## 1 Introduction
For InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\) alloys, there exist few experimental and theoretical studies, especially on the physics of those attributes which ascertain their prominence at a practical level [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. In the far-infrared (FIR) region, 5 meV \(\leq\) E \(\leq\) 100 meV, although SE is recognized as an efficient method for exploring lattice dynamics and free carrier concentration of binary materials, the method has not yet been applied to ternary alloys. Earlier analysis of RSS data on vibrational properties of InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\) using a modified random-element iso-displacement (MREI) model envisioned a two-phonon-mode behavior [25; 26; 27]. However, no gap (In\(P\):Sb for x \(\rightarrow\) 0) or localized vibrational mode (LVM) (In\(Sb\):P for x \(\rightarrow\) 1) was detected near the limiting values of x. Extensive PL measurements and extended X-ray absorption fine-structure (EXAFS) results on Gas-Source Molecular Beam Epitaxy (GS-MBE)-grown InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\)/n-InAs samples have recently provided valuable electronic and structural characteristics [51]. On the contrary, no attempts have been made to comprehend the optical properties of InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\) alloys in the near-IR (NIR) to ultraviolet (UV) energy range. The purpose of this paper is to report the results of both experimental (Section 2) and theoretical (Section 3) studies to assess the phonon and optical traits of nearly \(\sim\)1 um thick InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\)/n-InAs samples grown by the GS-MBE technique (Section 2.1). The TEM method was employed earlier for investigating the structural and chemical distributions of atoms. The composition of Sb in InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\) alloys has also been achieved by using electron probe microanalysis (EPMA). Room-temperature (RT) Hall measurements with van der Pauw methods have been performed to assess the electrical properties of Be- and Si-doped InP\({}_{1-\mathrm{x}}\)Sb\({}_{\mathrm{x}}\) epilayers [39; 40]. Here, we employed a Reinshaw InVia Raman (Section 2.2) spectrometer with a diode-pumped solid-state (DPSS) 532 nm laser as an excitation source for measuring the composition-dependent longitudinal optical (\(\omega_{\rm LO}\)) and transverse optical (\(\omega_{\rm TO}\)) phonons in InP\({}_{1-x}\)Sb\({}_{x}\)/n-InAs samples. The PL measurements are also reported by calibrating the radiation lines of a Xe lamp and employing the SPEX 500M monochromator (Section 2.3). Like HR-XRD, the PL studies on InP\({}_{1-x}\)Sb\({}_{x}\)/n-InAs samples with smaller values of x (\(\equiv\)0.10, 0.16, 0.17) have confirmed the two energy phases, and for x \(\geq\) 0.30, it provided a single energy phase. From a theoretical standpoint (Section 3.1), a classical \"Drude-Lorentz\"model is adopted by incorporating optical \(\omega_{\rm LO}\), \(\omega_{\rm TO}\) phonons to simulate (Section 3.2) the complex dielectric functions [\(\widetilde{\epsilon}(\omega)\), or \(\widetilde{\rm n}(\omega)\)] in the FIR \(\rightarrow\) MIR (5 meV \(\leq\) E \(\leq\) 100 meV) energy region for both binary and ternary alloys. Although the optical measurements by SE in the NIR \(\rightarrow\) UV (0. 5 eV to 6.0 eV) energy regions are known for InP and InSb materials [22; 23], little to no information is available for the ternary InP\({}_{1-x}\)Sb\({}_{x}\) alloys. From technical and scientific perspectives, it is crucial to derive analytical expressions for simulating the optical constants of both binary and ternary alloys. The systematic assessment of refractive indices \(\widetilde{\rm n}(\rm E)\) and absorption coefficients \(\alpha(\rm E)\) is especially important for selecting apposite materials in structural designs and the optimization of different optoelectronic devices.