Broadband Absorption in the Cavity Resonators with Changed Order

Agata Roszkiewicz

Institute of Fundamental Technological Research, Polish Academy of Sciences,

Adolfa Pawińskiego 5b, 02-106 Warsaw, Poland

Keywords: Broadband Absorption, Enhanced Absorption, Localized Surface Plasmons, Cavity Resonances, Diffraction

Gratings.

Abstract: This paper presents an analysis of phenomena leading to high and broadband absorption at a structure

combined of three elements: one-dimensional dielectric diffraction grating placed between silver grating

and a thick silver substrate. Each element of the dielectric grating consists of media of different dielectric

constants but of the same geometrical dimensions. A broad spectrum of high absorption in such a structure

is achieved as a result of two issues. First, due to the different excitation conditions the cavity resonances

are excited at different wavelengths. Second, the changed order of the resonators leads to further broadening

of the absorption band.

1 INTRODUCTION

High and broadband absorption of electromagnetic

waves is of interest in many nanophotonic

applications. Various kinds of configurations were

proposed to obtain near zero reflection and trapping

of light in the structure. Control of the reflection and

transmission is an important issue especially in

photodetectors and solar cells (Ferry et. al., 2010).

The total absorption of radiation by a metallic

structure has attracted significant interests over the

past few years (Liu et. al., 2010, Shchegolkov et. al.,

2010, Liu et. al., 2011). Many metallodielectric

structures designed as nearly perfect absorbers have

been proposed and some promising applications

have been discussed.

The near perfect absorption may be achieved

with use of localized plasmon resonances (Hu et. al.,

2009, Kravets et. al., 2010, Liu et. al., 2011, Pan et.

al., 2013), gap plasmons in bottle-like cavities

(Meng et. al., 2013), propagating surface plasmon

polaritons (Chen et. al., 2010) or Fabry-Perot

resonances in cavities between two metal surfaces

(Diem et. al., 2009, Hao et. al., 2010, Roszkiewicz

et. al., 2012, Song et. al., 2013). The designs based

on a Fabry-Perot resonance usually are composed of

periodic gratings. In order to obtain a wide

absorption band, each period of the structure can be

made of resonators of varied dimensions, supporting

resonances at different wavelengths (Song et. al.,

2013, Koechlin et. al., 2011, Zhang et. al., 2013,

Wang et. al., 2013). The continuation of such a

structure is a quasiperiodic structure (Dolev et. al.,

2011) and chirped grating with slowly varying

period (Chen et. al., 2010, Bouillard et. al., 2012,

Gan et. al., 2011). In those periodic configurations

the wide absorption band is a result of the existence

of similar resonances occurring at neighbouring

frequencies. However, in those examples all cavities

are filled with the same material and the resonators

are ordered according to their resonance

wavelengths.

In this paper we analyse a one-dimensional (1D)

absorptive structure. The presented configuration is

based on a 1D dielectric diffraction grating placed

between silver grating and a thick silver substrate.

The structure realizes simultaneous suppression of

reflection and transmission, leading to enhanced

absorption. Each element of the dielectric grating

consists of dielectric medium of different dielectric

constant but of the same geometrical dimensions. A

broad spectrum of high absorption in such a

structure is achieved as a result of the horizontal

cavity modes (HCMs) excited at different

wavelengths. Moreover, the changed order of the

resonators leads to further broadening of the

absorption band. It occurs that the sequence of the

resonators influences on the absorption

characteristics at normal as well as oblique

incidence.

Roszkiewicz A..

Broadband Absorption in the Cavity Resonators with Changed Order.

DOI: 10.5220/0005332900810086

In Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS-2015), pages 81-86

ISBN: 978-989-758-093-2

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

2 SIMULATION MODEL AND

METHOD

The analysed configuration is depicted in figure 1. A

TM polarized plane wave is incident normally from

air at a 1D stacked silver and dielectric gratings with

subwavelength slits placed at the silver substrate.

Each period of the structure consists of N = 5

identical metal stripes lying on the dielectric

resonators with different dielectric constants. The

relative change between dielectric constants of the

resonators is denoted by

Δε

. Hence the dielectric

constant of the n

stripe (n = 1, 2, ..., N) is

Δε

, where

= 1 is the dielectric constant of air and

Δε

= 0.8. We show, that the optimized structure

does not consist of resonators placed in order

according to the increasing resonance wavelength.

The structure characterized by the widest absorption

band is the structure, where the sequence of the

resonators is:

Numerical analysis of the optical response of the

structure was performed with use of Rigorous

Coupled Wave Analysis with implementation of the

scattering matrix algorithm, multilayer extension

and the factorization rules. The dielectric function of

silver was numerically fitted to the experimental

data (Johnson et. al., 1972).

3 SIMULATION RESULTS

It is known that by introducing different resonators

in one structure one can obtain a wide absorption

spectrum due to the excitation of resonances at

different wavelengths. In this paper we utilize the

concept of the 1D grating absorber presented in

figure 1. The main cause of high absorption in this

kind of structure is the excitation of the open metal-

dielectric-metal (MIM) horizontal cavity modes in

those dielectric resonators. The formation of the

cavity mode results in low reflection and strong

absorption, making most of electromagnetic field

focus inside the cavity. However, usually the

resonators are placed in an order accordingly to their

resonance wavelengths (Chen et. al., 2010, Song et.

al., 2013, Bouillard et. al., 2012). Here we change

this order.

Figure 2 gives the calculated absorption as a

function of the incident wavelength for

configurations with

Δε

= 0.8 and various orders of

dielectric resonators, among others the optimized

structure (green dashed line) and the ordered

configuration (red dashed-dotted line). The plot

Figure 1: (a) Configuration of the analysed problem. One

period of the structure

= 380 nm is presented. Silver 1D

grating of thickness h

= 25 nm is placed on the dielectric

grating of thickness h

= 21 nm. Dimensions of the

equally spaced ridges of identical dimensions: a = 30.4

nm, b = 45.6 nm and the filling factor f = 0.4. (b)

Imaginary part of the dielectric function of silver as a

function of wavelength. Blue line – experimental data

from (Johnson et. al., 1972), red dots – numerical fit.

Vertical dashed line denotes

= 330 nm.

shows also the absorption curve for different

configurations with constant

for comparison (dark

grey lines). The absorption spectrum differs for

structures with differently arranged resonators, even

under normal incidence. Other sequences of the

same resonators than the optimized one significantly

reduce the absorption bandwidth. It can be seen that

the non-optimized configurations are characterized

by narrower absorption band than the optimal

structure, despite the fact, that all of them consist of

the same resonators, however placed in different

order. Thus it appears, that the sequence of the

dielectric resonators in each grating period is also an

important parameter to be optimized. Moreover, the

maximal amplitudes of the resonances in structures

with constant

are at the level of ~60%, hence they

do not assure the high absorption. This behaviour

will be discussed later.

Each cavity resonator can be regarded as two

single metal-insulator interfaces brought close to

each other. In this situation, the dispersion curve of a

single interface splits into high and low-energy

modes. Here, due to the field symmetry matching,

only the low-energy mode is excited. Dispersion

curve for the symmetric mode in each cavity

depends on its dielectric constant

and thickness h

and can be described by the relation:

(a)

(b)

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

()

() ()

()

zdz

kkhk

εε

−=2tanh

(1)

where k

, k

(m)

and

(m)

are the z-components of

the wave vector and the dielectric constants in the

dielectric and metal media, respectively (Maier,

2007). A dispersion curve can be drawn for each

resonator with the consideration of its thickness and

dielectric constant

. Points at this dispersion curve

for a given cavity length a

≈

/2, where ν

= 1

denotes the resonance order in the horizontal cavity,

allow to obtain the plasmon resonance wavelength

for the wave vector k = 2

/a. Hence, the

energy in the resonator can be spatially restricted by

metal interfaces (in the vertical direction) and by

large wave vectors of the supported plasmon modes

(in the horizontal direction).

Figure 2: Absorption spectrum as a function of wavelength

for exemplary structures with differently ordered

resonators under normal incidence. Legend shows

configurations of the resonators in each period, green

dashed line and red dashed-dotted line show the

absorption of the optimized structure and the structure

with ordered resonators, respectively. Dark grey lines

show the absorption of the structures with all identical

resonators within the period. Horizontal dashed line

denotes absorption level of 80%. Vertical dashed line

denotes

= 330 nm.

The excitation conditions for cavity modes are

different in each resonator since, having the same

dimensions, the resonators are filled with media of

different dielectric constants. This results in

frequency splitting of the resonance curves

originating from the particular HCMs and thus

widening of the total absorption band. In the

presented configuration those electric dipole

resonances correspond to peaks between 380 – 500

nm wavelength.

High absorption at wavelengths shorter than 330

nm does not originate from any of the plasmonic

resonances. The limit value of the wavelength where

silver is characterized by low inner loss is about 330

nm. For shorter wavelengths the imaginary part of

the dielectric function of silver increases rapidly

(figure 1(b)). Hence, high absorption at wavelengths

lower than 330 nm visible in presented figures arises

from phenomena related to conduction and bound

electrons and it is caused by the interband transitions

of electrons in metal. For this reason the width of the

absorption band is calculated for wavelengths longer

than 330 nm. Resonances between ~330-380 nm are

connected with the excitation of localized surface

plasmons (LSPs), mainly at the metal ridges.

Figure 3: Absorption spectrum as a function of wavelength

and incident wave vector for (a) the optimized structure

and (b) structure with

The width of the band of more than 80%

absorption efficiency at normal incidence for the

optimized structure increased of ~121 nm in

comparison to the absorption band of the structure

with

, where n = 1, 2,...,5. Hence, the

absorption band width at normal incidence is

estimated to be ~141 nm, which can be compared

with ~23 nm bandwidth of the

structure. This

gives about 6.1-fold increase of the stop band width

in the optimized structure. Moreover, the bandwidth

of the ordered structure is ~116 nm, which gives

almost 1.2-fold increase of the absorption bandwidth

resulted from the changed order of the resonators.

In order to further analyse the properties of the

BroadbandAbsorptionintheCavityResonatorswithChangedOrder

modes responsible for high absorption, in figure 3

we present the absorption spectra as a function of

wavelength and in-plane component of the incident

field wave vector for the optimized structure and the

structure with

. First, it is worth to point out

that all resonances taking part in enhanced

absorption are dispersionless, which excludes

excitation of propagating surface plasmon

polaritons.

Second, since at λ =

= 380 nm the +/- 1

propagating diffraction orders appear, it is of interest

to design the structure so that all the HCMs are

excited at longer wavelengths, in the zero-order

regime, as presented. This prevents from unwanted

loss of energy which, otherwise, is distributed

between the propagating orders and may cause

lowering of the HCMs excitation efficiency.

Figure 4: Magnetic field intensity distribution under

normal incidence in one grating period of the optimized

structure at the peak wavelengths: 364, 387, 411, 428, 447

and 465 nm. Colour maps at each plot are scaled

independently.

Third, whilst the LSP resonances at wavelengths

330-380 nm do not exhibit any dependence on the

incidence angle sign, resonances at longer

wavelengths show this dependence. The asymmetry

in absorption is clearly visible at wavelength range

corresponding to the cavity modes. The absorption

remains very high for the illumination in the zero-

order regime, but outside it lowers and shows an

asymmetry withe regard to the incidence angle sign.

This indicates the energy losses by the existence of

the propagating orders and the coupling between

HCMs in neighbouring resonators, which therefore

are not independent from each other. Similar

asymmetry occurs also for structures with other

sequences of resonators.

In order to confirm the physical origin of the

suppressed reflection, in figure 4 we investigate the

magnetic field distribution at the peak wavelengths

under normal incidence. There is a distinct property

shown in those plots. Besides the LSP at shorter

wavelengths (figure 4(a)), the excitation of HCMs in

subsequent resonators is presented (figures 4(b-f)).

The sequence of the excited resonances corresponds

to the increased dielectric constant. Accordingly to

the standing wave model, the plasmon cavity mode

excited in each resonator at the upper and lower

metal/dielectric surface is reflected from both open

ends in a way that the magnetic field shows minima

at the ends. This feature is observed in the presented

magnetic field distribution plots.

4 DISCUSSION

In this paper, for simplicity, the relative change

between dielectric constants in dielectric resonators

is assumed constant (

Δε

) and the dimensions of all

of the resonators are equal. However, since slits of

the nanometric thickness can be regarded as media

with a large refractive index (Astilean et. al., 2000),

manipulation of the dielectric grating thickness can

also significantly change the resonance wavelength.

Accordingly to the simple standing wave model,

decrease of h

results in the decrease of the

resonance wavelength and increase of the separation

between HCMs absorption peaks. It is worth to point

out that when very narrow resonators are considered

of order of few nm), the nonlinear effects may

become important (Moreau et. al., 2013). Similar

results origin from increasing

Δε

. Hence, the

dielectric constants and thickness of the subsequent

resonators can be adjusted to create a desired

absorption bandwidth, since both parameters

influence the value of the cavity plasmon wave

vector.

The physical mechanism of the significant

fluctuations in absorption band caused by changed

order of the resonators is the mismatch of the phase

between individual resonators. It means that the

resonators are not independent and are close enough

to each other to influence their resonance conditions.

The optimized phase related to the spaces between

chirped resonators leads to wide and high absorption

(a)

(b)

(c)

(d)

(e) (f)

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

band (Song et. al., 2013). Additionally, the mutual

influence of the resonators is confirmed, when we

analyse the structures with constant

. This is

because the peak absorption in those structures is

about ~60%. However, the phase change introduced

by the change of

in neighbouring resonators alters

the resonance conditions in each resonator and leads

both to shift of the absorption peaks and high and

broadband absorption.

The ordered structure (with resonators in order:

), similarly as used in (Song et. al.,

2013), may not necessarily be the one with the

widest band width. Probably for this reason, in

(Song et. al., 2013) further optimization of the

structure (individually assorted widths and distances

between particular resonators) was performed to

achieve broad absorption band. This confirms that

the resonators are not independent on each other and

the resulted coupling modes play a role in forming

the broad absorption band. This indicated also, that

the further optimization of our structure by adjusting

separately widths of each space between resonators

may be possible.

5 CONCLUSIONS

A wide-band absorption over 80% was obtained in

the visible range in the periodic metallodielectric

structure with resonators filled with dielectrics of

varied dielectric constants. It occurred that this

device is sensitive to the change of the resonators'

order. The extended broadband absorption in such a

grating structure was attributed to the changed

sequence of those resonators in comparison to the

ordered structure. Those differences indicate that

those resonator are not independent on each other.

Change of the resonators' order allow for lowering

the mismatch of the phase between individual

resonators. The width of the absorption band at

normal incidence is estimated to be ~141 nm, which

is about 6.1 times wider than for a structure with five

identical resonators of

. Moreover, the

bandwidth of the optimized structure shows almost

1.2-fold increase with respect to the absorption

bandwidth of the ordered structure. This work shows

a way to obtain a wideband absorption by

optimizing order of the different resonators in a

grating period. The presented results may appear

useful in detection and imaging at visible

frequencies, angle-selective absorbers,

microbolometers, photodetectors and solar cell

technology.

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PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology