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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 19510–19521
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Anomalous optical absorption in metallic gratings with subwavelength slits

Ruey-Lin Chern, Yu-Tang Chen, and Hoang-Yan Lin  »View Author Affiliations


Optics Express, Vol. 18, Issue 19, pp. 19510-19521 (2010)
http://dx.doi.org/10.1364/OE.18.019510


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Abstract

The absorption in metallic gratings with subwavelength slits is theoretically investigated. Anomalous optical absorption occurs over a wide range of incident angles for TM and TE polarizations with different geometric parameters. In particular, a nearly perfect absorbance up to 99.5% with a significant bandwidth is attained for TM polarization with compound slits. Enhanced absorption is associated with extreme concentration of fields inside the structure. The respective field pattern depicts a special feature of surface plasmons excited on single interface only, which are identified as semibonding modes. The anomalous absorption is also achieved for TE polarization, when the compound grating is reduced to a simple grating. For this polarization, the anomalous absorption is attributed to the occurrence of trapped modes, with a slightly smaller absorbance (98.4%).

© 2010 Optical Society of America

1. Introduction

Extraordinary optical transmission through subwavelength holes or slits has been the subject of intensive research in the last decade [1

1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

, 2

2. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]

]. The transmission efficiency through subwavelength hole arrays can be orders of magnitude greater than predicted by the diffraction theory for small holes [3

3. H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163–182 (1944). [CrossRef]

]. The physical origin of enhanced transmission is attributed to the excitation of surface plasmons on the metal surfaces [1

1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

] as well as the waveguide modes associated with the holes [4

4. Z. Ruan and M. Qiu, “Enhanced Transmission through Periodic Arrays of Subwavelength Holes: The Role of Localized Waveguide Resonances,” Phys. Rev. Lett. 96, 233901 (2006). [CrossRef] [PubMed]

]. For thin metal films with periodic holes of infinite extent, a full transmission can even be attained [5

5. F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E 72, 016608 (2005). [CrossRef]

, 6

6. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007). [CrossRef]

]. In this situation, the fields scattered by the metal holes (under the plane wave incidence) are strongly confined near the surface, without causing reflection or attenuating transmission in the far field.

A similar resonance mechanism of light being concentrated into subwavelength region of an absorbing material leads to another interesting phenomenon, that is, extraordinary optical absorption, which may find important applications in ultrasmall detectors [7

7. J. Rosenberg, R. V. Shenoi, T. E. Vandervelde, S. Krishna, and O. Painter, “A multispectral and polarization-selective surface-plasmon resonant midinfrared detector,” Appl. Phys. Lett. 95, 161101 (2009). [CrossRef]

], selective thermal emitters [8

8. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009). [CrossRef]

], and high-efficiency solar cells [9

9. K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93, 121904 (2008). [CrossRef]

, 10

10. Y. Park, E. Drouard, O. E. Daif, X. Letartre, P. Viktorovitch, A. Fave, A. Kaminski, M. Lemiti, and C. Seassal, “Absorption enhancement using photonic crystals for silicon thin film solar cells,” Opt. Express 17, 14312–14321 (2009). [CrossRef] [PubMed]

]. The absorption enhancement factor through subwavelength slits can well exceeds the enhancement for transmission [11

11. J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009). [CrossRef] [PubMed]

]. Various designs of subwavelength structures may even give rise to nearly perfect absorbance [12

12. T. V. Teperik, V. V. Popov, and F. J. García de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005). [CrossRef]

, 13

13. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect Metamaterial Absorber,” Phys. Rev. Lett. 100, 207402 (2008). [CrossRef] [PubMed]

, 14

14. V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings,” Phys. Rev. B 78, 205405 (2008). [CrossRef]

, 8

8. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009). [CrossRef]

, 15

15. Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79, 045131 (2009). [CrossRef]

, 16

16. L. Dai and C. Jiang, “Anomalous near-perfect extraordinary optical absorption on subwavelength thin metal film grating,” Opt. Express 17, 20502–20514 (2009). [CrossRef] [PubMed]

]. In this situation, all incident electromagnetic power has been absorbed in the system, depicting an anomalous feature of no reflection and no transmission.

In contrast to the anomalous absorption in the medium having a large imaginary part of the permittivity [17

17. D. K. Gramotnev, “Anomalous absorption of TM electromagnetic waves by an ultrathin layer: optical analog of liquid friction,” Opt. Lett. 23, 91–93 (1998). [CrossRef]

], a small absorption coefficient is usually sufficient for the enhanced absorption in the subwavelength structures. The extreme light concentration can profoundly increase the optical absorption rate [18

18. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010). [CrossRef] [PubMed]

]. For thin metal films, the enhanced absorption is attributed to short range surface plasmons [19

19. J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How Holes Can Obscure the View: Suppressed Transmission through an Ultrathin Metal Film by a Subwavelength Hole Array,” Phys. Rev. Lett. 103, 203901 (2009). [CrossRef]

, 20

20. I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79, 161406 (2009). [CrossRef]

]. These waves are one of the two basic types of surface plasmons in metal films [21

21. E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539–554 (1969). [CrossRef]

], with the charge distribution being symmetric between the top and bottom surfaces [22

22. Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008). [CrossRef]

, 23

23. J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80, 205417 (2009). [CrossRef]

]. In this regard, short range surface plasmons are also termed as bonding modes. The associated electric fields in the metal film are essentially parallel to the surface. In the presence of a small damping, these waves are strongly damped.

Theoretically, the maximum absorbance in single-layer planar structures is 50% [6

6. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007). [CrossRef]

], where one half of the incident power is either reflected or transmitted. In order to reach the rather demanding condition of total absorption, where the reflection and transmission vanish simultaneously, some complexity has to be added in the system. From the scattering point of view, the scattered fields from a planar structure are expected to be drastically different between the two sides. On the incident side, the scattered field is evanescent and therefore no reflection exist in the far field. This is the typical feature of surface waves, which also appear in the enhanced transmission. On the transmission side, on the other hand, the scattered field has to be propagative so that the transmission through the structure is canceled out by a destructive interference with the incident field. Once the two distinct conditions are fulfilled by the same structure, the total absorption becomes feasible.

In the present study, we investigate the feature of anomalous optical absorption in metallic gratings with subwavelength slits. The metallic grating contains two slits in a unit cell and is sandwiched between two dielectric slabs. A nearly perfect absorbance up to 99.5% with a significant bandwidth (around 220 nm) is attained for TM polarization. The enhanced absorption is due to extreme concentration of fields inside the structure as the resonance occurs. In particular, the resonance field pattern is associated with surface plasmons excited on the top surface of the grating but not on the bottom. The highly asymmetric profile depicts the feature of semibonding modes, which are apparently different from either the bonding or antibonding modes that usually appear in thin metal films. For the present structure, the enhanced absorption is shown to occur over a wide range of incident angles. The extraordinary optical absorption is also achieved for TE polarization, with a slightly smaller absorbance (A ≈ 98.4%). This occurs when the two slits in the unit cell are merged into a larger slit. For this polarization, surface plasmons and the associated bonding structures do not exist. The enhanced absorption is attributed to the occurrence of trapped modes, with the fields being strongly confined within the structure.

Fig. 1. Schematic of the metallic grating with compound subwavelength slits sandwiched between two dielectric slabs, where a is the grating period, t is the grating thickness, h is the slab thickness, s is the slit width, and d is the distance between slits. The grating and slabs are made of aluminum (Al) and polysilicon (p-Si), respectively.

2. Results and discussion

Consider a metallic grating which contains two slits in a unit cell and is sandwiched between two dielectric slabs, as schematically shown in Fig. 1. The grating and slabs are made of aluminum (Al) and polysilicon (p-Si), respectively. A plane wave is incident from above and the frequency domain finite element method [24

24. J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, New York, 2002).

] is employed to solve the time-harmonic wave equations. The dielectric constants for Al and p-Si are taken from the solid handbook [25

25. E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, New York, 1985).

]. Once the electromagnetic fields are 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 [26

26. R. L. Chern and W. T. Hong, “Transmission resonances and antiresonances in metallic arrays of compound subwavelength holes,” J. Opt. 12, 065101 (2010). [CrossRef]

, 27

27. Y. T. Chen, R. L. Chern, and H. Y. Lin, “Multiple Fano resonances in metallic arrays of asymmetric dual stripes,” Appl. Opt. 49, 2819–2826 (2010). [CrossRef] [PubMed]

]. The absorbance A in the system is given as A = 1 − RT. According to the Poynting theorem [28

28. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

], the time-averaged power loss density (per unit volume) is given by dPlossdV=12ωεE2 , where ε″ is the imaginary part of the dielectric constant. 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.

2.1. Nearly perfect absorption

Consider the transverse magnetic (TM) polarization, where the magnetic fields are oriented perpendicular to the propagation direction. Figure 2(a) shows the absorbance, along with the reflectance and transmittance, for the metallic grating with compound subwavelength slits sandwiched between two dielectric slabs as sketched in Fig. 1, where a = 400 nm, s = 80 nm, d = 40 nm, t = 210 nm, and h = 50 nm. It is shown that a nearly perfect absorbance A ≈ 99.5% is attained at λ ≈ 891 nm with a significant bandwidth (full width at half maximum) about 220 nm.

Fig. 2. (a) Absorbance (along with reflectance and transmittance) of the metallic (Al) grating with compound subwavelength slits sandwiched between two dielectric (p-Si) slabs as sketched in Fig. 1, where a = 400 nm, s = 80 nm, d = 40 nm, t = 210 nm, and h = 50 nm. (b) Effect of the attachment of top and bottom dielectric slabs to the metallic grating on the absorbance.
Fig. 3. Effect of the Al grating on the absorbance. Solid line is the result for the same structure as in Fig. 2(a). Dashed line is the result of replacing the Al grating with a homogeneous Al slab of the same thickness (t = 210 nm). Dash-dotted and dotted lines are results for a single Al slab of thickness 210 nm and for a single p-Si slab of thickness 50 nm, respectively.

The transmittance T is rather small (T < 0.09) over the most wavelength range, while the reflectance R experiences significant variations. In particular, R has an inverse Lorentzian line shape and approaches zero near λ ≈ 891 nm. The coincidence of R ≈ 0 and T ≈ 0 gives rise to A ≈ 1. It is also shown in Fig. 2(b) that the attachment of a dielectric slab to the metallic grating from either top or bottom substantially increases the absorption. The top slab is obviously able to bring about a larger absorption than the bottom slab. When both the top and bottom slabs are included, the underlying grating structure is close to a perfect absorber at a certain frequency. In addition to the nearly perfect absorption, two extra enhanced absorptions occur at λ ≈ 614 nm and λ ≈ 414 nm, but with weaker absorbance A ≈ 67.8% and A ≈ 84%, respectively.

The effect of the Al grating on the absorption is shown in Fig. 3. When the Al grating is replaced by a homogeneous Al slab of the same thickness (t = 210 nm), the maximum absorption efficiency at λ ≈ 891 nm is substantially reduced to 72.3% (with the peak position shifted to λ ≈ 866 nm). This shows that the anomalous (nearly perfect) absorption at λ ≈ 891 nm is attributed to the presence of the grating with slits. A particular mode of resonance (which will be identified as the semibonding mode in Sec. 2.2) is associated with the underlying grating structure and reinforces the absorption efficiency up to 99.5%. Meanwhile, the absorption peak at λ ≈ 614 nm does not appear. Another absorption peak near 414 nm is due to p-Si and less affected by the grating structure. For comparison, the absorption efficiencies for a single Al slab of thickness 210 nm and for a single p-Si slab of thickness 50 nm are shown in the same plot.

The specific structure in the present study was chosen based on the following considerations. First, the metallic grating is a typical structure to produce the enhanced absorption up to 50% [20

20. I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79, 161406 (2009). [CrossRef]

], which is attributed to the excitation of surface plasmons. Second, the absorption of the metallic structure can be further enhanced by the attachment of dielectric slabs so that the fields can be guided inside the slabs to increase the absorption. Third, the compound slits are introduced to add certain degree of complexity in the grating structure so that the nearly 100% absorption could be obtained through optimization of geometric parameters.

Figure 4 shows the variations of absorbance with respect to the dielectric slab thickness h, metallic grating thickness t, slit width s, and distance between slits d. For all cases, the grating period a is 400 nm and the wavelength is fixed at 891 nm, where the maximum absorption occurs. It is shown that the absorbance is sensitive to the change of slab thickness h and the optimal value is around 50 nm [Fig. 4(a)]. The change of grating thickness t, on the other hand, has a less influence on the absorption. In the range between 100 nm to 300 nm, the absorption curve tends to be flat and is close to unity, the optimal value being around t = 210 nm [Fig. 4(b)]. The change of slit width s shows a smooth variation of the absorption about the optimal value s = 80 nm [Fig. 4(c)]. Narrower slits are in general likely to result in larger absorptions than wider slits. The effect of distance between slits d on the absorption is similar to that of slit width s and the optimal value is around d = 40 nm [Fig. 4(d)].

Fig. 4. Variations of absorbance (along with reflectance and transmittance) with respect to (a) dielectric slab thickness h, where t = 210 nm, s = 80 nm, and d = 40 nm, (b) metallic grating thickness t, where h = 50 nm, s = 80 nm, and d = 40 nm, (c) slit width s, where h = 50 nm, t = 210 nm, and d = 40 nm, and (d) distance between slits d, where h = 50 nm, t = 210 nm, and s = 80 nm. For all cases, the grating period a = 400 nm and λ ≈ 891 nm.

For oblique incidence, the absorbance as a function of parallel wave number (k a/2π) and frequency (ωa/2πc) is plotted in Fig. 5(b), where k = k 0 sin θ. There are three major absorption bands extending from the three absorption peaks at normal incidence (k =0) to the grazing incidence (k =k 0). The lowest absorption band (around λ ≈ 891 nm), where the nearly perfect absorption occurs, spreads a wide range of incident angles, with its center frequency basically unchanged. For instance, A ≈ 98.5% at λ ≈ 896 nm for θ = 30° and A ≈ 94.1% at λ ≈ 894 nm for θ = 50°. The second absorption band at a higher frequency (around λ ≈ 614 nm) shows a similar feature until it is partially blocked by the line of band folding (denoted by the black dashed line). The third absorption band is located near λa and extends toward the light line, becoming broadened and even intensified. The peak frequencies of these bands basically do not alter with k , showing a character of site resonance, that is, a resonance associated with individual slits rather than the whole lattice. Site and lattice (or grating) resonances are two basic types of resonances in periodic structures [29

29. F. J. García de Abajo, J. J. Sáenz, I. Campillo, and J. S. Dolado, “Site and lattice resonances in metallic hole arrays,” Opt. Express 14, 7–18 (2006). [CrossRef]

]. The two modes are in general coupled with each other. In the present configuration, the grating period is essential to give rise to the nearly perfect absorption. This can be realized that if the Al grating is replaced by a homogeneous Al slab, the maximum absorption is substantially reduced [cf. Fig. 3].

Fig. 5. (a) Power loss in the metallic grating (Al), the dielectric slabs (p-Si), and the whole system for the same grating structure as in Fig. 2. (b) Absorbance as a function of parallel wave number (k a/2π) and frequency (ωa/2πc). Black solid line stands for the light line ω = k c, which corresponds to the grazing incidence (θ = 90°). Black dashed line denotes the band folding due to periodicity.

2.2. Feature of semibonding mode

In order to illustrate the features of anomalous absorption for the underlying grating structure, the electric field patterns associated with the three absorption peaks at normal incidence are plotted in Fig. 6(a). The electric fields Ey at λ ≈ 414 nm and 614nm depict a symmetric and an antisymmetric pattern, respectively, about the top and bottom surfaces. The former is identified as the antibonding mode and the latter as the bonding mode. In particular, the bonding mode is characterized by a symmetric alignment of surface charges on the top and bottom surfaces, while the antibonding mode has an antisymmetric charge alignment [23

23. J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80, 205417 (2009). [CrossRef]

]. Therefore, the vertical electric fields associated with the bonding mode point in opposite directions on the two surfaces, leading to an antisymmetric pattern of Ey. The antibonding mode, on the other hand, is associated with a symmetric pattern of vertical electric fields. They are two standard modes that usually occur in thin metallic films [21

21. E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539–554 (1969). [CrossRef]

]. The bonding mode has a lower frequency and a larger decay rate (strongly damped), known as short range surface plasmon, while the antibonding mode has a higher frequency and a smaller decay rate (weakly damped), and is termed as long range surface plasmon [22

22. Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008). [CrossRef]

, 23

23. J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80, 205417 (2009). [CrossRef]

].

The occurrence of short range surface plasmon (bonding mode) has been identified as the cause of enhanced absorption (or suppressed transmission) in thin metallic structures [19

19. J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How Holes Can Obscure the View: Suppressed Transmission through an Ultrathin Metal Film by a Subwavelength Hole Array,” Phys. Rev. Lett. 103, 203901 (2009). [CrossRef]

, 20

20. I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79, 161406 (2009). [CrossRef]

].

Fig. 6. (a) Vertical electric fields Ey, (b) horizontal electric fields Ex, and (c) time-averaged power loss density dP loss/dV associated with the absorption peaks at λ ≈ 414 nm (left), 614nm (center), and 891nm (right) in Fig. 2. In (c), the signs of surface charges at the top and bottom surfaces are overlaid to illustrate the features of antibonding (left), bonding (center), and semibonding (right).

In the present problem, however, both the bonding and antibonding modes correspond to enhanced absorption. The antibonding mode at λ ≈ 414 nm even has a larger absorption than the bonding mode at λ ≈ 614 nm. This can be explained in two aspects. First, the sandwiched grating structure is considered a thick composite structure (the total thickness is 310 nm and the grating period is 400 nm). Although the typical features of bonding and antibonding modes as those in thin metal films are still present, their absorption properties may change. Second, the enhanced absorption associated with the long-range antibonding mode is attributed to its coupling with cavity resonance inside the slit. The corresponding fields are strongly concentrated inside the structure, leading to a large absorption rate [18

18. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010). [CrossRef] [PubMed]

]. This mechanism is similar to that of the short-range bonding mode.

A rather intriguing result is the field pattern associated with the nearly perfect absorption at λ ≈ 891 nm. The fields are strongly concentrated toward the top slab but are almost null on the bottom. This mode is characterized by the appearance of surface charges on only one side (top surface), which is different from the bonding or antibonding mode with the surface charges on two sides (top and bottom surfaces). The highly asymmetric pattern depicts a special character of semibonding mode, which is not observed in simple structures such as metal films. This feature is reminiscent of the secondary bonding (also named semibonding) structure of electric charges in atoms or molecules [30

30. N. W. Alcock, “Secondary bonding to nonmetallic elements,” Adv. Inorg. Chem. pp. 1–58 (1972). [CrossRef]

, 31

31. N. W. Alcock, Bonding and Structure: Structural Principles in Inorganic and Organic chemistry (Ellis Horwood, New York, 1990).

]. It is not a normal bonding as in simple molecules and may appear in a more complex system.

In the present problem, the excitation of semibonding mode provides a mechanism for the phenomenon of perfect (or nearly perfect) absorption. This can be understood from the aspect of scattered wave. On the one hand, the bonding on the top (incident) side gives rise to surface waves that decay exponentially away from the surface. No reflected waves will therefore go to infinity. The lack of bonding on the bottom (transmission) side, on the other hand, allows propagating waves through the structure and may destructively interfere with the incident wave. As a result, the concurrence of zero reflection and zero transmission is possible to occur, all the incident power being absorbed in the lossy medium. The drastically different nature of the scattered waves on the two sides responds to the special character of a semibonding mode. In Fig. 6(c), the features of bonding, antibonding, and semibonding are illustrated with the signs of surface charges on the top and bottom surfaces.

In another aspect, the electric fields Ex associated with the three absorption peaks are plotted in Fig. 6(b). The field component along the grating surface is mainly responsible for the absorption in the layered structure. In the present configuration, the fields Ex are much more intense on the top surface than on the bottom. When ε″ of the metal grating (Al) or dielectric slab (p-Si) becomes significant, the absorption tends to be large as well. To illustrate the distribution of absorption in the grating structure, the time-averaged power loss density (per unit volume) dP loss/dV associated with the three absorption peaks is plotted in Fig. 6(c). The pattern at λ ≈ 414 nm shows that the power loss density is mainly distributed over the top slab, while the pattern at λ ≈ 614 nm is largely concentrated on the upper and lower sides of the grating, with a small portion on the dielectric slab. In particular, the pattern at λ ≈ 891 nm shows an extreme concentration of power loss at the top side of the grating.

2.3. TE polarization

Next, consider the transverse electric (TE) polarization, where the electric fields are oriented perpendicular to the propagation direction. Figure 7(a) shows the absorbance, reflectance, and transmittance for the metallic grating structure, where the geometric parameters are the same as for TM polarization (cf. Fig. 2) except that d = 0, the two slits in the unit cell being merged into a larger slit. For TE polarization, the anomalous optical absorption, with a slightly smaller absorption efficiency than that for TM polarization, is still achieved. The maximum absorbance A ≈ 98.4% is attained at λ ≈ 721 nm with a resonance width (full width at half maximum) about 58 nm. Near this wavelength, the reflectance R also has an inverse Lorentzian line shape. The transmittance T is even smaller than that for TM polarization. Another absorption peak at λ ≈ 434 nm has a smaller absorbance A ≈ 91.1%, while the peak at λ ≈ 542 nm becomes much weaker (A ≈ 18.3%).

The absorbance as a function of parallel wave number (k a/2π) and frequency (ωa/2πc) is plotted in Fig. 7(b), which shows a very different character from that for TM polarization [cf. Fig. 5(b)]. As the incident angle increases, the lowest absorption peak at λ ≈721 nm for normal incidence splits into two bands. The two splitting bands correspond to a positive and a negative diffraction order, which is illustrated in Fig. 8 with the time-averaged Poynting vectors S=12Re[E×H*] at the two major absorption peaks for θ = 10° [indicated by the white circles in Fig. 7(b)]. At λ ≈ 687 nm, in particular, the vectors 〈S〉 near the top surface are directed to the right, showing a positive diffraction order associated with the higher frequency band, whereas the vectors 〈S〉 at λ ≈ 735 nm are directed to the left and correspond to a negative diffraction order with the lower frequency band. The feature of splitting indicates that the frequency of major absorption band no longer remains unchanged with the incident angle, as in the TM polarization. By the attachment of dielectric slabs, the frequency splitting occurs at a relatively lower frequency than that of the band folding (usually around λa). On the other hand, the higher absorption band maintains around the same frequency and becomes weakened as the incident angle increases.

Fig. 7. (a) Absorbance (along with reflectance and transmittance) of the grating structure for TE polarization, where the geometric parameters are the same as for TM polarization (cf. Fig. 2) except that d = 0. (b) Absorbance as a function of parallel wave number (k a/2π) and frequency (ωa/2πc) for the same grating structure. The dotted line indicates the oblique incident angle of θ = 10°, on which the white circles are crossing points with the two major absorption bands.
Fig. 8. Time-averaged Poynting vectors 〈S〉, overlaid with the color contours of electric fields Ez, associated with the two major absorption peaks for θ = 10° at λ ≈ 687 nm (left) and 735nm (right) [indicated by the white circles in Fig. 7(b)].
Fig. 9. (a) Electric field Ez and (b) time-averaged power loss density dP loss/dV associated with the absorption peaks at λ ≈ 434 nm (left) and 721nm (right) in Fig. 7(a).

As the electric fields are oriented in the z direction, which is parallel to the metal surface, surface charges do not exist. Surface plasmons and the associated bonding modes that occur in TM polarization are not present either. The enhanced absorption for TE polarization, instead, is attributed to the occurrence of trapped modes [32

32. A. G. Borisov, F. J. García de Abajo, and S. V. Shabanov, “Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials,” Phys. Rev. B 71, 075408 (2005). [CrossRef]

]. In these modes, the electromagnetic fields are largely confined within the structure. Figure 9(a) shows the electric fields Ez associated with the two larger absorption peaks. Note that the fields are strongly concentrated at the top slab for both peaks. In particular, the maximum of Ez for λ ≈ 721 nm is located at the center of the top slab, while for λ ≈ 434 nm it is located on the two edges, with a node at the center. This feature typically shows a low-order and a high-order oscillation pattern associated with the two absorption peaks. As the fields are trapped inside the structure, the enhanced absorption is likely to occur when the resonance condition is reached. In fact, the trapped modes have also been identified as the origin of enhanced transmission for TE polarization [32

32. A. G. Borisov, F. J. García de Abajo, and S. V. Shabanov, “Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials,” Phys. Rev. B 71, 075408 (2005). [CrossRef]

, 33

33. E. Moreno, L. Martin-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94–S97 (2006).

, 34

34. D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007). [CrossRef] [PubMed]

, 35

35. Y. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, “Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits,” Appl. Phys. Lett. 93, 061102 (2008). [CrossRef]

].

Finally, the distribution of power loss density dP loss/dV for the two absorption peaks is plotted in Fig. 9(b). For the low-frequency mode at λ ≈ 721 nm, the absorption is mainly due to the metallic grating (Al), while for the high-frequency peak λ ≈ 434 nm, the absorption is due to the dielectric slabs (p-Si). This feature is similar to that for TM polarization [cf. Fig. 6(c)] except that the power loss density in the dielectric slab for the high-frequency absorption peak is more concentrated near the slit.

3. Concluding remarks

In conclusion, we have investigated the anomalous optical absorption in metallic gratings of subwavelength slits. The absorption in the grating structure is substantially enhanced when it is sandwiched between two dielectric slabs. In particular, a nearly perfect absorption efficiency up to 99.5% with a significant bandwidth (220 nm) is attained at λ ≈ 891 nm for TM polarization. This value is significantly larger than the absorbance when the Al grating is replaced by a homogeneous Al slab (72.3%). The nearly perfect absorption is associated with the excitation of a special type of surface plasmon identified as the semibonding mode. The respective surface charges appear on only one of the two surfaces, which are apparently different from those for either the bonding or antibonding mode usually observed in metal films. The feature of anomalous absorption is also present for TE polarization, with a slightly smaller absorbance (98.4%). This occurs when the two slits in a unit cell are merged into a larger slit and the resulting structure is reduced to a simple grating. For this polarization, surface plasmons do not exist and the enhanced absorption is attributed to the occurrence of trapped modes.

Acknowledgments

This work was supported in part by National Science Council of the Republic of China under Contracts No. NSC 96-2221-E-002-190-MY3 and NSC 99-2221-E-002-140.

References and links

1.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

2.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]

3.

H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163–182 (1944). [CrossRef]

4.

Z. Ruan and M. Qiu, “Enhanced Transmission through Periodic Arrays of Subwavelength Holes: The Role of Localized Waveguide Resonances,” Phys. Rev. Lett. 96, 233901 (2006). [CrossRef] [PubMed]

5.

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E 72, 016608 (2005). [CrossRef]

6.

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007). [CrossRef]

7.

J. Rosenberg, R. V. Shenoi, T. E. Vandervelde, S. Krishna, and O. Painter, “A multispectral and polarization-selective surface-plasmon resonant midinfrared detector,” Appl. Phys. Lett. 95, 161101 (2009). [CrossRef]

8.

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009). [CrossRef]

9.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93, 121904 (2008). [CrossRef]

10.

Y. Park, E. Drouard, O. E. Daif, X. Letartre, P. Viktorovitch, A. Fave, A. Kaminski, M. Lemiti, and C. Seassal, “Absorption enhancement using photonic crystals for silicon thin film solar cells,” Opt. Express 17, 14312–14321 (2009). [CrossRef] [PubMed]

11.

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009). [CrossRef] [PubMed]

12.

T. V. Teperik, V. V. Popov, and F. J. García de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005). [CrossRef]

13.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect Metamaterial Absorber,” Phys. Rev. Lett. 100, 207402 (2008). [CrossRef] [PubMed]

14.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings,” Phys. Rev. B 78, 205405 (2008). [CrossRef]

15.

Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79, 045131 (2009). [CrossRef]

16.

L. Dai and C. Jiang, “Anomalous near-perfect extraordinary optical absorption on subwavelength thin metal film grating,” Opt. Express 17, 20502–20514 (2009). [CrossRef] [PubMed]

17.

D. K. Gramotnev, “Anomalous absorption of TM electromagnetic waves by an ultrathin layer: optical analog of liquid friction,” Opt. Lett. 23, 91–93 (1998). [CrossRef]

18.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010). [CrossRef] [PubMed]

19.

J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How Holes Can Obscure the View: Suppressed Transmission through an Ultrathin Metal Film by a Subwavelength Hole Array,” Phys. Rev. Lett. 103, 203901 (2009). [CrossRef]

20.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79, 161406 (2009). [CrossRef]

21.

E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539–554 (1969). [CrossRef]

22.

Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008). [CrossRef]

23.

J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80, 205417 (2009). [CrossRef]

24.

J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, New York, 2002).

25.

E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, New York, 1985).

26.

R. L. Chern and W. T. Hong, “Transmission resonances and antiresonances in metallic arrays of compound subwavelength holes,” J. Opt. 12, 065101 (2010). [CrossRef]

27.

Y. T. Chen, R. L. Chern, and H. Y. Lin, “Multiple Fano resonances in metallic arrays of asymmetric dual stripes,” Appl. Opt. 49, 2819–2826 (2010). [CrossRef] [PubMed]

28.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

29.

F. J. García de Abajo, J. J. Sáenz, I. Campillo, and J. S. Dolado, “Site and lattice resonances in metallic hole arrays,” Opt. Express 14, 7–18 (2006). [CrossRef]

30.

N. W. Alcock, “Secondary bonding to nonmetallic elements,” Adv. Inorg. Chem. pp. 1–58 (1972). [CrossRef]

31.

N. W. Alcock, Bonding and Structure: Structural Principles in Inorganic and Organic chemistry (Ellis Horwood, New York, 1990).

32.

A. G. Borisov, F. J. García de Abajo, and S. V. Shabanov, “Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials,” Phys. Rev. B 71, 075408 (2005). [CrossRef]

33.

E. Moreno, L. Martin-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94–S97 (2006).

34.

D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007). [CrossRef] [PubMed]

35.

Y. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, “Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits,” Appl. Phys. Lett. 93, 061102 (2008). [CrossRef]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(300.1030) Spectroscopy : Absorption

ToC Category:
Diffraction and Gratings

History
Original Manuscript: July 2, 2010
Revised Manuscript: August 8, 2010
Manuscript Accepted: August 20, 2010
Published: August 30, 2010

Citation
Ruey-Lin Chern, Yu-Tang Chen, and Hoang-Yan Lin, "Anomalous optical absorption in metallic gratings with subwavelength slits," Opt. Express 18, 19510-19521 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19510


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References

  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]
  2. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]
  3. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944). [CrossRef]
  4. Z. Ruan, and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006). [CrossRef] [PubMed]
  5. F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72, 016608 (2005). [CrossRef]
  6. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007). [CrossRef]
  7. J. Rosenberg, R. V. Shenoi, T. E. Vandervelde, S. Krishna, and O. Painter, “A multispectral and polarization-selective surface-plasmon resonant midinfrared detector,” Appl. Phys. Lett. 95, 161101 (2009). [CrossRef]
  8. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009). [CrossRef]
  9. K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93, 121904 (2008). [CrossRef]
  10. Y. Park, E. Drouard, O. E. Daif, X. Letartre, P. Viktorovitch, A. Fave, A. Kaminski, M. Lemiti, and C. Seassal, “Absorption enhancement using photonic crystals for silicon thin film solar cells,” Opt. Express 17, 14312–14321 (2009). [CrossRef] [PubMed]
  11. J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34, 686–688 (2009). [CrossRef] [PubMed]
  12. T. V. Teperik, V. V. Popov, and F. J. García de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005). [CrossRef]
  13. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). [CrossRef] [PubMed]
  14. V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Plasmonic blackbody: almost complete absorption of light in nanostructured metallic coatings,” Phys. Rev. B 78, 205405 (2008). [CrossRef]
  15. Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonics metamaterial,” Phys. Rev. B 79, 045131 (2009). [CrossRef]
  16. L. Dai, and C. Jiang, “Anomalous near-perfect extraordinary optical absorption on subwavelength thin metal film grating,” Opt. Express 17, 20502–20514 (2009). [CrossRef] [PubMed]
  17. D. K. Gramotnev, “Anomalous absorption of TM electromagnetic waves by an ultrathin layer: optical analog of liquid friction,” Opt. Lett. 23, 91–93 (1998). [CrossRef]
  18. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010). [CrossRef] [PubMed]
  19. J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How holes can obscure the view: suppressed transmission through an ultrathin metal film by a subwavelength hole array,” Phys. Rev. Lett. 103, 203901 (2009). [CrossRef]
  20. I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79, 161406 (2009). [CrossRef]
  21. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969). [CrossRef]
  22. Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008). [CrossRef]
  23. J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80, 205417 (2009). [CrossRef]
  24. J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 2002).
  25. E. D. Palik, and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1985).
  26. R. L. Chern, and W. T. Hong, “Transmission resonances and antiresonances in metallic arrays of compound subwavelength holes,” J. Opt. 12, 065101 (2010). [CrossRef]
  27. Y. T. Chen, R. L. Chern, and H. Y. Lin, “Multiple Fano resonances in metallic arrays of asymmetric dual stripes,” Appl. Opt. 49, 2819–2826 (2010). [CrossRef] [PubMed]
  28. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  29. F. J. García de Abajo, J. J. Sáenz, I. Campillo, and J. S. Dolado, “Site and lattice resonances in metallic hole arrays,” Opt. Express 14, 7–18 (2006). [CrossRef]
  30. N. W. Alcock, “Secondary bonding to nonmetallic elements,” Adv. Inorg. Chem. 15, 1–58 (1972). [CrossRef]
  31. N. W. Alcock, Bonding and Structure: Structural Principles in Inorganic and Organic chemistry (Ellis Horwood, 1990).
  32. A. G. Borisov, F. J. García de Abajo, and S. V. Shabanov, “Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials,” Phys. Rev. B 71, 075408 (2005). [CrossRef]
  33. E. Moreno, L. Martin-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A, Pure Appl. Opt. 8, S94–S97 (2006).
  34. D. Crouse, and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007). [CrossRef] [PubMed]
  35. Y. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, “Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits,” Appl. Phys. Lett. 93, 061102 (2008). [CrossRef]

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