Contrast-Enhanced OCT for Damage Detection in Polymeric Resins Embedded with Metallic Nanoparticles via Surface Plasmon Resonance

Abstract

Nanoparticle-embedded polymeric materials are an important subject in advanced structural applications due to their advantageous combination of low weight and high mechanical performance. Optical coherence tomography (OCT) is a high-resolution imaging technique that enables subsurface defect visualization, which can be used as one of the methods to reveal defects resulting from decomposition pathways or mechanisms of polymers. Nevertheless, the low contrast of polymeric materials, particularly PEEK-based polymers, does not allow for automatic geometry extraction for analytical input. To address the constraint of weak contrast, localized surface plasmon resonance (LSPR) of plasmonic nanoparticle-reinforced polymer materials has been used as an OCT contrast agent to provide the necessary contrast. The backscattering efficiency of light was also theoretically investigated, based on the Lorenz–Mie theory, with a single spherical nanoparticle embedded in a PEEK matrix as a non-absorptive, isotropic and homogeneous medium. In this study, the cases of a single homogeneous $Ti{O}_2$ nanoparticle and a hybrid $Ti{O}_2/Au$ core/shell nanoparticle configuration were considered separately. An examination of the influence of nanoparticle diameter and gold shell thickness on backscattering efficiencies of these nanostructures was performed. The results indicate that $Ti{O}_2/Au$ nanoshells demonstrate superior near-infrared (NIR) light backscattering capabilities at typical OCT operating wavelengths (830–1310 nm). Additionally, the potential of these nanoparticles for application in non-destructive testing-based light backscattering methods was investigated. The findings suggest that $Ti{O}_2/Au$ nanoshells have the ability to effectively backscatter near-infrared light in OCT operating central wavelengths, making them suitable to serve as effective NIR contrast-enhancing agents for OCT within the domain of NDT.

1. Introduction

The aerospace industry demands materials that simultaneously exhibit lightness, excellent thermal resistance and high durability capabilities. Traditionally, metals were employed for manufacturing aerospace components, but became obsolete due to their inability to meet modern requirements, particularly in terms of weight and corrosion resistance [1]. Composite materials made are often used to meet these criteria, with polymers serving as a basis for these innovative materials. Polymeric matrixes offer advantages such as low cost, versatile synthesis methods and a wide range of properties, including lightness, electrical conductivity, high thermal resistance and superior wear and corrosion resistance.

The development of nanoparticle-embedded polymeric materials has ushered in a new era of advanced materials that can satisfy these complex needs [2,3,4,5].When reinforced with nanomaterials, be they nanoparticles, nanofillers or nanometric-sized fibers, these polymers transform into nanocomposites with enhanced capabilities [5,6]. For instance, recent advancements in the field of nanocomposites have led to the successful integration of boron nitride nanoparticles into aluminum matrices, resulting in a high-performance composite material. This innovative material has now found practical application in the aerospace industry, specifically in the manufacture of intricate wing structures for aircraft [7].

Nanoparticle-embedded polymeric materials offer significant benefits in aircraft performance and safety. Conductive nanomaterials like graphene, when incorporated into aircraft structures, provide effective protection against environmental hazards such as lightning bolts. These lightweight alternatives can efficiently dissipate electrical energy, minimizing the risk of structural damage during lightning events [8].

Among the various metallic nanoparticles (MNPs) used to reinforce these composites, titanium dioxide ($Ti{O}_2$) nanoparticles, for example, are extensively used in aircraft and engine parts [9]. When incorporated into photocatalytic and self-cleaning coatings, $Ti{O}_2$ nanoparticles break down organic pollutants and provide protection against UV radiation, significantly reducing maintenance requirements for vehicles operating at high altitudes or in space [10,11].

Research shows that reinforcing PEEK with $Ti{O}_2$ nanoparticles significantly enhances its mechanical properties. Composites containing $Ti{O}_2$ nanoparticles demonstrate simultaneous improvements in tensile strength and elastic modulus [12,13], while PEEK/PEI blends with $Ti{O}_2$ nanoparticles are notably stiffened and strengthened compared to the base polymer [14]. In related polymer systems, $Ti{O}_2$ also contributes to improved stiffness and toughness [15]. Thermal and fire resistance are also significant factors in aerospace applications, particularly for ensuring the safety of high-performance and multifunctional aircraft and spacecraft parts. Nanoparticle-embedded polymeric materials, such as $Ti{O}_2$ nanopolymers and graphene-reinforced composites, demonstrate elevated heat resistance. To address the demands of aerospace materials, it is necessary to examine cutting-edge technologies in materials science beyond the macro level, across multiple scales and extending down to the nanoscale [8,16].

In this sense, microscopic methodologies, including scanning probe microscopy (SPM), scanning electron microscopy (SEM) and transmission electron microscopy (TEM), have been employed to investigate the structural modifications of composites at both micrometer and nanometer dimensions [17,18]. Although the foundational principles of these methodologies vary, their overarching objective is to generate highly magnified surface representations of the specimen. Nonetheless, the prerequisites for sample preparation, the limited probe dimensions, the elevated costs and the reliance on destructive techniques to obtain comprehensive insights pose significant challenges. Furthermore, the quality and extent of the information acquired are predominantly reliant upon the proficiency of the user and proper sample preparation.

In addition, small- and wide-angle scattering (SWAXS) are capable of providing structural information up to the atomic scale [19]. Nevertheless, the substantial financial investment required for their equipment makes these techniques less practical for on-the-spot analysis. In this sense, two other non-destructive methodologies, namely, ultrasonic scanning and X-ray computed tomography, have also been implemented [20]. Ultrasonic scanning is limited by its low resolution and requires a coupling medium, while X-ray tomography is costly, particularly for inline assessments [21].

While these methodologies can reveal surface representations at the atomic scale, their use for real-time, continuous evaluation of polymer composites is constrained by scanning duration, material preparation requisites, small probing dimensions and high cost. Conversely, the imaging technology of OCT has the potential to deliver non-destructive subsurface images of polymer and composite materials, thereby presenting a promising solution to some of these constraints [22]. OCT measures the interference signal created by the interaction between backscattered light from the sample and reflected light from a reference beam. Through demodulation and processing of this measured interference signal, OCT reconstructs sample structure information, generating both cross-sectional and volumetric images [23].

OCT employs low-coherence interferometry with a broadband light source to detect the depth information of samples without compromising their integrity. Initially employed for applications in biological imaging, including ophthalmology, dentistry and brain studies [24], OCT’s utility has significantly expanded its uses. With technological advancements, its applications have extended to non-destructive testing of polymer materials in industry; aeronautics, where it is used for detecting structural defects in polymer laminates for aircraft [21,25,26]; and various industrial products, such as light-emitting diodes, liquid crystal displays, optical thin films, optical modulators and touch-screen panels [27].

This photonic imaging technology shows great promise as a potential alternative for rapid analysis of polymer aeronautic materials. OCT is an interferometry method that exploits the phenomenon of light scattering from the illuminated target to measure the depth of the light penetrated in the sample. Since this technique identifies backscattered light that arises from variations in refractive indices due to the occurrence of fissures and delamination within the polymer film’s core, the incorporation of plasmonic nanoparticles exhibiting elevated backscattering at the OCT source wavelength may significantly augment the OCT signal emitted from the illuminated polymer substrate [28].

While OCT holds potential for enhancing NDT, it also has limitations. For instance, the ability to detect OCT signals depends on the intensity of the backscattered light. Thus, a weak scattering signal at low intensity due to the IR transparency in polymer materials significantly hampers the detection capability [29]. One potential solution to this issue involves incorporating plasmonic metallic nanoparticles (PMNPs) into the core of the polymer material, which serves to enhance the backscattered light signals in OCT [30]. Numerous experimental studies on this subject have been reported in the literature. These efforts focus on determining the effectiveness of incorporated (PMNPs) for more efficient and cost-effective nanoscale imaging in non-destructive testing [31,32,33].

Hybrid nanoparticles with acore/shell geometry with a dielectric core and a plasmonic goldshell, commonly known as plasmonic gold nanoshells, have also attracted particular interest over the past two decades. This interest in such heterostructures stems from their capability to provide not only more degrees of freedom in a core-and-shell-type material but also variation in the particle size and relative thickness of the core and the shell, allowing for tailored optical responses in specific non-destructive testing applications, particularly in OCT imaging [28,34]. The observation of Mie resonances in nanostructures, influenced by their morphology, size and composition, has led to additional simulation studies [35,36]. Optical behavior simulations of plasmonic nanoparticles have consistently proven to be a time- and cost-effective method for narrowing down experimental parameters in many research studies. In particular, prior research has shown that assessing the optical behavior of metallic nanostructures is essential for the efficient development of photonic applications [37,38]. The simulation-driven predictions were subsequently validated through physical experiments in these studies [39,40]. The validation process involved a comparison of experimental data and computational simulations. This approach not only confirmed the accuracy of the simulations but also reinforced their significance in early-stage design and testing of nanophotonic structures. The close agreement between simulated and experimental results underscores the reliability of computational methods in predicting the optical behavior of metallic nanostructures, thereby accelerating the development cycle.

The present study contributes to this domain by focusing on a detailed theoretical analysis of the backscattering properties of light with a single spherical nanoparticle embedded in a PEEK polymer layer, modeled to be a host unbounded and non-absorbing medium using the Lorenz–Mie theory. Two distinct cases are examined: a homogeneous $Ti{O}_2$ nanoparticle and a hybrid $Ti{O}_2/Au$ plasmonic nanoshell. The novelty of this work lies in the investigation of the influence of particle diameter and goldshell thickness on the backscattering cross-sections of these nanostructures. Furthermore, the efficacy of these nanoparticles in non-destructive testing applications based on light backscattering is evaluated. The incorporation of $Ti{O}_2/Au$ NP-doped PEEK has demonstrated a marked enhancement in OCT contrast, thereby enabling the segmentation of polymer twos and the visualization of micro-/nanometer-scale fissures.

2. Method and Theoretical Approach

The aim of the current study was to elucidate the optical response exhibited by a singular nanoparticle incorporated within a PEEK polymer laminated when subjected to irradiation by an electromagnetic wave, as schematically depicted in Figure 1. The surrounding medium is assumed to be unbounded and non-absorptive, and the electromagnetic wave is modeled as a plane wave polarized along the x-axis, propagating along the z-axis. This study investigates homogeneous nanoparticles employed as dielectric materials, such as titanium dioxide ($Ti{O}_2$), as well as hybrid nanoparticles composed of two distinct components, $Ti{O}_2$ and a noble metal, specifically gold (Au). Concentric core/shell nanoshells are characterized by a core radius denoted as $r_1$ and an overall particle radius indicated as $r_2$. The optical response of the nanoparticle can be delineated by dimensionless parameters, one of which is referred to as the backscattering efficiency,$Q_{back}$.

The backscattering properties of a single gold nanoshell may be described by the backscattering cross-section,$Q_{back}$. This parameter represents the equivalent cross-sectional area of the particle contributing to the backscattering of the incident electromagnetic wave. This parameter is normalized to the particle’s geometrical cross-section perpendicular to the direction of wave propagation.

The electromagnetic behavior of nanoparticles requires the resolution of Maxwell’s equations which govern the spatial distributions of the electric field, $\overrightarrow{E}$, and the magnetic field, $\overrightarrow{H}$. This solution must account for appropriate boundary conditions and continuity relations at material interfaces. For a spherical nanoparticles, Maxwell’s equations yield analytical solutions through Lorenz–Mie theory, comprehensively detailed in the seminal work of Bohren and Huffman [41].

According to Lorenz–Mie theory, the backscattering cross-section is defined as the differential scattering cross-section per unit solid angle in the backscattering direction. It consequently possesses the dimension of an area per unit solid angle. For an individual spherical particle, the backscattering cross-section can be expressed as a function of the Mie scattering coefficients $a_n$ and $b_n$.

In the case of a gold nanoshell, the backscattering efficiency ($Q_{back}$) can be calculated using an extension of Mie theory applicable to coated spheres [38]:

$${\mathrm{Q}}_{\mathrm{back}}={\displaystyle \frac{1}{4{\mathrm{k}}^2}}{\left|{\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{n}}\left(2\mathrm{n}+1\right){\left(-1\right)}^{\mathrm{n}}({\mathrm{a}}_{\mathrm{n}}-{\mathrm{b}}_{\mathrm{n}})\right|}^2$$

(1)

This extended theory accounts for the core/shell structure of the nanoparticle, allowing for accurate modeling of its optical properties.

The size parameter, $\mathrm{k}$, for a given wavelength, λ, is defined as $\mathrm{k}=2{\mathsf{\pi }\mathrm{r}}_2/\mathsf{\lambda }$. The scattering coefficients ${\mathrm{a}}_{\mathrm{n}}$ and ${\mathrm{b}}_{\mathrm{n}}$ are calculated using the algorithm outlined by Bohren and Huffman [41]. Numerical evaluations of these Mie coefficients and the resulting backscattering efficiency were conducted using commercial MATLAB software, version 2023B.

The computational model has several input parameters: the vacuum wavelength of incident light, λ; the core radius, ${\mathrm{r}}_1$; theoverall particle radius,${\mathrm{r}}_2$; the shell thickness fraction, ${\mathrm{t}}_{\mathrm{f}}={\mathrm{r}}_2-{\mathrm{r}}_1/{\mathrm{r}}_2$; and the refractive indices of the core (${\mathrm{n}}_1$), shell (${\mathrm{n}}_2$) and surrounding medium (${\mathrm{n}}_3$).

This study explores the use of plasmonic metallic nanoparticles as contrast agents for NDT imaging, especially to enhance the OCT signals from illuminated PEEK/polymer-grafted plasmonic nanoparticles. This is an interferometry technique that relies on the phenomenon of backscattering of light from an illuminated target. As OCT detects backscattered light arising from refractive index fluctuations in the laminated polymer, gold nanoshells exhibiting high backscattering at the OCT source wavelength may significantly improve the OCT signal from the illuminated PEEK/polymer-grafted gold nanoshells. Therefore, gold nanoshells with high backscattering efficiency in the near-infrared OCT operational wavelength range of 830–1310 nm are required [42].

The backscattering properties of a collection of gold nanoshells can be completely characterized by the backscattering coefficient, ${\mathsf{\mu }}_{\mathrm{back}}$; this parameter corresponds to their total backscattering cross-section per unit volume. Assuming negligible multiple scattering and a monodisperse gold nanoshell population (i.e., all gold nanoshells have identical dimensions), ${\mathsf{\mu }}_{\mathrm{back}}$ is specified by the following [34]:

$${\mathsf{\mu }}_{\mathrm{back}}={\mathrm{NC}}_{\mathrm{back}}=\mathrm{f}{\displaystyle \frac{{\mathrm{C}}_{\mathrm{back}}}{{\mathrm{V}}_{\mathrm{p}}}}$$

(2)

This formulation provides a basis for optimizing the design of gold nanoshells for enhanced OCT imaging in polymer composites, where $\mathrm{N}$ is the particle number density (particles per unit volume), $\mathrm{f}$ denotes the volume fraction of particles (particle volume per unit volume) and ${\mathrm{V}}_{\mathrm{p}}$ is the volume of a single particle. To facilitate unbiasedcomparison of backscattering properties, gold nanoshell ensembles with different dimensions are considered to have the same volume fraction. Consequently, a new quantity called the volume backscattering coefficient (${\mathrm{\alpha }}_{\mathrm{back}}$) is introduced. It represents the backscattering cross-section per unit particle volume. This normalized metric enables equitable assessment of the scattering performance across diverse nanoparticle architectures. ${\mathrm{\alpha }}_{\mathrm{back}}$ is given by the following:

$${\mathrm{\alpha }}_{\mathrm{back}}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{back}}}{{\mathrm{V}}_{\mathrm{p}}}}$$

(3)

In the context of polymer imaging, our focus is directed towards nanoparticles that exhibit elevated backscattering efficiency while simultaneously maintaining a diminutive size, thereby promoting their infiltration into the polymer matrix [43]. This objective is effectively achieved through the optimization of the ${\alpha }_{back}$ coefficient at the designated operating wavelengths of OCT. Furthermore, nanoparticles with dimensions less than 200 nm contribute to optimal dispersion and facilitate substantial interaction with the polymer matrix, thereby augmenting essential mechanical characteristics such as toughness and strength, which are imperative for applications in the aeronautical field [44]. In the context of polymer imaging, our focus is directed towards nanoparticles that exhibit elevated backscattering efficiency while simultaneously maintaining a diminutive size, thereby promoting their infiltration into the polymer matrix [43]. This objective is effectively achieved through the optimization of the ${\alpha }_{back}$ coefficient at the designated operating wavelengths of optical coherence tomography (OCT). Furthermore, nanoparticles with dimensions less than 200 nm contribute to optimal dispersion and facilitate substantial interaction with the polymer matrix, thereby augmenting essential mechanical characteristics such as toughness and strength, which are imperative for applications in the aeronautical field [44].

To simulate the backscattering efficiency of light by the nanostructures under consideration, it was necessary to obtain the complex refractive indices and permeabilities of the component materials, in this case the surrounding medium, titanium dioxide and gold. As previously mentioned, the polymer matrix was assumed to be non-absorbent, assigning a purely real refractive index. While this approximation is not universally valid across the electromagnetic spectrum, it is valid for certain intervals, particularly in the visible wavelength range of 380 to 750 nm. Following the approach of previous studies, the polymer host film was considered as a non-absorbing medium in the visible range [45]. Consequently, its refractive index was modeled as real and constant, neglecting the imaginary component. This assumption is justified by the polymer’s optical transparency in the studied spectral range, and it is further supported by the literature showing that polymers can be modeled as homogeneous, isotropic and non-absorbing media under certain conditions (near-infrared region), allowing for a simplified analysis of the optical response of the incorporated nanoparticles [46,47]. Thus, a constant refractive index of 1.55 was assumed in the calculations across the entire wavelength range studied [48].

Experimental data for the complex refractive indices were utilized for bulk crystalline titanium dioxide, $Ti{O}_2$, and bulk crystalline gold, as reported in previous studies [46,47]. In the absence of experimental data for other materials, the cubic spline interpolation technique was employed to estimate the missing values. The optical properties, specifically the refractive indices (n) and extinction coefficients (κ), of the materials under investigation are presented in Figure 2 for the wavelength range of 300–1100 nm.

Within the theoretical framework of Mie theory, our findings align with those of a previous work [49] which investigated the optical responses of homogeneous bismuth ferrite ($BiF{e}_3{O}_4$) nanospheres in air as agents in visible-light-induced photocatalysis and hybrid $BiF{e}_3{O}_4/Au$ nanoparticles in biological tissue as photothermal agents and contrast agents for OCT bioimaging. The study demonstrated that these two metallic nanoparticle models exhibit plasmonic resonances in the spectral range of 200–1400 nm, highlighting the efficacy of these nanoparticles in light absorption- and light scattering-based applications. This property is particularly intriguing when considering other types of homogeneous nanospheres as potential agents for NIR light-induced applications in OCT imaging and NDT. The ability to tune the backscattering optical response,$Q_{back}$, of nanoparticles could potentially enhance contrast and sensitivity in OCT imaging.

3. Results

3.1. $Ti{O}_2$ Nanoparticle

As a foundational assumption in the modeling approach, the analysis begins with a single homogenous ${\mathrm{TiO}}_2$ spherical nanoparticle. The homogeneous spherical nanoparticles have been the focus of some studies [50,51], wherein rutile ${\mathrm{TiO}}_2$ nanospheres were employed with air as the surrounding medium (host matrix). Considering that nanoparticles are subjected to analysis alongside others due to the high index of rutile,${\mathrm{TiO}}_2$, a multitude of backscattering peaks were detected within the visible spectrum. This observation supports the potential application of IR-reflective carbon-embedded rutile (${\mathrm{TiO}}_2$) nanospheres in the formulation of automotive paints with the aim of enhancing the visibility of vehicles during nocturnal conditions for light detection and ranging systems. Furthermore, recent research has focused on developing simplified analytical models to investigate backscattering phenomena and elucidate the influence of nanoparticle composition and material selection on enhanced energy harvesting capabilities [50].

The backscattering efficiency,${\mathrm{Q}}_{\mathrm{back}}$, of the ${\mathrm{TiO}}_2$ nanospheres is represented in two-dimensional color maps, defined as a function of the particle diameter, D, and the vacuum wavelength, λ; the resultant data are shown in Figure 3. The analysis encompasses particle diameters within the range of 10 to 500 nm, alongside wavelengths spanning from 300 to 1100 nm.

Examination of this map reveals that the phenomenon of light backscattering,$Q_{back}$, by $Ti{O}_2$ nanoparticles within the specified spectral range is only observable for particle diameters exceeding approximately 250 nm. This color map elucidates resonant backscattering phenomena linked to the renowned LSPR modes characteristic of the metallic nanoparticles that are the focus of this investigation. These modes are systematically arranged in branches, each encompassing a defined spectral domain and a corresponding range of particle diameters, represented within the radiation plane defined by diameter and wavelength. The branch representing the most prominent resonant modes is then identified as the fundamental branch, positioned at the lower end of the diameter axis. Specifically, this branch is observable within the wavelength range of 350–400 nm and the diameter range of 425–500 nm, specifically in the case of titanium dioxide. Moreover, the color map indicates that the backscattering ($Q_{back}$) spectrum intersects at a wavelength contingent upon the dimensions of the nanoparticle.

A thorough analysis of the $Q_{back}$ colour map emphasizes a critical wavelength threshold, abovewhich light backscattering is inexistent. This critical wavelength threshold demonstrates a linear increase with nanoparticle size, reaching 300, 400 and 420 nm for diameters of 280, 350 and 500 nm, respectively.

Moreover, spherical nanoparticles exhibit approximately constant backscattering efficiency for electromagnetic radiation with wavelengths (λ) shorter than 350 nm, regardless of particle size variations. This efficiency, although relatively modest, is approximately 1. However, this is not applicable for radiation wavelengths exceeding λ = 350 nm. Indeed, beyond this threshold, backscattering resonances emerge, exhibiting efficiencies that can attain values of 10, which are distributed across short linear branches within the critical wavelength threshold between 350 and 500 nm. These phenomena manifest from a threshold particle diameter of nearly 250 nm. The characteristics of these resonances, including their magnitude, quantity and spectral location, are contingent upon the diameter of the nanoparticle.

The backscattering efficiency remains nearly consistent across both wavelength and particle diameter, with values slightly exceeding unity. The profile of the light backscattering spectrum generated by individual $Ti{O}_2$ nanospheres embedded in a PEEK polymer material is presented in Figure 3; the spectrum is calculated for the particle diameter that corresponds to the highest efficiency of backscattering,$Q_{back}$. It is noteworthy that the backscattering efficiency spectra were computed using the Mie computations of the backscattering properties, as delineated in Equation (1). From the computed backscattering efficiency, it is evident that two distinct peaks are discernible within the backscattering spectra. The two primary peaks within the wavelength range below 400 nm correspond to the dipole oscillation modes of the LSPR spectra. The notably pronounced resonance peak at a wavelength of 350 nm is associated with the dipolar electric mode (ED), whereas the less intense peak appearing at 380 nm corresponds to the dipolar magnetic mode (MD) [52].

3.2. $Ti{O}_2/Au$ Core/Shell Nanoparticle

As previously discussed, the optical response exhibited by gold nanospheres within fused silica optical fibers has been subjected to a theoretical exploration in a previous work [28]. However, to date, no studies have documented backscattering phenomena in gold nanoshells possessing dielectric cores, presenting an unexpected literature gap. In the current study, this category of nanostructure was examined and had its optical response analyzed through the application of Lorenz–Mie theory across a broader spectrum of particle diameters and shell thicknesses. The backscattering efficiencies of a singular ${\mathrm{TiO}}_2/\mathrm{Au}$ core/shell spherical nanoparticle, embedded within a PEEK (polyetheretherketone) laminate, are depicted in two-dimensional color maps. These visual representations were calculated as functions of the outer diameter, D (=2${\mathrm{r}}_2$); the vacuum wavelength, λ; and various fractions of goldshell thickness, ${\mathrm{t}}_{\mathrm{f}}$ (=(${\mathrm{r}}_2-{\mathrm{r}}_1$)/${\mathrm{r}}_2$). Figure 4 presents the findings obtained for ${\mathrm{t}}_{\mathrm{f}}$ values of 0.15, 0.25, 0.5 and 0.75.

A comparative analysis of Figure 3 and Figure 5 reveals that the optical response of the $Ti{O}_2/Au$ nanoshell, as denoted by light backscattering, exhibits substantial discrepancies when juxtaposed with that of the pure $Ti{O}_2$ nanoparticle. Furthermore, the optical response of the $Ti{O}_2/Au$ nanoshell for shell thickness fractions exceeding 0.5 diverge significantly from those with shell thickness fractions lower than 0.5.

For goldshell thickness superior to 0.5 (${\mathrm{t}}_{\mathrm{f}}$ > 0.5), light backscattering trough a ${\mathrm{TiO}}_2/\mathrm{Au}$ spherical nanoshell becomes noticeable within the examined spectral range for diameters more than approximately 25 nm. In a case where the diameter is larger than this size threshold, the nanoshell is capable of backscattering light over a finite spectral range, which extends up to about 600 nm, regardless of further increases in diameter. Additionally, it also emits light in the finite spectral range with a cut-off wavelength, which experiences a large linear redshift when the size of the nanoparticle is increased. In numerical terms, the wavelength cut-off transitions (from 750 nm for D = 400 to 1100 nm for D = 150 nm).

A further investigation of ${\mathrm{Q}}_{\mathrm{back}}$ color maps reveals that the backscattering spectrum of ${\mathrm{TiO}}_2/\mathrm{Au}$ nanoshells is structured and displays distinct peaks with efficiencies higher than 1.6. These ${\mathrm{TiO}}_2/\mathrm{Au}$ nanoshells show consistent light backscattering within the spectral range of 300–600 nm with an efficiency of approximately 1.6, remaining virtually constant, regardless of the nanoshell dimensions. The backscattering resonance oscillations emerge at wavelengths beyond λ = 600 nm and are observed in nanoshells whose sizes which exceed the threshold dimension. Nevertheless, their attributes, such as magnitude, quantity and spectral range, are dependent on the nanoparticle diameter. When the goldshell thickness fractions are less than or equal to 0.5 (${\mathrm{t}}_{\mathrm{f}}$ ≤ 0.5), backscattering color maps reveal a significant distinction compared to those corresponding to shell thickness fractions exceeding 0.5. This distinction becomes increasingly pronounced as the shell thickness fraction decreases, resulting in the formation of three distinct branches. The phenomenon generates three branches, one of which exhibits resonant backscattering within a spectral region where such backscattering is typically suppressed in unmodified titanium dioxide (${\mathrm{TiO}}_2$) nanoparticles (Figure 3b), particularly at wavelengths that are longer (λ = 450 nm).

The three branches are linked to specific thresholds of particle size and wavelength. The size threshold remains constant at about 50 nm with respect to the fraction of gold shell thickness,${ \mathrm{t}}_{\mathrm{f}}$. Conversely, the wavelength threshold is dependent on the thickness of the shell, shifting towards longer wavelengths as the shell thickness fraction decreases. More precisely, this shift progresses from 800 nm for ${\mathrm{t}}_{\mathrm{f}}$ = 0.25 to 1008 nm for ${ \mathrm{t}}_{\mathrm{f}}$ = 0.15, represented by the black cross added to the ${\mathrm{Q}}_{\mathrm{back}}$ colour maps. These branches occur for a defined spectral range and for a narrow band of particle sizes. Both ranges broaden as the shellthickness fraction of the ${\mathrm{TiO}}_2/\mathrm{Au}$ nanoshell decreases. Specifically, the resonant backscattering of red light is facilitated by ${\mathrm{TiO}}_2/\mathrm{Au}$ nanoshells having a shellthickness fraction of ${ \mathrm{t}}_{\mathrm{f}}$= 0.25 and particle diameters in the interval of 50–150 nm. The effective backscattering of near-infrared light can be achieved by ${\mathrm{TiO}}_2/\mathrm{Au}$ nanoshells with a shellthickness fraction of 0.15 and outer diameters ranging from 50 to 150 nm.

These observations have been further elaborated in Figure 5, which shows the curves of backscattering efficiencies as functions of wavelength, each associated with a defined fraction of gold shell thickness and nanoparticle diameter; the chosen diameter aligns with an absolute maximum of backscattering efficiency for specified thickness fractions of 0.15, 0.25, 0.50 and 0.75. Thus, a redshift of the peaks associated with the maximum backscattering of light from nanoparticles of identical size (D = 100 nm) was observed following a reduction in the gold shell thickness fraction. More determinably, the backscattering peak at λ = 615 nm, supported by a ${ \mathrm{TiO}}_2/\mathrm{Au}$ core/shell nanoparticle with a diameter of 100 nm and a shell thickness of 26 nm, shifts to λ = 650 nm for the same shell thickness. According to the plasmon hybridization model, two internal boundaries are present in core/shell nanostructures; specifically, the inner and outer interfaces of the material shell layer [53].The electromagnetic wave induces plasmon modes at these two boundaries, namely, one at the core/shell interface and another at the shell/environment interface. The interaction between these two modes results in the splitting of the plasmon mode into two novel resonance modes: the Bonding Mode (BM) and the Antibonding Mode (ABM). The coupling between the electromagnetic wave and the Antibonding Mode is significantly weak, which accounts for its absence in the absorption spectrum [54,55]. As a result, the BM alone emerges for the gold shell layer.

As exhibited in Figure 5, this redshift is accompanied by an increase in the magnitude of the backscattering peak as the thickness fraction decreases from 0.75 to 0.50. As shown by the computed backscattering maps, represented as a function of wavelength and particle diameter (D), the optimal dimensions and thickness of the gold shell for maximal backscattering within the visible to NIR spectral range are elucidated (Figure 5). The peak backscattering efficiency of 11.90 is attained by a $Ti{O}_2/Au$ core/shell nanoparticle with an overall diameter of 110 nm and a shell thickness fraction of 0.15, corresponding to a gold shell thickness of 16.5 nm. This study presents a theoretical analysis of the optical properties of $Ti{O}_2/Au$ nanoshells, focusing on backscattering efficiency within the conventional OCT wavelength range (from 830 to 1310 nm). The results indicate that by modulating the dimensions of the core and shell, the backscattering resonance of gold nanoshells can be systematically adjusted across a wide spectrum, from the visible to the near infrared. The backscattering resonance of gold nanoshells can also be fine-tuned to manifest varying peak positions and peak intensities corresponding to different size parameters. By adjusting the core and shell dimensions, it is possible to maximize backscattering within the near-infrared spectral window typically (830–1310 nm), enhancing performance for OCT imaging in non-destructive testing of structural polymer material that is reinforced by these nanoparticles.

Building upon this framework, the methodology was extended to $F{e}_3{O}_4/Au$ spherical nanoshells embedded in human tissue [38]. The aim was to optimize their optical absorption properties for enhanced photothermal efficiency thanks to enabling the fine-tuning of particle geometry. This approach maximizes light-to-heat conversion in photothermal therapy applications.

4. Discussion

$Ti{O}_2/Au$ Nanoshells as Contrast Agents for Non-Destructive Testing by Optical Coherence Tomography

Figure 6 shows the curves of backscattering efficiencies as functions of the wavelength of nanoparticles with a selected diameter D = 110 nm and a selected thickness fraction ${\mathrm{t}}_{\mathrm{f}}=$ 0.15, corresponding to an absolute maximum of backscattering efficiencies. Herein, an interesting feature that we can note in this figure is that the backscattering of the optimized ${\mathrm{TiO}}_2/\mathrm{Au}$ nanoshell exhibited a strong light backscattering ability that was found to be 12 times that of the ${\mathrm{TiO}}_2$ nanoparticle with the same size, and the backscattering of light peaked at an excitation around 930 nm in the main wavelength range for lasers used in OCT from 830 nm to 1330 nm; the ${\mathrm{TiO}}_2$ nanoparticle with the same size made a negligible contribution to the backscattering intensity for wavelengths between 300 and 1000 nm.

This study focuses on the image analysis of polymeric materials, aiming to identify nanoparticles with high backscattering efficiency and reduced dimensions to improve their integration into a polymer matrix. This objective was achieved by optimizing the ${\mathrm{\alpha }}_{\mathrm{back}}$ coefficient at the operational wavelengths employed in OCT. The external dimensions and shellthickness proportions of the ${\mathrm{TiO}}_2/\mathrm{Au}$ nanoshells were fine-tuned, thus achieving peak values of ${\mathrm{\alpha }}_{\mathrm{back}}$ at a standard OCT source wavelength of around 930 nm. For comparison, an identical methodology was executed for pure ${\mathrm{TiO}}_2$ nanoparticles. Figure 6 shows the resulting ${\mathrm{\alpha }}_{\mathrm{back}}$ spectra for the optimized geometric parameters of the nanospheres. As illustrated at Figure 7, the ${\mathrm{TiO}}_2/\mathrm{Au}$ nanoshells effectively backscatter infrared light, whereas the ${\mathrm{TiO}}_2$ nanoparticles of same size contribute minimally to the backscattering intensity across 300 to 1000 nm wavelengths.

For comparison, we also summarized in

Table 1. The backscattering efficiency of various plasmonic and dielectric nanoparticles embedded in optical or polymeric matrices subjected to incident light of wavelength λ.

Type of Nanoparticles	Host Matrix	λ (nm)	Backscattering Efficiency
Au spherical NPs(~20–80 nm) [24]	Fused silica (optical fiber)	60,900	↗ by a factor of 5
${\mathrm{HfO}}_2$ NCs (4–6 nm) [32]	CFRP, polymer resin	930 nm	~3
$Ti{O}_2/Au$ spherical core/shell PMNPs (110 nm)	PEEK polymer	930 nm	10

a comparative analysis of the backscattering efficiency of various plasmonic and dielectric nanoparticles embedded in optical or polymeric matrices with respect to their contrast-enhancing performance for OCT. The ${\mathrm{TiO}}_2/\mathrm{Au}$ core/shell nanoparticles embedded in a PEEK matrix, as in this study, show a backscattering efficiency (${\mathrm{Q}}_{\mathrm{back}}$) of ~10 at 930 nm, outperforming previous approaches with fused silica fibers and epoxy matrices and demonstrating a tenfold enhancement of the OCT signal in polymer-based non-destructive imaging applications.

These findings corroborate previous studies where simulation-based approaches successfully guided experimental setups. The accurate prediction of optical responses for the investigated nanoparticles reinforces the efficacy of using computational simulations to prioritize experimental efforts and refine hypotheses. These theoretical observations suggest that $Ti{O}_2/Au$ core/shell nanostructures remain promising candidates for advanced imaging and NDT applications. However, translating these theoretical insights into practical applications presents a significant challenge for the scientific and technological community at present.

This study shows that gold nanoshells, particularly $Ti{O}_2/Au$ nanoparticles, represent some of the most promising materials examined as agents for enhancing backscattering contrast in OCT. Their potential stems from the highly tunable characteristics of LSPR. By varying the size and core composition of the gold nanoparticles, both the plasmonic resonance peak and the backscattering ratio can be precisely modulated across the visible to NIR spectral domains.

Enhanced backscattering leads to increased OCT signal intensity when dielectric–plasmonic nanoparticles are illuminated at their localized surface plasmon resonance wavelength, producing amplified backscattered signals within the surrounding medium. Since OCT detects backscattered light from refractive index variations in polymers, which typically exhibit minimal backscattering, the incorporation of gold nanoshells exhibiting strong resonance at the OCT source wavelength can enhance the signal detectability emitted from the polymer matrix. In contrast, homogeneous $Ti{O}_2$ nanospheres display negligible backscattering and lack significant plasmonic resonance in the near-infrared region. Therefore, the use of $Ti{O}_2/Au$ nanoshells with high backscattering efficiency at operational wavelengths is an effective way to generate contrast enhancement.

This spectral tunability leads to significant improvements in light scattering and an amplification in OCT signal intensity, particularly within PEEK$/Ti{O}_2/Au$ PMNP composite samples. This enhanced imaging capability can be attributed to the distinctive optical properties of the incorporated $Ti{O}_2/Au$ plasmonic metal nanoparticles (PMNPs), particularly their pronounced and efficient backscattering capabilities within the NIR spectrum.

This study demonstrates that leveraging the backscattering of integrated gold nanoshells enables the localization and quantification of defects via a non-destructive OCT-based approach. For homogeneous $Ti{O}_2$ nanoparticle-reinforced PEEK matrices, backscattering Mie calculations and OCT imaging confirmed the absence of detectable defects due to minimal backscattering across the spectrum. Conversely, $Ti{O}_2/Au$ nanoparticle-reinforced PEEK matrices exhibited a strong and distinguishable backscattering signal. Given the cost-effectiveness of dielectric $Ti{O}_2$ and the exceptional plasmonic properties of thin gold shells, these bifunctional nanocomposites represent a novel class of materials combining mechanical robustness with enhanced optical contrast in the near-infrared region, offering promising prospects for advanced NDT applications using OCT.

Although backscattering measurements alone may not precisely delineate or quantify all embedded features, they can proficiently ascertain the presence, localization and relative dimensions of structural imperfections within the material.

5. Conclusions

To elucidate the mechanisms underlying crack and delamination initiation and their propagation in polymeric materials, it is essential to first characterize their intrinsic optical properties. In situ characterization enables non-invasive and non-destructive visualization of potential damage, highlighting the relevance of techniques such as OCT. Given the low optical contrast of many polymer matrices, this study presents an approach for enhancing OCT imaging by incorporating plasmonic $Ti{O}_2/Au$ core/shell nanoparticles into a PEEK polymer laminate.

Numerical simulations based on Lorenz–Mie theory were used to model light backscattering from individual $Ti{O}_2$ and $Ti{O}_2/Au$ nanoparticles embedded in a non-absorbing, isotropic PEEK matrix across a spectral range of 300–1100 nm and particle diameters of 2–500 nm. The results reveal that $Ti{O}_2/Au$ nanoshells exhibit a tunable LSPR, producing a strong backscattering peak that can be aligned with OCT wavelengths (830–1310 nm). This resonance significantly enhances OCT signal intensity, overcoming the minimal backscattering typically observed in polymers and homogeneous $Ti{O}_2$ nanoparticles.

The findings demonstrate that $Ti{O}_2/Au$ nanoshells provide high scattering efficiency and are well-suited as OCT contrast agents for defect localization and quantification in polymeric materials. In contrast, PEEK/$Ti{O}_2$ composites show negligible backscattering and lack plasmonic resonance in the near-infrared range. By combining the cost-effectiveness of $Ti{O}_2$ with the remarkable plasmonic properties of thin gold shells, this work introduces a novel class of nanoparticle-embedded polymer nanocomposites optimized for non-destructive testing through OCT imaging.