Reflectance-Only Retrieval of Refractive Index and Extinction Coefficient Dispersions in an Absorbing Thin Film via a Paul-Wavelet Repetition-Frequency Method.

Accurate knowledge of the refractive index (n) and extinction coefficient (κ) dispersions is essential for understanding the optical response of thin-film materials used in photovoltaics, optoelectronics, and related photonic applications. However, transmission-based dispersion extraction becomes unreliable for turbid, colloidal, nanostructured, or strongly absorbing thin films, where low transmission or scattering prevents accurate spectral evaluation. In this work, we introduce a reflectance-only framework based on the Paul wavelet transform applied to normal-incidence reflectance spectra. The method exploits repetition frequency analysis of interference fringes to retrieve continuous dispersions of n and κ without requiring a predefined dispersion model. The wavelet order provides explicit control over the joint spectral-Fourier resolution, allowing optimization for a given data set. The approach is validated through simulation studies and a noisy signal test with 10% additive random noise, and benchmarked against Minkov's reflectance-based envelope/extrema method. Under noisy conditions, the proposed method preserves the refractive index trend close to the reference behavior, whereas the envelope-based approach shows larger deviations. The extinction coefficient is more sensitive to noise in both methods, although the wavelet-based retrieval remains comparatively stable. Experimental validation on a CdS thin film demonstrates consistency of the refractive index dispersion with literature data, while deviations in the extinction coefficient are attributed to its sensitivity to absorption-related and microstructural variations. The method requires independent film thickness information, as in all interference-based approaches, but is otherwise nondestructive and model-free, making it suitable for a broad range of thin-film systems including doped semiconductors, colloidal nanostructures, and hybrid organic-inorganic materials where conventional transmission or ellipsometric methods are difficult to apply.