nearly perfect absorption in intrinsically low-loss grating structures

Nearly perfect absorption in intrinsicallylow-loss grating structures

Ruey-Lin Chern* and Wei-Ting HongInstitute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan

∗[email protected]

Abstract: The feature of enhanced absorption in two-layered gratingstructures is theoretically investigated. The underlying structures make themost use of resonance mechanism to achieve a nearly perfect absorption inan intrinsically low-loss medium. For standalone gratings, the maximumabsorption efficiency is shown to be 50%, which is attributed to thecoupling of short range (bonding) or long range (antibonding) surfaceplasmons with cavity resonances. By attaching a dielectric slab on top orbottom to the metallic grating, the maximum absorption efficiency can beraised to nearly 100%. The presence of guided waves in the dielectric slabcauses the strong concentration of fields and reinforces the absorption toits extreme value. The efficient absorption mechanism is illustrated withthe pattern of resonance fields and the distribution of power loss density.A phenomenological theory is also used to characterize the absorptionanomaly in terms of complex pole and zero.

© 2011 Optical Society of AmericaOCIS codes: (050.1950) Diffraction gratings; (300.1030) Absorption.

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#143812 - $15.00 USD Received 14 Mar 2011; revised 10 Apr 2011; accepted 14 Apr 2011; published 22 Apr 2011(C) 2011 OSA 25 April 2011 / Vol. 19, No. 9 / OPTICS EXPRESS 8962

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1. Introduction

Extraordinary optical absorption in nanostructures has been the subject of intensive research inrecent years [1–10] due to the potential applications in photovoltaics [11–13] and photodectors[14]. The ultimate feature of enhanced absorption is the total absorption of incident power inthe structure, without either reflection or transmission. This special character can be realizedfrom the aspect of scattered waves, which are expected to be drastically different between twosides of the structure. On the incident side, the scattered field is evanescent and therefore noreflection exists in the far field. This is the typical feature of surface waves. On the transmissionside, on the other hand, the scattered field has to be propagative so that the transmission throughthe structure is possibly canceled out by a destructive interference with the incident field. Oncethe two distinct conditions are fulfilled in the same structure, the total absorption may appear.

The phenomenon of total absorption by metallic gratings has been discovered in the mid-1970s from a phenomenological theory and confirmed by numerical and experimental results[15–17]. The resonance generated by surface plasmons is attributed to the origin of absorptionanomaly. In most recent years, various designs of subwavelength structures also give rise tonearly perfect absorption, including porous metallic films [1], metallic resonators [6,9], crossedgratings [3], lamellar gratings [4, 5], and metallic gratings [7, 8, 10], among other structures.In contrast to the anomalous absorption in the medium having a large imaginary part of thepermittivity [18], a small absorption coefficient is usually sufficient for the enhanced absorptionin the subwavelength structures. The extreme light concentration can profoundly increase theoptical absorption rate [19].

A typical way to concentrate the field is to bring about the resonance. The metallic gratingserves as a simple structure with strong absorption. Due to the excitation of surface plasmons,the absorption efficiency can be as high as 50% [20]. For thin metal films, there are two basictypes of surface plasmons [21], characterized by the alignment of surface charges on the twosides of the film. The symmetric charge alignment is referred to as the bonding mode, whilethe antisymmetric alignment is called the antibonding mode [22,23]. In particular, the bondingmode is strongly damped (with the electric field essentially parallel to the surface inside themetal) and also named the short range surface plasmon, while the antibonding mode is weaklydamped (with the electric field predominantly normal to the surface) and is called the longrange surface plasmon [24, 25].

For metallic gratings with narrow slits, surface plasmon modes are coupled with cavity res-onances associated with the slits. The cavity-coupled surface plasmons have been identified asthe origin of enhanced transmission [26–28]. The same mechanism is also accompanied withthe enhanced absorption [29, 30]. For ideally thin planar structures, where the scattered fieldsare symmetric on the two sides, the theoretical limit of absorption efficiency is 50% [31]. Theother half incident power is either reflected from or transmitted through the structure. In orderto increase the absorption based on the grating design, a certain degree of complexity is to beadded in the system so that the scattered fields on the two sides could be as much different aspossible. The attachment of a dielectric slab to the metallic grating serves as a simple way to in-troduce such a complexity. In a previous study, the anomalous optical absorption was achievedin aluminum compound gratings in the near-infrared frequency [32]. Later on, three-layeredtungsten grating structures were designed to enhance the broad-band absorption in the visibleregime [33].

In the present study, we investigate the feature of nearly perfect absorption in more simplifiedgrating structures. They are two-layered structures consisting of a low-loss metallic grating(made of silver) and a lossless dielectric slab. The underlying structures make the most useof resonance mechanism to yield strong absorption in an intrinsically low-loss medium. Forstandalone metallic gratings with narrow slits, the maximum absorption efficiency is close to


50%, which is attributed to the coupling of short range (bonding) or long range (antibonding)surface plasmons with cavity resonances. By attaching a lossless dielectric slab on either top orbottom to the metallic grating, the maximum absorption efficiency can be raised to nearly 100%.The presence of guided waves in the dielectric slab causes the strong concentration of fieldsand reinforces the absorption in the underlying structure. In particular, the top slab enhancesthe absorption associated with the short range bonding mode, while the bottom slab enhancesthe absorption with the long range antibonding mode. These features are illustrated with theresonant field patterns associated with the absorption peaks. The distribution of time-averagedpower loss density is used to highlight the enhanced absorption in the underlying structure.Finally, the phenomenological theory [34] is used to characterize the absorption anomaly interms of complex pole and zero.

θ

k

θ

k

θ

k

Fig. 1. Schematics of the metallic grating with narrow slits (left), the grating structurewith a dielectric slab attached to the top surface (middle), and the grating structure witha dielectric slab attached to the bottom surface (right). The shaded region in yellow colorstands for the incident plane.

2. Problem description

Consider a metallic grating made of silver (Ag) with narrow slits as the baseline structure.A dielectric slab is attached to either the top or bottom of the grating to introduce a certaincomplexity into the system. The schematics of the underlying structures are depicted in Fig.1. A plane wave with the magnetic field oriented perpendicular to the propagation direction,that is, the transverse magnetic (TM) polarization, is incident from above. A frequency domainfinite element solver [35] is employed to solve the time-harmonic (with time dependance e−iωt )wave equation in terms of Hz:

∇ ·(

1ε

∇Hz

)+ k2

0Hz = 0, (1)

where the incident plane coincides with the xy plane, k0 = ω/c is the wave number in thesurrounding medium, which is assumed to be free space for simplicity, and ε is the dielectricconstant of the constituent materials. In the present study, ε for Ag is taken from the solidhandbook [36].

For periodic structures, it is sufficient to solve the problem in a unit cell, along with the Blochcondition, Hz (x+d,y) = eik‖dHz (x,y), imposed on the cell boundary, where d is the grating pe-riod (along the x direction), and k‖ = k0 sinθ is the wave number parallel to the surface, with θbeing the angle of incidence measured from the surface normal. Once the electromagnetic fieldsare solved, the reflectance R and transmittance T , the ratios of reflected and transmitted powers,respectively, to the incident one are determined by the fields at the far boundary. According tothe conservation of energy, the absorbance A in the system is given as A = 1−R−T .

The absorption of energy comes from the power loss in the system. For nonmagnetic materi-als, the power loss is associated with the nonzero imaginary part of the permittivity. According


to the Poynting theorem [37],∂u∂ t

+∇ ·S =−J ·E, (2)

the power loss in a system is due to the work done by the electromagnetic forces on electriccharges, where u is the electromagnetic energy density, S is the Poynting vector, and J is thetotal current density. The time-averaged power loss density (per unit volume) is given by

dPloss

dV=

12

Re[J ·E∗] =12

ωε ′′ |E|2 , (3)

where ε ′′ is the imaginary part of ε . This relation shows that the enhanced absorption can beattributed to high ε ′′ and/or large |E|2. For low-loss materials such as silver, a feasible way toenhance the absorption is to bring about the resonance so that the electric fields are intensifiedin the medium. In the present problem, the grating provides a mechanism to excite resonantmodes. The absorption mainly comes from silver when the resonance occurs. Note that thetime-averaged power loss Ploss, obtained by integrating dPloss/dV over the region of nonzeroε ′′, is equal to the absorbance A times the incident power Pinc, that is, A=Ploss/Pinc. The relation(3) can also be used to identify the distribution of absorbed energy in the system.

λ(nm)

Abs

orba

nce

550 600 650 7000

0.5

1

Absorb.Transmit.Reflect.

(a) (b)

6

0

- +++--- +--- + - +++

20

0

H

k

E

3

0

-3

0

3

-3

Fig. 2. (a) Absorbance, transmittance, and reflectance for the metallic (Ag) grating withnarrow slits, where d = 600 nm, w = 30 nm, and h = 30 nm. (b) Contours of verticalelectric field Ey (overlaid with electric field vectors) and time-averaged power loss densitydPloss/dV [cf. Eq. (3)] for the absorption peak A ≈ 0.497 at λ ≈ 612 nm. A schematicprofile of horizonal electric field Ex in the slit is plotted in the inset. The symbols ”+” and”-” denote the signs of surface charges.

3. Results and discussion

3.1. Single layer grating with maximum 50% absorbance

Figure 2(a) shows the absorbance A, transmittance T , and reflectance R for a thin metallic grat-ing with narrow slits, where a = 600 nm, w = 30 nm, and h = 30 nm. Note that the gratingthickness is on the order of skin depth for silver (Ag) around λ ≈ 600 nm, where the refractiveindex n ≡ n′+ in′′ ≈ 0.124+3.72i [36] and the skin depth δ = λ/(2πn′′)≈ 26 nm. An absorp-tion peak A ≈ 0.497 occurs at λ ≈ 612 nm, which is close to the transmission peak at λ ≈ 615nm. The maximum absorbance approaches the theoretical limit of absorption, A = 0.5, for thinplanar structures. This feature can be realized by noting that the total field is considered as the


sum of the incident field and the scattered field by the grating. As the wavelength is larger thanthe grating period, there exist a single reflected and a single transmitted wave of non-evanescentorder. For a very thin grating, the scattered fields on two sides tend to be symmetric with respectto the grating plane. The optimal absorbance is then achieved when the reflected power is equalto the transmitted power.

In Fig. 2(a), the transmission profile shows a peak and a dip located at nearby frequencies,which is the standard feature of Fano resonance [38]. This feature has been interpreted in thetransmission characteristic of hole arrays [39, 40]. In particular, the transmission peak for slitarrays can be characterized by the resonant condition: φ = 2nπ , where φ is the sum of scatte-ring phase due to the lattice and geometric phase determined by the optical path of the slit [41].For thin metal films, the total phase is dominated by the scattering phase and the transmissionresonance appears at a wavelength slightly larger than the grating period. Meanwhile, the trans-mission dip is very close to the grating period, indicating that it is lattice resonance in nature.The above phenomenon is also known as Wood’s anomaly [42], a feature referring to the drasticchange of transmission (or reflection) within a small frequency interval.

For the present configuration, the maximum absorption is accompanied with the Fano res-onance for transmission, which has also been identified in thin metal films [20, 43]. In thiscircumstance, both the enhanced transmission and enhanced absorption are attributable to theoccurrence of surface plasmons. For grating structures, the excitation of surface plasmons isfulfilled by the momentum matching condition [44]:

ksp = k0 sinθ ± 2nπa

, n = 0,1,2, ... (4)

where ksp is the wave number of surface plasmons. Compared to the parallel component of in-cident wave number k0 sinθ , ksp acquires an additional amount due to the multiple scattering offields over the grating structure. This amount covers the momentum deficit needed for couplingthe incident light with surface plasmons. The momentum of surface plasmon on a flat metallicsurface is given as [45]

ksp = k0

√εmεd

εm + εd, (5)

where εm and εd are the dielectric constants of the metal and surrounding dielectric, respec-tively. For a thin grating, Eq. (5) serves as an approximation to the actual surface plasmonmomentum.

The feature of surface plasmons is illustrated with the distribution of electric fields. In Fig.2(b), the pattern of vertical electric field Ey associated with the absorption peak at λ ≈ 612nm is antisymmetric with respect to the top and bottom surfaces. The surface charges on thetwo surfaces (denoted by the symbols ”+” and ”-”) are inphase. This alignment of charges isidentified as the bonding mode [22, 23], one of the two basic types of surface plasmons inmetal films [21]. For thin metal films, the bonding mode is strongly damped and referred to asshort range surface plasmon [24, 25]. The corresponding electric fields are essentially parallelto the surface inside the metal. Note that the horizontal electric field Ex inside the slit depicts atypical feature of even mode (sketched in the inset), which is therefore able to couple the shortrange surface plasmon. In particular, the short range surface plasmon is responsible for theenhanced absorption in thin metal films [20, 43]. The excitation of surface plasmons gives riseto strong enhancement of fields in the metal, and the extreme concentration of fields leads tolarge absorption rate [19]. In terms of the time-averaged power loss density dPloss/dV [cf. Eq.(3)], the absorption is shown to be distributed over a large portion of the grating, with higherstrength near the slits as well as in between.

If the grating thickness is increased to h = 100 nm, two absorption peaks appear, as shownin Fig. 3(a). The maximum absorbance A ≈ 0.496 moves to a longer wavelength (λ ≈ 640


λ(nm)

Abs

orba

nce

550 600 650 7000

0.5

1


(a) (b)

6

0

- +++--- +

- +++--- +

20

0

3

0

-3

0

3

-3

(c)

6

0

+ +++--- -

- ---+++ +

20

0

3

0

-3

0

3

-3

Fig. 3. (a) Absorbance, transmittance, and reflectance for the metallic (Ag) grating withnarrow slits, where d = 600 nm, w = 30 nm, and h = 100 nm. (b) Contours of verticalelectric field Ey (overlaid with electric field vectors) and time-averaged power loss den-sity dPloss/dV for the absorption peak A ≈ 0.467 at λ ≈ 606 nm. (c) Same as (b) for theabsorption peak A ≈ 0.496 at λ ≈ 640 nm.

nm), while another absorption peak with slightly weaker absorbance A ≈ 0.467 occurs aroundthe lattice period (λ ≈ 606 nm). Note that the two absorption peaks are very close to the twotransmission peaks (λ ≈ 641 nm and 605 nm). As mentioned earlier, the transmission throughslit arrays is characterized by the phase resonance, the total phase (sum of scattering phase andgeometric phase) being an integer times 2π . As the thickness increases, the geometric phase(determined by the optical path of the slit) becomes more dominated and the transmissionpeak moves to a longer wavelength than the grating period [41]. The role of cavity or Fabry-Perot resonance associated with the slit increases its importance and the coupling of surfaceplasmon with cavity resonance is more evident. Meanwhile, the Fano resonance feature of thetransmission becomes less significant.

The field pattern and surface charge alignment associated with the absorption peak at λ ≈ 606nm in Fig. 3(b) is analogous to the short range bonding mode as in the case of h = 30 nm [cf.Fig. 2(b)]. The time-averaged power loss density dPloss/dV [cf. Eq. (3)] is more concentratedtoward the top and bottom surfaces. On the other hand, the pattern of Ey at λ ≈ 640 nm in Fig.3(c), where the maximum absorption (A ≈ 0.496) occurs, is symmetric with respect to the topand bottom surfaces. The surface charges on the two surfaces are out of phase. This alignmentof charges is identified as the antibonding mode [22, 23], the other one of the two types ofsurface plasmons in metal films [21]. For thin metal films, the antibonding mode is weaklydamped and referred to as long range surface plasmon [24, 25]. The corresponding electricfields are predominantly normal to the surface inside the metal. In the present configuration,however, the long range surface plasmon is also associated with an enhanced absorption. This isbecause the antibonding mode is now coupled to a cavity resonance, the damping feature beingdifferent from that in thin films without slits. Note that the horizontal electric field Ex insidethe slit depicts a typical feature of odd mode (sketched in the inset), which is able to couple thelong range surface plasmon. In addition, the time-averaged power loss density dPloss/dV tendsto be distributed more around the slit.

For an even larger thickness h= 325 nm as shown in Fig. 4(a), the absorption peak A≈ 0.498at λ ≈ 665 nm becomes broader, while the other absorption peak A ≈ 0.365 at λ ≈ 609 nmis narrower. Unlike the case of h = 100 nm, the maximum absorption for the present caseis associated with the short range surface plasmon [cf. Fig. 4(c)], which is coupled with theeven mode of cavity resonance in the slit (sketched in the inset). Note that the cavity modehas a higher oscillation order than that in the case of h = 30 nm. Another absorption peak is


λ(nm)

Abs

orba

nce

550 600 650 700 7500

0.5

1


(a) (b)

6

0

+++---

---

++

+++--

++

--

20

0

3

0

-3

0

3

-3

(c)

6

0

+++---

+++----

++

-

+

--

+

0

20

3

0

-3

0

3

-3

Fig. 4. (a) Absorbance, transmittance, and reflectance for the metallic (Ag) grating withnarrow slits, where d = 600 nm, w = 30 nm, and h = 325 nm. (b) Contours of verticalelectric field Ey (overlaid with electric field vectors) and time-averaged power loss den-sity dPloss/dV for the absorption peak A ≈ 0.365 at λ ≈ 609 nm. (c) Same as (b) for theabsorption peak A ≈ 0.498 at λ ≈ 665 nm.

associated with the long range surface plasmon, coupled with the odd mode of cavity resonance[cf. Fig. 4(b)]. Note also that the bonding of charges occurs as well on the slit walls. This featureis consistent with the distribution of time-averaged power loss density dPloss/dV [cf. Eq. (3)],which is concentrated near the slit walls and less significant on the top and bottom surfaces.

λ(nm)

Abs

orba

nce

500 600 700 8000

0.5

1

Absorb.Transmit.Relfect.

(a) (b)

6

0

+ +++--- -

- +- +

20

0

3

0

-3

0

3

-3

3

Fig. 5. (a) Absorbance, transmittance, and reflectance for the same grating structure as inFig. 3, with a dielectric slab of thickness 70 nm and ε = 2 attached to the top. (b) Contoursof vertical electric field Ey (overlaid with electric field vectors) and time-averaged powerloss density dPloss/dV for the absorption peak A ≈ 0.997 at λ ≈ 623 nm.

3.2. Attachment of dielectric slab with nearly 100% absorbance

If a dielectric slab is attached to the metallic grating, the absorption can be greatly enhanced.Figure 5(a) shows the absorbance, transmittance, and reflectance for the same metallic gratingas in Fig. 3, with a dielectric slab of thickness 70 nm and dielectric constant ε = 2 attached tothe top surface. The maximum absorbance becomes nearly perfect: A ≈ 0.997 at λ ≈ 623 nm.In this configuration, the transmittance is small, especially in the range λ > a. The reflectanceexhibits an inverse Lorentzian line shape and reaches a rather small value at resonance, where


both the transmittance and reflectance approach zero. As a result, a nearly perfect absorptionoccurs.

The pattern of Ey in Fig. 5(b) associated with the absorption peak shows a typical featureof bonding mode or short range surface plasmon, as in the case of standalone grating [cf. Fig.3(b)]. The attachment of a dielectric slab to the top of the grating causes the fields to be stronglyconfined inside the slab, showing a typical feature of guided wave [46]. The hybridization ofa cavity-coupled surface plasmon with the guided wave significantly increases the absorptionfrom the theoretical limit of 50% for thin films to nearly 100%. Note that the fields in thedielectric slab change signs around the slit and the profile of Ex inside the slit (sketched inthe inset) depicts an odd mode with substantial asymmetry (due to the different environmentsbetween the top and bottom surfaces of the grating). In this situation, the short range surfaceplasmon is still able to couple with the odd mode of cavity resonance. The enhanced absorptionis manifest on the time-averaged power loss density dPloss/dV [cf. Eq. (3)], which is muchmore intense than for the standalone grating [cf. Fig. 3(b)].

λ(nm)

Abs

orba

nce

500 600 700 8000

0.5

1


(a)3

0

-3

0

3

-3

- - + +

6

0

---+++ -+

20

0

(b)

Fig. 6. (a) Absorbance, transmittance, and reflectance for the same grating structure asin Fig. 3, with a dielectric slab of thickness 70 nm and ε = 2 attached to the bottom. (b)Contours of vertical electric field Ey (overlaid with electric field vectors) and time-averagedpower loss density dPloss/dV for the absorption peak A ≈ 0.992 at λ ≈ 707 nm.

If the same dielectric slab is attached to the bottom of the grating, a nearly perfect absorptionA ≈ 0.992 is achieved at λ ≈ 707 nm, as shown in Fig. 6(a). As in the case with the topslab, the transmittance is small. The reflection dip moves to a longer wavelength, substantiallyaway from the lattice period. In Fig. 6(b), the pattern of Ey associated with the absorptionpeak shows a typical feature of antibonding mode or long range surface plasmon, which issimilar to that for the standalone grating [cf. Fig. 3(c)]. Note that the profile of Ex inside the slit(sketched in the inset) also depicts an odd mode with asymmetry. Compared to the case withthe top slab, the fields in the bottom slab show a more regular pattern and do not change signsaround the slit. The long range surface plasmon is able to couple with the odd mode of cavityresonance. In the bottom slab, the fields are concentrated and exhibit the character of a guidedwave [46]. Likewise, the hybridization of a cavity-coupled surface plasmon with the guidedwave leads to nearly perfect absorption, despite the fact that the long range surface plasmonis weakly damped in thin films. For this configuration, the corresponding time-averaged powerloss density dPloss/dV [cf. Eq. (3)] tends to be more concentrated toward the bottom surface.

Figure 7 is a plot showing the effect of the angle of incidence θ on the absorbance for thegrating structure with the attachment of a top slab (cf. Fig. 5) or a bottom slab (cf. Fig. 6).


Fig. 7. Effect of the angle of incidence θ on the absorbance for the grating structure with adielectric slab attached to the top as in Fig. 5 and (b) attached to the bottom as in Fig. 6.

As the angle of incidence is increased from zero (normal incidence), the enhanced absorptionsplits into two bands; one goes to longer wavelengths and the other to shorter wavelengths. Thetwo branches basically follow the onset of grating lobes with nonzero diffraction orders [47].For the case with the top slab [Fig. 7(a)], the right absorption branch forms an anticrossingscheme with the left branch of another pair of much weaker absorption bands located to theright. The appearance of an additional pair of branches is due to the asymmetric configurationby attaching a dielectric slab to the top of the grating. The latter branches are weakly damped asthey are not coupled with cavity resonances. For the case with the bottom slab [Fig. 7(b)], theenhanced absorption moves to the right pair of branches, which is complementary to the pairof absorption bands for the case with the top slab. Meanwhile, the left absorption branch formsan anticrossing scheme with the right branch of another pair of much weaker absorption bandslocated to the left. For either the case with the top slab or the bottom slab, the anticrossingphenomenon comes from the existence of like symmetry of modes between the two interactingbranches, the crossing being avoided due to the repulsion against each other [48]. In the presentconfiguration, the fields inside the slits present such a symmetry. This is manifest on the patternof Ex in the slit for the two cases [cf. the insets in Fig. 5(b) and Fig. 6(b)].

λ(nm)

Ref

lect

ion

phas

e

500 600 700 800-0.5π

0

0.5π

1π

top slabbottom slab

(a)

O

O

OO

OO

XXX

X

XX

O

O

O

O

O

O

XXXX

X

X

Re[λz,p]/d

Im[λ

z,p ]/d

0.9 1 1.1 1.2 1.3

-0.01

0

0.01

zero (top slab)pole (top slab)zero (bottom slab)pole (bottom slab)

O

X

O

X

(b)

15

1520

40

6080

203030

60w=80 nm

15

2030

40

6080

40

20

3040

60

w=80 nm

15

Fig. 8. (a) Reflection phase of the grating structure with a dielectric slab attached to thetop as in Fig. 5 and to the bottom as in Fig. 6. (b) Locations of the poles and zeros in thecomplex plane of wavelength for different slit width w.


3.3. The phenomenological theory

The feature of nearly perfect absorption is further interpreted from the phenomenological theory[16, 34], which characterizes the reflection (or transmission) coefficient in terms of a pole anda zero. Let r be the reflection coefficient, defined as the complex amplitude of reflected fieldnormalized by the incident field strength. The phenomenological formula for r is given as

r = r0λ −λ z

λ −λ p , (6)

where λ p and λ z are the pole and zero, respectively, in the complex plane of wavelength, and r0

is the reflection coefficient for a basis structure, which is taken here to be the structure withoutslits; that is, w = 0. The values of pole and zero are determined from the reflection coefficientin the vicinity of resonance, where a pair of local maximum and minimum appear. A similarformula can be used to characterize the transmission coefficient.

Figure 8(a) shows the phases of reflection coefficients for the same grating structures as inFigs. 5 and 6. Around the nearly perfect absorption, the reflection phase experiences a drasticvariation for both structures. This is a standard feature associated with the appearance of a poleand a zero. For the grating structure with a top slab [cf. Fig. 5], λ z ≈ (1.0372+0.0002i)dand λ p ≈ (1.0329−0.0053i)d. For the grating structure with a bottom slab [cf. Fig. 6], λ z ≈(1.1773−0.0009i)d and λ p ≈ (1.1809−0.0073i)d. Note that the zeros are very close to thereal axis, indicating the occurrence of nearly perfect absorption at real wavelengths. The poles,on the other hand, are deviated from the real axis. In addition, the real parts of the zero and thepole for each structure are close to each other. In Fig. 8(b), the locations of complex poles andzeros are plotted for different slit width w. As the slit width varies from its optimal value (aroundw = 30 nm), the zeros begin to move away from the real axis and the absorption anomalygradually disappears. The above features occur as well for the transmission coefficient. Thetransmission level in the present configuration, however, is rather low over a substantial rangenear the resonance [cf. Figs. 5(a) and 6(a)]. The corresponding features for the transmissionpoles and zeros are slightly inconspicuous than for the reflection.

4. Concluding remarks

In conclusion, we have investigated the feature of strong absorption in intrinsically low-lossgrating structures. A nearly perfect absorption was attained in two-layered structures made of alow-loss metallic grating and a lossless dielectric slab. The enhanced absorption is attributed tothe hybridization of cavity-coupled surface plasmons and guided waves. The former gives riseto enhanced absorption in standalone gratings, whereas the latter reinforces the absorption inthe composite grating structures to its extreme value. Due to the highly resonance nature, theabsorption spectrum depicts a very sharp profile and sensitive to the angle of incidence. Thesefeatures can be exploited for application in high quality detectors and sensors.

Acknowledgments

The authors thank Prof. C. T. Chan for his helpful comments and suggestions. This work wassupported in part by National Science Council of the Republic of China under Contract No.NSC 99-2221-E-002-121-MY3.


nearly perfect absorption in intrinsically low-loss grating structures

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