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Polarization-independent broad-band nearly perfect absorbers in the visible regime

Polarization-independent broad-band

nearly perfect absorbers in the visible

regime

Chia-Hung Lin,1Ruey-Lin Chern,2,?and Hoang-Yan Lin1

1Graduate Institute of Photonics and Optoelectronics and Department of Electrical

Engineering,National Taiwan University,Taipei106,Taiwan

2Institute of Applied Mechanics,National Taiwan University,Taipei106,Taiwan

?chernrl@https://www.sodocs.net/doc/a015532568.html,.tw

Abstract:Polarization-independent broad-band absorbers in the visible

regime are theoretically investigated.The absorbers are three-layered

structures consisting of a lossy dielectric grating on top of a low-loss

dielectric layer and a substrate of the same lossy dielectric placed at the

bottom.Enhanced absorption in the underlying structure is attained over a

broad range of frequency for both TE and TM polarizations.In particular,

a nearly perfect absorbance(over99.6%)is achieved atλ≈600nm,

around which the absorption spectra show a substantial overlap between

two polarizations.The enhanced absorption is attributed to cavity resonance

and its hybridization with a weakly bound surface wave.This feature is

illustrated with the electric?eld patterns and time-averaged power loss

density associated with the resonances.

?2011Optical Society of America

OCIS codes:(050.1950)Diffraction gratings;(300.1030)Absorption.

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1.Introduction

Extraordinary optical transmission through subwavelength holes or slits has been the subject of intensive research over the last decade[1–3].The enhanced transmission arises from the excitation of coupled surface plasmons on metal?lms and/or cavity resonances associated with the holes or slits[4,5].This mechanism may also lead to enhanced absorption due to the resonance nature in the underlying structure[6–8].On the one hand,the extreme light concentration can profoundly increase the optical absorption rate in the nanostructure[9].Ex-traordinary optical absorption or blackbody phenomenon becomes an intriguing topic in most recent years[10,11].On the other hand,the enhanced absorption may?nd important applica-#137566 - $15.00 USD Received 3 Nov 2010; revised 20 Dec 2010; accepted 21 Dec 2010; published 3 Jan 2011 (C) 2011 OSA17 January 2011 / Vol. 19, No. 2 / OPTICS EXPRESS 416

tions in solar cells [12,13],thermo-photovoltaics [14,15],photodetectors [16,17],and thermal emitters [18].

Various approaches have been proposed to greatly enhance the absorption in embedded nanostructures [19,20],metallic gratings with guiding layer [12,18],multilayer structures [21],and metamaterials [22–24].Under suitable conditions,a nearly perfect absorption can even be attained in a certain frequency range [10,18,22,24–26].This is a special feature that all the incident power is absorbed in the structure without re?ection from or transmission through the structure.The absorption ef?ciency is therefore far beyond the theoretical limit of absorption (50%)in thin planar structures [2].Most designs for enhanced absorption rely on the excitation of surface waves (that is,surface plasmons)at the metal/dielectric interface.The enhancement of ?eld near the surface gives rise to a large absorption.Some structures may also exploit the feature of cavity resonance to increase the absorption through ?eld con?nement.In fact,the two mechanisms can be supported in lossy dielectric structures with careful arrangement.A suitable material is tungsten,whose real part of the dielectric constant is positive in the optical regime [3,27].

In the present study,we investigate the feature of enhanced absorption for polarization-independent broad-band absorbers in the visible regime.The absorbers are three-layered struc-tures consisting of a lossy dielectric grating on top of a low-loss dielectric layer and a substrate of the same lossy dielectric placed at the bottom.Enhanced absorption in the underlying struc-ture is attained over a broad frequency range for both TE and TM polarizations.In particular,a nearly perfect absorbance (over 99.6%)is achieved around λ≈600nm,the absorption spectra showing a substantial overlap between the two polarizations.The enhanced absorption is at-tributed to the cavity resonance and its hybridization with a weakly bound surface wave.This feature is illustrated with the electric ?eld patterns and time-averaged power loss density asso-ciated with the resonances.x

z k

E (H )H (E )

θW p-Si

TE: E TM: H w a b h t θp Fig.1.Schematic diagram of the light absorber consisting of a grating layer and a substrate

made of tungsten (W),spaced by a polysilicon (p -Si)slab,where p is the grating period,b

is the grating depth,a is the slit width,w =p ?a ,h is the p -Si slab thickness,and t is the

W substrate thickness.

2.Results and discussion

Consider a three-layered structure consisting of a top layer of tungsten (W)grating,a middle layer of polysilicon (p -Si)slab,and a bottom layer of tungsten substrate.The schematic diagram and geometric parameters are shown in Fig.1.In the present study,the underlying structure serves as a nearly perfect absorber in the visible regime for TE and TM polarizations.Here,#137566 - $15.00 USD Received 3 Nov 2010; revised 20 Dec 2010; accepted 21 Dec 2010; published 3 Jan 2011

TE (TM)refers to the electric (magnetic)?eld parallel to the slits.In order to characterize the absorption,the frequency domain ?nite element solver is used to calculate the re?ectance (R ),transmittance (T ),and the corresponding ?eld distributions [28].The absorbance (A )is then obtained by the conservation of energy:1?R ?T .In another aspect,the absorption of light is related to the power loss in the material.The time-averaged power loss density (per unit volume):dP loss /dV =12ωε′′|E |2,where ε′′is the imaginary part of the dielectric constant,is used to illustrate the distribution of absorption in the structure.The power loss P loss ,obtained by integrating dP loss /dV over the region of nonzero ε′′,is equal to the absorbance A times the incident power P inc ,that is,A =P loss /P inc .In the present study,the optical constants for W and p -Si are taken from the solid handbook [29].

Wavelength λ[nm]A b s o r b a n c e 400500600700800

00.2

0.4

0.60.8

TE TM Fig.2.Absorbance of the light absorber as sketched in Fig.1for TE and TM polarizations,

where p =500nm,a =330nm,b =420nm,h =497nm and t =200nm.

2.1.Nearly perfect absorption

Figure 2shows the absorption spectra for the grating structure (cf.Fig.1)for normal incidence (θ=0?),where p =500nm,w =170nm,a =330nm,b =420nm,h =497nm and t =200nm.Strong absorption is observed over the whole visible regime for both TE and TM polarizations.The absorbance A exceeds 0.6in the wavelength range from 400nm to 800nm.Between 500nm and 700nm,the absorption ef?ciency is even greater than 80%.In particular,a nearly perfect absorption (A ≈1)is achieved around 600nm for either polarization;A ≈0.999at λ≈600nm for TE polarization and A ≈0.996at λ≈609nm for TM polarization.In this situation,all the incident power is absorbed in the system,without re?ection from or transmission through the structure.Due to the tungsten slab placed at the bottom,which acts as a re?ector as well as an absorber,the transmittance T is in fact negligible.The absorbance is equal to unity minus the re?ectance:A =1?R .

Note that there is a substantial overlap (roughly from λ≈520nm to 670nm)between the absorption curves for TE and TM polarizations.The present structure is therefore eligible to be a polarization-independent absorber.This property,however,is gradually changed as the angle of incidence increases from zero [cf.Fig.3].Note also that a small absorption peak is observed around λ≈500nm,which is more evident for TM polarization.This feature corresponds to the occurrence of Wood’s anomaly [2,30],where the re?ection experiences a rapid variation within a small frequency interval.The anomaly comes from the onset of a new diffraction order tangential to the surface [30].According to the grating equation

sin θm =sin θ+m λp ,(1)

#137566 - $15.00 USD Received 3 Nov 2010; revised 20 Dec 2010; accepted 21 Dec 2010; published 3 Jan 2011

the angle θm of the m th-order diffracted beam (m =0,±1,±2,...)is related to the angle of incidence θthrough the wavelength λand the grating period p .For normal incidence (θ=0?),the ?rst nonzero order of diffraction (m =±1)emerges as the wavelength approaches the grating period (λ≈p ).The respective diffracted wave goes into surface modes (θm =±90?)and a re?ection dip is associated with this wavelength (also known as the Rayleigh wavelength).As the transmission is negligible in the present con?guration,the anomaly appears as an absorption peak.

Wavelength λ[nm]A n g l e o f i n c i d e n c e θ(T M )10.50

Wavelength λ[nm]A n g l e o f i n c i d e n c e θ(T E )1

0.50(b)(a)Fig.3.Absorbance as a function of wavelength and angle of incidence for the same absorber

in Fig.2for (a)TE polarization and (b)TM polarization.White dashed lines indicate the

onset of grating lobes with nonzero diffraction order m .Black solid triangles denote the

absorption peaks (A >0.9)at different angles of incidence.

The absorbance as a function of wavelength and angle of incidence is plotted in Fig.3.It is shown that the absorption experiences a marked change when the angle of incidence exceeds the onset of grating lobe with diffraction order m =?1:θ=sin ?1(λ/p ?1)(denoted by the white dashed line).For TE polarization [Fig.3(a)],the absorption simply attenuates as the angle of incidence increases.The absorption peaks (denoted by the black solid triangles)are located around λ≈600nm until they are distracted along the onset of grating lobe to larger wavelengths,where the nonzero-order of diffracted wave emerges and adds to the zero-order re?ection.These waves are diffracted away from the structure and will not be absorbed in the system.The maximum absorption ef?ciency,however,is still over 80%for θ≈20?and 60%for θ≈50?.

For TM polarization [Fig.3(b)],the absorption pattern is somewhat complicated.The ab-sorption peaks basically move toward longer wavelengths as θincreases from zero.Beyond the onset of grating lobe (m =?1),the major absorption band is separated into three branches and spreads over a wider wavelength range.An array of absorption peaks is located around λ≈475nm (θ≈30?to 60?),while another array is situated near λ≈800nm (θ≈60?to 80?).The absorption for TM polarization is apparently stronger than for TE polarization,especially at large angles of incidence.The maximum absorbance is over 60%even at θ≈80?.

2.2.Mechanism of enhanced absorption

In order to identify the mechanism of enhanced absorption,the pattern of electric ?eld (E z )associated with the nearly perfect absorption (A ≈0.999)at λ≈600nm for TE polarization is plotted in Fig.4(a).It is shown that the ?eld is strongly con?ned within the slits of the grating and depicts a typical feature of cavity resonance.For an ideal cavity,the resonant wavelength #137566 - $15.00 USD Received 3 Nov 2010; revised 20 Dec 2010; accepted 21 Dec 2010; published 3 Jan 2011

(b)

(a)

Fig.4.Contours of the electric?eld E z at(a)λ≈600nm(TE11-like mode)associated

with the absorption peak and(b)λ≈407nm(TE12-like mode)for the same absorber in

Fig.2for TE polarization.In(b),the black arrows denote the directions of diffraction order

m=±1.

of the TE mn mode is given by

λmn=

(m/a)2+(n/b)2,(2)

where a and b are the width and length,respectively,of the cavity,and m and n are integers.The ?eld pattern in Fig.4(a)is analogous to the cavity mode with m=n=1.This feature has also been identi?ed as the origin of enhanced transmission through broad slits for TE polarization [31,32].Note that the?eld of the resonant mode extends somehow through the open end to the outside and partially penetrates into the layer of p-Si,leading to a weaker con?nement[33,34]. The?eld also penetrates into the side walls and effectively increases the cavity width due to the skin depth of tungsten.As a result,the effective resonant wavelength(λ≈600nm)of the TE11-like mode is slightly longer thanλ11≈519nm[cf.Eq.(2)].In fact,if the skin depth of tungsten(about33.5nm atλ≈600nm)is taken into account for the cavity width a in Eq.(2), the estimation ofλ11≈577nm is closer to the simulation result.

Meanwhile,the feature of Fabry-Perot like resonance with somewhat weaker strength is observed in the middle layer of p-Si.This layer acts as a parallel-plate waveguide with a higher-order oscillation of?eld than in the slits.Note that very little?eld penetrates into in the bottom layer of tungsten,where it is either re?ected or absorbed.

The origin of enhanced absorption has a strong correspondence with the quality of?eld con-?nement.For TE polarization,the fundamental TE11-like cavity mode depicts a higher quality of con?nement than the higher-order modes.For comparison,the TE12-like mode atλ≈407 nm is plotted in Fig.4(b).The respective absorbance is signi?cantly reduced(A≈0.7).On the one hand,the?rst-order diffraction emerges at a re?ection angle around±54.5?atλ≈407nm [cf.Eq.(1)with m=±1],which can be noticed by the interference pattern in Fig.4(b)(the re-?ected beams are denoted by the black arrows).On the other hand,both the real and imaginary parts of the complex refraction index n(=n′+in′′)of p-Si increase signi?cantly fromλ≈600 nm(n≈3.89+0.05i)toλ≈400nm(n≈5.22+0.44i).As a result,less?eld is allowed to enter into the p-Si layer and the W substrate.The absorption is therefore weaker.

The electric?eld associated with the nearly perfect absorption(A≈0.996)atλ≈609nm

(a)

(b)2

20Fig.5.(a)Contours of horizontal electric ?eld E x and (b)vertical electric ?eld E y associated

with the absorption peak at λ≈609nm for the same absorber in Fig.2for TM polarization.

for TM polarization is plotted in Fig.5.The pattern of horizonal electric ?eld E x in Fig.5(a)shows a typical feature of TM 02-like mode in the cavity.As in the case of TE polarization,the resonant mode is not completely con?ned within the cavity due to the open end at the top.The Fabry-Perot like resonance is also observed in the middle layer of p -Si.A special feature for TM polarization is the appearance of a surface wave,which is manifest on the pattern of vertical electric ?eld E y in Fig.5(b).The enhanced absorption is therefore characterized by the coupling of cavity modes with surface waves.This hybridization feature has also been identi?ed in the study of enhanced transmission in nanostructured materials [6].In the present study,the tungsten behaves as a lossy dielectric since its dielectric constant has a positive real part in the optical regime [27].The corresponding mode is weakly bound to the surface and known as the Zenneck wave [3],rather than the surface plasmon that usually occurs on the metal surface [35].This wave is also termed as structured surface plasmon or surface charge density wave

[36].

(a)

(b)126012

Fig.6.Contours of the time-averaged power loss density dP loss /dV associated with the

absorption peaks for the same absorber in Fig.2at (a)λ≈600nm for TE polarization and

(b)λ≈609nm for TM polarization.In (b),the alignment of surface charges are denoted

by symbols “+”and “-”.

#137566 - $15.00 USD Received 3 Nov 2010; revised 20 Dec 2010; accepted 21 Dec 2010; published 3 Jan 2011

The feature of enhanced absorption is further illustrated with the time-averaged power loss density dP loss /dV for the absorption peaks.For TE polarization in Fig.6(a),the incident power is mainly absorbed in the tungsten grating walls.A small portion of power is absorbed by the tungsten substrate and the polysilicon layer.This feature is consistent with the TE 11-like mode [cf.Fig.4(a)]associated with the absorption peak.For TM polarization in Fig.6(b),the absorption occurs on the grating top and bottom as well as on the walls.In addition,the absorption in the middle layer and substrate is more intensi?ed.This is due to the concurrence of cavity modes and surface waves.The alignment of surface charges is overlaid in the ?gure to show the feature of surface waves.

Wavelength λ[nm]P l o s s /P i n (T M )400500600700800

00.20.40.60.81Whole W grating p -Si layer W layer (b)Wavelength λ[nm]P l o s s /P i n (T E )40050060070080000.2

0.4

0.6

0.8

Whole W grating p -Si layer W layer (a)Fig.7.Ratios of the time-averaged power loss P loss in different layers of the same absorber

in Fig.2for (a)TE polarization and (b)TM polarization.

Figure 7shows the distribution of time-averaged power loss P loss by integrating dP loss /dV over separate layers.It is shown that for TE polarization [Fig.7(a)]the incident power is largely absorbed in the grating,especially at longer wavelengths.Around the absorption peak,80%of the power loss is due to the grating.For TM polarization [Fig.7(b)],the absorption in the substrate becomes more signi?cant.This is more evident at λ≈700nm,where 38%of the incident power is absorbed in the substrate.

2.3.Effect of geometrical parameters

Figure 8(a)shows the dependence of absorbance on the grating period p ,all other parame-ters being unchanged.The absorption band is basically centered around λ≈600nm for both polarizations as the grating period changes.This feature depicts that the absorption in the un-derlying absorber is more of the site resonance that depends on the individual structure in the unit cell.The absorption is,however,blocked by the line λ=p (denoted by the white dashed line),above which the nonzero order of diffractions emerge.A substantial portion of incident light is re?ected away from the absorber and the absorption is therefore signi?cantly reduced.Note that for TM polarization (right plot),the dependence of absorption on the grating period is a bit more complicated,due to the hybridization of cavity modes and surface waves.The main absorption band,however,is still around λ≈600nm and substantially blocked by the line λ=p .

The dependence of absorbance on the slit width a is shown in Fig.8(b).For TE polarization (left plot),the absorption peak moves to longer wavelengths as the slit width is increased.This feature is consistent with the character of TE 11-like mode associated with the enhanced absorption [cf.Fig.4(a)].The absorption is rather weak when the slit width is less than 200nm.Note that the strong absorption (A ≈96%)still occurs over a large wavelength range (λ≈610nm to 800nm)for a =490nm.The corresponding grating width w is 10nm,which is smaller than the skin depth of tungsten in the visible regime (20nm to 40nm).For TM polarization #137566 - $15.00 USD Received 3 Nov 2010; revised 20 Dec 2010; accepted 21 Dec 2010; published 3 Jan 2011

Wavelength λ[nm]P e r i o d p [n m ](T E )10.8

0.6

Wavelength λ[nm]P e r i o d p [n m ](T M )1

0.8

0.6

Wavelength λ[nm]S l i t w i d t h a [n m ](T E )10.7

0.4

(b)Wavelength λ[nm]S l i t w i d t h a [n m ](T M )10.7

0.4Fig.8.Dependence of absorbance on (a)the grating period p and (b)the slit width a for

TE polarization (left plots)and TM polarization (right plots).All geometry parameters are

the same as in Fig.2except the grating period p for (a)and the slit width a for (b).In each

plot,the white circle denotes the absorption peak for the optimized structure in Fig 2.

(right plot),the redshift of the absorption peak with the slit width is less obvious.This feature is consistent with the character of TM 02-like mode associated with the enhanced absorption.The change of slit width basically does not alter the resonant frequency.The enhanced absorption,however,is signi?cant when the slit width is larger than 150nm.

The effect of grating depth b on the absorption is shown in Fig.9(a).For TE polarization (left plot),the lower and higher absorption bands correspond to TE 11-like and TE 12-like modes,respectively,associated with the enhanced absorptions.The respective resonant modes are red-shifted with the grating depth,as they are with the slit width.For TM polarization (right plot),the three major absorption bands are associated with the TM 01-like,TM 02-like,and TM 03-like modes (from the lower to the higher bands).As in the case of TE polarization,more resonant modes are excited as the grating depth is increased.Meanwhile,the absorption bands move to longer wavelengths for larger grating depth.Finally,the dependence of absorption on the p -Si layer thickness h is shown in Fig.9(b).For TE polarization (left plot),the absorption band is nearly unchanged with the p -Si layer thickness,except that there are small variations near the band edges.For TM polarization (right plot),on the other hand,signi?cant variations occur on the absorption band edges,which is more evident on the long wavelength side.The peri-odic pattern along the layer thickness indicates that the Fabry-Perot like resonance in the p -Si layer increases its importance in the enhanced absorption.This feature is consistent with the increased portion of time-average power loss in the corresponding layer for TM polarization,as depicted in Fig.7.As the absorption band width for TM polarization is strongly dependent on h ,a suitable p -Si layer thickness is therefore required to give a maximum overlap of absorp-tion curves between TE and TM polarizations.In the present study,an optimal design for this purpose is attained with h =497nm (λ≈520nm to 670nm).

#137566 - $15.00 USD Received 3 Nov 2010; revised 20 Dec 2010; accepted 21 Dec 2010; published 3 Jan 2011

Wavelength λ[nm]G r a t i n g d e p t h b [n m ](T E )10.7

0.4

Wavelength λ[nm]G r a t i n g d e p t h b [n m ](T M )1

0.7

0.4Wavelength λ[nm]p -S i t h i c k n e s s h [n m ](T E )10.8

0.6

(b)Wavelength λ[nm]p -S i t h i c k n e s s h [n m ](T M )1

0.8

0.6

Fig.9.Dependence of absorbance on (a)the grating depth b and (b)the p -Si layer thickness

h for TE polarization (left plots)and TM polarization (right plots).All geometry parameters

are the same as in Fig.2except the grating depth b for (a)and p -Si layer thickness h .In

each plot,the white circle denotes the absorption peak for the optimized structure in Fig 2.

3.Concluding remarks

In conclusion,we have investigated the feature of polarization-independent broad-band ab-sorbers in the visible regime.Enhanced absorption (A >80%)occurs over a wide range of wavelength (200nm)for both polarizations.In particular,a nearly perfect absorption ef?ciency is achieved around λ≈600nm (A ≈99.9%at λ≈600nm for TE polarization and A ≈99.6%at λ≈609nm for TM polarization).The extraordinary optical absorption in the underlying structure comes from the occurrence of cavity-like resonance (for both polarizations)as well as the weakly bound surface wave (for TM polarization).The electromagnetic ?eld is trapped inside the grating structure,giving rise to a strong absorption.With careful arrangement of the geometric parameters of the absorber,the absorption spectra show a substantial overlap in the visible regime between two polarizations.The underlying grating structure is therefore eligible to be a polarization-independent absorber.

Acknowledgments

This work was supported in part by National Science Council of the Republic of China under Contracts No.NSC 99-2221-E-002-121-MY3and NSC 99-2221-E-002-140.

#137566 - $15.00 USD Received 3 Nov 2010; revised 20 Dec 2010; accepted 21 Dec 2010; published 3 Jan 2011

Polarization-independent broad-band nearly perfect absorbers in the visible regime

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