fibre and high radiation power. The efficiency of non-linear optical transformations can significantly increase when phase (wave) synchronism is achieved, as well as when external influences increase the non-linearity of the medium.
Non-linear optical transformations occurring during the propagation of optical radiation in an optical fibre are determined by the non-linear susceptibility tensor of amorphous silicon with impurities. The non-linear polarization of the fibre material induced by radiation occurs at mixed frequencies and is equal to
,
where is the electric constant, is the electric intensity of the interacting waves at frequencies ω1, ω2, while the non-linear susceptibility may depend on both the electric fields of the same and other waves in the optical fibre, and it also depends on external influences of an electric or other nature, e. g., from mechanical stresses existing or arising when twisting the optical fibre. In ideal crystals, the components of the non-linear susceptibility tensor are determined by symmetry, as in materials with an amorphous structure, the quadratic non-linearity is zero and third-order and higher-order non-linearities appear. In actual materials, there are structural inhomogeneities, external influences, which lead to the fact that the effective non-linear susceptibility may differ from the ideal one. Therefore, the effective quadratic non-linearity of amorphous SiO2 differs from the zero value, and when exposed to external fields it can take values sufficient to observe a second-order non-linear-optical transformation.
In addition to the above phenomena, other processes can take place in the fibre that are not taken into account when operating optical networks, since they do not have a significant impact on the transmission of information, but can be used as sources of informative signals for intercepting traffic.
Information signal [2–4,12]. Information is transmitted in optical networks by modulating an optical carrier, which uses radiation at wavelengths from transparency areas at frequencies ν = ω / 2π · 1014 Hz (λ = 850 nm), 2.3 ∙ 1014 Hz (1310 nm) and 1.9 ∙ 1014 Hz (1550 nm). When encoding information, amplitude and phase modulation is used at frequencies f = Ω / 2π = 108 Hz and above. The main way to increase the bandwidth of the communication line is associated with wave multiplexing of 40 or more wavelengths. The power of the information signal is determined by the optical budget of the line (without intermediate amplification) expressed in dB, i. e. total losses in the passive elements, which must be less than the difference in power source and the sensitivity of the receiver.
INFORMATIVE PARASITIC ELECTROMAGNETIC RADIATION
Based on the description of the information signal, line and communication channel in optical networks, it is possible to propose a simplified physical model of a fibre-optic information transmission system. The information transmission medium is a single-mode optical fibre with a stepped refractive index profile of n = 1.46 and a diameter of d = 125 / 10 μm with an absorption coefficient of α = 0.22 dB / km (5.1 ∙ 10–5 m–1). Information signal in the form of a monochrome optical carrier at a wavelength of λ = 1 550 nm (ν = 1,9 · 1014 Hz) with a source power of P0 = 1 mW modulated by a sinusoidal signal with a frequency of f = 1 GHz in amplitude with a modulation factor of m ≤ 1. The optical channel contains side optical radiation, generated mainly due to Rayleigh scattering, coherent carrier and having a power of about P1 = α λ P0 / 2, where Λ = c / f is the wavelengths of the modulating signal and c is the speed of light in vacuum, i. e. of the order of the spatial length of the bit.
In accordance with this approximation, the propagating optical radiation in the optical fibre consists in the forward direction of the flux of photons with energy and of photons of each type with energies and . The number of carrier photons in the stream decreases with the x distance travelled, so that
,
and modulated photons for each energy
.
In addition to direct photons that form the information optical signal, back-scattered photons are present in the optical fibre, which form side optical radiation with energies , and . Their number is determined by the Rayleigh and Mie scattering, the Fresnel reflection, and is equal to the carrier at the · distance from the source
.
The number of modulated photons for each energy
,
where the additional decrease is two times due to the symmetry of the scattering indicatrix.
The photons scattered from other distant parts of the optical fibre are not coherent with the information optical signal; therefore, their contribution to non-linear processes is insignificant and is not taken into account. The coherence length of the information optical signal with a spectrum width of 2Ω is equal to
,
i.e., the coherence length lc of the signal is slightly less than the bit length Λ / 2, therefore almost all photons of the information bit can participate in coherent processes.
Non-linear optical demodulation of the information signal can occur for any mutual direction of the wave vectors of photons [11–13] – collinear, anti-collinear and non-collinear (Fig. 2). In this case, the laws of conservation of energy and momentum , which are transformed into relations for the frequencies
for collinear interaction
and ,
hence the frequency of the generated radiation
;
for anti-collinear interaction
and ,
where ω is the polarization energy of the substance at zero frequency, hence the frequency of the generated radiation
;
for non-collinear interaction with an angle θ between the wave vectors
and ,
and for the frequency of the generated radiation
.
With collinear interaction, demodulation is possible only with three-wave mixing of photons, the probability of which is lower than two-wave interaction. With anti-collinear and noncollinear interactions, in the approximation of the proximity of frequencies , since , , and the smallness of the angle θ, we obtain
.
The differential frequency of the generated radiation is determined by the types of photons involved in the interaction, it can take values
,
where the first frequency is generated by the interaction of photons by the carrier frequency and one of the modulated waves , and doubled by the interaction of the modulated waves and with the opposite direction of the wave vectors. Demodulation leads to the generation of radiation at a frequency that belongs to the radio band and where the dielectric fibre is not a waveguide. This radiation propagates in all directions from the cable, forming an informative parasitic electromagnetic signal.
Let us estimate the radiation power at the frequency . Based on the present model of PEMR generation, the maximum value of its power is determined by the condition of non-linear optical transformation of all scattered waves of both carrier and modulated waves, i. e., it includes interaction processes carrier in the forward direction ( photons) and backscattered modulated wave ( photons);
backscattered carrier ( photons) and forward modulated wave ( photons)
Thus, determined by the smaller number of photons participating in the interaction, the total maximum possible number of demodulation photons is
or for the power of the informative signal at the frequency Ω
.
The power of the informative signal at the input (x = 0) for 100% modulation depth is equal to
= 7.3∙10–9 W,
which occurs at a frequency f = 1 GHz from a section of fibre with a length of Λ / 2 = 0.1 m.
In the case of registration of informative parasitic electromagnetic radiation from optical inhomogeneity such as a detachable connection with return losses of the order of β = –40 dB, their power can reach
,
and make at the input of
= 3∙10–7 W.
Received power of informative signals can be reliably received and decoded by public microwave receivers.
Let us estimate the optimal value of the effective non-linear susceptibility for type transformation . Since non-linear polarization at frequency
,
it can be represented as a connection between the incident , and generated photon fluxes in the form of
,
where the coefficient τ, having the dimension of time, is defined as
,
where is the cross-sectional area of the core.
The physical meaning of the coefficient τ is associated with the time of complete transformation of photons, limited by the limiting number of photons in the flux. Let the condition be satisfied in the photon flux, i. e. the flux of photons with energy exceeds the flux of photons with energy , where the flux of generated photons with energy cannot exceed a numerically smaller flux of photons, i. e. . The most effective transformation occurs when , i. e. when all photons from a smaller existing flux are converted to a forming flux . In this case, it is required that a greater photon flux
.
From here you can find the optimal value of the effective non-linear susceptibility
for full transformation of all photons. Thus, for 100% non-linear optical transformation, it is required that the value of the effective non-linear susceptibility exceed a certain critical value, which depends on the intensity of the larger flux and the frequency ratio of the generated and incident photons. The dependence on the ratio of frequencies leads to the fact that the process of generating the difference frequency occurs when the non-linearities are smaller by several orders of magnitude than to generate the second harmonic.
Estimation of the optimal value of the effective non-linear susceptibility for the generation of difference frequencies in optical fibre gives the value
10–8 м / В,
where it is assumed that the frequencies of the interacting waves are approximately equal to the carrier frequency = 3,8 π · 1014 rad / s, as well as the refractive indices = 1,46; the frequency of the generated wave is equal to the modulation frequency = 2 π · 109 rad / s, and the refractive index = 1; the intensity of the wave at a frequency is equal to the intensity of the carrier in the optical fibre = 1,27 · 107 W / m2.
The resulting value is quite achievable. In fused quartz, the linear susceptibility has a magnitude of the order of 1, the quadratic susceptibility is 10–11–10–13 m / V, and the cubic susceptibility is 10–21–10–23 m2 / V2 [11–13]. Since the magnitude of the non-linear susceptibility in the material of the defect-free fibre is 3 orders of magnitude less than that required for 100% transformation, hence the coefficient is 6 orders of magnitude less than the critical value, i. e. only 10–6 of the maximum possible number of photons will be converted. The power of informative parasitic electromagnetic radiation will take values less than 10–13 W, which is recorded in close proximity to the sources. In this case, to increase the transformation efficiency, an external effect can be used to increase the non-linearity of the medium.
FEATURES OF INTERCEPTION AND PROTECTION IN OPTICAL NETWORKS
The implementation of traffic interception in optical networks is associated with the choice of technical reconnaissance equipment, its optimal location. The main element is a receiving antenna, the design of which depends on the type of cable system installation (underground, underwater, air), cable design (dielectric or metal protective / carrying elements), the number of optical fibres. For a cylindrical informative parasitic electromagnetic wave radiating from a cable, the antenna can be in the form of a conductive film or wire screw cylinder around a fibre of the order of the Λ / 2 bit length, the signal from which is transmitted to the amplifier and receiver (Fig.3).
Metallic protective and supporting cable elements can weaken the informative electromagnetic signal, so they perform the functions of the first protective echelon. At modulation Ω = 2 π · 109 rad / s, the penetration depth of electromagnetic radiation is about 2.5 μm for iron with a specific conductivity of 107 Ohm / m, which is much less than the thickness of protective shells. To overcome it, the intruder must destroy the protective steel cable sheaths and gain access to the internal surfaces of the metal protective sheaths, in which case the internal surfaces themselves can act as antennas.
The power of the informative signal is influenced by the power of the information optical signal (carrier); therefore, the most dangerous are sections of the optical network near active elements, such as a transmitter / amplifier / repeater, and less dangerous – sections at the input in front of the receiver / amplifier / repeater. Of these considerations, the most dangerous are the parts of the optical network with optical inhomogeneities, such as couplings, where welded fibres are placed; distribution cabinets where fibre detachable joints are placed; as well as any other fibre areas with increased local losses.
The power of the informative signal can be increased by increasing the optical non-linearity in the fibre by external influence by constant electric, magnetic fields, or mechanical action. The magnitude of the impact can be determined experimentally or theoretically by the physical characteristics of the optical fibre, but in any case, the additional effect increases the power of informative parasitic electromagnetic radiation, as it increases not only the optical non-linearity, but also increases the local loss in the optical fibre.
Countering threats of interception can be accomplished in many ways. For example, by feeding a coherent noise signal into the shell at frequencies other than the information one, but with a bandwidth close to the bandwidth of the information signal, the same can be applied when multiplexing the information and noise signals directly in the core. In this case, the informative parasitic electromagnetic signal generated from the information signal will be noised by the parasitic electromagnetic radiation from the noise signals.
CONCLUSION
A theoretical analysis of non-linear optical processes with an information optical signal in optical fibres of communication networks shows the possibility of generating information parasitic electromagnetic signals that can be used for remote (i. e., without destroying the protective shells of an optical cable) to intercept traffic in optical networks. The effectiveness of interception is determined by the location of technical intelligence relative to the active elements, the proximity of the receiving antenna to the optical fibre, external influence on the optical fibre to increase its non-linear susceptibility. The revealed features of interception allow us to formulate requirements for means of technical protection of traffic, such as the use of a noise signal, etc.
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