Sangmo Kang

Optical resonances in multilayer cavities arise from constructive interference of electromagnetic waves and govern field enhancement, energy localization, and photothermal energy conversion. Although resonance phenomena are commonly characterized through real-frequency spectral responses, their underlying modal structure remains insufficiently understood. Here, a complex-frequency framework is developed to investigate optical resonance modes in metal–polymer–metal (M–P–M) cavities. Analytical solutions of the frequency-domain Maxwell–Helmholtz equation are assembled through interfacial continuity conditions to construct a global field-response function, whose poles define the intrinsic resonance modes of the cavity. The framework is applied to a Cr–PDMS–Cr cavity to investigate how complex-frequency resonance poles underlie resonance matching, field localization, and energy redistribution as functions of polymer-layer thickness, refractive index, and metal-layer thickness. Resonance matching to a 532 nm excitation wavelength is achieved through cavity-thickness tuning, and the corresponding complex-frequency resonance poles are systematically tracked as the structural and material parameters are varied. The pole-based predictions are validated by real-frequency electric-field calculations, confirming the correspondence between the resonance pole associated with the excitation wavelength and the resonance-matching condition. The results further show that refractive-index contrast and metal-layer attenuation govern resonance-pole migration and the resulting resonance characteristics of the cavity. Resonance matching produces strong electric-field localization within the polymer cavity while substantially reducing metallic heat generation through resonance-induced energy redistribution. These findings establish a consistent physical relationship between complex-frequency resonance poles and real-frequency optical and thermal responses, providing a unified modal framework for interpreting resonance matching, field localization, and resonance-mediated energy redistribution and a basis for the analysis and design of photothermal multilayer structures.

Frequency-dependent acoustic attenuation plays a central role in shaping photoacoustic wave propagation in biological media. However, its interaction with interfacial reflections and wave interference in multilayered media remains insufficiently understood. This study investigates the physical effects of frequency-dependent acoustic attenuation on photoacoustic wave propagation in multilayered human skin using a Fourier-domain semi-analytical approach. The formulation extends a previously developed lossless model by incorporating attenuation and its associated dispersion while preserving explicit interface-resolved wave interactions. Analytical expressions for the frequency-domain pressure field are obtained in each layer, and time-domain responses are reconstructed via inverse Fourier transformation. The results show that, in multilayered media, attenuation not only reduces signal amplitude but also alters the relative contributions of reflected and transmitted waves through preferential suppression of high-frequency components. This leads to systematic modification of interference patterns and corresponding changes in waveform structure and temporal broadening. Dispersion introduces additional phase variation but has a comparatively minor influence on the overall waveform under the conditions considered. These results provide a unified framework for interpreting attenuation effects in layered media, highlighting the dominant role of attenuation in shaping photoacoustic signals while retaining physically consistent wave propagation.

The basal layer (BL) of human skin is an ultrathin, melanin-rich absorber that plays a dominant role in near-surface optical absorption and photoacoustic (PA) wave generation. In many PA skin models, the epidermis is treated as a single effective layer to reduce anatomical complexity and computational cost; however, the impact of explicit BL resolution on time-domain PA waveforms remains unclear. This study aims at determining whether the BL must be modeled as an independent ultrathin absorber for quantitatively reliable time-domain PA analysis and reduced-layer representations of human skin. Because skin is a strongly scattering stratified medium, optical transport is diffusion-dominated. To address this question, a coupled optical–thermal–acoustic semi-analytical framework is applied to a physiologically representative nine-layer skin model and to reduced configurations with and without an explicitly resolved BL. Under excitation at a visible wavelength ( λ e = 532  nm ), increasing BL absorption raises the peak PA pressure by more than a factor of three, demonstrating the strong sensitivity of the PA amplitude to this localized source. Variations in BL thickness modify the amplitude and temporal-spectral characteristics of the PA waveform. Reduced models that preserve the BL reproduce the full-model response, whereas merging the BL into the epidermis leads to attenuation and temporal broadening due to source delocalization. These results show that preserving the spatial localization of the dominant absorber, rather than the anatomical layer count itself, is the governing physical criterion for model reduction and is essential for physically consistent time-domain PA analysis and inverse reconstruction in layered biological tissues.

This work presents a frequency-domain semi-analytical framework for modeling photoacoustic wave generation and propagation in strongly scattering multilayered human skin. The approach extends previous semi-analytical methods for non-scattering multilayered media by incorporating photon diffusion and its coupling with heat conduction and thermoelastic wave generation within a unified Fourier-domain formulation, enabling accurate characterization of frequency-dependent acoustic responses. A key contribution is the physically consistent treatment of photon transport at refractive-index discontinuities, resolving inconsistencies that can arise when Robin-type conditions are applied at internal interfaces in some diffusion-based layered models. This ensures photon-flux continuity and optical energy conservation across anatomical interfaces, which is critical for accurate predictions in scattering-dominant media. The formulation is validated against benchmark reference results, demonstrating excellent agreement in pressure amplitude and phase. Application to a realistic nine-layer anatomical skin model enables depth-resolved analysis of photon fluence, thermal behavior, and acoustic pressure under physiologically relevant conditions. The proposed framework provides an energy-conserving and generalizable foundation for quantitative photoacoustic analysis in layered biological media, offering improved physical fidelity for biomedical ultrasound and photoacoustic imaging applications.

This study presents a semi-analytical modeling framework for photoacoustic ultrasound generation in multilayered metal–polymer structures, integrating optical, thermal, and acoustic dynamics. The model solves the Maxwell–Helmholtz equation in the frequency domain to determine heat generation distributions, capturing complex optical phenomena, such as multiple reflections, interference, and Fabry–Pérot resonance, surpassing the limitations of the conventional Beer–Lambert law. This optical response is coupled with Fourier transform-based solutions to the heat conduction and elastic–acoustic wave equations, yielding closed-form expressions for the spatiotemporal evolution of temperature and pressure. The unified semi-analytical formulation rigorously incorporates multilayer heterogeneity, interfacial continuity, and realistic boundary conditions. Model predictions are validated against finite-difference (finite-difference frequency-domain and finite-difference time-domain) simulations and experimental measurements, demonstrating excellent agreement and confirming its high accuracy and physical fidelity. The results further reveal how parameters, such as layer thickness, acoustic impedance mismatch, and optical resonance, affect heat localization and acoustic wave generation. This framework offers predictive insight and design guidance for optimizing multilayered photoacoustic structures that generate ultrasound through light absorption in biomedical imaging, non-destructive testing, and optoacoustic devices.

This study presents a Fourier transform–based semi-analytical approach for analyzing the generation and propagation of photoacoustic ultrasound in multilayered thermal-acoustic structures. Laser-induced heat generation, described by the Beer–Lambert law, is incorporated into the heat conduction and acoustic wave equations, which are solved semi-analytically in the frequency domain. The general solutions are obtained analytically, while the arbitrary constants are determined numerically using interface and boundary conditions. Inverse Fourier transforms are then applied to reconstruct the time-domain responses. The approach is validated through comparisons with finite-difference time-domain simulations and experimental data. To demonstrate its applicability, it is applied to a water-substrate-polymer-water structural configuration, where the polymer layer serves as the light-absorbing medium, enabling detailed investigation of photoacoustic phenomena in both the time and frequency domains. The results show that laser heating raises the polymer temperature, generating bi-directional pressure waves and inducing acoustic resonances in both the polymer and the substrate. The proposed method accurately captures these coupled thermal and acoustic dynamics, providing new insights into ultrasound propagation in multilayered structures.