General design method of ultra-broadband perfect ... - OSA Publishing

Vol. 25, No. 20 | 2 Oct 2017 | OPTICS EXPRESS A980

General design method of ultra-broadband perfect absorbers based on magnetic polaritons YUANBIN LIU,1 JUN QIU,1,2 JUNMING ZHAO,1 AND LINHUA LIU1,3 1

School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, China 2 [email protected] 3 [email protected]

Abstract: Starting from one-dimensional gratings and the theory of magnetic polaritons (MPs), we propose a general design method of ultra-broadband perfect absorbers. Based on the proposed design method, the obtained absorber can keep the spectrum-average absorptance over 99% at normal incidence in a wide range of wavelengths; this work simultaneously reveals the robustness of the absorber to incident angles and polarization angles of incident light. Furthermore, this work shows that the spectral band of perfect absorption can be flexibly extended to near the infrared regime by adjusting the structure dimension. The findings of this work may facilitate the active design of ultra-broadband absorbers based on plasmonic nanostructures. ©2017 Optical Society of America OCIS codes: (350.2770) Gratings; (300.1030) Absorption; (260.5740) Resonance; (160.3918) Metamaterials.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

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https://doi.org/10.1364/OE.25.00A980 Received 31 Jul 2017; revised 5 Sep 2017; accepted 20 Sep 2017; published 26 Sep 2017


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1. Introduction The utilization of solar energy or radiative cooling can serve as an important and effective way to reduce the excessive consumption of traditional energy resources [1, 2]. These applications are involved with many fields such as thermophotovoltaic (TPV) systems, solar cells and thermal emitter. As a matter of fact, the broadband perfect absorption is of critical significance in these fields. With remarkable progress of nanoscience, metamaterials have been demonstrated to achieve the exotic optical properties unattainable with naturally-existing materials by creating independent tailored magnetic and electric responses to incident electromagnetic radiation [3–5]. In particular, magnetic and electric responses can excite magnetic polaritons (MPs) and surface plasmon polaritons (SPPs) through the coupling of external electromagnetic fields to induced electric currents and oscillations of the conductor’s electron plasma, respectively. Both resonance modes can make the electric and magnetic fields associated with light confined to metamaterials [6, 7]. Such as split-ring resonators [4], arrays of pairs of parallel nanorods [8] and rectangular gratings [9] are typical cases of applications of MPs and SPPs to induce a resonance absorption. Nowadays, numerous researchers have been attracted to fabricate an ideal absorber by metamaterials. Dramatic progress has been made, yet plenty of them concentrate mainly on wide-angle and polarization independent perfect absorbers with one or several narrow peaks [10–13]. It is because the design of plasmonic nanostructures is still challenging to effectively couple broadband and close resonance wavelengths together and keep high performance [14–21]. Even so, there is still great essentiality and interest in achieving broadband perfect absorption by the use of metamaterials supporting plasmonic modes. The one-dimension (1D) rectangular grating in Fig. 1(a) is well known as its simple structure and remarkable property of enhancing the absorption of metals in specific wavelengths. The resonances for transverse magnetic (TM) waves in 1D gratings have been successfully predicted and elucidated by the theory of MPs [22]. The MP resonance can be described by an inductor-capacitor (LC) circuit. The metal ridge and substrate act as inductive elements L and the dielectric in the trench acts as capacitive elements C. The fundamental resonance wavelength can be obtained from λR = 2π c0 LC . Compared with SPPs, the unique property of MPs is its robustness to the incident angle of light [10, 22, 23]. However, the 1D rectangular grating also suffers from the common disadvantage of narrow bandwidth. Figure 1(b) shows five cases of 1D Ag gratings with different trench widths b, where


period Λ = 500 nm and height h = 300 nm are fixed. The trench widths change from 6 nm to 10 nm and the step size is 1 nm. The optical constants of Ag are derived from a Drude model [24]. The rigorous coupled-wave analysis (RCWA) is applied to compute the spectral absorptance of gratings at normal incidence of TM waves. Five narrow peaks corresponding different trenches are shown in Fig. 1(c) and peak positions make a red shift with the trench width decreasing. In addition, peak positions are close to each other due to the near trench widths. If the difference of trench widths reduces further, there are more narrow peaks with closer positions and the family of their absorptance curves can be encompassed by an envelope curve as shown in Fig. 1(c). The envelope curve shows that if there are plenty of gratings with close resonance wavelengths or continuous trench widths blended together, the absorption band will be broadened. Though directly packing so many gratings together is not feasible in practice, it provides a useful enlightenment for the design of the ultra-broadband perfect absorber. Figure 1(d) shows that the five cases of different trench widths in Fig. 1(b) are marked with black dashed rectangles and packed along the direction of Z axis where trench widths are tapering. When the number of gratings with different trench widths is enough large and trench widths change linearly and continuously, in limited cases of geometry, we can take the metal-dielectricmetal structure in Fig. 1(d) as an approximate substitute of plentiful gratings with continuous variation in trench widths. Yellow regions in Fig. 1(d) represent the dielectric material sandwiched between metals. As a result, the 1D sandwich structure in Fig. 1(d) can excite MPs in a wide wavelength band for TM waves at various parts of the structure. Besides, the MP resonance can simultaneously happen in both the metal-air-metal and metal-dielectricmetal regions. Resonances from the two places make joint efforts to enhance absorption. The coupling of resonances at different wavelengths brings about the broadband absorption.

Fig. 1. (a) One-dimension rectangular grating with plane of incidence and polarization. (b) Five cases of 1D grating with different trench widths, other parameters are fixed: Λ = 500 nm and h = 300 nm. (c) Spectral absorptance of five cases of 1D gratings corresponding Fig. 1(b). (d) Schematic of 1D metal-dielectric-metal sandwich structure proposed in this work.

Because the transverse electric (TE) waves cannot excite MPs in 1D grating, to make the absorber insensitive to both TM and TE waves, the metal-dielectric-metal pyramid


nanostructure with four-fold rotational symmetry is proposed in this work and shown in Fig. 2(a) as the 2D counterpart of the 1D sandwich structure. The structure period is represented by Λx and Λy (Λx = Λy); lx and ly are the edge lengths of inner dielectric pyramid (lx = ly); β shows the dihedral angle; δ represents the thickness of the metal membrane. As shown in Fig. 2(a), the left half part represents the external view of the proposed nanostructure and the right half part is the perspective neglecting the uppermost metal membrane. For the practical devices, the electron beam lithography is a potential and effective fabrication method to obtain the pyramid geometry in the dielectric layer, which has been utilized to manufacture similar nanocone structures [25, 26]. Then using physical vapor deposition (PVD) can grow a metallic thin film over the dielectric pyramid. To facilitate the application of the pyramid nanostructured absorber, this work gives the design process of the structure dimension in the target wavelength band firstly. Based on the proposed design method, the spectral absorptance of the obtained nanostructure is investigated from 0.2 μm to 4 μm. Furthermore, the feature of wide-angle and polarization independent absorption of the pyramid grating has been demonstrated.

(b)

(a)

β

Λy Λx

ly lx

δ δ

(c)

C L

L C

Fig. 2. (a) Schematic of the proposed pyramid nanostructure, external view in left half and perspective drawing in right half. (b) Model of calculating equivalent impedance which is intercepted from the whole pyramid. (c) Equivalent LC circuit of the calculation model.

2. Theoretical model and analysis The MP resonance can be described by an inductor-capacitor (LC) circuit. The resonance in the pyramid is taken for study due to the advantage of four-fold rotational symmetry of pyramid which can simplify the formulas of inductance and capacitance. It is noting that the MP resonance generated in the space between ridges of two pyramids has been similarly studied [27]. In the pyramid, the metal membrane acts as inductive elements L and the dielectric part acts as capacitive elements C. Inductive elements include both kinetic inductance Lk and mutual inductance Lm. Because the incident radiation with different wavelengths can be accumulated and absorbed in various parts of the pyramid nanostructure, we have intercepted a part of the pyramid shown in Fig. 2(b) to obtain specific expressions of L and C shown in Fig. 2(c). Lk is contributed by the drifting electrons in metal and its formula is [22]:


Lk =

−ε ′

ε 0ω (ε ′ 2

2

 + ε ′′ ) 2

s

0

−ε ′ tan γ ds l = ln 2 2 2 δ (l − 2 s / tan γ ) 2ε 0ω (ε ′ + ε ′′ ) l − 2s / tan γ

(1)

where s is the total length of current path in the metal; ε ′ and ε ′′ are the real and imaginary part of dielectric function of metals, respectively. Via the mean value theorem of integrals and simplification treatment, Eq. (1) can be changed as another form: Lk ≈

−ε ′

s

ε 0ω (ε ′ + ε ′′ ) δ (l − s / tan γ ) 2

2

2

(2)

In the later analysis, it can be found that the form of Eq. (2) is helpful. Through integration, the mutual inductance is Lm = 0.5μ0 s . And the capacitance of two metallic plates is C = c ′ε 0ε d 

l ds

s y

0

lx

=c′ε 0ε d s

(3)

where ε d represents the dielectric function of the dielectric material; the numerical factor c′ between 0 and 1 accounts for the non-uniform charge distribution. The resonance wavelength can be predicted by λR = 2π c0 (2 Lk + 2 Lm )C . After some manipulations, it can be shown that:

λR = 2π s

c′ε d 1+ A

(4)

where the parameter A has been defined as A=

2ε ′ s 2 c′ε d

(5) (ε ′2 + ε ′′2 )δ (l − s / tan γ ) Equation (4) is an implicit function about the resonance wavelength due to the fact that materials are usually dispersive for different wavelengths. The optical constants of solid materials can be described by the Lorentz-Drude (LD) oscillator model [28]. The LD model shows that a complex dielectric function is expressed in the form: ε = ε D + ε L , which consists of the intraband part (Drude model, referred to free-electron effects) and interband part (Lorentz model, referred to bound-electron effects). Because the interband part is the semiquantum model, it is complicated and infeasible to obtain the explicit expression about λR of Eq. (4). However, in the low frequency limit ( A