Supplemental Document

High-efficient photoacoustic generation with anultrathin metallic multilayer broadbandabsorber: supplementCHUNQI ZHENG,1,4 HUANZHENG ZHU,1,4 ZIQUAN XU,1 RAVINDRA K.SINHA,2,3 QIANG LI,1 AND PINTU GHOSH1,∗

1State Key Laboratory of Modern Optical Instrumentation, College of Optical Science and Engineering,Zhejiang University, Hangzhou 310027, China2CSIR-Central Scientific Instruments Organization, Chandigarh 160030, India3TIFAC-CORE in Fiber Optics and Optical Communication, Applied Physics Department, DelhiTechnological University, Bawana Road, Delhi-110042, India4Equal contribution∗ghosh@zju.edu.cn

This supplement published with The Optical Society on 3 March 2021 by The Authors under theterms of the Creative Commons Attribution 4.0 License in the format provided by the authorsand unedited. Further distribution of this work must maintain attribution to the author(s) and thepublished article’s title, journal citation, and DOI.

Supplement DOI: https://doi.org/10.6084/m9.figshare.14099651

Parent Article DOI: https://doi.org/10.1364/OE.420138

High-efficient photoacoustic generation with ultrathin metallic multilayer broadband absorber: supplemental document 1. Simulation

In the thermoelastic regime, stress confinement condition needs to be required, that is, the heating caused by the incident light is faster than the thermal expansion [1]. Therefore, the incident light should be intensity-modulated waves. When the PA conversion structure is illuminated by the incident light, the spatial electric field can be calculated via the Helmholtz equation [2] ∇ × ∇ × − − = 0, (S1)

where μr, εr, σ and k0 are relative permeability, relative permittivity, conductivity and wavenumber, respectively. The resistive heating caused by light absorption can be expressed as = ∙ , (S2)

where and are current density at a given location and electric field at that location.

The temporal temperature change is determined by the product of resistive heating and light pulse shape and can be written as [3] − ∇ ∇ = ∙ , (S3)

where , , and are the mass density, heat capacity and heat conductivity, respectively. represents the temporal light pulse shape. Then the thermal strain can be calculated via

the product of material thermal expansion coefficient and temperature change as = − , (S4)

where is the thermal expansion tensor and − is the temperature change due to resistive heating. For a linear elastic material, Hooke’s law relates the stress tensor s to the elastic strain as [4] = : − , (S5)

where is the fourth-order elasticity tensor of the material, “:” represents for the double-dot tensor product, and is the total strain. The structural displacement can be calculated by = ∇ , (S6)

where is the displacement normal to the acoustic-structural boundary and is mass density. The acoustic pressure can be correlated with the normal acceleration of the structural displacement at the boundary of acoustic generation as ∙ ∇ + = 0, (S7)

where the direction of is the outward surface normal.

The acoustic wave propagating in the surrounding medium can be described by the acoustic wave equation

where is t

The optical aMultiphysics nanostructuresubstrate and thermal expanport in silica gsimulate the in

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2. The emission spectrum of the white light LED

The emission spectrum of the white lifht LED used to excite the photoacoustic signal is shown in figure S1.

Fig. S2. The emission spectrum of the white light LED used to excite the PA signal.

3. Determination of the thickness of the PDMS layer

The thickness of the PDMS layer can be determined by referring to the curves of film thickness varies with different dilution ratios of PDMS and hexane [5].

Fig. S3. PDMS film thickness for different ratios of dilution with n-hexane.

References

1. T. Lee, H. W. Baac, Q. Li, and L. J. Guo, "Efficient Photoacoustic Conversion in Optical Nanomaterials and Composites," Advanced Optical Materials 6, 1800491 (2018).

2. E. P. Furlani, I. H. Karampelas, and Q. Xie, "Analysis of pulsed laser plasmon-assisted photothermal heating and bubble generation at the nanoscale," Lab Chip 12, 3707-3719 (2012).

3. A. O. Govorov, W. Zhang, T. Skeini, H. Richardson, J. Lee, and N. A. Kotov, "Gold nanoparticle ensembles as heaters and actuators: melting and collective plasmon resonances," Nanoscale Research Letters 1, 84-90 (2006).

4. A. Hatef, B. Darvish, A. Dagallier, Y. R. Davletshin, W. Johnston, J. C. Kumaradas, D. Rioux, and M. Meunier, "Analysis of photoacoustic response from gold–silver alloy nanoparticles irradiated by short pulsed laser in water," The Journal of Physical Chemistry C 119, 24075-24080 (2015).

5. A. L. Thangawng, R. S. Ruoff, M. A. Swartz, and M. R. Glucksberg, "An ultra-thin PDMS membrane as a bio/micro-nano interface: fabrication and characterization," Biomed Microdevices 9, 587-595 (2007).