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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>N. Dzyanyi);</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Layered model for protecting speech information against leakage through an optoelectronic channel⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Nazarii Dzyanyi</string-name>
          <email>nazarii.r.dzianyi@lpnu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ivan Opirskyy</string-name>
          <email>ivan.r.opirskyi@lpnu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Mariia Shved</string-name>
          <email>mariia.y.shved@lpnu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Olha Liubchyk</string-name>
          <email>olha.liubchyk@gmail.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Lviv Polytechnic National University</institution>
          ,
          <addr-line>12 Stepan Bandera str., 79000 Lviv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0002</lpage>
      <abstract>
        <p>The article presents the results of a scientific and technical analysis and the development of a layered model for protecting speech information against leakage via an optoelectronic channel. It is determined that the primary factors influencing the effectiveness of protection against laser acoustic reconnaissance systems include not only the physical properties of materials but also their comprehensive multilayer arrangement. A model that describes the interaction of a laser beam with a multilayer structure (glass, films, coatings) and accounts for both forward propagation and the backscattered response is proposed. The model is formalized as a system of interrelated coefficients (K1−Kn) that represent the qualitative and quantitative composition of materials, properties of protective coatings, angle of incidence, and instrument technical specifications. The use of a “minimum-loss” principle is proposed for quantitatively assessing protection effectiveness. The study substantiates the feasibility of employing both aggregate and composite models to forecast the protective properties of window assemblies, thereby enabling the optimization of material selection and their combinations. It is shown that protection effectiveness depends on the damping characteristics of polymer films, the absence of resonance effects in insulated glazing units with panes of differing thicknesses, and the ability of smart glass to scatter laser radiation. The obtained results confirm the relevance of passive protection methods and provide a scientific basis for the development and implementation of high-technology solutions to ensure information security.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;speech information</kwd>
        <kwd>optoelectronic channel of information leakage</kwd>
        <kwd>laser acoustic reconnaissance systems</kwd>
        <kwd>protective coatings</kwd>
        <kwd>information protection</kwd>
        <kwd>layered model</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        The problem of unauthorized acquisition of confidential information is among the most pressing
challenges in today’s information environment. Technical channels of information leakage—
particularly acoustic, vibroacoustic, and hybrid forms—are evolving alongside technological
advances. The optoelectronic leakage channel that employs laser acoustic reconnaissance systems
(LARS) poses a significant threat due to its high effectiveness, long operational range, and covert
nature. Numerous methods for protecting information against leakage through various channels
have been developed over recent decades. One of the key directions in ensuring information
security is the detection and localization of potential technical channels of acoustic information
leakage. In this field, a wide range of methods has been investigated, including both active and
passive means of protecting speech information, leveraging specialized instruments, magnetostatics
and electrostatics, and optical properties [
        <xref ref-type="bibr" rid="ref1 ref2 ref3 ref4 ref5 ref6 ref7">1–7</xref>
        ].
      </p>
      <p>Among the most timely and promising directions in passive protection of speech information is
the development of specialized coatings and films whose use can substantially reduce the risk of
confidential information leakage by: absorbing or scattering the probing laser radiation; reducing
the vibration amplitude of reflective surfaces, thereby hindering audio reconstruction; and
deploying combinations of layered elements that yield a maximal degree of room protection.
The protection level of premises against LARS-based interception of speech exhibits a complex
dependence shaped by many interrelated quantities. Addressing this problem requires a
comprehensive approach that accounts for material properties (glass, protective films), their
multilayer combinations, and the interaction of the laser beam with surfaces. Developing a
mathematical model that incorporates all these factors is critically important for creating effective
solutions.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Theoretical Foundations of the Study</title>
      <p>The operating principle of LARS is based on laser vibrometry methods. The system uses an
invisible infrared (IR) laser beam for remote probing of a surface that vibrates under the action of
an acoustic wave. A speech signal inside a room creates an acoustic field which, upon reaching the
window glass, causes it to oscillate (vibrate). These oscillations modulate the reflected laser beam,
converting acoustic information into an optical signal.</p>
      <p>The key physical phenomenon used to read out this information is the Doppler effect.
According to this effect, the frequency of light reflected from a moving object changes
proportionally to the object’s velocity. Because vibration is an oscillatory motion, it has a velocity
that varies continuously. A laser beam reflected from a vibrating surface experiences a Doppler
frequency shift. This shift is linearly dependent on the velocity of the glass’s oscillation, enabling
high-precision measurement of vibration parameters and reconstruction of the original acoustic
signal.</p>
      <p>The choice of the IR range for LARS is not arbitrary. It is dictated by the properties of the
propagation medium—the atmosphere. Air exhibits so-called atmospheric transmission windows in
the IR band (e.g., 3–4 μm and 8–12 μm), where atmospheric absorption is minimal. This allows the
laser beam to maintain high power over substantial distances (300–1000 m), which is one of LARS’s
principal advantages. In addition, the invisibility of IR radiation to the unaided eye enhances the
covert nature of reconnaissance. However, atmospheric conditions such as rain, fog, or snow can
substantially attenuate the reflected signal through scattering, which is a key drawback of this
channel.</p>
      <p>The optoelectronic information leakage channel can be represented as a classical
three-component system: “source of the hazardous signal—propagation medium—technical
reconnaissance means.” In this context:



the source is the speech signal in the premises, which generates the acoustic field.
the propagation medium is the air inside the room, which conveys the acoustic wave to the
window glass.
the reconnaissance means is the laser system that irradiates the vibrating surface and
receives the modulated reflected signal.</p>
      <p>The window glass plays an essential role in this chain. Under the influence of the acoustic field,
it transforms from a passive barrier into an active source of vibrational motion, which becomes the
carrier of the informative signal for LARS interception. Consequently, the effectiveness of room
protection directly depends on the window system’s ability to attenuate these vibrations and/or
alter the characteristics of the reflected laser beam in a way that renders it unintelligible.</p>
      <p>Prevention of information leakage through the acousto-optoelectronic channel can be achieved
using vacuum and other protected window units, and frosting the exterior glass surface.
applying vibrational noise masking to windows and other reflective objects.
by:

</p>
      <p>
        Speech information protection is a set of measures aimed at preventing unauthorized access,
use, dissemination, or alteration of speech data.
In studies [
        <xref ref-type="bibr" rid="ref10 ref11 ref12 ref8 ref9">8–12</xref>
        ], local researchers consider the protection of speech information from leakage
through the optoelectronic channel. The proposed passive methods employing solar-control films
do not deliver the desired anti-laser effect.
      </p>
      <p>
        Copper-based films that protect windows against ultraviolet and visible infrared radiation, as
described in [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ], operate most effectively around 500 nm, which cannot provide the desired
protection against laser probing because operational laser wavelengths are typically in the 650–
3000 nm range.
      </p>
      <p>
        Foreign authors in [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] analyzed options for reducing glass vibration and preventing laser
eavesdropping, taking into account the influence of insulated glass unit design on LARS protective
properties. The results show that only about 1% of the glass’s vibrations are transmitted through
the window frames, with the remainder concentrated in the glazing itself.
      </p>
      <p>
        The effect of anti-laser aerosols on the intensity of acoustic signals is considered in [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ]. It was
found that the optimal signal strength corresponds to the amount of ablative material. This allows
appropriate adjustment of laser focus during sampling to achieve optimal ablation based on the
acoustic signal intensity.
      </p>
      <p>
        For remote laser capture of voice, the backscattering characteristics of objects were analyzed in
[
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. The results showed that the reconstructed speech amplitude gradually decreases as surface
roughness increases. Moreover, the reconstructed acoustic signal amplitude increases with an
increase in the metal’s attenuation coefficient.
      </p>
      <p>
        Based on photonic crystal superlattices and nanomaterials, multifrequency multilayer films and
coatings have been developed [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ]. These materials provide filtering of specific optical wavelengths
while maintaining transparency across other parts of the spectrum.
      </p>
      <p>Analysis of local and foreign research supports the conclusion that protecting speech data from
potential leakage through technical channels is a critical task for ensuring information security in
both governmental and business domains.</p>
      <p>
        Any information leakage channel is formed from three components: a transmitter (source of the
hazardous signal), a propagation medium for that signal, and a receiver (the information capture
device). The optoelectronic channel is no exception. The hazardous signal in this case is the
interlocutors’ speech—i.e., sensitive information expressed aloud. The propagation medium for the
hazardous signal, in our case, may include windows, paintings, mirrors, and other household
objects located in the room. These structures exhibit membrane-like properties and are strongly
affected by acoustic vibrations [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
      <p>Thus, to exploit the optoelectronic information leakage channel, an adversary does not need to
enter the premises; it is sufficient to gain access to adjacent buildings and install
information-collection devices that convert structural vibrations within the controlled area into
electrical signals.</p>
      <p>Protection of speech information can proceed along two lines. First, protecting conversations
that take place in enclosed rooms or within a controlled area. Second, protecting speech
information within communication channels.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Problem statement</title>
      <p>Existing architectural and construction solutions used in building or retrofitting premises do not
always provide an adequate level of protection for speech information against laser acoustic
reconnaissance systems (LARS). This is because LARS operation relies on remotely reading surface
micro-vibrations (e.g., of window glass) induced by sound waves inside the room. Even minute
vibrations can be converted back into intelligible speech using sensitive optical equipment.</p>
      <p>Protection against LARS is an extremely complex, multifactorial task that depends on a large
number of interrelated parameters. The challenge in countering LARS lies in the fact that window
glass—typically perceived as a passive protective barrier—actually becomes an active element of the
information-leakage channel. The security of a room depends on myriad interdependent factors,
from the glass’s chemical composition and geometric parameters to the type of protective coatings
and environmental conditions. Therefore, the development of effective countermeasures requires a
systematic approach that enables not only the identification but also the quantitative assessment of
each factor’s impact on the overall level of protection.</p>
      <p>The absence of comprehensive, scientifically grounded models that account for combinations of
layered elements and the bidirectional response to laser-beam propagation (into the premises and
back) complicates the design of truly secure facilities. As a result, security measures are often
inadequate, ineffective, or excessively costly without achieving the desired level of protection.</p>
      <p>Thus, a current scientific and technical problem is the development and application of an
effective model that permits quantitative assessment, forecasting, and minimization of the risks of
speech information leakage through the optoelectronic channel from LARS, ensuring maximum
protection of premises under contemporary information-security threat conditions.</p>
      <p>Aim of the study: to advance and substantiate the proposed layered model for protecting
speech information from LARS by detailing the physico-chemical and modeling factors that
influence its effectiveness, and by formalizing these factors as predictive mathematical
relationships.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Research Methodology</title>
      <p>The methodology of this study relies on a comprehensive approach to examining the security
parameters of the optoelectronic information-leakage channel, enabling investigation of the
layer-by-layer interdependence and the influence of protective optical layers and the internal
structure of glass on its protective characteristics against LARS. Specifically, based on assessments
of the protection afforded by glass and film coatings against laser reconnaissance—carried out
using X-ray fluorescence (XRF) and spectral analysis, as well as simplex-lattice (mixture) design in
modeling glass characteristics—it can be generalized that the employed methods, the procedures
developed from them, and the experimental investigations together constitute a methodology that
fully accomplishes the stated objectives.</p>
      <p>To construct a protective layered model of a multicomponent, architecturally configured
structure for the optoelectronic information-leakage channel, we used results obtained in our prior
studies.</p>
      <p>
        In particular, we investigated the protective capability of glass against laser probing as a
function of its elemental composition, including the influence of the elemental makeup of float
glass on the reflectance and absorption coefficients of the probing radiation. Systematizing the
elemental and quantitative composition of the studied window glass by periods and groups of the
periodic table revealed a dependence between the electronic structure of the constituent chemical
elements and the protective properties of the glass. The results showed that reflectance and
absorption vary with changes in the glass’s chemical composition, which makes it possible to
predict properties and to design the glass composition with prescribed protective characteristics
[
        <xref ref-type="bibr" rid="ref18">18</xref>
        ].
      </p>
      <p>To ensure that all investigations were conducted correctly we created an experimental setting
which helped us to receive precise numbers on protective capabilities of studied glass against laser
probing (Figure 1). It includes: L—laser, —sample, D1 and D2—detectors (laser power
measuring device).</p>
      <p>
        Based on studying the reflectance of glass with a sputtered single-layer hafnium dioxide (HfO2)
coating through its spectral characteristics, we proposed the use of protective films with high
reflectivity that complicate or preclude optical interception. We substantiated the advantages of
dielectric HfO2 films, since the reflectance of glass with such a deposited film is significantly higher
compared to bare glass, which increases the glass’s protective performance against speech
information leakage by multiples. Moreover, the costs of producing and depositing such coatings
are substantially lower than the costs of developing and manufacturing active countermeasures in
the modern context, underscoring the advantages of passive methods for protecting speech
information from optoelectronic readout [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ].
      </p>
      <p>
        We also conducted studies and an effectiveness assessment of a protective semiconductor film,
BaCuTeF, and proposed a method for obtaining an improved amorphous, electrically conductive
protective film structure with subsequent crystallization through annealing in an argon
atmosphere. Depending on the annealing temperature, this approach can significantly improve
visible-light transmittance, increase the power of the reflected laser beam, and more strongly
absorb laser radiation power compared with simple metallized films. This study led to the
conclusion that installing such a protective film in combination with a high-reflectance dye layer
on the exterior window glass of a building reduces or completely negates the effectiveness of laser
interception of voice information, primarily due to the sharp drop in the power of the reflected or
absorbed signal by the outer glass layer with the film coating [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ].
      </p>
      <p>
        Analyzing the results of the study describing the deposition methodology for a single-layer
hafnium coating and the subsequent investigation of glass reflectance with the deposited film,
together with [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ], which examined the protective characteristics of textured films deposited on
glass, we concluded that changing the tilt angle of the insulating glass unit and using textured films
on the exterior side of the glass significantly influence the reflectance. This can provide effective
protection against LARS at minimal cost.
      </p>
      <p>Based on the analysis and synthesis of prior research results, it became possible to construct a
comprehensive model of a multicomponent, architecturally configured structure for the
optoelectronic information-leakage channel.</p>
    </sec>
    <sec id="sec-5">
      <title>5. Results</title>
      <p>The composite optoelectronic information leakage channel is formed by capturing information
with an IR laser beam (LARS) from a flat glass surface vibrating under the influence of an acoustic
wave carrying information. In the classical structure of an optoelectronic leakage channel, the
sources of the acoustic signal in a room are, first and foremost, the person speaking and any
reflected signal sources. In our case, window glass in a particular placement, of a specified chemical
composition, and with various deposited layers and films, ceases to be only part of the propagation
path and also acts as a source of vibrational oscillations. Depending on the number of protective
layers on the glass, it can attenuate or, conversely, enhance the signal components available to
LARS.</p>
      <p>
        At the same time, based on experiments and studies [
        <xref ref-type="bibr" rid="ref22">22</xref>
        ], we note that vibration propagation
differs depending on the configuration of barrier materials (glass and other enclosing structures)
through which they propagate, as well as on the prior response to the scanning action of the laser
beam.
      </p>
      <p>Accordingly, we propose to represent the structure of the optoelectronic information leakage
channel as a layered model (Figure 2).</p>
      <p>
        Thus, the protection level of premises against speech interception by laser reconnaissance
systems exhibits a complex dependence shaped by the configuration of many interrelated
quantities [
        <xref ref-type="bibr" rid="ref23">23</xref>
        ]:








      </p>
      <p>K1: qualitative protection coefficient (elemental composition of the glass).</p>
      <p>K2: quantitative protection coefficient (stoichiometry of glass constituents).</p>
      <p>K3: protective coatings coefficient (films).</p>
      <p>K4: angular coefficient (tilt angle of the insulating glass unit).</p>
      <p>K5: angular coefficient (angle of incidence of the laser beam).</p>
      <p>K6: “sandwich” coefficient (arrangement/configuration of protective layers).</p>
      <p>K7: instrument technical characteristics coefficient.</p>
      <p>Kn: nth protection coefficient.</p>
      <p>Coefficients K1 (qualitative, elemental composition) and K2 (quantitative, stoichiometry) are
fundamental characteristics that determine the protective properties of glass. They influence both
mechanical and optical parameters.</p>
      <p>
        The glass composition directly affects its stiffness, described by Young’s modulus (E), which for
silicate glass ranges from approximately 48 to 83 GPa. The higher the Young’s modulus, the smaller
the amplitude of glass vibrations [
        <xref ref-type="bibr" rid="ref24">24</xref>
        ] under acoustic pressure. The introduction of oxides such as
CaO, ZnO, Al2O3, and PbO can increase glass stiffness. Density also depends on composition;
increasing the content of lead or barium oxides raises density, which in turn increases inertia and
can affect the frequency response of vibrations.
      </p>
      <p>
        Chemical composition and stoichiometry determine the glass’s absorption and transmission
spectrum [
        <xref ref-type="bibr" rid="ref25">25</xref>
        ]. Even glass that is transparent in the visible band exhibits significant absorption in
the IR region, which is critical for countering LARS. This absorption is due to various oxides and to
hydroxyl (OH−) vibrational modes. For example, adding lead and barium oxides can increase
transparency in the 2.5–4.5 μm range. Conversely, the formation of more ordered polycrystalline
phases such as BaF2 and CuxTe1−x can reduce transparency due to increased absorption.
Thus, K1 and K2 establish the baseline physical parameters that serve as inputs for modeling glass
vibrations induced by the acoustic signal and for modeling laser-beam attenuation.
      </p>
      <p>Coefficients K3 (protective coatings) and K6 (the “sandwich” coefficient) describe how the
glass’s baseline properties are modified by additional materials and constructions.</p>
      <p>
        One of the most effective passive methods is laminated glass (triplex) [
        <xref ref-type="bibr" rid="ref26">26</xref>
        ], where two or more
glass layers are bonded by a polymer interlayer, typically polyvinyl butyral (PVB). The key
technical advantage is that the polymer acts as a damping layer, absorbing vibrational energy
transferred from one glass ply to another and substantially reducing the overall vibration
amplitude. This mechanism is fundamentally different from simple sound insulation and directly
counters LARS-based interception. Damping effectiveness depends on the polymer’s acoustic
properties, such as sound speed and absorption coefficient.
      </p>
      <p>The “sandwich” coefficient (K6) further accounts for the layer combinations within the glazing
unit. Robust protection is achieved by using panes of differing thicknesses (e.g., 6 and 8 mm), which
helps avoid resonance effects that occur when panes share identical natural frequencies and can
amplify vibration. Additionally, employing air gaps of different thicknesses improves sound
insulation by promoting the scattering of sound waves.</p>
      <p>A state-of-the-art solution is integrating PDLC (Polymer-Dispersed Liquid Crystal) films into
insulating glass units. This “smart” glass can instantaneously switch from transparent to frosted
under an applied electric field. In the frosted state, the liquid crystals are randomly oriented,
producing strong light scattering. This effect can be leveraged against LARS, as it prevents
acquisition of a well-defined reflected signal and complicates laser beam aiming.</p>
      <p>Table 1 presents a comparative description of several protective materials for window systems.
High transparency in Low cost; brittle; no
the visible range; low protection
in the IR</p>
      <p>Coefficients K4, K5, and K7 describe not intrinsic material properties, but external factors and
technical characteristics that influence the effectiveness of the leakage channel.
The angular coefficients K4 (tilt angle of the Insulating glass unit) and K5 (angle of incidence of the
laser beam) are important for successful interception. When the laser beam strikes the glass at a
non-normal angle, the reflected spot becomes elliptical. This spreads the beam energy over a larger
area, which can reduce the intensity of the signal returned to the receiver.</p>
      <p>
        Coefficient K7 accounts for the technical capabilities of the LARS apparatus, including laser
power, photodetector sensitivity, and signal processing algorithms [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. The effectiveness of any
protection is evaluated not in absolute terms but relative to the adversary’s reconnaissance
capability. The main criterion is the signal-to-noise ratio (SNR) at the detector output. The goal of
protective measures is to reduce this ratio to a level at which the informative signal becomes
unintelligible.
      </p>
      <p>The mathematical model describes minimizing information leakage through the optoelectronic
channel against LARS, which corresponds to maximizing the room’s protection. The total
information loss consists of several components that are layered on the base material (glass). For
each hypothetical layer there exists an optimal magnitude of risk reduction for LARS leakage that
corresponds to a minimum. This minimum of losses correlates with a practical numerical
characteristic K lmarins, which takes into account the composition and combination of layered elements
involved in solving the room’s security problem. In the general case, the final K lmarins is composed of
n protective layers, that is:</p>
      <p>n
K lmarins = i ∑=1 K n ,
(1)
where K lmarins is the coefficient of minimal loss of speech information, K n is the minimal-loss
coefficient contributed by the n-th protective layer.</p>
      <p>We can posit that the layered model of the multicomponent, architecturally composed structure
of the optoelectronic leakage channel unfolds at two levels: an aggregate model and a holistic
(complex) model.</p>
      <p>The aggregate model of a complex (layered) system consists of separate subsystems and a
description of their interactions (in the classical manner). In this model, subsystems are represented
by individual equations that relate outputs to inputs and subsystem parameters. In compact form:
{ K 2 =</p>
      <p>K 1 =
K n =
f 2 ( x 1 , x 2 , x n ... ) }
f 1 ( x 1 , x 2 , x n ... )
f n ( x 1 , x 2 , x n ... )</p>
      <p>The interaction between subsystems (glass, deposited layers, protective films, arrangement, etc.)
is such that the outputs of one subsystem serve as inputs to another and share the same identifiers
in the aggregate model.</p>
      <p>The complex (system-level) model views the source—propagation—receiver chain as a whole,
without decomposing it into subsystems and internal processes. The overall protection coefficient
can be expressed as:</p>
      <p>Moreover, for specific tasks the complex model can be obtained and represented as a
consolidated aggregate model by reducing the system of equations to a single expression linking
the system’s inputs and outputs (through substitution), depending on the configuration of the
elements used to protect against optoelectronic leakage.</p>
      <p>This two-tier structure—aggregate and complex—is methodologically sound because it allows
analysis both at the level of individual components (glass, films) and of the system as a whole.
Кprot = f Kn.
However, to achieve scientific rigor, these models must be populated with concrete physical
relationships.</p>
      <p>The foundation for describing window vibrational behavior is the equation of forced
oscillations. In the simplest case, the acoustic pressure acts as the external driving force, and the
glass’s elastic and damping properties are included:</p>
      <p>The expression for the acoustic pressure force F(t) can be written as:</p>
      <p>F(t)=P(t)⋅ A,
where P(t) is the acoustic pressure and A is the surface area.</p>
      <p>Equation of motion with damping for an effective mass m:
,
(4)
(5)
where m is the effective mass of the glass, x is the displacement from equilibrium, β is the
damping coefficient, k is the stiffness.</p>
      <p>Coefficients K1 and K2 influence m and k, while K3 and K6 primarily affect β.</p>
      <p>Modern methods such as the finite element method are used to model the complex vibrations of
multilayer structures. The finite element method captures interlayer coupling between glass plies
and polymer films, as well as the nonuniform spatial distribution of vibrations—effects that lie
beyond simple analytical models. In this way, the complex model can be realized as a numerical
simulation that integrates all coefficients into a unified system.</p>
      <p>The terminal protection objective (Kprot) can be posed as minimizing the SNR at the
photodetector input:</p>
      <p>Kprot=min(SNR),
(6)
where SNR depends on the vibration amplitude, which in turn is a function of all coefficients
K1...Kn.</p>
      <p>The advantage of these approaches is that, depending on the system’s objectives and component
specifications, one can flexibly compose the overall behavior from modular elements with known
parameters or criteria, even without delving into internal structure, focusing solely on the required
outcome. Evidently, the proposed model enables both approaches: experimental studies of
individual layers and forecasting the theoretical capabilities of an integrated protection system for
speech information against LARS.</p>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusions</title>
      <p>As a result of this study, we have constructed a protective model for a multicomponent,
architecturally composed structure of the optoelectronic information leakage channel. The model
accounts for combinations of layered elements, the forward and backward response of a laser beam
propagating into and out of the premises, and is formulated at both aggregate and complex levels.</p>
      <p>It has been established that the protection of premises against LARS-based interception of
speech is not a linear function; rather, it is shaped by a complex combination of interrelated
parameters, including the bidirectional response of the laser beam as it traverses multilayer
elements of building structures (e.g., glass, protective films, and coatings).</p>
      <p>The developed mathematical model, which describes the minimization of information losses
through the optoelectronic channel under LARS probing, makes it possible to determine the
optimal reduction of risk for each hypothetical layer of the base material. This, in turn, corresponds
to the maximum achievable level of premises protection.</p>
      <p>The “minimum-loss” concept reflects a practical numerical measure of the effectiveness of
specific combinations of layered elements that form the room’s security system. Accordingly, the
study provides a scientific foundation for the design and optimization of protective systems,
enabling the most effective countermeasures against laser acoustic reconnaissance through
targeted manipulation of the physical properties of multilayer architectural components.</p>
      <p>The conducted scientific and technical analysis confirms the high relevance of protection
against the optoelectronic leakage channel and substantiates the systems approach proposed in the
layered model. The research offers concrete justification for each protection coefficient (K1–Kn),
linking them to material properties such as Young’s modulus, absorption spectra, and damping
characteristics.</p>
      <p>It is shown that effective protection requires a comprehensive approach that combines passive
methods aimed at attenuating structural vibrations and the laser beam with active systems that
introduce interference. Despite its high effectiveness and stealth, the optoelectronic channel
exhibits vulnerabilities stemming from its dependence on material properties and atmospheric
conditions.</p>
      <p>Development of the mathematical model using the equations of forced oscillations and
numerical techniques such as the finite element method enables a transition from theoretical
assumptions to precise calculations. This opens the way to high-technology solutions—including
smart glass and laser interference systems—that can ensure robust protection of confidential speech
information under contemporary conditions.</p>
      <p>Declaration on Generative AI
While preparing this work, the authors used the AI programs Grammarly Pro to correct text
grammar and Strike Plagiarism to search for possible plagiarism. After using this tool, the authors
reviewed and edited the content as needed and took full responsibility for the publication’s content.</p>
    </sec>
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