806
J. Opt. Soc. Am. B / Vol. 31, No. 4 / April 2014
Li et al.
Unexpected unidirectional perfect absorption of light in a freestanding optical thin metallic grating with extremely small filling factor Hu-Quan Li, Ke-Jia Wang, Zhen-Gang Yang, and Jin-Song Liu* Wuhan National Laboratory for Optoelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China *Corresponding author:
[email protected] Received January 17, 2014; revised February 19, 2014; accepted February 19, 2014; posted February 19, 2014 (Doc. ID 204764); published March 13, 2014 In this paper, we predict an unexpected enhanced optical absorption (OA) phenomenon in an optical thin (60 nm) freestanding metallic grating. After introducing periodical back grooves to the grating, the absorption could be enhanced up to 95% for light incident from the topside, which is inhibited lower than 10% for light incident from the bottom side. Physically it is ascribed to the strong modulation effect of the surface plasmons (SPs)/or charge distribution on the back surface of the grating by the grooves. As a result, the reflection at the SPs resonant position is greatly inhibited. It indicates a new mechanism to achieve high OA in a freestanding subwavelength structure by directly controlling the SPs. More counterintuitively, the highly enhanced absorption will increase as the filling factor of the grating decreases, rather than decrease as the filling factor decreases. So even for a very small filling factor (0.5), unexpected high OA up to 95% could be attained at SPs resonance. The underlying physical mechanism is analyzed with a dipole moment description. © 2014 Optical Society of America OCIS codes: (240.0240) Optics at surfaces; (240.6680) Surface plasmons; (050.0050) Diffraction and gratings; (290.5880) Scattering, rough surfaces. http://dx.doi.org/10.1364/JOSAB.31.000806
1. INTRODUCTION In recent years, lots of functional devices have been designed based on the extraordinary optical absorption (EOA) phenomena in metallic films with periodical subwavelength defects, such as photodetectors [1], narrowband thermal emitters [2], thermophotovoltaics (TPV) [3], and thin film solar cells [4]. The physical origins of these EOA phenomena are generally admitted as the excitation of surface plasmons (SPs) [or spoof surface plasmons (SSPs) for highly conducting structures [5]] on the metallic-dielectric interfaces, and/or the Fabry–Perot (FP)-like cavity mode (CM) resonances in the defects [6]. Recently, Spevak reported strong OA (∼50%) in a nearly transparent ultrathin metallic film by introducing periodical defects (slits) to it [7]. The absorption is ascribed to the excitation of short range SPs [8–10] on the metal surface. In their simulation, the grating slits are filled with an absorptive dielectric material with permittivity of εslit 0.2εgold to absorb the lights localized by the metallic grating, which is a commonly used method to achieve high absorption in subwavelength structures. Another mechanism is also evidenced by Roszkiewicz and Nasalski [11] to realize strong OA (∼75%) in an optical thin (∼50 nm) metallic grating with a high filling factor up to 0.94. In the structure, the grating thickness is well chosen to simultaneously excite the SPs and the CMs. Three conditions are necessary for their strong OA: first, the grating must be thin enough to permit additional coupling between SPs through the metal stripes; second, the grating must be thick enough to sustain CMs in the slits; third, the filling factor must be very large (∼0.94). Meanwhile, the strong OA is only attained under normal incidence of TM polarized lights and 0740-3224/14/040806-04$15.00/0
will be strongly suppressed for oblique incidence. However, the underlying physical mechanisms for EOA in an ultrathin metallic film are quite complex if asymmetric defects are introduced. So it still requires more investigations, especially when it concerns the modulation of SPs. In this paper, we predict a new mechanism that can achieve much stronger (∼95%) OA in a freestanding optical thin (h 60 nm) silver grating by introducing periodical back grooves to it (Fig. 1, up). The absorption peak locates near the SPs resonance. However, due to the direct modulation effect of the back grooves on the charge distribution/or SPs on the bottom metallic surface, the absorption is greatly enhanced. However, the above-mentioned strong OA can only be obtained for light incident on the structure from topside due to the asymmetry. If light is inversely incident from the bottom side, absorption is greatly inhibited [Fig. 2(b)]. More counterintuitively, the absorbance at SPs resonance will increase as the filling factor decreases. So even for a very small filling factor, f w∕p 0.5, the absorbance at resonance could reach 95%; this exceeds the expectation for such a thin and small filled metallic structure. Moreover, it is evidenced that the strong OA is not limited to the normal incidence, only if the filling factor is relative large (≥0.8).
2. RESULTS AND DISCUSSION The grating period p and thickness h h1 h2 are fixed to be 500 and 60 nm, respectively. s is the slit width, and s21 and h2 are the width and depth of back groove, respectively. The ridge widths r 21 and r 22 are equal. The bottom part in Fig. 1 presents the charge distribution schematically according © 2014 Optical Society of America
Li et al.
Vol. 31, No. 4 / April 2014 / J. Opt. Soc. Am. B
xE+3
−0.36
z(µm)
to field pattern when the incident lights excite SPs on the metallic surface. Red circles indicate the positive charges, and green the negative charges. A rigorous coupled wave analysis [12] method is used to calculate the propagation of electromagnetic (EM) fields. The dielectric permittivity of silver is taken from the tabulated experimental datum by interpolation [13]. Figure 2 presents the transmittance (T, blue lines), reflectance (R, black lines) and absorbance (A, red lines) for a freestanding simple grating [(a), without back grooves] and the proposed structure [(b), with back grooves] under the normal incidence of TM polarized light. The dashed lines in Fig. 2(b) indicate the results for light incident on the structure from bottom side. The structural parameters are given as s 0.25 μm, s21 0.1 μm, and h2 10 nm. For the simple grating (a), the SPs resonant absorption peak locates at λ 0.5171 μm with absorbance of 53.45%. When back grooves are introduced to the simple grating, however, the absorption is highly enhanced up to 95% for light incident from topside [Fig. 2(b), red solid line], with resonant wavelength being slightly shifted to λ 0.5200 μm. It is clearly seen that introducing the back grooves has strongly suppressed the reflection at SPs resonance, which results in the highly enhanced absorption. In such a case, the incident light is well converted into SPs on the top surface of the grating; however, its propagation and back-transformation into outgoing photons [8–10] is strongly suppressed on the bottom surface of the grating. In contrast, if the light is inversely incident from the bottom side, the absorption will be strongly inhibited (red dashed lines) because the lights cannot be transformed into SPs successfully in this case. Hereafter, we focus on the enhanced absorption.
In order to interpret the physical mechanism behind the unexpected enhanced OA, we compute the EM field distributions (Fig. 3) in the vicinity of the grating at the resonant absorption peaks in Figs. 2(a) and 2(b). According to Fig. 3, the OA peaks clearly originate from the SPs excited by the incident lights and its resonant coupling on both surfaces. The EM fields at resonances are strongly localized near the grating in a range of resonant wavelengths. When the back grooves are introduced, as shown in (b1) and (b2), the ability of confinements of EM fields is strongly enhanced (the amplitudes). But how the back groove enhances the absorption needs more analysis. A dipole moment interpretation (Fig. 1, bottom) is used to explain the enhancement of the absorption in this paper. Following the previous discussion of Huang et al. [6], the TM-polarized light incident on the metallic grating from topside is first converted to SPs, which then propagate along the top conducting surface, until impeded by the slit corners to form oscillating dipoles at the entrances of the slits (ba). These oscillating dipoles act as light sources, which radiate some new wavelets into the slits to drive the free electrons on the slits walls moving toward the exits of slits. Consequently, new oscillating dipoles (cd) will be constructed at the exits of slits that act as light sources contributing to the transmission. Meanwhile, parts of wavelets are radiated back into the slits as a feedback. For a simple grating, the charge distribution on the bottom surface of the grating is nearly antisymmetric to that on the top surface except for some decrease in density. The charges are mostly localized at the openings of the slits in this case. From the results given in Fig. 2(a), we can see that the reflection at SPs resonance is relative high (∼40%) for a simple grating, which is different from the case of CMs resonance in an optical thick grating where reflection is strongly inhibited. The high reflection here is directly related to the feedback of oscillating dipoles (charges) formed at the exits of slits (cd) However, when back grooves are introduced, some of the charges that are previously localized at the exits of slits will be pulled to the exits of the grooves according to the tip effect (Fig. 1, bottom), which decreases the charge density at the exits of slits, i.e., weakens the dipoles cd equivalently. As a result, the reflection is strongly suppressed [Fig. 2(b)]. In fact, one may also
|E|
(a1)
−0.18
6
0
4 0.18
2
0
z(µm)
−0.36
(a2)
|H|
1
0.18
5
−0.36
6
0.25 x(µm)
|H|
0.5
(b2)
−0.18 4
0
2 0
0.25 x(µm)
0.5
10 8
0
6
0.18
4 2
0.36
0.36
15
0
0
−0.18
0.18
Fig. 2. Transmittance (T), reflectance (R), and absorbance (A) of (a) a simple silver grating (without back grooves) with parameters:p 0.5 μm, s 0.25 μm, and h 60 nm. (b) A dug grating (with back grooves) with parameters: p 0.5 μm, s 0.25 μm, s21 0.1 μm, h2 10 nm, and h 60 nm. Dashed lines represent the results for light incident from the bottom side.
(b1)
−0.18
0.5
z(µm)
(b)
0.25 x(µm)
|E|
0.36
0.36
(a)
xE+3
−0.36
8
z(µm)
Fig. 1. Structure of the silver grating under study. The red (positive) and green (negative) points represent the charges accumulated at the corners.
807
0
0.25 x(µm)
0.5
Fig. 3. (a1) (jEj) and (a2) (jHy j) correspond to the absorption peak in Fig. 2(a); (b1) (jEj) and (b2) (jHy j) correspond to the absorption peak in Fig. 2(b).
808
J. Opt. Soc. Am. B / Vol. 31, No. 4 / April 2014
Li et al.
wonder that the reflection prohibition may also originate from the destructive interference between the reflection of grooves and that of slits, since the incident light will penetrate the thin metal film and reach the groove. To clarify this query, we have also studied the case of thick grating in which the hypothetical destructive interference between the reflection of grooves and that of slits does not exist. Thick grating’s parameters are given as p 100 μm, h2 4 μm, h 8 μm, and s 20 μm. For a simple grating case (s21 0.0 μm), the reflection at SPs resonance (λ 100.3 μm) is as high as 82.44%, and the absorption is as low as 16.84%. However, when back grooves are introduced (s21 20 μm), the reflection at SPs resonance (been shifted to λ 100.9 μm) is nearly all inhibited, resulting in highly enhanced absorption 94.7%. In addition, the field distributions were also calculated. All these results support our opinion on the mechanism of reflection prohibition. On the other hand, new dipoles ef and ig are formed at the exits of grooves, which are inverse to cd. Accordingly, the wavelets emitted by them will interfere destructively in output region III, resulting in transmission inhibition. As a consequence, the energy at SPs resonance is strongly confined to the grating. Based on the above interpretation, the key to effectively inhibit the reflection and realize strong OA at the SPs resonance is weakening the oscillating dipoles (charge density) at the exits of the slits. In Fig. 4, we calculated the absorbance as functions of the structural parameters f ; h2 ; s21 and incident angle θ. The resonant positions (wavelengths) are also calculated but not plotted for (a), (b), and (c), because they vary in a very small range (∼10 nm) around the SPs resonant wavelength 0.52 μm when the structural parameters f ; h2 ; s21 change. Figure 4(a) shows that even for a simple grating (black line with squares), if the filling factor is decreased to lower the 1.0 0.9 0.8 0.7 A 0.6 0.5 0.4 0.3
0.9
A sg A pg
0.8 0.7
A 0.6
(a)
0.5
(b)
0.4 0
0.3 0.4 0.5 0.6 0.7 0.8 0.9
5
10 15 20 25 30 35 40 (×E-2)
s21(µm)
f
A
1.0 0.9
1.0
0.7
0.8
0.9
λ sg(µm) λ pg (µm)
0.7 0.5
0.6
(c) 0.3 0.0 0.5 1.0 1.5 2.0 2.5 (×E-2)
h 2( µm)
0.5
(d)
A sg A pg
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
-10 0 10 20 30 40 50 60 70 80 θ (degree)
Fig. 4. Absorbance as functions of (a) filling factor f; (b) groove width; (c) groove depth; and (d) incident angle (red line). The remaining parameters for each subgraph are given as (a) p 0.5 μm, s21 0.1 μm, h 60 nm, and h2 10 nm; (b) p 0.5 μm, s 0.1 μm, h 60 nm, and h2 10 nm; (c) p 0.5 μm, s 0.25 μm, s21 0.1 μm, and h 60 nm; (d) simple grating (lines with squares): p 0.5 μm, s 0.25 μm, s21 0.0 μm, h 60 nm, and h2 10 nm; proposed structure: p 0.5 μm, s 0.25 μm, s21 0.1 μm, h 60 nm, and h2 10 nm. The black lines represent the resonant positions and red dashed lines represent absorbance. The subscripts sg and pg represent simple grating and proposed grating, respectively.
direct contribution of the dipoles cd to the reflection, absorption will be enhanced. After introducing the back grooves, the charge density located at the exits of slits is further decreased. Consequently, much higher absorptions [red line with circles] are obtained compared to the case of simple grating. However, when the filling factor becomes too small, the stripes at the bottom interface will be narrow because the groove width is fixed, which increases the charge density at the exits of slits and consequently recover the reflection. On the other hand, the transmission becomes non-negligible for too small filling factors (
