Rotational Effects on Magneto-Photo-Thermoelastic Wave Propagation in a Fiber-Reinforced Anisotropic Semiconductor Half-Space Under Optical Excitation

Summary

We present an analytical model to investigate the propagation of rotating magneto-photo-thermoelastic waves in anisotropic fiber-reinforced semiconductors under optical excitation. The method can be used to analyze temperature, carrier density, displacement, and stress distributions in advanced semiconductor materials.

Abstract

This study investigates the coupled rotating magneto-photo-thermoelastic behavior of an anisotropic fiber-reinforced semiconductor half-space subjected to optical excitation and an applied magnetic field. The governing equations, incorporating thermal, elastic, carrier-density, electromagnetic, and rotational effects, are formulated within a unified multiphysical framework. The normal mode method is employed to transform the coupled partial differential equations into a system of ordinary differential equations, which is subsequently rewritten as a first-order matrix differential system. An eigenvalue-based formulation is then developed to construct the analytical solution of the coupled problem. The resulting eigenvalue problem, boundary-condition system, and field quantities are evaluated numerically. Numerical results are presented for the temperature, carrier density, displacement components, and stress distributions to examine the effects of the rotation parameter and magnetic field intensity on the coupled physical fields. The results demonstrate the important role of rotational and electromagnetic interactions in modifying wave propagation, attenuation characteristics, and field distributions within the anisotropic semiconductor medium. Numerical computations were carried out for a silicon-based semiconductor medium.

Introduction

Photo-thermoelasticity has become an active area of research owing to its capability to describe the coupled interactions among thermal, mechanical, optical, and carrier-density fields in semiconductor materials subjected to laser irradiation and photothermal excitation. These coupled phenomena play an important role in modern optoelectronic devices, semiconductor technologies, laser-processing systems, and microelectronic applications. Saeed et al.¹ investigated wave propagation in semiconductor solids with temperature-dependent properties, while Abbas et al.² examined photo-thermal interactions in semiconductors containing cylindrical cavities and variable thermal conductivity. Subsequently, Ihtisham Ullah et al.³ analyzed the influence of variable thermal conductivity and laser pulses on reflected elastic waves in semiconductor media. In addition, Yadav⁴ studied magneto-photothermal plasma wave propagation in diffusion semiconductors under a two-temperature multi-phase-lag thermoelastic framework. More recently, Lute et al.⁵ and Lute et al.⁶ developed advanced photo-thermoelastic semiconductor models incorporating photothermal heat generation, memory effects, and nonlocal interactions, whereas Alaofi and El-Dali⁷ proposed a multiphysics photo-thermo-hygroelastic formulation for semiconductor materials. Furthermore, several generalized photo-thermoelastic models based on phase-lag theories and nonlocal formulations have been reported to improve the description of coupled thermal and carrier transport phenomena in semiconductors^8,9,10,11.

The increasing demand for lightweight and high-performance engineering structures has stimulated extensive research on anisotropic and fiber-reinforced materials. Owing to their superior mechanical characteristics and enhanced thermal resistance, fiber-reinforced composites have been widely employed in aerospace, civil, and electronic engineering applications. Khan et al.¹² developed a unified micropolar thermoelastic model for temperature-dependent fiber-reinforced composites and demonstrated the significant influence of microstructural parameters on wave propagation characteristics. Pitarresi et al.¹³ investigated the thermoelastic response of fiber-reinforced plastics and highlighted the role of material heterogeneity on thermal stress distributions. Escalante-Solís et al.¹⁴ examined the effect of fiber curvature on the micromechanical behavior of reinforced composites, while Abo-Dahab et al.¹⁵ studied wave reflection phenomena in fiber-reinforced thermoelastic media. More recently, Purkait and Kanoria¹⁶ analyzed a rotating fiber-reinforced magneto-thermoelastic medium subjected to pulsed laser excitation, whereas Akai et al.¹⁷ and Quinlan et al.¹⁸ investigated thermoelastic responses in fiber-reinforced composite structures under different loading conditions. These studies confirmed that reinforcement characteristics and anisotropy substantially affect thermal transport, stress concentrations, and wave propagation behavior. Nevertheless, most of the available investigations were devoted to thermoelastic composite materials and did not simultaneously account for photo-thermoelastic semiconductor coupling together with carrier transport mechanisms.

The interaction between magnetic fields and thermoelastic semiconductor media has also attracted considerable attention because of its importance in electromagnetic devices and conducting materials. Yadav¹⁹ investigated wave reflection in a rotating orthotropic magneto-thermoelastic half-space with diffusion effects, while Selvamani et al.²⁰ studied magnetoelastic wave propagation in nonlocal fractional nanobeams. Abouelregal et al.²¹ examined coupled laser-thermomagnetic stimulation in magnetized porous structures with memory-dependent effects, whereas Chandel et al.²² proposed a nonlocal magneto-thermoelastic framework based on Moore-Gibson-Thompson heat conduction. In the context of semiconductors, Abouelregal²³ developed a modified fractional photo-thermoelastic model for a rotating semiconductor half-space subjected to a magnetic field, and Sur²⁴ investigated magneto-photo-thermoelastic interactions in media exhibiting hereditary characteristics. More recently, Saidi et al.²⁵ and Rashid et al.²⁶ analyzed magneto-photo-thermoelastic disturbances in generalized rotating semiconductor media and demonstrated the significant influence of magnetic intensity on the propagation of coupled waves. Similar observations were reported in advanced photo-thermo-viscoelastic and Moore-Gibson-Thompson semiconductor models^27,28,29.

Rotational effects are another important aspect of generalized thermoelasticity, as rotation introduces additional Coriolis and centripetal forces that considerably modify wave propagation characteristics. Khan et al.³⁰ performed a sensitivity analysis of wave behavior in rotating thermoelastic solids subjected to laser-induced thermal loading. Yadav³¹ investigated magnetothermoelastic waves in rotating orthotropic media with diffusion effects, whereas Abouelregal et al.³² examined fractional dual-phase-lag thermoelastic responses in rotating stressed media containing spherical cavities. Furthermore, Khan et al.³³ studied wave propagation in a rotating porous thermoelastic half-space under a nonlocal fractional three-phase-lag model. Rotational influences on semiconductor thermoelastic nanostructures were also examined by Abo-Dahab et al.³⁴, who demonstrated that rotation can significantly alter thermal and mechanical field distributions. Despite these efforts, rotational effects have rarely been investigated simultaneously with anisotropy, fiber reinforcement, optical excitation, carrier transport, and magnetic field interactions within a unified semiconductor framework.

Although substantial progress has been achieved in the aforementioned studies, most existing investigations have focused on selected combinations of photo-thermoelastic, magnetic, rotational, or reinforcement effects. A comprehensive analytical model that simultaneously incorporates optical excitation, carrier transport dynamics, anisotropy, fiber reinforcement, magnetic field interactions, and rotational influences in a semiconductor medium remains largely unavailable. Therefore, there is still a need for a unified formulation that accurately describes the mutual coupling among these physical mechanisms and clarifies their combined influence on wave propagation.

Motivated by these observations, the present work develops a two-dimensional analytical model to investigate magneto-photo-thermoelastic wave propagation in a rotating, fiber-reinforced, anisotropic semiconductor half-space subjected to optical excitation. The governing equations are formulated within a unified framework that incorporates thermal, mechanical, carrier-density, and electromagnetic fields, and are solved using the normal-mode technique together with the eigenvalue approach. It is noteworthy that Alaofi et al.³⁵ recently investigated the coupled thermo-photoelastic response of anisotropic fiber-reinforced silicon using an eigenvalue formulation. However, magnetic field effects and rotational contributions were not considered in their model. The novelty of the present work lies in extending that formulation by simultaneously incorporating magnetic interactions, rotational effects, carrier transport dynamics, anisotropic reinforcement, and optical excitation within a single magneto-photo-thermoelastic framework. Consequently, the proposed model provides a more comprehensive description of coupled wave propagation phenomena and enables a detailed assessment of the combined influence of magnetic intensity and rotation on the physical fields of interest. Unlike Alaofi et al.³⁵, which considered the thermo-photoelastic response of an anisotropic fiber-reinforced semiconductor without magnetic field and rotational effects, the present formulation incorporates the simultaneous interaction of rotation, magnetic field, optical excitation, carrier transport, and anisotropic reinforcement within a unified framework. In addition, the eigenvalue implementation is extended to this more general coupled system, enabling analysis of coupled physical effects not addressed in the earlier model. Furthermore, a distinctive feature of the present work is the implementation of the eigenvalue approach. While many related studies, including Alaofi et al.³⁵, rely on elimination procedures to reduce the governing system before obtaining the solution, the present formulation is constructed and solved using a matrix-based eigenvalue framework. This implementation is applied to a more general coupled system involving rotation, magnetic field, optical excitation, carrier transport, and fiber reinforcement, thereby extending the scope of the previously published models.

Protocol

The present work is based entirely on analytical modeling, symbolic computation, and numerical simulations to investigate coupled rotating magneto-photo-thermoelastic interactions in anisotropic semiconductor media. No human participants, animal experiments, clinical data, or biological specimens were involved in this study. Therefore, ethical approval and informed consent were not required.

Mathematical formulation of the magneto-photo-thermoelastic problem in a rotating fiber-reinforced anisotropic semiconductor half-space

In the present study, a two-dimensional rotating fiber-reinforced anisotropic semiconductor half-space is investigated under optical excitation and an applied magnetic field. The medium occupies the semi-infinite region x ≥ 0, where the boundary at x = 0 represents the exposed surface subjected to external optical loading. The coordinate system is chosen such that the x - axis extends into the medium, while the y - axis lies along the surface, representing the in-plane behavior of the structure. The applied magnetic field and angular velocity vector are both taken along the z - axis. The semiconductor medium is assumed to be homogeneous and linearly elastic, while anisotropy is introduced through aligned reinforcing fibers embedded in the x - direction. Optical absorption at the boundary produces localized heating and excess charge carriers, resulting in coupled thermal, mechanical, and carrier interactions within the medium. In addition, the magnetic field introduces electromagnetic coupling effects, whereas the rotational motion contributes inertial effects that significantly influence the propagation of thermoelastic waves and the overall physical response. Accordingly, the physical state of the medium is represented by the temperature field T(x, y, t)(K), carrier density N(x, y, t)(m^-3), and displacement components u(x, y,t)(m) and v(x,y,t)(m), under the assumption of small deformations. Figure 1 illustrates the geometry of the problem, including the coordinate system, optical excitation, magnetic field, rotational effect, and fiber orientation. The present formulation is applicable to homogeneous anisotropic fiber-reinforced semiconductor media operating within the small-deformation regime and the framework of linear thermoelasticity. The model assumes a fixed fiber orientation and constant material properties throughout the medium. Consequently, nonlinear material behavior, large deformations, material damage, and spatial variations of material properties are not considered in the current study. Therefore, the proposed model is intended for moderate loading conditions where the response remains within the linear range. In the present study, the optical excitation is modeled using prescribed boundary conditions for surface temperature and photo-generated carrier density. The detailed laser-matter interaction process, including optical absorption, penetration depth, and intensity distribution, is not treated explicitly. Instead, its net effect is represented by the boundary amplitudes θ₀ and N₀, which characterize the thermal and carrier excitations induced by the incident optical field.

Figure 1: Schematic representation of the rotating anisotropic fiber-reinforced semiconductor half-space subjected to optical excitation and an external magnetic field. The figure illustrates the physical configuration of the problem, including the coordinate system, optical excitation, applied magnetic field, fiber orientation, and rotational effects considered in the present formulation. Please click here to view a larger version of this figure.

The constitutive relation for the stress tensor in a fiber-reinforced anisotropic thermoelastic semiconductor medium can be expressed in the generalized form as follows^12,15,16.

   (1)

Here, σ_ij denotes the stress tensor components, C_ijkl are the elastic stiffness coefficients, e_kl represents the strain tensor, T is the temperature increment relative to the reference temperature T₀, and N denotes the excess carrier density. The tensors β_ij and η_ij correspond to the thermoelastic and carrier coupling coefficients, respectively. Accordingly, the constitutive relation including the explicit influence of fiber reinforcement may be written as^12,15:

  (2)

In this formulation, λ and μ_T are the Lamé elastic constants, while μ_L denotes the longitudinal shear modulus along the fiber direction. The parameters α and β describe the reinforcement effects associated with the embedded fibers. The quantity δ_ij is the Kronecker delta symbol, and a_i are the components of the unit vector defining the fiber orientation. For the present model, the reinforcing fibers are aligned along the x -direction such that a = (1,0). The terms involving β_ijθ and η_ijN represent thermal and carrier coupling effects, respectively. For the present two-dimensional configuration, the governing stress components reduce to the following forms^12,15:

.    (3)

.    (4)

.    (5)

Here,  and  denote the displacement components along the x - and y -directions, respectively, while A_ij are the effective elastic coefficients of the anisotropic fiber-reinforced medium. The thermoelastic and carrier coupling coefficients are defined as follows

,

,

,

.

In the above relations, α_ij represent the thermal expansion coefficients, whereas ξ_ij denote the carrier expansion coefficients associated with the semiconductor medium. The effective elastic coefficients of the fiber-reinforced anisotropic medium are given by

, , , .

These coefficients characterize the anisotropic elastic response of the reinforced semiconductor material and describe how fiber orientation influences the coupled thermoelastic behavior. To account for the influence of electromagnetic interactions in the present magneto-photo-thermoelastic formulation, a uniform magnetic field is assumed to be applied along the z -direction, which is normal to the x - y plane of deformation. Accordingly, the magnetic field vector is considered in the form^23,25 , , where H₀ denotes the constant magnetic field intensity. Since the present formulation is restricted to two-dimensional deformations, the displacement field of the medium is taken as , where  and  represent the displacement components along the x- and y- directions, respectively.

Under the assumptions of small deformations and a slowly moving electrically conducting semiconductor medium, the interaction between the particle velocity and the applied magnetic field generates an induced electric field.

Based on Maxwell's electromagnetic relations for moving conductive media, the induced electric field vector can be expressed as^19,23

.     (6)

where μ₀ denotes the magnetic permeability and  is the particle velocity vector. Substituting the expressions of  and  into the above relation gives

.    (7)

which yields

.   (8)

Taking the time derivative of the induced electric field, we obtain

. (9)

The magnetic perturbation vector generated due to the deformation of the semiconductor medium is defined as²³˒²⁵

. (10)

The above expression automatically satisfies Maxwell’s divergence condition for the magnetic perturbation field, namely

. (11)

To determine the electric current density, the curl of the magnetic perturbation vector is first evaluated. In determinant form, the curl operator can be written as²³

. (12)

Expanding the determinant leads to

. (13)

The electric current density vector is then obtained from Maxwell’s electromagnetic equation²³

. (14)

where ε₀ denotes the electric permittivity of the medium.

The electromagnetic body force acting on the semiconductor medium is determined using the Lorentz force relation²³

. (15)

The vector product  may be evaluated in determinant form as

. (16)

Substituting the previous expressions into Eq. (15), the components of the electromagnetic body force vector become

. (17)

. (18)

These relations clearly indicate that the applied magnetic field contributes additional coupling mechanisms to the governing equations through both stiffness-like electromagnetic terms and modified inertial terms proportional to . Consequently, the magnetic field significantly affects the propagation characteristics of thermoelastic waves and the overall dynamic behavior of the fiber-reinforced anisotropic semiconductor medium. In addition to the electromagnetic effects, the influence of rotation is incorporated into the present formulation in order to describe the dynamic response of the medium when observed from a rotating frame of reference. The fiber-reinforced semiconductor medium is assumed to undergo a uniform rigid-body rotation with a constant angular velocity vector given by³³ , where  denotes the constant angular velocity about the z -axis. Since the rotation axis is normal to the x - y plane, when the equations of motion are formulated in a rotating coordinate system, additional inertial accelerations arise due to the non-inertial nature of the rotating frame. These accelerations consist mainly of the Coriolis and centrifugal accelerations. The Coriolis acceleration is associated with the particle velocity field and is expressed as³¹˒³³

. (19)

Substituting the expressions of  and , we obtain

. (20)

Therefore, the Coriolis acceleration becomes

. (21)

The centrifugal acceleration depends directly on the displacement field itself and is represented by^31,35

. (22)

First, the vector product  is evaluated as

. (23)

Then, substituting the obtained result into the centrifugal acceleration relation yields

. (24)

Accordingly, the total rotational contribution appearing in the governing equations can be expressed as

. (25)

Hence, the rotational acceleration components in the x-  and y- directions become

, (26)

. (27)

The above expressions demonstrate that rotational motion introduces additional coupling between the displacement components via the Coriolis acceleration, in addition to displacement-dependent inertial effects due to the centrifugal acceleration. Therefore, the combined action of the magnetic field and rotation produces significant modifications to the dynamic response and wave-propagation characteristics of the rotating fiber-reinforced anisotropic semiconductor medium. To incorporate the combined influence of electromagnetic interactions and rotational motion, the equations of motion for the fiber-reinforced anisotropic semiconductor medium are generalized to include both the electromagnetic body force and the additional inertial accelerations arising in a rotating frame of reference. Accordingly, the general equation of motion for a deformable rotating continuum can be expressed as follows³¹˒³²

. (28)

Here, ρ denotes the mass density, and F_i represents the electromagnetic body force components. Moreover,  denotes the angular velocity vector of the rotating frame. The Eqs. (22) and (24) correspond to the Coriolis and centrifugal accelerations, respectively. The equations of motion in the x- and y- directions may be written as

. (29)

. (30)

Substituting the previously obtained electromagnetic body force components into the above equations gives

. (31)

. (32)

Next, substituting the constitutive relations corresponding to the fiber-reinforced anisotropic semiconductor medium into the above equations yields the coupled equations of motion in terms of the displacement components, temperature field, and carrier density³²

. (33)

. (34)

Finally, using the expression of the magnetic perturbation field given previously in Eq. (15), and substituting it into the above equations, the governing equations of motion can be written in their final coupled form as

. (35)

. (36)

These equations reveal the coupled influence of rotational and magnetic field effects on the medium's thermoelastic response. The rotational terms account for both Coriolis and centrifugal contributions, whereas the magnetic field introduces additional electromagnetic coupling and modifies the system's dynamic behavior. Consequently, the governing equations establish a unified framework for analyzing wave propagation and multiphysical interactions in rotating magneto-photo-thermoelastic fiber-reinforced semiconductors. Under optical excitation, the thermal behavior of the semiconductor medium is significantly influenced by the interplay among heat conduction, carrier transport, and mechanical deformation, leading to a strongly coupled thermo-photoelastic process. Unlike the classical heat conduction model, the temperature distribution in semiconductor materials is influenced not only by thermal diffusion but also by carrier recombination and thermoelastic coupling. Consequently, the generalized heat conduction equation for the anisotropic fiber-reinforced semiconductor medium can be expressed as follows⁷˒²³.

. (37)

The above equation clearly demonstrates that the thermal field inside the rotating magneto-photo-thermoelastic semiconductor medium is governed by the combined influence of anisotropic heat conduction, carrier recombination processes, and thermoelastic interactions. The term describes the thermal energy generated due to carrier recombination under optical excitation, while the coupling terms involving  and  indicate the influence of time-dependent mechanical deformation on the thermal response of the medium. Consequently, the temperature field becomes strongly coupled with both the carrier density and the elastic field, which plays an important role in the propagation characteristics of thermoelastic waves in fiber-reinforced semiconductor materials. In the present formulation, the evolution of the carrier concentration N(x, y, t) inside the semiconductor medium is governed by the combined effects of carrier diffusion, recombination processes, and thermal activation generated by optical excitation. Accordingly, the carrier transport equation describing the nonequilibrium carrier dynamics can be written as follows^4,23

. (38)

Here, D_E denotes the carrier diffusion coefficient, while  represents the two-dimensional Laplacian operator in the x -y plane. The term  corresponds to the carrier recombination effect associated with the carrier lifetime τ. Furthermore, κ is the thermo-carrier coupling parameter defined by , where N₀ denotes the equilibrium carrier concentration. The coupling term κT describes the influence of the temperature field on the generation of excess carriers within the semiconductor medium. The above equation demonstrates that the carrier concentration is strongly coupled with the thermal field through thermally activated carrier generation mechanisms. Consequently, the carrier dynamics become highly dependent on both thermal diffusion and recombination effects, which significantly influence the coupled photo-thermoelastic response of the rotating fiber-reinforced anisotropic semiconductor medium. The governing equations and mathematical formulation of the coupled magneto-photo-thermoelastic semiconductor system have now been completely established. The physical and material parameters for the silicon medium are summarized in Table 2, along with their numerical values, units, and corresponding references. These parameters are subsequently utilized in the numerical computations and nondimensionalization procedure.

Nondimensional formulation of the rotating magneto-photo-thermoelastic fiber-reinforced semiconductor model

To simplify the governing equations and obtain a compact mathematical representation of the coupled rotating magneto-photo-thermoelastic system, appropriate characteristic scales are introduced to nondimensionalize the physical variables. This nondimensionalization procedure reduces the number of governing material parameters and facilitates the analytical and numerical treatment of the coupled equations. The selected characteristic quantities are chosen consistently with the thermoelastic, electromagnetic, rotational, and carrier transport properties of the semiconductor medium^16,21 Accordingly, the following dimensionless variables are introduced:

, , , , , , , , , , .

Here, C_T denotes the characteristic elastic wave velocity, while t* represents the characteristic thermal relaxation time associated with the coupled thermoelastic process. Furthermore, the parameter defines the nondimensional rotational parameter  that characterizes the influence of rotational motion on the medium's dynamic behavior. Substituting the above dimensionless quantities into the previously derived governing equations transforms the coupled system into normalized form. This transformation considerably simplifies the equations' mathematical structure and provides a suitable framework for investigating the combined effects of magnetic field, optical excitation, rotation, anisotropy, and carrier-transport interactions. For simplicity, the prime notation associated with the dimensionless quantities is omitted in the subsequent analysis. Accordingly, the governing equations of the coupled rotating magneto-photo-thermoelastic system can be written in the following nondimensional form^16,20:

, (39)

, (40)

, (41)

. (42)

The corresponding nondimensional stress components of the rotating anisotropic fiber-reinforced semiconductor medium are obtained as follows:

, (43)

, (44)

. (45)

The nondimensional coefficients a_i (i = 1,2,...,18) represent combinations of the physical, thermal, electromagnetic, carrier, and rotational parameters of the coupled semiconductor medium. These coefficients characterize the influence of anisotropy, fiber reinforcement, magnetic field, thermoelastic coupling, carrier transport, and rotational motion on the overall behavior of the system. Consequently, the obtained nondimensional governing equations provide a compact and efficient mathematical model for analyzing the coupled wave propagation phenomena and multiphysical interactions in rotating magneto-photo-thermoelastic fiber-reinforced semiconductor media. The nondimensional parameters a_i, γ_i, and δ_i were introduced to represent compact combinations of the physical and material properties governing the coupled rotating magneto-photo-thermoelastic behavior of the fiber-reinforced anisotropic semiconductor medium. Each coefficient reflects a specific interaction mechanism within the coupled system and provides insight into the relative influence of the underlying physical processes. For clarity, the dimensionless parameters and their corresponding definitions are summarized in Table 1.

Table 1: Definitions and physical interpretations of the dimensionless parameters used in the present formulation. The table summarizes the dimensionless parameters appearing in the governing equations together with their physical meanings and their roles in describing the coupled thermoelastic, electromagnetic, carrier-density, and rotational interactions. Please click here to download this Table.

Analytical solution using the normal mode technique

To derive the analytical solution of the coupled rotating magneto-photo-thermoelastic system, the normal mode technique is employed. This method is widely used in generalized thermoelasticity and semiconductor theories due to its effectiveness in transforming the coupled partial differential equations into a reduced system of ordinary differential equations. Such an approach is particularly useful in the analysis of wave propagation, attenuation, and multiphysical interactions in anisotropic semiconductor media. Following the normal mode analysis, all physical field quantities are assumed to vary harmonically with respect to time and the transverse spatial coordinate . Accordingly, the temperature field, carrier-density, displacement components, and stress quantities are represented in the exponential form^24,27

. (46)

Here, ω denotes the complex frequency parameter governing the temporal variation of the physical fields. The real part of ω is associated with the temporal attenuation (or growth) of the wave amplitude, whereas the imaginary part represents the oscillatory behavior of the propagating mode. These interpretations are consistent with the conventional normal mode analysis adopted in the present study, while a represents the wave number associated with the spatial variation along the y-direction. The quantities , and  correspond to the field amplitudes depending only on the spatial coordinate x. Substituting the above normal mode representations into the previously obtained nondimensional governing equations and simplifying the resulting expressions, the original coupled partial differential system is transformed into a set of ordinary differential equations with respect to the spatial coordinate x. Consequently, the governing equations in the transformed domain take the following form:

, (47)

, (48)

, (49)

. (50)

Furthermore, the corresponding transformed stress components are obtained as

, (51)

, (52)

. (53)

Here, , denotes the differential operator with respect to the spatial coordinate . The obtained transformed system forms the mathematical foundation for constructing the characteristic equation and deriving the complete analytical solution of the coupled rotating magneto-photo-thermoelastic problem. The coefficients appearing in the transformed equations are defined as follows:

, , , , , , , , , , , .

These coefficients contain the combined contributions of anisotropic elasticity, magnetic field interaction, thermal coupling, carrier transport, and rotational effects. Therefore, the transformed system provides a compact representation suitable for obtaining the characteristic roots and investigating the coupled wave propagation behavior within the rotating fiber-reinforced semiconductor medium.

Supplementary File 1: Analytical Solution Using Matrix Form. This file contains the detailed matrix formulation, the eigenvalue solution procedure, characteristic equation derivation, and intermediate analytical steps used to obtain the general solution of the coupled magneto-photo-thermoelastic model.Please click here to download this file.

The detailed matrix formulation, eigenvalue solution procedure, and characteristic equation derivation are provided in Supplementary File 1.

Boundary conditions and determination of the unknown constants

To complete the analytical formulation, the obtained general solutions were substituted into the prescribed boundary conditions imposed at the surface x = 0. This substitution generated a coupled algebraic system involving the unknown amplitude constants . Each boundary requirement associated with temperature, carrier density, mechanical displacement, and stress constraints was expressed in terms of the admissible eigenmodes, yielding a linear set of equations relating the coefficients . For convenience, the resulting algebraic system was rewritten in compact matrix form as BC = D, where B denotes the coefficient matrix constructed from the eigenvector components evaluated at the boundary surface,  represents the vector of unknown constants, and D corresponds to the vector generated from the imposed boundary conditions, including the thermal loading parameter θ₀, the carrier excitation term N₀, and the prescribed displacement conditions. After evaluating these constants, they were substituted back into the general expressions of the field variables in order to obtain the complete analytical solutions. These expressions were subsequently employed in the numerical computations and graphical visualization of the thermoelastic, carrier-density, and displacement fields within the rotating fiber-reinforced anisotropic semiconductor medium. The adopted boundary conditions represent an optically illuminated semiconductor surface subjected to simultaneous thermal and carrier excitations. The prescribed temperature condition models the thermal loading generated by the incident optical field, while the carrier-density condition accounts for the photo-generated excess carriers produced by optical illumination. In addition, the transverse displacement constraint represents mechanical confinement of the surface in the -direction, whereas the vanishing shear-stress condition corresponds to a tangentially traction-free boundary. Consequently, the selected mixed thermal, electronic, and mechanical boundary conditions provide a physically consistent representation of coupled photo-thermoelastic interactions at the semiconductor surface and supply the necessary constraints required for determining the unknown constants of the solution. The imposed boundary conditions are given as follows:

Temperature constraint:

. (78)

This condition represents a harmonically varying surface temperature induced by periodic optical heating. It acts as the primary thermal excitation driving the coupled thermoelastic and carrier transport processes within the medium. The amplitude θ₀ characterizes the intensity of the applied thermal load.

Carrier density constraint:

. (79)

This boundary condition describes the photo-generated carrier density resulting from optical illumination. It reflects the electronic excitation due to photon absorption and its harmonic modulation consistent with the incident optical field.

Displacement constraint:

. (80)

This condition indicates that the boundary is mechanically constrained in the transverse direction. Hence, no displacement occurs along the -direction at the surface.

Shear stress constraint:

. (81)

This condition corresponds to a traction-free boundary with respect to shear stress. It ensures that no tangential forces act on the surface, which is consistent with a mechanically free boundary in the tangential direction. In addition to the boundary conditions at x = 0, the physical requirement at infinity was imposed as:  ensuring bounded physical solutions within the semi-infinite domain. To provide a clear overview of the analytical and computational procedure adopted in the present study, the main steps of the solution methodology are summarized in Figure 2.

Figure 2: Flowchart of the analytical solution procedure adopted in the present study, including the formulation of the governing equations, normal mode analysis, eigenvalue solution, application of boundary conditions, and evaluation of the physical field variables. The diagram summarizes the main computational steps for obtaining the analytical solution and subsequently evaluating the coupled magneto-photo-thermoelastic response numerically. Please click here to view a larger version of this figure.

Results

To obtain the numerical results presented in this study, silicon (Si) was selected as the representative semiconductor material due to its wide applicability in semiconductor and thermoelastic engineering applications. The physical, thermal, elastic, electromagnetic, and carrier-related material properties employed in the computations are summarized in Table 2. These material constants were substituted into the dimensionless governing equations to generate the numerical results discussed in the subsequent sections. In addition, the numerical computations were carried out over the dimensionless spatial domain  using a spatial step size of . This choice was found to provide sufficient numerical resolution and ensure that the complete spatial behavior of the physical fields under consideration is accurately captured within the computational domain.

Table 2: Material properties and corresponding constants of silicon (Si) used in the present analysis, given in SI units. The listed material parameters are employed in the numerical computations and represent the thermophysical, elastic, semiconductor, and electromagnetic properties required for the implementation of the proposed model.Please click here to download this Table.

Influence and local sensitivity assessment of the rotation parameter

To investigate the influence of the rotation parameter on the coupled magneto-photo-thermoelastic response of the fiber-reinforced anisotropic semiconductor medium, the spatial distributions of the temperature field , carrier density , displacement components u and v, and stress components , , and  were evaluated over the interval . Three representative values of the rotation parameter, namely , 0.4, and 0.7, were considered. The case  corresponds to the non-rotating configuration and serves as a reference state, while the remaining values illustrate the influence of rotational effects on wave attenuation, field localization, and coupled thermoelastic interactions within the medium.

Figure 3 presents the temperature distribution for different values of the rotation parameter. The limiting case  reproduces the thermal response reported in Alaofi et al.³⁵, while increasing rotation produces a slight enhancement in the thermal field near the boundary. This behavior reflects the additional thermoelastic coupling generated by rotational inertia. Despite the change in amplitude, all curves preserve the same attenuation pattern and approach zero as x increases, confirming the physical consistency of the obtained solutions. Quantitatively, the peak temperature remains nearly unchanged as Ω increases from 0 to 0.4 and 0.7, with a maximum value of approximately 2.1273 in all cases. This confirms that the thermal field exhibits only weak sensitivity to variations in the rotation parameter. Figure 4 illustrates the carrier-density distribution. The non-rotating profile agrees with the expected diffusion-recombination behavior of the reference model. The introduction of rotation produces only moderate quantitative modifications while preserving the overall decaying trend. This observation confirms that the present formulation reduces correctly to the established photo-thermoelastic semiconductor model when rotational effects are removed. Quantitatively, only negligible variations are observed in the peak carrier density as Ω increases. The close agreement between the corresponding peak values confirms the weak influence of rotation on the carrier transport process. Figure 5 depicts the longitudinal displacement component u. A noticeable influence of rotation appears near the boundary region, where increasing alters both the peak value and the local deformation pattern. Physically, this behavior results from the additional inertial forces associated with rotation, which modify the elastic response of the medium. Nevertheless, all profiles remain bounded and decay smoothly away from the boundary. The peak value of the longitudinal displacement decreases from approximately 1.4970 at Ω = 0 to 0.4978 and 0.3179 for Ω = 0.4 and 0.7, respectively. These changes demonstrate the pronounced influence of rotation on the longitudinal mechanical response of the medium. Figure 6 shows the transverse displacement component . Unlike the temperature and carrier fields, the transverse displacement exhibits a stronger sensitivity to rotational effects. The increase in Ω significantly enhances the amplitude of the response, indicating the important contribution of Coriolis-type coupling between the displacement components. The limiting profile corresponding to  is recovered smoothly and remains fully consistent with the reference formulation. The peak value of the transverse displacement increases from approximately 0.0490 at  to 0.1546 and 0.2454 for Ω = 0.4 and 0.7, respectively. This significant increase highlights the strong sensitivity of the transverse displacement field to rotational effects. The normal stress component , shown in Figure 7, demonstrates that rotation substantially modifies the stress localization near the boundary. Although the stress magnitude changes with increasing rotational speed, all profiles maintain the same qualitative behavior and converge toward zero as the distance increases. This confirms the stability and boundedness of the stress response. The minimum value of σ_yy changes from approximately -6.6088 at  to -5.5898 and -4.8856 for Ω = 0.4 and 0.7, respectively. This behavior confirms that rotation substantially modifies the magnitude and localization of the normal stress field. Figure 8 presents the variation of the transverse normal stress . The effect of rotation remains relatively moderate compared with that observed for , yet a systematic variation in stress magnitude can still be identified. The smooth evolution of the profiles from the limiting case confirms the robustness of the proposed formulation. The minimum value of changes from approximately -0.4852 at  to -0.4744 and -0.4670 for Ω = 0.4 and 0.7, respectively. Although the effect is less pronounced than that observed for σxx, the results still indicate a measurable dependence on the rotation parameter.

Finally, Figure 9 illustrates the shear stress distribution . The limiting case reproduces the non-rotating behavior reported previously, whereas finite rotational values modify both the magnitude and spatial localization of the shear response. This result highlights the role of rotation in coupling the longitudinal and transverse mechanical fields and demonstrates the capability of the present model to capture additional physical effects absent in the earlier formulation. Overall, the comparison with the limiting case  confirms that the proposed model correctly recovers the previously established non-rotating solution reported in Alaofi et al.³⁵. The peak value of σxy increases from approximately 0.0037 at  to 0.0143 and 0.0182 for Ω = 0.4 and 0.7, respectively. These results demonstrate the significant contribution of rotation to the shear stress response and the coupling between the longitudinal and transverse mechanical fields. The smooth transition from the reference case to finite rotational states, together with the bounded and physically admissible behavior of all field variables, provides strong validation for the correctness and physical consistency of the present generalized formulation. A brief local sensitivity analysis with respect to the rotation parameter Ω has been included by examining the responses of the temperature, carrier density, displacement, and stress fields for Ω = 0, 0.4, and 0.7. The results show that the model remains stable and physically admissible under moderate variations of Ω. While the temperature and carrier-density fields exhibit relatively limited sensitivity, the displacement and stress fields display a more pronounced sensitivity to the rotation parameter. Furthermore, the limiting case  reproduces the previously published results of Alaofi et al.³⁵, providing additional validation of the proposed formulation.

Figure 3: Dimensionless temperature distribution versus the dimensionless distance for different values of the rotation parameter . All remaining parameters are fixed as listed in Table 2. Rotational motion modifies the thermal response near the boundary while preserving the attenuating behavior throughout the medium. Please click here to view a larger version of this figure.

Figure 4: Dimensionless carrier-density distribution N versus the dimensionless distance x for different values of the rotation parameter Ω. All remaining parameters are fixed as listed in Table 2. The carrier concentration decreases away from the illuminated surface, while rotation affects the carrier transport characteristics. Please click here to view a larger version of this figure.

Figure 5: Dimensionless longitudinal displacement u versus the dimensionless distance x for different values of the rotation parameter Ω. All remaining parameters are fixed as listed in Table 2. The rotational inertia influences the amplitude and localization of the longitudinal deformation field. Please click here to view a larger version of this figure.

Figure 6: Dimensionless transverse displacement v versus the dimensionless distance x for different values of the rotation parameter Ω. All remaining parameters are fixed as listed in Table 2. The transverse displacement exhibits noticeable sensitivity to rotational coupling effects. Please click here to view a larger version of this figure.

Figure 7: Dimensionless normal stress σ_xx versus the dimensionless distance for different values of the rotation parameter Ω. All remaining parameters are fixed as listed in Table 2. Rotation alters the stress localization and magnitude near the boundary region. Please click here to view a larger version of this figure.

Figure 8: Dimensionless normal stress σ_yy versus the dimensionless distance for different values of the rotation parameter Ω. All remaining parameters are fixed as listed in Table 2. The transverse stress response reflects the combined influence of anisotropy and rotational motion. Please click here to view a larger version of this figure.

Figure 9: Dimensionless shear stress σ_xy versus the dimensionless distance for different values of the rotation parameter Ω. All remaining parameters are fixed as listed in Table 2. The shear stress remains concentrated near the excitation boundary and attenuates rapidly within the medium. Please click here to view a larger version of this figure.

Effect of the magnetic field intensity on the coupled physical fields

To examine the influence of the external magnetic field on the coupled magneto-photo-thermoelastic response of the fiber-reinforced anisotropic semiconductor medium, the spatial distributions of the temperature T, carrier density N, displacement components u and v, and stress components , , and  were evaluated over the interval . Three representative values of the magnetic field intensity were considered, namely , 4 × 10⁸, and 8 × 10⁸. The case H₀ = 0 corresponds to the absence of magnetic effects and serves as a reference configuration, whereas the other values illustrate the influence of magnetoelastic coupling on the propagation and attenuation characteristics of the coupled fields.

Figure 10 illustrates the variation of the temperature distribution for different magnetic field intensities. It is observed that the temperature profiles almost coincide throughout the entire spatial domain, indicating that the thermal field is only weakly influenced by the applied magnetic field. The dominant thermal behavior remains governed by heat conduction and photothermal interactions, while the magnetic contribution introduces only negligible modifications to the temperature evolution. The peak temperature remains essentially unchanged as H₀ increases from 0 to 4 × 10⁸ and 8 × 10⁸, with a maximum value of approximately 2.1273 in all cases. This confirms the weak sensitivity of the thermal field to variations in the magnetic field intensity. Figure 11 shows the carrier-density distribution N. The carrier-density profiles remain practically unchanged for all considered values of H₀, indicating that the magnetic field has only a minor effect on the diffusion and recombination processes governing the carrier dynamics. Consequently, the carrier field preserves its exponential attenuation behavior throughout the computational domain, while the magnetic field mainly influences the mechanical stress and displacement responses rather than the carrier transport process. The peak carrier density remains nearly unchanged with a maximum value of approximately 2.1273 for all considered values of H₀. This observation further confirms that the carrier-density field is only weakly affected by the applied magnetic field. Figure 12 illustrates the displacement component . Increasing the magnetic field intensity decreases the positive displacement amplitude near the boundary and enhances the magnitude of the subsequent negative region. Physically, the induced electromagnetic force acts against the mechanical motion, restricting longitudinal deformation and producing a stronger localization of the displacement field within the vicinity of the excitation source. The peak value of the longitudinal displacement decreases from approximately 1.4970 at H₀ = 0 to 1.1149 and 0.4983 for 4 × 10⁸ and 8 × 10⁸, respectively. These results demonstrate the significant influence of the magnetic field on the longitudinal mechanical response. Figure 13 depicts the displacement component v. In contrast to the behavior of u, the peak amplitude of the transverse displacement decreases as the magnetic field increases. The magnetic field therefore suppresses the transverse mechanical response and reduces the extent of lateral deformation. This behavior is a direct consequence of the electromagnetic body forces generated by the interaction between the magnetic field and the electrically conducting semiconductor medium. The peak value of the transverse displacement decreases from approximately 0.0490 at H₀ = 0 to 0.0411 and 0.0346 for H₀ = 4 × 10⁸ and 8 × 10⁸ , respectively. This behavior confirms the suppressing effect of the magnetic field on the transverse displacement response. Figure 14 depicts the normal stress component  for different values of H₀. A significant influence of the magnetic field is observed near the boundary region, where increasing H₀ noticeably reduces the magnitude of the compressive stress. The induced Lorentz force generates an additional mechanical resistance that counteracts the deformation process, leading to a redistribution of the internal stress field and a reduction in stress concentration close to the illuminated surface. The minimum value of changes from approximately −6.6088 at H₀ = 0 to -5.8387 and -4.5859 for H₀ = 4 × 10⁸ and 8 × 10⁸, respectively. This reduction in stress magnitude confirms the pronounced influence of magnetoelastic interactions on the normal stress field. Figure 15 presents the transverse stress component . The influence of the magnetic field on this component is comparatively small, although a slight reduction in the compressive stress magnitude can be observed near the boundary. Away from the illuminated surface, all curves gradually converge toward zero, indicating that the magnetic effect is primarily localized within the near-surface interaction region. The minimum value of  changes from approximately -0.4852 at H₀ = 0 to -0.4771 and -0.4639 for H₀ = 4 × 10⁸ and 8 × 10⁸, respectively. Although the variation is relatively moderate, the results still indicate a measurable dependence on the magnetic field intensity. Figure 16 presents the shear stress distribution . The application of the magnetic field decreases the magnitude of the initial negative shear stress and shifts the transition toward positive values closer to the boundary. Furthermore, the positive peak slightly increases and moves toward smaller values of x as H₀ increases. This behavior reflects the coupling between the induced electromagnetic force and the shear deformation mechanisms within the rotating semiconductor medium. Overall, the results demonstrate that the magnetic field primarily affects the mechanical part of the coupled response through magnetoelastic interactions and Lorentz-force effects, whereas the thermal and carrier-density fields remain comparatively insensitive to variations in H₀. The minimum value of changes  from approximately -0.0167 at H₀ = 0 to -0.0115 and -0.0037 for H₀ = 4 × 10⁸ and 8 × 10⁸, respectively. This progressive reduction in the shear-stress magnitude demonstrates the important role of the magnetic field in modifying the coupled mechanical response of the medium. The strongest magnetic influence is therefore observed in the displacement and stress components, particularly in the near-boundary region where the coupled interactions are most pronounced. A brief local sensitivity analysis with respect to the magnetic field intensity H₀ has been included by examining the responses of the temperature, carrier density, displacement, and stress fields for H₀ = 0, 4 × 10⁸ and 8 × 10⁸. The results indicate that the temperature and carrier-density fields exhibit relatively weak sensitivity to variations in H₀, whereas the displacement and stress fields show a more pronounced response, particularly in the near-boundary region where magnetoelastic coupling effects are strongest. The obtained solutions remain bounded and physically admissible for all investigated values of H₀, confirming the stability and robustness of the proposed formulation under moderate variations of the applied magnetic field.

Figure 10: Dimensionless temperature distribution T versus the dimensionless distance x for different values of the magnetic field intensity H₀. All remaining parameters are fixed as listed in Table 2. The magnetic field modifies the thermal response through magneto-thermoelastic coupling effects. Please click here to view a larger version of this figure.

Figure 11: Dimensionless carrier-density distribution N versus the dimensionless distance x for different values of the magnetic field intensity H₀. All remaining parameters are fixed as listed in Table 2. Variations in the magnetic field influence carrier redistribution within the semiconductor medium. Please click here to view a larger version of this figure.

Figure 12: Dimensionless longitudinal displacement u versus the dimensionless distance x for different values of the magnetic field intensity H₀. All remaining parameters are fixed as listed in Table 2. Electromagnetic coupling modifies the displacement amplitude and attenuation behavior. Please click here to view a larger version of this figure.

Figure 13: Dimensionless transverse displacement v versus the dimensionless distance x for different values of the magnetic field intensity H₀. All remaining parameters are fixed as listed in Table 2. The magnetic field alters the transverse deformation characteristics of the medium. Please click here to view a larger version of this figure.

Figure 14: Dimensionless normal stress σ_xx versus the dimensionless distance x for different values of the magnetic field intensity H₀. All remaining parameters are fixed as listed in Table 2. The stress distribution near the boundary is affected by the applied magnetic field. Please click here to view a larger version of this figure.

Figure 15: Dimensionless normal stress σ_yy versus the dimensionless distance x for different values of the magnetic field intensity H₀. All remaining parameters are fixed as listed in Table 2. The magnetic interaction modifies the attenuation characteristics of the transverse stress field. Please click here to view a larger version of this figure.

Figure 16: Dimensionless shear stress σ_xy versus the dimensionless distance x for different values of the magneti field intensity H₀. All remaining parameters are fixed as listed in Table 2. Magnetoelastic coupling influences the spatial distribution of the shear stress response. Please click here to view a larger version of this figure.

Validation, stability, and physical consistency of the proposed model

To further assess the physical consistency and reliability of the proposed formulation, additional validation and stability considerations are presented in this section. The analysis focuses on the admissibility of the obtained eigenmodes, the boundedness of the associated solutions in the semi-infinite domain, and the consistency of the model through appropriate limiting cases and comparisons with previously published results. In addition to the stability considerations discussed below, the proposed formulation was further verified through appropriate limiting cases. The numerical results presented in Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 include the case , corresponding to the non-rotating configuration, while Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16 include the case H₀ = 0, corresponding to the absence of magnetic field effects. These limiting cases recover previously established configurations reported in the literature and exhibit smooth, physically consistent transitions to the generalized rotating and magnetized cases. The obtained agreement provides additional validation of the correctness of the proposed formulation and its numerical implementation. Furthermore, a quantitative comparison with the previously published results of Alaofi et al.³⁵ is presented in Table 3 for the limiting case . The results show excellent agreement with negligible relative errors, confirming the accuracy and numerical reliability of the present implementation.

Table 3: Comparison of the present model in the limiting case (Ω = 0) with previously published results of Alaofi et al.³⁵ for the temperature field T at t = 0.6. The comparison demonstrates excellent agreement between the present results and the published data, confirming the correctness, accuracy, and numerical reliability of the present formulation and its implementation. Please click here to download this Table.

DATA AVAILABILITY:

The raw numerical data used to generate all figures in this study have been provided in Supplementary File 2 . These datasets include the spatial distributions of all computed variables for the considered time instances, enabling full reproducibility of the presented results.

Supplementary File 2: Numerical datasets used to generate Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, and Figure 16. The Excel workbook contains multiple worksheets corresponding to the temperature (T), carrier density (N), displacement components (u, v), and stress components  under different values of the rotation parameter Ω and magnetic field parameter H₀. The datasets provide the numerical values used to construct all figures presented in the manuscript.Please click here to download this file.

Discussion

Eigenvalue admissibility, stability, and boundedness analysis

The admissibility of the obtained eigenvalues is governed by the physical requirement that all field variables remain bounded within the semi-infinite domain x ≥ 0. The general eigensolution is expressed in terms of exponential modes of the form . Consequently, the asymptotic behavior of the solution depends directly on the real part of the eigenvalues . To satisfy the boundedness condition at infinity, only eigenvalues satisfying , are retained. Under this condition, , ensuring that all physical fields decay away from the boundary and remain finite throughout the medium. In contrast, eigenvalues with  produce exponentially growing terms, which lead to unbounded solutions and violate the physical requirements of the semi-infinite semiconductor half-space. Therefore, such roots are discarded from the admissible solution set. The adopted root-selection criterion is consistent with the standard eigenvalue-based treatment of coupled thermoelastic and semiconductor wave-propagation problems in semi-infinite media and guarantees the physical admissibility and stability of the obtained analytical solution. Similar admissibility conditions have been employed in related studies dealing with decaying eigenmodes and bounded solutions in generalized thermoelastic media.

In this work, a coupled magneto-photo-thermoelastic model for a rotating fiber-reinforced anisotropic semiconductor half-space subjected to optical excitation and an applied magnetic field was developed and analyzed. The governing equations describing the thermal, carrier-density, displacement, and stress fields were formulated within a unified theoretical framework and solved analytically using the normal mode method together with the eigenvalue approach. The obtained solutions satisfy the boundedness condition in the semi-infinite domain and were verified through eigenvalue admissibility requirements and limiting-case comparisons with previously published results. The numerical results demonstrated that rotational motion introduces additional inertial coupling effects through the Coriolis and centrifugal accelerations, leading to noticeable modifications in the temperature, carrier-density, displacement, and stress distributions. Increasing the rotation parameter Ω alters the amplitudes and attenuation characteristics of the coupled fields, with the most significant influence observed in the displacement and stress responses near the boundary surface. The applied magnetic field intensity H₀ was also found to play a crucial role in the coupled behavior of the medium. Variations in H₀ modify the electromagnetic–mechanical interaction through the Lorentz-force contribution, resulting in appreciable changes in the magnitudes and spatial distributions of all physical field quantities. The results indicate that both rotational and magnetic effects strongly influence the propagation and attenuation characteristics of the coupled waves within the semiconductor medium. Furthermore, the limiting case corresponding to the absence of rotation and magnetic field effects was examined and shown to recover previously published photo-thermoelastic results, confirming the consistency and reliability of the proposed formulation. Overall, the present model provides a generalized analytical framework for investigating coupled wave propagation phenomena in rotating fiber-reinforced semiconductor media under optical and electromagnetic excitations. The obtained results contribute to a better theoretical understanding of multiphysical interactions in semiconductor structures and may serve as a useful basis for future studies of coupled thermoelastic and optoelectronic systems. The present study is formulated within the framework of deterministic generalized magneto-photo-thermoelasticity, where all material and physical parameters are taken from established values reported in the literature. The primary objective is to investigate the coupled influence of rotation, magnetic field, and optical excitation on wave propagation characteristics. A comprehensive stochastic treatment of parameter uncertainties is beyond the scope of the present work and will be considered in future investigations.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Computational software (symbolic and numerical analysis)	Wolfram Research	Wolfram Mathematica (Version 12.0) was used	Used for eigenvalue computation, analytical solution implementation, and numerical evaluation
Material parameter dataset (silicon semiconductor properties)	Various literature sources	N/A	Physical constants (elastic, thermal, carrier-related) used in computations (Table 1)
Personal computer/workstation	HP	N/A	Computations were performed on a standard personal computer running Windows OS with sufficient memory for numerical simulations
Equation editor	Microsoft  Word and MathType	N/A	Used for formatting and presenting mathematical expressions in the manuscript
Reference management software	Elsevier	N/A	Used for managing references and formatting citations (Vancouver style)