Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices

Tsegaye Atnaf; Shewa Getachew

doi:doi:10.11648/j.am.20241304.13

Research Article |

| Peer-Reviewed

Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices

Tsegaye Atnaf

, Shewa Getachew^*

Published in Advances in Materials (Volume 13, Issue 4)

Received: 13 November 2024 Accepted: 28 November 2024 Published: 30 December 2024

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Abstract

We theoretically and numerically investigated the local field enhancement factor (LFEF), absorption coefficient, refractive index, and group velocity of spherical core-shell nanocomposites (NCs) using the quasi-static approach. By solving Laplace’s equations, we derived expressions for the enhancement factor, polarizability, absorption coefficient, refractive index, and group velocity for each core-shell NCs. Our findings show that the LFEF, absorption coefficient, and group velocity of spherical core-shell NCs exhibit two peaks, while the real part of the refractive index shows four distinct peaks. Additionally, the core-shell nanocomposites demonstrate greater tunability and a higher intensity of the enhancement factor when the host matrix is changed from CdSe to SiO₃. The study further reveals that, for spherical nanocomposites, the first two peaks of the enhancement factor and extinction cross-sections occur at the same frequencies. Moreover, all extinction cross-section peaks are lowest when the dielectric function of the host matrix is SiO₃, whereas the peaks are highest for CdSe. The variation in peak values, despite having the same number of peaks for different shapes, indicates that the shape of the core-shell NCs significantly influences the intensity, number, and positions of the peaks in the enhancement factor and optical cross-sections. Such nanocomposites hold potential for applications in optical sensing, biosensing, as well as in photonic and electronic devices.

Published in	Advances in Materials (Volume 13, Issue 4)
DOI	10.11648/j.am.20241304.13
Page(s)	80-91
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Absorption Coefficient, Host Matrix, Nanocomposites, Fast Light, Slow Light

1. Introduction

Over the past three decades, the optical properties of nanoparticles have been extensively studied using various approaches. Among them, core-shell NCs have shown vast applications in numerous fields of science and technology

[1]

. It has been observed that the optical properties of dielectric core-metallic shell NCs are strongly influenced by factors such as size, metal fraction, spatial distribution of the core-shell structure, and the surrounding medium

[2-5]

. Additional research has further demonstrated that although size and the embedding medium are important parameters, the surface plasmon resonances of core-shell nanoparticles are much more sensitive to particle shape

[6]

. Therefore, altering the shape of core-shell NCs is an effective method to tune surface plasmon resonances and, consequently, their optical properties. Due to their geometric shape, which allows tunability of optical properties, spheroidal core-shell NCs have garnered significant interest

[7]

. Since this geometry supports plasmon resonances, spheroidal core-shell NCs consisting of a dielectric core coated with a metallic shell are among the most useful structures for achieving a wide tunability range from the visible to the infrared regions of the electromagnetic spectrum

[8, 9]

Among various combinations of core-shell nanostructures, metal@metal core-shell nanocomposites exhibit novel properties that are valuable for numerous applications. These unique characteristics Preprint submitted to primarily stem from the interaction between metallic (plasmonic) materials and the incident electro-magnetic field, significantly enhanced by the surface plasmon resonance (SPR) phenomenon and the interaction of metal shell plasmons with the metal interior material

[10]

. At the SPR frequencies, the collective oscillations of conducting electrons in the metallic nanoparticle are driven by incident resonant light, which acts as electric radiating dipoles. A two-layer bimetallic core-shell nanostructure has been investigated for desired applications both experimentally

[11-14]

and theoretically

[15, 16]

. sThe position of the surface plasmon band in core-shell nanostructures can be tuned based on size, shape, and surface morphology

[17, 18]

. Among these substrates, SiO₂@Au NCs have been completely studied in various research in chemistry and biomedicine fields over the past year due to their unique Physicochemical and plasmonic characteristics

[19, 20]

At the nanoinclusion, nanoparticles (NPs) of both ZnO and Ag exhibit distinctive catalytic and optical properties, making them well-suited for medical applications. The uncoated Ag and ZnO nanoparticles have demonstrated significant antibacterial properties, leading to their widespread use in fields such as in cosmetic industry and the biomedicine

[21]

. In comparison to other metallic NPs, Ag NPs exhibit Ag NPs demonstrate reduced toxicity, outstanding biocompatibility, and antimicrobial characteristics

[22-24]

. SiO₂ coated quantum dots are instrumental in biomedical applications, particularly for sensing, probing, and labeling cells and tissues due to their long-term chemical and optical stability. Furthermore, their photonic conversion capabilities make them ideal candidates for optoelectronic devices

[25]

. Si₃N₄ thin films play a crucial role in modern electronic device production as diffusion masks and passivation layers. Additionally, the combination of SiO₂ and Si₃N₄ films has enabled the realization of a new generation of electronic devices with memory properties

[26]

Moreover, since zinc telluride (ZnTe) can be easily doped, it finds applications in blue light emitting diodes, laser diodes, and solar cells, making it essential for optoelectronic device design. In CdTe/ZnTe solar cells, the ZnTe semiconductor enhances efficiency by reducing the high electron affinity of CdTe

[27]

. ZnTe is also utilized in nonlinear optics for producing terahertz radiation and as an electro-optical detector. Some applications of the CdTe semiconductor binary compound include electro-optical modulators in infrared optical materials

[28, 29]

. Numerous experimental, computational, and theoretical studies have explored the effect of shape on the optical properties of core-shell NCs, such as SiO₂@Au

[30]

, Ag@SiO₂

[31]

, CdSe@Ag

[32]

, and ZnO@Au

[33]

This paper presents computational results obtained from the study of the absorption coefficient, refractive index, and group velocity in metal-coated dielectric NCs with spherical nanoinclusions embedded in an active dielectric host matrix. We demonstrate that NCs with spherical nanoinclusions featuring dielectric cores embedded in various host matrices strongly absorb light at two resonant frequencies, unlike NCs with dielectric-coated metal spherical nanoinclusions, which have only one resonant frequency. The research indicates that the dielectric function (DF) of various host matrices substantially amplifies the intensity, absorption coefficient, refractive index, gains, and group velocity. This amplification facilitates the transmission of strongly attenuated narrow pulses of slow, backward, and fast light within the NCs media. The author asserts that this investigation is the first to examine the absorption coefficient, refractive index, and the occurrence of slow and fast light in NCs featuring spherical nanoinclusions, particularly those with metal-coated dielectric cores. These findings are considered original contributions to the field.

2. Theoretical Bases and Mathematical Computations

Our work focused on a type of nanocomposite material called spherical metal coated dielectric NCs. These NCs consist of a core made of a dielectric material with a radius of r₁ and a dielectric function represented by

ε_{d}

. The shell surrounding the core has a radius of r₂ and its dielectric function varies depending on the electric field applied to it, which we denote as

ε_{m}

. The entire nanocomposite is embedded within a host matrix made of a dielectric material with a dielectric function of

ε_{m}

. The nanocomposite is then exposed to incident electromagnetic radiation

[8, 11]

. In order to investigate the impact on the absorption coefficient, refractive index and group velocity, we explored four different dielectric function of the host matrices. Those are CdSe, ZnO, Si₃N₄ and SiO₃ host matrices. In this study, we separately examined both components of the DFs to analyze their individual effects.

2.1. Electric Potential Distribution in Spherical Metal NCs

By applying boundary conditions and solving Laplace’s equation for spherical metal-coated dielectric NCs, the electric potential distributions within the core-shell structure and surrounding host matrix are determined. The core-shell nanocomposite consists of a dielectric core with radius r₁ and dielectric function

ε_{d}

, and a metallic shell characterized by radius r₂ and dielectric function

ε_{m}

(where r₁ < r₂). The host material is described by its dielectric function,

ε_{h}

. The electric potential distributions are expressed by three distinct functions:

ϕ_{d}

for the dielectric core,

ϕ_{m}

for the metallic shell, and

ϕ_{h}

for the host matrix. These functions are derived based on the equation referenced in

[12, 13]

Φ_{d} = - E_{h} Ar \cos θ, r \leq r_{1}

Φ_{m} = - E_{h} (Br - \frac{C}{r^{2}}) cosθ, r_{1} \leq r \leq r_{2}

Φ_{h} = - E_{h} (r - \frac{D}{r^{2}}) \cos θ, r > r_{2}

In this scenario, E_h denotes the applied electric field, while r and θ refer to the spherical coordinates of the observation point. The z-axis is aligned with the direction of the vector E_h. The coefficients A, B, C, and D are unknowns that must be determined by applying the continuity conditions for the electric potential and displacement vector at the boundaries between the core-shell and shell-host matrix interfaces. At the boundary between the dielectric core and the metallic shell of a metal-dielectric nanocomposite, the electric potential remains continuous. This is because there cannot be a discontinuous change in the potential across the interface; thus, the potential in both the dielectric (core) and metallic (shell) regions must be equal at the interface. This condition can be expressed as:

ϕ_{d} = ϕ_{m}, r = r_{1}

(1)

ϕ_{m} = ϕ_{d}, r = r_{2}

(2)

The continuity of the displacement vector (which is related to the electric field) must also be maintained at the interface. This condition can be expressed as:

ε_{d} \frac{\partial ϕ_{d}}{\partial r} = ε_{m} \frac{\partial ϕ_{m}}{\partial r}, r = r_{1}

(3)

ε_{m} \frac{\partial ϕ_{m}}{\partial r} = ε_{h} \frac{\partial ϕ_{h}}{\partial r}, r = r_{2}

(4)

The dielectric constants of the dielectric core, metal shell, and dielectric host are represented by

ε_{d}

ε_{m}

, and

ε_{h}

, respectively. By solving equations 1, 2, 3 and 4 an simultaneously, the values of the unknown coefficients can be determined as listed below.

A = \frac{9 ε_{h} ε_{m}}{2 pη}

(5)

B = \frac{3 ε_{h} (ε_{d} + 2 ε_{m})}{2 pη}

(6)

C = \frac{3 ε_{h} (ε_{d} - ε_{m})}{2 pη} {r_{1}}^{3}

(7)

D = (1 - \frac{3 p ε_{h} (ε_{d} - ε_{m}) + 9 ε_{h} ε_{m}}{2 pη}) {r_{2}}^{3}

(8)

Where,

p = 1 - {(\frac{r_{1}}{r_{2}})}^{3}

is the metal volume fraction in the inclusion,

η = {ε_{m}}^{2} + \prod ε_{m} + ε_{d} ε_{h}

(9)

\prod = (\frac{3}{2 p} - 1) ε_{d} + (\frac{3}{p} - 1) ε_{h}

(10)

The Drude-Sommerfeld model is a theoretical framework that describes the behavior of electrons in metals, offering a simplified yet effective method for understanding their electrical and optical properties. This model yields a straightforward expression for the metal’s dielectric function (

ε_{m}

), which indicates how the material responds to an external electric field and influences its optical characteristics. According to the Drude-Sommerfeld model, the DF of the metal (

ε_{m}

) is expressed as follows

[8, 9]

ε_{m} = ε_{\infty} - \frac{1}{z (z + iγ)}

(11)

In this context,

ε_{\infty}

denotes the effect of bound electrons on polarizability. The variable z represents the ratio of the incident radiation frequency (

ω

) to the frequency of the bulk plasmon (

ω_{p}

), while

γ

indicates the ratio of the electron damping constant (

ν

) to the plasma frequency (

ω_{p}

). Additionally, the real and imaginary components of

ε_{m}

can be expressed as

ε_{m} = ε_{m}^{'} + i ε_{m}^{''}

(12)

Let's denote the parts, both real and imaginary of the equations above as follows:

ε_{m}^{'} = ε_{\infty}^{'} - \frac{1}{z (z + γ)}

ε_{m}^{''} = ε_{\infty}^{''} + \frac{1}{z (z^{2} + γz)}

2.2. Dispersion Properties of Metal-Dielectric Composites with Spherical Nanoinclusions

Dispersion is the phenomenon in which the refractive index or other optical properties of a material change with the frequency or wavelength of light. In the case of composites containing spherical nanoinclusions, dispersion occurs due to the interaction between the nanoinclusions and the sur-rounding matrix material. The incorporation of spherical nanoinclusions within a nanocomposite (NCs) creates additional interfaces, leading to complex interactions with incident electromagnetic waves. These interactions can result in dispersion phenomena, such as a frequency-dependent refractive index, absorption, and scattering. The polarization of an individual metal covered spherical nanoinclusion with a dielectric core embedded in a dielectric host matrix can be presented as follows

[2, 14, 15]

D = α r_{2}^{2} = α = 1 - \frac{3}{2} \frac{Δ}{η}

(13)

Where,

Δ = ε_{h} ((\frac{3}{2 p} - 1) ε_{m} + ε_{d})

Here, D represents the effective polarizability of the inclusion, while p denotes the metal fraction of the inclusion (r₁ and r₂ are the radii of the dielectric core and the metal shell, respectively). Since

ε_{m}

is complex, the terms

Δ, α, \prod

and

η

are also complex.

2.3. Refractive Index of Composite with Passive Host Matrix

The effective dielectric function (

ε_{e}

) of the composite can be determined using the Clausius Mossotti formula

[15]

\frac{ε_{e} - ε_{h}}{ε_{e} + 2 ε_{h}} = \frac{4 π}{3} DN

(14)

Where D is defined by equation (13), and N represents the density of the inclusions. The effective dielectric function,

ε_{e}

, is provided by the equation below.

ε_{e} = ε_{h} (1 + 3 f \frac{α}{1 - fα} = n^{2}

(15)

Where,

f = \frac{4 π}{3} r_{2}^{3} N

represents the volume fraction of spherical inclusions, and

α

denotes the polarizability of the inclusions.

n^{2} = ε_{h} (1 + 3 f \frac{α^{'} + i α^{″}}{1 - f (α^{'} + i α^{″})})

n^{2} = ε_{h} (1 + 3 f \frac{α^{'} - f | {α |}^{2} + i α^{″}}{{(1 - f α^{'})}^{2} + ({{fα}^{″})}^{2})}) = b_{1} + i b_{2}

(16)

Where,

b_{1} = ε_{h} (1 + 3 f \frac{α^{'} - f | {α |}^{2} + i α^{″}}{{(1 - f α^{'})}^{2} + ({{fα}^{″})}^{2})})

b_{2} = ε_{h} 3 f \frac{α^{″}}{{(1 - f α^{'})}^{2} + ({{fα}^{″})}^{2})}

Equating the real and the imaginary parts

n = n^{'} + i n^{″}

with equation (16) can give us the expressions

n^{' 2} - n^{″ 2} = b_{1}

(17)

{2 n}^{'} n^{″} = b_{2}

(18)

In this representation, the refractive index is divided into its real part, denoted as

n^{'}

, and its imaginary part, denoted as

n^{″}

. By isolating these real and imaginary components, we can effectively express the refractive index in terms of b₁ and b₂.

n^{' 2} = \frac{1}{2} (\sqrt{b_{1}^{2} + b_{2}^{2}} + b_{1})

(19)

n^{″ 2} = \frac{1}{2} (\sqrt{b_{1}^{2} + b_{2}^{2}} + b_{1})

(20)

These equations are utilized to numerically compute the

n^{'}

and

n^{″}

of composites that contain metal coated dielectric inclusions for various host matrices.

2.4. Absorption Coefficient

The wave equation allows for a solution represented as a plane wave given by E=

E_{0} e^{i (k^{'} x - ωt)}

. The wave number k = nω/c is a complex quantity that can be expressed in the form

k = k^{'}

i k^{''}

. Therefore, we can rewrite the equation above as

[34]

E = E_{0} e^{i (k^{'} x - ωt)} e^{- i k^{''} x}

(21)

The term

e^{- i k^{''} x}

indicates that the wave diminishes as it travels. The intensity of an electromagnetic wave is proportional to the square of the electric field (i.e., I ≈ E²). According to Beers law, we can express the relationship as follows:

I = I_{0} e^{- α_{abs}^{''} x}

(22)

where

α_{abs}

is known as the absorption coefficient. Therefore, we can write the absorption coefficient as

α_{abs} = 2 k^{''} = 2 n^{''} ω / c

(23)

α_{abs} = 2 n^{''} z ω_{p} / c

(24)

2.5. Group Velocity

The group velocity

v_{g}

of a wave packet is the velocity at which the overall shape of the wave packet (or pulse) travels. This is particularly important when dealing with wave packets composed of multiple waves with different wave numbers

k

. If the angular frequency

ω (k)

is a linear function of

k

, the wave packet will move without distortion, maintaining its shape. This is because all components of the wave packet travel at the same speed. The group velocity

v_{g}

is defined as the derivative of the angular frequency

ω (k)

with respect to the wave number

k

. In the case where the angular frequency

ω (k)

is approximately linear near the central wave number

k_{0}

, the group velocity

v_{g}

around that point

k_{0}

is given by:

v_{g} = \frac{dω}{dk}

(25)

This expression shows that the velocity at which the pulse travels is determined by the slope of the ω(k) versus

k

curve at the central wave number

k_{0}

. When the wave packet moves with this velocity, it remains undistorted, as all components of the wave packet move together coherently. The group velocity

v_{g}

of a wave packet can be expressed in terms of the group refractive index

n_{g}

as follows:

v_{g} = \frac{c}{n_{g}}

(26)

Where,

c

is the speed of light in a vacuum. The group refractive index

n_{g}

is related to the ordinary refractive index

n (z)

by:

n_{g} = n (z) + ω \frac{dn (z)}{dz}

(27)

This expression reflects that different frequency components of a wave packet propagate at varying speeds due to dispersion, which ultimately affects the overall group velocity of the wave packet. Slow light occurs when the group velocity v g of light is significantly less than the speed of light in a vacuum

c

. The condition

\frac{dn}{dω} ≪ c

signifies that the dispersion is such that the group velocity is considerably diminished. In the context of normal dispersion (

\frac{dω}{dk} > 0

), where the refractive index

n

exceeds 1, the group velocity is lower than the phase velocity. This occurs because the refractive index

n

increases with frequency, resulting in a reduction in group velocity. Conversely, fast light pertains to scenarios where the group velocity

v_{g}

surpasses the speed of light in a vacuum

c

or even turns negative. This phenomenon is typically linked to anomalous dispersion. In regions characterized by anomalous dispersion, where

\frac{dω}{dk} < 0

(indicating that the refractive index decreases with frequency), the group velocity can indeed become negative. However, this does not mean that information or energy travels faster than

c

; rather, it suggests that the peak of the pulse appears to move in the opposite direction to the wave vector.

3. Results and Discussion

In this study, we examined the enhancement factor, absorption coefficients, refractive index, and group velocity of ZnTe@Ag core-shell spherical nanoparticles embedded in various host matrices. The model taken into account in this study specifically includes a dielectric core of ZnTe, a silver (Ag) shell, and different host materials. The parameters selected for numerical calculations are as follows

[35, 36]

ε_{d} = 9.8

ε_{\infty} = 4.5

ω_{p} = 1.45 x 10^{14} rad / s

υ = 1.67 x 10^{14} rad / s

, and z = 0.2.

3.1. Effect of Core-Shell Radii on LFEF of Metal Coated Dielectric Spherical NCs

Figure 1 illustrates the plot of the LFEF for five different core-shell radii, while maintaining a constant shell thickness (r₂) of 40nm. The analysis indicates that the LFEF of the spheroidal core-shell NCs displays two distinct peaks. As the core-shell radii increase from 0.4 to 0.6, the first resonance peak (counted from left to right) of the LFEF for the spherical core-shell NCs moves toward lower frequencies, whereas the second peak of resonance (counted from right to left) shifts toward higher frequencies. This behavior can be understood through the plasmon hybridization theory within the quasi-static limit

[37, 38]

. In this theory, sphere and cavity plasmons are generated on the outer and inner surfaces of the nanoshell, respectively., and these plasmons hybridize to produce two new resonance modes: the lower energy plasmon mode is symmetric, while the higher energy plasmon mode is antisymmetric

[39]

. The intensity of these plasmon modes is influenced by the metallic shell’s thickness. The asymmetric and antisymmetric plasmonic modes are represented by the first and second peaks of resonance peaks, respectively. The first set of peaks increases in value and experiences a blue shift as the metallic shell’s thickness increases (i.e., as r₁/r₂ decreases). This enhancement is attributed to a rise in the number of available free electrons that participate in the surface plasmon oscillations at the Ag/ZnO interface

[40]

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Figure 1. LFEF (|A|²) as a function of frequency for different core-shell radii. r₂= 0.40nm fixed constant.

When the magnitude of the NPs is increased (i.e., the magnitude of the ZnTe@Ag core-shell, while keeping the shell thickness constant) from r₁/r₂= 0.4 to r₁/r₂ = 0.6, the values of the two resonance peak sets are are enhanced, although the peak positions remain unchanged. This indicates that the magnitude of the NCs does not influence the locations of the resonant peaks; rather, it is the shift in the ratio r₁/r₂ that is the role of adjusting the peak locations to the intended wavelength, supposing that all other variables stay constant. Figures 1 and 2 emphasizes the significance of both the core-shell radii and the size of the nanoparticles in determining the optical properties of spheroidal core-shell NCs, especially in tuning and enhancing the resonance peaks of the LFEF. The findings presented in

[13]

are consistent with these findings.

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Figure 2. LFEF for spherical nanoparticles versus core-shell radii (R₁/R₂) and frequency z in linear host matrix.

The ability to adjust the resonance peaks of the LFEF by modifying the core-shell ratio offers a powerful tool for engineering the optical and plasmonic properties of spheroidal core-shell NCs, with important implications for various applications in photonics, optoelectronics, sensing, and nanoscale energy technology. Figure 2 presents a 3D view of figure 1.

3.2. Effect of Metal Volume Fractions on Refractive Index of Metal Coated Dielectric Spherical NCs

The study reveals that the number of maximum peaks in the absorption cross-section for nanocomposites varies based on the host matrix. In particular, it was observed that spherical nanocomposites exhibit two distinct peaks.

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Figure 3. (a) Absorption cross section (

α_{abs}

) and (b) refractive index as a function of frequency for different host matrix, r₂ = 0.40nm fixed constant.

Using equation (24), figure 3 illustrates that the imaginary part of the refractive index and the absorption coefficient are directly proportional to each other. The typical light propagation length in the medium can be determined using the formula

l

≈ 1/

α_{abs}

[41]

. To create conditions that allow for significant light wave propagation, it is essential to change the dielectric within the host matrix from CdSe to SiO₃. It is possible to succeed by introducing various dielectric functions for the host matrix. The host matrix containing SiO₃ enhances the incident electromagnetic wave instead of absorbing it.

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Figure 4. (a) Real of refractive index (

α_{abs}

) and (b) imaginary of refractive index for different core-shell radii.

Additionally, the study demonstrates that even when the amount of peaks remains consistent across various host matrices, their magnitudes can vary. This indicates that the host matrix of core-shell NCs influences both the number and the relative intensities of the absorption cross-section peaks. Figure 3(a) also shows that the resonance position of the first peak experiences a slight red shift when the host matrix of the spherical NCs transitions from CdSe to SiO₃. Conversely, a blue shift is observed when the host matrix has been modified in the opposite direction.

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Figure 5. Real refractive index versus resonate dimensionless frequency (z) and core-shell radii r₁/r₂ in SiO₃ host matrix.

These shifts result in the first and second peaks becoming closer together in the SiO₃ host matrix compared to the other dielectric constants investigated. The study emphasizes the substantial the host matrix influence on the number, magnitudes, and resonance positions of the absorption cross-section peaks in spherical NCs. These findings offer valuable insights for a deeper understanding and optimization of the optical properties of these nanostructures. Figure 3(b) shows that there are two maximum peaks in the refractive index, which occur at different frequencies and volume fractions. When the dielectric host matrix of the spherical NCs changes from CdSe to SiO₃, the amount of the first peak decreases, while the second peak experiences a slight increase. Furthermore, both the first and second resonance peaks of the refractive index shift toward higher frequencies. Importantly, the shift of the first maximum peak toward higher frequencies is more pronounced than that of the second maximum peak. This observation indicates that the varying host matrix of the spherical NCs influences the first and second resonance peaks of the refractive index.

In Figure 4(a),

n^{'}

is plotted against z, while Figure 4(b) presents

n^{''}

versus z. These figures focus on the resonant frequencies of a composite material composed of metal-coated dielectric spherical inclusions within a passive dielectric core, with different metal fractions indicated by p. The results reveal two peak values for both

n^{'}

and

n^{''}

at distinct resonant frequencies.

Notably, the peak on the left side of the graph is of greater magnitude than the peak on the right, as shown in both

n^{'}

and

n^{''}

. This difference indicates an asymmetry in the refractive index properties of the composite material. Similarly, Figure 4(a) and (b), as well as Figures 5 and 6, illustrate the impact of core-shell radii on the real and imaginary parts of the refractive index of the composite material. As the ratio of the core radius to the shell radius (r₁/r₂) decreases, the first resonance peak increases (blue shift), while the second maximum peak slightly decreases (red shift). The relationship between the absorption coefficient (

α_{abs}

) and the refractive index (

n^{''}

) is illustrated in Figure 7(a) and (b), as outlined in equation (24).

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Figure 6. Refractive index imaginary part (

n^{''}

) versus resonate dimensionless frequency (z) and core-shell radii r₁/r₂ in SiO₃ host matrix.

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Figure 7. (a) Absorption cross section (

α_{abs}

) and (b) refractive index as a function of frequency for different core-shell radii in SiO₃ host matrix.

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Figure 8. Absorption coefficient (

α_{abs}

) versus resonate dimensionless frequency (z) and core-shell radii r₁/r₂ in SiO₃ host matrix.

The figure displays the absorption coefficients and refractive index as functions of frequency for various core-shell ratios of the spherical nanoparticles. The absorption of the effective medium composite reaches a maximum at two distinct frequencies. As the core-shell radii of the spherical nanoparticles decrease, the first resonance peak not only increases but also shifts toward higher frequencies (a blue shift). This indicates that the composite material demonstrates stronger absorption at the first resonance frequency as the core-shell ratio decreases. The second resonate peak shows a slight decrease and shifts towards lower frequencies (red shift). This indicates that the absorption at the second resonance frequency decreases marginally as the core-shell ratio declines.

These findings illustrate the essential role of the SiO₃ host matrices in modulating the absorption coefficients and refractive index of the effective composite material. The study emphasizes the considerable impact of the core-shell structure on the resonance peaks and optical properties of the NCs material that includes spherical nanoparticles. Similarly, Figure 8 depicts the effect of core-shell radii on the absorption coefficients of the composite material. As the ratio of the core radius to the shell radius (r₁/r₂) decreases, the first resonance peak increases (blue shift), while the second maximum peak experiences a slight decrease (red shift). The study also performed numerical calculations and plotted the absorption coefficient of the composite material, taking into account various volume fractions (f) of spherical nanoparticles, as illustrated in Figure 9.

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Figure 9. Absorption cross section (

α_{abs}

) as a function of frequency for different volume fraction in SiO₃host matrix and r₂ = 0.40nm fixed constant.

The results indicate the existence of two maxima in the absorption coefficient, which occur at two distinct frequencies and volume fractions. As the volume fraction of the spherical nanoparticles rises from 0.001 to 0.003, the magnitude of the first peak increases, while the second peak exhibits a slight rise. Additionally, neither the first nor the second resonance peaks of the absorption coefficient shift; instead, they increase at two constant frequencies. This finding implies that the first and second resonance peaks of the absorption coefficient are influenced by the changing volume fraction of the spherical nanoparticles.

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Figure 10. Absorption cross section (

α_{abs}

) versus frequency and volume fraction in SiO₃ host matrix and r₂=0.40nm fixed constant.

The investigation of the absorption coefficient (

α_{abs}

) is currently being conducted in both 2D and 3D formats. While the primary focus is on the 2D analysis, Figure 10 illustrates the absorption coefficient in a 3D context. Interestingly, the physical quantities depicted in Figures 9 and 10 are the same, despite the differences in dimensionality. However, there are significant distinctions between the 2D and 3D graphs regarding the volume fraction of spherical nanoparticles (NPs) within the composite material. Figure 10 demonstrates a clear relationship between the dimensionless frequency, the volume fraction of the composite, and the absorption coefficient (

α_{abs}

) of the spherical nanocomposites. Specifically, as the volume fraction of the composite decreases, the

α_{abs}

also declines accordingly. This observed trend has important implications for the light propagation properties of the nanocomposite material. The results suggest that as the

α_{abs}

of the nanocomposites decreases, the typical light propagation length within the medium increases, as described by the inverse relationship l= 1/

α_{abs}

Consequently, the main observation is that as the volume fraction of the composite material decreases, the absorption coefficient also decreases, resulting in an increased light propagation length within the nanocomposites. The ability to adjust the light propagation length in these nanocomposites facilitates the optimization of light-matter interactions, which is essential for developing efficient and versatile photonic and optoelectronic devices. Controlling light propagation can enhance light harvesting, trapping, guiding, and manipulation, ultimately leading to improved performance across various applications.

3.3. Effect of Varying Host Matrix on Group Velocity

Figures 11 and 12 present the group index and group velocity for spherical nanoparticles (NPs) in different host matrices, specifically SiO₃ and Si₃N₄, respectively. The numerical results presented in Figure 11(b) demonstrate that the group velocity of light within the SiO₃ host matrix displays two distinct behaviors. In the proximity of the first resonant frequency, the group velocity corresponds to that of “fast light”, with a value of v_g=1.86c. Conversely, in the region of the second resonant frequency, the group velocity reflects that of “slow light”, with a value of v_g=0.96c. Altering the dielectric host matrix of the spherical NPs significantly influences the results.

Download: Download full-size image

Figure 11. Group index (n_g) and group velocity (v_g/c) in SiO₃ host matrix and r₂=0.40nm fixed constant.

The plots of the normalized group velocity (v_g/c) against the parameter z in Figure 11(b) and Figure 12(b) for the SiO₃ and Si₃N₄ host matrices, respectively, exhibit similar types of curves. In the SiO₃ host matrix, the first peak on the left displays fast-light group velocities, with v_g = 1.86c, while the second peak on the right shows slow-light group velocities, with v_g = 0.95c, as illustrated in figure 11. For the Si₂N₄ host matrix in figure 11, both the first peak on the left and the second peak on the right exhibit slow-light group velocities. The first peak has a group velocity of v_g = 0.94c, while the second peak has a group velocity of v_g = 0.58c. These results indicate that the dielectric host matrix of the spherical NCs is critical in determining the group velocities of light, resulting in the observed fast-light and slow-light phenomena.

Download: Download full-size image

Figure 12. Group index (n_g) and group velocity (v_g/c) in Si₃N₄ host matrix and r₂ =0.40nm fixed constant.

This study emphasizes the importance of the host matrices in influencing the optical properties of the nanocomposite material containing spherical nanoparticles.

Download: Download full-size image

Figure 13. Group index (n_g) versus dimensionless frequency (z) and volume fraction (f) in SiO₃ host matrix and r₂=0.40nm fixed constant.

Figure 13 illustrates the relationship among the group index, dimensionless frequency, and volume fraction. The results indicate that as the volume fraction increases, the group index decreases into the negative range while remaining constant in the positive range. The resonant frequencies of the nanoparticles are significantly influenced by the dielectric environment of the host matrices. In the SiO₃ matrix, the first and second resonant frequencies correspond to fast light and slow light behaviors, respectively. Conversely, in the Si₂N₄ matrix, both the first and second resonant frequencies display slow light behavior. The differences in dielectric properties, resonant frequencies, light-matter interactions, and dispersion characteristics between the SiO₃ and Si₂N₄ host matrices are key factors affecting the observed variations in group velocity, particularly the contrast between fast light and slow light behaviors.

4. Conclusions

In this study, we explored the optical properties of core-shell spherical nanoinclusions embedded in various host matrices. We conducted both theoretical and numerical analyses of the LFEF, absorption coefficient, refractive index, and group velocity of the system using the quasistatic approximation. Our findings indicate that there are two maximum values of the local field enhancement factor for different core-shell radii and host matrices. Consequently, the behavior of local field enhancement is significantly influenced by the core-shell radii and the host matrix. As the core-shell radii increase from 0.4 to 0.6, the first resonance peak (counted from left to right) of the LFEF for the spherical core-shell nanocomposites shifts towards lower frequencies, while the second resonance peak (counted from right to left) shifts towards higher frequencies. Furthermore, our study shows that both the first and second resonate peaks of the refractive index shift towards higher frequencies, with the first peak demonstrating a more significant shift compared to the second. This observation suggests that the varying host matrix of the spherical nanocomposites plays a crucial role in controlling the first and second resonance peaks of the refractive index.

The effective medium composite absorption reaches a maximum at two distinct frequencies. As the core-shell radii of the spherical nanoparticles decrease, the first resonance peak increases and shifts towards higher frequencies (a blue shift), indicating that the composite material exhibits stronger absorption at the first resonance frequency as the core-shell ratio decreases. Conversely, the second resonate peak slightly decreases and shifts towards lower frequencies (a red shift), suggesting that absorption at the second resonance frequency is slightly lower as the core-shell ratio decreases. These results demonstrate that the SiO₃ host matrices significantly influence the absorption coefficients and refractive index of the effective composite material. The interaction between the incident light and the nanoparticles is affected by the dielectric properties of the host matrix. In the SiO₃ matrix, the light-matter interaction is stronger, leading to more pronounced fast light and slow light effects. In contrast, the light-matter interaction in the Si₂N₄ matrix is less pronounced, resulting in a more uniform slow light behavior. The differences in dielectric properties, resonant frequencies, light-matter interaction, and dispersion characteristics between the SiO₃ and Si₂N₄ host matrices are key factors influencing the observed differences in group velocity, particularly regarding the contrast between fast light and slow light behaviors. We hope that the results obtained will have potential applications in optoelectronic and photonic devices based on ZnTe@Ag spherical nanocomposites.

Abbreviations

LFEF	Local Field Enhancement Factor
NCs	Nanocomposites
NPs	Nanoparticles
ZnTe	Zinc Telluride
DFs	Dielectric Functions
SPR	Surface Plasmon Resonance
SERS	Surface Enhanced Raman Spectroscopy

Author Contributions

Shewa Getachew: Conceptualization, Formal analysis, Investigation, Methodology, Software, Supervision, Visualization, Writing - original draft, Writing - review & editing

Tsegaye Atnaf: Conceptualization, Formal analysis, Methodology, Investigation, Supervision, Validation, Writing - review & editing

Data Availability Statement

This manuscript has no associated data or the data will not be deposited.

Conflicts of Interest

The authors declare no conflicts of interest.

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Atnaf, T., Getachew, S. (2024). Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices. Advances in Materials, 13(4), 80-91. https://doi.org/10.11648/j.am.20241304.13

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Atnaf, T.; Getachew, S. Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices. Adv. Mater. 2024, 13(4), 80-91. doi: 10.11648/j.am.20241304.13

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Atnaf T, Getachew S. Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices. Adv Mater. 2024;13(4):80-91. doi: 10.11648/j.am.20241304.13

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@article{10.11648/j.am.20241304.13,
  author = {Tsegaye Atnaf and Shewa Getachew},
  title = {Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices},
  journal = {Advances in Materials},
  volume = {13},
  number = {4},
  pages = {80-91},
  doi = {10.11648/j.am.20241304.13},
  url = {https://doi.org/10.11648/j.am.20241304.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.am.20241304.13},
  abstract = {We theoretically and numerically investigated the local field enhancement factor (LFEF), absorption coefficient, refractive index, and group velocity of spherical core-shell nanocomposites (NCs) using the quasi-static approach. By solving Laplace’s equations, we derived expressions for the enhancement factor, polarizability, absorption coefficient, refractive index, and group velocity for each core-shell NCs. Our findings show that the LFEF, absorption coefficient, and group velocity of spherical core-shell NCs exhibit two peaks, while the real part of the refractive index shows four distinct peaks. Additionally, the core-shell nanocomposites demonstrate greater tunability and a higher intensity of the enhancement factor when the host matrix is changed from CdSe to SiO3. The study further reveals that, for spherical nanocomposites, the first two peaks of the enhancement factor and extinction cross-sections occur at the same frequencies. Moreover, all extinction cross-section peaks are lowest when the dielectric function of the host matrix is SiO3, whereas the peaks are highest for CdSe. The variation in peak values, despite having the same number of peaks for different shapes, indicates that the shape of the core-shell NCs significantly influences the intensity, number, and positions of the peaks in the enhancement factor and optical cross-sections. Such nanocomposites hold potential for applications in optical sensing, biosensing, as well as in photonic and electronic devices.},
 year = {2024}
}

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TY  - JOUR
T1  - Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices
AU  - Tsegaye Atnaf
AU  - Shewa Getachew
Y1  - 2024/12/30
PY  - 2024
N1  - https://doi.org/10.11648/j.am.20241304.13
DO  - 10.11648/j.am.20241304.13
T2  - Advances in Materials
JF  - Advances in Materials
JO  - Advances in Materials
SP  - 80
EP  - 91
PB  - Science Publishing Group
SN  - 2327-252X
UR  - https://doi.org/10.11648/j.am.20241304.13
AB  - We theoretically and numerically investigated the local field enhancement factor (LFEF), absorption coefficient, refractive index, and group velocity of spherical core-shell nanocomposites (NCs) using the quasi-static approach. By solving Laplace’s equations, we derived expressions for the enhancement factor, polarizability, absorption coefficient, refractive index, and group velocity for each core-shell NCs. Our findings show that the LFEF, absorption coefficient, and group velocity of spherical core-shell NCs exhibit two peaks, while the real part of the refractive index shows four distinct peaks. Additionally, the core-shell nanocomposites demonstrate greater tunability and a higher intensity of the enhancement factor when the host matrix is changed from CdSe to SiO3. The study further reveals that, for spherical nanocomposites, the first two peaks of the enhancement factor and extinction cross-sections occur at the same frequencies. Moreover, all extinction cross-section peaks are lowest when the dielectric function of the host matrix is SiO3, whereas the peaks are highest for CdSe. The variation in peak values, despite having the same number of peaks for different shapes, indicates that the shape of the core-shell NCs significantly influences the intensity, number, and positions of the peaks in the enhancement factor and optical cross-sections. Such nanocomposites hold potential for applications in optical sensing, biosensing, as well as in photonic and electronic devices.
VL  - 13
IS  - 4
ER  -

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Author Information

Tsegaye Atnaf

Department of Chemistry, Wolkite University, Addis Ababa, Ethiopia

Biography: Tsegaye Atnaf is a Chemistry Lecturer at Wolkite University. He earned his Bachelor of Science degree in Applied Chemistry from Dilla University is 2017–2019, followed by a Master of Science in Organic chemistry in 2023. In his professional role, Tsegaye is responsible for teaching undergraduate courses and conducting research in natural product. He has extensive experience in reviewing and editing academic papers, particularly focusing on natural product.

Research Fields: Refractive index, group velocity of spherical Nanocomposites; Optical properties of core-shell nanocomposite of nanoparticles

Contact Email

http://orcid.org/0009-0006-0106-3646
Shewa Getachew

Department of Physics, Wolkite University, Addis Ababa, Ethiopia

Biography: Shewa Getachew is a Physics Lecturer at Wolkite University. He earned his Bachelor of Science degree in Applied Physics from Wolkite University is 2017–2019, followed by a Master of Science in Condensed Matter Physics in 2023. In his professional role, Shewa is responsible for teaching undergraduate courses and conducting research in material science. He has extensive experience in reviewing and editing academic papers, particularly focusing on optical properties and nanocomposites. His research interests span astronomy, space science, and material science, with a specific emphasis on the optical properties of nanocomposites, local field enhancement, and depolarization effects. Shewa's contributions have earned him notable recognition, including an award from the Ethiopian Physics Society in North America in 2022 and the SHEN Research Award in 2024. He is proficient in various technical tools such as Mathematica, MATLAB, Python, Fortran, and LaTeX, with expertise in scientific computing, optical simulations, and material science research.

Research Fields: Local field enhancement of cylinderical Nanocomposites; Optical bistability of cylinderical Nanocomposites; Local field enhancement of spherical Nanocomposites; Optical bistability of spherical Nanocomposites; Refractive index, group velocity of spherical Nanocomposites

Contact Email

http://orcid.org/0009-0005-8265-0115

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Atnaf, T., Getachew, S. (2024). Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices. Advances in Materials, 13(4), 80-91. https://doi.org/10.11648/j.am.20241304.13

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Atnaf, T.; Getachew, S. Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices. Adv. Mater. 2024, 13(4), 80-91. doi: 10.11648/j.am.20241304.13

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AMA Style

Atnaf T, Getachew S. Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices. Adv Mater. 2024;13(4):80-91. doi: 10.11648/j.am.20241304.13

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@article{10.11648/j.am.20241304.13,
  author = {Tsegaye Atnaf and Shewa Getachew},
  title = {Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices},
  journal = {Advances in Materials},
  volume = {13},
  number = {4},
  pages = {80-91},
  doi = {10.11648/j.am.20241304.13},
  url = {https://doi.org/10.11648/j.am.20241304.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.am.20241304.13},
  abstract = {We theoretically and numerically investigated the local field enhancement factor (LFEF), absorption coefficient, refractive index, and group velocity of spherical core-shell nanocomposites (NCs) using the quasi-static approach. By solving Laplace’s equations, we derived expressions for the enhancement factor, polarizability, absorption coefficient, refractive index, and group velocity for each core-shell NCs. Our findings show that the LFEF, absorption coefficient, and group velocity of spherical core-shell NCs exhibit two peaks, while the real part of the refractive index shows four distinct peaks. Additionally, the core-shell nanocomposites demonstrate greater tunability and a higher intensity of the enhancement factor when the host matrix is changed from CdSe to SiO3. The study further reveals that, for spherical nanocomposites, the first two peaks of the enhancement factor and extinction cross-sections occur at the same frequencies. Moreover, all extinction cross-section peaks are lowest when the dielectric function of the host matrix is SiO3, whereas the peaks are highest for CdSe. The variation in peak values, despite having the same number of peaks for different shapes, indicates that the shape of the core-shell NCs significantly influences the intensity, number, and positions of the peaks in the enhancement factor and optical cross-sections. Such nanocomposites hold potential for applications in optical sensing, biosensing, as well as in photonic and electronic devices.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Investigation Optical Properties of ZnTe@Ag Core-Shell Spherical Nanocomposites Within Varies Dielectric Host Matrices
AU  - Tsegaye Atnaf
AU  - Shewa Getachew
Y1  - 2024/12/30
PY  - 2024
N1  - https://doi.org/10.11648/j.am.20241304.13
DO  - 10.11648/j.am.20241304.13
T2  - Advances in Materials
JF  - Advances in Materials
JO  - Advances in Materials
SP  - 80
EP  - 91
PB  - Science Publishing Group
SN  - 2327-252X
UR  - https://doi.org/10.11648/j.am.20241304.13
AB  - We theoretically and numerically investigated the local field enhancement factor (LFEF), absorption coefficient, refractive index, and group velocity of spherical core-shell nanocomposites (NCs) using the quasi-static approach. By solving Laplace’s equations, we derived expressions for the enhancement factor, polarizability, absorption coefficient, refractive index, and group velocity for each core-shell NCs. Our findings show that the LFEF, absorption coefficient, and group velocity of spherical core-shell NCs exhibit two peaks, while the real part of the refractive index shows four distinct peaks. Additionally, the core-shell nanocomposites demonstrate greater tunability and a higher intensity of the enhancement factor when the host matrix is changed from CdSe to SiO3. The study further reveals that, for spherical nanocomposites, the first two peaks of the enhancement factor and extinction cross-sections occur at the same frequencies. Moreover, all extinction cross-section peaks are lowest when the dielectric function of the host matrix is SiO3, whereas the peaks are highest for CdSe. The variation in peak values, despite having the same number of peaks for different shapes, indicates that the shape of the core-shell NCs significantly influences the intensity, number, and positions of the peaks in the enhancement factor and optical cross-sections. Such nanocomposites hold potential for applications in optical sensing, biosensing, as well as in photonic and electronic devices.
VL  - 13
IS  - 4
ER  -

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