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Parallel LC circuit model for multi-band absorption and preliminary design of radiative cooling

Rui Feng, Jun Qiu, Linhua Liu, Weiqiang Ding, and Lixue Chen

Open Access Open Access

Abstract

We perform a comprehensive analysis of multi-band absorption by exciting magnetic polaritons in the infrared region. According to the independent properties of the magnetic polaritons, we propose a parallel inductance and capacitance(PLC) circuit model to explain and predict the multi-band resonant absorption peaks, which is fully validated by using the multi-sized structure with identical dielectric spacing layer and the multilayer structure with the same strip width. More importantly, we present the application of the PLC circuit model to preliminarily design a radiative cooling structure realized by merging several close peaks together. This omnidirectional and polarization insensitive structure is a good candidate for radiative cooling application.

© 2014 Optical Society of America

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Figures (10)
Fig. 1
Fig. 1 (a) Schematic of the multi-sized dual-band absorber. (b) Absorption spectra of the multi-sized dual-band absorber at normal incidence. Insets are structure with only one subunit.

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Fig. 2
Fig. 2 Distributions of the normalized magnetic field and electric field vector at the resonant peaks of (a) 5.59 μm and (b) 8.19 μm. (c) Schematic of the equivalent LC circuit model for grating-film structure. (d) Illustration of the PLC circuit model for multi-sized structure. Each subunit corresponds to one impedance and two impedances are connected in parallel.

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Fig. 3
Fig. 3 Absorption spectra of the multi-sized structure with varying the refractive index of the spacing layer, while keeping the geometry parameters unchanged. Green triangles indicate the resonance wavelength calculated from the LC circuit model.

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Fig. 4
Fig. 4 (a) Schematic of the multilayer dual-band absorber. (b) Absorption spectra of the multilayer dual-band absorber at normal incidence. Insets are structure with a single Al2O3 (n1) or ZnTe (n2) dielectric spacing layer.

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Fig. 5
Fig. 5 Distributions of the normalized magnetic field and electric field vector at the resonant peaks of (a) 6.36 μm, and (b) 10.63 μm. (c) Schematic of the equivalent LC circuit model for double-layer arrays. (d) Illustration of the PLC circuit model for multilayer structure. The impedances of two subunits are still connected in parallel.

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Fig. 6
Fig. 6 Absorption spectra of the multilayer dual-band absorber with various strip lengths while keeping the other parameter fixed. Green triangles indicate the resonance wavelength predicted from the PLC circuit model.

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Fig. 7
Fig. 7 (a) Absorption spectra of the radiative cooling structure for the TM polarization. Inset is schematic of the radiative cooling structure. (b) Absorptivity as a function of wavelength and angle of incidence.

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Fig. 8
Fig. 8 (a) Schematic of the two dimensional radiative cooling structure. (b) Absorption spectra with different polarization angles from 0° (TM) to 90° (TE) in a step of 10° at normal incidence.

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Fig. 9
Fig. 9 Absorption spectra for different azimuthal angles of φ = 0°(red), and φ = 45°(green), and φ = 90°(blue) at a fixed incident angle of 25° for (a) TE and (b) TM polarization. Insets are propagation configuration.

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Fig. 10
Fig. 10 (a) Absorption spectra for different incident angles 10° and 25° at a fixed azimuthal angle of 0° under the TM polarization. (b) Distributions of the magnetic field on the x-z cross-section in the middle of the biggest patch w4 at the wavelength 7.63 μm.

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Equations (12)

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Z w = iω( L m + L e ) 1− ω 2 C g ( L m + L e ) + 2 iω C m +iω( L m + L e )
1 Z tot = 1 Z w 1 + 1 Z w 2 ⋯ 1 Z w n
Z tot = Z w 1 ⋅ Z w 2 Z w 1 +Z w 2
Z n = 2 i ω ( L m + L e ) 1 − ω 2 C g ( L m + L e ) + 2 i ω C m
Z tot = Z n 1 ⋅ Z n 2 Z n 1 +Z n 2
Z subunit = 2 i ω ( L m + L e ) + 2 i ω C m
Z n 1 , w 1 = 2 i ω 1 ( A w 1 t + B w 1 ) + 2 i ω 1 C ( w 1 / t )
Z n 1 , w 2 = 2 i ω 2 ( A w 2 t + B w 2 ) + 2 i ω 2 C ( w 2 / t )
Z upper = Z n 1 , w 1 ⋅ Z n 1 , w 2 Z n 1 , w 1 +Z n 1 , w 2
Z n 2 , w 1 = 2 i ω 3 ( A w 1 t + B w 1 ) + 2 i ω 3 C ( w 1 / t )
Z n 2 , w 2 = 2 i ω 4 ( A w 2 t + B w 2 ) + 2 i ω 4 C ( w 2 / t )
Z lower = Z n 2 , w 1 ⋅ Z n 2 , w 2 Z n 2 , w 1 +Z n 2 , w 2
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