双波长窄带宽介质超材料吸收器

双波长窄带宽介质超材料吸收器

方晓敏 江孝伟 武华

Dual-wavelength narrow-bandwidth dielectric metamaterial absorber

FANG Xiao-min, JIANG Xiao-wei, WU Hua

引用本文:

方晓敏,江孝伟,武华. 双波长窄带宽介质超材料吸收器[J]. 中国光学, 2021, 14(6): 1327-1340. doi: 10.37188/CO.2021-0075

FANG Xiao-min, JIANG Xiao-wei, WU Hua. Dual-wavelength narrow-bandwidth dielectric metamaterial absorber[J].

第 14 卷 第 6 期

2021年11月

中国光学

Chine Optics

Vol. 14 No. 6

Nov. 2021

文章编号 2095-1531（2021）06-1327-14

Dual-wavelength narrow-bandwidth dielectric metamaterial absorber

FANG Xiao-min

11 *2

，JIANG Xiao-wei，WU Hua

（1. Faculty of Information Engineering, Quzhou College of Technology, Quzhou 324100, China；

2. College of Physics and Electronic Information, Gannan Normal University, Ganzhou 341000, China）

* Corresponding author，E-mail: JophJiangquzhi@126

Abstract: In order to reduce the manufacturing cost of the narrow-bandwidth Metamaterial Absorber (MA)

and broaden its application field, a dual-wavelength dielectric narrow-bandwidth MA, compod of Au sub-

strate, SiO dielectric layer and Si dielectric asymmetric grating, is designed bad on the finite-difference

2

time-domain method using dielectric materials. It is found by simulation that the propod narrow-band-

width MA has ultra-high absorption efficiency at λ = 1.20852 μm and λ = 1.23821 μm, and the FWHM is

12

only 0.735 nm and 0.077 nm, respectively. The main principle that MA achieves the narrow-bandwidth ab-

sorption at λ is mainly due to the formation of Fabry-Pérot (FP) cavity resonance in the SiO layer, while the

12

narrow-bandwidth absorption of MA at λ is mainly due to the guided mode resonance effect of the incident

2

light in the asymmetric grating. The theoretical calculations show that the absorption characteristics can be

affected more significantly by changing the structural parameters of the MA.

Key words: metamaterial absorber; dual-wavelength; narrow-bandwidth; Fabry-Pérot cavity resonance;

guided mode resonance

双波长窄带宽介质超材料吸收器

方晓敏

11 *2

，江孝伟，武 华

（1. 衢州职业技术学院 信息工程学院，浙江 衢州 324100；

2. 赣南师范大学 物理与电子信息学院，江西 赣州 341000）

摘要：为降低窄带宽超材料吸收器（Metamaterial Absorber，MA）制造成本的同时拓宽其应用领域，本文基于时域有限差分

法利用介质材料设计出双波长窄带宽介质MA，其由Au衬底、SiO介质层和Si介质非对称光栅构成。经模拟计算发

2

现，本文提出的双波长窄带宽介质MA在λ

12

=1.20852 μm和λ=1.23821 μm具有超高吸收效率，而且FWHM也分别只

有0.735 nm和0.077 nm。MA在λ实现窄带宽吸收主要是因为光在SiO层形成了法布里-珀罗(Fabry-Pérot, FP)腔共

12

收稿日期：2021-04-13；修订日期：2021-05-11

基金项目：国家自然科学基金(No. 61575008, No. 61650404)、江西省自然科学基金（No. 20171BAB202037）、江西省

教育厅科技项目(No. GJJ170819)、衢州市科技计划项目(No. 2019K20)

Supported by National Natural Science Foundation of China (No. 61575008, No. 61650404), Jiangxi Natural

Science Foundation (No. 20171BAB202037), Technology Project of Jiangxi Provincial Education Department

(No. GJJ170819), Quzhou Science and Technology Project (No. 2019K20)

1328

中国光学

第 14 卷

振，而MA在λ实现窄带宽吸收主要是由于入射光在介质非对称光栅中形成了导模共振效应。经理论计算可知，通过

2

改变MA的结构参数可对其吸收特性产生较为显著的影响。

关 键 词：超材料吸收器；双波长；窄带宽；法布里-珀罗腔共振；导模共振

中图分类号：TN256 文献标志码：A doi：10.37188/CO.2021-0075

1 Introduction

Perfect absorption of electromagnetic waves is

required in many applications, such as solar cells,

thermal emitters, radiation cooling, communi-

cation. However, the absorbers made of natural

[1-4]

materials can lead to impedance mismatch due to

the lack of magnetic respon, and therefore they

cannot completely suppress light reflection, thus

reducing the light absorption capacity of the ab-

sorber. Therefore, metamaterial-bad absorbers

[5]

have been propod, and becau the Metamaterial

Absorber (MA) has high absorption efficiency for

electromagnetic wave, and has the advantages of

compact size and ttable operating wavelength, it is

gradually gaining attention and becoming one of the

rearch hotspots.

[6]

With further in-depth rearch, different types

of MA have been gradually designed and fabricated,

such as wide-bandwidth MA, narrow-bandwidth

MA, terahertz MA, and tunable MA. The reason

[7-9]

why narrow-bandwidth MAs have received atten-

tion is that narrow-bandwidth MAs are more effi-

cient in detection and thermal emitters compared to

wide-bandwidth MAs, and only narrow-band-

[10-11]

width in optical modulation, optical detection, and

tailoring of thermal radiation MA can meet the re-

quirements. Different structures of narrow-

[12-13]

bandwidth MA have been propod, such as narrow-

bandwidth MA bad on Split Ring Resonator

(SRR) arrays, metal/dielectric periodic gratings, and

metal/dielectric slits (narrow slits). In 2014, Min

Qiu et al. (KTH Royal Institute of Technology) pro-

pod etching metal grating on a silver (Ag) metal

substrate, and bad on the surface plasmon exciton-

ic resonance formed by Ag grating and air mediumstrate, and the FWHM of this narrow-bandwidth

they successfully enabled MA with narrow-band-

width absorption at wavelength 1400 nm, and its

linewidth (Full Width Half Maximum, FWHM) can reach

0.4 nm; in 2018, FENG A et al. (the Chine Uni-

[14]

versity of Hong Kong) propod a narrow-band-

width MA consisting of asymmetric metal grating

and metal substrate, and a SiO transition layer was

2

added between the grating and the substrate, and the

narrow-bandwidth MA was found to achieve ultra-

narrow absorption in the optical communication

band with a FWHM of 0.28 nm; In 2019, KANG

[15]

S et al. (Southeast University) propod to etch a

cross-shaped nanoarray compod of gold (Au) on a

silicon dioxide substrate, while growing a thin layer

of Au on the other side of the silicon dioxide to sup-

press transmission, and the MA was tested and

found to achieve narrow-bandwidth absorption in

the terahertz band.

[16]

From the above, it can be found that the materi-

als ud in the micro-nano structures in the nar-

row-bandwidth MAs are metallic materials, but

metallic materials have ohmic loss and there are

processing problems for fine metallic materials at

high frequencies, both of which will affect the ap-

plication promotion of MAs in the future to some

extent. For this reason, some rearch groups have

propod to design and fabricate narrow-bandwidth

MAs using dielectric materials. In 2019, Zhibin Ren

et al. (Harbin Institute of Technology) designed and

prepared MAs with narrow-bandwidth absorption in

the infrared band using silicon nitride and indium tin

oxide materials, which were tested to have a FWHM

of up to 2.6 nm; in 2020, Yan Zhao et al. (Anhui

[17]

University) propod a dielectric grating compod

of silicon material etched directly on a metal sub-

第 6 期

FANG Xiao-min, et al. : Dual-Wavelength Narrow-Bandwidth Dielectric ......

1329

MA was calculated by simulation up to 0.38 nm.substrate, a silicon dioxide (SiO) dielectric layer,

[18]

Although the design and preparation of narrow-

bandwidth MAs using dielectric materials can re-

duce fabrication costs and improve absorption effi-

ciency, and the absorption bandwidth can be main-

tained at the sub-nanometer level, it can be en that

few MAs that achieve multi-wavelength narrow-

bandwidth (sub-nanometer level) absorption are cur-

rently available. This can limit the application of

narrow-bandwidth MAs in some applications, such

as in spectral detection and gas detection, where

multi-wavelength narrow-bandwidth MAs are more

efficient in improving their efficiency. To this

[19-20]

end, a dual-wavelength narrow-bandwidth dielec-

tric MA consisting of an asymmetric dielectric grat-

ing, a dielectric transition layer, and a metal sub-

strate is propod in this paper, and the MA is de-

signed and analyzed using the Finite Difference

Time Domain (FDTD) method. The differential

form of Maxwell's equations can be numerically

solved in the time domain through FDTD, in which

the differential quotient can be substituted for the

differential in the equation. In the solution, the elec-

tric and magnetic fields are alternately distributed,

and the electric and magnetic fields in the simula-

tion region are solved over time. Through simula-

tion calculations, it is found that the FWHM of the

dual-wavelength narrow-bandwidth MA is as low as

0.077 nm and the quality factor (figure of merit,

FOM) is up to 1524/RIU, and it can also be found

that the narrowest absorption bandwidth of the nar-

row-bandwidth MA designed in this paper de-

cread by an order of magnitude compared to the

reference [14-18]. This study can provide high-qual-

ity dual-wavelength narrow-bandwidth dielectric

MAs for bionsors, thermal emitters, light modulat-

ors, etc.

2 Device structure

A dual-wavelength narrow-bandwidth dielec-

tric MA, as shown in Figure 1, consists of an Aucoefficient and incident light angle frequency, re-

2

and an asymmetric grating formed by silicon (Si)

material from the bottom up. The main function of

the Au substrate is to suppress light transmission, so

its thickness must be greater than the skinning depth

of the incident electromagnetic wave, and the thick-

ness of Au is t to 0.2 μm in this paper. It can be

en from Figure 1 that there are two gratings with

the same height h but different widths, W and W,

12

in a period, and the distance between the gratings in

the same period is g, and the thickness of SiO is t.

2

In the future practical device preparation, the pre-

paration process of the dual-wavelength narrow-

bandwidth dielectric MA in this paper is compatible

with the current micro-nano processing process.

First, SiO and Si thin layers are grown success-

2

ively on the Au substrate by magnetron sputtering,

followed by spin-coating electron beam resist on the

Si thin layer, forming asymmetric grating patterns

on the resist after electron beam exposure and devel-

opment, and then debonding and transferring the

patterns to the Si thin layer using inductively

coupled plasma etching to finally prepare the dual-

wavelength narrow-bandwidth dielectric MA.

[21]

TE

z

k

H

θ

P

x

W

1

W

2

g

Si

h

SiO

t

2

Au

Fig. 1 Dual-wavelength narrow-bandwidth dielectric MA

structure diagram

图 1 双波长窄带宽介质MA结构图

The dielectric constant of Au is reprented by

the Drude model as shown in Equation (1), where

ω, γ and ω are the plasma frequency, damping

p

1330

中国光学

第 14 卷

spectively. To ensure the correctness of the simula-

tion calculation results, ω and γ are obtained from

p

the experimental data, and according to the refer-

ence [22], ω=1.32×10 rad/s, γ=1.2×10 rad/s. The

p

1614

refractive indices of SiO and Si are =1.45 and

2

n

SiO

2

n

Si

=3.45, respectively.

ε=1−.

Au

ω

2

p

（1）

ω+iγω

2

3 Results and discussion

3.1 Realization of dual-wavelength narrow-

bandwidth and high absorption

Firstly, a two-dimensional physical model of a

single period of the dual-wavelength narrow-band-

width dielectric MA is established using FDTD, and

then periodic boundary conditions are added in the

x-direction, perfect matching layer boundary condi-

tions are added in the z-direction, and the y-direc-

tion is t to grating infinite length by default. Fi-

nally, a light source is added directly above the

dual-wavelength narrow-bandwidth dielectric MA,

the light source polarization is t to TE polariza-

tion, the incident angle is t to 0°, and the MA is

surrounded by air with refractive index n=1.

Figure 2 shows the absorption spectrum of the

dual-wavelength narrow-bandwidth dielectric MA,

where P=1.05 μm, t=1.2 μm, h=0.78 μm, W=0.2 μm,

1

W=0.3 μm and g=0.2 μm. The above grating para-

2

meters were obtained bad on FDTD optimization.

It can be en from the figure that the MA has ultra-

high absorption efficiency at wavelengths λ=

1

1.2085 μm and λ=1.2382 μm, respectively, and

2

the absorption linewidths FWHM are 0.735 nm

and 0.077 nm, respectively. By comparing with

references [14-15, 17], the linewidth of the dual-

wavelength narrow-bandwidth dielectric MA at

wavelength λ is significantly decread and narrow-

2

bandwidth absorption is achieved. All parameters

mentioned above were kept constant for subquent

calculations if not otherwi stated.

1.0

λ

1

1.0

λ

2

n

o

0.8

0.8

i

t

p

r

0.6

FWHM=0.077 nm

o

)

s

.

u

b

.

A

0.4

a

(

n

0.6

0.2

o

1.237 51.238 01.238 51.239 0

0

i

t

p

r

FWHM=0.735 nm

Wavelength/µm

o

P=1.05 µm

s

0.4

b

h=0.78 µm

A

t=1.2 µm

0.2

W

1

=0.2 µm

W

2

=0.3 µm

0

g=0.2 µm

1.201.211.221.231.241.25

Wavelength/µm

Fig. 2 Absorption spectroscopy of dual-wavelength nar-

row-bandwidth dielectric MA

图 2 双波长窄带宽介质MA吸收光谱

MA can achieve ultra-narrow bandwidth high

absorption at wavelengths λ=1.2085 μm and λ=

12

1.2382 μm becau the effective impedance of MA

at the two wavelengths just matches the free-space

impedance and thus the reflection of MA at

wavelengths λ and λ can be effectively suppre-

12

sd. Becau the absorption efficiency A of MA

[23]

can be expresd as A=1-T-R, becau the thickness

of Au substrate is greater than the skinning depth of

light, so T=0, and when the reflection of MA at

wavelengths λ and λ is suppresd, the absorption

12

efficiency of MA at the two wavelengths can be

clo to 1. The effective impedance Z of MA can be

expresd by Equation (2), where S and S are the

1121

scattering matrix coefficients of reflection and trans-

mission under vertical irradiation of TE polarized

light, respectively, and R=(S), T=(S), and since

1121

22

T=0, S=0. Figure 3 shows the effective impedance

21

of MA calculated by Equation (2).

From Figure 3(a), it can be en that the real

part of impedance Z is clo to 1 at wavelengths

real

λ and λ, while from Figure 3(b) it can be found that

12

the imaginary part of impedance Z is clo to 0 at

imag

wavelengths λ and λ.

12

√

Z=

√

(1+S)

11

2

−S

2

21

(1−S)

11

2

−S

=.

1+S

11

2

1−S

11

（2）

21

第 6 期

FANG Xiao-min, et al. : Dual-Wavelength Narrow-Bandwidth Dielectric ......

1331

1.0

(a)

0.8

0.6

l

a

e

r

Z

0.4

0.2

0

1.151.201.251.30

Wavelength/µm

10

(b)

8

6

g

a

m

i

Z

4

2

1.151.201.251.30

0

Wavelength/µm

Fig. 3 Effective impedance of dielectric MA. (a) Real part

of impedance; (b) imaginary part of impedance

图 3 介质MA的有效阻抗。（a）阻抗实部；（b）阻抗虚部

In order to explore the intrinsic physical mech-

anisms of MA achieving dual-wavelength narrow-

bandwidth absorption, the electric field distribution

of MA at wavelengths λ and λ respectively, is cal-

12

culated in this paper, as shown in Figure 4 (Color

online). From Figure 4(a), it can be en that the

narrow-bandwidth dielectric MA has high narrow-

bandwidth absorption at wavelength λ becau

1

most of the light is confined in the SiO dielectric

2

layer, and a small portion of the light is confined in

the asymmetric grating. It can be en that the incid-

ent light forms a Fabry-Pérot (FP) cavity resonance

in the SiO dielectric layer. Figure 4(b) shows the

2

electric field distribution of the narrow bandwidth

dielectric MA at wavelength λ. Unlike the electric

2

field distribution at wavelength λ, the light is no

1

longer confined in the SiO dielectric layer, but in

2

the grating. Bad on the electric field distribution,

it can be judged that this is due to the formation of a

guided mode resonance in the grating by the incid-

ent light, which also leads to a narrower band-

[24]

width of the MA at wavelength λ.

2

(a)

24

3.3

21

18

2.4

15

m

μ

12

/

z

1.5

9

0.6

6

3

0

−1.5−0.70.10.9

x/μm

(b)

60

3.3

50

Si

2.4

40

m

30

μ

/

z

1.5

20

0.6

SiO

2

10

0

−1.5−0.70.10.9

x/μm

Au

Fig. 4 Electric field distribution of dual-wavelength nar-

row-bandwidth dielectric MA at different

wavelengths. (a) λ; (b) λ

12

图 4 双波长窄带宽介质MA在不同波长处的电场分布。

（a）λ；（b）λ

12

3.2 Effect of structural parameters on absorp-

tion characteristics of MA

In order to investigate the effect of MA struc-

ture parameters on the absorption characteristics of

dual-wavelength narrow-bandwidth dielectric, the

effect of MA structure parameters on its absorption

characteristics is simulated and calculated in this pa-

per. Figure 5 (Color online) shows the effect of dif-

ferent SiO dielectric layer thickness t on MA ab-

2

sorption characteristics. From Figure 5(a), it can be

en that the absorption wavelength λ of MA is red-

1

shifted as t increas, however, the change in t has a

very weak effect on the absorption wavelength λ.

2

From Figure 5(b), it can be en when t increas

1332

中国光学

第 14 卷

from 1.2 μm to 1.215 μm, the absorption wave-weaker effect on the absorption wavelength λ of

length λ is red-shifted from 1.2085 μm to

1

1.2115 μm, an increa of 3 nm. The change in t has

a significant effect on the MA absorption

wavelength λ, which is due to the FP cavity reson-

1

ance formed by the light in the SiO dielectric layer

2

as en in Figure 4(a). The relationship between FP

cavity resonance wavelength and SiO layer thick-

2

ness t is shown in Equation (3),

[25]

2

nt+Φλ

eqFPFP

=Nλ,

（3）

where n is the equivalent refractive index of FP

eq

cavity, Φ is the sum of the phas of the upper and

lower interfaces of the FP cavity, and N is an in-

teger, λ is the resonant wavelength of the FP cav-

FP

ity. According to Equation (3), it is known that an

increa in t increas the FP cavity resonance

wavelength λ which leads to a red shift in the ab-

FP

sorption wavelength λ of MA.

1

1.0

(a)

λ

12

1.0

λ

n

0.8

o

0.8

i

t

p

r

0.6

o

)

s

.

b

0.4

u

A

.

a

0.2

(

0.6

n

o

1.2371.2381.2391.240

0

i

t

p

r

o

0.4

s

b

t=1.200 µm

A

t=1.205 µm

0.2

t=1.215 µm

0

1.201.211.221.231.241.25

Wavelength/µm

1.211 5

(b)

1.211 0

P=1.05 µm

h=0.78 µm

1.210 5

W

1

=0.2 µm

m

µ

W

2

=0.3 µm

/

1.210 0

1

λ

g=0.2 µm

1.209 5

1.209 0

1.208 5

1.2001.2041.2081.2121.216

t/µm

Fig. 5 Effect of t on the absorption characteristics of the

dual-wavelength narrow-bandwidth dielectric MA.

(a) Absorption spectra; (b) absorption wavelength

图 5 t对双波长窄带宽介质MA吸收特性的影响。（a）吸

收光谱；（b）吸收波长

However, the reason why the increa in t has a

2

MA is that the narrow-bandwidth and high-absorp-

tion of MA at wavelength λ are caud by guided

2

mode resonance, which can be en from Figure

4(b). According to Ref. [26], the guided mode res-

onance wavelength is mainly related to the grating

parameters and the incident angle. However, the ab-

sorption efficiency of MA at the absorption wave-

length λ will gradually decrea as t increas,

2

which can be explained by Figure 6 (Color online).

Figure 6 is the electric field distribution of MA at

wavelength λ when t=1.205 μm. Comparing Figure

2

6 with Figure 4(b), it can be found that the electric

field focud in the grating in Figure 6 is signific-

antly lower than Figure 4(b). Therefore, the absorp-

tion rate of MA will decrea after t becomes larger.

3.3

42

36

2.4

30

m

24

μ

/

z

1.5

18

12

0.6

6

0

−1.5−0.70.10.9

x/μm

Fig. 6 Electric field distribution of MA at wavelength λ

2

when t = 1.205 μm

图 6 t=1.205 μm时MA在波长λ处的电场分布

2

Figure 7 (Color online) shows the effect of

grating width W on the absorption characteristics of

1

dual-wavelength narrow-bandwidth dielectric MA.

It can be en from Figure 7(a) that the absorption

wavelengths λ and λ of MA both have red shifted

12

as W becomes larger, respectively. It can be en

1

from Figure 7(b) that when W increas from

1

0.2 μm to 0.202 μm, the absorption wavelength λ of

2

MA is red-shifted by nearly 7 nm, while the absorp-

tion wavelength λ of MA is red-shifted by 1.46 nm.

1

第 6 期

FANG Xiao-min, et al. : Dual-Wavelength Narrow-Bandwidth Dielectric ......

1333

1.0

(a)

0.8

=0.200 µm

W

1

=0.201 µm

W

1

)

.

u

W

.

1

=0.202 µm

a

(

0.6

n

o

i

t

p

r

o

0.4

s

b

A

0.2

0

1.201.211.221.231.241.25

Wavelength/µm

(b)

1.246

1.210 0

P=1.05 µm

h=0.78 µm

1.244

1.209 5

t=1.2 µm

m

W

1.242

m

µ

2

=0.3 µm

µ

/

/

1

2

λ

g=0.2 µm

λ

1.209 0

1.240

1.208 5

1.238

0.200

0.2010.202

W/µm

1

Fig. 7 Effect of W on the absorption characteristics of the

1

dual-wavelength narrow-bandwidth dielectric MA.

(a) Absorption spectra; (b) absorption wavelength

图 7 W对双波长窄带宽介质MA吸收特性的影响。（a）

1

吸收光谱；（b）吸收波长

The change of W can have an impact on the

1

absorption wavelength λ becau it can be known

1

that the change of the grating width will lead to a

change in the equivalent refractive index of the

asymmetric grating, and the equivalent refractive in-

dex of the FP cavity n is effectd by the equivalent

eq

refractive index of the asymmetric grating n.

w

Moreover, it has been shown in Ref. [27] that the in-

crea of the grating width will lead to the increa

of the equivalent refractive index of the FP cavity

n. From Equation (3), it is known that an increa

eq

in n will increa the FP cavity resonance

eq

wavelength λ. And the increa of λ will lead to

FPFP

the red-shift of the absorption wavelength λ of MA.

1

Figure 8 shows n varying with W and it is calcu-

eq1

lated by FDTD. From Figure 8, it can be found that

when W increas from 0.2 μm to 0.202 μm, n in-

1eq

creas from 1.510 to 1.512.

1.512 5

1.512 0

q

e

n

1.511 5

1.511 0

1.510 5

0.200 00.200 50.201 00.201 50.202 0

W

1

/μm

Fig. 8 Effect of W on n

1eq

图 8 W对n的影响

1eq

The grating, SiO layer, and air form an optical

2

waveguide, and according to the grating guided-

mode resonance theory, it is known that the grating

equivalent refractive index change will affect the

guided-mode resonance wavelength, as shown in

[26]

Equation (4).

n

w

=nsinθ+m.

λ

g

P

（4）

where λ is the guided-mode resonance wavelength

g

and m is the diffraction order of the grating. Accord-

ing to the equivalent medium theory, an increa in

W will increa the grating equivalent refractive in-

1

dex n, and from Eq. (4), an increa in n will red-

ww

shift the guided-mode resonance wavelength λ and

g

thus the MA absorption wavelength λ will red-shift.

2

The effect of W on MA absorption characteristics is

2

not shown in this paper, becau the effect of the

change in W on MA absorption characteristics is

2

similar to that of W on MA, and the intrinsic phys-

1

ical mechanism of the effect is esntially the same.

The electric field distribution in Figure 4(b)

shows that a part of the electric field is distributed

among the slits of the dielectric grating, so it can be

en that the change of the surrounding gas will

have an effect on the absorption wavelength λ of

2

MA. Therefore, the narrow bandwidth dielectric

MA propod in this paper can be applied in the

fields of gas or biological detection. In order to eval-

uate the performance of the narrow-bandwidth

dielectric MA in gas detection, two parameters,

1334

中国光学

第 14 卷

nsitivity and quality factor, are defined, and thescription, the grating refractive index will lead to a

specific expressions are shown in equations (5) and

(6). Where S is the nsitivity of narrow-bandwidth

MA, n and λ are the amount of change in re-

△△

fractive index and the amount of change in absorp-

tion wavelength of the surrounding gas, respect-

ively.

[18]

S=

∆λ

∆n

,

（5）

FOM=

S

FWHM

.

（6）

From Figure 9 (a) (Color online), it can be en

that the absorption wavelengths λ and λ of MA are

12

redshifted as n increas. This is becau a larger n

leads to a larger refractive index n of the grating's

l

low refractive index material, which in turn leads to

a larger equivalent refractive index of the grating for

different wavelengths. And from the previous de-

1.0

(a)

n=1.00

0.8

n=1.01

n=1.02

)

.

u

n=1.03

.

a

(

0.6

n

o

i

t

p

r

o

0.4

s

b

A

0.2

0

1.201.221.24

Wavelength/µm

1.242 0

(b)

1.241 5

P=1.05 µm

h=0.78 µm

1.241 0

W

1

=0.2 µm

1.240 5

W

2

=0.3 µm

m

µ

/

1.240 0

g=0.2 µm

2

λ

1.239 5

1.239 0

1.238 5

1.238 0

1.0001.0051.0101.0151.0201.0251.030

n

Fig. 9 Effect of n on the absorption characteristics of the

dual-wavelength narrow-bandwidth dielectric MA.

(a) Absorption spectra; (b) absorption wavelength

图 9 n对双波长窄带宽介质MA吸收特性的影响。（a）

吸收光谱；（b）吸收波长

larger equivalent refractive index n of FP cavity,

eq

so according to Equation (3), the increa of n will

lead to a red shift of MA absorption wavelength λ.

1

Unlike the mechanism that caus the red shift of

MA absorption wavelength λ, λ is red-shifted as n

12

becomes larger, becau the grating equivalent re-

fractive index n increas, which means that it in-

w

creas the refractive index of the central layer of

the optical waveguide, and this must lead to the red

shift of the grating guided mode resonance wave-

length according to the guided mode resonance the-

ory and Equation (4).

[27]

From Figure 9(b), when n increas from 1 to

1.03, the absorption wavelength λ increas from

2

1.2382 μm to 1.2417 μm, which is red-shifted by

3.5 nm, and according to Eqs. (5) and (6), S=

117.3 nm/RIU and FOM = 1524/RIU. It can be

found that the FOM in this paper is significantly im-

proved compared to the references [14-15, 18].

Finally, the effect of the asymmetric grating

period P on the absorption characteristics of the

dielectric MA was analyzed, and the specific results

are shown in Figure 10 (Color online). From

Figure 10, it can be found that the absorption

wavelengths λ and λ of MA are red-shifted with

12

the increa of P. When P increas from 1.05 μm

to 1.1 μm, the wavelength λ increas from

1

1.2085 μm to 1.2249 μm, while the wavelength λ

2

increas from 1.2382 μm to 1.2525 μm. From

Equation (4) we can know the reason why the

wavelength λ increas with the increa of P.

2

[24]

When the period increas, if the guided mode res-

onance is to be maintained, the resonance

wavelength must be shifted to the long wavelength

direction.

As P increas, the pha Φ of the FP cavity

decreas significantly becau the effect of the

change of P on n is not as significant as the pha

eq

Φ. Therefore, according to Equation (3), it is known

that the FP cavity resonance wavelength λ in-

FP

第 6 期

FANG Xiao-min, et al. : Dual-Wavelength Narrow-Bandwidth Dielectric ......

1335

creas with the increa of P, which leads to the

red-shift of the absorption wavelength λ of MA.

1

The trend of the effect of P on the pha Φ is calcu-

lated by FDTD and is shown in Figure 11, from

which it can be en that Φ decreas from 4.64 rad

to 0.22 rad when P increas from 1.05 μm to

1.1 μm.

1.0

P=1.050 µm

P=1.075 µm

0.8

P=1.100 µm

)

.

u

.

a

t=1.2 µm

(

0.6

n

h=0.78 µm

o

i

t

W

p

1

=0.2 µm

r

o

0.4

W

2

=0.3 µm

s

b

A

g=0.2 µm

0.2

0

1.201.211.221.231.241.251.26

1.27

1.28

Wavelength/µm

Fig. 10 Effect of P on the absorption characteristics of the

dual-wavelength narrow-bandwidth dielectric MA

图 10 P对双波长窄带宽介质MA吸收特性的影响

5

4

3

d

a

r

/

Φ

2

1

0

1.051.061.071.081.091.10

P/μm

Fig. 11 Effect of P on Φ

图 11 P对Φ的影响

——中文对照版——

1 引 言

在许多应用中都有需要对电磁波实现完美吸

收，如太阳能电池、热发射器、辐射冷却、通信

等。但是由自然界存在的材料构成的吸收器

[1-4]

因缺乏磁响应导致阻抗失配，因此它们不能完全

抑制光反射，从而降低了吸收器光吸收能力。

[5]

因此，人们提出了基于超材料的吸收器，由于超材于宽带宽MA效率更高，而且在光调制、光探

4 Conclusion

In order to broaden the application field of nar-

row-bandwidth MA, a medium MA is designed in

this paper that can achieve dual-wavelength narrow-

bandwidth absorption in the infrared band bad on

the finite-difference time-domain method. Through

simulation analysis, the narrow bandwidth dielec-

tric MA in this paper has ultra-high absorption effi-

ciency at wavelength λ = 1.2085 μm and λ = 1.238

12

2 μm, and the FWHM is only 0.735 nm and

0.077 nm, respectively. Becau of the different

mechanisms of MA forming narrow-bandwidth and

high absorption on λ and λ, the study found that λ

121

is very nsitive to the change of the thickness t of

the SiO transition layer, while λ is very nsitive to

22

the change of the dielectric grating width W. With

1

the increa of t and W, the absorption wavelengths

1

λ and λ of MA will red-shift respectively. When

12

the grating period P increas, the absorption wave-

lengths λ and λ of MA will shift to the long

12

wavelength direction at the same time. From the

electric field distribution of MA at λ, a large part of

2

its electric field is distributed in the gap between the

gratings, so the change of air refractive index has a

significant effect on λ. This allows it to be ud in

2

the field of detection. It is calculated that the FOM

of the narrow-bandwidth dielectric MA in this pa-

per can reach 1524/RIU.

料吸收器（Metamaterial Absorber，MA）对电磁波

具有高吸收效率，且具有体积小、可设定工作波

长等优点，逐渐被人们所关注并成为研究热点之

一。

[6]

经深入研究，人们设计并制备出了不同类型

的MA，如宽带宽MA、窄带宽MA、太赫兹MA、

可调谐MA等。窄带宽MA被人们所关注是

[7-9]

因为窄带宽MA用在探测和热发射器上时相比

[10-11]

1336

中国光学

第 14 卷

测和热辐射剪裁中只有窄带宽MA才能满足要式进行数值求解，以差商代替方程中的微分。在

求。目前已经有不同结构的窄带宽MA被提

[12-13]

出，如基于裂环谐振器阵列（Split Ring Resonator，

SRR）、金属/介质周期光栅、金属/介质狭缝（nar-

row slits）等。2014年瑞典皇家理工学院的Min-

Qiu等人提出在银（Ag）金属衬底上刻蚀金属光

栅，基于Ag光栅与空气介质形成的表面等离子

激元共振成功使MA在波长1400 nm处实现了

窄带宽吸收，其线宽（Full Width Half Maximum，

FWHM）可以达到0.4 nm

[14]

；2018年香港中文大

学的FENG A等人提出一种由非对称金属光栅和

金属衬底构成的窄带宽MA，而且在光栅和衬底

之间添加了一层二氧化硅过渡层，经模拟计算发

现该窄带宽MA在光通信波段实现了超窄吸收，

FWHM仅有0.28 nm

[15]

；2019年，东南大学

KANG S等人提出在二氧化硅衬底上刻蚀出由金

（Au）材料构成的十字型纳米阵列，与此同时在二

氧化硅另一面生长一层Au薄层抑制透射，经测

试发现该MA可在太赫兹波段实现窄带宽吸收。

[16]

从以上研究可以发现，这些窄带宽MA中的

微纳结构所使用的材料都是金属材料，但是金属

材料存在欧姆损耗，而且在高频处精细金属材料

存在加工问题，这会在一定程度上影响MA在将

来的应用推广。因此，一些课题组提出利用介质

材料设计、制造窄带宽MA。2019年哈尔滨工业

大学的Zhibin Ren等人利用氮化硅、氧化铟锡材

料设计并制备出在红外波段具有窄带宽吸收的

MA，经测试可得该窄带宽MA的FWHM可达

2.6 nm

[17]

；2020年，安徽大学的Yan Zhao等人提

出在金属衬底上直接刻蚀出由硅材料构成的介质

光栅，经模拟计算可知该窄带宽MA的FWHM

可达0.38 nm。

[18]

虽然利用介质材料设计制备窄带宽MA可

以降低制造成本，提高吸收效率，而且吸收带宽可

保持在亚纳米级别，但目前鲜有实现多波长窄带

宽亚纳米级别吸收的MA，这会限制窄带宽MA

在一些场合的应用，如在光谱探测、气体探测中，

多波长窄带宽MA更能提高它们的工作效率。

[19-20]

针对上述需求，本文提出由非对称介质光栅、介

质过渡层、金属衬底构成的双波长窄带宽介质

MA，并利用时域有限差分法(Finite Difference

Time Domain, FDTD)对该MA进行设计和分

析。FDTD在时域中对麦克斯韦方程组的微分形质MA单个周期的二维物理模型，然后在x方向

求解时电场与磁场交替分布，随着时间的推移求

解出仿真区域的电场和磁场。经模拟计算发现双

波长窄带宽MA的FWHM最低可达0.077 nm，

品质因素（Figure Of Merit，FOM）可达1524/RIU，

而且经对比可以发现本文设计的窄带宽MA最

窄的吸收带宽相比文献[14-18]都下降了一个数

量级。本文研究可为生物传感器、热发射器、光

调制器等提供高质量的双波长窄带宽介质MA。

2 器件结构

图1是双波长窄带宽介质MA结构图，它自

下而上由Au衬底、二氧化硅（SiO）介质层、硅

2

（Si）材料形成的非对称光栅组成。Au衬底的主

要作用是抑制光的透射，因此它的厚度必须大于

入射电磁波的趋肤深度，本实验中Au的厚度设

为0.2 μm。从图1中可以看到，一个周期内具有

两个同高度（h）、不同宽度的光栅，它们的宽度分

别是W和W，同周期内光栅之间的间距为g，另

12

外SiO的厚度为t。在将来实际器件制备中，本

2

文的双波长窄带宽介质MA的制备工艺与现今

的微纳加工工艺兼容，通过磁控溅射在Au衬底

上先后生长SiO和Si薄层，紧接着在Si薄层上

2

旋涂电子束抗蚀胶，经电子束曝光和显影后在抗

蚀胶上形成非对称光栅图形，去胶并利用感应耦

合等离子体刻蚀技术，将图形转移到Si薄层上，

最终制备出双波长窄带宽介质MA。

[21]

Au的介质常数由Drude模型表示，即

ε=1−.

p

Au

ω

2

ω+iγω

2

（1）

式中ω、γ和ω分别是等离子体频率、阻尼系数

p

和入射光角频率。为了保证模拟计算结果正确，

ω

p

和γ均是从实验数据中获得，根据文献[22]可

知，ω和

p2

=1.32×10 rad/s，γ=1.2×10 rad/s。SiO

1614

Si的折射率分别为=1.45和=3.45。

nn

SiOSi

2

3 结果与讨论

3.1 双波长窄带宽高吸收的实现

首先利用FDTD软件建立双波长窄带宽介

第 6 期

FANG Xiao-min, et al. : Dual-Wavelength Narrow-Bandwidth Dielectric ......

1337

添加周期性边界条件，在z方向添加完美匹配层的电场分布，与在波长λ的电场分布不同，此

边界条件，y方向默认为光栅无限长。最后在双

波长窄带宽介质MA正上方添加光源，光源偏振

设为TE偏振，入射角设为0°，并且MA周围为空

气，折射率n=1。

图2所示的是双波长窄带宽介质MA的吸

收光谱，此时P=1.05 μm、t=1.2 μm、h=0.78 μm、

W=0.2 μm、W=0.3 μm、g=0.2 μm，上述光栅参数

12

是基于FDTD优化后获得的。从图2中可以看

到MA分别在波长λ

12

=1.2085 μm和λ=1.2382 μm

处具有超高吸收效率，吸收线宽FWHM分别为

0.735 nm和0.077 nm。相比于文献[14-15, 17]结

果，双波长窄带宽介质MA在波长λ处的线宽明

2

显下降，实现了窄带宽吸收。若无特殊说明，上述

所有参数保持不变。

MA能在波长λ=1.2085 μm和λ=1.2382 μm

12

实现超窄带宽高吸收，是因为MA在这两个波长

处的有效阻抗刚好与自由空间阻抗相匹配，这可

有效地抑制MA对波长λ和λ的反射。因为

12

[23]

MA的吸收效率A可表示为A=1-T-R，由于Au衬

底的厚度大于光的趋肤深度，所以T=0，而当

MA在波长λ

12

和λ的反射得到抑制后，MA对这

两个波长的吸收效率就接近1。MA的有效阻抗

Z可由式（2）表示：

√

Z=

√

(1+S)

11

2

−S

2

21

=.

1+S

11

）（2

(1−S)

11

2

−S

2

1−S

11

21

式中S和S分别是TE偏振光垂直照射下反射

1121

和透射的散射矩阵系数，其中R=(S，由

1121

),T=(S)

22

于T=0，所以S

21

=0。图3是由式（2）计算得到的

MA的有效阻抗，从图3（a）中可知阻抗的实部

Z

real12

在波长λ和λ处接近为1，而从图3（b）中可

以发现阻抗的虚部Z在波长λ和λ接近为0。

imag12

为了探索MA实现双波长窄带宽吸收的内

在物理机制，本文计算了MA分别在波长λ和

1

λ

2

处的电场分布，具体如图4（彩图见期刊电子

版）所示。从图4（a）中可知，窄带宽介质MA之

所以在波长λ出现窄带宽高吸收是因为大部分

1

光被限制在SiO介质层当中，少部分光限制在非

2

对称光栅当中。由此可知，入射光在SiO介质层

2

当中形成了法布里-珀罗(Fabry-Pérot, FP)腔共

振。图4（b）所示的是窄带宽介质MA在波长为根据等效介质原理可知光栅宽度的变化会导致

λ

21

时光不再被限制在SiO介质层当中，反而是被限

2

制在光栅当中，依据电场分布可以判断这是由于

入射光在光栅中形成了导模共振，也因为导模

[24]

共振导致MA在波长λ处的带宽更窄。

2

3.2 结构参数对MA吸收特性的影响

为了探究双波长窄带宽介质MA结构参数

对其吸收特性的影响规律，本文模拟计算了

MA结构参数对其吸收特性的影响。图5（彩图见

期刊电子版）是不同SiO介质层厚度t对MA吸

2

收特性的影响。从图5（a）中可知，随着t的增加，

MA的吸收波长λ

1

会出现红移现象，但是t的变

化对吸收波长λ的影响非常微弱。由图5（b）可

2

得，当t从1.2 μm增加到1.215 μm，吸收波长λ

1

从1.2085 μm红移到1.2115 μm，增加了3 nm。

t的变化能够对MA吸收波长λ

1

有显著影响，是

因为由图4（a）可知光在SiO介质层中形成了

2

FP腔共振。FP腔共振波长与SiO

2

层厚度t的关

系为：

[25]

2

nt+Φλ

eqFPFP

=Nλ,

（3）

式中，n是FP腔的等效折射率，Φ是FP腔上下

eq

界面相位之和，N是整数，λ是FP腔共振波长。

FP

根据式（3）可知t增大会导致FP腔共振波长λ

FP

增大，从而导致MA的吸收波长λ出现红移现象。

1

由图4（b）可知，MA在波长λ处实现窄带宽

2

高吸收是因为导模共振效应，而根据文献[26]可

知，导模共振波长主要与光栅参数、入射角等有

关。但是可以发现随着t的增大，MA在吸收波

长λ的吸收效率会逐渐下降，这可由图6（彩图见

2

期刊电子版）解释。图6是t=1.205 μm时MA在

波长λ处电场分布，将图6与图4（b）相比，可以

2

发现在图6中聚集在光栅中的电场明显低于

图4（b），故此导致MA在t变大后的吸收率会下降。

图7（彩图见期刊电子版）所示的是光栅宽度

W

1

对双波长窄带宽介质MA吸收特性的影响。

由图7（a）可知，随着W的变宽，MA的吸收波长

1

λ

12

和λ都分别出现了红移现象。从图7（b）可知，

当W从0.2 μm增加到0.202 μm，MA的吸收波

1

长λ红移了将近7 nm，而MA的吸收波长λ红

21

移了1.46 nm。

W

11

的变化能够对吸收波长λ产生影响是因

1338

中国光学

第 14 卷

非对称光栅的等效折射率发生变化，而FP腔的红移。与导致MA吸收波长λ红移的机理不

等效折射率n又受非对称光栅等效折射率n的

eqw

影响。而且文献[27]也已经证明，光栅宽度增加是因为其增大了光栅等效折射率n，这意味着增

会导致FP腔等效折射率n增大，由式（3）可知，大了光波导中心层的折射率，而根据导模共振理

eq

n

eqFPFP

增大，FP腔共振波长λ也将会增大。λ增论和式（4）可知，这必定会导致光栅导模共振波

大就会导致MA的吸收波长λ红移。图8是当

1

W

1eq

取不同值时n的变化情况，它是由FDTD计

算获得。从图8中可以发现，当W从0.2 μm增

1

加到0.202 μm，n则从1.510增加到1.512.

eq

光栅、SiO层、空气形成了光波导，根据光栅

2

导模共振理论可知，光栅等效折射率的改变将会

影响导模共振波长，即

[26]

n

nsinθ+m=.

λ

g

w

P

（4）

式中λ是导模共振波长，m为光栅的衍射阶数。

g

由等效介质理论可知，W增大将会使光栅等效折

1

射率n增大，而根据式（4）可知，n增大则使导

ww

模共振波长λ红移，从而使MA吸收波长λ红

g2

移。在本文中之所以没有展示W对MA吸收特

2

性的影响，是因为W的变化对MA吸收特性的

2

影响与W对MA的影响相似，而且内在物理机

1

理也基本相同。

通过图4（b）的电场分布可知，有一部分电场

分布在介质光栅缝隙中，由此可知，周围气体的变

化将会对MA的吸收波长λ产生影响，因此本文

2

提出的窄带宽介质MA可应用在气体或生物探

测等领域当中。为了评估窄带宽介质MA在气

体探测中的工作性能，定义了灵敏度和品质因素

两个参数，即

S=

∆λ

∆n

,

（5）

FOM=

S

FWHM

,

（6）

式中S是窄带宽MA的灵敏度，△n和△λ分别是